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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What is the equation of a ellipsoid in motion and how to obtain its semi-axes? [closed]

The equation of an ellipsoid is given by $$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{p^2}=1$$ where $a,b,p$ are the length of the semi-axes. If $a=b=p=R$ then this ellipsoid is a sphere of radius ...
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Warp Drive conundrum - Speculative science question [closed]

Let me begin by stating that this question about Warp Engines/Drives, which i understand is a speculative, also I am not a Professional scientist or someone with a degree in physics. The question will ...
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How to prove a symmetric tensor is indeed a tensor?

Our professor defined a rank $(k,l)$ tensor as something that transforms like a tensor as follows: $$T^{\mu_1' \mu_2'...\mu_k'}{}_{\nu_1'\nu_2'...\nu_l'} ~=~ ...
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Are photons inside the media massive? If yes, why there is no Meissner effect?

We all know in vacuum travels with speed $c$, hence its rest mass has to be 0. In the media the light speed $v<c$. Then the photon renormalized by the medium (call it "quasi-photon" if you like), ...
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De Broglie wavelength of a massive particle as v approaches c

We understand that from a relativistic version of De Broglie's wavelength-momentum relation that as velocity approaches 0 the wavelength trends to infinity and as velocity approaches the speed of ...
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Electromagnetism and a simple doubt [duplicate]

Why don't electromagnetic waves need a medium to propagate? How does light get such a magnificent velocity?
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Can light travel with a speed less than its speed at same time?

I know that the velocity of light with respect to anything is constant ($c$) . What, then, is velocity of light with respect to light?
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Heisenbergs Uncertainty Principle in different intertial frames

Say there is a single particle in a box. If we switch to a different inertial frame (without the box) travelling close to the speed of light we see the box get smaller. At a high enough speed the ...
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How is $\dfrac{A^2}{8\pi}$ is the energy per unit volume of light?

In his 1905 paper, under the section: 8. Transformation of the Energy of Light Rays. Theory of the Pressure of Radiation Exerted on Perfect Reflectors, Einstein states: Since $\dfrac{A^2}{8\pi}$ ...
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What do we mean by saying that one clock had been “running slower” than another clock; or that two clocks had been “running equally”?

Several posts on this site, especially on the topic of relativity, refer to comparisons between clocks in terms of their "running"; one having "run faster" than the other, one having "run slower" than ...
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Explanation of Supplee's paradox

I was reading about Supplee's paradox, which is about whether a relativistic projectile, subject to uniform gravitational acceleration, would float or sink underwater. However the solution of the ...
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Time Dilation When In Orbit

Imagine a space ship orbiting the sun at near relativistic speeds, when compared to Earth (say from the reference frame of the sun) there would be x amount of time dilation. This would mean people on ...
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Is the amplitude proportional to frequency in electromagnetic waves?

In Einstein's 1905 paper, under the section: § 7. Theory of Doppler’s Principle and of Aberration Einstein derived the relativistic Doppler effect: $$f'=f\dfrac{1-\cos\phi \cdot ...
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Is there any way to measure the one-way speed of light?

Is there any way (practical or theoretical) to measure the one-way speed of light? The two methods that come to mind are: Stellar aberration, and Using adiabatic clocks: synchronize clocks, then ...
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1answer
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Why $x=-ct$ line in a spacetime diagram?

I can understand why the $x=ct$ line is needed as follows: If $c \Delta t \geq \Delta x$ then the event can be causally related to your current position, so the event could not appear in reverse ...
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Alongside a light ray (in another medium)

It is a said fact that the speed of light is insurmountable. But can the validity of this fact be questioned in another medium? If I pass a beam of light in, say water (here the light speed is ...
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Is the relativistic mass of a photon non-zero?

A photon has rest $m=0$, but it is never at rest, so it has no rest mass, then the relativistic mass is according to me non-zero because: $E = \text{work}=m \times \text{acceleration} \times ...
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Can a baseball travel through the Sun?

A baseball moving sufficiently close to the speed of light could theoretically spend less than a nanosecond inside of the Sun in the balls frame. If a baseball were traveling close enough to the speed ...
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Lorentz transformation in “On the Electrodynamics of Moving Bodies”? [duplicate]

I must be certainly wrong, but there is something I don't understand when reading the paper on "On the Electrodynamics of Moving Bodies" from Albert Einstein. All the sources I found give the same ...
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Why does a function $\psi(v)$ appear when a Lorentz transformation is applied on Maxwell's equations?

In his 1905 paper, Einstein applies Lorentz transformation on Maxwell's equations, and relates the electric force $(X,Y,Z)$ and magnetic force $(L,M,N)$ in an inertial frame $K$ with spectime ...
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What is the intuitive meaning of $Q^2$?

In particle physics, $-Q^2$ is defined by the four momentum transfer squared: $$Q^2 = -(p_i - p_f)^2 = (\vec{p}_i-\vec{p}_f)^2-(E_i-E_f)^2$$ For elastic scattering, the meaning of $Q^2$ is clear - it ...
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Twin Paradox in a closed universe: who is younger when they meet? [duplicate]

Assuming that our universe is like a great balloon-- if you travel far and long enough, you will eventually come back to the original position. Now, a pair of twins are "travelling around the ...
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Twins Paradox - Does ageing depend on motion?

I am trying to understand the Twins Paradox (relativity) and its implications. Can we infer from the Twins Paradox that the ageing process (cell decay or other biological processes) depends on ...
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Why does the Lorentz transformation have to be a linear transformation? [duplicate]

In my textbook, they say the following statements before doing a proof for the Lorentz transformation: We know that the Galilean transformation $x' = x - vt$ is incorrect, but what is the ...
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Why is there a universal speed limit?

