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Direct interrupts are even more rarely supplied.
- To emit special directives for the linker or assembler, for example to change sectioning, macros, or to make symbol aliases.
On the other hand, inline assembler poses a direct problem for the compiler itself as it complicates the analysis of what is done to each variable, a key part of register allocation. This means the performance might actually decrease. Inline assembler also complicates future porting and maintenance of a program.
Alternative facilities are often provided as a way to simplify the work for both the compiler and the programmer. Intrinsic functions for special instructions are provided by most compilers and C-function wrappers for arbitrary system calls are available on every Unix platform.
## Syntax
### In language standards
The ISO C++ standard and ISO C standards (annex J) specify a conditionally supported syntax for inline assembler:
An asm declaration has the form
asm-declaration:
( string-literal ) ;
The asm declaration is conditionally-supported; its meaning is implementation-defined. C++, [dcl.asm]
This definition, however, is rarely used in actual C, as it is simultaneously too liberal (in the interpretation) and too restricted (in the use of one string literal only).
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asm declaration is conditionally-supported; its meaning is implementation-defined. C++, [dcl.asm]
This definition, however, is rarely used in actual C, as it is simultaneously too liberal (in the interpretation) and too restricted (in the use of one string literal only).
### In actual compilers
In practical use, inline assembly operating on values is rarely standalone as free-floating code. Since the programmer cannot predict what register a variable is assigned to, compilers typically provide a way to substitute them in as an extension.
There are, in general, two types of inline assembly supported by C/C++ compilers:
- (or ) in GCC. GCC uses a direct extension of the ISO rules: assembly code template is written in strings, with inputs, outputs, and clobbered registers specified after the strings in colons. C variables are used directly while register names are quoted as string literals.
- in Microsoft Visual C++ (MSVC), Borland/Embarcadero C compiler, and descendants. This syntax is not based on ISO rules at all; programmers simply write ASM inside a block without needing to conform to C syntax. Variables are available as if they are registers and some C expressions are allowed. ARM Compiler used to have a similar facility.
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Variables are available as if they are registers and some C expressions are allowed. ARM Compiler used to have a similar facility.
The two families of extensions represent different understandings of division of labor in processing inline assembly. The GCC form preserves the overall syntax of the language and compartmentizes what the compiler needs to know: what is needed and what is changed. It does not explicitly require the compiler to understand instruction names, as the compiler is only needed to substitute its register assignments, plus a few operations, to handle the input requirements. However, the user is prone to specifying clobbered registers incorrectly. The MSVC form of an embedded domain-specific language provides ease of writing, but it requires the compiler itself to know about opcode names and their clobbering properties, demanding extra attention in maintenance and porting. It is still possible to check GCC-style assembly for clobber mistakes with knowledge of the instruction set.
GNAT (Ada language frontend of the GCC suite), and LLVM uses the GCC syntax. The D programming language uses a DSL similar to the MSVC extension officially for x86_64, but the LLVM-based LDC also provides the GCC-style syntax on every architecture. MSVC only supports inline assembler on 32-bit x86.
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The D programming language uses a DSL similar to the MSVC extension officially for x86_64, but the LLVM-based LDC also provides the GCC-style syntax on every architecture. MSVC only supports inline assembler on 32-bit x86.
The Rust language has since migrated to a syntax abstracting away inline assembly options further than the LLVM (GCC-style) version. It provides enough information to allow transforming the block into an externally-assembled function if the backend could not handle embedded assembly.
Examples
### A system call in GCC
Calling an operating system directly is generally not possible under a system using protected memory. The OS runs at a more privileged level (kernel mode) than the user (user mode); a (software) interrupt is used to make requests to the operating system. This is rarely a feature in a higher-level language, and so wrapper functions for system calls are written using inline assembler.
The following C code example shows an x86 system call wrapper in AT&T assembler syntax, using the GNU Assembler. Such calls are normally written with the aid of macros; the full code is included for clarity. In this particular case, the wrapper performs a system call of a number given by the caller with three operands, returning the result.
To recap, GCC supports both basic and extended assembly.
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In this particular case, the wrapper performs a system call of a number given by the caller with three operands, returning the result.
To recap, GCC supports both basic and extended assembly. The former simply passes text verbatim to the assembler, while the latter performs some substitutions for register locations.
```c
extern int errno;
int syscall3(int num, int arg1, int arg2, int arg3)
{
int res;
__asm__ (
"int $0x80" /* make the request to the OS */
: "=a" (res), /* return result in eax ("a") */
"+b" (arg1), /* pass arg1 in ebx ("b") [as a "+" output because the syscall may change it] */
"+c" (arg2), /* pass arg2 in ecx ("c") [ditto] */
"+d" (arg3) /* pass arg3 in edx ("d") [ditto] */
: "a" (num) /* pass system call number in eax ("a") */
: "memory", "cc", /* announce to the compiler that the memory and condition codes have been modified */
"esi", "edi", "ebp"); /* these registers are clobbered [changed by the syscall] too */
/* The operating system will return a negative value on error;
- wrappers return -1 on error and set the errno global variable */
if (-125 <= res && res < 0) {
errno = -res;
res = -1;
}
return res;
}
```
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To recap, GCC supports both basic and extended assembly. The former simply passes text verbatim to the assembler, while the latter performs some substitutions for register locations.
```c
extern int errno;
int syscall3(int num, int arg1, int arg2, int arg3)
{
int res;
__asm__ (
"int $0x80" /* make the request to the OS */
: "=a" (res), /* return result in eax ("a") */
"+b" (arg1), /* pass arg1 in ebx ("b") [as a "+" output because the syscall may change it] */
"+c" (arg2), /* pass arg2 in ecx ("c") [ditto] */
"+d" (arg3) /* pass arg3 in edx ("d") [ditto] */
: "a" (num) /* pass system call number in eax ("a") */
: "memory", "cc", /* announce to the compiler that the memory and condition codes have been modified */
"esi", "edi", "ebp"); /* these registers are clobbered [changed by the syscall] too */
/* The operating system will return a negative value on error;
- wrappers return -1 on error and set the errno global variable */
if (-125 <= res && res < 0) {
errno = -res;
res = -1;
}
return res;
}
```
### Processor-specific instruction in D
This example of inline assembly from the D programming language shows code that computes the tangent of x using the x86's FPU (x87)
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The former simply passes text verbatim to the assembler, while the latter performs some substitutions for register locations.
```c
extern int errno;
int syscall3(int num, int arg1, int arg2, int arg3)
{
int res;
__asm__ (
"int $0x80" /* make the request to the OS */
: "=a" (res), /* return result in eax ("a") */
"+b" (arg1), /* pass arg1 in ebx ("b") [as a "+" output because the syscall may change it] */
"+c" (arg2), /* pass arg2 in ecx ("c") [ditto] */
"+d" (arg3) /* pass arg3 in edx ("d") [ditto] */
: "a" (num) /* pass system call number in eax ("a") */
: "memory", "cc", /* announce to the compiler that the memory and condition codes have been modified */
"esi", "edi", "ebp"); /* these registers are clobbered [changed by the syscall] too */
/* The operating system will return a negative value on error;
- wrappers return -1 on error and set the errno global variable */
if (-125 <= res && res < 0) {
errno = -res;
res = -1;
}
return res;
}
```
### Processor-specific instruction in D
This example of inline assembly from the D programming language shows code that computes the tangent of x using the x86's FPU (x87) instructions.
```d
// Compute the tangent of x
real tan(real x)
{
asm
{
fld x[EBP] ; // load x
fxam ; // test for oddball values
fstsw AX ;
sahf ;
jc trigerr ; // C0 = 1: x is NAN, infinity, or empty
// 387's can handle denormals
SC18: fptan ;
fstp ST(0) ; // dump X, which is always 1
fstsw AX ;
sahf ; // if (!(fp_status & 0x20)) goto Lret
jnp Lret ; // C2 = 1: x is out of range, do argument reduction
fldpi ; // load pi
fxch ;
SC17: fprem1 ; // reminder (partial)
fstsw AX ;
sahf ;
jp SC17 ; // C2 = 1: partial reminder, need to loop
fstp ST(1) ; // remove pi from stack
jmp SC18 ;
}
trigerr:
return real.nan;
Lret: // No need to manually return anything as the value is already on FP stack
;
}
```
The followed by conditional jump idiom is used to access the x87 FPU status word bits C0 and C2. stores the status in a general-purpose register; sahf sets the FLAGS register to the higher 8 bits of the register; and the jump is used to judge on whatever flag bit that happens to correspond to the FPU status bit.
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### Processor-specific instruction in D
This example of inline assembly from the D programming language shows code that computes the tangent of x using the x86's FPU (x87) instructions.
```d
// Compute the tangent of x
real tan(real x)
{
asm
{
fld x[EBP] ; // load x
fxam ; // test for oddball values
fstsw AX ;
sahf ;
jc trigerr ; // C0 = 1: x is NAN, infinity, or empty
// 387's can handle denormals
SC18: fptan ;
fstp ST(0) ; // dump X, which is always 1
fstsw AX ;
sahf ; // if (!(fp_status & 0x20)) goto Lret
jnp Lret ; // C2 = 1: x is out of range, do argument reduction
fldpi ; // load pi
fxch ;
SC17: fprem1 ; // reminder (partial)
fstsw AX ;
sahf ;
jp SC17 ; // C2 = 1: partial reminder, need to loop
fstp ST(1) ; // remove pi from stack
jmp SC18 ;
}
trigerr:
return real.nan;
Lret: // No need to manually return anything as the value is already on FP stack
;
}
```
The followed by conditional jump idiom is used to access the x87 FPU status word bits C0 and C2. stores the status in a general-purpose register; sahf sets the FLAGS register to the higher 8 bits of the register; and the jump is used to judge on whatever flag bit that happens to correspond to the FPU status bit.
## References
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https://en.wikipedia.org/wiki/Inline_assembler
|
instructions.
```d
// Compute the tangent of x
real tan(real x)
{
asm
{
fld x[EBP] ; // load x
fxam ; // test for oddball values
fstsw AX ;
sahf ;
jc trigerr ; // C0 = 1: x is NAN, infinity, or empty
// 387's can handle denormals
SC18: fptan ;
fstp ST(0) ; // dump X, which is always 1
fstsw AX ;
sahf ; // if (!(fp_status & 0x20)) goto Lret
jnp Lret ; // C2 = 1: x is out of range, do argument reduction
fldpi ; // load pi
fxch ;
SC17: fprem1 ; // reminder (partial)
fstsw AX ;
sahf ;
jp SC17 ; // C2 = 1: partial reminder, need to loop
fstp ST(1) ; // remove pi from stack
jmp SC18 ;
}
trigerr:
return real.nan;
Lret: // No need to manually return anything as the value is already on FP stack
;
}
```
The followed by conditional jump idiom is used to access the x87 FPU status word bits C0 and C2. stores the status in a general-purpose register; sahf sets the FLAGS register to the higher 8 bits of the register; and the jump is used to judge on whatever flag bit that happens to correspond to the FPU status bit.
## References
## External links
- GCC-Inline-Assembly-HOWTO
- Clang Inline assembly
- GNAT Inline Assembler
- GCC Inline Assembler Reference
- Compiler Explorer
Category:Assembly languages
Category:Articles with example C code
Category:Articles with example D code
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The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford at the University of Manchester based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron in 1932, models for a nucleus composed of protons and neutrons were quickly developed by Dmitri Ivanenko and Werner Heisenberg. An atom is composed of a positively charged nucleus, with a cloud of negatively charged electrons surrounding it, bound together by electrostatic force. Almost all of the mass of an atom is located in the nucleus, with a very small contribution from the electron cloud. Protons and neutrons are bound together to form a nucleus by the nuclear force.
The diameter of the nucleus is in the range of () for hydrogen (the diameter of a single proton) to about for uranium. These dimensions are much smaller than the diameter of the atom itself (nucleus + electron cloud), by a factor of about 26,634 (uranium atomic radius is about ()) to about 60,250 (hydrogen atomic radius is about ).
The branch of physics involved with the study and understanding of the atomic nucleus, including its composition and the forces that bind it together, is called nuclear physics.
## History
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The branch of physics involved with the study and understanding of the atomic nucleus, including its composition and the forces that bind it together, is called nuclear physics.
