Invariance Definition and 454 Threads

[SOLVED] invariance of maxwell's equations under Gauge transformation Homework Statement Show that the source-free Maxwell equations \partial_{\mu} F^{\mu\nu}=0 are left invariant under the local gauge transformation A_{\mu}(x^{\nu})\rightarrow...

Proof that pressure is invariant on the front and back faces of the moving box. (We are already agreed in another thread that the pressure is invariant on the other faces) Pressure in the rest frame of the box: (Frame S) When a gas particle of mass M and velocity U collides with a face...

Many textbooks derive the formulas which account for the Doppler shift and for aberration of light from the invariance of the phase of an electromagnetic wave. Do you know an explanation for the invariance?

Homework Statement Is the following input/output (x is input, y is output) system linear, time invariant, causal, and memoryless? Answer yes or no for each one.Homework Equations y(t)=2x(t)+3The Attempt at a Solution My instinct tells me it's linear, but for some reason I have trouble showing...

Please tell me if it is possible to derive the formula which accounts for the Lorentz contraction from the invariance of the space-time interval. Thanks

I am having trouble going about proving the Lorentz invariance and non-Galilean invariance of Maxwell's equations. Can someone help me find a simple way to do it? I've looked online and in textbooks, but they hardly give any explicit examples.

On p. 32 of Quantum field theory in a nutshell, Zee tries to derive the propagator for a spin 1 field: D_{\nu\lambda} = \frac{-g_{\nu\lambda} + k_\nu k_\lambda /m^2}{k^2 - m^2} using the Lorentz invariance of the equation k^\mu \varepsilon_\mu^{(a)}=0 where \varepsilon_\mu^{(a)} denotes the...

Please tell me if there are motivated physical reasons to consider that combinations of dimensionless physical quantities that appear at the exponent of e in distribution functions have the same magnitude in all inertial reference frames in relative motion, Thanks in advance

Simple question.. How do you prove the volume element of momentum space (d3k/Ek) is Lorentz Invariant? I tried making it proportional to "velocity volume element" derived from the Lorentz transformations but didn't seem to get very far.

Homework Statement Prove that the quantity 2EN^2 dx^3 is a relativistic invariant. Homework Equations Well we want to prove that this quantity is the same in all inercial frames. My doubt is with the energy transformation, E=\gamma E_0 does it transforms like that? If...

What is the physical significance of tensors? Occasionally, motivating statements are made roughly along the lines of "if an equation can be expressed purely in terms of tensors, then it is true for all observers". But that doesn't seem quite complete because different tensor-users would have...

I just wanted to know say a matrix X is invariant under some transformation T. So: T:X->Y is invariant... does that mean all the elements of X are the same as the elements of Y? Or is the elements in Y a scalar multiple of the elements in X?

Homework Statement Show that y(t) = \frac{d}{dt}\left[e^{-t}x(t)\right] is time invariant. 2. Relevant Information I don't think this is TI! I'm told it is TI, but I think I proved that it is not TI! My proof is below. Am I wrong or is the question wrong in assuming that the...

On page 3 of the following pdf: http://pdg.lbl.gov/2005/reviews/numixrpp.pdf the paragraph after equation 13.12, there's a line that says: "Thus, if U is not real, the neutrino... When CPT holds, any difference between these probabilities indicates a violation of CP invariance." I don't...

I have noticed that questions about this subject get either ignored or receive some confusing answers. So I decided to write a "brief" but self-contained introduction to the subject. I'm sure you will find it useful. It is going to take about 13 or 14 post to complete the work. Be patient with...

In Feynman lectures in physics v2 28-6, Feynman points out that we can add a constant times \phi to D'Alembertian without distrupting the relativistic invariance. How and why?? Can someone work out a mathematical proof? Thanks in advance.

Homework Statement Consider the following input-output relationship: y(t) = \int_0^\infty e^{-\sigma}x(t-\sigma) d\sigma A) Is the system time-invariant? B) Find the output y(t) when the input to the system is x(t) = \mid t \mid , -\infty < t < \infty Homework Equations These are the...

Hi everyone, How would I go about proving that the scalar product of two four-vectors (A,B) is invariant under a Lorentz transformation?

The problem is, rather briefly: Show that the wave equation is INVARIANT The equation is given as: [the Laplacian of phi] - 1/(c^2)*[dee^2(phi)/dee(t^2)] dee being the partial derivative.. phi is a scalar of (x, y, z, t) Now, i want, and think i should be able, to solve this problem...

Please inform me if you know places where the invariance of the product velocityxphase velocity=cc is discussed (derived?). Thanks

It is clear that a conserved current \partial_{\mu} J^\mu = 0 implies the existence of a conserved charge Q= \int d^3x J^0 . Now I want to go the other way round: Suppose we have a basis of momentum eigenstates, such that these states are also eigenstates of the charge. Then clearly the charge...

I recently read an author making the following argument in QFT: if <m|A^0(t,0)|n>=B then <m|A^mu(t,0)|n>=(B/p^0)*p^mu by Lorentz invariance. Can anybody tell me under which circumstances this holds and how it comes about? I understand that <m|A^mu(t,0)|n> had to transform as a 4-vector but why...

I recently studied supersymmetry breaking and read there that for Supersymmetry breaking we have the energy of the vacuum state >0. However what I do not really see is why such a vacuum would not break Poincare invariance as well as the energy is part of the momentum 4-vector and so transforms...

How do we prove that the spacetime interval is invariant? Also why is it so important?

do you kinow a simple and convincing argument for the fact that proper time is a relativistic invariant?

Since there's another thread on the same subject in the GR forum, but on this forum about 8 months ago an interesting discussion on the same subject took place, https://www.physicsforums.com/showthread.php?t=114620, i want to draw everyone's attention on the post \#24 in that thread in which the...

