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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226 views

How is 4-current a 4-vector?

I am looking at Jackson sec 11.9, where he states that the $\rho,\bf{J}$ form the 4-current $$J^\alpha=(c\rho,\bf{J})$$ Jackson says this is from the invariant of the 4-divergence $\partial^\alpha ...
2
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4answers
430 views

Is this a Lorentz-scalar? How do I tell?

I'm struggling to identify whether a scalar is a Lorentz-scalar. E.g: $$\partial_i A^i \quad i \in {1,2,3}.$$ How do I determine if this is a Lorentz-scalar or not? If got the same problem with ...
-2
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1answer
46 views

Do we have rest mass according to quantum physics? [closed]

I know wave must be in motion and resonant waves are actually in motion. So I don't understand what is a rest mass of a particle. If a particle is just a wave in a particular field, it should be ...
-2
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2answers
89 views

How can we know that the speed of light is constant?

Science say that within a constant time frame the light travels a constant distance. But if time is relative how can it be possible to use it as a reference to say that something is constant?
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1answer
44 views

Does momentum scale linearly with time, assuming a constant nonzero net force, even at relativistic speeds?

I would expect it to, since you'd think the loss of velocity due to relativity would be made up for by the gain in relativistic mass. I'd like this to be confirmed, though. and if so, in whose ...
2
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1answer
47 views

4-Gradient Lorentz Transformation

I am currently studying the behavior of a scalar field $\phi$ under a Lorentz transformation $\Lambda$. However I am having trouble understanding why the following holds true: $$\partial_{\mu}\left(\...
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0answers
7 views

Head-on collision near lightspead [duplicate]

Assume two objects moving near light-speed (for this experiment let's say $0.9c$) towards each other. The speed is measured from an observation platform at the collision point (as I understood ...
-3
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2answers
55 views

Dark Matter vs. Mass from Kinetic Energy

I was thinking about dark matter, and was wondering if the extra mass due to kinetic energy has been taken into account. Here's what I mean: let's talk about any cosmological object that is known to ...
0
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2answers
2k views

Why magnetic field lines and force are not orthogonal with magnets?

The below explanation why magnetism exists is superb in this video. The explanation about magnets is also great in this video. A magnet has atoms with unpaired electrons forming mini magnets. The ...
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1answer
30 views

Differences in notation of momentum 4 vector

I have noticed three ways to write the 4 momentum vectors: $P = (E/c, \vec{p})$ $P = (E, \vec{p})$ $P = (E, c\vec{p})$ I know how to derive equation 1, and as far as I know, one can use the ...
0
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2answers
119 views

How to interpret Hermann Minkowski's comments on the construction of spacetime

What did Minkowski mean by his statement: "The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are ...
0
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1answer
86 views

If photons end up having a tiny mass, say $10^{-54}~\rm kg$, what would be the universal speed of massless particles?

First, I'm no expert so sorry if I get anything confused but I tried to research as much as could before asking this. So while it is pretty much accepted that photons are massless (Despite this ...
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2answers
57 views

Is the rate of light emissions actually the frequency of the light?

I am confusing with the concept of frequency in the context of Doppler effect studying SR. The Schutz says, if the source emits pulses more frequently, then the observer would see the lights not only ...
8
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5answers
503 views

Can one deduce absolute motion through magnetism? [closed]

I am trying to understand forces in relativity: Suppose there are two electrons A , B travelling side by side at 1 cm distance at .99 c (in space or at lHC, ignoring all other factors). I know that ...
0
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1answer
35 views

Is proper time and proper length relative or absolute in relation to two events?

This question concerns with a problem encountered when doing a question on special relativity. A scenario in which the question is based will be described and the problem will be explained. Scenario: ...
4
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2answers
847 views

Point charge 4-current derivation

How do I derive that the 4-current of a point charge is $$j^{\mu}(x)=e\int_{-\infty}^{+\infty}\dot{z}^{\mu}(s)\delta^4(x-z(s))ds$$ where $\dot{z}^{\mu}(s)$ is the 4-velocity of the charge and $s$ is ...
0
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0answers
29 views

Applications of octonions in special relativity?