## History
The nucleus was discovered in 1911, as a result of Ernest Rutherford's efforts to test Thomson's "plum pudding model" of the atom. The electron had already been discovered by J. J. Thomson. Knowing that atoms are electrically neutral, J. J. Thomson postulated that there must be a positive charge as well. In his plum pudding model, Thomson suggested that an atom consisted of negative electrons randomly scattered within a sphere of positive charge. Ernest Rutherford later devised an experiment with his research partner Hans Geiger and with help of Ernest Marsden, that involved the deflection of alpha particles (helium nuclei) directed at a thin sheet of metal foil. He reasoned that if J. J. Thomson's model were correct, the positively charged alpha particles would easily pass through the foil with very little deviation in their paths, as the foil should act as electrically neutral if the negative and positive charges are so intimately mixed as to make it appear neutral. To his surprise, many of the particles were deflected at very large angles.
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He reasoned that if J. J. Thomson's model were correct, the positively charged alpha particles would easily pass through the foil with very little deviation in their paths, as the foil should act as electrically neutral if the negative and positive charges are so intimately mixed as to make it appear neutral. To his surprise, many of the particles were deflected at very large angles. Because the mass of an alpha particle is about 8000 times that of an electron, it became apparent that a very strong force must be present if it could deflect the massive and fast moving alpha particles. He realized that the plum pudding model could not be accurate and that the deflections of the alpha particles could only be explained if the positive and negative charges were separated from each other and that the mass of the atom was a concentrated point of positive charge. This justified the idea of a nuclear atom with a dense center of positive charge and mass.
### Etymology
The term nucleus is from the Latin word , a diminutive of ('nut'), meaning 'the kernel' (i.e., the 'small nut') inside a watery type of fruit (like a peach). In 1844, Michael Faraday used the term to refer to the "central point of an atom". The modern atomic meaning was proposed by Ernest Rutherford in 1912.
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In 1844, Michael Faraday used the term to refer to the "central point of an atom". The modern atomic meaning was proposed by Ernest Rutherford in 1912. The adoption of the term "nucleus" to atomic theory, however, was not immediate. In 1916, for example, Gilbert N. Lewis stated, in his famous article The Atom and the Molecule, that "the atom is composed of the kernel and an outer atom or shell. "
Similarly, the term kern meaning kernel is used for nucleus in German and Dutch.
## Principles
The nucleus of an atom consists of neutrons and protons, which in turn are the manifestation of more elementary particles, called quarks, that are held in association by the nuclear strong force in certain stable combinations of hadrons, called baryons. The nuclear strong force extends far enough from each baryon so as to bind the neutrons and protons together against the repulsive electrical force between the positively charged protons. The nuclear strong force has a very short range, and essentially drops to zero just beyond the edge of the nucleus. The collective action of the positively charged nucleus is to hold the electrically negative charged electrons in their orbits about the nucleus. The collection of negatively charged electrons orbiting the nucleus display an affinity for certain configurations and numbers of electrons that make their orbits stable.
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The collective action of the positively charged nucleus is to hold the electrically negative charged electrons in their orbits about the nucleus. The collection of negatively charged electrons orbiting the nucleus display an affinity for certain configurations and numbers of electrons that make their orbits stable. Which chemical element an atom represents is determined by the number of protons in the nucleus; the neutral atom will have an equal number of electrons orbiting that nucleus. Individual chemical elements can create more stable electron configurations by combining to share their electrons. It is that sharing of electrons to create stable electronic orbits about the nuclei that appears to us as the chemistry of our macro world.
Protons define the entire charge of a nucleus, and hence its chemical identity. Neutrons are electrically neutral, but contribute to the mass of a nucleus to nearly the same extent as the protons. Neutrons can explain the phenomenon of isotopes (same atomic number with different atomic mass). The main role of neutrons is to reduce electrostatic repulsion inside the nucleus.
## Composition and shape
Protons and neutrons are fermions, with different values of the strong isospin quantum number, so two protons and two neutrons can share the same space wave function since they are not identical quantum entities. They are sometimes viewed as two different quantum states of the same particle, the nucleon.
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## Composition and shape
Protons and neutrons are fermions, with different values of the strong isospin quantum number, so two protons and two neutrons can share the same space wave function since they are not identical quantum entities. They are sometimes viewed as two different quantum states of the same particle, the nucleon. Two fermions, such as two protons, or two neutrons, or a proton + neutron (the deuteron) can exhibit bosonic behavior when they become loosely bound in pairs, which have integer spin.
In the rare case of a hypernucleus, a third baryon called a hyperon, containing one or more strange quarks and/or other unusual quark(s), can also share the wave function. However, this type of nucleus is extremely unstable and not found on Earth except in high-energy physics experiments.
The neutron has a positively charged core of radius ≈ 0.3 fm surrounded by a compensating negative charge of radius between 0.3 fm and 2 fm. The proton has an approximately exponentially decaying positive charge distribution with a mean square radius of about 0.8 fm.
The shape of the atomic nucleus can be spherical, rugby ball-shaped (prolate deformation), discus-shaped (oblate deformation), triaxial (a combination of oblate and prolate deformation) or pear-shaped.
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The proton has an approximately exponentially decaying positive charge distribution with a mean square radius of about 0.8 fm.
The shape of the atomic nucleus can be spherical, rugby ball-shaped (prolate deformation), discus-shaped (oblate deformation), triaxial (a combination of oblate and prolate deformation) or pear-shaped.
## Forces
Nuclei are bound together by the residual strong force (nuclear force). The residual strong force is a minor residuum of the strong interaction which binds quarks together to form protons and neutrons. This force is much weaker between neutrons and protons because it is mostly neutralized within them, in the same way that electromagnetic forces between neutral atoms (such as van der Waals forces that act between two inert gas atoms) are much weaker than the electromagnetic forces that hold the parts of the atoms together internally (for example, the forces that hold the electrons in an inert gas atom bound to its nucleus).
The nuclear force is highly attractive at the distance of typical nucleon separation, and this overwhelms the repulsion between protons due to the electromagnetic force, thus allowing nuclei to exist. However, the residual strong force has a limited range because it decays quickly with distance (see Yukawa potential); thus only nuclei smaller than a certain size can be completely stable.
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The nuclear force is highly attractive at the distance of typical nucleon separation, and this overwhelms the repulsion between protons due to the electromagnetic force, thus allowing nuclei to exist. However, the residual strong force has a limited range because it decays quickly with distance (see Yukawa potential); thus only nuclei smaller than a certain size can be completely stable. The largest known completely stable nucleus (i.e. stable to alpha, beta, and gamma decay) is lead-208 which contains a total of 208 nucleons (126 neutrons and 82 protons). Nuclei larger than this maximum are unstable and tend to be increasingly short-lived with larger numbers of nucleons. However, bismuth-209 is also stable to beta decay and has the longest half-life to alpha decay of any known isotope, estimated at a billion times longer than the age of the universe.
The residual strong force is effective over a very short range (usually only a few femtometres (fm); roughly one or two nucleon diameters) and causes an attraction between any pair of nucleons. For example, between a proton and a neutron to form a deuteron [NP], and also between protons and protons, and neutrons and neutrons.
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The residual strong force is effective over a very short range (usually only a few femtometres (fm); roughly one or two nucleon diameters) and causes an attraction between any pair of nucleons. For example, between a proton and a neutron to form a deuteron [NP], and also between protons and protons, and neutrons and neutrons.
## Halo nuclei and nuclear force range limits
The effective absolute limit of the range of the nuclear force (also known as residual strong force) is represented by halo nuclei such as lithium-11 or boron-14, in which dineutrons, or other collections of neutrons, orbit at distances of about (roughly similar to the radius of the nucleus of uranium-238). These nuclei are not maximally dense. Halo nuclei form at the extreme edges of the chart of the nuclides—the neutron drip line and proton drip line—and are all unstable with short half-lives, measured in milliseconds; for example, lithium-11 has a half-life of .
Halos in effect represent an excited state with nucleons in an outer quantum shell which has unfilled energy levels "below" it (both in terms of radius and energy). The halo may be made of either neutrons [NN, NNN] or protons [PP, PPP].
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The halo may be made of either neutrons [NN, NNN] or protons [PP, PPP]. Nuclei which have a single neutron halo include 11Be and 19C. A two-neutron halo is exhibited by 6He, 11Li, 17B, 19B and 22C. Two-neutron halo nuclei break into three fragments, never two, and are called Borromean nuclei because of this behavior (referring to a system of three interlocked rings in which breaking any ring frees both of the others). 8He and 14Be both exhibit a four-neutron halo. Nuclei which have a proton halo include 8B and 26P. A two-proton halo is exhibited by 17Ne and 27S. Proton halos are expected to be more rare and unstable than the neutron examples, because of the repulsive electromagnetic forces of the halo proton(s).
## Nuclear models
Although the standard model of physics is widely believed to completely describe the composition and behavior of the nucleus, generating predictions from theory is much more difficult than for most other areas of particle physics. This is due to two reasons:
- In principle, the physics within a nucleus can be derived entirely from quantum chromodynamics (QCD).
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This is due to two reasons:
- In principle, the physics within a nucleus can be derived entirely from quantum chromodynamics (QCD). In practice however, current computational and mathematical approaches for solving QCD in low-energy systems such as the nuclei are extremely limited. This is due to the phase transition that occurs between high-energy quark matter and low-energy hadronic matter, which renders perturbative techniques unusable, making it difficult to construct an accurate QCD-derived model of the forces between nucleons. Current approaches are limited to either phenomenological models such as the Argonne v18 potential or chiral effective field theory.
- Even if the nuclear force is well constrained, a significant amount of computational power is required to accurately compute the properties of nuclei ab initio. Developments in many-body theory have made this possible for many low mass and relatively stable nuclei, but further improvements in both computational power and mathematical approaches are required before heavy nuclei or highly unstable nuclei can be tackled.
Historically, experiments have been compared to relatively crude models that are necessarily imperfect. None of these models can completely explain experimental data on nuclear structure.
The nuclear radius (R) is considered to be one of the basic quantities that any model must predict.
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None of these models can completely explain experimental data on nuclear structure.
The nuclear radius (R) is considered to be one of the basic quantities that any model must predict. For stable nuclei (not halo nuclei or other unstable distorted nuclei) the nuclear radius is roughly proportional to the cube root of the mass number (A) of the nucleus, and particularly in nuclei containing many nucleons, as they arrange in more spherical configurations:
The stable nucleus has approximately a constant density and therefore the nuclear radius R can be approximated by the following formula,
$$
R = r_0 A^{1/3} \,
$$
where A = Atomic mass number (the number of protons Z, plus the number of neutrons N) and r0 = 1.25 fm = 1.25 × 10−15 m. In this equation, the "constant" r0 varies by 0.2 fm, depending on the nucleus in question, but this is less than 20% change from a constant.
In other words, packing protons and neutrons in the nucleus gives approximately the same total size result as packing hard spheres of a constant size (like marbles) into a tight spherical or almost spherical bag (some stable nuclei are not quite spherical, but are known to be prolate).
Models of nuclear structure include:
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In other words, packing protons and neutrons in the nucleus gives approximately the same total size result as packing hard spheres of a constant size (like marbles) into a tight spherical or almost spherical bag (some stable nuclei are not quite spherical, but are known to be prolate).
Models of nuclear structure include:
### Cluster model
The cluster model describes the nucleus as a molecule-like collection of proton-neutron groups (e.g., alpha particles) with one or more valence neutrons occupying molecular orbitals.
### Liquid drop model
Early models of the nucleus viewed the nucleus as a rotating liquid drop. In this model, the trade-off of long-range electromagnetic forces and relatively short-range nuclear forces, together cause behavior which resembled surface tension forces in liquid drops of different sizes. This formula is successful at explaining many important phenomena of nuclei, such as their changing amounts of binding energy as their size and composition changes (see semi-empirical mass formula), but it does not explain the special stability which occurs when nuclei have special "magic numbers" of protons or neutrons.
The terms in the semi-empirical mass formula, which can be used to approximate the binding energy of many nuclei, are considered as the sum of five types of energies (see below).
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This formula is successful at explaining many important phenomena of nuclei, such as their changing amounts of binding energy as their size and composition changes (see semi-empirical mass formula), but it does not explain the special stability which occurs when nuclei have special "magic numbers" of protons or neutrons.
The terms in the semi-empirical mass formula, which can be used to approximate the binding energy of many nuclei, are considered as the sum of five types of energies (see below). Then the picture of a nucleus as a drop of incompressible liquid roughly accounts for the observed variation of binding energy of the nucleus:
Volume energy. When an assembly of nucleons of the same size is packed together into the smallest volume, each interior nucleon has a certain number of other nucleons in contact with it. So, this nuclear energy is proportional to the volume.
