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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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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26 views

How does the idea of a scalar potential for a 3-vector field generalize to Minkowski space?

How does the idea of a scalar potential for a 3-vector field generalize to Minkowski space? As I guess, I thought one way would be to generalize 3-force to 4-force and replace the 3-gradient with the ...
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4answers
1k views

Which one to learn first: Special or general relativity? [closed]

I am extremely interested in self-learning Einstein's theory of relativity, but I don't know where to start. Can I make general relativity my starting point, and later look at special relativity as ...
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1answer
189 views

Time-reversed twin paradox

This started with wondering about the nature of certain physical quantities under time-reversal - chiefly, that acceleration retains its magnitude and direction at a given time regardless of the ...
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2answers
202 views

Difference between locality and causality?

I ask this question as the two seem to be very closely related and are sometimes taken to be one and the same (in the notion of microcausality in QFT), which has left me confused as to what meaning of ...
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2answers
104 views

Twin paradox caused by gravitational difference in space

I am not a physicist, but have always been curious about the twin paradox. So, here is my question. There are two twins in space - Twin A and Twin B (both stationary). They are apart from each other ...
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1answer
66 views

do relativistic velocities change the apparent entropy content of the moving object?

Imagine a box of hot gas. It has a certain (large) amount of entropy, which we can relate to the amount of information needed to completely specify the position and velocity of every gas particle in ...
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4answers
1k views

What is the speed of light relative to?

Consider the scenario where you measure the time it takes for light to travel to the left 10 meters and to the right 10 meters. Both measurements will take the same time, even though we are moving ...
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5answers
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Relativistic momentum

I have been trying to derive why relativistic momentum is defined as $p=\gamma mv$. I set up a collision between 2 same balls ($m_1 = m_2 = m$). Before the collision these two balls travel one ...
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1answer
76 views

Vector product in a 4-dimensional Minkowski spacetime

I'm studying relativity and I lost track of interpretation along the mathematical formalism. What does vector product mean as an event? I mean, how must one interpret the result of the vector product ...
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1answer
125 views

Proving the conservation of 4-momentum for a particle collision $A+B\to C+D$

Let me say that particle A hits particle B and two particles come out - C and D; In system S I can write: $$p_A^μ+p_B^μ=p_C^μ+p_D^μ;\tag{1}$$ here $p_N^μ$ is the 4-momentum. Using the Lorentz ...
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2answers
724 views

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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2answers
138 views

Universe without a fixed universal speed limit

What would a universe without a fixed universal speed limit (like $c$ in the actual universe) look like? Would it be paradoxical? Would time travel into the past become possible?
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1answer
25 views

Using relative velocity between two frames and the time elapsed between events in one frame to find the time elapsed/event separation in the other [closed]

Q from text: A second transporternaut is beamed to a much more remote galaxy that is moving away form Earth at .87c. This time, too, she stays in the remote galaxy for one year as measured by clocks ...
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1answer
209 views

Doppler shift for a uniformly accelerating observer

This was given in textbook as an example. An observer on a spaceship with a four velocity $u$ is approaching from $x = +\infty$ a star at rest in the reference frame $S$ while undergoing constant ...
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2answers
359 views

Does space between objects contract?

I had a question, let us assume a coordinate system where there is 2 objects moving at relativistic speeds (at same velocity) for the observer therefore the observer will observe the length ...
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2answers
113 views

Special relativity: where does this naive calculation go wrong?

Inspired by the recent question, "If all motion is relative, how does light have a finite speed?", I tried to work out a little calculation. Where does it go wrong? My friend Buzz is traveling in a ...
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3answers
72 views

How do I sum up speed though space and time to obtain c (in terms of units)?

