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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Plane waves in special relativity

I don't understand how there can be plane waves that by definition are spread through all of space if nothing can travel faster than light. Wouldn't every wave have to spread over time with at most ...
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80 views

As electron is accelerated nearly to the speed of light what would occur? [on hold]

What would occur if an electron at rest was accelerated nearly to the speed of light? Would the photons emitted by the electron approach a gamma wave photon as it approached the speed of light, or ...
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Parenthetical tensor notation

Just out of curiosity, what does it mean to be a type $(n,m)$ tensor? For instance in the context of special and general relativity, the Minkowski metric $\eta$ is considered a type $(0,2)$ tensor. I ...
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Bell inequality violations evidence for 1935 EPR claims?

Is it possible that Bell inequality tests provide experimental evidence in support for the EPR claims in their 1935 paper titled "Can Quantum-Mechanical Description of Physical Reality Be Considered ...
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1answer
45 views

Time dilation of a body A with respect to B [duplicate]

Let there be two bodies a and b. Let a be on Earth and b in space with velocity $(√3/2)c$. Then let the time interval which has passed (on the earth) be twice that of the time interval of which passed ...
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1answer
104 views

Does the factor $k$ in Hooke's law change in special relativity? [on hold]

let's say an object is tied to a spring and it's oscillating. But this system is moving in 0.5c. Then, the period of this oscillation increases. But the problem is $k$. I think the $k$ increases ...
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Constancy of the speed of light in the hypotenuse of the triangle in the Michelson and Morley experiment [on hold]

In Michelson and Morley experiment, Michelson calculated that the total time traveled by light with respect to the stationary observer standing at ether field was $2L/c$. Here, Michelson followed ...
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$(1/2, 0)$ representation of the Lorentz Group $SO(1,3)$

Let us consider the $(j, j') = \left(\frac{1}{2}, 0\right)$ representation of $SO(1, 3)\cong SU(2) \otimes SU(2)$. $j = \frac{1}{2}$ corresponds to $SU(2)$ generated by $$ \tag{1} N_i^+ = \frac{1}{...
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trouble reconciling doppler shift for energy and momentum of light

[See late addition at bottom for what currently remains unresolved in this question.] I have seen the assertion in a couple of places that if you trap light in a reflective resonator, or any other ...
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1answer
57 views

Can we work out how fast we are traveling by looking at our mass?

If we (the galaxy) were traveling close to the speed of light; relativity says we would need proportionally more energy to go faster. Given that relative to the cosmic microwave background, the Local ...
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1answer
59 views

Is there energy output when mass moves between two spacetimes [on hold]

Is there energy output when mass $m$ moves between two spacetimes? Say, it starts in a flat spacetime and then falls into a black hole (other examples don't come to mind, but this doesn't mean they ...
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The “Other” mechanical clock appears to click slower from both observers point of view. How? [duplicate]

In professor Shankar's Yale University lecture Lorentz transformation video, https://www.youtube.com/watch?v=202fU9qIVK4 , at the time period between 49:00 to 53:00, he describes light clocks and how ...
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5answers
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Why Sun light can reach us if Time is dilating?

I understand that if something is moving with constant speed in respect to an observer, the time of the moving one runs slower, so the more your speed is, the more your time ticks slower. Which ...
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2answers
244 views

Performing Wick Rotation to get Euclidean action of scalar field

I'm working with the signature $(+,-,-,-)$ and with a Minkowski space-stime Lagrangian $$ \mathcal{L}_M = \Psi^\dagger\left(i\partial_0 + \frac{\nabla^2}{2m}\right)\Psi $$ The Minkowski action is $$ ...
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Relativistic Doppler effect derivation

This is about a step in a derivation of the expression for the relativistic Doppler effect. Consider a source receding from an observer at a velocity $v$ along the line joining the two. Light is ...
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2answers
283 views

Lorentz-invariance of step function

I was reading about the Lorentz invariant integration measure $\int \frac{d^3k}{2E_K}$, and ways to prove that this was Lorentz invariant. Many of the proofs I have read use the step function (or ...
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1answer
79 views

Why does the Klein-Gordon propagator $D(x)$ depend on the sign of $x^0$?

