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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What if a particle falls into the center of a central field? [closed]

Given a central field $U(r)$ satisfies $U(r) \rightarrow -\infty$ when $r \rightarrow 0$, then What if a particle falls into the center of a central field? Can you help me analysis this question in ...
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1answer
1k views

Lorentz Invariant Integration Measure [closed]

When we canonically quantize the scalar field in QFT, we use a Lorentz invariant integration measure given by $$\widetilde{dk} \equiv \frac{d^3k}{(2\pi)^3 2\omega(\textbf{k})}.$$ How can I show that ...
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2answers
626 views

Spacelike and timelike photons

I know the definition of space-like and time-like intervals. How do you show that in some reaction the virtual photon(s) is spacelike/timelike? On page 191 Peskin and Schroeder, it says "since ...
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2answers
147 views

Distance travelled in spaceship Newton vs Einstein

If you get in the canonical 1G windowless spaceship and accelerate for 5 years as determined by your trusty wristwatch, then decelerate for 5 years, then decide its time to see where you are would the ...
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5answers
330 views

Could velocity be taken as fundamental instead of time?

In physics time and length are taken as fundamental in the SI system and, as it seems, in the thinking of physicists. Could one instead take velocity, with c as its unit, together with length as ...
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0answers
225 views

Non-zero charge density due to Lorentz contraction in current carrying wires

In trying to answer this question I came across the following problem. The original question relates to the idea that what looks like a magnetic field in one reference frame, ends up as an ...
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2answers
736 views

current in wire + special relativity = magnetism

Current in wire + moving charge next to wire creates magnetic force in the stationary reference frame OR electric force in the moving reference frame from special relativity due to change in charge ...
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8answers
25k views

How does velocity cause time dilation?

I've been trying to learn about the speed of light and time dilation, but I'm at an impasse. The presented facts say that if I travel around the solar system at 50% the speed of light and then come ...
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0answers
50 views

Momentum of light in medium [duplicate]

Maybe this has been asked before, but I didn't find anything about it. I am wondering about the momentum of light in media with refractive index n>1 (so to say, not in vacuum). There are two ...
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1answer
509 views

Lorentz transformation of the Spinor Field

I'm reading chapter 3 of Peskin and Schroeder and am stuck on page 43 of P&S. They have defined the Lorentz generators in the spinor representation as: \begin{equation} S^{\mu \nu} = ...
2
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1answer
148 views

Reduction in gravity from photon exchange

Let's say you have two bodies at are held at rest relative to each other exchanging (real, not virtual) photons back and forth. Then we let them go (maybe push them apart slightly), so they will ...
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1answer
103 views

Why is general relativity only formulated in continuum terms?

So, when we are discussing Newtonian mechanics, we treat particles as point particles. In continuum mechanics, which I understand to be a version in which mass is continuously distributed, we have ...
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2answers
983 views

How is the speed of light an absolute maximum speed in the universe? [closed]

Under the heading which came first, the chicken or the egg, which came first: the maximum velocity of electrons orbiting the atom, or the speed of light as the maximum velocity limit? Is it possible ...
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4answers
199 views

Defining simultaneity with a central light vs with clocks

So there's the classic example of the relativity of simultaneity involving two people on a train, with a light source exactly between them. Moments after the lights turn on, observers on the train ...
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2answers
184 views

Is there an official name for “Lorentz Pairs” like energy and momentum?

In learning about relativity I've noticed that in the construction of Lorentz invariants (specifically four-vectors) two physical quantities that were previously considered distinct are instead ...
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0answers
50 views

Do two synchronous clocks have simultaneous indications?

Considering two clocks, $C$ and $D$, which were at rest to each other throughout a sufficiently extended trial, and given their time parametrizations $t_C : {\text{ ordered set of}}C{\text{'s ...
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1answer
285 views

What do subatomic particles look like for a 'speed of light - observer'?

