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<p>I am studying an example problem, concerning the very topic mentioned in the title. In this example problem, a car has a head-on collision with the wall; the initial and final velocity are known, as well as the mass. My question is, why does the car rebound off of the wall? Why doesn't the normal force of the wall reduce the car's velocity to zero, with the car remaining there, instead of reducing the car's velocity to zero, and then giving it a velocity in the opposite direction?</p>
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] |
<p>I was playing around with <a href="http://www.lpta.univ-montp2.fr/users/kneur/Suspect/">SuSpect</a> to generate some SUSY mass spectrums and I'm often encountering situations where I get a negative neutralino mass. </p>
<ol>
<li><p>What is the physical meaning of this negative mass I am getting? </p></li>
<li><p>Does this mean the parameters I am putting in is giving an unphysical spectrum?</p></li>
</ol>
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<p>I'd like to calculate the distance between the Earth and an asteroid at a given date. Is this possible using the data from <a href="http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=433" rel="nofollow">JPL's small-body database</a>? Is there a better way?</p>
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<p>This might be an incredibly naive question, but I'm wondering if there are a set of rules for "translating" between Standard Model and SUSY. For instance, if I want want to go from a Standard Model feynman diagram to a SUSY diagram, can one write down a set of rule including things like:</p>
<p>"replace quarks with the corresponding squark"</p>
<p>with the caveat of course that R-parity is conserved (so two SUSY particles at each vertex). Given the underlying symmetry between SM particles and their superpartners, it seems like there should be some type of correspondence between SM feynman rules and the SUSY feynman rules. It seems like it would be incredibly difficult to go through and learn a completely new set of interactions and rules for SUSY. Are there things that carry over from SM Feynman rules that can be used as rules of thumb for figuring out what are the allowed SUSY diagrams for a particular process?</p>
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<p>I was attempting to do some calculations of apparent magnitude to help solidify my understanding of the topic, but have been running into some confusion.</p>
<p>According to <a href="http://en.wikipedia.org/wiki/Apparent_magnitude#Calculations" rel="nofollow">Wikipedia</a>, the apparent magnitude can be given as:</p>
<p>$m_x = -2.5\log_{10}(F_x/F^0_x)$</p>
<p>where $F_x$ is the observed flux and $F^0_x$ is a reference flux (in other words, this equation provides the <em>difference</em> of apparent magnitude between two observed values). Also, this is assuming that the same wavelength band is used in both flux measurements.</p>
<p><a href="http://en.wikipedia.org/wiki/Luminosity#Computing_between_brightness_and_luminosity" rel="nofollow">Flux</a>, in turn, can be calculated as:</p>
<p>$F = \frac{L}{A}$</p>
<p>where $L$ is the star's luminosity and $A$ is the flux density. Since stars act as point sources, this can be simplified to:</p>
<p>$F = \frac{L}{4\pi r^2}$</p>
<p>where $r$ is the distance to the star.</p>
<p>Since, historically, Vega has been used as the reference zero-point (having an apparent magnitude around 0.03), I tried doing a simple calculation to find out the apparent magnitude of Fomalhaut using the values for luminosity and distance given in Wikipedia for <a href="http://en.wikipedia.org/wiki/Vega" rel="nofollow">both</a> of <a href="http://en.wikipedia.org/wiki/Fomalhaut" rel="nofollow">them</a>.</p>
<p>First, the flux of Vega:</p>
<p>$F_{Vega} = \frac{37\,L_\odot}{4\pi (25.3\,ly)^2}$</p>
<p>$F_{Vega} = 4.5999\times 10^{-3}\,L_\odot/ly^2$</p>
<p>Next, the flux of Fomalhaut:</p>
<p>$F_{Fomalhaut} = \frac{17.66\,L_\odot}{4\pi (25\,ly)^2}$</p>
<p>$F_{Fomalhaut} = 2.2485\times 10^{-3}\,L_\odot/ly^2$</p>
<p>Now, to calculate the apparent magnitude:</p>
<p>$m_{Fomalhaut} = -2.5\log_{10}(\frac{2.2485\times 10^{-3}\,L_\odot/ly^2}{4.5999\times 10^{-3}\,L_\odot/ly^2})$</p>
<p>$m_{Fomalhaut} = 0.7777$</p>
<p>Huh?? Fomalhaut's apparent magnitude is supposed to be <strong>1.16</strong>. Even correcting for Vega's offset of 0.03, we still come up with <strong>0.8077</strong>. Why are the calculations failing? I don't think I've made a mistake in the mathematics. Am I using the wrong values?</p>
| 9,172 |
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<p>When we first learn elementary geometrical optics, the first thing taught to us is the two broad divisions of the type of reflection.-Regular and Irregular or Diffused.<br>
The difference in cause for both of these is that in case of regular reflection an incoming ray is perfectly reflected in a specific direction but in diffused reflection, the reflected ray are diffused in several direction probably owing to minor irregularities of the surface. Hence the diffuse reflection does not form our image as a mirror does but instead produces general luminance. But then in case of multi-media-projectors or when we use a paper or a wall as a screen for real images, an otherwise diffuse surface (wall, paper, etc) produces an image which can be seen by us. Is this not only possible when the incoming rays are REGULARLY reflected on to our eyes? </p>
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<p>In his QFT book, Weinberg claims what follows (Vol I, pag. 144-145): given a (free) representation of the Poincaré group with generators $\bf P$ (spatial translations), $H_0$ (time translations), $\bf J$ (rotations), and ${\bf K}_0$ (boosts), one obtains another (interacting) reprentation by replacing $H_0$ and ${\bf K}_0$ with
$$
H = H_0 + \int \mathcal{H}({\bf x}, 0) d^3x \; \; \text{ and } \; \; {\bf K} = {\bf K}_0 - \int {\bf x} \mathcal{H}({\bf x}, 0) d^3x,
$$
respectively, where $\mathcal{H}(x)= \mathcal{H}({\bf x}, t)$ is a self-adjoint operator density which is covariant and causal, that is:
$$
U_0(\Lambda, a) \mathcal{H}(x) U_0(\Lambda, a)^{-1}= \mathcal{H}(\Lambda x + a)
\; \; \text{ and } \; \; [\mathcal{H}(x), \mathcal{H}(y )] = 0 \text{ for } (x - y)^2 \geq 0,
$$
where $U_0(\Lambda, a)$ is the free representation.</p>
<p>Weinberg provides only a partial proof of this claim. Does somebody know if this is a rigorous result, and where one can possibly find a complete/rigorous proof?</p>
| 9,174 |
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<p>I study physics and am attending a course on quantum field theory. It is hard for me to draw connections from there to the old conventional theories.</p>
<p>In quantum field theory spin originates from the Dirac equation in the case of fermions. </p>
<p>I don't remember where it comes from in quantum mechanics. I just remember that there was the Stern Gerlach experiment where you shoot neutral spin 1/2 Ag atoms in. Is there also a electrically neutral elementary particle? If this is the case, how would this experiment look like in quantum field theory?
Of course I ask this for the lowest order, otherwise we would have to calculate an infinite number of Feynman graphs, won't we?</p>
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<p>Non-unital completely positive (<a href="http://en.wikipedia.org/wiki/Choi%27s_theorem_on_completely_positive_maps" rel="nofollow">CP</a>) maps take a maximally mixed quantum state (aka a normalized identity matrix aka an infinite temperature state) and map it to something else. This necessarily decreases its von Neumann entropy and, depending on how you define it, reduces its temperature.</p>
<p>Can a stronger connection be made between thermodynamics and CP maps? To what extent do non-unital CP maps reliably cool states that <em>aren't</em> infinite temperature?</p>
| 9,175 |
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<p>It is experimentally known that the equation of motion for a charge $e$ moving in a static electric field $\mathbf{E}$ is given by:</p>
<p>$$\frac{\mathrm{d}}{\mathrm{d}t} (\gamma m\mathbf{v}) = e\mathbf{E}$$</p>
<p>Is it possible to show this using just Newton's laws of motion for the proper frame of $e$, symmetry arguments, the Lorentz transformations and other additional principles?</p>
| 9,176 |
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<p><strong>1.a</strong> In paragraph at <a href="http://en.wikipedia.org/wiki/Entropy#Relating_entropy_to_energy_usefulness">Wikipedia/Entropy</a> it is stated:</p>
<blockquote>
<p>This is because energy supplied at a <strong>high temperature (i.e. with low entropy)</strong>
tends to be more useful than the same amount of energy
available at room temperature</p>
</blockquote>
<p><strong>1.b</strong> But at <a href="http://www.nmsea.org/Curriculum/Primer/what_is_entropy.htm">What is Entropy?</a> there is:</p>
<blockquote>
<p>The higher the temperature of the gas, the faster the gas particles
are moving on average, so the wider the range of possible velocities
for the gas particles, and hence, the more uncertainty we have about
the velocity of any particular particle. <strong>Thus, higher temperature</strong>, as
well as greater volume, <strong>mean higher entropy</strong>.</p>
</blockquote>
<p><strong>2.a</strong> I was trying to obtain information on relation between entropy and work. Basically, if an external process modifies a system so that its entropy is reduced, then it is expected by me that work was done on the system and energy was contributed to it. I received good answers ( <a href="http://physics.stackexchange.com/questions/24134/connection-between-entropy-and-energy/24147">Connection between entropy and energy</a> ). However I feel that I was not properly understood.</p>
<p><strong>2.b</strong> In 1953 paper of L. Brillouin ("The Negentropy Principle of Information") wrote what I basically had in mind when I asked the question. I am not aware if the approach is correct and accepted. </p>
<blockquote>
<p>An isolated system contains negentropy if it reveals a possibility for
doing mechanical or electrical work. If the system is not at a uniform
temperature T, but consists of different parts at different
temperatures, it contains a certain amount of negentropy. This
negentropy can be used to obtain some mechanical work done by the
system, or it can be simply dissipated and lost by thermal conduction.