I'm still learning SR and only recently I could scratch the surface of such beautiful, complex and deep topic. This post here was really enlightening, and even though it is somewhat basic, it helped ...
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2answers
38 views

Relative Velocity Problem: Light? [duplicate]

Assume 2 rockets coming towards each other at each other at 99% of speed of light, and so as they pass each other the relative velocity between 2 rockets would be 198% of Speed of Light and so what ...
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1answer
159 views

Two apparent contradictions in SR involving time dilation and length contraction

So I've encountered the site "Alternative Physics" – a website proposing "alternative" theories to theories in modern physics. Of course, the site claims that both SR and GR are wrong. To show "why" ...
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1answer
112 views

How can the 'choice' of a photon said to be delayed?

My question arises from two ideas that seem to be contradictory. Idea One: Wheeler's Delayed Choice experiment is an interesting variation of the double slit experiment. Idea Two: In the "reference ...
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1answer
120 views

Physical interpretation of distances

Suppose we have a universe with only two distinguishable particles, neglecting gravitation. These particles start off next to each-other, ostensibly "touching" each-other and at rest. If it takes ...
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2answers
301 views

Reunion condition in the Twin Paradox

In the Twin Paradox two twins initially at rest in the same reference frame are separated and take different journeys through spacetime. Eventually they are reunited. What is the condition for the ...
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0answers
56 views

Sum according to a function - composition of velocities

An observation more than a question. Take any function $f$ (additional hypotheses may follow) and evaluate it on any two points $x_1, x_2\in\mathcal{D}_f$. Define then the sum of these two points as ...
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2answers
222 views

Why do we consider Lagrangian densities in QFT?

My question is: Why do we consider Lagrangian densities in QFT (as opposed to Lagrangians as in classical mechanics)? Is it simply because of the following? We wish the theories to be Lorentz ...
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1answer
47 views

Exact meaning of locality and its implications on the formulation of a QFT

As far as I understand it, locality in physics is the statement that interactions can only occur between physical objects if the spacetime interval separating them is null or time-like. Thus, if the ...
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2answers
150 views

Commutation relations in QFT and the principle of locality

My question is, given two space-time points $x^{\mu}$ and $y^{\mu}$, if the events that occur at these points are simultaneous, i.e. $x^{0}=y^{0}$, are the two events necessarily space-like separated? ...
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1answer
168 views

Finding the total energy in centre of mass frame

I'm working through a problem in a special relativity textbook (Woodhouse) and I'm having some difficulty. I have to show that if I have a particle of rest mass $M$, total energy $E$ colliding with a ...
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3answers
109 views

The relation between mass and speed

Massless particles (or luxons) have no (rest) mass ($m = 0$) and a speed equal to the speed of light ($v = c$). Massive particles (or bradyons) have mass ($m > 0$) and a speed lower than the speed ...
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2answers
132 views

Simple Harmonic Motion in Special Relativity

I was trying to see what results I would get if I were to incorporate relativistic corrections into the case of a harmonic oscillator in one dimension. I thought that if the maximum velocity of the ...
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6answers
377 views

Detecting absolute motion inside a box

This is not a contradiction and I know it is impossible but still consider a thought experiment by me and point out if something is wrong. See the following picture and then the explanation follows. ...
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1answer
68 views

Is it possible for the light (photons) to turns into normal electromagnetic signal?

I want a theoretical opinion about this question: The relativistic Doppler Shift equation for the light is $$\frac{f_s}{f_o}=\sqrt{\frac{1+\beta}{1-\beta}}$$ where $\beta=v/c$ is the velocity of the ...
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2answers
111 views

Proof of conservation of energy with the relativistic definition of force

Professor Susskind proved conservation of energy in one of his lectures by taking the classical definition of force ($F = ma$) and by showing that its time derivative is zero. How can we do that with ...
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Proving the speed of light to be an invariant and the “ultimate” speed limit using Minkowski diagrams

Can one show that a certain speed, denoted $c$, is invariant and the ultimate speed limit in all reference frames using Minkowski diagrams? As we define $c = 1$, one can find the angle $\tan^{-1}(1) ...
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1answer
91 views

On the Lorentz Group representation [closed]

I am going through the notes on QFT by Srednicki (which is certainly a worth reading on the subject, and can be found online, see http://web.physics.ucsb.edu/~mark/qft.html). When describing ...
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60 views

Is it true that whenever any non rigid body moves, there must be a delay between the ends? [duplicate]

Very sorry if this is still considered a duplicate to this, but unfortunately the answer to this question cannot address this because mine is a nonrigid body and involve biological locomotion concepts ...
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2answers
81 views

Is this an inertial frame of reference in relativistic context?

