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's the connection between the pole contours of propagators and their causality?

Wikipedia distinguishes between three kinds of propagators for a scalar field: The Retarded propagator's contours have $\mathrm{Im}(k^0)>0$ on both poles, so its limit is completely in the first ...
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3answers
80 views

The motion-independent definition of force

I think we must be able to accomodate a definition of a force on some particle which is independent of the motion of the particle, for all kinds of forces, to surely verify the statement like 'force ...
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1answer
79 views

Determining Proper Time and Distance in Relativistic Systems

I'm having a heck of a time understand how to account for time dilation and space contraction in the following problem: A mothership traveling at 0.620 c toward the Earth launches a landing craft. ...
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1answer
41 views

Funny Time Dilation Relation

Today I was curiously calculating/comparing the times of moving observers and the time recorded by a corresponding stationary observer using Einstein's time dilation equation as detailed in Special ...
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1answer
48 views

If the universe is closed, does the twin paradox really matter? [duplicate]

By closed universe, I mean just something like 3-D analog of a closed ring or a sphere. I think it can be one of arguments that the universe must not be closed. Is that right? The paradox is just the ...
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1answer
127 views

How far does a photon move in the 4th dimension when it travels one light second? [closed]

In one second a photon moves 3x10^8 meters through the three spatial dimensions. Light's velocity is 3x10^8 m/s. If the photon moved at all in the fourth dimension, it's velocity would no longer be ...
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5answers
143 views

Simple length contraction question

The question I'm doing states that the nearest star to earth is 4 light years away, as measured on earth and a spaceship can get there in 5 years, as measured by an observer on earth. It asks how long ...
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0answers
41 views

Coulomb Gauge under Lorentz Boost

In the Coulomb gauge for the Maxwell potential we have $$ A^0 = 0 \\ \partial_i A^i = 0 $$ Under an infinitesimal Lorentz Transformation with parameter $\epsilon$, we have $$ A^\mu(x) \rightarrow ...
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1answer
103 views

Integrating elements of a Lie group with respect to parameters of the corresponding Lie algebra

I am working with an operator $\textbf{M}$ that is represented by the Lie group SO(1,3), thus it can be written as, $$ \textbf{M} = \exp{\textbf{L}} $$ where, $$ \textbf{L} = \begin{bmatrix} 0&a&...
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1answer
43 views

Could we find relativistic energy in a simple way?

I asked a couple of questions on mass(-energy) increasing with speed, but there is still a very simple aspect I cannot understand, I hope you can give a simple and direct answer: The formula to find ...
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2answers
54 views

Centripetal effect or curved space time

I think I understand both the centrepedal effect and Einsteins curved space time. However I am confused about which best describes the motion of a planet ( or other orbiting body ). Simply put, does ...
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2answers
72 views

Why don't people use Hamilton's equations for a relativistic free charged particle?

A charged relativistic free particle has the Hamiltonian in general: $$ \mathcal{H} = \sqrt{p^2c^2+m^2c^4}.$$ I read somewhere that says, it is possible to go further and say that the EoM are ...
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2answers
95 views

Do mechanical waves also carry momentum as well as energy? [closed]

I have read that electromagnetic waves carry momentum because they carry energy, while energy is equivalent to mass. So they carry momentum. But this explanation is in the context of special ...
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1answer
104 views

Why is a theory Lorentz invariant if the Lagrangian is Lorentz invariant?

For if I started by trying to make the Hamiltonian Lorentz invariant, I would have failed. Indeed, the Hamiltonian is part of a covariant tensor. But how do I know that the Lagrangian is not a part of ...
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0answers
35 views

Twin Paradox when both twins are moving [duplicate]

Let's say twin scientists A and B start on Earth. Twin A moves east at speed v comparable to light, and Twin B moves west at speed v comparable to light. After some time, they reverse directions and ...
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1answer
79 views

At what speeds does time dilations start to occur?

My question is, is it possible for time dilation to occur at a speed less than that of speed of light?
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1answer
110 views

What happens to a ball spinning with peripheral speed near to the speed of light?

I can't imagine such phenomenon. Would it becomes an ellipsoid, or maybe a straight line?
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1answer
84 views

How is time dilation consistent between both observer?

