Invariance Definition and 454 Threads

Does anyone know of any website that has animations of what this Diffeomorphism Invariance in General Relativity can do? I read a lot of articles about it but can't seem to get the essence or visualize how it actually occurs exactly. Thanks.

Is it possible that Lorentz invariance is just a lower limit of a larger manifold that has a priveleged frame? Even if Bell's experiments can't transmit signal faster than light. The spirit of relativity is still violated by say instantaneous correlation between 10 billion light years. As...

Hi everybody, i have a question concerning potential energy (in all its forms, which basically means all forms of energy except the kinetic one). The kinetic energy of a system is always well defined: in the rest frame it is m² (convention c=1), in a frame moving at a relative speed v compared...

Hello! Hopefully somebody could give me a push from behind on this one :) Homework Statement Show that the classical wave equation is lorentz invariant. The Attempt at a Solution I tried to exchange all derivatives by the chain rule: (c^2 \frac{d^2 }{dt^2} + \frac{d^2 }{dx^2} + \frac{d^2...

Hi, Assume the following action: \int d^4 x L[\phi,A]+ \int d^4 x A_{\mu} (x) J^{\mu}(x) What are the conditions on the form of action to have space/time translational invariance for a two point function: \left\langle J_{\mu}(x) J_{\nu}(y) \right\rangle = G_{\mu \nu}(x-y)...

Is it proved that the bosonic string and superstring partition functions are modular-invariant for arbitrarily high loop order? If not, how many loops have been analyzed?

Hello, I don't understand two steps in solution to the problem: I. Homework Statement Show that QED action is invariant under gauge transformation. II. Relevant equations QED action: S= \int{d^{4} x \left[\overline{\Psi}\left(i\gamma^{\mu} D_{\mu} -m \right)\Psi...

How is Lorentz invariance handled in GR? I know that there is no global Lorentz invariance in GR, instead it only holds locally, meaning that it is obeyed in the limit at infinity:when r goes to infinity by considering infinite distance or infinitely small point mathematical objects. But when...

We know basic classical mechanics is time-reversal invariant while there is a concept of irreversibility in thermodynamics. Is there a simple (by which I mean undergrad level and more preferably lower undergrad level) explanation for this apparent paradox? Someone please either explain this or...

Yesterday there was a thread here on a claimed violation of Lorentz invariance, but I can't locate it today. Was the thread moved? Can someone point me to its new location? (I don't remember the exact title of the thread, but the posts referred to a letter in the Sep 2010 issue of European...

In section 1.2 of Taylor and Wheeler's Spacetime Physics, a rocket moves past a laboratory (on Earth). Attached to the rocket is a pin. From that pin a spark is emitted at two locations in the lab, separated by 2 meters. The observer in the rocket measures the elapsed time between the sparks, as...

I have been trying to teach myself Lagrangian mechanics from a textbook “Lagrangian and Hamiltonian Mechanics” by MC Calkin. It has covered virtual displacements, generalised coordinates, d’Alembert’s principle, the definition of the Lagrangian, the Euler-Lagrange differential equation and how...

First of all, let me remind about an older thread on this topic: https://www.physicsforums.com/showthread.php?t=330517 Here I'd like to thank again to everybody, who participated in that discussion. However, I still find myself at a deadlock with some questions about Gauge Invariance (GI)...

Covariance and Invariance We consider the equation: {\frac {{d}^{2} {x^{\alpha}}}{{d }{{\tau}^{2}}}}{=}{-}{{\Gamma}^{\alpha}}_{\beta\gamma}{\frac{{d}{x^{\beta}}}{{d}{\tau}}}{\frac{{d}{x^{\gamma}}}{{d}{\tau}}} The covariant form is preserved in all coordinate systems. But the Christoffel...

Hi I am confused about these two related but different terms Lorentz invariance/covariance and General invariance/covariance As I understand it a Lorentz invariant is a scalar which is the same in all inertial reference frames i.e. it acts trivially under a Lorentz transformation an example...