In A. Zee's Quantum filed theory in a nutshell, it says the Klein-Gordon propagator depend on the sign of $x^0$. Here $x=(x^0,x^1,x^2,x^3)$. $$D(x)=-i\int \frac{d^3k}{(2\pi)^32\omega_k}[e^{-i(\...
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Watching a live stream in spaceship traveling away from earth close to speed of light

My name is Dennis. This might sound just straight up ignorant of basic concepts of physics. I was having a conversation with my friend in regards to streaming a live event on earth to a spaceship ...
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97 views

What is the velocity of the photon through the fourth dimension x4? [on hold]

Photons are real, physical objects. The fourth dimension is a real, physical entity. Therefore, photons must have a relationship with the fourth dimension. They must have some velocity relative to ...
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Question on the Derivation of Lorentz Invariance of Electric Charge

On Zwiebach's "A First Course in String Theory" textbook, there is a problem 8.2 that derives the invariance of electric charge given a few assumptions: 1. Conservation of Maxwell 4-current $j = (c\...
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Does Special Relativity require a “ruler postulate” analogous to the “clock postulate”?

It's fairly well known that the clock postulate is needed in Special Relativity when dealing with accelerated clocks, so does something analogous exist when dealing with accelerated spatial ...
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1answer
326 views

In QFT, why do fermions have to anticommute in order to insure causality?

I have seen this question and I believe I understand the answer to it. However, AFAIK, only for bosons the causality condition is a vanishing commutator. For fermions we expect the anticommutator $[\...
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How do clocks in inertial frames speed up from the point of view of accelerating observers, like in the twin paradox thought experiment? [closed]

At the end of a twin's space voyage just as he starts decelerating, I know that the traveling twin sees his brother's clock on Earth speed up, which makes sense...EXCEPT that conclusion elicits the ...
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3answers
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If something is not moving in space, is it moving on the time axis at the speed of light? [duplicate]

I heard this theory yesterday: If something is not moving in space, then it is moving on the time axis at the speed of light. I realize that in essence there is no object which can be considered as "...
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4answers
8k views

Does inertia increase with speed? [duplicate]

I have heard that when the speed of the object increase, the mass of the object also increase. (Why does an object with higher speed gain more (relativistic) mass?) So inertia which is related to ...
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A rocket is receding from the earth at [closed]

A rocket is receding from the Earth at speed of $0.2 c$ where $c$ is velocity of light. It emits signals of frequency $4 \times 10^7 $Hz. The apparent frequency observed by an observer on earth is
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1answer
2k views

Does the increase of (relativistic) mass, while flying near speed of light, has any impact on astronauts? [duplicate]

Possible Duplicate: Would travelling at relativistic speeds have any impact on human biology? I am asking myself this question for a few days. What is the correct answer on: Does the increase ...
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2answers
155 views

Have scientists ever experimentally proved the Andromeda paradox-like events? [closed]

We all know that a light year is of the order of 1016 metres and all the objects in the space are beyond a light year. So the Andromeda paradox should give considerable difference in time while ...
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4answers
961 views

Energy-Momentum Tensor under Lorentz Transformation

In relativity, the symmetric energy-momentum tensor is given by $$ T^{ij}, $$ where $T^{00}$ is the energy density and $\frac{1}{c}T^{10}$ is the momentum density. Thus: $$ \left(\frac{1}{c}T^{00}dV, ...
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Is the light in a Lorentzclock going slower when you travel with it with 0.9c? [closed]

In a Lorentzclock the light is bounced between the two mirrors with his speed of appr. 300.000km/s. Now when things speed up their time goes slower. But the light is always c, so in the Lorentsclock ...
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Rotation matrix for aligning x-axis in an arbitrary direction

I want to align the x-axis of my coordinate system, with an arbitrary direction in space $\hat{n}$. About which axis should I rotate? Ceratinty rotation about x-axis or $\hat{n}$-axis will not serve ...
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2answers
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Wouldn't a photon disappear because of length contraction? [duplicate]

I was experimenting with the formula for length contraction, when I realized that anything traveling at the speed of light shrinks out of existence. This is the formula for length contraction: $$T=T'\...
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2answers
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Space-Time Geometry that shortens time intervals?

