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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Lorentz transformations: Which coordinate system is marked?

I am confused about a basic special relativity question. So we have the Lorentz transformations $$\begin{align} x' &= \gamma(x-ut) \\ t' &= \gamma(t-ux/c^2)\ , \end{align}$$ where frame $S'$ ...
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2answers
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Why photon only have helicity other than spin? [duplicate]

When learning angular momentum in quantum mechanics, a spin 1 particle have 3 states. Then I saw from sakurai's modern quantum mechanics that photon's two polarization are just like spins, but with ...
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3answers
124 views

Time slowed by gravity

If time moves more slowly on Earth (due to our proximity to a gravitational body) than for someone orbiting Earth in a spaceship, yet the opposite occurs in the frequently cited "twin paradox" of the ...
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50 views

How much real and how much relative is our universe?

Apologies in advance if my question appears more philosophical than practical. It is indeed philosophy, but a philosophy relating to our scientific understanding of the universe as a whole. Special ...
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4answers
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Why is coordinate time frame dependent? [duplicate]

Here is what I understand by coordinate time. It is the time difference measured between two events, using two synchronized clocks, one present at each event, and the difference is measured in an ...
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1answer
70 views

Is there a mathematical reason that the Lagrangian is Lorentz invariant?

The Hamiltonian is directly related to the energy, which is just one component of a four-vector and therefore not Lorentz invariant. The Lagrangian is the Legendre transform of the Hamiltonian and I ...
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56 views

Can the Cosmos itself be assumed as a reference frame?

Einstein believed that there are no reference frame in the universe in accord to his Special Relativity (SR). Now imagine a man, as the first observer, and his cat, as the second, are both at rest in ...
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Vector spaces for the irreducible representations of the Lorentz Group

The definition of a representation is a map to the space of linear operators over a vector space. My question is: What are the corresponding vector spaces for the $(0,0)$ Representation ...
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2answers
93 views

Why does time slow down when traveling at high speeds [duplicate]

One of the effects of traveling at high speeds is slowing down of clocks. I can understand gravity time dilation effect but not how would velocity affect clock speeds. How correct it is, if I say ...
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Confusion about Length Contraction (ex in Muon decay)

I am a bit confused about the implications of length contractions; For example, in the muon decay problem, we assume that the distance between the muon and the earth is contracted only in the frame ...
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16 views

Is uncertainty in velocity via HUP reference frame dependent? [duplicate]

Simply put HUP involves position and momentum, further more consider a mass of 1kg. as momentum is mass X velocity = 1X velocity = velocity for calculation purposes. now for a stationary observer the ...
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39 views

Maxwell's Equations for Accelerated Conductors

I asked a question about accelerated conductors in a magnetic field but nobody unfortunately answered. That is: Ohm's Law for Accelerated Conductors Maybe, I could not state my question well. I ...
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2answers
59 views

If a photon is exists in 'timeless' state, how can objects around it move? [duplicate]

My understanding is that light does not experience time. In attempting to understand what the universe would be like from the perspective of a photon, the answer I get is that the universe would be ...
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86 views

Why scalar function of vector can only depend on norm of vector?

In Field Quantization by Greiner and Reinhardt as well as The Qunatum Theory of Fields by Weinberg, concerning the spectral function, the authors say a scalar function of the four-vector $p^\mu$ can ...
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1answer
124 views

Lever “paradox”?