A difference in pressure between different parts of the system is
another case of negentropy. A difference of electrical potential
repre-sents another example. A tank of compressed gas in a room at
atmospheric pressure, a vacuum tank in a similar room, a charged
battery, any device that can produce high-grade energy (mechanical
work) or be degraded by some irreversible process (thermal
con-duction, electrical resistivity, friction, viscosity) is a source
of negentropy.</p>
</blockquote>
<p><strong>3.a</strong> There is often a contradict intuition about information entropy. Shannon approach sees maximum entropy as maximum uncertainty / information.</p>
<p><strong>3.b</strong> Joe Rosen in "The Symmetry Principle" states that maximum entropy is maximum symmetry – which means maximum redundancy, so minimum amount of information.</p>
<p><strong>4.</strong> Non-equilibrium thermodynamics – the branch is not mature and does not serve as a tool to solve issues like in 2.a, AFAIK.</p>
<p>I was seeing <a href="http://arxiv.org/abs/0707.3400">The Physics of Maxwell's demon and information</a> as very good guide through <strong>equilibrium</strong> (what about non-equilibrium?) thermodynamics, its connection with work and information. The authors did, however, when elaborating on entropy of a system in Brillouin's view, put an equal sign to it and Shannon entropy – which I think is contradict to Brillouin itself – who as I cited in 2.b stated that it is disequilibrium that allows system to work – meaning a complex, information-rich system (in other paragraph he also explicitly sates that negentropy is information). This conforms to Rosen 3.b.</p>
<p><strong>Are there other good compilations on entropy, information, maybe complexity science? Such that solve the contradictions, form compatible non-equilibrium foundation?</strong></p>
| 9,177 |
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<p>I read a few times that a knot can reduce the strenght of a rope, but I can't understand why this happens. Can someone explain me what happens to a rope tied with a generic knot and stretched? Is there a way to calculate the reduction of resistance from the form of the knot?</p>
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<p>First of all, does the expansion of spacetime solely cause the expansion of universe?</p>
<p>Secondly, if spacetime is the sole cause, do objects(matter with mass) themselves expand?</p>
<p>Thirdly, by spacetime expansion, does time also expand? (at least in general relativity)</p>
<p>Thanks.</p>
| 56 |
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<p>A hydrogen atom is characterized by the wavefunction</p>
<p>$$\mid \psi \rangle =\sqrt{\frac{2}{7}}\mid 4\,2\,1\rangle +\sqrt{\frac{1}{7}}\mid 2 \,1\,\bar{1}\rangle+\sqrt{\frac{4}{7}}\mid 3\,2\,0\rangle$$</p>
<p>I want to know the possible outcomes and the probability for obtaining each outcome from measuring $E$, $L^2$, and $L_z$, while also calculating the expectation value of the energy expressed as some number times $E_1$ (for $E$), $\hbar^2$ (for $L^2$), and $\hbar$ (for $L_z$). I know the possible outcomes are the eigenvalues for the observable, but we didn't really go over any examples, and there are few examples of this sort in the textbook, so I don't know where to begin. For example, I know when we act $L^2$ on the system, we will get</p>
<p>$$ L^2\mid \psi\rangle=6\hbar^2\sqrt{\frac{2}{7}}\mid 4\,2\,1\rangle +2\hbar^2\sqrt{\frac{1}{7}}\mid 2 \,1\,\bar{1}\rangle+6\hbar^2\sqrt{\frac{4}{7}}\mid 3\,2\,0\rangle$$</p>
<p>However, what does this tell me about the possible outcomes? Would the probabilities for each outcome be the coefficient multiplying each successive term squared divided by the Pythagorean sum of the all three terms? How do I find the expectation value? Any help would be appreciated. </p>
| 9,179 |
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<p>If the earth left the solar system for some reason. Assuming its moving at the same velocity it's currently exhibiting. How long would it take for the atmosphere to freeze. Would we get methane clouds like Titan. Would there be an atmosphere or would it all be frozen on the ground? </p>
| 918 |
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<p>If we have a sphere which has $σ$ surface charge density and rotate it in axis z will this create current ? Is it possible without any potential difference ? </p>
| 9,180 |
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<p>I've been digging into emission spectra of different elements and found that such things as the Rydberg equation, Bohr's model, and quantum mechanics can only fully describe the single electron in the Hydrogen atom. How did we then make the leap to s,p,d,f shells of multi-electron atoms? How accurate is our analysis of these more complicated elements?</p>
<p>Rydberg Equation (side-note: Is this an empirical 'data-fitting' equation? What's the significance of that?)</p>
<p>$$\frac{1}{\lambda}=R_H\left( \frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$$ </p>
<p>Hydrogen:
<img src="http://i.stack.imgur.com/9yWL5.jpg" alt="enter image description here"></p>
<p>Helium:
<img src="http://i.stack.imgur.com/EyQi5.jpg" alt="enter image description here"></p>
<p>Iron:
<img src="http://i.stack.imgur.com/Tx0Vp.jpg" alt="enter image description here"></p>
<p>Potassium:
<img src="http://i.stack.imgur.com/g23gw.jpg" alt="enter image description here"></p>
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<p>At a very basic level I know that gravity isn't generated by mass but rather the <a href="https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor">stress-energy tensor</a> and when I wave my hands a lot it seems like that implies that energy in $E^2 = (pc)^2 + (mc^2)^2$ is the source of gravity.</p>
<p>If the total energy of a particle contributes to the generation of a gravitational field, that seems to imply some strange things. For example, you could accelerate a particle like an electron to such a high velocity that it has enough momentum / kinetic energy to collapse into a black hole. An observer traveling with the electron would see an electron and stationary observers would see an arbitrarily massive black hole flying by. These observations seem to be contradictory. The same would be true of an extremely high energy photon.</p>
<p>Another consequence is that a stationary particle could appear to have so much mass that it could attract / deflect the trajectory of a rapidly moving observer. It seems odd that at low velocities you wouldn't even notice a stationary electron as you pass it by but at high velocities the gravitational field you observe could be significant enough to alter your path.</p>
<p>Am I correct that non-mass-energy generates a gravitational field? If it does, how are these strange observations like a particle looking like a black hole in one reference frame but not another reconciled?</p>
| 112 |
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<p>In quantum electrodynamics, the classical Hamiltonian is obtained from the classical electromagnetic Lagrangian. Then the classical electric and magnetic fields are promoted to operators, as is the classical 4-vector potential $A_{\mu}$. The appropriate commutation relations are expected between the fields and their conjugate momenta.</p>
<p>Now, my question is, do the principles of quantum electrodynamics follow as a consequence of the fact that the charged particle producing the field is a quantum particle which must follow the principles of quantum mechanics?</p>
<p>Let me give a specific example. Consider a slow moving(for simplicity) free electron moving with a constant velocity initially.</p>
<p>Now, classically, the magnetic field at a point $P$ would be given by a function $\vec{B} = \vec{f}(\vec{r},\vec{x},\vec{p})$, where $\vec{r}$ is the position vector of the point at which the field is being 'measured' and $x$ and $p$ are the position and momenta of the charged particle evaluated at the retarded time.</p>
<p>Now, supposing I apply the principles of quantum mechanics to this electron and promote the above mentioned expression for the magnetic field at point $P$ to an operator by the usual quantum mechanical prescription. Would this prescription yield the correct values for the measured magnetic field at point $P$? Why? or Why not?</p>
<p>The bottom line of my entire question is whether the quantum field theory of an electron is a direct consequence of the fact that the particle producing the field is a quantum particle (and not a classical one) or does it involve much more than that?</p>
<p>EDIT: Thank you for your responses. I would also like to know if the above mentioned prescription for obtaining the magnetic field would yield accurate results for slow moving electrons(non-relativistic)?</p>
| 9,182 |
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] |
<ol>
<li><p>If gravity is the force of attraction between masses, does this force is an intrinsic property of every atoms? </p></li>
<li><p>Is there any possibility of some other particles within atom which is yet to be discovered? </p></li>
<li><p>Or is it simply a result of cosmic waves which created due to big bang?</p></li>
<li><p>Does anyone have any information regarding variations in gravitational force? </p></li>
<li><p>If its not there then is it simply be "something like plasma which entire universe in within its plume and huge masses simply accelerate the attraction"?</p></li>
</ol>
| 9,183 |
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<p>In <a href="http://www.youtube.com/watch?v=EYPapE-3FRw" rel="nofollow">this video of Feynman discussing the scientific method</a>, starting at around eight minutes and 30 seconds, Feynman describes the proposition that space consists of a cubic lattice of points (as opposed to space being continuous). Feynman says "then we can prove that [the proposition] immediately is wrong," but he doesn't elaborate on the proof.</p>
<blockquote>
