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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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22 views

Why is Velocity defined as 4-vector in Relativity?

In Classical Field Theory class my professor first defined velocity as $$v^{\mu} = \frac{dx^{\mu}}{dt}$$ where, $ \frac{dx^{0}}{dt} = 1$ Then he said it doesn't transform like $${v^{'}}^{\mu} = L^{\...
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3answers
92 views

Faster-than-light communication using Taylor's theorem?

I was thinking about Taylor's theorem and how if a function $f(x)$ is analytic at a point $a$ and one can measure all the derivatives at $a$, $f^{(n)}(a)$ then one knows the complete behaviour of the ...
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4answers
61 views

Hypothetical mass-energy equivalence

2 questions: Hypothetically, if in an imaginary universe, the speed of light squared were 90% or 110% of what is is in our universe...would the math require another constant such as 1.1 or .9 next ...
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1answer
33 views

Falling towards black hole with lorentz factor

Falling at rest from infinity to black hole. I calculated the velocity when an object fall from infinity to a black hole or vicinity of one. $c\Big(1-\frac{2GM}{c^2r}\Big)\sqrt{\Big(\frac{2GM}{c^2r}\...
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1answer
22 views

How to find time transformation given certain coordinate transformations?

Let’s say that you’re given a coordinate transformation (say, from Cartesian to spherical), how do you find the time coordinate transformation? Or is the time coordinate the same if not otherwise ...
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0answers
28 views

The Lorentz symmetry and structure of the universe

I know that the Lorentz symmetry group is one of two (other is Galilean) that is compatible with the homogeneity and isotropy of the universe. A consequence of Lorentz symmetry is that the speed of ...
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0answers
51 views

An object near the speed of light can become a black hole at high speeds? [duplicate]

If we use the Lorentz equation for the length contraction, and the Schwarzschild equation for the lightlike sphere, we can calculate the velocity for the object to form a black hole: $ \Delta x^{'}=\...
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3answers
131 views

QFT = QM + SR? for everyday people

I understand that originally QM was a successful theory that has been experimentally proven, and was non-relativistic. Now its successor was said to be QFT. Later on, it incorporated effects of SR, ...
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2answers
86 views

Yet another question about time dilation

I thought I had understood special relativity, at least the idea of the clocks with light pulses and rods from the book The Meaning of Relativity. But going through the basic illustration of the time ...
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1answer
113 views

Do people around the globe have different rest frames?

This is an intuition check. Maybe I'm starting to get it, or maybe I'm not. I apologize ahead for my potential ignorance and naivety, but I've been trying to curve the space in my head around special ...
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1answer
52 views

Generalization of the Coulomb Force to the Lorentz-Force - Is it “guessing”?

it's me again, and I'm still stuck with the paper Generalization of Coulomb’s law to Maxwell’s equations using special relativity by Kobe, like in my previous question. My problem now lies in ...
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1answer
58 views

Light has Mass or not? [duplicate]

If there is no mass for the light, it should penetrate. But light is not penetrating through solid medium. If the speed of light is constant there is some work should be done to maintain the speed. ...
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0answers
53 views

Name of vector related to metric tensor?

Suppose we have a locally Minkowskian metric $g_{\mu \nu}$, and we explicitly diagonalize it: $$ g_{\mu \nu} = U_\mu^\lambda (\delta_{\lambda \kappa} - 2 \delta_{0 \lambda} \delta_{0 \kappa}) U_\nu^\...
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0answers
17 views

How long would it take sunlight to reach our spaceship? [closed]

If we are on a spaceship that left the Earth at 0.9999c, how long would it take for the light from the sun to reach our spaceship - from our point of view (on the spaceship)? From Earth, wouldn't it ...
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1answer
52 views

Proof that an observer cannot be in two places at once [closed]

If you went at light speed, you would literally and instantly teleport from the sun to the Earth. Any slower would create the perception of time. In other words, we appear frozen to the light (or ...
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1answer
56 views

Lorentz transformations in non-Euclidean geometries

I have an assessment/investigation coming up in my math class and I plan to investigate Lorentz transformations in geometries other than Euclidean such as spherical or hyperbolic. For spherical/polar, ...
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2answers
49 views

Energy mass equivalence

Regarding $E=mc^2$, in a hypothetical parallel universe. If in that universe the speed of light squared were let’s say 10% slower, would everything still work but just slightly different? Or would an ...
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0answers
36 views

