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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Non-relativistic limit in a Lagrangian density

What criteria should I consider when determining the non-relativistic limit of a Lagrangian density? For example, how would I take the non-relativistic limit of the following Lagrangian density: $$\...
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620 views

How can photons interact with anything?

I read photons do not age because they move at the speed of light. So when a photon interacts with my eyes, aren't they apart in space-time by the difference of the time in the frame of reference of ...
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Speed of light that is traveling away from the observer

The second postulate of Special Relativity states: The speed of light in a vacuum is the same for all observers, regardless of their motion relative to the source. Now imagine the observer ...
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258 views

Can relativistic momentum (photons) be used as propulsion for 'free' after the initial generation?

In discussing this question about propelling a spacecraft with photons and their relativistic momentum, the author asked that I restate my comment as another question. If photons can really be used ...
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Relativistic momentum finding

Kinetic energy of an object $mc^2$. I want to evaluate the momentum. We know Kinetic energy, $$E_k = \frac{p^2}{2m}$$ $$mc^2 = \frac{p^2}{2m}$$ $$ p = \sqrt{2}mc$$ Note that the momentum is the ...
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In space I am moving wrt to what?

Let us suppose I am running on a street. When my eyes are open, I can see many things moving backward, and thus it gives me an idea that I am moving wrt those things. Not even this, even if I close my ...
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218 views

Special relativity: moving charge and twisting bar magnet

ETA: Huh. It's been more than three months since I posed this question. Is it really possible that no one knows the answer? I thought for sure someone would know. Oh well. You have a small bar ...
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195 views

Units in time dilation calculation

I am currently working through Brian Greene's "World Science U" course on special relativity, and I have a question regarding one of the calculations performed for an exercise on time dilation (MODULE ...
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722 views

Why isn't general relativity the obvious thing to try after special relativity?

To preface my question, I ask this as a mathematics student, so I don't have a very good sense of how physicists think. Here is the historical context I'm imagining (in particular taking into account ...
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Are signal fronts in a beam not at rest to each other?

I'd like to investigate how the notion of "mutual rest" might be applied consistently, but distinctively, in the following thought experiment: Consider a light source ("$A$") which directs a beam ...
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0answers
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If a photon is a boson and has spin 1, shouldn't it have 3 spin orientations since spin 1 is a triplet? [duplicate]

I've gotten used to the fact that a spin can be described by its total spin and its $z$-component. And I've learned that a particle (really, anything) with spin 1 forms a triplet with three possible ...
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Fate of largest scale structures?

In $\Lambda\mathrm{CDM}$, structures form "bottom up" with larger structures forming later. Structures are generally speaking supported by the velocity dispersion of their constituent objects (e.g. ...
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Observers in Special Relativity

Suppose I am an observer in Minkowski space, observing a particle traveling with a constant velocity $v$. If I want to calculate the particle's Lorentz factor, given that the particle is traveling at ...
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40 views

Special Relativity Textbooks Request [duplicate]

I have a copy of David Bohm's Special Theory of Relativity and also a copy of T.M. Helliwell's Special Relativity. I was wondering if anyone has used these texts and if they're sufficient in providing ...
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2answers
607 views

Weird case for relative velocities and special relativity

This has bothered me for a while. I've been taught that the formula for determining the perceived velocity on an object from another moving object's reference frame under special relativity is: $$v = ...
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0answers
241 views

Including special relativistic effects in momentum in Heisenberg's Uncertainty Principle

I've been told that an electron is somewhere within the space of $10^{-10}m$ and am supposed to find the uncertainty in its velocity. Simply applying $m\Delta x \Delta v \geq \frac{h}{4\pi}$ results ...
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351 views

What is the role of the speed of light in mass-energy equivalency? [duplicate]

Where does $c$ squared come into play in the equation $E=mc^2$. Multiplication obviously but how does energy equal mass times the speed of light?
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151 views

All possible electromagnetic Lorentz invariants that can be built into the electromagnetic Lagrangian?

