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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How can one motivate the relativistic momentum?

Motivating the classical momentum $\mathbf{p} = m\mathbf{v}$ is quite easy: it is meant to represent the quantity of motion of the particle, and since the mass is one measure of quantity of matter it ...
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2answers
105 views

How to visualize the world while travelling near the speed of light? [closed]

I have been having some trouble with this for a while. I think in terms of vivid , moving images and i haven't been able to visualize this completely. I wondered if a person, like the Flash from the ...
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1answer
84 views

How does the Lorentz boost change if we introduce transformation to the minkowski metric

Let's say we have the Lorentz boost given by the $ \Lambda^\mu_\nu$ in the Minkowski metric $diag\{1,-1,-1,-1\}$. Now if I do a transformation on the Minkowski metric such that the new metric is ...
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Time Dilation: One observer at rest, two observers in motion

I am currently taking a course in Modern Physics mainly focused on Special Relativity and came up with the following problem: Let $O_1$ be an observer at rest. A second observer $O_2$ is moving to ...
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45 views

Double-slit experiment [closed]

Given the following wavelength: $\lambda = 1.75 \cdot 10^{-12}\ m$ This leads to the velocity of the electron (matter wave). First approach: $p = \dfrac{h}{\lambda}=m(v)v=m_e\gamma v$ [...] $v ...
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107 views

Off-diagonal terms in metric for 4D space-time [closed]

Consider a delta between two events in 4D space-time written as a 4-vector, $x^\mu=(dt, dR)$. The time $dt$ is a scalar difference in time. The 3-vector $dR$ points some direction in space. One ...
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372 views

Faster than light signals and the price to be paid if we accept them : a very simple protocol

Most physicists currently understand entanglement as transferring information instantaneously, yet not violating causality. Is this really a satisfactory explanation, or should be look for something ...
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89 views

Deriving the equations for a moving inertial reference frame [closed]

I assume $c=1$ in the following derivation: In order to derive the equations for a moving inertial reference frame, I immediately wrote down the following: $$ x'=Ax+Bt, \tag{1}$$ $$t'= Dx+Et. ...
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75 views

Can a point in empty space be motionless with respect to light?

Being that the speed of light is constant throughout the universe, can a point in empty space be motionless with respect to light?
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1answer
48 views

Parity transformation is proper orthochronous?

In 3+1 dimensional spacetime the parity transformation is $$P^\mu_{\;\,\nu}=\begin{pmatrix}+1&&&\\&-1&&\\&&-1&\\&&&-1\end{pmatrix}.$$ This is ...
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1answer
145 views

Biot-Savart law from relativity

Few days ago I came by a derivation of STR from Bio-Savart law. Since then I have been trying to derive Bio-Savart law from STR. The derivation mentioned previously used two parallel current-carrying ...
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4answers
115 views

What is the mass of a sphere?

A solid sphere of mass M is rotating along an axis. We can consider it as a collection of large number of point masses, every point mass is moving with respect to center of mass with velocity which ...
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32 views

Does the algebraic number field used to define spacetime always have to be the real numbers?

When we talk about Minkowski space, do we assume the field $K$ we are using is the real numbers? Why couldn't spacetime be made up of the rational numbers or something? Also, I was reading Arnold and ...
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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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178 views

How can a Physical law not be invariant?

In Relativity, both the old Galilean theory or Einstein's Special Relativity, one of the most important things is the discussion of whether or not physical laws are invariant. Einstein's theory then ...
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Can quaternion math be used to model spacetime?

Quaternions are commonly used to model 4 dimensional systems where the quaternion consists of a real 3 dimensional vector and an imaginary scalar. So on the surface Quaternions seem well suited to ...
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1answer
44 views

Why do we restrict the maximal supercharge to 32?

Many supersymmetry textbook state that the maximal supersymmetry in any dimension has 32 hermitian supercharges. (Actually for lowest number of supersymmetry $N=1$ the highest dimension is $D=11$) I ...
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2answers
96 views

Is there any theory in physics that might support the existence of tachyons?

According to Einstein, we all know that light is the fastest thing and it's impossible to beat it's speed. But isn't there a way to go around this? I read somewhere that tachyons gain speed per the ...
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2answers
185 views

What spacelike, timelike and lightlike really mean?

Suppose we have two events $(x_1,y_1,z_1,t_1)$ and $(x_2,y_2,z_2,t_2)$, then we can define $$\Delta s^2 = -(c\Delta t)^2 + \Delta x^2 + \Delta y^2 + \Delta z^2$$ which is called the spacetime ...
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76 views

Through relativity could a person be dead and alive at the same time?

For the purposes of the question ignore the fact that radiation and several other things would kill humans long before this. You and another person are jumping into a black hole and the other person ...
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51 views

Two spaceships are accelerating equally, uniformly on exactly parallel tracks. Does a rope suspended between them eventually rip?

This question is a variant of "Bell's spaceships problem". Rather than one spaceship following the other "on the same track", let the two spaceships accelerate "side by side", on exactly parallel ...
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24 views

Averaged energies in particle collisions

Let's have (in CM frame) process $x + y \to x + y + z$, where $x, y, z$ correspond to (in general) different particles with non-zero masses. The total energy of process is $E$. How to calculate ...
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Rest masses, binding energy - mechanism for negative mass

Let us have an two objects (in a box) both of mass $m_0$ far from each other. They attract each other and at some moment their distance is close and they have substantial kinetic energy. Something ...
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2answers
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Is FTL communication compatible with Lorentz ether theory?

I have come to understand, that faster-than-light communication is problematic with special relativity, because it leads to the possibility of sending signals into the past. I also read about the ...
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$V_{\rm ball}=V_{\rm train}+V_{\rm ball}$?