Surface energy. A nucleon at the surface of a nucleus interacts with fewer other nucleons than one in the interior of the nucleus and hence its binding energy is less. This surface energy term takes that into account and is therefore negative and is proportional to the surface area.
Coulomb energy. The electric repulsion between each pair of protons in a nucleus contributes toward decreasing its binding energy.
Asymmetry energy (also called Pauli Energy).
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The electric repulsion between each pair of protons in a nucleus contributes toward decreasing its binding energy.
Asymmetry energy (also called Pauli Energy). An energy associated with the Pauli exclusion principle. Were it not for the Coulomb energy, the most stable form of nuclear matter would have the same number of neutrons as protons, since unequal numbers of neutrons and protons imply filling higher energy levels for one type of particle, while leaving lower energy levels vacant for the other type.
Pairing energy. An energy which is a correction term that arises from the tendency of proton pairs and neutron pairs to occur. An even number of particles is more stable than an odd number.
### Shell models and other quantum models
A number of models for the nucleus have also been proposed in which nucleons occupy orbitals, much like the atomic orbitals in atomic physics theory. These wave models imagine nucleons to be either sizeless point particles in potential wells, or else probability waves as in the "optical model", frictionlessly orbiting at high speed in potential wells.
In the above models, the nucleons may occupy orbitals in pairs, due to being fermions, which allows explanation of even/odd Z and N effects well known from experiments.
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These wave models imagine nucleons to be either sizeless point particles in potential wells, or else probability waves as in the "optical model", frictionlessly orbiting at high speed in potential wells.
In the above models, the nucleons may occupy orbitals in pairs, due to being fermions, which allows explanation of even/odd Z and N effects well known from experiments. The exact nature and capacity of nuclear shells differs from those of electrons in atomic orbitals, primarily because the potential well in which the nucleons move (especially in larger nuclei) is quite different from the central electromagnetic potential well which binds electrons in atoms. Some resemblance to atomic orbital models may be seen in a small atomic nucleus like that of helium-4, in which the two protons and two neutrons separately occupy 1s orbitals analogous to the 1s orbital for the two electrons in the helium atom, and achieve unusual stability for the same reason. Nuclei with 5 nucleons are all extremely unstable and short-lived, yet, helium-3, with 3 nucleons, is very stable even with lack of a closed 1s orbital shell. Another nucleus with 3 nucleons, the triton hydrogen-3 is unstable and will decay into helium-3 when isolated.
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Nuclei with 5 nucleons are all extremely unstable and short-lived, yet, helium-3, with 3 nucleons, is very stable even with lack of a closed 1s orbital shell. Another nucleus with 3 nucleons, the triton hydrogen-3 is unstable and will decay into helium-3 when isolated. Weak nuclear stability with 2 nucleons {NP} in the 1s orbital is found in the deuteron hydrogen-2, with only one nucleon in each of the proton and neutron potential wells. While each nucleon is a fermion, the {NP} deuteron is a boson and thus does not follow Pauli Exclusion for close packing within shells. Lithium-6 with 6 nucleons is highly stable without a closed second 1p shell orbital. For light nuclei with total nucleon numbers 1 to 6 only those with 5 do not show some evidence of stability. Observations of beta-stability of light nuclei outside closed shells indicate that nuclear stability is much more complex than simple closure of shell orbitals with magic numbers of protons and neutrons.
For larger nuclei, the shells occupied by nucleons begin to differ significantly from electron shells, but nevertheless, present nuclear theory does predict the magic numbers of filled nuclear shells for both protons and neutrons.
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Observations of beta-stability of light nuclei outside closed shells indicate that nuclear stability is much more complex than simple closure of shell orbitals with magic numbers of protons and neutrons.
For larger nuclei, the shells occupied by nucleons begin to differ significantly from electron shells, but nevertheless, present nuclear theory does predict the magic numbers of filled nuclear shells for both protons and neutrons. The closure of the stable shells predicts unusually stable configurations, analogous to the noble group of nearly-inert gases in chemistry. An example is the stability of the closed shell of 50 protons, which allows tin to have 10 stable isotopes, more than any other element. Similarly, the distance from shell-closure explains the unusual instability of isotopes which have far from stable numbers of these particles, such as the radioactive elements 43 (technetium) and 61 (promethium), each of which is preceded and followed by 17 or more stable elements.
There are however problems with the shell model when an attempt is made to account for nuclear properties well away from closed shells. This has led to complex post hoc distortions of the shape of the potential well to fit experimental data, but the question remains whether these mathematical manipulations actually correspond to the spatial deformations in real nuclei.
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There are however problems with the shell model when an attempt is made to account for nuclear properties well away from closed shells. This has led to complex post hoc distortions of the shape of the potential well to fit experimental data, but the question remains whether these mathematical manipulations actually correspond to the spatial deformations in real nuclei. Problems with the shell model have led some to propose realistic two-body and three-body nuclear force effects involving nucleon clusters and then build the nucleus on this basis. Three such cluster models are the 1936 Resonating Group Structure model of John Wheeler, Close-Packed Spheron Model of Linus Pauling and the 2D Ising Model of MacGregor.
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The word "mass" has two meanings in special relativity: invariant mass (also called rest mass) is an invariant quantity which is the same for all observers in all reference frames, while the relativistic mass is dependent on the velocity of the observer. According to the concept of mass–energy equivalence, invariant mass is equivalent to rest energy, while relativistic mass is equivalent to relativistic energy (also called total energy).
The term "relativistic mass" tends not to be used in particle and nuclear physics and is often avoided by writers on special relativity, in favor of referring to the body's relativistic energy. In contrast, "invariant mass" is usually preferred over rest energy. The measurable inertia of a body in a given frame of reference is determined by its relativistic mass, not merely its invariant mass. For example, photons have zero rest mass but contribute to the inertia (and weight in a gravitational field) of any system containing them.
The concept is generalized in mass in general relativity.
## Rest mass
The term mass in special relativity usually refers to the rest mass of the object, which is the Newtonian mass as measured by an observer moving along with the object. The invariant mass is another name for the rest mass of single particles.
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## Rest mass
The term mass in special relativity usually refers to the rest mass of the object, which is the Newtonian mass as measured by an observer moving along with the object. The invariant mass is another name for the rest mass of single particles. The more general invariant mass (calculated with a more complicated formula) loosely corresponds to the "rest mass" of a "system". Thus, invariant mass is a natural unit of mass used for systems which are being viewed from their center of momentum frame (COM frame), as when any closed system (for example a bottle of hot gas) is weighed, which requires that the measurement be taken in the center of momentum frame where the system has no net momentum. Under such circumstances the invariant mass is equal to the relativistic mass (discussed below), which is the total energy of the system divided by c2 (the speed of light squared).
The concept of invariant mass does not require bound systems of particles, however. As such, it may also be applied to systems of unbound particles in high-speed relative motion. Because of this, it is often employed in particle physics for systems which consist of widely separated high-energy particles. If such systems were derived from a single particle, then the calculation of the invariant mass of such systems, which is a never-changing quantity, will provide the rest mass of the parent particle (because it is conserved over time).
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Because of this, it is often employed in particle physics for systems which consist of widely separated high-energy particles. If such systems were derived from a single particle, then the calculation of the invariant mass of such systems, which is a never-changing quantity, will provide the rest mass of the parent particle (because it is conserved over time).
It is often convenient in calculation that the invariant mass of a system is the total energy of the system (divided by ) in the COM frame (where, by definition, the momentum of the system is zero). However, since the invariant mass of any system is also the same quantity in all inertial frames, it is a quantity often calculated from the total energy in the COM frame, then used to calculate system energies and momenta in other frames where the momenta are not zero, and the system total energy will necessarily be a different quantity than in the COM frame. As with energy and momentum, the invariant mass of a system cannot be destroyed or changed, and it is thus conserved, so long as the system is closed to all influences. (The technical term is isolated system meaning that an idealized boundary is drawn around the system, and no mass/energy is allowed across it.)
##
### Relativistic mass
The relativistic mass is the sum total quantity of energy in a body or system (divided by ).
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##
### Relativistic mass
The relativistic mass is the sum total quantity of energy in a body or system (divided by ). Thus, the mass in the formula
$$
E = m_\text{rel} c^2
$$
is the relativistic mass. For a particle of non-zero rest mass moving at a speed
$$
v
$$
relative to the observer, one finds
$$
m_\text{rel} = \frac{m}{\sqrt{1 - \dfrac{v^2}{c^2}}}.
$$
In the center of momentum frame,
$$
v = 0
$$
and the relativistic mass equals the rest mass. In other frames, the relativistic mass (of a body or system of bodies) includes a contribution from the "net" kinetic energy of the body (the kinetic energy of the center of mass of the body), and is larger the faster the body moves. Thus, unlike the invariant mass, the relativistic mass depends on the observer's frame of reference. However, for given single frames of reference and for isolated systems, the relativistic mass is also a conserved quantity.
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Thus, unlike the invariant mass, the relativistic mass depends on the observer's frame of reference. However, for given single frames of reference and for isolated systems, the relativistic mass is also a conserved quantity.
The relativistic mass is also the proportionality factor between velocity and momentum,
$$
\mathbf{p} = m_\text{rel}\mathbf{v}.
$$
Newton's second law remains valid in the form
$$
\mathbf{f} = \frac{d(m_\text{rel}\mathbf{v})}{dt}.
$$
When a body emits light of frequency
$$
\nu
$$
and wavelength
$$
\lambda
$$
as a photon of energy
$$
E = h \nu = h c / \lambda
$$
, the mass of the body decreases by
$$
E/c^2 = h/ \lambda c
$$
, which someKetterle, W. and Jamison, A. O. (2020). "An atomic physics perspective on the kilogram’s new definition", "Physics Today" 73, 32-38 interpret as the relativistic mass of the emitted photon since it also fulfills
$$
p = m_\text{rel}c = h/\lambda
$$
.
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The relativistic mass is also the proportionality factor between velocity and momentum,
$$
\mathbf{p} = m_\text{rel}\mathbf{v}.
$$
Newton's second law remains valid in the form
$$
\mathbf{f} = \frac{d(m_\text{rel}\mathbf{v})}{dt}.
$$
When a body emits light of frequency
$$
\nu
$$
and wavelength
$$
\lambda
$$
as a photon of energy
$$
E = h \nu = h c / \lambda
$$
, the mass of the body decreases by
$$
E/c^2 = h/ \lambda c
$$
, which someKetterle, W. and Jamison, A. O. (2020). "An atomic physics perspective on the kilogram’s new definition", "Physics Today" 73, 32-38 interpret as the relativistic mass of the emitted photon since it also fulfills
$$
p = m_\text{rel}c = h/\lambda
$$
. Although some authors present relativistic mass as a fundamental concept of the theory, it has been argued that this is wrong as the fundamentals of the theory relate to space–time. There is disagreement over whether the concept is pedagogically useful.
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Although some authors present relativistic mass as a fundamental concept of the theory, it has been argued that this is wrong as the fundamentals of the theory relate to space–time. There is disagreement over whether the concept is pedagogically useful. It explains simply and quantitatively why a body subject to a constant acceleration cannot reach the speed of light, and why the mass of a system emitting a photon decreases. In relativistic quantum chemistry, relativistic mass is used to explain electron orbital contraction in heavy elements.
The notion of mass as a property of an object from Newtonian mechanics does not bear a precise relationship to the concept in relativity.
Relativistic mass is not referenced in nuclear and particle physics, and a survey of introductory textbooks in 2005 showed that only 5 of 24 texts used the concept, although it is still prevalent in popularizations.
If a stationary box contains many particles, its weight increases in its rest frame the faster the particles are moving. Any energy in the box (including the kinetic energy of the particles) adds to the mass, so that the relative motion of the particles contributes to the mass of the box. But if the box itself is moving (its center of mass is moving), there remains the question of whether the kinetic energy of the overall motion should be included in the mass of the system.
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Any energy in the box (including the kinetic energy of the particles) adds to the mass, so that the relative motion of the particles contributes to the mass of the box. But if the box itself is moving (its center of mass is moving), there remains the question of whether the kinetic energy of the overall motion should be included in the mass of the system. The invariant mass is calculated excluding the kinetic energy of the system as a whole (calculated using the single velocity of the box, which is to say the velocity of the box's center of mass), while the relativistic mass is calculated including invariant mass plus the kinetic energy of the system which is calculated from the velocity of the center of mass.
