# Questions tagged [special-relativity]

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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### For a given object in the sky, the red shift due to the relativistic Doppler effect is greater than the cosmological red shift. Why is this?

Measure the red shift of a galaxy at 1. Use a standard candle measurement and you will determine the distance of the galaxy from us at around 10 billion light years. Using Hubble's Law we can ...
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### Did Einstein himself ever follow up on his theory that light travels with infinite velocity? [closed]

In reading the freely available English translation of "On the electrodynamics of moving bodies" I find on page 10 Einstein himself conducts a critical evaluation of the domain of validity ...
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### How does the eigenvector interpretation of Lorentz transformations generalise to higher dimensions?

When I came across this video, I immediatly realised how Lorentz transform corresponds to a linear transformation where the vectors representing the speed of light ($\vec{c}$ and $-\vec{c}$) are in ...
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### What physical argument to say that time is a dimension? [closed]

To demonstrate Lorentz transformations mathematically, we assume that time is a dimension (via linear transformations, etc.), what physical argument requires us to do this? Details for the reason for ...
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### How can light never tire? [closed]

The question has been asked before, by myself and others, for various reasons: Why assume that all observed redshift is the result of cosmological expansion and not the light itself expanding due to ...
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### Relativistic Lagrangian for a System of Massive Particles

The standard Lagrangian $L$ written in local coordinates for a free, relativistic particle of mass $m > 0$ is given by $$L(q, \dot{q}) = -m \sqrt{-g_{\mu\nu}(q) \dot{q}^\mu \dot{q}^\nu}\tag{1}$$ ...
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### Importance of orthogonality in Minkowski space [closed]

I am currently studying Minkowski space. Orthogonality in this space is new to me. I have seen in a blog post, in 1 that states that, orthogonality is important in this space. It will be helpful, if ...
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### What is happening when you take into account distances with the twin paradox?

The twin paradox is based on special relativity alone. Bob is the reference (immobile), and measure the speed of Alice: 0.99c (Lorentz factor =7), they both set their clock at zero. After one year of ...
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### Differences between QED and relativistic quantum mechanics? [closed]

Differences between QED and relativistic quantum mechanics? Can you please explain, what are the differences between QED and relativistic quantum mechanics (RQM)? I have read that QED focuses on the ...
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### Could a crossterm in the energy–momentum relation be missing? [closed]

Could it be that $E^2 = (mc^2)^2 + (pc )^2$ is really $E^2 = (mc^2)^2 + 2mpc^3 + (pc )^2$ or $E^2 = (mc^2)^2 - 2mpc^3 + (pc )^2$ so that it comes from $E^2 = (mc^2 + pc)^2$ or $E^2 = (mc^2 - pc)^2$? ...
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### Discrepancy with a result from Peskin & Schroeder's QFT

I'm trying to understand a result in Peskin and Schroeders chapter 3 on the dirac equation, during the free particle calculation for the case $p^0=E>0$. Peskin and schroeder derived this expression:...
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### Can Lorentz invariance turn out to be an approximate symmetry in string theory?

I don't know whether I need to ask much but the essential question is at scales either approaching or at $M_{pl}$, can Lorentz invariance be broken? I am especially interested in the context of string ...
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### Doppler Shift in Moving Medium

Would the medium between a stationary source and observer moving cause a shift if the source and observer are on opposite sides of the medium? The reason for this question is that I was noticing how ...
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### Did Einstein say the one-way speed-of-light is "not a fact of nature"? [closed]

If so is there a published paper where he said as much?
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### Why cant I measure proper length on spacetime curvature with the following formula? [closed]

I'm struggling right now from the definition of proper length along spacetime curvature, it is said as I found online the length that object covered on his spacetime rest frame , so why cant I use the ...
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### Is $\hat{H}^2 = c^2\left(\hat{p}^2+m^2c^2\right)$ valid quantum physics?