30 years after reading Einstein's books I'm having another go at understanding astrophysics, but one thing I didn't understand back then still doesn't make sense to me. It is the example of a ball ...
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37 views

Travelling at the speed of light [closed]

more of a philosophical questions normally if you are travelling at some speed and you bump into some object, you generally would get slowed down and the force from your acceleration would be ...
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1answer
160 views

Phase velocity greater then the speed of light?

It is my understanding the the phase velocity of a wave can be greater then the speed of light. So imagine we had a wave packet consisting of a single sinusoidal wave; $$y=sin(\omega t-kx)$$ Then ...
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4answers
476 views

Can we change a photon's frequency in mid-air?

Can we have a light source emitting photons in the infrared range and after, lets say, 5 meters, these photons become a photon in the x-ray range? The only way I know we can change a photon's ...
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4answers
477 views

What is the universal speed limit relative to? [duplicate]

If all speeds are relative, then what "governing" force is that speed limit relative to? Is there some sort of fixed or absolute grid with locations everything is compared to? Does this also mean ...
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3answers
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Is it possible to stop time? [duplicate]

Assuming the spacetime principle, if the space is modified the time does too. So if the velocity in the space is increase, does the time slow down? What happens if the speed is the speed of light, ...
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1answer
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Special relativity: can the velocity of a free object be discontinuous relative to an accelerated observer who stops accelerating?

Suppose an observer ${\it {\mathcal O}}$ leaves point O*, origin of the Minkowski frame K*, in the $O^{*}x^{*} $ direction, with a uniform acceleration $a_{0} $ (as measured by himself) ...
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1answer
81 views

Relativistic addition of velocities in the y-direction? [closed]

I've been having some difficulty with the problem described below, please have a look: Two particles with identical masses (m) undergo a collision. Before the collision they move with velocities ...
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Length contraction alongside acceleration

Let's have a ship, a target and a ship traveler which we use as point of view. Assuming no other object are observed and we are so far from any other object that gravity distortion are negligible, I'm ...
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Behavior of mass approaching the speed of light

I would like some clarification on the behavior of relativistic mass as it approaches the speed of light. I am a high school student with an interest in physics so chances are I will have a hard time ...
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1answer
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Simultaneous observations in relativity

Consider an object which responds to two different signals A and B: it responds to signal A with blue color and signal B with red color. Also, it responds only to the signal that reached first. In ...
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The limited Computing Capabilities of Space, Increased quantized info leads to time-dilation?

Are there any approaches to Special and General Relativity using space as a computing medium? With space having a maximum computing capability and time dilation as lag? Could this idea describe the ...
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80 views

Minkowski Diagram for Time-Like Separated Events

A while ago, I asked a question if two events are always simultaneous in some reference frame. I received excellent answers. The point is that if $E_1$ and $E_2$ are time-like separated with time ...
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Doppler shift and special relativity

I have been listening to an audio course on Special Relativity. In the course the teacher repeatedly says that the "laws of physics are equally valid for all uniformly moving frames of reference". ...
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2answers
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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1answer
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How did special relativity change physicists views on the two prominent inverse square laws (ie Newton grav and Coulomb's law)?

On page 107 in Hartle's Gravity -- An introduction to Einstein's General Relativity, he says the following With the success of special relativity it became apparent that the Newtonian theory of ...
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To what fraction of the speed-of-light has any multi-atom molecule (or polyatomic ion) been accelerated?

Of course photons go $c$ in a vacuum, and seems there's data on electrons getting to $0.999999999976c$ and protons to $0.99999912c$. For the twins paradox to be plausible, one of the twins must ...
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Why is the scalar product of four-velocity with itself -1?

My GR book Hartle says the scalar product of four-velocity with itself $-1$? Consider the definition of four velocity $\mathbf{u} = \frac{dx^{\alpha}}{d\tau}$. Suppose I take the scalar product of ...
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477 views

Are length contractions limited by Planck length?

While we are getting closer to speed of light our length in the direction of the movement is according to Lorentz transformation getting shorter. But we can not (even theoretically) consider length ...
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Why is the relativistic Lorentz factor defined this way? [duplicate]

My question is: why has the Lorentz factor the form $$\gamma = \dfrac{1}{\sqrt{1 - \dfrac{v^2}{c^2}}}$$ and not, for example one of those: $$\gamma = \dfrac{1}{\sqrt{1 - \dfrac{v}{c}}}$$ or ...
0
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2answers
110 views

What is the fastest speed that a massive object can travel at? [duplicate]

What is the fastest speed (in miles per hour) that a massive object can travel at? I have heard that an object can travel at the speed of light, but I've also heard that massive objects cannot travel ...
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62 views

Quantum relativistic effects

I was performing a thought experiment: let us assume an object is traveling so close to the speed of light that the length of the object is small enough for quantum effects to become noticeable to a ...
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6answers
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Confused about Lorentz contraction

My son asked me the following question which I can't answer in a simple way. A frame $O'$ has speed $v$ relative to $O$. A photon travelling along the $x'$-axis in frame $O'$ over a distance $L'$ ...
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2answers
84 views

Time dilation due to change in speed

I can't get something strait... Lets use the usual example: A man is flying away from earth on a very fast spaceship. So, His time is now not moving in the same "speed" like earth time but slower. But ...
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1answer
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Has light been used to measure relative velocity?

Here we have 2 lasers. Both are in the same frame of reference as is top box. Laser #1 sends the light directly through the hole in the top box on one side and the light eventually exits the hole ...
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Mass-velocity-relation for tachyon

Suppose that $m = \gamma m_0$ with $$\gamma = \left(1-\frac{u^2}{c^2}\right)^{-\frac{1}{2}}$$ is valid for tachyons, where $m$ is the mass of the tachyon and $u$ its velocity. Since $u>c$, the rest ...