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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Colliding particles at speeds aproaching c [closed]

(In natural units where $\hbar=c=1$.) Two particles are to be collided. Each of these particles has a rest mass of 0.9 GeV and they will be collided at equal but opposite speeds. What is the minimum ...
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State of constant motion

Why does an object remains in its state of constant motion if there are no forces acting on that object? My understanding is that all the energy of the motion will be kept inside and a change in the ...
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Is the existence of electromagnetic standing waves dependent on the observers reference frame?

If I take two plane EM waves travelling in opposite direction e.g. $E = E_0 \sin(kx-\omega t)$ and $E=E_0 \sin (kx + \omega t)$, they sum to give a standing wave with a time-averaged Poynting vector ...
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Is speed of light ( Sun-to-Earth ) related to the movement speed of solar system?

The speed of light has been measured to be 299 792 458 m/s. Now, the Solar System is traveling at an average speed of 828,000 km/h (230 000 m/s). Summing up the numbers we get close to 300 000 000 m/s ...
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Taking signal travel time into account in Special Relativity

I am having problems taking the time it takes for a light signal from an event to reach an observer into account: For instance, if we have two observers $A$ and $B$ who synchronize their clocks when ...
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206 views

Learning the stress-energy tensor

I am learning dynamics in special relativity and come across the stress-energy tensor. I have real trouble understanding it. I would love answers on How to motivate the definition of this tensor. ...
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171 views

Magnetism due to relativity?

So I have been reading in some books that magnetism does not have to be assumed a priori, but can be obtained from the electric field + special relativity. And I have seen how this leads to the common ...
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What happens when relativistic effects stop?

I'm currently learning special relativity in high school and we only primarily deal with what happens when an object is moving at constant relativistic speeds. But what if the object slowed back down ...
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255 views

Is there a graphical representation of the Lorentz transformation equations?

I always loved theoretical physics as a kid and when I came upon this site while seeking computer advice via superuser I had to stick my silly little head into an oasis of intelligence. I have often ...
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Are there 'special' cases for when special relativity can be applied for accelerating bodies?

I have the following theoretical situation: A space station modeled as a ring in free space is rotating about its centre point at a high speed. I am trying to work out where time flows slower. From ...
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Velocity measurement in relativistic perspectives

I understand the precepts of relativistic time dilation, but I'm looking to nail down the local perception of velocity in each frame. My question is threefold: Given two observers $A$ (rest frame) ...
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139 views

In Minkowski space, why does the hyperboloid appear to each observer as a circle whose radius is increasing faster than the speed of light?

I read the assumption in the above question in the paper Hyperbolic geometry on a Hyperboloid by William F. Reynolds (see here, page 444), but it was not clarified further (the discussion was rather ...
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Homogeneity of space implies linearity of Lorentz transformations

In the derivation of Lorentz transformations, the Wikipedia article mentions a couple of times that the linearity comes from the homogeneity of space. I am looking for a thorough explanation on this. ...
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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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615 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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197 views

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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253 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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49 views

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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161 views

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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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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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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710 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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134 views

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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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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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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585 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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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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335 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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150 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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499 views

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
161 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
208 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
254 views

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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2answers
561 views

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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1answer
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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115 views

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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1answer
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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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153 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
289 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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2answers
294 views

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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1answer
297 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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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 ...