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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Would Special Relativity Predict Time Dilation of a Geostationary Satellite Compared to an Observer on Earth?

Consider a geostationary satellite at some arbitrary distance above the Earth's equator and consider a person directly below it, standing on the Earth's equator. Both satellite and person exist on the ...
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Composition of Lorentz Transformations

If a particle is moving in the $x$-direction with velocity $c/2$, then the Lorentz transformation $\Lambda = \begin{pmatrix}\gamma & -\beta \gamma & 0 & 0 \\ -\beta \gamma & \gamma ...
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Special Relativity - Distance Not Increased?

I just watched the movie Interstellar and the question was asked of why/how high-speed travel would slow time within an area. Curious as I am, I watched several YouTube videos to quickly 'educate' ...
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Intrinsic CPT phase

Under charge conjugation C, spatial inversion P and time reversal T transformations, there are possible intrinsic phases (more for this on Chapter 9, The Quantum Theory of Field v1 by S. Weinberg): ...
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Relativistic Kinematics - 2-Body Particle Decay

Consider the scenario where a particle of mass $M$ decays into two lighter particles of mass $m_1$ and $m_2$. In the center of mass frame (i.e. $\mathbf{p}_1$ and $\mathbf{p}_2$, the momenta of the ...
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Charged particle under a uniform electric field

Suppose a charge particle $q$ starts to move without initial velocity under the influence of a uniform electric field $E$ pointing in the positive $x$ direction. Express its position vector in ...
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Speed of light yes or no? [closed]

First off I am not a physics student: I am more of a science enthusiast. My question pertains to time and the speed of light: According to Einstein, no mass can travel at the speed of light. Now, ...
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5answers
198 views

What is the significance of the “squared” in $E =mc^2$? [duplicate]

If $c$ is just an arbitrary constant, why don't we say $E=mc$ and define the value of $c$ to be $\sqrt{299 792 458} \approx 17314$ meters per second? Or, why not use $E=mc^3$?
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Why does the minus sign in the Minkowski metric mean that nothing can move backwards in time?

I just watched this video: http://www.youtube.com/watch?v=GkCWywO93b8#t=27 and there Mr. Cox states that because of the minus sign in the Minkowski metric nothing can move backwards in time. It's ...
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31 views

SR: constant acceleration wordline simultaneity

A worldline $W$ with constant acceleration $a$ is given parametrically by $$t=\frac{c}{a} \sinh(\frac{a \tau}{c}), \quad x=\frac{c^2}{a} \cosh(\frac{a \tau}{c}).$$ Let $E=(0,0,0,0)$. I showed that for ...
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Polarization vector identity in Minkowski space?

Playing around with numerical light-like momenta $p^\mu_1,p^\mu_2$ (light-like meaning ${p_1}^\mu {p_1}_\mu={p_2}^\mu {p_2}_\mu=0$) and corresponding circular polarization vectors ...
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Could any object have zero mass? [duplicate]

Energy and mass are interrelated. As everything has energy could any object be massless? For example a photon is a packet of energy but still it is considered to be a massless particle. Why is it so?
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Would you be able to see yourself in a mirror in front of you as you two are in a room traveling at the speed of light? [duplicate]

Veritasium talked about this in one video. If you are in a room or a train, plane, car or whatever just a closed space traveling at the speed of light and you put a mirror in front of you, could you ...
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86 views

Special relativity mirror clock experiment inconsistency

Say I set up a relativistic mirror clock experiment in which a spaceship contains a set of mirrors with a photon bouncing between them. Say the photon's motion is parallel to the direction of motion ...
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Space and time variant? But together invariant?

I admit I'm having difficulty with spacetime. I don't understand how unifying space and time, seemingly variant quantities, results in an invariant spacetime. All texts and references talk about using ...
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2answers
151 views

Does the speed of light have a range of speeds due to medium-dependency?

An EM particle-wave propagates in a vacuum at a constant speed $c$, independent of the source/receiver but dependent on most mediums it moves through. Since the vacuum is a medium, and if logically ...
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53 views

Is there experimental evidence supporting the equivalence principle between different particles?

Knowing virtually nothing of GR, and only hints of particle theory, this might be something of a naive question. If I've misunderstood somethings, I would gladly like to know why. Perhaps a more ...
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How can we justify dropping the absolute time hypothesis?

In some approaches to Special Relativity the theory is motivated talking about the Michelson-Morley experiment and how this relates to the postulate that the speed of light is the same in every ...
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Deriving the Lorentz factor

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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29 views

SR: vector field and change of reference [closed]

If $U$ and $V$ are vector fields, then the derivative of $U$ along $V$ is the vector field $\nabla _V U$ with components $$\nabla _V U^a=V^b \frac{\partial U^a}{\partial x^b}.$$ 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 [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 ...
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138 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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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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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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129 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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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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73 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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81 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? [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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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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65 views

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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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 ...