Let's say that an observer is moving with the speed of light relatively to an atom that he wants to look into. He has equipment that precise that he can observe the atom and what is inside. From ...
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1answer
35 views

Flat space current conservation sign confusion

It is said that in Minkowski spacetime, the current conservation law for the number current $N^\mu$ where $N^0$ is the number density and $N^i, i=1,2,3$ is the particle flux in the $x^i $ direction, ...
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1answer
194 views

Properties of Lorentz transformation generator?

In chapter 2 of Srednicki, the author defines: $$ U(1+\delta \omega) = I +\frac{i}{2h}\delta \omega_{\mu \nu} M^{\mu \nu} $$ where the $M^{\mu\nu}$s are hermitian operators and are the generators of ...
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1answer
47 views

Does a “midpoint between” 2 members of an inertial system belong to the same IS?

This answer to a recent question related to Einstein's thought-experimental definition of (how to determine) simultaneity contained the following statement: Suppose two people, $C$ and $D$, stand ...
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1answer
80 views

How to make appropriate statements concerning simultaneity or sequence of pitches

This answer to a recent question related to Einstein's thought-experimental definition of (how to determine) simultaneity contained the following statement: Suppose two people, $C$ and $D$, stand ...
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1answer
135 views

Lorentz transformation - need a little clarification

So the question states: A's and B's systems are related by the standard Lorentz transform. B simultaneously fires off two photons from transmitters distance D apart along the x' axis, and in the ...
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0answers
95 views

What is wrong in following arguments about connection of local gauge invariance and causality?

There is a question and corresponding downvoting of my answer, so I decided to ask this question. There is my answer on it: "...The most theories of free fields are invariant under global gauge ...
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0answers
65 views

Time reversal invariance and statistics

To what extend does the behaviour of time reversal invariance depend on the statistics of the particle under consideration? More explicitly: To what extend does the action of the time reversal ...
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1answer
257 views

Is $E=mc^2$ false?

Recently, I found a YouTube video saying that $$E=mc^2$$ is false. It says that the real one is $$ E^2=m^2 c^4 + p^2 c^2 $$ where $E$: energy, $m$: mass, $c$: speed of light and $p$: momentum. Is ...
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1answer
497 views

The example of relativity of simultaneity given by Einstein

I understand (supposedly) the mathematics concerning the relativity of simultaneity in Special Relativity, but I have a nagging question regarding the original example given by Einstein supporting it ...
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0answers
176 views

does light beam bend when moving with a constant velocity?

I'm studding special relativity and there is a famous example where there is a moving train witch has a light source on its floor and a mirror attached to its roof. an observer in the train sees a ...
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2answers
389 views

twin paradox question

I'm trying to wrap my mind around the twin paradox, but I can't figure out this one problem from my textbook. It uses the relativistic Doppler effect to demonstrate how the paradox works. The first ...
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2answers
128 views

Length contraction as $v>c$

What would theoretically happen to an observed object's length (let it be a 5 meter line) moving at some speed greater than that of light in a straight path?
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1answer
2k views

How do I derive the Lorentz contraction from the invariant interval?

Reviewing some basic special relativity, and I stumbled upon this problem: From the definition of the proper time: $$c^2d\tau^2=c^2dt^2-dx^2$$ I was able to derive the time dilation formula by using ...
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1answer
270 views

Is mass an inherent property?

Suppose I have an electronic weighing machine placed in a uniform gravitational field. Now I put a mass above it and register the reading. Now I give the system (mass + machine) an impulse so that it ...
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4answers
3k views

What is so special about speed of light in vacuum?

I will try to be as explanatory as possible with my question. Please also note that I have done my share of googling and I am looking for simple language preferable with some example so that I can get ...
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4answers
325 views

A question abou $E=pc$ for massless particles

Since photon has no (rest)mass and $$E^2=(pc)^2+(mc^2)^2$$ we derive that $E=pc$ for particle with no (rest)mass. However, if we transform the non-relativistic formula for kinetic energy ...
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1answer
391 views

Speed of approach between image and object

A plane mirror image approaches the object at the same rate the object approaches the mirror. So the speed of approach is twice the speed at which the object approaches the mirror. If the object ...
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172 views

What axiomatizations exist for special relativity?

