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Why do we use two stationary clocks to compare the time elapsed in one moving clock?

Because it is the clearest way to show the underlying physical effect. If you try to compare the elapsed time on one clock in one frame with a single clock in another frame, you can only do it by ...
Marco Ocram's user avatar
0 votes

What if an object is approaching us at near the speed of light?

I don't think there's any surprise or contradiction here. Imagine that you were looking with a super-duper telescope at that object and see it 100 light-years away turning on its engines. At that ...
Nadav Har'El's user avatar
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1 vote

What if an object is approaching us at near the speed of light?

If the object turned on its headlights when passing a milestone 100 light years away in the Earth's frame, then the object would arrive at Earth not long after you had first seen its blue-shifted ...
Marco Ocram's user avatar
5 votes

How is special relativity explained by general relativity?

Let me expand on the comment by WillO. In order to be able to formulate newtonian mechanics we grant Pythagoras' relation: $$ r^2 = x^2 + y^2 + z^2 \tag{1} $$ Interestingly, back when Isaac Newton ...
Cleonis's user avatar
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Does time dilation will only reflect on clock only after we accelerate for the return journey in a round trip

You are mixing up ideas here- I suspect three of them, namely time-dilation, the Doppler effect and the twin paradox. Let's take time dilation first. The object moving to the right is time dilated in ...
Marco Ocram's user avatar
3 votes

Twin paradox without accelaration, having been together or making any semblance of a roundtrip

I'm not sure how this is a twin paradox situation. You simply have two synchronized clocks a distance $L$ apart and at rest with respect to one-another, and a moving clock which goes from one to the ...
J. Murray's user avatar
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6 votes
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Understanding orthochronous, proper and improper Lorentz transformations

You've incorrectly written down your components. They are: $\det \Lambda = +1$ and $\Lambda^0{}_0 \geq 1$: These are the proper orthochronous Lorentz transformations. $\det \Lambda = +1$ and $\Lambda^...
Prahar's user avatar
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3 votes

Can we regard metric as the Higgs field of gravity?

We will be using Trautman's unifying formulation of both general relativity and Yang-Mills gauge theories as theories of a $G$-principal bundle $P\to M$ over spacetime $M$. For an exposition of this ...
ACuriousMind's user avatar
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1 vote
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Understanding spinors, double cover and professor's expanation

Why is $Spin(1,3)$ the double cover of $SO(1,3)$? You have first to realize that $Spin(1,3)$ is related to how spinor/fermion $\psi$ transforms, whereas $SO(1,3)$ is related to how vector $X$ ...
MadMax's user avatar
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1 vote

Thermodynamics and Special Relativity

What happens to the temperature of a body (not in the body frame) as it approaches the speed of light? As discussed in this article, no one can tell you the answer, at least unless you choose a ...
hft's user avatar
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0 votes

Relativistically, shouldn't a current loop produce an electric field that is negative perpendicular to the loop and positive in the plane of the loop?

So what happens is that the number of field lines emanating from a charge does not change if the charge accelerates, but the field lines concentrate to some direction. So in the case of an infinitely ...
stuffu's user avatar
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Seeming contradiction between Lorentz equations and length contraction

I think that in both frames of reference (the ships and the astronauts) the ship fires its photon at the moment when the ship and UFO are symmetrically positioned around the astronaut. This is false. ...
naturallyInconsistent's user avatar
0 votes

Ehrenfest paradox and the link to general relativity

In order to demonstrate that c is a constant Einstein needed to show that two two coincidental ligt beams movind in opposite directions to one another still have the velocity of c (one in reference to ...
Jimski's user avatar
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-1 votes

Pair production in vacuum

Maybe we should clarify here something subtle that can cause confusion among readers by other information sources. You are right, spontaneous pair production of stable particles (i.e. an electron-...
Markoul11's user avatar
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4 votes

What is the time dilation due to acceleration?

There are two answers here, depending on your viewpoint. Inertial observer An inertial observer sees a rocket whose occupants experience constant acceleration, what motion does the inertial observer ...
CR Drost's user avatar
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3 votes

What is the time dilation due to acceleration?

The problem here is that the phrase 'time dilation' has a particular meaning which refers to the difference in the time interval between two events in an inertial frame in which they occur in the ...
Marco Ocram's user avatar
8 votes

What is the time dilation due to acceleration?

There is no time dilation due to acceleration. Kinematic time dilation is due to velocity in an inertial frame and gravitational time dilation is due to gravitational potential.
Dale's user avatar
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1 vote

Cannot understand this identity between kronecker and metric tensor

Assuming that you mistyped and $\alpha$ is actually meant to be $\sigma$, then you obtain this relation as follows: \begin{align*}\omega_{\rho \sigma} \eta^{\rho\mu} \delta^{\sigma}_{\nu} &= \frac{...
Octavius's user avatar
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How to see that the electromagnetic stress-energy tensor satisfies the null energy condition?