<p>My question is: What are the objection(s) to a cubic lattice universe that Feynman refers to in this video?</p>
</blockquote>
<p>I'm not looking for every possible objection to a cubic lattice universe. I'm wondering what in particular the (apparently immediate and obvious) objections are that made Feynman so dismissive of the idea.</p>
| 114 |
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] |
<p>Are there any theories out there that discuss the idea that space itself could be made out of particles?</p>
| 302 |
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<p>I can't find an answer of why the lowest temperature is -273.15ºC. Is it deduced theoretically or is it experimental?</p>
<p>An explanation is that when any gas volume tends to zero, the temperature will be -273.15ºC (Charles law). But shouldn't this number have some kind of error? And this would only apply to ideal gases.</p>
<p><img src="http://i.stack.imgur.com/LOk7j.jpg" alt="enter image description here"></p>
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<p>I know that
$A_{[a} B_{b]} = \frac{1}{2!}(A_{a}B_{b} - A_{b}B_{a})$</p>
<p>But how can write $E_{[a} F_{bc]}$ like the above?</p>
<p>Can you provide a reference where this notational matter is discussed?</p>
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<p>Why do hurricane winds rotate? I know it´s about <a href="http://en.wikipedia.org/wiki/Coriolis_effect" rel="nofollow">Coriolis force</a> but how can I be quantitative? My problem is that I can´t imagine the direction velocity of wind and the angle with earth angular velocity rotation. Also, when can we explain other things like bathtubs, toilets.. using Coriolis? I mean when this force is relevant to explain the motion and the direction of rotation, CCW or CW(clock wise)?</p>
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<p>I am looking for an introduction (textbook or paper, or if someone wouldn't mind writing a memo on it) to canonical quantum gravity, specifically the concept of minisuperspaces. I have been reading the paper of Wheeler (in Phys Review) but he doesn't speak about minisuperspaces, maybe they were not used/invented at the time.</p>
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<p>The circuit under consideration has two inductively coupled loops, one with a DC battery, inductor, and resistor in series. The other loop has two inductors, one inductively coupled to the first, the other not, and a resistor, all in series. </p>
<p>I would like to know the current in the top loop (the one without the battery) as a function of the given quantities after the battery is connected.</p>
<p>I tried adding the three inductors and using that value to find the bottom loop's current, then substituting that into the top loop to find d(phi)/dt and then current. This gives me the standard RL current expression for the bottom loop and an exponential decay model for the current in the top loop. This is counter-intuitive for me; I believed that the current in the top loop should start at zero, peak, and decay rather than start high and decay.</p>
<p>Thanks in advance.</p>
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<p>Let me create a very artificial experimental set up. Take a bathtub the size of Delaware and suspend it a mile above the ground. Fill it with water (though I'm not sure to what depth - and it might matter). Now pull the plug out.</p>
<p>The effect is that you have a waterfall with an endless supply of water, high above the ground, and, in my idealization, the stream of water is an arbitrarily thick, cylinder of water.</p>
<p>The question is, how fast does the water travel at the center of the waterfall? Obviously, I'm not looking for a numerical answer here, but I just want to understand the limits. Water at the edges of the waterfall are subject to wind resistance and will therefore quickly reach terminal velocity. But water at the center of the stream is removed from the effects of air resistence, so if the stream was thick enough and the waterfall high enough, would the center of the waterfall be unboundedly fast?</p>
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<p>Will a plant grow faster when you would apply more upward gravitational force?</p>
<p>and/or</p>
<p>Will a plant grow slower when you would apply more downward gravitational force?</p>
| 9,190 |
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<p>I'm interested in a QFT model featuring a fermion derivative coupling like $XX^* \chi^*\gamma^\mu∂_\mu \psi$ where X is some other field operator.
Has anybody seen a paper containing something like this?
How would Feynman-Graphs for such an interaction look like?
Are derivatives of fermions ruled out by some consideration i am missing?</p>
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] |
<p>Is there field theory which describe a second order phase transition without upper critical dimension ? Mermin-Wagner says something about lower critical dimension but nothing about upper dimension.</p>
| 9,192 |
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<p>I'm a beginner in quantum mechanics, and I'm a bit confused about states and the probability to measure certain values. I would like to understand at least the following simplified situation:</p>
<p>Suppose the operator $S_z$ is measuring the spin in the $z$ direction of a free particle. Let $$\{e_s\},\quad s = -L, -L+1, \dots, L-1, L$$ be a basis of eigenstates for $S_z$, with $S_z(e_s) = s e_s$.</p>
<p>If at time $t<0$ the system is constantly in the pure state $P_{\psi}$, where $\psi$ is one basis vector, how can I compute the probability that the measuring the spin in the $z$ direction has result $-L/2$?</p>
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<p>Can anyone explain what metric signature is?</p>
<p>I have a basic knowledge regarding tensors, btw.</p>
<p>Also, how is it related to fundamental understanding of general relativity?</p>
<p>Thanks.</p>
| 9,194 |
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] |
<p>How do <a href="http://en.wikipedia.org/wiki/Stirling_engine" rel="nofollow">Stirling engines</a> work? I understand the heating and cooling of air, but how much faster (or more force, I'm not sure which to use) does the piston move per degree Celsius that the temperatures differ?</p>
| 9,195 |
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<p>So for a complex dielectric constant $\epsilon = \epsilon_a + i\epsilon_b$, the wave vector and index of refraction are related to it through $k = \frac{\omega}{c}n$ and $n = \sqrt{\frac{\mu \epsilon}{\mu_0 \epsilon_0}}$. According to Jackson, the real part of the dielectric is related to polarization and anomalous dispersion, while the imaginary part is associated with dissipation of energy into the medium.</p>
<p>If you write the wavevector as $k = \beta + i \alpha/2$ and plug it in the general wave formula (just in 1D right now) of $e^{ikr} = e^{-\alpha r/2}e^{i\beta r}$, the intensity drops as $e^{-\alpha r}$, so $\alpha$ is the attenuation constant, which tells you how quickly the wave dies out in the medium.</p>
<p>But, if you plug that form of $k$ into the above equations to solve for $\alpha$ and $\beta$ as a function of $\epsilon_a$ and $\epsilon_b$, you find that $\alpha$ and $\beta$ are both a function of both $\epsilon_a$ and $\epsilon_b$.</p>
<p>This is counterintuitive to me, because intuitively I'd think that the attenuation constant $\alpha$ would only be based on $\epsilon_b$, due to dissipation, and the same with $\beta$ and $\epsilon_a$.</p>
<p>Can anyone give a good physical explanation for this "mixing"?</p>
| 9,196 |
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<p>What is the physics behind a normal human jump ?</p>
<p><img src="http://www.wired.com/images_blogs/wiredscience/2012/04/drawings_spring_12key_23.jpg" alt="a human jump"></p>
<p>when a normal human wants to jump.</p>
<ol>
<li>First, some energy is stored in their thighs and The elastic tendons Just like a spring.
In mechanics and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load applied to it. Many materials obey this law as long as the load does not exceed the material's elastic limit</li>
</ol>
<p>$$F=-k.x$$
where
<strong>x</strong> is the displacement of the spring's end from its equilibrium position (a distance, in SI units: metres); <strong>F</strong> is the restoring force exerted by the spring on that end (in SI units: N or kg·m/s^2); and k is a constant called the rate or spring constant (in SI units: N/ m</p>
<p>what is human rate constant <strong>k</strong>?</p>
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<p>I always thought that high voltage power lines would attract a lightning strike more than other structures in the same area. Turns out I was wrong. My neighbor's chimney got struck by lightning and it destroyed a lot of stuff (street lamps, wifi APs, small home electronics). We live very close to high voltage power lines - so, is my premise wrong? Do power lines not attract a lightning strike more that other objects?</p>
<p>Also, if a chimney isn't connected to the power grid (or am I wrong?), then how is it possible, that almost all of the street lamps don't work and other electronic devices were destroyed?</p>
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<p>This question follows on previous work on connections between (other) areas of physics and thermodynamics as in <a href="http://physics.stackexchange.com/q/115026/">here</a>, <a href="http://physics.stackexchange.com/q/114697/">here</a> and <a href="http://cs.stackexchange.com/q/26049/">even here</a>.</p>
<p><a href="http://en.wikipedia.org/wiki/Paul_Dirac" rel="nofollow">P. Dirac</a> (an electrical engineer initially) was one of the first to pose the possible existence of magnetic monopoles (<a href="http://users.physik.fu-berlin.de/~kleinert/files/dirac1931.pdf" rel="nofollow">original paper</a>)(for example as solenoids). This would allow more symmetric forms of certain equations (physicist fetish?). Anyway, this (a-)symmetry is also the starting point for possible connections to thermodynamical concepts.</p>