Short intro.: I'm a 2nd year M.Sc. student in particle physics, with basic quantum field theory and knowledge of the SM and perhaps a bit more. I've read the forums before and tried to find questions/answers that were similar to my own until I decided, "why not just join so I can ask exactly...

Homework Statement For each of the following systems, determine whether or not the system is linear, time-invariant, and causal. a) y[n] = x[n]cos(0.2*PI*n) b) y[n] = x[n] - x[n-1] c) y[n] = |x[n]| d) y[n] = Ax[n] + B, where A & B are constants. Homework Equations The Attempt...

hi, is it correct to say that any particle or object that is invariant under rotation of 2 pi is a boson, whereas fermions need 4 pi? what is the accurate statement about this? thank you for your reply

The invariance of Lagrange's equations with a given "time" Homework Statement What is the change in the Lagrangian in order that the Lagrangian equations of motion retain their form under the transformation to new coordinates and "time" give by: q = q(Q, \tau) t = t(Q, \tau)Homework Equations...

Hallo I'm new to this (wonderful) forum, and to SR too... I've a general question about the space time interval invariance. Say we have two points A and B, at rest each other, at distance AB. Now A and B simultaneously in their reference frame emit a flash of light. The space time interval...

If one observer in an inertial reference measures a collision to be elastic, then all observers in an inertial reference frame will measure the collision to be elastic - can this be explained with the conservation of energy? What exactly does the conservation of energy principle say in regards...

Homework Statement Hi everyone, in Peskin & Schroeder, P36, the derivative part of KG field is transformed as eqn (3.3). But why does the partial derivative itself not transform? Homework Equations \partial_{\mu} \phi (x) \rightarrow \partial_{\mu} ( \phi ( \Lambda^{-1} x) ) = (...

I've read that GR is diffeomorphism invariant, I asked a math buddy of mine and I have a VERY BASIC idea of what that means in this case - the theory is the same regardless of your choice of coordinates? Noether's theorem states that for every symmetry there's a corresponding conservation...

This is related to the thread on the meaning of diffeomorphism invariance but is adressing a distinct point (at least I think so, but I may be proven wrong). As Rovelli discusses in his book, the action of the Standard Model coupled to gravity has three types of invariance: under the gauge...

I am trying to establish whether the force defined by the Lorentz equation below is invariant under the Lorentz transforms: [1] F = F_E + F_B = qE + qvB In the context of this equation, [q] is moving with velocity [v] such that it is acted on by both an electric E-force and magnetic...

I am posting my question in this forum because it is about a basic conceptual aspect of LQG discussed in Rovelli's book Quantum Gravity. He makes the following statement on page 67 (here, "e" refers to the vierbein): I do not understand the part in boldface. First, he means that the...

Hi, I have been taking a classical electrodynamics course, in which we established the classical well-known larmor formula for the radiation of a classically accelerated point charge in vacuum. Then, since the radiated power is a Lorentz invariant, we just assumed that the correct...

Hello! Quite some time ago I'd asked for help with a proof that proves that area of a closed curve is invariant i.e : its independent of the way it is spliced into. Say we splice a closed curve into one set of rectangles with parallel sides and we then splice an identical curve with...

In electrodynamics, the Coulomb gauge is specified by \nabla \cdot A=0 , i.e., the 3-divergence of the 3-vector potential is zero. This condition is not Lorentz invariant, so my first question is how can something that is not Lorentz invariant be allowed in the laws of physics? My second...

I've tried proving the invariance of the spacetime interval from Lorentz transformations 3 times now, but every time I end up with two extra terms that don't cancel! Could I have some help?

Having some generic curved spacetime, what are the Noether currents that are guaranteed to exist by diffeomorphism invariance? Is the energy-momentum tensor such a current?

My friend is moving in my inertial frame and receives light in the two directions parallel to her movement: from behind and from ahead. The photons that reach her travel at c in my frame, so I presume they will approach my friend at different speeds (as I view it): faster from ahead and slower...

I'm trying to show that \frac{d}{dt}\; g_{\mu \nu} u^{\mu} v^{\nu} = 0 in the context of parallel transport (or maybe not zero), and I'm rather insecure about the procedure. This is akin to problem 3.14 in Hobson's et al. book (General Relativity an introduction for physicists). As a guess, I...