## Relativistic vs. rest mass
Relativistic mass and rest mass are both traditional concepts in physics, but the relativistic mass corresponds to the total energy. The relativistic mass is the mass of the system as it would be measured on a scale, but in some cases (such as the box above) this fact remains true only because the system on average must be at rest to be weighed (it must have zero net momentum, which is to say, the measurement is in its center of momentum frame). For example, if an electron in a cyclotron is moving in circles with a relativistic velocity, the mass of the cyclotron+electron system is increased by the relativistic mass of the electron, not by the electron's rest mass.
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this fact remains true only because the system on average must be at rest to be weighed (it must have zero net momentum, which is to say, the measurement is in its center of momentum frame). For example, if an electron in a cyclotron is moving in circles with a relativistic velocity, the mass of the cyclotron+electron system is increased by the relativistic mass of the electron, not by the electron's rest mass. But the same is also true of any closed system, such as an electron-and-box, if the electron bounces at high speed inside the box. It is only the lack of total momentum in the system (the system momenta sum to zero) which allows the kinetic energy of the electron to be "weighed". If the electron is stopped and weighed, or the scale were somehow sent after it, it would not be moving with respect to the scale, and again the relativistic and rest masses would be the same for the single electron (and would be smaller). In general, relativistic and rest masses are equal only in systems which have no net momentum and the system center of mass is at rest; otherwise they may be different.
The invariant mass is proportional to the value of the total energy in one reference frame, the frame where the object as a whole is at rest (as defined below in terms of center of mass). This is why the invariant mass is the same as the rest mass for single particles.
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The invariant mass is proportional to the value of the total energy in one reference frame, the frame where the object as a whole is at rest (as defined below in terms of center of mass). This is why the invariant mass is the same as the rest mass for single particles. However, the invariant mass also represents the measured mass when the center of mass is at rest for systems of many particles. This special frame where this occurs is also called the center of momentum frame, and is defined as the inertial frame in which the center of mass of the object is at rest (another way of stating this is that it is the frame in which the momenta of the system's parts add to zero). For compound objects (made of many smaller objects, some of which may be moving) and sets of unbound objects (some of which may also be moving), only the center of mass of the system is required to be at rest, for the object's relativistic mass to be equal to its rest mass.
A so-called massless particle (such as a photon, or a theoretical graviton) moves at the speed of light in every frame of reference. In this case there is no transformation that will bring the particle to rest. The total energy of such particles becomes smaller and smaller in frames which move faster and faster in the same direction. As such, they have no rest mass, because they can never be measured in a frame where they are at rest.
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The total energy of such particles becomes smaller and smaller in frames which move faster and faster in the same direction. As such, they have no rest mass, because they can never be measured in a frame where they are at rest. This property of having no rest mass is what causes these particles to be termed "massless". However, even massless particles have a relativistic mass, which varies with their observed energy in various frames of reference.
## Invariant mass
The invariant mass is the ratio of four-momentum (the four-dimensional generalization of classical momentum) to four-velocity:
$$
p^\mu = m v^\mu
$$
and is also the ratio of four-acceleration to four-force when the rest mass is constant. The four-dimensional form of Newton's second law is:
$$
F^\mu = m A^\mu.
$$
## Relativistic energy–momentum equation
The relativistic expressions for and obey the relativistic energy–momentum relation:
$$
E^2 - (pc)^2 = \left(mc^2\right)^2
$$
where the m is the rest mass, or the invariant mass for systems, and is the total energy.
The equation is also valid for photons, which have :_
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## Relativistic energy–momentum equation
The relativistic expressions for and obey the relativistic energy–momentum relation:
$$
E^2 - (pc)^2 = \left(mc^2\right)^2
$$
where the m is the rest mass, or the invariant mass for systems, and is the total energy.
The equation is also valid for photons, which have :_ BLOCK1_and therefore
$$
E = pc
$$
A photon's momentum is a function of its energy, but it is not proportional to the velocity, which is always .
For an object at rest, the momentum is zero, therefore
$$
E = mc^2.
$$
Note that the formula is true only for particles or systems with zero momentum.
The rest mass is only proportional to the total energy in the rest frame of the object.
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Note that the formula is true only for particles or systems with zero momentum.
The rest mass is only proportional to the total energy in the rest frame of the object.
When the object is moving, the total energy is given by
$$
E = \sqrt{\left(mc^2\right)^2 + (pc)^2}
$$
To find the form of the momentum and energy as a function of velocity, it can be noted that the four-velocity, which is proportional to
$$
\left(c, \vec{v}\right)
$$
, is the only four-vector associated with the particle's motion, so that if there is a conserved four-momentum
$$
\left(E, \vec{p}c\right)
$$
, it must be proportional to this vector. This allows expressing the ratio of energy to momentum as
$$
pc = E \frac{v}{c} ,
$$
resulting in a relation between and :_
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When the object is moving, the total energy is given by
$$
E = \sqrt{\left(mc^2\right)^2 + (pc)^2}
$$
To find the form of the momentum and energy as a function of velocity, it can be noted that the four-velocity, which is proportional to
$$
\left(c, \vec{v}\right)
$$
, is the only four-vector associated with the particle's motion, so that if there is a conserved four-momentum
$$
\left(E, \vec{p}c\right)
$$
, it must be proportional to this vector. This allows expressing the ratio of energy to momentum as
$$
pc = E \frac{v}{c} ,
$$
resulting in a relation between and :_ BLOCK8_This results in
$$
E = \frac{mc^2}{\sqrt{1 - \dfrac{v^2}{c^2}}}
$$
and
$$
p = \frac{mv}{\sqrt{1 - \dfrac{v^2}{c^2}}}.
$$
these expressions can be written as
$$
\begin{align}
E_0 &= mc^2 , \\
E &= \gamma mc^2 , \\
p &= mv \gamma ,
\end{align}
$$
where the factor
$$
\gamma = {1}/{\sqrt{1-\frac{v^2}{c^2}}}.
$$
When working in units where , known as the natural unit system, all the relativistic equations are simplified and the quantities energy, momentum, and mass have the same natural dimension:
$$
m^2 = E^2 - p^2.
$$
The equation is often written this way because the difference
$$
E^2 - p^2
$$
is the relativistic length of the energy momentum four-vector, a length which is associated with rest mass or invariant mass in systems.
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This allows expressing the ratio of energy to momentum as
$$
pc = E \frac{v}{c} ,
$$
resulting in a relation between and :_ BLOCK8_This results in
$$
E = \frac{mc^2}{\sqrt{1 - \dfrac{v^2}{c^2}}}
$$
and
$$
p = \frac{mv}{\sqrt{1 - \dfrac{v^2}{c^2}}}.
$$
these expressions can be written as
$$
\begin{align}
E_0 &= mc^2 , \\
E &= \gamma mc^2 , \\
p &= mv \gamma ,
\end{align}
$$
where the factor
$$
\gamma = {1}/{\sqrt{1-\frac{v^2}{c^2}}}.
$$
When working in units where , known as the natural unit system, all the relativistic equations are simplified and the quantities energy, momentum, and mass have the same natural dimension:
$$
m^2 = E^2 - p^2.
$$
The equation is often written this way because the difference
$$
E^2 - p^2
$$
is the relativistic length of the energy momentum four-vector, a length which is associated with rest mass or invariant mass in systems. Where and , this equation again expresses the mass–energy equivalence .
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BLOCK8_This results in
$$
E = \frac{mc^2}{\sqrt{1 - \dfrac{v^2}{c^2}}}
$$
and
$$
p = \frac{mv}{\sqrt{1 - \dfrac{v^2}{c^2}}}.
$$
these expressions can be written as
$$
\begin{align}
E_0 &= mc^2 , \\
E &= \gamma mc^2 , \\
p &= mv \gamma ,
\end{align}
$$
where the factor
$$
\gamma = {1}/{\sqrt{1-\frac{v^2}{c^2}}}.
$$
When working in units where , known as the natural unit system, all the relativistic equations are simplified and the quantities energy, momentum, and mass have the same natural dimension:
$$
m^2 = E^2 - p^2.
$$
The equation is often written this way because the difference
$$
E^2 - p^2
$$
is the relativistic length of the energy momentum four-vector, a length which is associated with rest mass or invariant mass in systems. Where and , this equation again expresses the mass–energy equivalence .
##
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Where and , this equation again expresses the mass–energy equivalence .
## The mass of composite systems
The rest mass of a composite system is not the sum of the rest masses of the parts, unless all the parts are at rest. The total mass of a composite system includes the kinetic energy and field energy in the system.
The total energy of a composite system can be determined by adding together the sum of the energies of its components. The total momentum
$$
\vec{p}
$$
of the system, a vector quantity, can also be computed by adding together the momenta of all its components.
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The total energy of a composite system can be determined by adding together the sum of the energies of its components. The total momentum
$$
\vec{p}
$$
of the system, a vector quantity, can also be computed by adding together the momenta of all its components. Given the total energy and the length (magnitude) of the total momentum vector
$$
\vec{p}
$$
, the invariant mass is given by:
$$
m = \frac{\sqrt{E^2 - (pc)^2}}{c^2}
$$
In the system of natural units where , for systems of particles (whether bound or unbound) the total system invariant mass is given equivalently by the following:
$$
m^2 = \left(\sum E\right)^2 - \left\|\sum \vec{p} \ \right\|^2
$$
Where, again, the particle momenta
$$
\vec{p}
$$
are first summed as vectors, and then the square of their resulting total magnitude (Euclidean norm) is used. This results in a scalar number, which is subtracted from the scalar value of the square of the total energy.
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Given the total energy and the length (magnitude) of the total momentum vector
$$
\vec{p}
$$
, the invariant mass is given by:
$$
m = \frac{\sqrt{E^2 - (pc)^2}}{c^2}
$$
In the system of natural units where , for systems of particles (whether bound or unbound) the total system invariant mass is given equivalently by the following:
$$
m^2 = \left(\sum E\right)^2 - \left\|\sum \vec{p} \ \right\|^2
$$
Where, again, the particle momenta
$$
\vec{p}
$$
are first summed as vectors, and then the square of their resulting total magnitude (Euclidean norm) is used. This results in a scalar number, which is subtracted from the scalar value of the square of the total energy.
For such a system, in the special center of momentum frame where momenta sum to zero, again the system mass (called the invariant mass) corresponds to the total system energy or, in units where , is identical to it.
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This results in a scalar number, which is subtracted from the scalar value of the square of the total energy.
For such a system, in the special center of momentum frame where momenta sum to zero, again the system mass (called the invariant mass) corresponds to the total system energy or, in units where , is identical to it. This invariant mass for a system remains the same quantity in any inertial frame, although the system total energy and total momentum are functions of the particular inertial frame which is chosen, and will vary in such a way between inertial frames as to keep the invariant mass the same for all observers. Invariant mass thus functions for systems of particles in the same capacity as "rest mass" does for single particles.
Note that the invariant mass of an isolated system (i.e., one closed to both mass and energy) is also independent of observer or inertial frame, and is a constant, conserved quantity for isolated systems and single observers, even during chemical and nuclear reactions. The concept of invariant mass is widely used in particle physics, because the invariant mass of a particle's decay products is equal to its rest mass. This is used to make measurements of the mass of particles like the Z boson or the top quark.
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The concept of invariant mass is widely used in particle physics, because the invariant mass of a particle's decay products is equal to its rest mass. This is used to make measurements of the mass of particles like the Z boson or the top quark.
## Conservation versus invariance of mass in special relativity
Total energy is an additive conserved quantity (for single observers) in systems and in reactions between particles, but rest mass (in the sense of being a sum of particle rest masses) may not be conserved through an event in which rest masses of particles are converted to other types of energy, such as kinetic energy. Finding the sum of individual particle rest masses would require multiple observers, one for each particle rest inertial frame, and these observers ignore individual particle kinetic energy. Conservation laws require a single observer and a single inertial frame.
In general, for isolated systems and single observers, relativistic mass is conserved (each observer sees it constant over time), but is not invariant (that is, different observers see different values). Invariant mass, however, is both conserved and invariant (all single observers see the same value, which does not change over time).
The relativistic mass corresponds to the energy, so conservation of energy automatically means that relativistic mass is conserved for any given observer and inertial frame.
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Invariant mass, however, is both conserved and invariant (all single observers see the same value, which does not change over time).