Real light-time in special relativity & the Lorentz Transformation

In special relativity, why does $x_1 = vl$, where $x_1$ is a position coordinate for the inertial reference frame $K$, $v$ is the velocity of the inertial reference frame $K'$ relative to $K$, and $l$ ...
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0answers
27 views

Lorentz transformation of absorption coefficient

My question is about the properties of the Boltzmann equation under Lorentz transformations. In Misner, Thorne, Wheeler (chapter 22, eq. 22.47) it is shown that the collisionless Boltzmann equation ...
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2answers
58 views

Difficulties Understanding “Summary” of Dirac $\gamma$-Matrices using Minkowski Metric

While studying the Dirac equation, $$\left(i\gamma^{\mu} \partial_{\mu} - m\right)\psi = 0$$ I have been finding difficulty understanding the following summarisation of the algebra that the $\gamma$-...
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0answers
40 views

Argument for a priori discovery of special relativity [closed]

Time are those dimensions along which information is conserved. Space are those dimensions along which it is not. Information needs time to travel in space. Therefore, information has a speed limit ...
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1answer
112 views

Check where am I wrong. Here is how information can be sent faster than light [duplicate]

If I have a very long rigid rod which is of rectangular cross section and small mass. Let it's length be 1 light year and total mass be 1 kg now at one end if I rotate that rod, since the rod is rigid ...
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0answers
94 views

Motion of a particle near a charged plane

Consider a positive charge density in the $x-y$ plane, its electric field is $\vec{E}=\frac{\sigma}{2\epsilon_0}\hat{z}$. At moment $t=0$ a particle with positive charge $q$ begins to move with ...
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0answers
24 views

Theoretical meridian tower - what do You think [closed]

What do You think about theoretical high tower on meridian? Let's say 25 light hours height. Considering three observers, at the bottom, at the top and in space next to the top passing him. The linear ...
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0answers
18 views

To prove the Lorentz invariance of density distribution functions for massless particles in phase space

One defines the density distribution function of a collection of $N$ particles in phase space as follows, $$f(\vec{x},\vec{p},t)=\sum_{i=1}^N\delta^{(3)}(\vec{x}-\vec{x}_i)\delta^{(3)}(\vec{p}-\vec{p}...
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0answers
41 views

Chain rule related to relativistic momentum

I am having trouble deriving the chain rule in the following: $$\frac{\partial}{\partial p^i}=\frac{\partial p_0}{\partial \vec{p}}\frac{\partial}{\partial p_0}+\frac{\partial}{\partial \vec{p}}.$$ ...
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0answers
28 views

Is there a mathematical singularity in the relativistic contraction of valence orbitals as a function of nuclear charge?

I'm looking at Figure 1 on p. 2 of Jansen, "Effects of relativistic motion of electrons on the chemistry of gold and platinum" (2005) (should be a free download). From the bottom curve, there is such ...
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0answers
73 views

Why spatial infinity is a point and not an $S^2$?

First a disclaimer, this question already has been asked here, but as pointed out in comments, more detail was required. So this is a more detailed version. Let $(\mathbb{R}^4,\eta)$ be Minkowski ...
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0answers
28 views

Do relativistically-contracted electron states have the same energy and angular momentum values?

I've been reading that electron bound states are defined by four quantum numbers, $n$, $l$, $m_l$, and $m_s$, respectively the principal quantum number, the azimuthal quantum number, the magnetic ...
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0answers
23 views

Contracted product of matrices with Lorentz indices

Let $\mathbf{A}_\mu$ and $\mathbf{B}_\mu$ be two matrix-valued spacetime vectors, i.e. $(A_\mu)_{ab}$ and $(B_\mu)_{ab}$ and let $\mathbf{C}$ be a matrix in the same space (external to spacetime), i.e....
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1answer
62 views

Generalization of the Gauss' Law to a lorentz-covariant law in Paper of Kobe: Is it “guessed”?

In the Paper Generalization of Coulomb's law to Maxwell's equations using special relativity by Donald H. Kobe, he tries to derive Maxwell's equations by trying to find covariant laws between tensor ...
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3answers
95 views

Problem in understanding energy-mass equivalence

From whatever approach (either from modern approach by Hamiltonian or from Einstein's original approach by considering momentum), we can derive that $p_{i} = \gamma mv_{i}$ and $$H = \gamma mc^2 = \...
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2answers
51 views

Does Wave-Particle duality exist at high speed?