Einstein 1905 gives the following axiomatization of special relativity (Perrett and Jeffery's translation): The laws by which the states of physical systems undergo change are not affected, whether ...
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4answers
459 views

Is special relativity axiomatic?

Can special relativity be somewhat described by the following statement? If the speed of light is a universal constant, and if light can be placed in separate frames of motion, then time must be ...
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3answers
732 views

The reference frame of $c$

I don't have a lot of knowledge of special relativity and associated topics; some of the few things I know are that "all motion is relative" (that is, there is no 'stationary reference frame'), and ...
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2answers
721 views

The relation between electric field and magnetic potential

In every electrodynamics book there is one chapter on special relativity which includes one section about" covariant formulation of electrodynamics" which uses tensor to describe the two fields and ...
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0answers
123 views

Does light initially accelerate? [duplicate]

Light travels with a speed of $3\times10^8{m\over s}$. My question is that was the light initially accelerating or it archived the speed in an instance? If it was accelerating then why it did not ...
4
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1answer
844 views

Galilean invariance of a subset of Maxwell equations

I read in Feynman's proof of Maxwell equations the statement that the subset of Maxwell equations comming from the Bianchi identity: $$ \nabla \cdot {\bf B} = 0, \quad \nabla \times {\bf E} + ...
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1answer
249 views

Magnetic induction in Relativity

As we know magnetic phenomenon is a mere relativistic effect.My question is how to explain the magnetic induction in a relativistic manner?
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1answer
213 views

Classically, how can an electron orbiting a proton radiate given its relativistic energy

In classical relativistic Electrodynamics, we are often told that any accelerating point charge inherently radiates (Bremstrallung). (This is the basis for the need for a QM conception of electrons.) ...
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2answers
1k 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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2answers
717 views

Why moving charges causes Magnetic Field (module and direction)?

Why an constant electric current in a wire produces a magnetic field, that circles that wire? I know that this question was posted before. However, all answers talk about Maxwell equations, axioms, ...
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2answers
401 views

Can a scalar field model gravity? How accurate would be the results? Are there any difficulties with such a model?

Newtonian gravity can be described by the equation: $$ \nabla^2 \phi = 4 \pi \rho G $$ where $\rho$ is the mass density, $\phi$ is the gravitational potential, and G is the universal gravitational ...
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6answers
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If I am travelling on a car at around 60 km/h, and I shine a light, does that mean that the light is travelling faster than the speed of light?

The title says it all. If I was on a bus at 60 km/h, and I started walking on the bus at a steady pace of 5 km/h, then I'd technically be moving at 65 km/h, right? So my son posed me an interesting ...
4
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4answers
1k views

Why acceleration is not relative in General Relativity?

I was thinking of it, If I say: "I'm moving at a velocity $v_1$ relative to a reference frame $M$ then the acceleration will be the derivative of $v_1$ relative to the reference frame $M$." In other ...
2
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2answers
228 views

How is relativity equation approximated

What is the technique with which I can approximate the equation $$\frac{mc^2}{\sqrt{1-(\frac{v}{c})^2}}-mc^2$$ when $v\ll c$? Any hint would be much appreciated
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1answer
218 views

Why there is the requirement for derivatives no higher than second order in free quantum field equations? [duplicate]

Why there is the requirement for derivatives no higher than second order in free quantum fields equations? We can get the equations for the free fields of an arbitrary spin by using the requirements ...
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1answer
101 views

Finding the EOM for a charged relativistic particle

For an exercise sheet of a course in general relativity I'm asked to derive the equations of motion for a charged particle in an EM-field given by a potential $A^\mu$. I am give the action: $$S = ...