<blockquote>
<p>Is there any relation to the (non-) existence of <a href="http://en.wikipedia.org/wiki/Magnetic_monopole" rel="nofollow">magnetic
monopoles</a> and <a href="http://en.wikipedia.org/wiki/Second_law_of_thermodynamics" rel="nofollow">2nd
law</a>?</p>
<p>Would the possible existence of magnetic monopoles violate the 2nd
law, or does the 2nd law predict magnetic monopoles, or it is just
irrelevant (sth many physicists would not assume lightly)?</p>
</blockquote>
<p>Relevant physics areas include the intersection of materials magnetization and thermodynamics.</p>
<p>Relevant articles include <a href="http://www.nature.com/nphys/journal/v9/n6/full/nphys2611.html" rel="nofollow">this one</a> on <a href="http://en.wikipedia.org/wiki/Spin_ice" rel="nofollow">spin ice</a> and <a href="http://www.ncbi.nlm.nih.gov/pubmed/23443563" rel="nofollow">this one</a> on Brownian motion</p>
<p><strong>NOTE:</strong> have not actually read the articles as i do not have access, however mentioned as part of existing literature on the question's subject.</p>
<p>Relevant papers and outlines: <a href="http://www.int.washington.edu/talks/WorkShops/int_11_2c/People/Sondhi_S/sondhi.pdf" rel="nofollow">here</a>, <a href="http://arxiv.org/abs/1005.3557" rel="nofollow">here</a>, <a href="http://phys.org/news/2014-01-physicists-synthetic-magnetic-monopole-years.html" rel="nofollow">here</a> and <a href="http://arxiv.org/abs/0708.1783" rel="nofollow">an arxiv paper</a> by P. Davies on this issue (circa 2007)</p>
<p>UPDATE: An "unorthodox" critical view on mainstream mathematical physics (specifically <a href="http://milesmathis.com/yang.html" rel="nofollow">Yang-Mills theory</a>)</p>
| 9,199 |
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] |
<p>I'm aware of the so-called <a href="http://en.wikipedia.org/wiki/Refractive_index#Group_index" rel="nofollow">group index</a> but why is the phase velocity used in the <a href="http://en.wikipedia.org/wiki/Refractive_index#Definition" rel="nofollow">standard definition</a> of the index of refraction? What advantage does this offer?</p>
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<p>Sorry, since the question has been posed, but I insist that others posed not from this position.</p>
<p>Can any listener deduce whether we could measure, by analyzing electromagnetic disturbance, a particle$^1$ traveling faster than light? (or current measuring device, for the sake of assuming for questioning)</p>
<p>Studying to understand cosmic rays, inductance, and capture technologies by the artifacts of Tesla.. The name most studied by us uneducated electrical folk.</p>
<p>--</p>
<p>$^1$ For the 2011 OPERA neutrino experiment, see <a href="http://physics.stackexchange.com/q/14968/2451">this</a> Phys.SE post.</p>
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<p>The limit of microscopes is 200nm, but apparently STED improves this according to this coverage of the Kavil prizes 2014 : </p>
<p><a href="http://www.photonics.com/Article.aspx?AID=56255" rel="nofollow">http://www.photonics.com/Article.aspx?AID=56255</a> </p>
<p>What is the current limit for microscopy ? </p>
| 9,202 |
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<p>I have searched the internet and have not found any actual test results.</p>
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<p>While deriving lagrange's equation, for an infinitesimal displacement $\vec{dr}$, we express it using taylor series in terms of general coordinates as $\frac{\vec{dr}}{dq} \delta q$. Where $\frac{\vec{dr}}{dq}$ means derivative of $\vec{r}$. What does it mean?(this derivative term). What is the function whose derivative we are taking ?</p>
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<p>we are given a problem with spring with its own mass $m$. I am confused how to set up the
PE term in the Lagrangian.</p>
<p>Assume the spring has length of $L_{0}$ when it is laying on a table
horizontally. Now when we hold the spring upright and hang it vertically from
a pivot in the ceiling to make a pendulum, it will stretch a little due to its
own weight by $\frac{(m/3)g}{k}$ where $k$ is the spring constant. I use
$m/3$ there since that is the common factor used to generate an effective mass
used for a spring with its own weight.</p>
<p><a href="http://en.wikipedia.org/wiki/Effective_mass_%28spring-mass_system%29" rel="nofollow">http://en.wikipedia.org/wiki/Effective_mass_%28spring-mass_system%29</a></p>
<p>Hence now the length of the spring is $L_{0}+\frac{(m/3)g}{k}$ before we even
put the bob mass at the end of it. Should one use $L_{0}+\frac{(m/3)g}{k}$ as
the relaxed length of the spring or use $L_{0}?$</p>
<p>Will the PE for the spring be $\frac{1}{2}k\left( y-L_{0}\right) ^{2}$ or
$\frac{1}{2}k\left( y-(L_{0}+\frac{(m/3)g}{k})\right) ^{2}$? </p>
<p>Assuming one is measuring $y$ here from the ceiling where the spring is hanging from</p>
<pre><code> +---------
\ |
/ |
\ |
/ | y(t)
\ |
/ |
M V
</code></pre>
<p>Which term should be used for PE? </p>
<p>I know there will be additional PE term for the spring due to its own mass,
which is $-mg\frac{y}{2}\cos\theta$ </p>
<p>Hence total PE from the spring is</p>
<p>$PE=\frac{1}{2}k\left( y-L_{0}\right) ^{2}-mg\frac{y}{2}\cos\theta
-Mgy\cos\theta$</p>
<p>or</p>
<p>$PE=\frac{1}{2}k\left( y-(L_{0}+\frac{(m/3)g}{k})\right) ^{2}-mg\frac{y}
{2}\cos\theta-Mgy\cos\theta
$</p>
<p>where $\theta$ is angle of rotation of the spring pendulum.</p>
<p>not sure which to use.</p>
| 9,205 |
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] |
<p>Are the ions in a fluorescent lamps concentrated near the electrodes , and just the electrons move to the other electrode or the positive mercury ions move too?</p>
| 9,206 |
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<p>An electron is orbiting two protons. With the Born-Oppenheimer approximation that the protons do not move, I'd write the Hamiltonian of the electron's movement as:</p>
<p>$$ \mathbf{H} = -\frac{\hbar^2}{2m}\nabla^2 + E_p$$</p>
<p>with</p>
<p>$$E_p = -\frac{e^2}{4\pi \epsilon_0}\left(\frac{1}{r_1}+\frac{1}{r_2}\right) $$</p>
<p>as the potential caused by the protons, with $r_1$ and $r_2$ denoting distances to the protons. Apparently it should be</p>
<p>$$E_p = -\frac{e^2}{4\pi \epsilon_0}\left(\frac{1}{r_1}+\frac{1}{r_2}-\frac{1}{r_0}\right), $$</p>
<p>where $r_0$ denotes the distance between the protons. How can that term be explained?</p>
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<p>I want to know if dimensional regularization has any issues if the theory has IR divergences or is scale invariant. </p>
<ul>
<li><p>Does dimensional regularization see "all" kinds of divergences? </p>
<p>I mean - what does it <em>exactly</em> mean when one says that power law divergences and IR divergences disappear in the dimensional regularization. So is more regularization needed in general over and above dimensional regularization? </p></li>
<li><p>Does anything about the divergences get specially constrained if the theory is scale invariant? </p>
<p>I have often heard it being said that dimensional regularization "preserves" scale invariance. </p></li>
</ul>
| 9,208 |
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<p>Kinetic energy conservation in collision.</p>
<p>In any type of collision type of collision if we take the system to comprised of both bodies then the net external force is zero. So the work done by external force is also zero. By the relation $W=K_f-K_i$ as $W$ is zero hence kinetic energy is conserved. But this not the case. </p>
<p>Can you tell me what is the flaw in my argument? Some people say that the argument has neglected the fact that some kinetic energy is transformed into heat. But heat is created due to the interactions between bodies during collision which is thus an internal force and thus shouldn't affect kinetic energy. </p>
| 9,209 |
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<p>I wonder whether $\sigma$ or $\sigma / \sqrt{N}$ is error of a measurement. When I measure, say $0, 1, -1, 1, -1$, I have a $\sigma = 1$. I just measure $0, 1, -1$, I also have $\sigma = 1$.</p>
<p>But in the former case, I had more measurements, so the error should be smaller. So would the error be 1 or rather $1/\sqrt{5}$ and $1/\sqrt{3}$ respectively?</p>
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] |
<p>Does <a href="http://en.wikipedia.org/wiki/Chaos_theory">chaos theory</a> occur in quantum mechanics? Or in any non-newtonian physics? Apart from perhaps thermodynamics?</p>
| 9,211 |
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<p>Good evening,</p>
<p>I haven't had physics since year 7 and now I need to use elementary things in university. Since I lack a lot of basics I am now trying my best to fill these holes. Currently I am stuck at solving circuits and I hope one of you can help me with the following circuit. I've also attached an image at the bottom of the post (large image).</p>
<p>Given:<br>
$R_1 = 20\Omega$<br>
$R_2 = 100\Omega$<br>
$R_3 = 50\Omega$<br>
$R_6 = 100\Omega$<br>
$U_0 = 2V$<br>
$U_5 = 900mV$<br>
$U_6 = 1V$<br>
$I_5 = 10mA$<br>
$I_7 = 80mA$ </p>
<p>What needs to be calculated: $U_3, I_4, R_5, R_8, U_8, I_8$</p>
<p>My attempt on solving the circuit:</p>
<p>1) Since $U_5$ and $I_5$ are given we can use Ohm's law to calcualte $R_5 = 90\Omega$.<br>
2) Knowing $U_6$ we can use the Mesh-Current Method to determine $U_7 = 1V$.<br>
3) Again I used Ohm's law to calculate $I_7 = 80mA$ with $U_7 = 1V$ from 2)<br>
4) Ohm's law to determine $I_6 = 10mA$ since we have $U_6, R_6$ given.<br>
5) Now I used the Mesh-Current Method between $U_1, U_5 and U_6$. Since $U_1, U_2, U_3, U_4$ are parallel to each other I assumed that they must be equal (? not quite sure on this one). However this assumption lead to the following result for $U_1, U_2, U_3, U_4 = 100mV$.<br>
6) Knowing $R_1, R_2, R_3$ and now $U_1, U_2, U_3$ I calculated $I_1 = 5mA, I_2 = 1mA, I_3 = 2mA$ with Ohm's law.