I know that relativistic DeBroglie wavelength is given by $λ = h/γmv$. And $γ ≥ 1$, so at higher speed $λ$ will get shorter and shorter, does this mean it will start behaving like a particle and wave ...
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1answer
44 views

If 2 spaceship fly in opposit directions at 99.9% of speed of light what is the distance between them would be in …?

2 ship fly in opposite directions from each other each one at the 99.9% speed of light relative to the zero point. I assume that at the zero point time in 1 seconds the ship will be 2 light seconds ...
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1answer
36 views

Large Lorentz Boost

I understand the general concept of a lorentz transformation and a lorentz boost. What does it mean for a lorentz boost to be large however? My current guess is that this is referring to a large ...
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2answers
35 views

How can I calculate time dilation between our clock, and clock in satellite? [duplicate]

We know satellite is moving , so there should be time dilation due to motion, also we know due to Earth's Gravitational field there should be time dilation, what should I do, just calculate both of ...
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votes
1answer
60 views

Consolidating maxwells equation with relativity [closed]

I know that maxwells equations are consistent with relativity. The following thought experiment seems to imply otherwise so I am wondering where my mistake lies. Lets say we have some very large ...
2
votes
1answer
159 views

What is kinetic mass of photon?

Today an unusual thought stroke my mind. A mass moving will some velocity has energy called kinetic energy. Everyone knows that nature loves symmetry so why doesn't moving energy ( photon ) has mass ( ...
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0answers
40 views

Simple question about Lorentz matrix

I am confused between orthogonal automorphism and Lorentz matrix : For example, a 2D rotation matrix represents an orthogonal automorphism and its inverse is equal to the transposed matrix. But the ...
0
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1answer
28 views

electric field of a static charge very far away and basic question about electromagnetic waves

I have learned about the electric fields of static charges and those of moving charges. From what I gather(although I have not really learned the specifics) when charges are accelerated they emit ...
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2answers
129 views

Bullet hits Earth at speed $0.99c$ [closed]

According to wikipedia, the speed of the neutrino is as close as we can get to the speed of light with an object with rest mass. As per the comments, since neutrinos come in different energies, let's ...
2
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0answers
41 views

Analytic cotinuation between Minkowskian and Euclidean space, and causality

We can flip between Minkowkian and Euclidean signature by Wick rotation, and it is a well defined operation, provided there are no non - trivial singularities. Now, Unitarity in Minkowskian space ...
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2answers
96 views

How would an event appear to an observer circling it near the speed of light? [closed]

An observer is circling $\text{Point A}$ once per second with a tangential velocity arbitrarily close to the speed of light $\left(v \lesssim c\right).$ When an event occurs at $\text{Point A},$ what ...
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0answers
39 views

So, there is a mistake in veritasium video, and fixed positive charge will attract to DC wire? [duplicate]

(for those, who always don't see an actual question it's in question above) This is the continuation of this Yes, again about the same video of Veritasium question. Short Overview Consider a DC ...
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1answer
47 views

From non-relativistic to relativistic action

There is a derivation of relativistic action that treats space and time symetricaly which is just playing arround with the square of kinetic energy in the non-relativistic action and plugging in speed ...
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1answer
57 views

Meaning of “stars being already dead when we look at them” in relativity

It is a very common statement that when we look at a star, it might already be dead because its light took time to arrive to us. But I am puzzled by this statement, since it seems to assume that we ...
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2answers
71 views

Can we deduce the principle of relativity from some more basic principles?

I was reading "Relativity" by Albert Einstein. In chapter 5 page 14, it is written that If K is a Galilean co-ordinate system, then every other co-ordinate system K' is a Galileian one, when, in ...
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2answers
76 views

“Now-plane” of a particle

I am currently reading the book "Classical charge particle" by Fritz Rohrlich, and I struggle a lot with the appendix "space-like planes and Gauss's integral theorem". He says "the world line of a ...
2
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0answers
18 views

Can we convert energy to mass? [duplicate]

I am in class 12 and I have read Einstein's equation E=mc^2 it relates the amount of energy we can get by destroying a given mass but can we reverse it means can we produce mass from a given amount of ...
-3
votes
1answer
51 views

Why all EM waves have same speed in vacuum? [duplicate]

As far as I know different electromagnetic waves including light have different frequency and wavelength in Vacuum and other medium as well then which factor makes their speed equal to $c$?