Given the electromagnetic Lagrangian density $$ \mathcal{L}~=~-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}~=~\frac{1}{2}(E^2-B^2) $$ is a Lorentz invariant, how many other electromagnetic invariants exists that ...
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Local EPR-experiments with photons in vacuum?

The principle of non-locality states "that an object is influenced directly only by its immediate surroundings." (Wikipedia) When two entangled particles are measured in an EPR experiment, we ...
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Derivation of the general Lorentz transformation

The standard Lorentz transformation or boost with velocity $u$ is given by $$\left(\begin{matrix} ct \\ x \\ y \\ z \end{matrix}\right) = \left(\begin{matrix} \gamma & \gamma u/c & 0 & 0 \...
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Special relativity: how to prove that $g = L^t g L$?

We have $$X^\textrm{t}gX = 0 \iff X^\textrm{t}L^\textrm{t}gLX = 0,$$ where $X$ is a column vector of length four, $L$ is a non-singular $4 \times 4$ matrix, 't' denotes matrix transpose, and $$g = \...
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Is there a fourth component to the electric field and magnetic field?

The Question If the three vector electric and magnetic fields come from the four component four-potential, then is there a fourth component to the electric and magnetic field? Related Question I ...
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1answer
168 views

What happens if a body free-falls at a certain speed?

It is known that a body falling to the ground is affected by gravity, and its velocity increases by 9.8 m/s per second. But when this body is falling, and it reaches the speed of 340 m/s (the speed of ...
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1answer
225 views

Does the light speed change in media? [duplicate]

Does the light speed change? The Theory of Relativity says that the speed of light in vacuum is the same and unchangeable, while I read that the speed of light in glass is lower than in air, and that ...
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4answers
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Challenge: Answer this gedanken (PFP - Perpendicularly Fired Photon)

I'm challenging anyone who can answer the following question objectively: As usual, imagine a railway station and trains which are equipped with single photon sources (one each in the platform and ...
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Reason why $F^{\mu\nu}F_{\mu\nu}$ and $\tilde{F}_{\mu\nu}F^{\mu\nu}$ are Lorentz invariant

I'm trying to think of an intuitive reasoning for why $F^{\mu\nu}F_{\mu\nu}$ and $\tilde{F}_{\mu\nu}F^{\mu\nu}$ are Lorentz invariant. By this I mean that I don't simply want to show that they remain ...
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86 views

How does time dilation work in this situation?

It is my understanding that when moving near the speed of light, time slows down relative to other things not moving so fast. Based on this principle, would it be theoretically possible to travel a ...
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62 views

Simple question about the tidal force (Leibniz's notation confuses me)

I started going through Taylor and Wheeler's Spacetime physics (standard textbook on special relativity). This is from exercise 2.8. Basically we're dropping a bearing ball from a 315 m height above ...
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does an object travelling close to the speed of light in an inertial frame of reference behave Relativistically

The two tenants of Special Relativity are: The laws of physics are the same in all inertial frames of reference. The speed of light in free space has the same value $c$ in all inertial frames of ...
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What is the formula for determining time dilation (as the object in motion)? [duplicate]

The formula for calculating how much time passes for a still observer is T=TO/(1-v^2/c^2)^1/2. How do I calculate what TO is?
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1answer
160 views

Confused about length contraction and aberration [duplicate]

Einstein states that a moving object's shape changes due to the length contraction. But people had done such an experiment: Taking photos to a moving object, but they didn't find Lorentz contraction, ...
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1answer
294 views

Is time dilation an illusion? Variation on the twins paradox [duplicate]

Consider the twins paradox with a slight variation: Twins A and B are in separate space ships both capable of going at the speed of light instantly (i.e. without any acceleration). Both ships are ...
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Time dilation in special relativity?