What I've learned from our special relativity lectures is that an inertial frame of reference in relativity is one that experiences no gravitational forces. Also, it is a frame where if a particle is ...
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0answers
48 views

Question on time dilation [duplicate]

When i studied physics we had this example where someone climbes into a rocked flyes into space comes back the time that passes for him one year time on earth 86 years. I think most know what thinking ...
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122 views

Lorentz transformation of Gamma matrices $\gamma^{\mu}$

From my understanding, gamma matrices transforms under Lorentz transformation $\Lambda$ as \begin{equation} \gamma^{\mu} \rightarrow S[\Lambda]\gamma^{\mu}S[\Lambda]^{-1} = ...
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1answer
127 views

Perfect fluid and Cauchy momentum equation

The stress-energy tensor of a perfect fluid is given by $$T^{\mu\nu}=\left(\rho+pc^{-2}\right)u^\mu u^\nu+pg^{\mu\nu}$$ The divergence of the stress-energy tensor is zero: $\nabla_\mu T^{\mu\nu}=0$. ...
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3answers
579 views

Why does nonlinearity in quantum mechanics lead to superluminal signaling?

I recently came across two nice papers on the foundations of quantum mechancis, Aaronson 2004 and Hardy 2001. Aaronson makes the statement, which was new to me, that nonlinearity in QM leads to ...
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1answer
35 views

Energy and momentum of a relativistic electron

The question is to find the magnitude, $p$ of the electron's momentum in the unit of MeV/$c$, given that the kinetic energy of the electron is 2.53 MeV. The answer provided by the book says, ...
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4answers
114 views

Can a photon have little to no energy and/or speed?

Can a photon move more slowly than the speed of light and behave 'non-relativistically,' so to speak. Perhaps another way to express my thought is: could we stop a photon from moving?
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2answers
608 views

Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
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1answer
70 views

Hafele-Keating revisited with a gravity clock

Most modern clocks use electromagnetic phenomena to measure time. There are perhaps some older clocks that involve gravity to some degree (hour glass, pendulum), but I believe they still have a ...
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5answers
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I know light's speed in vacuum is constant, but what about its velocity?

Is the velocity of light in vacuum constant? It seems it would be different depending on whether it is coming toward you or away from you, but I just want to make sure. Does the direction of light ...
8
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1answer
1k views

Lorentz Invariant Integration Measure [closed]

When we canonically quantize the scalar field in QFT, we use a Lorentz invariant integration measure given by $$\widetilde{dk} \equiv \frac{d^3k}{(2\pi)^3 2\omega(\textbf{k})}.$$ How can I show that ...
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228 views

Proving the Lorentz invariance of the Lorentz invariant phase space element

I have been looking around for a satisfactory answer to prove that $$\frac{d^3\vec{p}}{2E_{\vec{p}}}$$ where $E_{\vec{p}}=+\sqrt{(|\vec{p}|c)^2+(mc^2)^2}$, is Lorentz invariant. The standard answer ...
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3answers
134 views

What can change a photon's frequency?

I found this question: Is it possible to apply force to a light particle? As it states, gravity can change the frequency of light by changing its momentum. My question regards other phenomena that ...
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1answer
52 views

Polarization vector identity in Minkowski space?

Playing around with numerical light-like momenta $p^\mu_1,p^\mu_2$ (light-like meaning ${p_1}^\mu {p_1}_\mu={p_2}^\mu {p_2}_\mu=0$) and corresponding polarization vectors ...