According to the Wikipedia article on octonions: Octonions [...] have applications in fields such as string theory, special relativity, and quantum logic. However, I couldn't find any ...
-1
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2answers
87 views

What particles travel near the speed of a photon? [closed]

I know photons travel at the speed of light. How does the size of a particle determine its maximum velocity? Phonons, Preons, Electron ect. Is there a scale in from the smallest particle's maximum ...
1
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2answers
95 views

Why does Special Relativity apply to more than just light?

It is my understanding that time dilation is derived from the constancy of the speed of light in vacuum. I would assume this implies that the quirky consequences would therefore apply only to light. ...
0
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1answer
65 views

Is the time dilation experiment for real?

A popular experiment is described in books on special relativity, that claims that an atomic clock was flown at high speed and later compared with a similar atomic clock on earth, and it was found ...
3
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2answers
58 views

Pole and Barn Paradox w/ Spacetime Interval

I'm having trouble with a pole and barn paradox problem. The problem is as follows: A pole vaulter is running with a pole at $ v=\frac{\sqrt3}{2}c $. Her pole has a proper length of $L$. She runs ...
0
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0answers
21 views

Relativistic Mass and Potential Energy

In the chapter 16–4 of the Feynman Lectures, Feynman employs a thought experiment to explain why "if two particles come together and produce potential or any other form of energy; if the pieces are ...
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4answers
2k views

Am I just some energy traveled at light speed? [closed]

I don't understand $E=mc^2$ very well, and here is my question: Does this equation mean masses are just condensed energy? And does this mean that the extra energy an object has when traveling at ...
2
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1answer
110 views
20
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6answers
2k views

Proving that interval preserving transformations are linear

In almost all proofs I've seen of the Lorentz transformations one starts on the assumption that the required transformations are linear. I'm wondering if there is a way to prove the linearity: Prove ...
1
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1answer
56 views

Einsteins theory of relativity and formula of kinetic energy [duplicate]

After seeing both Einstein's theory of relativity ($E=mc^2$) and the formula of kinetic energy (K.E=$\frac{mv^2}{2}$), I noticed that that they are mostly the same, with the only difference that ...
2
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0answers
40 views

Is the helicity of photon Lorentz invariant? [closed]

If the helicity of a photon is $+1$ in an inertial frame, then is the helicity of this photon $+1$ in another inertial frame? The helicity operator is $$ h=\mathbf{S}\cdot\hat{\mathbf{p}} $$ with $$ ...
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1answer
76 views

Where is the mistake in the following rationament [duplicate]

Well... kind of hard to translate in English so bare with me :). Let's consider a wheel that spins in the void. Each point of the wheel has the speed $v = ω r$. That means that for any $ω$, there is ...
4
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2answers
166 views

Nature of light in Special Relativity

What is the nature of light in the context of Special Relativity? Is it a photon, or an electromagnetic wave, or something else? I have doubts, because a photon seems to me a quantum mechanical ...
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6answers
1k views

Relativistic Cellular Automata

Cellular automata provide interesting models of physics: Google Scholar gives more than 25,000 results when searching for "cellular automata" physics. Google Scholar still gives more than 2.000 ...
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4answers
6k views

Relativistic Doppler effect derivation

This is about a step in a derivation of the expression for the relativistic Doppler effect. Consider a source receding from an observer at a velocity $v$ along the line joining the two. Light is ...
5
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3answers
1k views

How do Doppler Effect and Time Dilation differ?

Above, I have drawn a diagram showing Doppler Effect (here we are using space-time but in a non-relativistic sense. Time and distance are the same for A and B). Edit: I am adding a relativistic ...
0
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2answers
69 views

Is time a coordinate or a parameter in Newtonian mechanics?