First notice that $$k^\mu k^\nu \eta_{\mu\nu}F_{\rho \sigma} F^{\rho\sigma} = k_\mu k^\mu F_{\rho \sigma} F^{\rho\sigma} = 0 \,.$$ Then notice that $$ k^\mu F_{\mu\rho} k^\nu F^{\rho}{}_{\nu} $$ is ...
my2cts's user avatar
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0 votes

A problem of relative time when two observers in different frame of reference try to calculate the time experienced by another object

You are making the mistake of thinking that time dilation means that a clock in one frame runs more slowly than a clock in another, which is just not true. All good clocks in SR run at the same rate. ...
Marco Ocram's user avatar
0 votes

Thought experiment in Mach's principle - Can a void universe be considered with special relativity?

I believe that an empty spacetime would not be flat because a positive cosmological constant is a property of the vacuum. The rate of cosmic expansion is accelerating because the expansive force of ...
rjpetti's user avatar
1 vote

What Do We Envision the Fabric of Space to Be? Physical or Immaterial?

Whatever spacetime is, we have to grant that it has the capacity to support propagation of gravitational waves. The LIGO observatory registers the passage of gravitational waves. The frequency range ...
Cleonis's user avatar
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0 votes
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Is there a mistake in this special relativity question? Partial derivative

It looks like the RHS should be $0_{\beta}$, but nobody does that. Compare to the homogenous field equation(s): $$\partial_{[\alpha}F_{\beta\gamma]}=0$$
JEB's user avatar
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0 votes

Hall voltage vs frame dependent electric field in conductor

In both cases - Hall voltage due to current flowing in magnetic field, and voltage due to conductor moving in magnetic field - are due to separated charges, a polarized free charge distribution on ...
Ján Lalinský's user avatar
4 votes
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The effects of light needing to reach observers from observed objects

Some of the teaching of relativity is awful, and a common problem in text books is that they are written in a way that blurs the meaning of the word observer. As you point out, a literal observer ...
Marco Ocram's user avatar
4 votes

"Pure Energy" in special relativity and why does the rest energy follow from a derivation at the speed of light?

As a consequence of the postulates of special relativity, it can be shown that the total energy possessed by a moving object is: $$E=\frac{mc^2}{\sqrt{1-\left(\frac v c\right)^2}}=\gamma~ mc^2$$ If we ...
RC_23's user avatar
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0 votes

Analyticity and Causality in Relativity

But Aharonov, in page 66 of his book " Quantum Paradoxes " seems to agree with your first thought because he says literally: If we change a quantum wave at one spacetime point, the rest of ...
Evariste's user avatar
3 votes

Lorentz transform causes Faster than light motion for Spacelike-separated object?

It's worse than that, and you don't even need relativity to see why! Your first two points are $(x=0,t=0)$ and $(x=1,t=0)$. So $dx/dt=1/0$, which is infinite. In other words, a stationary rod has ...
WillO's user avatar
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-1 votes
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Can we regard metric as the Higgs field of gravity?

A version of this idea is discussed at the end of section 1.1.1 of https://inspirehep.net/literature/1823987 which also cites the following as precursors https://inspirehep.net/literature/150700 https:...
Mitchell Porter's user avatar
1 vote

Continuity equation as a four-divergence. Possible misunderstanding of contravariance, covariance, or metric signature

You should use the Minkowski metric to give the sign you need. Zangwill does it a different way, using ict. The problem is that no one else does it that way, so you can't compare with other references....
Jerrold Franklin's user avatar
4 votes
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Continuity equation as a four-divergence. Possible misunderstanding of contravariance, covariance, or metric signature

What am I misunderstanding and how can I correct it? Equation $(1)$ is wrong. With your definition of $j$ we clearly obtain $$\partial_\mu j^\mu= \frac{\partial\rho}{\partial{ t}}+ \boldsymbol{\...
Filippo's user avatar
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-1 votes

Special Relaticity and Uniform Circular Motion, a (Seemingly) Elementary Problem?

One approach might be to assume Y's path to be a regular n-gon, and calculate the time recorded assuming Y is in free float when in travelling in each of the n-sides, then calculating the limit as n ...
stuffu's user avatar
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1 vote

Does a photon in vacuum have a rest frame?

