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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Einstein's mass-energy equivalence [closed]

Einstein's wonder equation $E=m c^2$,if we take energy is proportional to the mass, we can put single constant to make that equivalent equation. We all know that $\mathrm{constant}\cdot\mathrm{...
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Why are the proper time and the proper length not defined in the same frame of reference?

I've just read this interesting Wikipedia article about time dilation and length contraction in special relativity. . Derivation of time dilation Applying the above postulates, consider the ...
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Relativity asymmetry?

If you have two bodies that move towards each other at a constant velocity, each body will observe the other body experience time faster. This does not make sense to me because if you had a person ...
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What is the difference between these two equation dealing with time dilation?

In my textbook, the time dilation equation is presented as $\Delta t' = \gamma \Delta t,$ where $ \gamma = 1/ \sqrt{1 - v^2/c^2} $. My understanding of this equation is as follows (correct me if I'm ...
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Relativistic doppler effect in three dimensions

Consider a sphere that travels through space with a velocity $v$. I wish to investigate the relative intensities of the CMB on all points on the sphere. For the microwaves approaching from the direct ...
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106 views

How to motivate this approach on Special Relativity?

One of the most common approaches to Special Relativity is that based on the two Einstein's postulates: The laws of Physics are invariant in every inertial reference frame The speed of light ...
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Perception at relatavistic speeds

If one were to be traveling at near the speed of light, their mass would be $m_{rel}= m_0 / \sqrt{1 - \frac{v^2}{c^2}}$. For the mass to double the speed would have to be $86.6\%c$ [edit] To better ...
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About Lorentz Group

In definition of orthogonal matrices we say that the a matrix $A$ is orthogonal if $A^TA = I$, while for Lorentz Group it is written as $\Lambda^Tg\Lambda = g $. And we say that Lorentz transformation ...
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Is a nuclear bomb in some sense a bullet travelling at the speed of light, but along time rather than along space?

Apologies if this is a silly or perhaps obvious question, but $E=mc^2$ just looks so much like classical kinetic energy (except for the factor of 2). So I'm thinking of the to-be-fissioned-away ...
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247 views

Sign convention for the Minkowski metric $\eta_{\mu\nu}$

In special relativity, one is confronted with a quadratic form called proper time, which is $c^2t^2-(x^2+y^2+z^2)$, $t$ being time and $x,y,z$ being the space coordinates. One usually introduces a ...
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65 views

Boyles law & relativity

In relativity when an object approaches the speed of light, $c$,its volume decreases due to length contraction. As a thought experiment, consider a rectangular metal box travelling at a relativistic ...
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Why collide a moving particle with a particle at rest, rather than two moving particles?

I was just reading some lecture notes about relativistic and quantum mechanics, and in the later part of this page the author demonstrates that any relativistic particle collision in the "lab" ...
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Is there a formula that gives the position of an object depending on the time, but which doesn't allow the object to surpass the speed of light?

I have found these two formulas: $v = at + v_0$ $x = \frac{1}{2}at^2 + v_0t + x_0$ a is the acceleration v is the velocity x is the position t is the time $v_0$ is the initial velocity $x_0$ is ...
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Proving the conservation of 4-momentum for a particle collision $A+B\to C+D$

Let me say that particle A hits particle B and two particles come out - C and D; In system S I can write: $$p_A^μ+p_B^μ=p_C^μ+p_D^μ;\tag{1}$$ here $p_N^μ$ is the 4-momentum. Using the Lorentz ...
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Gravity's Rainbow

What is it? I've seen it in context of a few research papers such as Absence of black holes at LHC due to gravity's rainbow and Thermodynamics of black holes in gravity’s rainbow formalisms My best ...
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1answer
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Special relativity and Lorentz transformation

I recently learned about special relativity and different reference frames. The conversion from two inertial reference frames is given by Lorentz transformations: $$x' = \frac{x-ut}{\sqrt{1-\frac{u^2}...
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3answers
103 views

How does an electromagnetic field oscillate if time does not pass for the speed of light?

As far as I'm aware, traveling at $c$ will prevent time passing due to time dilation. Electromagnetic waves rely upon oscillations to propagate. Since oscillations rely upon the passing of time, how ...
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why is the magnetic field circular

According to relativity, If magnetic field is just an electric field viewed from a different frame of reference, why is the magnetic field around the wire is circular?
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Are reversible and irreversible processes frame dependent?

since it is all about time. If I have a look at an irreversible process from a frame where time runs really slow. is there a possibility of considering that process reversible from that frame?
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Rigorous computation of four-velocity

In Special Relativity we can consider spacetime to be the Minkowsky space $\mathbb{R}^{1,3}$ which is just $\mathbb{R}^4$ together with the non degenerate symmetric bilinear form $g$ that in some ...
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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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137 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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119 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 $diag\...
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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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51 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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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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Faster than light signals and the price to be paid if we accept them : a very simple protocol

Some 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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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. \tag{...
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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
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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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343 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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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, ...