The relativistic mass corresponds to the energy, so conservation of energy automatically means that relativistic mass is conserved for any given observer and inertial frame. However, this quantity, like the total energy of a particle, is not invariant. This means that, even though it is conserved for any observer during a reaction, its absolute value will change with the frame of the observer, and for different observers in different frames.
By contrast, the rest mass and invariant masses of systems and particles are conserved also invariant. For example: A closed container of gas (closed to energy as well) has a system "rest mass" in the sense that it can be weighed on a resting scale, even while it contains moving components. This mass is the invariant mass, which is equal to the total relativistic energy of the container (including the kinetic energy of the gas) only when it is measured in the center of momentum frame. Just as is the case for single particles, the calculated "rest mass" of such a container of gas does not change when it is in motion, although its "relativistic mass" does change.
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This mass is the invariant mass, which is equal to the total relativistic energy of the container (including the kinetic energy of the gas) only when it is measured in the center of momentum frame. Just as is the case for single particles, the calculated "rest mass" of such a container of gas does not change when it is in motion, although its "relativistic mass" does change.
The container may even be subjected to a force which gives it an overall velocity, or else (equivalently) it may be viewed from an inertial frame in which it has an overall velocity (that is, technically, a frame in which its center of mass has a velocity). In this case, its total relativistic mass and energy increase. However, in such a situation, although the container's total relativistic energy and total momentum increase, these energy and momentum increases subtract out in the invariant mass definition, so that the moving container's invariant mass will be calculated as the same value as if it were measured at rest, on a scale.
### Closed systems
All conservation laws in special relativity (for energy, mass, and momentum) require isolated systems, meaning systems that are totally isolated, with no mass–energy allowed in or out, over time.
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However, in such a situation, although the container's total relativistic energy and total momentum increase, these energy and momentum increases subtract out in the invariant mass definition, so that the moving container's invariant mass will be calculated as the same value as if it were measured at rest, on a scale.
### Closed systems
All conservation laws in special relativity (for energy, mass, and momentum) require isolated systems, meaning systems that are totally isolated, with no mass–energy allowed in or out, over time. If a system is isolated, then both total energy and total momentum in the system are conserved over time for any observer in any single inertial frame, though their absolute values will vary, according to different observers in different inertial frames. The invariant mass of the system is also conserved, but does not change with different observers. This is also the familiar situation with single particles: all observers calculate the same particle rest mass (a special case of the invariant mass) no matter how they move (what inertial frame they choose), but different observers see different total energies and momenta for the same particle.
Conservation of invariant mass also requires the system to be enclosed so that no heat and radiation (and thus invariant mass) can escape.
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This is also the familiar situation with single particles: all observers calculate the same particle rest mass (a special case of the invariant mass) no matter how they move (what inertial frame they choose), but different observers see different total energies and momenta for the same particle.
Conservation of invariant mass also requires the system to be enclosed so that no heat and radiation (and thus invariant mass) can escape. As in the example above, a physically enclosed or bound system does not need to be completely isolated from external forces for its mass to remain constant, because for bound systems these merely act to change the inertial frame of the system or the observer. Though such actions may change the total energy or momentum of the bound system, these two changes cancel, so that there is no change in the system's invariant mass. This is just the same result as with single particles: their calculated rest mass also remains constant no matter how fast they move, or how fast an observer sees them move.
On the other hand, for systems which are unbound, the "closure" of the system may be enforced by an idealized surface, inasmuch as no mass–energy can be allowed into or out of the test-volume over time, if conservation of system invariant mass is to hold during that time.
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This is just the same result as with single particles: their calculated rest mass also remains constant no matter how fast they move, or how fast an observer sees them move.
On the other hand, for systems which are unbound, the "closure" of the system may be enforced by an idealized surface, inasmuch as no mass–energy can be allowed into or out of the test-volume over time, if conservation of system invariant mass is to hold during that time. If a force is allowed to act on (do work on) only one part of such an unbound system, this is equivalent to allowing energy into or out of the system, and the condition of "closure" to mass–energy (total isolation) is violated. In this case, conservation of invariant mass of the system also will no longer hold. Such a loss of rest mass in systems when energy is removed, according to where is the energy removed, and is the change in rest mass, reflect changes of mass associated with movement of energy, not "conversion" of mass to energy.
### The system invariant mass vs. the individual rest masses of parts of the system
Again, in special relativity, the rest mass of a system is not required to be equal to the sum of the rest masses of the parts (a situation which would be analogous to gross mass-conservation in chemistry).
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### The system invariant mass vs. the individual rest masses of parts of the system
Again, in special relativity, the rest mass of a system is not required to be equal to the sum of the rest masses of the parts (a situation which would be analogous to gross mass-conservation in chemistry). For example, a massive particle can decay into photons which individually have no mass, but which (as a system) preserve the invariant mass of the particle which produced them. Also a box of moving non-interacting particles (e.g., photons, or an ideal gas) will have a larger invariant mass than the sum of the rest masses of the particles which compose it. This is because the total energy of all particles and fields in a system must be summed, and this quantity, as seen in the center of momentum frame, and divided by , is the system's invariant mass.
In special relativity, mass is not "converted" to energy, for all types of energy still retain their associated mass. Neither energy nor invariant mass can be destroyed in special relativity, and each is separately conserved over time in closed systems. Thus, a system's invariant mass may change only because invariant mass is allowed to escape, perhaps as light or heat.
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Neither energy nor invariant mass can be destroyed in special relativity, and each is separately conserved over time in closed systems. Thus, a system's invariant mass may change only because invariant mass is allowed to escape, perhaps as light or heat. Thus, when reactions (whether chemical or nuclear) release energy in the form of heat and light, if the heat and light is not allowed to escape (the system is closed and isolated), the energy will continue to contribute to the system rest mass, and the system mass will not change. Only if the energy is released to the environment will the mass be lost; this is because the associated mass has been allowed out of the system, where it contributes to the mass of the surroundings.
## History of the relativistic mass concept
### Transverse and longitudinal mass
Concepts that were similar to what nowadays is called "relativistic mass", were already developed before the advent of special relativity. For example, it was recognized by J. J. Thomson in 1881 that a charged body is harder to set in motion than an uncharged body, which was worked out in more detail by Oliver Heaviside (1889) and George Frederick Charles Searle (1897). So the electrostatic energy behaves as having some sort of electromagnetic mass
$$
m_\text{em} = \frac{4}{3} E_\text{em}/c^2
$$
, which can increase the normal mechanical mass of the bodies.
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For example, it was recognized by J. J. Thomson in 1881 that a charged body is harder to set in motion than an uncharged body, which was worked out in more detail by Oliver Heaviside (1889) and George Frederick Charles Searle (1897). So the electrostatic energy behaves as having some sort of electromagnetic mass
$$
m_\text{em} = \frac{4}{3} E_\text{em}/c^2
$$
, which can increase the normal mechanical mass of the bodies.
Then, it was pointed out by Thomson and Searle that this electromagnetic mass also increases with velocity. This was further elaborated by Hendrik Lorentz (1899, 1904) in the framework of Lorentz ether theory. He defined mass as the ratio of force to acceleration, not as the ratio of momentum to velocity, so he needed to distinguish between the mass
$$
m_\text{L} = \gamma^3 m
$$
parallel to the direction of motion and the mass
$$
m_\text{T} = \gamma m
$$
perpendicular to the direction of motion (where
$$
\gamma = 1/\sqrt{1 - v^2/c^2}
$$
is the Lorentz factor, is the relative velocity between the ether and the object, and is the speed of light).
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This was further elaborated by Hendrik Lorentz (1899, 1904) in the framework of Lorentz ether theory. He defined mass as the ratio of force to acceleration, not as the ratio of momentum to velocity, so he needed to distinguish between the mass
$$
m_\text{L} = \gamma^3 m
$$
parallel to the direction of motion and the mass
$$
m_\text{T} = \gamma m
$$
perpendicular to the direction of motion (where
$$
\gamma = 1/\sqrt{1 - v^2/c^2}
$$
is the Lorentz factor, is the relative velocity between the ether and the object, and is the speed of light). Only when the force is perpendicular to the velocity, Lorentz's mass is equal to what is now called "relativistic mass". Max Abraham (1902) called
$$
m_\text{L}
$$
longitudinal mass and
$$
m_\text{T}
$$
transverse mass (although Abraham used more complicated expressions than Lorentz's relativistic ones). So, according to Lorentz's theory no body can reach the speed of light because the mass becomes infinitely large at this velocity.
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Max Abraham (1902) called
$$
m_\text{L}
$$
longitudinal mass and
$$
m_\text{T}
$$
transverse mass (although Abraham used more complicated expressions than Lorentz's relativistic ones). So, according to Lorentz's theory no body can reach the speed of light because the mass becomes infinitely large at this velocity.
Albert Einstein also initially used the concepts of longitudinal and transverse mass in his 1905 electrodynamics paper (equivalent to those of Lorentz, but with a different
$$
m_\text{T}
$$
by an unfortunate force definition, which was later corrected), and in another paper in 1906. However, he later abandoned velocity dependent mass concepts (see quote at the end of next section).
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Albert Einstein also initially used the concepts of longitudinal and transverse mass in his 1905 electrodynamics paper (equivalent to those of Lorentz, but with a different
$$
m_\text{T}
$$
by an unfortunate force definition, which was later corrected), and in another paper in 1906. However, he later abandoned velocity dependent mass concepts (see quote at the end of next section).
The precise relativistic expression (which is equivalent to Lorentz's) relating force and acceleration for a particle with non-zero rest mass
$$
m
$$
moving in the x direction with velocity v and associated Lorentz factor
$$
\gamma
$$
is
$$
\begin{align}
f_\text{x} &= m \gamma^3 a_\text{x} &= m_\text{L} a_\text{x}, \\
f_\text{y} &= m \gamma a_\text{y} &= m_\text{T} a_\text{y}, \\
f_\text{z} &= m \gamma a_\text{z} &= m_\text{T} a_\text{z}.
\end{align}
$$
Relativistic mass
In special relativity, an object that has nonzero rest mass cannot travel at the speed of light. As the object approaches the speed of light, the object's energy and momentum increase without bound.
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The precise relativistic expression (which is equivalent to Lorentz's) relating force and acceleration for a particle with non-zero rest mass
$$
m
$$
moving in the x direction with velocity v and associated Lorentz factor
$$
\gamma
$$
is
$$
\begin{align}
f_\text{x} &= m \gamma^3 a_\text{x} &= m_\text{L} a_\text{x}, \\
f_\text{y} &= m \gamma a_\text{y} &= m_\text{T} a_\text{y}, \\
f_\text{z} &= m \gamma a_\text{z} &= m_\text{T} a_\text{z}.
\end{align}
$$
Relativistic mass
In special relativity, an object that has nonzero rest mass cannot travel at the speed of light. As the object approaches the speed of light, the object's energy and momentum increase without bound.
In the first years after 1905, following Lorentz and Einstein, the terms longitudinal and transverse mass were still in use. However, those expressions were replaced by the concept of relativistic mass, an expression which was first defined by Gilbert N. Lewis and Richard C. Tolman in 1909.
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In the first years after 1905, following Lorentz and Einstein, the terms longitudinal and transverse mass were still in use. However, those expressions were replaced by the concept of relativistic mass, an expression which was first defined by Gilbert N. Lewis and Richard C. Tolman in 1909. They defined the total energy and mass of a body as
$$
m_\text{rel} = \frac{E}{c^2},
$$
and of a body at rest
$$
m_0 = \frac{E_0}{c^2},
$$
with the ratio
$$
\frac{m_\text{rel}}{m_0} = \gamma.
$$
Tolman in 1912 further elaborated on this concept, and stated: "the expression m0(1 − v/c)−1/2 is best suited for the mass of a moving body. "
In 1934, Tolman argued that the relativistic mass formula
$$
m_\text{rel} = E / c^2
$$
holds for all particles, including those moving at the speed of light, while the formula
$$
m_\text{rel} = \gamma m_0
$$
only applies to a slower-than-light particle (a particle with a nonzero rest mass). Tolman remarked on this relation that "We have, moreover, of course the experimental verification of the expression in the case of moving electrons ...
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"
In 1934, Tolman argued that the relativistic mass formula
$$
m_\text{rel} = E / c^2
$$
holds for all particles, including those moving at the speed of light, while the formula
$$
m_\text{rel} = \gamma m_0
$$
only applies to a slower-than-light particle (a particle with a nonzero rest mass). Tolman remarked on this relation that "We have, moreover, of course the experimental verification of the expression in the case of moving electrons ... We shall hence have no hesitation in accepting the expression as correct in general for the mass of a moving particle."