I am going to approach the matter otherwise. I do not dispute the arguments made in answers in [1] or answers in [2]. However, based on my learning style, these arguments do not work for me. This is ...
Michael Levy's user avatar
0 votes

Time Dilation According to Stationary Object

Einstein's view of special relativity can lead to many paradoxes like this , the correct view of special relativity is the Minkwoski metric.It says that the spacetime interval is the same for all ...
Root Groves's user avatar
0 votes
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Time Dilation According to Stationary Object

Usually in physics we talk about events as being instantaneous, so if you have an event in the everyday sense that takes 2 seconds we would treat that as an interval between a pair of events, namely a ...
Marco Ocram's user avatar
2 votes
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Explaining Faraday's Law With Lorentz Transformations of $E$ and $B$ Fields

Just a small detail, Faraday's law is about inducing electromotive forces (emf's), not currents. To make the link between current and emf, you'll need to go beyond Faraday's law and make some ...
LPZ's user avatar
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-1 votes
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Why an accelerated electron can emit a photon if energy is conserved?

"Emission of a photon" is a figure of speech used either to refer to integral terms/diagrams in mathematical calculations in QED, or to refer to a simplified and flawed/inaccurate mechanical ...
Ján Lalinský's user avatar
0 votes

Why an accelerated electron can emit a photon if energy is conserved?

Either the acceleration is low, energy of emitted photon is low, and time when the photon is emitted is uncertain, and the speed at the time of the event of emitting is uncertain, or the acceleration ...
stuffu's user avatar
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3 votes
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Commutation of the Hamiltonian with the generator of boost

...From the above, we see that $$\{M^{0i}, H\} = P^i$$ No, you should have: $$ \{M^{0i}, H\} = -P^i $$ ...Why is it that $\frac{d}{dt}M^{0i}\neq \{H, M^{0i}\}$? Can someone please explain? It's ...
hft's user avatar
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1 vote
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From Faraday's Paradox to the design of a One Piece Axial Flux Motor

Yes, there is a separation of charges. See the Hall effect, which in principle is no different from the Lorentz force. What you are describing is an electric generator. For the generator to work ...
HolgerFiedler's user avatar
0 votes

One-Way Speed of Light and the Big Bang

If the speed of light is not isotropic, then there would be a discrepancy as to the age our distant alien friends would assess the universe (14.8 billion years old) when they receive the message (...
Dale's user avatar
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2 votes

Definition of four-velocity: why define it with proper time of the object?

One thing that the other answers haven't mentioned is the Hamiltonian formulation of special relativity. The vector transformation property of the four velocity can be obtained by differentiation wrt ...
Ryder Rude's user avatar
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0 votes

One-Way Speed of Light and the Big Bang

… the Big Bang did happen everywhere all at once. <…> Can this be used to synchronize clocks across a frame? Yes. Here is a paper that provides definition for such cosmological time function: ...
A.V.S.'s user avatar
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3 votes
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Which experimental setup replicating Michelson-Morley experiment had the longest path of light?

Experimental setup in Ligo uses replica of Michelson Morley interferometer with additional etalon used to increase the optical path length .The effective path length along each arm by adding etalon ...
Questioningmind's user avatar
2 votes

Sending photons in opposite directions in a closed universe leads to different proper time before we see them again?

The chart map that you have used does not cover the entirety of the spacetime because the underlying (1+1)D manifold's global topology is $\mathbb{R}\times\mathbb{S}$ while the topology of the chart ...
S.G's user avatar
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0 votes

Sending photons in opposite directions in a closed universe leads to different proper time before we see them again?

The metric for rotating reference frame is:$$ ds^{2}=\left(c^{2}-\omega^{2}r^{2}\right)dt^{2}-2\omega r^{2} d\phi dt-dr ^{2}-r ^{2}d\phi ^{2}\;\;\;\; \,(*)$$ with $\;r\omega=v$ As in any stationary ...
The Tiler's user avatar
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4 votes

Sending photons in opposite directions in a closed universe leads to different proper time before we see them again?

Nothing in this problem depends essentially on the spacetime signature, so consider instead a Euclidean cylinder, which you might take to be the subspace of $\mathbb R^3$ (with standard Euclidean ...
benrg's user avatar
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3 votes

Sending photons in opposite directions in a closed universe leads to different proper time before we see them again?

If the circumference in the frame of a comoving FLRW observer who observes no dipole in the CMB was x lightyears, the circumference in the frame of an observer travelling with v relative to the ...
Yukterez's user avatar
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1 vote

Can I find $\frac{dm}{dt}$ where $m$ is the relativistic mass of a particle?

Your assumption that $F = m \frac{dv}{dt}\gamma$ is not correct. You should instead have $$F = \frac{d}{dt} (\gamma m_0v) = v\frac{dm}{dt} + m\frac{d}{dt}(v)$$ where note $m = \gamma m_0$. However, to ...
S.G's user avatar
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0 votes

Is Bohmian mechanics really incompatible with relativity?

Yes, for a very basic reason: Relativity has $E = mc^2$ - which sets the stage for particle creation and annihilation - processes where the particle number changes. The whole point of Bohmian ...
NinjaDarth's user avatar
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