From Schrödinger equation we know that $\hat{H}=\hat{E}$ for non-relativistic systems. For relativistic scenarios we use the usual $\hat{E}^2 = c^2\left(\hat{p}^2+m^2c^2 \right)$. From this we can ...
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### Terrell Rotation

In David Tong's lecture notes on special relativity (p.158 in Section 7.6.2), it is mentioned that Terrell rotation (also known as the Penrose-Terrell effect) does not alter the shape of a sphere ...
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### Derivation of "Euclidean Lorentz transforms" without the one-way speed-of-light constancy postulate but with the relativity principle [closed]

Here is the derivation of Euclidean "Lorentz transformations" by Gemini 1.5 Pro from the basic postulates but without the one-way speed light constancy postulate. Do you find any faults in ...
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### Why don't non-local theories typically have any energy-momentum tensor?

This great answer by @AccidentalFourierTransform says that for energy momentum tensors we need locality and Lorentz invariance. The rest of the answer focuses on metric dependence of partition ...
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### Special relativity thought experiment using light

I have a clock using lights bouncing off two mirrors in a moving train as shown below. The train is moving in the left direction as shown. In this situation, the light in direction 1 takes more ...
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### Absence of length contraction for a translating rod in one dimension

I was reading Section 2 of Einstein's paper, and began thinking about the idea of a rod translating with a horizontal velocity $v$. The rod has two ends, end A and end B. If the rod is translating ...
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### Constant velocity motion should be undetected

In special relativity, the constant velocity motion cannot be detected by any experiment. Even when light is used we end up with phenomenon of length contraction and time dilation but that is the case ...
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### Difficulty Understanding Special Relativity Time Dilation [closed]

Joe and I have agreed to shoot a photon at each other when our clocks count 10 seconds. Suppose I am approaching Joe at relativistic speeds such that I think Joe’s clock is ticking at half my clock’s ...
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### Relativistic mass of neutron almost at speed of light [duplicate]

What will be the relativistic mass of the neutron moving almost at the speed of light? I am considering the relation Binding Energy, $$E = m c^2 \ .$$ Technically speaking, velocity would inversely be ...
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### Two Photons are Traveling [duplicate]

Two photons, photon A and photon B, are traveling in the same direction at the speed of light, $c$. How fast does photon B appear to be traveling from the perspective of photon A?
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### General Relativity an inevitable consequence of the constancy of light-speed and the equivalence principle: Is this really true?

Quite a long time ago, longer than I'd like to admit, I had heard what is said in the title -- that General relativity is the inevitable result of the constancy of the speed of light and the ...
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### Deducing the (special) relativistic Lagrangian only using Lorentz transform [duplicate]

I feel like there must be a way to deduce the (special) relativstic Lagrangian using only the Lorentz transform (without other knowledge of special relativity). So far, all the derivations I have seen ...
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### $G$-invariant field equations

It is easily verifiable that if we are given a field theory with the Klein Gordon equation, it is Poincaré-invariant. So is the Dirac equation. More generally, for arbitrary spin, the Poincaré-...
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### Why is Special Relativity preferred over Lorentz Ether Theory?

Special Relativity and Lorentz Ether Theory make the same predictions, so they cannot be experimentally differentiated. (Are Lorentz aether theory and special relativity fully equivalent?). As such, ...
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### Some confusion about understanding the relativistic quantum mechanics

S. Weinberg in his book "The quantum theory of fields" chapter 2 introduced the notion of symmetry in quantum mechanic as follows: Physical states are represented by rays in Hilbert space. ...
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### When is the Lagrangian a Lorentz scalar?

The Lagrangian $\mathcal{L}$ can be defined as the Legendre transform (when it exists) of the Hamiltonian $\mathcal{H}$, a non-Lorentz scalar quantity (as $\mathcal{H} =T^{00}$). My questions are, ...
According to Wikipedia, the relativistic Doppler effect is simply the classical Doppler effect for a stationary source, $1-v/c$, times the relativistic time dilation, $1/\sqrt{1-v^2/c^2}$ (where v is ...