In classical (Newtonian) mechanics we only ever seem to consider 3-dimensional space, with physical quantities being represented by 3-vectors. My understanding for this is because in classical (...
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1answer
2k views

4-momentum of photon

The 4-momentum is defined as $p=mU$ where m is the rest mass of the particle and $U$ is the 4-velocity. Now I am confused as to how this applies to a photon for which one can't define $U$ since there ...
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2answers
51 views

Motivation for usage of 4-vectors in special relativity

I understand that if one considers a 4-dimensional space-time from the outset then 4-vectors are the natural quantities to consider (as opposed to 3-vectors as in Newtonian mechanics), since the ...
3
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1answer
67 views

Relativistic correction to Hydrogen atom - Perturbation theory

Given the relativistic correction $$ H_1' = - \frac{p^4}{8m^3 c^2} $$ to the Hamiltonian (i.e. a perturbation), what does it mean when $[H_1', \mathbf{L}] = 0$? The book I'm reading says this implies ...
2
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2answers
106 views

Is acceleration relative in relativity?

Suppose a box A is moving relative to a Box B, then by time dilation equation if I take 1 sec passed for an observer in A then for an observer in B will be little longer. Now if I suppose that the box ...
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0answers
62 views

Galileo's ship experiment with a laser pen instead of a rock

Ship's mast experiment with the boat moving at speed v: If a rock is dropped from the mast, then for an observer inside the boat they will see this: For an observer outside the boat and on the ...
0
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1answer
39 views

Momentum equation of a beam hitting a stationary target to create antiprotons

I'm struggling with the solution of a physics exercise which is to calculate the minimum energy needed to create antiprotons when a proton beam scatters on a stationary proton target: $$p + p \...
1
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2answers
75 views

Definition of the Lorentz transformations [closed]

Until very recently I believed that the Lorentz transformations were defined as "the transformations that carry one inertial reference frame into another". In Wikipedia's page we find something along ...
3
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1answer
79 views

Homogeneity and isotropy and derivation of the Lorentz transformations

In deriving the Lorentz transformations I have found (from reading a few different sets lecture notes) that it is argued that they must be linear and thus there general form must be $$x'=Ax+Bt,\quad t'...
1
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0answers
69 views

Zeroth component of 4-momentum and relativistic energy-momentum relation

As I understand it one is forced to use 4-vectors since we require objects that transform as vectors under application of Lorentz transformations and 3-vectors do not (technically they do under ...
0
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0answers
49 views

Speed of the Coulomb Field Measured To Be “Infinite”

The paper "Measuring Propagation Speed of Coulomb Fields" by R. de Sangro et al points out that: ...the Lienard-Weichert retarded potential leads to the same formula as the one obtained assuming ...
0
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0answers
31 views

Inertial coordinate systems [duplicate]

In Newtonian mechanics, by the following two assumptions: (i) The time is absolute. (ii) The length is absolute. it is easy find the relations betweem two coordinate systems with uniform motion ...
1
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0answers
64 views

Path integral (sum over paths where $v>c$) [closed]

The path integral formalism is used to get for example the propagator of particles. In this formalism we integrate over all mathematically possible paths (and weight them with the non-relativistic ...
2
votes
2answers
63 views

How do we determine if a certain physical quantity is a vector?

For instance in Newtonian physics we treat position of objects, displacements, velocities, forces, momenta, angular velocities etc all as vector quantities (little arrows in space which have a certain ...
0
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3answers
47 views

Frames of reference, relativity, and a ball thrown in the air

Ever since my high school physics days I found relativity fascinating but I don't think I have great insight even into special relativity. For example, in almost every lesson or video they give an ...
2
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1answer
82 views

What is really sought when we purpose Einstein's postulates in Special Relativity?

Special Relativity can be motivated by looking at Maxwell's Electrodynamics and noticing that there is some kind of inconsistency between it and Newtonian Mechanics. Indeed, as Einstein pointed out on ...
17
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3answers
4k views

Deriving the speed of the propagation of a change in the Electromagnetic Field from Maxwell's Equations

I've been told that, from Maxwell's equations, one can find that the propagation of change in the Electromagnetic Field travels at a speed $\frac{1}{\sqrt{\mu_0 \epsilon_0}}$ (the values of which can ...
3
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2answers
916 views

Exact definition of momentarily comoving reference frame (MCRF)

Consider a particle $P$ in the framework of special relativity with position $r(t)=(ct,x(t),y(t),z(t))$ respect to an inertial reference frame $\Sigma=(ct,x,y,z;O)$. I need to know if the following ...