After the first explanation of superconductivity by Bardeen, Cooper and Schrieffer, it was for several years a matter of concern to render the theory charge conserving and gauge invariant. I have been reading the article by Y. Nambu, Phys. Rev. Vol. 117, p. 648 (1960) who uses Ward identities to...

Hi; I am pretty sure that sqrt(-g) is diffeomorphism-invariant. I am wondering if all powers of this are diffeo-invariant too. For example, are -g, g^2, etc. all invariants too?

I am trying to learn tensor calculus, but I must be confused about tensor invariance. I know the definition of a tensor is a number or function that transforms according to certain rules under a change of coordinates. The transformation leaves the number or function invariant if it is a...

Hey, I've come across a part in my notes which I can't figure out. Essentially it says: \frac{\partial^{2}y}{\partial t^{2}} = v^{2} . \frac{\partial^{2}y}{\partial x^{2}} is space and time invariant. Whereas: \frac{\partial y}{\partial t} = -v . \frac{\partial y}{\partial x} is not...

Hi, In the derivation of scattering amplitudes (e.g. page 94 in http://kcl.ac.uk/content/1/c6/06/20/94/LecturesSM2010.pdf ) does anyone have a clue as to how to prove that the momentum uncertainty element (\delta p)^3/E is Lorentz invariant? I know how to do it for the measure d^3p/E...

The existence of entropy in gravity implies that there are microscopic degrees of freedom in space that carries the entropy. This implies space is discrete. Discrete space breaks lorentz invariance, which has been strongly constrained by both FERMI and thought experiments. String theory...

I'm trying to prove that the helicity operator \pmb{\sigma}\cdot\pmb{\hat{p}} is invariant under rotations. I found in Sakurai: Modern Quantum Mechanics page 166 that the Pauli matrices are invariant under rotations. Clearly that is sufficient for the helicity operator to be invariant under...

Homework Statement Explain which of the following quantities are invariant in Newtonian mechanics. Position Distance between two points Velocity Acceleration Momentum Kinetic Energy Potential Energy (I presume gravitational) Homework Equations N/A The Attempt at a Solution I understand...

Homework Statement So I was doing a problem out of Merzbacher 3rd edition (end of chapter 4 problem 3); the homework set has already been turned in but I wanted to run this by you all and see what you thought. I am essentially working with a particle in a 1-d ring constrained to the x-y plane...

If we start with minkowski spacetime in 4 dimensions and then add several curled up spatial dimensions attached at every spacetime point, then: I'll label a spacetime point as: (ct,x,y,z)[a1,a2,a3,..,an] where the bracketted coordinates are the 'curled' coordinates. - If we label the...

How do you prove x2-c2t2 is invariant under the lorentz transformations given that;

Hi, I have a question which to many may seem quite stupid but it honestly has been perplexing me for a while now. I'm actually not sure if this is the correct place to post this but the question does seem to be based on the theory of relativity so here goes. I think I'm correct in supposing...

Seasons greetings all, I am trying to dissect a really interesting article: http://www.nature.com.libproxy.ucl.ac.uk/nature/journal/v462/n7271/full/nature08574.html but I am struggling with some of the more technical terms in it. I have shown it to some lecturers at my uni and even they...

please anyone can help me how make check the linearity and shift invarient for the system I want to determine whether the system is linear and shift invarientby steps g(m,n) = f(m,-1) + f(m,0) + f(m,1) g(x) = (integration from +infinety to - infinety) f(x,z) dz please help me...

Hi, I've been reading Vic. Stenger's book "The comprehensible Cosmos" and have a question about the example he gives for Galilean invariance. In his example, Galileo drops a weight from the tower of Pisa and to a person standing near the tower (and thus in the same inertial? frame of the tower)...

The physics building is based on the invariance of the atom. Is there any principle or law or experiment ? I think that we only presume. What if there is no foundation for our 'truth' ?

Hi I have a simple question what is the conserved quantity corresponding to the symmetry of galilean invariance? and Lorentz invariance? cheers M