7) Now this is the point where I am stuck at. I'm not sure if it is allowed to reduce the circuit to only a specific area. For Instance I reduced the circuit to the upper left corner to determine $I_4 = 2mA$ with the Branch-Current Method. Having that given allows me to easily calculate $R_4 = 50\Omega$ with the help of Ohm's law.
8) Knowing that $U_0 = 2V$ I used the Mesh-Current Method for the whole outer part of the circuit to calculate $U_8 = 1V$.
9) Using the Branch-Current Method I determined the value of $I_8 = 110mV$
10) Now I used Ohm's law to get the value of $R_8 = 9.09091\Omega$. </p>
<p>$U_3 = 100mV, I_4 = 2mA, R_5 = 90\Omega, R_8 = 9.09091\Omega, U_8 = 1V, I_8 = 110mV$</p>
<p>I somehow cannot attach any images yet so I hope it is okay if I post an outisde link:</p>
<p><a href="https://www.dropbox.com/s/bfj64pkm0kg36ht/01.jpg" rel="nofollow">https://www.dropbox.com/s/bfj64pkm0kg36ht/01.jpg</a> (link to the circuit, large file, same as shown below)</p>
<p><img src="http://i.stack.imgur.com/04zfe.png" alt="circuit"></p>
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] |
<p>Is there any dependence of the impurities ionization energy on temperature in silicon? I mean if there are any interactions between localized electron and phonons which leads to renormalization of electron binding energy.</p>
| 9,213 |
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<p>Liquid-gas transition critical point is believed to share the same universality class as the 3D Ising model.</p>
<p>We know that the liquid-gas transition is characterized by a phenomenon called critical opalescence that occurs at the critical point and which in short happens because the system becomes correlated at all length scales and thus scatters all frequency of the incident light, thus making the liquid-gas look opaque.</p>
<p><strong>Q</strong> : What is the analogous phenomenon of critical opalescence in a spin system ? Say one takes a material that may be described by a 3D Ising model and does neutron scattering with a broad range of neutron energy : At the critical magnetic ordering temperature, will he see critical opalescence of the neutrons, i.e a diffuse scattering of the neutrons at all wave-length at the critical temperature ?</p>
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<p>I really like to do research in physics and like to calculate to see what happen. However, I really find it hard to write a paper, to explain the results I obtained and to put them in order. One of the reasons is the lack of my vocabulary. </p>
<p>How do I write physics well? I think that writing physics is more dependent of an author's taste than writing mathematics is. Are there any good reference I can consult when writing? Or could you give me advice and tips on writing a paper? What do you take into account when you start writing a paper? What are your strategies on the process such as structuring the paper, writing a draft, polishing it, etc?</p>
<p>In addition, it is helpful to give me examples of great writing with the reason why you think it is good. Do you have specific recommendations?</p>
| 9,215 |
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<p>(for a more muddled version, see physics.stackexchange: <a href="http://physics.stackexchange.com/questions/14020/whats-with-mandelstams-argument-that-only-linear-regge-trajectories-are-stable">http://physics.stackexchange.com/questions/14020/whats-with-mandelstams-argument-that-only-linear-regge-trajectories-are-stable</a>)</p>
<p>There is a 1974 argument of Mandelstam's that linear Regge trajectories implies stability, from "Dual-Resonance Models" from 1974, sciencedirect.com/science/article/pii/0370157374900349. Expand the Regge trajectory function $\alpha(s)$ in a dispersion relation with two subtractions:</p>
<p>$$ \alpha(s) = b + as + {1\over i\pi} \int_0^\infty {\mathrm{Im}(\alpha(s'))\over s-s'} ds'$$</p>
<p>The imaginary part of $\alpha(s)$ gives the decay of the string states, since where it hits an integer tells you where the poles are. So if the string resonances are exactly stable, then the imaginary part is zero, and the trajectory is linear.</p>
<p>This argument bugged me for these reasons:</p>
<ul>
<li>It seems to work just as well with two subtractions, three subtractions, etc. Can you conclude that exactly quadratic or exactly cubic Regge trajectories are also stable? What is a quadratic or cubic trajectory?</li>
<li>The Regge trajectory function appears in the exponent, so you have to take a log to extract it. Why is it clear that it has a representation like the above, without a cut contribution at negative s? </li>
<li>In string theory, the trajectories are linear when they are long-lived, but the trajectory function doesn't look as fundamental today. Is there a more modern formulation of this, which would tell you which string limits are non-interacting just from a condition on the spectrum?</li>
</ul>
<p>Mandelstam generously emailed me a short remark, saying essentially that the trajectory function imaginary part is a lifetime, and indeed this is obvious from the fact that it gives the position of the resonances, but I am still confused regarding the questions above.</p>
<p>Even a partial answer would be appreciated.</p>
| 9,216 |
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<p>In his work on information processing in GPTs <a href="http://arxiv.org/abs/quant-ph/0508211">http://arxiv.org/abs/quant-ph/0508211</a> Barrett speculates that the trade-off between allowed states and the allowed dynamics in a GPT is optimal in quantum theory, allowing for information processing capabilities not all of which occur in either the generalized no-signalling theory (GNST) or the generalized local theory (GLT). I'm wondering if this optimality is related to the symmetry of the associated polytope (of allowed states) in the theory, and in what exact manner. Any ideas?</p>
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<p>It always fascinate me that time is symmetrical classical physics while in life we all experience flow of time in only one direction. There is no preference direction of time in classical physics. The only exception being in thermodynamics where with the introduction of entropy, there is a prefer direction for the time axis. Physical systems evolve in the direction where the entropy increases (sorry for not being precise...) Personally, I have never truly accepted thermodynamics as a full theory as it never truly "explain" why entropy must increase. </p>
<p>But, in quantum theory, there seems to be a preferred direction for time too. And, this has nothing to do with entropy? The collapse of a wave function in a measurement seems to dictate a direction of time. Could this be a better explanation for the direction of time or maybe even for thermodynamics? (Ok, maybe not thermodynamics...)</p>
| 303 |
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] |
<p>Why do spinless fermions behave in the same way as weakly interacting bosons.</p>
| 9,218 |
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<p>Would we all parish due to excessive heat? Or would that be only limited to the area near the impact while as the people on rest of the earth would die from other phenomenons such as mega earthquakes, volcanic activities, tsunamis etc. Does it matter where the impact is - if it landed in antarctica we would have massive floods but if it landed in the middle of eurasian continent, the effect would be different? </p>
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] |
<p>I would like to know the ballistic device characteristics and illustrations (if any) to understand how can we overcome the dependence of current on carrier mobility .</p>
| 9,220 |
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<p>I'm performing an experiment with a 2D <a href="http://en.wikipedia.org/wiki/Double_pendulum" rel="nofollow">double pendulum</a>, and in part of it I want to investigate the normal modes of the double pendulum, where the pendula are not of equal length or of equal mass. My question is - how will I actually know when I've successfully excited a normal mode? </p>
<p>I start by setting the initial angles to be in (roughly) the correct proportion to one another in order for the initial setup to be an eigenvector, but of course once I release the pendulum there is a slight 'jolt' which means I can't be sure the initial conditions were exactly an eigenvector (of course, realistically I'm only going to be closely approximating one). Then, once data is recorded I can generate a phase portrait with the computer, and the phase portrait I see when I get quite close to an eigenvector looks kind of like a tilted cylinder (sorry, don't know how to post a Matlab graph here). Is there a way to tell from this phase portrait (with the angles $\theta_1$ and $\theta_2$) whether I've hit a normal mode or not? Would appreciate some help.</p>
<p>(ie. if someone could post a picture of a phase portrait of the normal modes of a double pendulum, so that I know what I'm looking for, that would be very appreciated)</p>
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<p>Is light electromagnetic waves or quantum physical particle waves. Or are they the same?</p>
<p>Note: My question is specifically how electromagnetism plays into the quantum physics and the double slit experiment.</p>
| 304 |
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] |
<p>Question: The melting point of copper is 1080 degrees Celsius and its heat of fusion is 200 kJ/kg. If a copper coin at this temperature is completely melted by the absorption of 2000 J of heat, what is the mass of the coin in kg?</p>
<hr>
<p>I am not sure which formula(s) to use. Is the melting point even needed in this particular problem with it's given information?</p>
<p>Thank you.</p>
| 9,222 |
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] |
<p>How is the Lorenz gauge condition $\partial_\mu \overline{h}^{\mu \nu}=0$ equivalent to the <a href="http://en.wikipedia.org/wiki/Harmonic_coordinate_condition">harmonic gauge condition</a> $\Box x^\mu=0 $?</p>
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<p>How do the wave properties of an electron change with its motion? What about when it is stationary?</p>
| 9,224 |
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<p>A student conducts an experiment to measure the motion of two unknown masses (A and B) along a smooth table. A constant force of 1 N was applied by means of a string connected by a falling weight. </p>
<p>A motion sensor recorded the position (measured from the start line) of each mass at regular time intervals as they slid along the table. The results displayed by the data logger are tabulated: </p>
<p><img src="http://i.stack.imgur.com/RDHr0.png" alt="enter image description here"></p>
<p>What would be the best way of describing the motion of both masses? Do you use acceleration? </p>
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<p>When quantizing Yang-Mills theory, we introduce the ghosts as a way to gauge-fix the path integral and make sure that we "count" only one contribution from each gauge-orbit of the gauge field $A_\mu\,^a$, because physically only the orbits themselves correspond to distinct physical configurations whereas the motion within the gauge-orbit should not contribute to the path-integral.</p>
<p>How come we don't run into this problem when we quantize the Fermions, which also have gauge transformations, and also have a gauge orbit? Shouldn't we include a gauge-fixing term for the Fermions as well, or does the term introduced for the Boson fields already pick out the gauge orbit for the Fermions as well? How does this technically come to be?</p>
<p>So far I introduce a gauge fixing term into the Lagrangian as $$ 1 = \int d\left[\alpha\right]\det\left(\frac{\delta G\left[A_{\mu}\left[\alpha\right]\right]}{\delta\alpha}\right)\delta\left(G\left[A\left[\alpha\right]\right]\right) $$ where $\alpha(x)$ are the gauge functions, and $G[]$ is a functional which is non-zero only for a unique gauge-representative in each gauge-orbit, where we have the transformations as: $$ \begin{cases}
\psi_{c_{i}} & \mapsto\left(1+i\alpha^{a}t^{a}\right)_{c_{i}c_{j}}\psi_{c_{j}}+\mathcal{O}\left(\left(\alpha^{a}\right)^{2}\right)\\
A_{\mu}\,^{a} & \mapsto A_{\mu}\,^{a}+\frac{1}{g}D_{\mu}\,^{ab}\alpha^{b}+\mathcal{O}\left(\left(\alpha^{a}\right)^{2}\right)
\end{cases} $$</p>
| 9,226 |
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<p>I'm searching for references, articles and books, that discussed the geometrization of modern (and contemporary) physics, in a philosofical point of view. Something in the way that Michael Friedman did in "Space-time foundations theories" or Tian Yu Cao did in "The conceptual foundations and philosophical aspects of renormalization theory" or yet, what Roberto Torreti did in "Relativity and Geometry".</p>
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<p>I have a question that I can't seem to get my head around. I'm really rusty on my physics, but I'm sitting here trying to think this out, but I'm missing a really big part of the equation.</p>
<p>So lets say I have a turbine in space. It's purpose is to convert the energy given to it, in joules to watts. So I realize we will have friction, and we need to overturn the static friction before turning can be achieved. </p>
<p>I want the device to turn at a relatively high speed, therefore F > Ff. However, this will create a situation where the device will constantly accelerate, because there is F and not being apposed by friction, Fn = ma.</p>
<p>So here is my thought process for the situation.</p>
<p>Force needed to start turning...<br>
F = Fn - Ff<br>
Energy needed to start turning...<br>
W = Fd<br>
where...<br>
W = (KEf - KEi) where KEi = 0<br>
Therefore,<br>
a = F/m </p>
<p>Since there will always be force, and constant supply of energy, the device will accelerate to infinity, supplying infinite energy in watts?