When the relative velocity is zero,
$$
\gamma
$$
is simply equal to 1, and the relativistic mass is reduced to the rest mass as one can see in the next two equations below. As the velocity increases toward the speed of light c, the denominator of the right side approaches zero, and consequently
$$
\gamma
$$
approaches infinity.
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When the relative velocity is zero,
$$
\gamma
$$
is simply equal to 1, and the relativistic mass is reduced to the rest mass as one can see in the next two equations below. As the velocity increases toward the speed of light c, the denominator of the right side approaches zero, and consequently
$$
\gamma
$$
approaches infinity. While Newton's second law remains valid in the form
$$
\mathbf{f} = \frac{d(m_\text{rel}\mathbf{v})}{dt},
$$
the derived form
$$
\mathbf{f} = m_\text{rel} \mathbf{a}
$$
is not valid because
$$
m_\text{rel}
$$
in
$$
{d(m_\text{rel}\mathbf{v})}
$$
is generally not a constant (see the section above on transverse and longitudinal mass).
Even though Einstein initially used the expressions "longitudinal" and "transverse" mass in two papers (see previous section), in his first paper on
$$
E = mc^2
$$
(1905) he treated as what would now be called the rest mass. Einstein never derived an equation for "relativistic mass", and in later years he expressed his dislike of the idea:
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Even though Einstein initially used the expressions "longitudinal" and "transverse" mass in two papers (see previous section), in his first paper on
$$
E = mc^2
$$
(1905) he treated as what would now be called the rest mass. Einstein never derived an equation for "relativistic mass", and in later years he expressed his dislike of the idea:
### Popular science and textbooks
The concept of relativistic mass is widely used in popular science writing and in high school and undergraduate textbooks. Authors such as Okun and A. B. Arons have argued against this as archaic and confusing, and not in accord with modern relativistic theory. Also in
Arons wrote:
For many years it was conventional to enter the discussion of dynamics through derivation of the relativistic mass, that is the mass–velocity relation, and this is probably still the dominant mode in textbooks. More recently, however, it has been increasingly recognized that relativistic mass is a troublesome and dubious concept. [See, for example, Okun (1989).]... The sound and rigorous approach to relativistic dynamics is through direct development of that expression for momentum that ensures conservation of momentum in all frames: rather than through relativistic mass.
C. Alder takes a similarly dismissive stance on mass in relativity.
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The sound and rigorous approach to relativistic dynamics is through direct development of that expression for momentum that ensures conservation of momentum in all frames: rather than through relativistic mass.
C. Alder takes a similarly dismissive stance on mass in relativity. Writing on said subject matter, he says that "its introduction into the theory of special relativity was much in the way of a historical accident", noting towards the widespread knowledge of and how the public's interpretation of the equation has largely informed how it is taught in higher education. He instead supposes that the difference between rest and relativistic mass should be explicitly taught, so that students know why mass should be thought of as invariant "in most discussions of inertia".
Many contemporary authors such as Taylor and Wheeler avoid using the concept of relativistic mass altogether:
While spacetime has the unbounded geometry of Minkowski space, the velocity-space is bounded by and has the geometry of hyperbolic geometry where relativistic mass plays an analogous role to that of Newtonian mass in the barycentric coordinates of Euclidean geometry. The connection of velocity to hyperbolic geometry enables the 3-velocity-dependent relativistic mass to be related to the 4-velocity Minkowski formalism.
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A search engine is a software system that provides hyperlinks to web pages and other relevant information on the Web in response to a user's query. The user inputs a query within a web browser or a mobile app, and the search results are often a list of hyperlinks, accompanied by textual summaries and images. Users also have the option of limiting the search to a specific type of results, such as images, videos, or news.
For a search provider, its engine is part of a distributed computing system that can encompass many data centers throughout the world. The speed and accuracy of an engine's response to a query is based on a complex system of indexing that is continuously updated by automated web crawlers. This can include data mining the files and databases stored on web servers, but some content is not accessible to crawlers.
There have been many search engines since the dawn of the Web in the 1990s, but Google Search became the dominant one in the 2000s and has remained so. It currently has a 90% global market share. The business of websites improving their visibility in search results, known as marketing and optimization, has thus largely focused on Google.
## History
+ Timeline (full list) Year Engine Current status1993W3CatalogALIWEBJumpStationWWW Worm1994WebCrawlerGo.com, redirects to Disney
### Lycos
Infoseek, redirects to Disney1995
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Year Engine Current status1993W3CatalogALIWEBJumpStationWWW Worm1994WebCrawlerGo.com, redirects to Disney
### Lycos
Infoseek, redirects to Disney1995
### Yahoo!
Search, initially a search function for Yahoo! DirectoryDaumSearch.chMagellan
### Excite
MetaCrawlerAltaVista, acquired by Yahoo!
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in 2003, since 2013 redirects to Yahoo!SAPO1996RankDex, incorporated into Baidu in 2000DogpileHotBot (used Inktomi search technology)Ask Jeeves (rebranded ask.com)1997AOL NetFind (rebranded AOL Search since 1999)goo.ne.jpNorthern LightYandex1998GoogleIxquick as Startpage.comMSN Search as Bingempas (merged with NATE)1999AlltheWeb (URL redirected to Yahoo!)GenieKnows, rebranded Yellowee (was redirecting to justlocalbusiness.com)NaverTeoma (redirect to Ask.com)2000BaiduExaleadGigablast2001Kartoo2003Info.com2004A9.comClusty (redirect to DuckDuckGo)MojeekSogou2005SearchMeKidzSearch, Google Search2006Soso, merged with SogouQuaeroSearch.comChaChaAsk.comLive Search as Bing, rebranded MSN Search2007wikiseekSprooseWikia SearchBlackle.com, Google Search2008Powerset (redirects to Bing)PicollatorViewziBoogamiLeapFishForestle (redirects to Ecosia)DuckDuckGoTinEye2009Bing, rebranded Live SearchYebolScout (Goby)NATEEcosiaStartpage.com, sister engine of Ixquick2010Blekko, sold to IBMCuilYandex (English)Parsijoo2011YaCy, P2P2012Volunia2013Qwant2014Egerin, Kurdish / SoraniSwisscowsSearx2015YoozCliqz2016Kiddle, Google Search2017Presearch2018Kagi2020Petal2021Brave SearchQueyeYou.com
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### Pre-1990s
In 1945, Vannevar Bush described an information retrieval system that would allow a user to access a great expanse of information, all at a single desk. He called it a memex. He described the system in an article titled "As We May Think" that was published in The Atlantic Monthly. The memex was intended to give a user the capability to overcome the ever-increasing difficulty of locating information in ever-growing centralized indices of scientific work. Vannevar Bush envisioned libraries of research with connected annotations, which are similar to modern hyperlinks.
Link analysis eventually became a crucial component of search engines through algorithms such as Hyper Search and PageRank.
### 1990s: Birth of search engines
The first internet search engines predate the debut of the Web in December 1990: WHOIS user search dates back to 1982, and the Knowbot Information Service multi-network user search was first implemented in 1989. The first well documented search engine that searched content files, namely FTP files, was
### Archie
, which debuted on 10 September 1990.
Prior to September 1993, the World Wide Web was entirely indexed by hand. There was a list of webservers edited by Tim Berners-Lee and hosted on the CERN webserver. One snapshot of the list in 1992 remains, but as more and more web servers went online the central list could no longer keep up.
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There was a list of webservers edited by Tim Berners-Lee and hosted on the CERN webserver. One snapshot of the list in 1992 remains, but as more and more web servers went online the central list could no longer keep up. On the NCSA site, new servers were announced under the title "What's New!".
The first tool used for searching content (as opposed to users) on the Internet was Archie. The name stands for "archive" without the "v". It was created by Alan Emtage, computer science student at McGill University in Montreal, Quebec, Canada. The program downloaded the directory listings of all the files located on public anonymous FTP (File Transfer Protocol) sites, creating a searchable database of file names; however, Archie Search Engine did not index the contents of these sites since the amount of data was so limited it could be readily searched manually.
The rise of Gopher (created in 1991 by Mark McCahill at the University of Minnesota) led to two new search programs,
### Veronica
and Jughead. Like Archie, they searched the file names and titles stored in Gopher index systems. Veronica (Very Easy Rodent-Oriented Net-wide Index to Computerized Archives) provided a keyword search of most Gopher menu titles in the entire Gopher listings.
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Like Archie, they searched the file names and titles stored in Gopher index systems. Veronica (Very Easy Rodent-Oriented Net-wide Index to Computerized Archives) provided a keyword search of most Gopher menu titles in the entire Gopher listings. Jughead (Jonzy's Universal Gopher Hierarchy Excavation And Display) was a tool for obtaining menu information from specific Gopher servers. While the name of the search engine "Archie Search Engine" was not a reference to the Archie comic book series, "Veronica" and "Jughead" are characters in the series, thus referencing their predecessor.
In the summer of 1993, no search engine existed for the web, though numerous specialized catalogs were maintained by hand. Oscar Nierstrasz at the University of Geneva wrote a series of Perl scripts that periodically mirrored these pages and rewrote them into a standard format. This formed the basis for W3Catalog, the web's first primitive search engine, released on September 2, 1993.
In June 1993, Matthew Gray, then at MIT, produced what was probably the first web robot, the Perl-based World Wide Web Wanderer, and used it to generate an index called "Wandex". The purpose of the Wanderer was to measure the size of the World Wide Web, which it did until late 1995. The web's second search engine Aliweb appeared in November 1993.
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The purpose of the Wanderer was to measure the size of the World Wide Web, which it did until late 1995. The web's second search engine Aliweb appeared in November 1993. Aliweb did not use a web robot, but instead depended on being notified by website administrators of the existence at each site of an index file in a particular format.
JumpStation (created in December 1993 by Jonathon Fletcher) used a web robot to find web pages and to build its index, and used a web form as the interface to its query program. It was thus the first WWW resource-discovery tool to combine the three essential features of a web search engine (crawling, indexing, and searching) as described below. Because of the limited resources available on the platform it ran on, its indexing and hence searching were limited to the titles and headings found in the web pages the crawler encountered.
One of the first "all text" crawler-based search engines was WebCrawler, which came out in 1994. Unlike its predecessors, it allowed users to search for any word in any web page, which has become the standard for all major search engines since. It was also the search engine that was widely known by the public. Also, in 1994, Lycos (which started at Carnegie Mellon University) was launched and became a major commercial endeavor.
The first popular search engine on the Web was Yahoo! Search.
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The first popular search engine on the Web was Yahoo! Search. The first product from Yahoo!, founded by Jerry Yang and David Filo in January 1994, was a Web directory called Yahoo! Directory. In 1995, a search function was added, allowing users to search Yahoo! Directory. It became one of the most popular ways for people to find web pages of interest, but its search function operated on its web directory, rather than its full-text copies of web pages.
Soon after, a number of search engines appeared and vied for popularity. These included Magellan, Excite, Infoseek, Inktomi, Northern Light, and AltaVista. Information seekers could also browse the directory instead of doing a keyword-based search.
In 1996, Robin Li developed the RankDex site-scoring algorithm for search engines results page rankingYanhong Li, "Toward a Qualitative Search Engine", IEEE Internet Computing, vol. 2, no. 4, pp. 24–29, July/Aug. 1998, and received a US patent for the technology. It was the first search engine that used hyperlinks to measure the quality of websites it was indexing, predating the very similar algorithm patent filed by Google two years later in 1998. Larry Page referenced Li's work in some of his U.S. patents for PageRank.
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It was the first search engine that used hyperlinks to measure the quality of websites it was indexing, predating the very similar algorithm patent filed by Google two years later in 1998. Larry Page referenced Li's work in some of his U.S. patents for PageRank. Li later used his Rankdex technology for the Baidu search engine, which was founded by him in China and launched in 2000.
In 1996, Netscape was looking to give a single search engine an exclusive deal as the featured search engine on Netscape's web browser. There was so much interest that instead, Netscape struck deals with five of the major search engines: for $5 million a year, each search engine would be in rotation on the Netscape search engine page. The five engines were Yahoo!, Magellan, Lycos, Infoseek, and Excite.
Google adopted the idea of selling search terms in 1998 from a small search engine company named goto.com. This move had a significant effect on the search engine business, which went from struggling to one of the most profitable businesses in the Internet.