Let's say we have a lever with two weights A and B with the same mass overlapping at the midpoint. Suppose they start to separate with each other at the speed of light simultaneously. From our point ...
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28 views

Extreme temperatures, relativity and kinetic theory

According to kinetic theory, average kinetic energy is proportional to temperature. Supposing $k_BT/2$ per particle, can we use relativity and kinetic theory to calculate, e.g., the temperature and ...
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0answers
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2 questions on 4-velocity

Firstly 4-velocity is defined by $u^\mu=\frac{dx^\mu}{d\tau}$ let us consider the component $x_i$ of $x^\mu$ then this derivative can be written as: ...
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$E=mc^2$ what is unique about the speed of light? [duplicate]

What unique property of light, makes it the conversion factor between energy and mass? It has to be more than a coincidence that the speed of light, just happens to be the correct number number to ...
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49 views

$E=mc^2$ is incomplete? [duplicate]

So I was going through youtube and I found out these: http://www.youtube.com/watch?v=mkiCPMjpysc http://www.youtube.com/watch?v=NnMIhxWRGNw Can anyone here explain to me (with derivation if ...
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39 views

Is time dilation a mechanical slowdown only? [duplicate]

I've recently read about the time dilation occurs at very high speeds. But I'm really wondering if it is just a mechanical slowdown of the clock only? What if we use clocks that does not use moving ...
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Does spinning actually decrease the time experienced by the spinner?

In this xkcd, Megan spins around to attempt to take momentum away from the Earth to slow its spinning. I was wondering, if Megan spinned around, wouldn't this cause her relative velocity to the rest ...
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2answers
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How to understand non-associative composition of velocities in STR?

In STR the composition of non parallel movements is in general non-associative. The formula is $\displaystyle\bar{u}\oplus\bar{v}= \frac{\bar{u}+\bar{v}_{\|}+\bar{v}_\bot/\gamma}{1+\bar u\cdot\bar ...
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Decoherence, collpse, and WHEN does the collapse occur?

The idea that decoherence stands behind the so-called collapse (reduction) of the wave-function doesn't seem satisfactory. Consider a quantum particle whose wave-function is of the form (1) ...
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“Reality” of length contraction in SR

I was in argument with someone who claims that length contraction is not "real" but only "apparent", that the measurement of a solid rod in its rest reference frame is the "real length" of the rod and ...
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1answer
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Twin paradox…what happens to the ship?

The earth bound twin looks up and sees his travelling twin moving slower inside his spaceship because he is whizzing by at some percent speed of light. But what does the motion of the ship itself ...
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Books on special and general relativity? [duplicate]

I have idea about all the theories related to space and time and stuff. But I wanna dig deep into it and understand all the theories like special and general relativity to begin with for now. Can ...
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1answer
75 views

Einsteins idea about solving the ether problem [duplicate]

I'm struggling a bit with my Special Relativity course. Most exercises are quite trivial and can be done without much effort, but when you really start to think and analyse why and how certain things ...
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Center of mass of two $\gamma$ rays moving in opposite directions

Suppose there are two $\gamma$ rays with frequencies $\nu_1$ and $\nu_2$ moving in opposite directions according to a reference frame $S$. I want to find the velocity of the center of mass of this ...
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Are virtual particles limited by the speed of light? [duplicate]

I have recently been reading about Quantum Electrodynamics which I found very interesting, but even more confusing. I understand photons mediate the electromagnetic force and interactions between ...
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1answer
50 views

Passage of time on a faster-than-light (FTL) vessel [closed]

Yes, this is already wild speculation. I'll retract this question if it isn't well received. As I understand, within an event horizon, spacetime gets rotated so that the singularity is in the future, ...
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Ohm's Law for Accelerated Conductors

My questions are about the Ohm's law for a moving conductor in a stationary magnetic field. As we know this law is stated based on following relation with respect to the fixed frame of reference ...
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What do physicists mean by “information”?

On the question why certain velocities (i.e. phase velocity) can be greater than the speed of light, people will say something like: since no matter or "information" is transferred, therefore the ...
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Recommendation for contra-variant and contra-variant vectors in the context of special relativity [duplicate]

I have just started studying covariant and contra-variant vectors in special relativity. I am finding difficulty understanding this topic. Can anyone recommend a book (with a detailed chapter) or ...
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156 views

How to theoretically define a concrete operation to perform in order to measure the length of an object?