So we've all heard of the concept of time dilation and length contraction (from both general and special relativity). Suppose we work with a metric of a black hole, and person A is far, far away and ...
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Is there a limit in angular speed in special relativity? [duplicate]

I was thinking in the following problem: Suppose I have a bar of lenght $l$. If I spin it with constant angular velocity $\omega$, according to the special theory of relativity, is there a limit ...
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Why moving charges cause magnetic field (module and direction)?

Why an constant electric current in a wire produces a magnetic field, that circles that wire? I know that this question was posted before. However, all answers talk about Maxwell equations, axioms, ...
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59 views

Synchronization of clocks using material waves

I am not a physicist by training, but I have studied special relativity enough to understand why simultaneity is a relative concept, and so why if you synchronize clocks in one inertial frame, an ...
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1answer
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Is it possible to introduce 4-velocity very early on?

I was wondering if it would be possible to teach new physics students about 4-velocity straight away at the beginning of their studies. Keeping the regular notion of the three dimensional velocity $\...
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2answers
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Presentism: doesn't everything exist at the same moment? [closed]

The Help Center recommends I 'fix' this question: (original question) "It seems self-evident that everything exist in the Now. Notwithstanding time-dilation and different rates of the passage of ...
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1answer
78 views

Inference of relativistic time dilation wrong?

One popular example of relativistic time dilation uses the idea of a Light clock where time is measured in terms of cycles the light between the two mirrors (which are at distance L from each other) ...
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1answer
120 views

Relativistic action is negative or positive number? [duplicate]

Possible Duplicate: Why lagrangian is negative number? In the special relativistic action for a massive point particle, $$\int_{t_i}^{t_f}\mathcal {L}dt,$$ where the Lagrangian $$\mathcal {L}...
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Does the speed of light in vacuum define the universal speed limit?

Is light the thing causing the universal speed limit to be $299\,792\,458\,\mathrm{m/s}$? So the universal speed limit would be different if light travelled faster or slower? Or, is $299\,792\,458\,\...
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70 views

In a moving light clock, does the velocity of the clock add to the velocity of the light?

Currently going through the class Space, Time and Einstein from worldscienceu. On module Time in Motion an example is given of 2 light clocks, one moving and one stationary. The point is made that ...
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635 views

Does a interstellar spacecraft traveling at relativistic velocity require continous thrust to maintain velocity?

Assuming completely empty space, does a spacecraft traveling at 0.5 C require continuous thrust to avoid deceleration? If the spacecraft is traveling at 0.5 C, does it's relativistic mass act upon ...
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How long does it take to travel 36 light years with tolerable acceleration and deceleration?

The recent discovery of HD85512b only 36 light years from Earth has promising attributes to harbor life. Assuming we want to travel there, we cannot instantaneously jump to light speed, (StarTrek ...
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In relativity, perpendicular motion does not show contraction… Isn't the whole concept lost?

I read in HC Verma's Concept of Physics that a body moving in direction perpendicular to length, doesn't show Length Contraction. And Length Contraction, they said, is to maintain the velocity of ...
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1answer
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Can anyone clarify this example of Relativity of Simultaneity [closed]

While doing this course: http://www.worldscienceu.com/ I couldn't understand this example http://www.youtube.com/watch?v=53oAxycVhhg. (full example here https://www.youtube.com/watch?v=Iiugtmt18W4) ...
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2answers
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Expanding Universe [closed]

So an expanding universe has the metric $$ds^2 = g_{\mu \nu} dx^\mu dx^\nu = -dt^2 + a(t) ( dr^2+r^2 d\Omega^2)$$ where $d\Omega^2 = d\theta^2 + \sin^2\theta d\varphi^2$ as the usual spherical ...
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Can sound waves be used as simple explanation of relativity effects in STR?

There are so many similarities (Doppler Effect, independence of wave velocity from source speed etc..). Try moving in your car with music and ask you friend outside record it while you moving towards ...
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Why under Lorentz transformations the Higgs boson is a scalar field and under $SU(2)$ it is a doublet?

I am a bit confused about this difference. My understanding is that when we build a $G$-bundle, where $G$ is a gauge group, we have a representation $\rho:G\to GL(V)$ that acts on the fibers of the $G$...
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108 views

Conservation of linear momentum (classical mechanics and special relativity)

How did Newton deduce the law of conservation of linear momentum? Can it be derived only by Newton's laws, or does it follow from practical experiments? If the law of conservation of linear momentum ...