Today my professor gave us an argument in favor of why charge was frame invariant. It went like "if it were not, then moving neutral object would become charged, which is not something that we observe". It's not exactly that and it made sense at the time, but I'm missing a piece in the argument...

i usually have such a hard time determining whether a signal is time invariant or not ... for example, why would x[-n] not be time-invariant? please don't just tell me why x[-n] would not be time invariant ... tell me techniques that I can apply to other signals too

Derivation of Poincare Invariance from general quantum field theory C.D. Froggatt, H.B. Nielsen Annalen der Physik, Volume 14, Issue 1-3 , Pages 115 - 147 (2005) Special Issue commemorating Albert Einstein Starting from a very general quantum field theory we seek to derive Poincare...

The "hole argument" and diffeomorphism invariance First, let me give a summary of my understanding of the "hole argument": Consider a space-time completely filled with matter with exception of a finite space-time volume that contains no matter (a hole). The hole is located between two spatial...

Gents, Is it possible to have the not singular chiral current (singularity is due to the product of fermionic operators) and at the same time the translational invariance. Normaly to get rid of singularity in chiral current one is useing the point splitting regularisation (little shift of...

Recently a question asked by sparsh stimulated my gray matter regarding the invariance of lengths in galilean relativistic classical mechanics. First I state the question. A man X is sitting at the rear end of a long compartment of a train running at constant horizontal velocity with respect...

Hi, I'm hoping someone can give a little guidance, my taks is to prove that the Lagrangian equations are invariant under a change of coordinates. So what I've done is said if we have a set of coordinates say \left{ q_{i} \right\} , i = 1, \ldots ,N where I'll assume this first set is...

Hi, I was wondering if there was a way to prove the invariance of the space-time interval just from postulating a constant speed of light and an isotropic space-time. Most arguments go "from the Lorentz transformations it can be seen that the interval is invariant." Can we show the...

Right or wrong? Specifically, an equation is said to be Galilean invariant if a substitution x \rightarrow x \pm v_x t y \rightarrow y \pm v_y t z \rightarrow z \pm v_z t t \rightarrow t doesn't change the equation. If right, would simply showing that x \rightarrow x \pm vt y...

Is someone able to proove the invariance under Galilean transformations of F=dp/dt within a system of variable mass? In particular is the momentum invariant? i.e. p=p', as Goldstein states? Please answer me! :wink:

Just need a couple of things confirmed for me guys. Firstly, lines of invariance are always real eigenvectors right? Secondly, how is this line of invariance related to rotational matrices? My line of invariance happens to be the same axis. Finally, how is the angle of the rotation...

Maybe this is really easy, but... Can someone show me how the sign reversal between the space and time components of Minkowski spacetime make its intervals Lorentz invariant (mathematical derivation) ? Thanks... :wink:

Hi, I know I'm probably going to get shot down in flames. I'm a total amateur to all of this. But I do try to read things and I do try to understand them - so I hope you guys will at least be patient with me. But in any case I have been reading around about Noether's theorem and about the...

http://arxiv.org/abs/hep-th/0507020 Title: Charge Conjugation Invariance of the Vacuum and the Cosmological Constant Problem Authors: J. W. Moffat Comments: 14 pages, Latex file, No figures We propose a method of field quantization which uses an indefinite metric in a Hilbert space of...

For a positive natural number n, we use |n|= \log_{2}n as the measure of the size of n (which is the number of bits in n's binary representation). however, in most cases the size of n can be written as log n without giving an explicit base (the omitting case is the natural base e). Show...

Clauset and Young, in their new paper http://www.arxiv.org/PS_cache/physics/pdf/0502/0502014.pdf , apply standard modern statistics to a database of terrorist strikes ordered by the number of people killed or injured. They find that extreme cases, such as 9/11, are not outliers, but find their...

In non-relativistic QM when one transforms to a different frame the wavefunction is also transformed: (1) \psi ' = \psi e^{-\frac{imvx}{\hbar}-\frac{imv^{2}t}{2\hbar}} This looks a hell of a lot like: (2) \psi ' = \psi e^{-i\frac{<p>x+<E>t}{\hbar} where <p> and <E> are obviously...

Hi All, I'm new to this forum. I'm a third-year undergrad Physics Major in Australia, about to go on to Honours, very exciting project in Helium atom detection. To the point. My 3rd year Special Rel project is an investigation of the development of relativistic QM (RQM). I have to...

I know what a diffeomorphism is. But what is diffeomorphism invariance? And why is it important in physics? Thanks.

This principle is needed for a theory on the quantization of spacetime at the infinitesimal region. The properties of this principle are: 1. Top-right-front 2. Top-left-front 3. Top-right-back 4. Top-left-back 5. Down-right-front 6. Down-left-front 7. Down-right-back 8. Down-left-back...

Does anyone know where I can find a mathematical proof that the norm of any four-vector is Lorentz invaraint?

The following is a thought experiment devised by David Chalmers which suggests that the physical constitution of a conscious system doesn't have any bearing on that system's state of consciousness. Rather, Chalmers argues that the only relevant properties of a system in determining its state of...

The more I read about group theory and SU(3), the stronger is my suspicion that they are very similar to the principle of directional invariance, which is based on the ideas of describing a dynamic one-dimensional cube and its eight properties. Maybe I am wrong and too engross in my own ideas...

In trying to get my head round GR and quantum gravity, I'm puzzled about the following questions: Is the gauge group for gravity defined as the group of all possible Weyl tensors on a general 4D Riemann manifold? How is this group defined in matrix algebra? Is it a subgroup of GL(4). How do...