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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Deriving the Relativistic Mass Equation

Recently, I learned how to derive E = mc^2. However, to do so, one must accept the relativistic mass equation. How does one derive this?
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Rindler and Minkowski space future/past infinity

In my black holes course, we are looking at the Penrose diagram for 1+1 D Minkowski space. My notes don't specifically describe $i^{\pm}$ (future/past timelike infinity) but do say all timelike curves ...
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Simultaneity hypersurface, local rest frame in special relativity

I am reading the book "Special Relativity in General Frames" by Eric Gourgoulhon for its more axiomatic approach to flat Minkowski spacetime geometry. In this book, the author defines something called ...
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SR: vector field and change of reference

If $U$ and $V$ are vector fields, then the derivative of $U$ along $V$ is the vector field $\nabla _V U$ with components $$\nabla _V U=V^b \frac{\partial U^a}{\partial x^b}.$$ I would like to verify ...
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In $1$-dimensional space, how would the gravity generated by an electron affect a photon moving away from the electron if the photon can’t slow down?

Suppose we had a universe obeying the same physical laws as our own. But it had only one spatial dimension (represented by the $x$ axis) and it was totally empty. There are just two point-like ...
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What is $E$ in the Planck-Einstein relation?

The Planck-Einstein relation was first given for photons $$E = h\nu$$ But later, de Broglie extended it to matter waves, and showed that it would hold for all particles as well. The $E$ for a photon ...
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Propagation speed of photons when taking higher-order QFT corrections into account

In our group of experimental physicist who have nothing to do with and know very little about quantum field theory, we recently had a question concerning the propagation speed of photons in vacuum: ...
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Einstein's mass-energy equivalence [on hold]

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 ...
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73 views

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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41 views

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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22 views

proper time according to rocket frame [on hold]

A space traveler with a wristwatch started from the origin and traveled a distance of 2.5 years with a constant speed of 0.357 according to the lab frame. What is the time recorded by the space ...
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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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Photon collides with electron. (Special relativity) [on hold]

A photon of zero rest mass collides with an electron of rest mass $m$ that is initially at rest in the laboratory frame. Show that the angle $ \theta $ by which the photon is deflected (measured in ...
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Special relativity revisited [on hold]

I had a query about Einstein's special relativity, particularly when it came to the notion of $c$ being the ultimate speed. I resolved such a query by treating an imaginary particle traveling at an ...
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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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60 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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34 views

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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Threshold energy, does this indicate particle annihilation?

If we have a question on threshold energy like the following: Two particles A and B collide to create C and D. Find the threshold energy required for particle A given that particle B is at rest. ...
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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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108 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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51 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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Does the assumption of $c$ being perfectly defined mislead us about the fundamental nature of space and time? [closed]

To explain my reasoning and understand my question, I must develop and present my thoughts as I have below. Background The one-way speed of light has been called 'a postulate which could never ...
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247 views

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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Is the Time Dilation Formula For Special Relativity Too Simple? [closed]

If you look up Time Dilation in Wikipedia, scrolling down to the section "Simple inference of time dilation due to relative velocity" not only shows you the formula for time dilation, but actually ...
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Time, time perception and time dilation [closed]

I'm new to this stackexchange, I usually wander in the worldbuilding one and there I've read time and time again questions and answers about the different "passings of time" depending on where you are ...
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65 views

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' = ...
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76 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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How to visualize the world while travelling near the speed of light? [on hold]

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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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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39 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

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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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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Special relativity: Two particles are accelerated to $.99c$ in opposite directions, what is their relative velocity? [duplicate]

Special relativity makes sense to me for objects moving at small fractions of $c$, but I am puzzled by how it works as we approach the limit. We are able to accelerate particles at CERN to speeds of ...
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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
38 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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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 ...