I'm trying to understand the concepts of time dilation and spatial compression. I've been using the classic example of firing a photon of light inside a ship (spaceship, boxcar, etc.) moving at a ...
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306 views

Huggins Displacement Theory and Retrocausality

I was looking at the Wikipedia entries on Time Travel and the Grandfather paradox and noticed a paragraph on the so-called Huggins Displacement Theory. I haven't been able to find the source although ...
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Inertial Frames in Special Relativity

According to the postulates of special relativity, all inertial frames are equal in all respects. Then how does it follow from this, that the space is isotropic and homogenous for an inertial frame ...
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103 views

Can we travel faster than light? [duplicate]

Consider two cars going in opposite direction one at speed $c/2$ and other just greater than $c/2$, then one bus will appear to other moving at speed more than $c$. How can an object travel at speed ...
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Why is radiation for an ultrarelativistic charge zero on axis?

I attribute it to the fact that for an ultrarelativistic charge the field is contracted and essentially there are only fields in the transverse direction and nothing longitudinally (wrt the charges ...
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Can special/general relativity be derived from the standard model?

Can special/general relativity be derived from the standard model? For example the time dilatation in strong gravitation? My feeling is yes, but I am not quite sure.
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Theoretically if you passed the speed of light in a medium, would there be a sonic boom equivalent?

I know that it is technically impossible to reach the speed of light in vacuum since the mass of the object travelling would reach infinity. However in a medium, would there be some sort of ...
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The question about MTW 4-momentum integral expression and lorentz nature

In section 5.8 of Misner, Thorne, and Wheeler's "Gravitation" there is a proof that 4-momentum determined as $$ \tag 1 p^{\mu} = \int T^{\mu 0}\,\mathrm{d}^{3}\mathbf r , \quad \partial^{\mu}T_{\mu \...
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How would an electron bunch/beam look different in the rest and lab frames?

With respect to special relativity, I was wondering how the spatial dimensions would differ between the rest and LAB frame of an electron beam. System: Electron bunch/beam traveling in linear motion. ...
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Why in the relativistic quantum mechanics $ \gamma_4$ name is not used instead of $ \gamma_5$?

I have seen in the in the Dirac equation $$\gamma_0,\gamma_1,\gamma_2,\gamma_3.$$ Then I have seen the definition of a new matrix $$\gamma_5=i\gamma_0\gamma_1\gamma_2\gamma_3.$$ Now my question is why ...
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Length contraction and angle change

I am new to special theory of relativity and it puzzles me at some points. For example, if we have a rod of length 1 meter, tilted at angle of 45 degrees ( x axis) and it moves at the speed of $v=0....
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5answers
301 views

Two clocks along different worldlines [duplicate]

I have been reading and watching videos about this subject for a while now. I just can not seem to grasp the idea. Let's say we have two clocks. I leave one at home and keep one in my pocket. Then, ...
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4answers
871 views

What will be the relative speed of a photon in a light ray to another photon of opposite direction light ray?

If two light rays start simultaneously in the space from exactly opposite ends in opposite direction that is separated by a distance of 600000 km in a way they meet at the mid point (300000 km from ...
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A problem with $E = mc^2$

(Rest) mass of proton = (rest) mass of neutron (approximately) = $1.67 \times 10^{-27}$ kg. let $m$ be the mass of nitrogen atom then $m = 2.32 \times 10^{-26}$ kg. $c = 3 \times 10^8$ m/s (approx). ...
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Integral of energy-momentum tensor

On Weinberg's Gravitation and Cosmology section 8 chapter 2, he introduced the energy-momentum tensor of a system of $n$ particals: $$ T^{\alpha\beta}=\sum_np_n^{\alpha}(t)\frac{dx_n^\beta(t)}{dt}\...
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twin paradox inferring cosmic speed limit

As I understand it, the twin paradox was integral to Einstein's conclusion that nothing can travel faster than the speed of light. Why wasn't there a similar conclusion for a hypothetical scenario ...
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Unitary representations of the diffeomorphism group in curved spacetime

In (special) relativistic quantum mechanics there is a standard argument that says that the (rigged) Hilbert space of states $H$ should be equipped with a projective unitary representation $U$ of the ...