I understand this to be fundamentally impossible... So where am I going wrong? I feel like this will be a facepalm moment, but I just can't seem to remember what I'm missing here.</p>
<p>Best Regards.</p>
| 9,228 |
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<p>Why doesn't diamond show up in X-ray imaging? Diamond is the hardest substance ever known, and as we know, X-ray radiation is produced when a cathode ray of high frequency hits a very high atomic mass target. But I am amazed: why doesn't diamond show up in X-ray imaging?</p>
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<p><a href="http://en.wikipedia.org/wiki/Particle_in_a_ring" rel="nofollow">Particle in ring</a> is a well-known example where a solution of the Schrodinger equation exists. My question is: In principle we also want that $\psi'(\theta) = \psi'(\theta + 2\pi)$. The thing is that this condition is never explicitly stated ( probably because it is fulfilled anyway, but in principle we would also need this condition, right?</p>
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<p>This year in college we"ve had a lot of quantum stuff thrown at us, and we"ve only been doing classical mechanics till last year. We"ve been introduced to Schrodinger"s equation, electron waves, what have you. This is my understanding(rather rudimentary) so far. When you solve Schrodinger"s equation for an atom, you get a set of wave functions(what are the inputs and outputs exactly in this function?). Each wave function can describe a maximum of 2 electrons. It was stated in one place that the wave function represents the amplitude of the electron wave, and its square gives the probability of finding the electron at a place.An orbital is a surface diagram that includes the regions where the electron described by a particular wave function is most likely to be found within the surface.
NOTE: I know the basic quantum formulae even though I may not understand what they mean.</p>
<p>Is my understanding right?(I realize I had forgotten to put this sentence when I first posted the question, and it would"ve seemed rather confusing as to what it was I actually wanted to know.)</p>
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] |
<p>If I immerse a rod vertically in a liquid with a relative permittivity gradient (the permittivity decreases with depth), will the rod stretch (will the spacing of the atoms in the rod be affected by the varying permittivity)?</p>
| 9,232 |
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<p>There was some experiment that I read about some time back in which two particles (or the same particle, but split into two) were sent in opposite directions, but when something happened to one, it happened to the other at the same moment, as if they were the same particle.</p>
<p>I thought the word for this was "entrainment", but looking that up does not lead back to this experiment.</p>
<p>What is the term for this, assuming that I am not remembering something that never happened.</p>
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<p>If I have a laser light incident on the double slit at an angle O < 90 what kind of interference pattern will I see? Will i see the same with less intensity or different pattern? </p>
| 9,234 |
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] |
<p>Temperature is a measure of kinetic energy transferred to particles, henceforth, <a href="http://en.wikipedia.org/wiki/Outer_space#Environment" rel="nofollow">space</a> being vacuum, temperature cannot be measured.
But then, there is cosmic background radiation. It is the leftover heat from the Big Bang, but then heat in space doesn't make sense, how does this radiation, heat up space time when it technically cannot be heated up?
Moreover why is it referred to as heat when it is approximately just $2.5$ Kelvin, which is just above absolute zero?</p>
| 9,235 |
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] |
<p>I have a uniform electric field $E$ projected from left to right and I placed an insulator or dielectric right in the middle of it. To the left of the insulator, the $E$ is the original $E$. Inside the insulator, there is an induced field and thus the net field is less than the original. What happen to the $E$ to the right of the insulator? Will it be the same as the original? If it does, then the $E$ will have to increase back? Why?</p>
| 9,236 |
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<p>I have the following homework problem in theoretical electrodynamics:</p>
<blockquote>
<p>Show that the gauge invariant Lagrange density $\epsilon_{\mu\nu\alpha\beta} F^{\mu\nu} F^{\alpha\beta}$ can be written as a total divergence of a four-vector.</p>
</blockquote>
<p>This total divergence should be something like $\partial_\mu G^\mu$, right?</p>
<p>With
$$
\hat F^{\mu\nu} = \frac 12 \epsilon^{\mu\nu\alpha\beta} F_{\alpha\beta}
$$
I figured that I write this Lagrange density (I'll refer to it as $L_2$) could be written as:
$$
L_2 = 2 \hat F^{\mu\nu} F_{\mu\nu}
$$</p>
<p>I simplified this by using the matrix representations of each $F$ and got it down to:
$$
L_2 = -\frac 4c B_i E^i
$$</p>
<p>$B$ and $E$ can be expressed in Terms of $A$ like so:
$$
B_i = \epsilon_{ijk} \partial_j A^j
,\quad
E_i = -\partial_i A^0 -\partial_0 A^i
$$</p>
<p>How would I continue to find that four-vector $G$?</p>
| 9,237 |
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<p>Will a person on top of hill will age faster than one at sea level due to Time Dilation?</p>
| 9,238 |
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<p>I'm a first year graduate student in Mathematical Physics, and I am trying to generalise a certain method involving the so-called "Differential realizations" of certain algebras. The problem I'm having is that in papers <a href="http://arxiv.org/pdf/hep-th/9810074.pdf" rel="nofollow">here</a> (Page 8) and <a href="http://arxiv.org/pdf/hep-th/9804191.pdf" rel="nofollow">here</a> (Page 5-6), they express a certain type of algebra in terms of differential operators and I'm not sure how that is done. My goal is to see if such methods can be generalised to other algebras to test for a certain property called "Shape Invariance" which is mentioned in the latter paper. I'm wondering if anyone here has ever heard of differential realizations and has any idea how they can be derived for other algebras?</p>
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<p>All know that Inflation may solve some of the problems of the Standard Model of Cosmology and today we suppose that the field responsible for that is the inflaton. The properties of the potential $V(\varphi)$ allow via the momentum-energy tensor to define a barotropic fluid for which $$p=-\rho$$ and when the slow-roll conditions $\epsilon\ll1$, $|\eta|\ll1$ are satisfied, this fluid with $w=-1$ has some sort of negative pressure or repulsive gravity that allow the expansion of Universe. So a scalar field may act like a cosmological constant $\Lambda$ giving some energy to the vacuum. Now seems that the Universe undergoes an epoch of "second inflation" with $$\ddot{a}>0.$$ My question is: why there is no exponential inflation like the old one if today the dominant fraction of the Universe budget is again a sort of cosmological constant $\Lambda$?
