# Tagged Questions

The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.

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### What do things move relative to?

When someone says that a spacecraft in otherwise empty space is traveling at a constant velocity of 10 km/h (for the sake of convenience) then what is the reference point for which this measurement ...
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### How can I tell that a Lagrangian has an $SU(2)\times SU(2)$ symmetry?

this is a very basic question and it probably has a very simple answer. I was reading through some handouts when I came over something that I did not understand. One considered the simple Lagrangian ...
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### What is the matrix representation of the momentum operator (generator of translations) that is used in the commutators of the Poincaré Group?

So the commutators of the Poincareé group are given by \begin{eqnarray} [J_{i},P_{j}]=i\epsilon_{ijk}P_{k}, \quad [J_{i},J_{j}]=i\epsilon_{ijk}J_{k}, \quad [J_{i},K_{j}]=i\epsilon_{ijk}K_{k}, \quad [...
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### Construction of vector bundles of relativistic fields by Mackey's method of induced representation

I recently stumbled on Sternberg's book on group theory and physics. The ideas expressed in the book are really great, but the detailed reasoning is very hard to follow, I find. I am kind of stuck ...
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### Rotating rod viewed in standard frames S and S' [on hold]

I am doing a problem in relativity book by Rindler and for one question I do not have the answer. It states that in the rest frame a rod centred on the origin rotates uniformly (frame S'). What will ...
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### Does the use of $\gamma=\left(1-v^{2}/c^{2}\right)^{-1/2}$ automatically assume a (+ - - - ) metric? [on hold]

In Special Relativity, does the use of $\gamma=\left(1-v^{2}/c^{2}\right)^{-1/2}$ automatically assume a (+ - - - ) metric convention? For introductory textbooks, the Lorentz factor is is always ...
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### Why does time dilation cause you to age slower? And is time considered relative to the observer?

I understand that the higher your velocity the slower light will move. But how does time itself slow down while you are moving faster?
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### If the four velocity of a photon is undefined, what can we say about the velocity of a photon? Is Brian Greene right about motion through spacetime? [on hold]

Edit: THIS QUESTION IS ASKING ABOUT THE FOUR VELOCITY OF A PHOTON. THE PREVIOUS QUESTION DOES NOT. PLEASE ANSWER THIS QUESTION, WHICH HAS NOT BEEN ASKED. If the four velocity of a photon is ...
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### Do electronic energy levels of an atom effectively shift for scattering processes if the atom is moving in the lab frame?

When an electron of low energy scatters off an atom it interacts with one of the electrons in its shell and can transfer energy to it. The energy transfers would be discrete, since the shell electron ...
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### One particle states in an interacting theory

Question: What is the general definition of one particle states $|\vec p\rangle$ in an interacting QFT? By general I mean non-perturbative and non-asymptotic. Context. 1) For example, in Weigand'...
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### Why can't massless particle exceed speed of light?

Why massless particle can't exceed speed of light?
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### If a photon has no mass why doesn't it have infinite speed? [duplicate]

Please help a naïve layperson understand -- if a photon has no mass, why is its velocity limited at all? Shouldn't a particle with no mass be able to travel at an infinite speed?
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### Lorentz Transformations in Minkowski space

If $\Lambda$ represents the Lorentz transformation matrix, then the transformation of contravariant components $x^\mu$ is given by $$x'^\mu=\Lambda^{\mu}{}_{\nu} x^\nu$$ and that of the covariant ...
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### Hidden momentum

I'm trying to learn about hidden momentum. After reading what I could find with a google search, I understand that it is equal to the momentum carried by radiation, calculated with the Poynting vector....
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### Deriving invariance of interval

I'm reading a book called A First Course In General Relativity, and when I got to the invariance of the interval, the book didn't derive it. Also, when the book derived time dilation and Lorentz ...
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### Special relativity paradox and gravitation/acceleration equivalence

One of the features of the black hole complementarity is the following : According to an external observer, the infinite time dilation at the horizon itself makes it appear as if it takes an ...
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### Twin paradox without gravity [on hold]