I am looking for an answer that does not rely on Special or General Relativity -and without recourse to the fact that the speed of light is frame invariant. Is there another way of showing this ...
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The effect of relativistic near misses

Alice and Bob are both floating in free, empty space. Alice does not like Bob very much. Thus one day, believing that there is no such thing as overkill, Alice takes her programmable hyper-energetic ...
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Confusion I have regarding Einstein's 1905 derivation of LT

In his 1905 paper, Einstein derives the Lorentz transformation using the two postulates of SR;constancy of $c$ for all inertial frames and the Invariance of the laws of physics for all inertial ...
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The action of a relativistic point particle, the meaning of its parametrization invariance and possible potential terms

i am currently toying around with the behaviour of a classical relativistic point particle a bit. For a free one we get the action \begin{align} S =\int_\tau - m\sqrt{- \dot X_\mu \dot X^\mu}. ...
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4-vectors in special relativity and spacetime interval

In one of my vector mechanics lectures, the lecturer said the the space time interval was the dot product of the four position vector. But then he proceeded to show it was this: $s^2$ = $\Delta r^2$ - ...
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Does motion with constant proper acceleration, in a flat region, necessarily mean straight hyperbolic motion?

Is motion of a participant with constant proper acceleration, in a flat region, necessarily straight, hyperbolic motion (with respect to members of any inertial system, in that region)? Or is for ...
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Regarding synchronization of clocks in special relativity

I am trying to read of synchronization of two clocks in same inertial frame in special relativity. Suppose we have two synchronized clocks in an inertial frame placed at positions $x_1$ and $x_2$ in ...
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Why is this 4x4 tensor a 16-dimensional representation of SO(3,1)?

In his QFT book "A Modern Introduction to Quantum Field Theory" (http://www.nucleares.unam.mx/~alberto/apuntes/maggiore.pdf, pages 20-21), Michele Maggiore describes the tensor product of the ...
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Best twin paradox trajectory for constant acceleration rocket?

Let's say I have a rocket that can provide constant (proper) acceleration (let's say of 1 gee) for an infinte amount of time. Let's say I want to use this rocket as a means of "suspended animation," ...
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Why is the Mixed Faraday Tensor a matrix in the algebra so(1,3)?

The mixed Faraday tensor $F^\mu{}_\nu$ explicitly in natural units is: ...
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Doubts regarding Einstein's 1905 derivation of mass-energy equivalence

This is a follow up on this question. In his [paper][2] under the title:Does the inertia of a body depend upon its energy-content, Einstein drives the famous $E=mc^2$ equation. His argument can be ...
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Does space expansion change value when traveling near the speed of light?

To draw an analogy, we receive roughly the same amount of cosmic background radiation from all directions. However if we were to travel near the speed of light relative to the reference frame where ...
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Is potential energy frame dependent in special relativity?

In newtonian mechanics, As far as I'm aware, only kinetic energy is dependent on frames of reference, since kinetic energy is a function of velocity(squared) and velocity is dependent on frames of ...
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tensor products in special realitivity

Use the definition of a tensor as a linear function on vectors and 1-forms. For a one (2,1) tensor T, use a single vector as argument e.g. T(V) which converts it to a (1,1) tensor. However, if you ...
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What is disadvantageous about measuring time events using light signals sent from events?

In his paper: On the electrodynamics of moving bodies, under the section entitled I. KINEMATICAL PART: § 1. Definition of Simultaneity, Einstein discusses time and gives it an operational definition. ...
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Do relativistic electrons have more charge?

Gauss's law tells us that the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. When a charged particle is moving close to the speed of light ...
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Are relativistic spacecraft slowed down by oncoming gamma ray photons?

I recently read that a proton having an energy of ten billion GeV can travel across our galaxy in about 5 minutes from the frame of the proton. From the Earths frame we would see it take roughly ...
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Derivation of relativistic mean free path

I am working through a short derivation found in Abramowicz 1991 regarding the mean free path of a photon. We have a fluid moving in a particular direction with velocity $v$ and in an inertial rest ...
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The Twin Paradox using reference frame following the ship

The Twin Paradox is undoubtedly one of the most discussed things in special relativity and have a tendency to confuse most of us. Classically, it's resolved by either stick to one of the three ...
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Time relativity

Lets say that I am on a spaceship moving with the speed of 0,90c and I am looking on my friend who stayed back on earth. My friend is looking on me. From my perspective, my friend is moving 7 times ...
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Is heavier object falls slower according to special theory of relativity?

I'm newbie in physics, but have some idea want to know whether it is correct! I saw some information about special theorey of relativity. It just like says "when objects go faster it becomes more ...
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Gauge transformation and Special relativity

While explaining gauge theories, a book makes a comment that the U(1) transformation definition, $ U= e^{i q \lambda(x)}$ is analogous to a special relativity transformation in freely falling ...
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How does work function transform in Einstein's special theory of relativity?

A photon with energy greater than the work function hits the metal, and an electron is knocked off. Now, suppose we were in an inertial frame moving with a velocity $v$ with respect to the metal such ...
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Humans on earth seen from traveling space ship

If I would stand on a space ship traveling with a speed of 0,99c I would be moving 7 times slower from Earth's perspective. But if I would look back on Earth I would see everything moving 7 times ...
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Is there a standard of rest in the universe? [duplicate]

If you measure the cosmic background radiation you will find that in any direction it is roughly the same. However, if you were to travel near the speed of light relative to the Earth in a particular ...
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Why did Compton use X-rays in his experiment?

Why did Compton use X-rays in his famous experiment? Can it be done using other types of electromagnetic waves?