Maybe the two fluids are of completely different kind, or the behavior depends on the energy and temperature conditions or i am wrong something? </p>
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<p>Ohm's Law tells us that $V = IR$. This implies that $I \propto \frac{1}{R}$. But, $R \propto l$, where l is the length of the conductor. This would mean that $I \propto \frac{1}{l}$. But this does not fit with the definition of current that says that current is the amount of charge $Q$ passing through a given point per unit time. Clearly, the amount of charge passing through a given point per second does not vary with the length of the conductor. How can this contradiction exist?</p>
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<p>As our homework, we were asked to derive $P = I^2R$. </p>
<p>Now, I started off with the basic relation $P = \frac{W}{T}$. I was not able to think of anything from here, so I started plugging in random formulas from a purely algebraic point of view. </p>
<p>I tried the one for voltage $V = \frac{W}{q} \implies Vq = W$ and got $P = \frac{Vq}{T}$. And since $I = \frac{q}{T}$, $IT = q$, plugging this in we get $P = IV$. A simple application of Ohm's Law gives us the required equation. But, when I tried to get an intuitive grasp of what I'd just done, I found a few discrepancies:</p>
<ol>
<li><p>In the definition of voltage, $W$ refers to the energy an electron loses when it goes from the negative to the positive terminal. In the definition of power, $W$, refers to the total energy consumed by the appliances. How can you relate the two?</p></li>
<li><p>In the definition of current $T$, refers to the time taken by the electron to go from one terminal to the other, whereas, in power $T$ refers to the time for which the appliances run or the energy is supplied. How can these two be the same?</p></li>
</ol>
<p>Is my derivation incorrect? If not, then how would you counter the arguments I mentioned above?</p>
| 9,242 |
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<p><img src="http://i.stack.imgur.com/H9uwm.jpg" alt="enter image description here"></p>
<p>If the above image is a cross section of a conductor, the field at the point shown is not zero. So the field inside a conductor is not zero at all points. </p>
<p>You could argue that the electrons would rearrange themselves so that the field inside is zero. But if that were true, all the positive charges would not be on the surface. For example, in the diagram above, the electron at the point shown, would move, leaving a charge in the centre.</p>
<p>What am I missing?</p>
<h1><em><strong>I am not looking for a proof that the field inside a conductor is zero. Please address the problem I discussed above.</em></strong></h1>
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<p>Say I'm given the following Schrodinger equation</p>
<p>$$\frac{d^2u}{dx^2}+ \left[E - V(x)+ \frac{a}{x^2}\right]u(x) =0$$</p>
<p>Where $a \in \mathbb{R}$. What are the physical interpretations of this equation? I understand that it means the angular momentum is fixed, but are there any other implications associated with this?</p>
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<p>This is a question triggered by <a href="http://physics.stackexchange.com/questions/93124/divergent-series">this post</a></p>
<p><a href="http://en.wikipedia.org/wiki/Madelung_constant" rel="nofollow">Madelung's constant</a> is defined to the coefficient of electrostatic potential energy in a ionic crystal. In the example of $NaCl$,
\begin{equation}
M = \sum_{ijk}{}^{'}\frac{(-1)^{i+j+k}}{\sqrt{i^2+j^2+k^2}}
\end{equation}
is conditionally convergent. </p>
<blockquote>
<p><em>Since this sum is conditionally convergent it is not suitable as definition of Madelung's constant unless the order of summation is also specified. There are two "obvious" methods of summing this series, by expanding cubes or expanding spheres. The latter, though devoid of a meaningful physical interpretation (there are no spherical crystals) is rather popular because of its simplicity. Thus, the following expansion is often found in the literature:[2]</em>
$$ M = -6 +12/ \sqrt{2} -8/ \sqrt{3} +6/2 - 24/ \sqrt{5} + \dotsb = -1.74756\dots. $$
<em>However, this is wrong as this series diverges as was shown by Emersleben in 1951.[3][4] The summation over expanding cubes converges to the correct value. An unambiguous mathematical definition is given by Borwein, Borwein and Taylor by means of analytic continuation of an absolutely convergent series.</em></p>
</blockquote>
<p>I have the following questions.</p>
<p>1) Expanding sphere leads to a divergent series. OK, what if I make a perfect spherical sample of $NaCl$, will the experimentally measured Madelung's constant to be infinity?</p>
<p>(<strong>EDIT</strong>: I maybe have some misunderstanding of divergence: it could be the case that the series is bounded but don't have a definite limit. So is the series for expanding sphere bounded? and if there is no definite limit, what's the experimentally measured value for a perfect spherical crystal?)</p>
<p>2) What physical principle dictates the order of summation? or why does finite number obtained by analytic continuation should be consistent with the observed value?</p>
<p>3) What is the role of charge neutrality here? I ever programed to compute Madelung's constant using the fractional charge idea((assign $\frac{1}{8}$ charge to the corner, $\frac{1}{4}$ to the edge, $\frac{1}{2}$ to the face ), which makes the expanding cube charge neutral. Does that mean charge neutrality is one of conditions that <em>must</em> be enforced? or it is just for the sake of computational efficiency?</p>
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] |
<p>While studying reflection through a plane mirror, I have been told that when the object is real the image will be virtual and <strong>the image will be real while the object is virtual</strong>.</p>
<p>What are virtual objects? Do they really exist in nature? </p>
| 209 |
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<p>If $|\psi \rangle$ represents a wavefunction through a column matrix and $\langle \psi |$ represents the dual vector in a row matrix and $|\psi \rangle \langle \psi | = \rho $ is the probability density of the wavefunction collapse to a particular value in $\mathbb{R}$ by a measurement, and matter is also a wave (DeBroglie), how does one represent matter by using Dirac notations - how about anti-matter? Would there be something similar to $\langle \psi |\psi \rangle = n \in \mathbb{R} $ ?</p>
<p>I apologize if the question is quite ignorant, i.e. Dirac's equations don't relate matter/anti-matter, it just seems they should - and I would like to know how ;)</p>
<p>Thanks,</p>
<p>Brian</p>
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<p>Suppose we havean uniform slender rod of dimensions : $L$( length) and $A$( cross sectional area). Now at different points on the rod we apply different forces. So, in this situation how are we expected to find the elongation in the rod?</p>
<p>I tried in 2 different ways:</p>
<ul>
<li>I considered each part and found the elongation for each part, and then added them up.</li>
<li>I considered cumulative segments, that is: from part A to B then from part A to C ( hence taking the forces at junction B as internal force and not taking them into account) and then adding them up.</li>
</ul>
<p>My question is, as these two processes yield different results, which is the correct method and why? Also if anyone has a better method, please share it with me.</p>
<p>The type of the question can be found in Timoshenko & Young : Elements of Strengths of Materials, Exercise 1.2 figure A.</p>
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<p>In Rindler's book: Relativity, Special, General and Cosmological, is stated on page 40 that the Relativity Principle (RP), when applied to just one Inertial Frame (IF), guarantees the homogeneity and isotropy of tha IF. By inertial frame Rindler means an ideal infinity extended rigid body moving freely in a world without gravity. This is distinct from an inertial coordinate system, that should be understood as an IF plus, in it, a choice of standard coordinates $x$, $y$, $z$ and $t$.
As he says, the RP concerns inertial coordinate systems: the laws of physics are invariant under a change of inertial coordinate systems.</p>
<p>I can't understand why this imply homogeneity and isotropy of an IF. If I suppose the existence of an special direction in some inertial reference frame, I could imagine some physical law governig the propagation of some signal (it can be light if you want, but it's not necessary), and if by measuring the velocity of this signal in two different directions and I get two different results, this would violate the isotropy of the IF and at the same time I could write the physical law in an invariant way under coordinate changes inside de IF (sure, it would depend on the special direction) and this would be in accordance with the RP as stated above. What is wrong with my reasoning?</p>
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<p>Doppler redshift of distant galaxies gave first hint that the universe is expanding. I am curious to know how this redshift is actually measured and interpreted from observation. Suppose I observe some visible line say red with wavelength \lambda_1. This is not enough to tell that this line is redshifted, i.e., the original line emitted from that galaxy had a smaller wavelength. How do I know the value of that particular line when it was emitted from that galaxy? It appears that mere observation of a line is not enough. So how do we proceed?</p>
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<p>In the canonical quantization of fields, CCR is postulated as (for scalar boson field ):
$$[\phi(x),\pi(y)]=i\delta(x-y)\qquad\qquad(1)$$
in analogy with the ordinary QM commutation relation:
$$[x_i,p_j]=i\delta_{ij}\qquad\qquad(2)$$
However, using (2) we could demo the continuum feature of the spectrum of $x_i$, while (1) raises the issue of $\delta(0)$ for the searching of spectrum of $\phi(x)$, so what would be its spectrum? <br><br>
I guess that the configure space in QFT is the set of all functions of $x$ in $R^3$, so the QFT version of $\langle x'|x\rangle=\delta(x'-x)$ would be $\langle f(x)|g(x)\rangle=\delta[f(x),g(x)]$, <br>but what does $\delta[f(x),g(x)]$ mean?<br><br> If you will say it means $\int Dg(x) F[g(x)]\delta[f(x),g(x)]=F[f(x)]$, then how is the measure $Dg(x)$ defined?<br><br>