EDIT: Some answerers pointed out that the title of this question is in contrast with what is actually been asked in the body of the question, so I changed the title accordingly. The original title was ...
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How, in practice, could instantaneous signalling violate causality?

I know that instantaneous signalling can result in different observers not agreeing on the order of events, but how can that result in causality violation in practice? In other words, if one had two ...
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If we traveled at almost light speed with a mirror in hand [duplicate]

What would we see if we hold the mirror in front of us and behind us.
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Bound electrons don't move, right?

I've never been satisfied with the explanation that electrons have a “speed” and move close to the speed of light, thus incurring relativistic effects that make gold pretty and mercury wet. I learned ...
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4answers
107 views

Twin paradox where the twins start at different locations

Suppose we have this scenario with twins A and B: 1) Instead of the twins starting at the same location, let's say the twins start out some distance apart, in the same reference frame. 2) The ...
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Applying Lorentz Transformations and Time Dilation

My question is based on a popular question, usually posed in introductory courses on the special theory of relativity. Two rockets are on a collision course. Rocket 1 is traveling at the speed ...
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Interferometers and Earth's motion relative to the Aether

Why was the Michelson and not the Fabry-Perot interferometer used to detect the motion of Earth relative to the Aether? Maybe the Fabry-Perot was used but we all know that the most famous experiment ...
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Question about dot product of four vectors?

I am looking back over some old notes and see that I have written $\bar{p}=\left(\overset{E}{\vec p}\right)$ and $\bar{x}=\left(\overset{t}{\vec x}\right)$ (using Plank units) And then $\bar{p} ...
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Does rotation increase mass?

If an object is rotated on its axis near the speed of light would its mass increase? Normally if the object was moving (in relationship to the Earth for example) I would agree that its mass would ...
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3answers
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Is it really possible to create some mass only from equivalent energy? [duplicate]

From Special theory of relativity we know that $E=m_0 c^2$, which says about mass energy equivalency. But my question : **Is there any real experiment where some mass is created purely from energy? ...
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$2\to3$ Phase space Integration

I have a $2\to3$ process ($P=p_1+p_2 \to p_3+p_4+p_5$) where all particles in the initial state and one of the particles in the final state ($p_3$) are massless. The other two ($p_4$ and $p_5$) have ...
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How to identify a “measuring rod”, and how to compare separated “measuring rods” with each other?

The notion of "measuring rod" has appeared in PSE here and there, and outside PSE as well. As far as I understand (and as perhaps all who refer to this notion do agree on), important constituents of ...
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Measuring speed of the moving train, if I'm inside it

So I am inside a coach in a train that is fully sealed (with no windows and a locked door). I have a torch, photo & time sensor and a scale with me. So, I place the sensor at one of the walls and ...
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2answers
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If the vacuum is not “emptiness” why the speed of the electromagnetic wave is independent of the frame of reference?

If the vacuum were "emptiness" it were easy to accept that there is no "preferred frame of coordinates" and the light velocity is the same in any inertial frame of coordinates. But the vacuum is an ...
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Is it possible to propagate a relativistic system of particles in time using Verlet?

The Verlet algorithm and its derivations are very popular methods to integrate Newton's equations of motion in time and obtain a trajectory for a system with $N$ particles. I work with classical ...
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Circumference of a circle in a co-rotating frame of reference

According to Einstein it should be greater than $2 \pi R$ for a co-rotating observer, i.e. $L' = \gamma L$ where $L = 2 \pi R$ in a non-rotating frame and $\gamma$ is the usual Lorentz factor, which ...
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How does the Lorentz transformation $\Lambda^{\mu}{}_{\nu}$ transform?

For example the Four-velocity transforms as $$U^{a'}=\Lambda^{a'}{}_{\nu}U^{\nu},$$ the Faradaytensor as $$F^{a'b'}=\Lambda_{\,\,\mu}^{a'}\Lambda_{\,\,\nu}^{b'}F^{\mu\nu}$$ or in Matrixnotation: ...