Suppose we have 3 people Person1 was already born on a spaceship that travels in the speed of 0.5c toward person2 Person2 was born in a point in point in the space also in the exact time of person1 ...
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### Is mass relative? [duplicate]

This question has to do with the relativistic mass of an object. I have been reading that as energy increases, so does mass to a much lesser extent, and that this applies to kinetic energy as well. ...
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### Lorentz transformation: Can distance between two observers depend on the observers? [on hold]

Consider reference frames S and S'. S' is moving in positive x direction at speed v relative to S. Time measured by S is t and that measured by S' is t'. When t = 0, then t'= 0. Coordinate systems ...
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### Proof of two Lorentz-algebra identities

I am currently working through the QFT introduction text by Peskin and Schroeder and try to fill in two identities that I wasn't able to prove (it should be fairly simple, but my experience with this ...
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### What is the irreducible decomposition of the tensor product of left and right weyl spinor representations, i.e. $(1/2,0)⊗(0,1/2)$?

What is the irreducible decomposition of the tensor product of left and right weyl spinor representations of the group $SL(2,\mathbb{C})$, i.e. $(1/2,0)⊗(0,1/2)$? I mean, the tensor product of two ...
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### Length contraction in special relativity: can space be at rest in any frame?

Suppose a rod is moving at speed $v$ relative to me along its length. $L_0 = {}$length of the rod in the frame in which the rod is at rest $L = {}$length of the rod in my frame Then L = L_0 \sqrt{1-...
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### Special Relativity Problem: What's wrong here? [on hold]

Two 1 kg blocks float in space. After an explosion, they move left and right at 0.6 c. Consider their momentum relative to a frame of reference moving a 0.6 c to the right relative to their center of ...
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### What is the geometric explanation for why the interior angles of a triangle sum to 180 degrees in both Euclidean space and Minkowski spacetime?

Four-dimensional Euclidean space has the same topology and affine structure as Minkowski spacetime, though the two have different metric structures. Given that the interior angles of a triangle ...
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### Speed of light and relativity [duplicate]

Suppose there are two observers $A$ & $B$ both are in motion, now $A$ sees $B$ is moving with speed $'u'$. A says that another object $'d'$ is moving with speed $c+u$ w.r.t. A in the same ...
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### Reflection At Speed of Light

I have looked online to no avail. There is two competing answers and I am curious to know which one is right. Someone asked me this question. If you are traveling at the speed of light can you see ...
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### Why must $v$ be $< c$ in the Lorentz transformations? Do these equations not apply to light? [duplicate]

I was trying to understand how things look from the perspective of light. Looking at the Lorentz transformations, it seems that the universe would contract along the direction of movement into a plane,...
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### A puzzler in induction and special relativity

Some reading I was doing jogged my memory about a puzzle in E&M that hit me back in my undergrad days, but I just let it go at the time and never found an answer. A pretty common undergrad E&...
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### Can orbiting a black hole 99.99% speed of light make other object with relatively fast clock travel faster than light, relative to me?

If i orbit a black hole, 99.9% speed of light, time for me is moving slowly, relative to me, planet earth is aging fast, and i have traveled 10 years into the future(relatively) in 1 second, suppose ...
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### Imagine I'm on a spacecraft that was accelerated to 1.0$c$ could I only move backwards? [duplicate]

Imagine I'm in a sapcecraft1 that is moving with 1.0$c$ or at least is so close to that speed that a few miles per hour would just be left to reach $c$. So when I'm traveling now in the direction ...
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### What exactly were the “asymmetries which do not appear to be inherent in the phenomena” in Einstein's 1905 SR paper?

The first ¶ of Einstein's "On the Electrodynamics of Moving Bodies" says (my emphases): It is known that Maxwell's electrodynamics—as usually understood at the present time—when applied to moving ...
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### What is problematic about the Moving magnet and conductor problem?

The problem is posed as follows: There is a conductor and a magnet in relative motion. This motion induces emf in the conductor. The value of the induced emf is independent of whether it's the ...