And what is the cardinality of the set $\{g(x)\}$? Is the state space of QFT a separable Hilbert sapce also? Then are field operators well defined on this space?</p>
<p>Actually if you choose to quantize in an $L^3$ box, many issues will not emerge, but many symmetries cannot be studied in this approximation, such as translation and rotation, so that would not be the standard route, <br>so I wonder how the rigor is preserved in the formalism in the whole space rather than in a box or cylinder model?<br>
<br>
I'm now beginning learning QFT, and know little about the mathematical formulation of QFT, so please help me with these conceptual issues.</p>
| 9,250 |
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<p>Can anyone explain the process required to make a Hadamard gate that acts on 1st, 2nd and 3rd qbits?</p>
<p>For Hgates acting on the first qubit i realise the matrix is $H=\begin{pmatrix} 1&1\\1&-1\end{pmatrix}$, but I am unsure how to formulate such a gate. As to acting on the second qubit I have read this <a href="http://en.wikipedia.org/wiki/Hadamard_transform" rel="nofollow">web page 1 </a>but I am not really sure if it is correct, because it is just a 4x4 matrix without any zeroes. I found this $\begin{pmatrix} 1 & 1 \\-1 & 1 \end{pmatrix} $ on another website which will obviously have zeroes when it is multiplied by $I$. Simply can anyone explain how Hadarmd gates can be formulated and built to n qubits? </p>
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] |
<p><img src="http://i.stack.imgur.com/jHugn.png" alt="enter image description here"></p>
<p>The electric field in a wire is parallel to the wire's surface (it is always pointing "to the front"). If the electric field did not point in this direction, surface charges would build up and change the electric field to make it point the correct way.</p>
<p>In the above diagram the electric field vectors are pointing the wrong direction, but there will be no charge build up, since the current flowing into the junction is same as the current flowing out. So in this scenario how would the surface charges rearrange to make the electric field point in the correct direction?</p>
| 9,252 |
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<p>A black hole engulfs the matter nearby, how does it store the mass inside? We know that matter is composed of particles, does a black hole store the mass in massive particles? Or can we assume that it's composed of extremal black holes? what are theories about it?</p>
<p>EDIT:
I checked out <a href="http://physics.stackexchange.com/questions/35150/black-holes-are-in-which-state-of-matter">Black-holes are in which state of matter?</a>
it doesn't provide a definite answer.</p>
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<p>If the Alice sends to Bob an q-bit $\alpha\left|\mathbf{0}\right> + \beta\left|\mathbf{1}\right>$ in quantum key exchange (such as BB84) it is assumed that Eve cannot copy the state (due to no cloning theorem) and attempts to read the state requires guessing the base which would allow to detect interception.</p>
<p>However if the Eve put $\left|\mathbf{1}\right>$ through C-Not gate than the state would be:</p>
<p>$$\phi_0 = (\alpha\left|\mathbf{0}\right> + \beta\left|\mathbf{1}\right>)\otimes\left|\mathbf{1}\right>$$
$$\phi_1 = \alpha\left|\mathbf{00}\right> + \beta\left|\mathbf{11}\right>$$</p>
<p>Now Eve can store her q-bit somewhere and send the 'original' one to Bob. Since the base disclosure is on public channel she can measure her q-bit in correct base (the state would be collapsed but it shouldn't matter).</p>
<p>Why then quantum entanglement doesn't break quantum cryptography?</p>
<p><strong>Edit:</strong> To clarify what I understand (I haven't read the text about density matrices).</p>
<p>Alice sends to Bob two qubits - $\left|\mathbf{0}\right>$ and $\left|\mathbf{+}\right>$. Let's assume they are not discarded then in first case after Eve entangle it's qubit with sent qubit the state in case one:</p>
<p>$$\phi_{\left|\mathbf{0}\right>} = \left(\begin{array}{rrrr} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{array}\right)\left(\begin{array}{r} 0 \\ 1 \\ 0 \\ 0\end{array}\right) = \left(\begin{array}{r} 1 \\ 0 \\ 0 \\ 0\end{array}\right) = \left|\mathbf{00}\right>$$</p>
<p>Now the only possible value read by Bob is $\mathbf{0}$ assuming he guessed base. Eve can then overhear the disclosure of bases and measure the reduced state on previously stored entangled qubit.</p>
<p>In second case:</p>
<p>$$\phi_{\left|\mathbf{+}\right>} = \left(\begin{array}{rrrr} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{array}\right)\frac{1}{\sqrt{2}}\left(\begin{array}{r} 0 \\ 1 \\ 0 \\ 1\end{array}\right) = \frac{1}{\sqrt{2}}\left(\begin{array}{r} 1 \\ 0 \\ 0 \\ 1\end{array}\right) = \left|\mathbf{++}\right>$$</p>
<p>Assuming that the Bob guessed the base correctly the Eve would also measured $\mathbf{+}$ in similar way as previously. If Bob didn't guessed it correctly Eve can discard particular qubit.</p>
<p>Now if quantum cryptography works:</p>
<ul>
<li>For some reasons the entanglement is forbidden (if yes - what is the difference between sending qubit and processing it inside quantum computer?)</li>
<li>Reduction of state by Bob does not happen in a way I think (possibly due to not knowing the density matrix).</li>
</ul>
| 9,254 |
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<p>I know there are theories (or postulates) that hold that our Universe could be a simulation. I was wondering, if Special Relativity states that two events which are not causally linked can be judged to have happened simultaneously or not, depending on the reference frame of the observer, can someone (or something) simulating the Universe reproduce this effect (if one observer says that two events were simultaneous, and the other disagrees, and they are both equally justified in their claims, what would the simulator conclude regarding their simultaneity)? </p>
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<p>What sort of no-slip zone is in place when liquid water flows from a faucet through air at room temperature? Does the water drag a layer of air molecules along with it?</p>
| 9,256 |
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<p>Is there a way to see that <a href="http://en.wikipedia.org/wiki/Bertrand%27s_theorem" rel="nofollow">Bertrand's theorem</a> is true intuitively. I mean without getting into too much mathematics ?</p>
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] |
<p><code>Person A</code> and <code>Person B</code> are same person (theortically). They both weigh 800N. They both can vertically
lift 1000N. They want to check something out.</p>
<p><code>G -> Gravity; N -> "Normal"; M -> Muscular active</code></p>
<p><code>R -> Netto; 1 -> Person A; 2 -> Person B</code></p>
<p>$F_{g1} = 800N$</p>
<p>$F_{g2} = 800N$</p>
<p>$F_{m1} = 0N$</p>
<p>$F_{m2} = 0N$</p>
<p>$F_{n1} = F_{g1} - F_{m2} = 800N$</p>
<p>$F_{n2} = F_{g2} - F_{m1}= 800N$</p>
<p>$F_{r1} = F_{g1} - F_{n1} - F{m2} = 0N$ (no move)</p>
<p>$F_{r2} = F_{g2} - F_{n2} - F{m1} = 0N$ (no move)</p>
<ul>
<li><code>Person A</code> grabs <code>Person B</code> with both hands shirt of <code>Person B</code> in region of a bit lower than collarbone (like "tough" guys do on films).</li>
<li><code>Person A</code> lifts <code>Person B</code> with 1000N in air, about 135 degrees relative to his torso.</li>
</ul>
<p>$F_{g1} = 800N$</p>
<p>$F_{g2} = 800N$</p>
<p>$F_{m1} = 800N$</p>
<p>$F_{m2} = 0N$</p>
<p>$F_{n1} = F_{g1} + F_{g2} = 1600N$</p>
<p>$F_{n2} = F_{g2} - F_{m1} = 0N$</p>
<p>$F_{r1} = F_{g1} - F_{n1} - F{m2} = 0N$ (no move; on ground)</p>
<p>$F_{r2} = F_{g2} - F_{n2} - F{m1} = 0N$ (no move; in air)</p>
<ul>
<li>Seems till now, perfectly understandable and normal to me. In my perception of physics.</li>
<li><code>Person B</code> grabs <code>Person A</code> with both hands whatever of <code>Person A</code> in region of whatever. By whatever I mean, somewhere on body that person is still able to pull <code>Person A</code> in air.</li>
<li><code>Person B</code> lifts(?) <code>Person A</code> with 1000N in air(?), about 135 degrees relative to his torso.</li>
<li>This is when I lose it. Following rules, are total non-sense and also cause why I write this.</li>
</ul>
<p>$F_{g1} = 800N$</p>
<p>$F_{g2} = 800N$</p>
<p>$F_{m1} = 800N$</p>
<p>$F_{m2} = 800N$</p>
<p>$F_{n1} = F_{g1} - F_{m2} = 0N$</p>
<p>$F_{n2} = F_{g2} - F_{m1} = 0N$</p>
<p>$F_{r1} = F_{g1} - F_{n1} - F_{m2} = 0N$ ("floating")</p>
<p>$F_{r2} = F_{g2} - F_{n2} - F_{m1} = 0N$ ("floating")</p>
<p>"My brain", that gummy moisten tube in my head filled with baloney, tells me that first gravity and muscle force count. Then the normal one. This would cause $F_{r_{both}} = 0N$. They both have effect of being "freed" from effect of "normal" force. As <code>Person 2</code> was when he/she was in air, being lifted by <code>Person 1</code>. But it's impossible. There is still gravity pulling them to earth. And at this point. There is "floating" going on and explaining this with "Normal force" would make it even worse because both of them separately will be either flying or falling through ground.</p>
<p>@edit - When <code>Person A</code> will pull <code>Person B</code> up. <code>Person B</code>'s attitude would decrease till on feet. What then?</p>
<p>As if, if they normally stay on ground turning to tomatoes because of pulling each other up. What happens to that all the force they put in it? This 1600N.</p>
<p>"Definables": T-Shirt is untearable, won't fall off and does not hurt body at all. Both of them stay right on their feet. Please explain as plain as possible. I am really really really low with my knowledge. Relatively to you, I am idiot. I'm sorry for grammar.</p>
<p><strong>Question:</strong> What happens to <code>Person 1</code> and <code>Person 2</code>? Could you explain forces influencing their bodies, please?</p>
<p>If you are about to think "Goddammit, you're so stupid, answer is so obvious!" keep in mind I am teenager (17) without real physics knowledge. Answer may just lay around my point of view/knowledge/logic. In place of getting offensive try to explain where I made my mistake so it won't happen again :).</p>
| 9,258 |
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