Search engines were also known as some of the brightest stars in the Internet investing frenzy that occurred in the late 1990s. Several companies entered the market spectacularly, receiving record gains during their initial public offerings. Some have taken down their public search engine and are marketing enterprise-only editions, such as Northern Light.
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Several companies entered the market spectacularly, receiving record gains during their initial public offerings. Some have taken down their public search engine and are marketing enterprise-only editions, such as Northern Light. Many search engine companies were caught up in the dot-com bubble, a speculation-driven market boom that peaked in March 2000.
### 2000s–present: Post dot-com bubble
Around 2000, Google's search engine rose to prominence. The company achieved better results for many searches with an algorithm called PageRank, as was explained in the paper Anatomy of a Search Engine written by Sergey Brin and Larry Page, the later founders of Google. This iterative algorithm ranks web pages based on the number and PageRank of other web sites and pages that link there, on the premise that good or desirable pages are linked to more than others. Larry Page's patent for PageRank cites Robin Li's earlier RankDex patent as an influence. Google also maintained a minimalist interface to its search engine. In contrast, many of its competitors embedded a search engine in a web portal. In fact, the Google search engine became so popular that spoof engines emerged such as Mystery Seeker.
By 2000, Yahoo! was providing search services based on Inktomi's search engine. Yahoo! acquired Inktomi in 2002, and Overture (which owned AlltheWeb and AltaVista) in 2003.
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By 2000, Yahoo! was providing search services based on Inktomi's search engine. Yahoo! acquired Inktomi in 2002, and Overture (which owned AlltheWeb and AltaVista) in 2003. Yahoo! switched to Google's search engine until 2004, when it launched its own search engine based on the combined technologies of its acquisitions.
Microsoft first launched MSN Search in the fall of 1998 using search results from Inktomi. In early 1999, the site began to display listings from Looksmart, blended with results from Inktomi. For a short time in 1999, MSN Search used results from AltaVista instead. In 2004, Microsoft began a transition to its own search technology, powered by its own web crawler (called msnbot).
Microsoft's rebranded search engine, Bing, was launched on June 1, 2009. On July 29, 2009, Yahoo! and Microsoft finalized a deal in which Yahoo! Search would be powered by Microsoft Bing technology.
As of 2019 active search engine crawlers include those of Google, Sogou, Baidu, Bing, Gigablast, Mojeek, DuckDuckGo and Yandex.
## Approach
A search engine maintains the following processes in near real time:
1. Web crawling
1. Indexing
1. Searching
Web search engines get their information by web crawling from site to site. The "spider" checks for the standard filename robots.txt, addressed to it.
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Searching
Web search engines get their information by web crawling from site to site. The "spider" checks for the standard filename robots.txt, addressed to it. The robots.txt file contains directives for search spiders, telling it which pages to crawl and which pages not to crawl. After checking for robots.txt and either finding it or not, the spider sends certain information back to be indexed depending on many factors, such as the titles, page content, JavaScript, Cascading Style Sheets (CSS), headings, or its metadata in HTML meta tags. After a certain number of pages crawled, amount of data indexed, or time spent on the website, the spider stops crawling and moves on. "[N]o web crawler may actually crawl the entire reachable web. Due to infinite websites, spider traps, spam, and other exigencies of the real web, crawlers instead apply a crawl policy to determine when the crawling of a site should be deemed sufficient. Some websites are crawled exhaustively, while others are crawled only partially".
Indexing means associating words and other definable tokens found on web pages to their domain names and HTML-based fields. The associations are stored in a public database and accessible through web search queries. A query from a user can be a single word, multiple words or a sentence.
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The associations are stored in a public database and accessible through web search queries. A query from a user can be a single word, multiple words or a sentence. The index helps find information relating to the query as quickly as possible. Some of the techniques for indexing, and caching are trade secrets, whereas web crawling is a straightforward process of visiting all sites on a systematic basis.
Between visits by the spider, the cached version of the page (some or all the content needed to render it) stored in the search engine working memory is quickly sent to an inquirer. If a visit is overdue, the search engine can just act as a web proxy instead. In this case, the page may differ from the search terms indexed. The cached page holds the appearance of the version whose words were previously indexed, so a cached version of a page can be useful to the website when the actual page has been lost, but this problem is also considered a mild form of linkrot.
Typically when a user enters a query into a search engine it is a few keywords. The index already has the names of the sites containing the keywords, and these are instantly obtained from the index. The real processing load is in generating the web pages that are the search results list: Every page in the entire list must be weighted according to information in the indexes.
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The index already has the names of the sites containing the keywords, and these are instantly obtained from the index. The real processing load is in generating the web pages that are the search results list: Every page in the entire list must be weighted according to information in the indexes. Then the top search result item requires the lookup, reconstruction, and markup of the snippets showing the context of the keywords matched. These are only part of the processing each search results web page requires, and further pages (next to the top) require more of this post-processing.
Beyond simple keyword lookups, search engines offer their own GUI- or command-driven operators and search parameters to refine the search results. These provide the necessary controls for the user engaged in the feedback loop users create by filtering and weighting while refining the search results, given the initial pages of the first search results.
For example, from 2007 the Google.com search engine has allowed one to filter by date by clicking "Show search tools" in the leftmost column of the initial search results page, and then selecting the desired date range. It is also possible to weight by date because each page has a modification time. Most search engines support the use of the Boolean operators AND, OR and NOT to help end users refine the search query. Boolean operators are for literal searches that allow the user to refine and extend the terms of the search.
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Most search engines support the use of the Boolean operators AND, OR and NOT to help end users refine the search query. Boolean operators are for literal searches that allow the user to refine and extend the terms of the search. The engine looks for the words or phrases exactly as entered. Some search engines provide an advanced feature called proximity search, which allows users to define the distance between keywords. There is also concept-based searching where the research involves using statistical analysis on pages containing the words or phrases you search for.
The usefulness of a search engine depends on the relevance of the result set it gives back. While there may be millions of web pages that include a particular word or phrase, some pages may be more relevant, popular, or authoritative than others. Most search engines employ methods to rank the results to provide the "best" results first. How a search engine decides which pages are the best matches, and what order the results should be shown in, varies widely from one engine to another. The methods also change over time as Internet usage changes and new techniques evolve. There are two main types of search engine that have evolved: one is a system of predefined and hierarchically ordered keywords that humans have programmed extensively. The other is a system that generates an "inverted index" by analyzing texts it locates.
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There are two main types of search engine that have evolved: one is a system of predefined and hierarchically ordered keywords that humans have programmed extensively. The other is a system that generates an "inverted index" by analyzing texts it locates. This first form relies much more heavily on the computer itself to do the bulk of the work.
Most Web search engines are commercial ventures supported by advertising revenue and thus some of them allow advertisers to have their listings ranked higher in search results for a fee. Search engines that do not accept money for their search results make money by running search related ads alongside the regular search engine results. The search engines make money every time someone clicks on one of these ads.
### Local search
Local search is the process that optimizes the efforts of local businesses. They focus on change to make sure all searches are consistent. It is important because many people determine where they plan to go and what to buy based on their searches.
## Market share
As of January 2022 Google is by far the world's most used search engine, with a market share of 90%, and the world's other most used search engines were Bing at 4%, Yandex at 2%, Yahoo! at 1%. Other search engines not listed have less than a 3% market share. In 2024, Google's dominance was ruled an illegal monopoly in a case brought by the US Department of Justice.
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Other search engines not listed have less than a 3% market share. In 2024, Google's dominance was ruled an illegal monopoly in a case brought by the US Department of Justice.
### Russia and East Asia
In Russia, Yandex has a market share of 62.6%, compared to Google's 28.3%. Yandex is the second most used search engine on smartphones in Asia and
### Europe
. In China, Baidu is the most popular search engine. South Korea-based search portal Naver is used for 62.8% of online searches in the country. Yahoo! Japan and Yahoo! Taiwan are the most popular choices for Internet searches in Japan and Taiwan, respectively. China is one of few countries where Google is not in the top three web search engines for market share. Google was previously more popular in China, but withdrew significantly after a disagreement with the government over censorship and a cyberattack. Bing, however, is in the top three web search engines with a market share of 14.95%. Baidu is top with 49.1% of the market share.
Europe
Most countries' markets in the European Union are dominated by Google, except for the Czech Republic, where Seznam is a strong competitor.
The search engine Qwant is based in Paris, France, where it attracts most of its 50 million monthly registered users from.
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Europe
Most countries' markets in the European Union are dominated by Google, except for the Czech Republic, where Seznam is a strong competitor.
The search engine Qwant is based in Paris, France, where it attracts most of its 50 million monthly registered users from.
## Search engine bias
Although search engines are programmed to rank websites based on some combination of their popularity and relevancy, empirical studies indicate various political, economic, and social biases in the information they provide and the underlying assumptions about the technology. These biases can be a direct result of economic and commercial processes (e.g., companies that advertise with a search engine can become also more popular in its organic search results), and political processes (e.g., the removal of search results to comply with local laws). For example, Google will not surface certain neo-Nazi websites in France and Germany, where Holocaust denial is illegal.
Biases can also be a result of social processes, as search engine algorithms are frequently designed to exclude non-normative viewpoints in favor of more "popular" results. Indexing algorithms of major search engines skew towards coverage of U.S.-based sites, rather than websites from non-U.S. countries.
Google Bombing is one example of an attempt to manipulate search results for political, social or commercial reasons.
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Indexing algorithms of major search engines skew towards coverage of U.S.-based sites, rather than websites from non-U.S. countries.
Google Bombing is one example of an attempt to manipulate search results for political, social or commercial reasons.
Several scholars have studied the cultural changes triggered by search engines, and the representation of certain controversial topics in their results, such as terrorism in Ireland, climate change denial, and conspiracy theories.
## Customized results and filter bubbles
There has been concern raised that search engines such as Google and Bing provide customized results based on the user's activity history, leading to what has been termed echo chambers or filter bubbles by Eli Pariser in 2011. The argument is that search engines and social media platforms use algorithms to selectively guess what information a user would like to see, based on information about the user (such as location, past click behaviour and search history). As a result, websites tend to show only information that agrees with the user's past viewpoint. According to Eli Pariser users get less exposure to conflicting viewpoints and are isolated intellectually in their own informational bubble. Since this problem has been identified, competing search engines have emerged that seek to avoid this problem by not tracking or "bubbling" users, such as DuckDuckGo. However many scholars have questioned Pariser's view, finding that there is little evidence for the filter bubble.
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Since this problem has been identified, competing search engines have emerged that seek to avoid this problem by not tracking or "bubbling" users, such as DuckDuckGo. However many scholars have questioned Pariser's view, finding that there is little evidence for the filter bubble. On the contrary, a number of studies trying to verify the existence of filter bubbles have found only minor levels of personalisation in search, that most people encounter a range of views when browsing online, and that Google news tends to promote mainstream established news outlets.
## Religious search engines
The global growth of the Internet and electronic media in the Arab and Muslim world during the last decade has encouraged Islamic adherents in the Middle East and Asian sub-continent, to attempt their own search engines, their own filtered search portals that would enable users to perform safe searches. More than usual safe search filters, these Islamic web portals categorizing websites into being either "halal" or "haram", based on interpretation of Sharia law. ImHalal came online in September 2011. Halalgoogling came online in July 2013. These use haram filters on the collections from Google and Bing (and others).
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Halalgoogling came online in July 2013. These use haram filters on the collections from Google and Bing (and others).
While lack of investment and slow pace in technologies in the Muslim world has hindered progress and thwarted success of an Islamic search engine, targeting as the main consumers Islamic adherents, projects like Muxlim (a Muslim lifestyle site) received millions of dollars from investors like Rite Internet Ventures, and it also faltered. Other religion-oriented search engines are Jewogle, the Jewish version of Google, and Christian search engine SeekFind.org. SeekFind filters sites that attack or degrade their faith.
## Search engine submission
Web search engine submission is a process in which a webmaster submits a website directly to a search engine. While search engine submission is sometimes presented as a way to promote a website, it generally is not necessary because the major search engines use web crawlers that will eventually find most web sites on the Internet without assistance. They can either submit one web page at a time, or they can submit the entire site using a sitemap, but it is normally only necessary to submit the home page of a web site as search engines are able to crawl a well designed website. There are two remaining reasons to submit a web site or web page to a search engine: to add an entirely new web site without waiting for a search engine to discover it, and to have a web site's record updated after a substantial redesign.
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They can either submit one web page at a time, or they can submit the entire site using a sitemap, but it is normally only necessary to submit the home page of a web site as search engines are able to crawl a well designed website. There are two remaining reasons to submit a web site or web page to a search engine: to add an entirely new web site without waiting for a search engine to discover it, and to have a web site's record updated after a substantial redesign.
Some search engine submission software not only submits websites to multiple search engines, but also adds links to websites from their own pages. This could appear helpful in increasing a website's ranking, because external links are one of the most important factors determining a website's ranking. However, John Mueller of Google has stated that this "can lead to a tremendous number of unnatural links for your site" with a negative impact on site ranking.
## Comparison to social bookmarking
## Technology
Archie
The first web search engine was Archie, created in 1990 by Alan Emtage, a student at McGill University in Montreal. The author originally wanted to call the program "archives", but had to shorten it to comply with the Unix world standard of assigning programs and files short, cryptic names such as grep, cat, troff, sed, awk, perl, and so on.
The primary method of storing and retrieving files was via the File Transfer Protocol (FTP).
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The author originally wanted to call the program "archives", but had to shorten it to comply with the Unix world standard of assigning programs and files short, cryptic names such as grep, cat, troff, sed, awk, perl, and so on.
The primary method of storing and retrieving files was via the File Transfer Protocol (FTP). This was (and still is) a system that specified a common way for computers to exchange files over the Internet. It works like this: Some administrator decides that he wants to make files available from his computer. He sets up a program on his computer, called an FTP server. When someone on the Internet wants to retrieve a file from this computer, he or she connects to it via another program called an FTP client. Any FTP client program can connect with any FTP server program as long as the client and server programs both fully follow the specifications set forth in the FTP protocol.
Initially, anyone who wanted to share a file had to set up an FTP server in order to make the file available to others. Later, "anonymous" FTP sites became repositories for files, allowing all users to post and retrieve them.
Even with archive sites, many important files were still scattered on small FTP servers. These files could be located only by the Internet equivalent of word of mouth: Somebody would post an e-mail to a message list or a discussion forum announcing the availability of a file.
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Even with archive sites, many important files were still scattered on small FTP servers. These files could be located only by the Internet equivalent of word of mouth: Somebody would post an e-mail to a message list or a discussion forum announcing the availability of a file.
Archie changed all that. It combined a script-based data gatherer, which fetched site listings of anonymous FTP files, with a regular expression matcher for retrieving file names matching a user query. (4) In other words, Archie's gatherer scoured FTP sites across the Internet and indexed all of the files it found. Its regular expression matcher provided users with access to its database.
Veronica
In 1993, the University of Nevada System Computing Services group developed Veronica. It was created as a type of searching device similar to Archie but for Gopher files. Another Gopher search service, called Jughead, appeared a little later, probably for the sole purpose of rounding out the comic-strip triumvirate. Jughead is an acronym for Jonzy's Universal Gopher Hierarchy Excavation and Display, although, like Veronica, it is probably safe to assume that the creator backed into the acronym. Jughead's functionality was pretty much identical to Veronica's, although it appears to be a little rougher around the edges.
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Jughead is an acronym for Jonzy's Universal Gopher Hierarchy Excavation and Display, although, like Veronica, it is probably safe to assume that the creator backed into the acronym. Jughead's functionality was pretty much identical to Veronica's, although it appears to be a little rougher around the edges.
### The Lone Wanderer
The World Wide Web Wanderer, developed by Matthew Gray in 1993 was the first robot on the Web and was designed to track the Web's growth. Initially, the Wanderer counted only Web servers, but shortly after its introduction, it started to capture URLs as it went along. The database of captured URLs became the Wandex, the first web database.
Matthew Gray's Wanderer created quite a controversy at the time, partially because early versions of the software ran rampant through the Net and caused a noticeable netwide performance degradation. This degradation occurred because the Wanderer would access the same page hundreds of times a day. The Wanderer soon amended its ways, but the controversy over whether robots were good or bad for the Internet remained.
In response to the Wanderer, Martijn Koster created Archie-Like Indexing of the Web, or ALIWEB, in October 1993. As the name implies, ALIWEB was the HTTP equivalent of Archie, and because of this, it is still unique in many ways.
ALIWEB does not have a web-searching robot.
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As the name implies, ALIWEB was the HTTP equivalent of Archie, and because of this, it is still unique in many ways.
ALIWEB does not have a web-searching robot. Instead, webmasters of participating sites post their own index information for each page they want listed. The advantage to this method is that users get to describe their own site, and a robot does not run about eating up Net bandwidth. The disadvantages of ALIWEB are more of a problem today. The primary disadvantage is that a special indexing file must be submitted. Most users do not understand how to create such a file, and therefore they do not submit their pages. This leads to a relatively small database, which meant that users are less likely to search ALIWEB than one of the large bot-based sites. This Catch-22 has been somewhat offset by incorporating other databases into the ALIWEB search, but it still does not have the mass appeal of search engines such as Yahoo! or Lycos.
Excite
Excite, initially called Architext, was started by six Stanford undergraduates in February 1993. Their idea was to use statistical analysis of word relationships in order to provide more efficient searches through the large amount of information on the Internet.
Their project was fully funded by mid-1993. Once funding was secured. they released a version of their search software for webmasters to use on their own web sites.
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Once funding was secured. they released a version of their search software for webmasters to use on their own web sites. At the time, the software was called Architext, but it now goes by the name of Excite for Web Servers.
Excite was the first serious commercial search engine which launched in 1995. It was developed in Stanford and was purchased for $6.5 billion by @Home. In 2001 Excite and @Home went bankrupt and InfoSpace bought Excite for $10 million.
Some of the first analysis of web searching was conducted on search logs from Excite
Yahoo!
In April 1994, two Stanford University Ph.D. candidates, David Filo and Jerry Yang, created some pages that became rather popular. They called the collection of pages Yahoo! Their official explanation for the name choice was that they considered themselves to be a pair of yahoos.
As the number of links grew and their pages began to receive thousands of hits a day, the team created ways to better organize the data. In order to aid in data retrieval, Yahoo! (www.yahoo.com) became a searchable directory. The search feature was a simple database search engine. Because Yahoo! entries were entered and categorized manually, Yahoo! was not really classified as a search engine. Instead, it was generally considered to be a searchable directory.
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entries were entered and categorized manually, Yahoo! was not really classified as a search engine. Instead, it was generally considered to be a searchable directory. Yahoo! has since automated some aspects of the gathering and classification process, blurring the distinction between engine and directory.
The Wanderer captured only URLs, which made it difficult to find things that were not explicitly described by their URL. Because URLs are rather cryptic to begin with, this did not help the average user. Searching Yahoo! or the Galaxy was much more effective because they contained additional descriptive information about the indexed sites.
Lycos
At Carnegie Mellon University during July 1994, Michael Mauldin, on leave from CMU, developed the Lycos search engine.
### Types of web search engines
Search engines on the web are sites enriched with facility to search the content stored on other sites. There is difference in the way various search engines work, but they all perform three basic tasks.
1. Finding and selecting full or partial content based on the keywords provided.
1. Maintaining index of the content and referencing to the location they find
1. Allowing users to look for words or combinations of words found in that index.
The process begins when a user enters a query statement into the system through the interface provided.
Type Example Description Conventional librarycatalog Search by keyword, title, author, etc.
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The process begins when a user enters a query statement into the system through the interface provided.
Type Example Description Conventional librarycatalog Search by keyword, title, author, etc. Text-based Google, Bing, Yahoo! Search by keywords. Limited search using queries in natural language. Voice-based Google, Bing, Yahoo! Search by keywords. Limited search using queries in natural language. Multimedia search QBIC, WebSeek, SaFe Search by visual appearance (shapes, colors,..) Q/A Stack Exchange, NSIR Search in (restricted) natural language Clustering Systems Vivisimo, Clusty Research Systems Lemur, Nutch
There are basically three types of search engines: Those that are powered by robots (called crawlers; ants or spiders) and those that are powered by human submissions; and those that are a hybrid of the two.
Crawler-based search engines are those that use automated software agents (called crawlers) that visit a Web site, read the information on the actual site, read the site's meta tags and also follow the links that the site connects to performing indexing on all linked Web sites as well. The crawler returns all that information back to a central depository, where the data is indexed. The crawler will periodically return to the sites to check for any information that has changed.
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The crawler returns all that information back to a central depository, where the data is indexed. The crawler will periodically return to the sites to check for any information that has changed. The frequency with which this happens is determined by the administrators of the search engine.
Human-powered search engines rely on humans to submit information that is subsequently indexed and catalogued. Only information that is submitted is put into the index.
In both cases, when you query a search engine to locate information, you're actually searching through the index that the search engine has created —you are not actually searching the Web. These indices are giant databases of information that is collected and stored and subsequently searched. This explains why sometimes a search on a commercial search engine, such as Yahoo! or Google, will return results that are, in fact, dead links. Since the search results are based on the index, if the index has not been updated since a Web page became invalid the search engine treats the page as still an active link even though it no longer is. It will remain that way until the index is updated.
So why will the same search on different search engines produce different results? Part of the answer to that question is because not all indices are going to be exactly the same. It depends on what the spiders find or what the humans submitted. But more important, not every search engine uses the same algorithm to search through the indices.
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It depends on what the spiders find or what the humans submitted. But more important, not every search engine uses the same algorithm to search through the indices. The algorithm is what the search engines use to determine the relevance of the information in the index to what the user is searching for.
One of the elements that a search engine algorithm scans for is the frequency and location of keywords on a Web page. Those with higher frequency are typically considered more relevant. But search engine technology is becoming sophisticated in its attempt to discourage what is known as keyword stuffing, or spamdexing.
Another common element that algorithms analyze is the way that pages link to other pages in the Web. By analyzing how pages link to each other, an engine can both determine what a page is about (if the keywords of the linked pages are similar to the keywords on the original page) and whether that page is considered "important" and deserving of a boost in ranking. Just as the technology is becoming increasingly sophisticated to ignore keyword stuffing, it is also becoming more savvy to Web masters who build artificial links into their sites in order to build an artificial ranking.
Modern web search engines are highly intricate software systems that employ technology that has evolved over the years. There are a number of sub-categories of search engine software that are separately applicable to specific 'browsing' needs.
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Modern web search engines are highly intricate software systems that employ technology that has evolved over the years. There are a number of sub-categories of search engine software that are separately applicable to specific 'browsing' needs. These include web search engines (e.g. Google), database or structured data search engines (e.g. Dieselpoint), and mixed search engines or enterprise search. The more prevalent search engines, such as Google and Yahoo!, utilize hundreds of thousands computers to process trillions of web pages in order to return fairly well-aimed results. Due to this high volume of queries and text processing, the software is required to run in a highly dispersed environment with a high degree of superfluity.
Another category of search engines is scientific search engines. These are search engines which search scientific literature. The best known example is Google Scholar. Researchers are working on improving search engine technology by making them understand the content element of the articles, such as extracting theoretical constructs or key research findings.
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In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation
$$
i^{2}= -1
$$
; every complex number can be expressed in the form
$$
a + bi
$$
, where and are real numbers. Because no real number satisfies the above equation, was called an imaginary number by René Descartes. For the complex number is called the , and is called the . The set of complex numbers is denoted by either of the symbols
$$
\mathbb C
$$
or . Despite the historical nomenclature, "imaginary" complex numbers have a mathematical existence as firm as that of the real numbers, and they are fundamental tools in the scientific description of the natural world. "Complex numbers, as much as reals, and perhaps even more, find a unity with nature that is truly remarkable. It is as though Nature herself is as impressed by the scope and consistency of the complex-number system as we are ourselves, and has entrusted to these numbers the precise operations of her world at its minutest scales. ", .
Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers.
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", .
Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex coefficients has a solution which is a complex number. For example, the equation
$$
(x+1)^2 = -9
$$
has no real solution, because the square of a real number cannot be negative, but has the two nonreal complex solutions
$$
-1+3i
$$
and
$$
-1-3i
$$
.
Addition, subtraction and multiplication of complex numbers can be naturally defined by using the rule
$$
i^{2}=-1
$$
along with the associative, commutative, and distributive laws. Every nonzero complex number has a multiplicative inverse. This makes the complex numbers a field with the real numbers as a subfield. Because of these properties, , and which form is written depends upon convention and style considerations.
The complex numbers also form a real vector space of dimension two, with
$$
\{1,i\}
$$
as a standard basis. This standard basis makes the complex numbers a Cartesian plane, called the complex plane. This allows a geometric interpretation of the complex numbers and their operations, and conversely some geometric objects and operations can be expressed in terms of complex numbers.
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