There is a special variant of time dilation paradox bugs me. Imagine there are 2 small spaceships moving toward each other in constant speed. Each ship has an observer on-board. According to both ...
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2answers
396 views

Stanford: “Objects in spacetime all move at constant speed $c$.” Are they right? [duplicate]

In this Stanford University lecture on Relativity, it is stated: Likewise, objects in spacetime all move at constant speed c in spacetime but if you change its direction, say by moving at speed v in ...
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0answers
25 views

Error in deriving constant acceleration relativistic distance

Bob accelerates away from Carol at proper acceleration $a$ (in light seconds per second), and Carol wants to know how far Bob has traveled when $t$ seconds pass in Bob's frame. Using http://math....
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2answers
75 views

Do Einstein's postulates of relativity emerge from the Minkowski spacetime metric?

Does the constancy of the speed of light for all observers naturally emerge from the Minkowski spacetime metric? Do Einstein's two postulates of relativity emerge from the Minkowski spacetime metric? ...
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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 ...
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1answer
107 views

Can $E=mc^2$ be derived from the Minkowski spacetime metric? $s^2=x^2+y^2+z^2-(ct)^2$?

Can $E=mc^2$ be derived from the Minkowski spacetime metric? $s^2=x^2+y^2+z^2-(ct)^2$? If so, how? Can the equivalence of mass and energy be derived from the Minkowski spacetime metric? Has someone ...
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1answer
74 views

What is the Lorentz group representation for a general spin?

Setup, as I understand things so far: One way to think about where the spin of a quantum field comes from is that it is a consequence of the ways that different types of fields transform under ...
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1answer
30 views

Synchronization of clocks

I have read the book "Introduction to special relativity " by Robert Resnick In the book I have found that "If the distance between the clocks is L, one observer will see the other clock lag his by ...
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1answer
70 views

Plane Wave Solutions of the Dirac Equation

I'm trying to understand the plane wave solutions of the Dirac Equation. But I'm still a newbie on indices notation and contravariant and covariant objects. What I don't understand is how to get: $$(\...
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2answers
141 views

Meaning and logic of Einstein's train thought experiment

This seems to be a recurrent topic but I wasn't able to find any satisfactory discussion about this tought experiment. I will quote the original story from Einstein's and put my doubts inside: Up ...
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1answer
67 views

Force, Mass, Motion? $E = mc^2$

Does any object needs force to move? If 'yes', does the matter needs mass to form a force? These questions arises from me because $E = mc^2$ and $F = ma$ does not relate and one does not agrees with ...
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1answer
60 views

Radiative equilibrium of a relativistic black body

A black body in empty space in the CMB rest frame should (discounting starlight) come to an equilibrium temperature of around 2.7 K. However, if the body is moving relative to the CMB frame, one side ...
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1answer
86 views

Why is the speed of light being invariant and finite in all inertial reference frames?

I understand the basics of Lorentz transformation and Riemann Geometry but I still cannot understand why the speed of light is the same in all inertial references. Has anyone ever researched about ...
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2answers
3k views

Were the Michelson-Morley results a surprise?

How unexpected were the Michelson-Morley experiment results? Did physicists have theoretical reasons to predict that the speed of light would result to be invariant?
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1answer
62 views

How time and speed of light are related? [closed]

I want to know how speed and light and time are related? How will motion with highspeed effect time? I am not a physics student. I want an answer which is free of mathematical relations. I want an ...
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1answer
53 views

Behaviour of Dirac Bilinears

Dirac bilinears transform in the Lorentz indices as, $\bar{\psi}\psi$ scalar $\bar{\psi}\gamma^\mu\psi$ vector $\bar{\psi}\sigma^{\mu\nu}\psi$ 2nd rank (antisymmetric) tensor $\bar{\psi}\gamma^{\mu}\...
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1answer
25 views

How to express in terms of spacetime intervals the average speed of one participant having moved between two suitable others

Given a flat region of spacetime as set $\mathcal S$ of events together with values of spacetime intervals (up to a common non-zero constant) for each pair of events, $s^2 : \mathcal S \times \mathcal ...
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1answer
16 views

How to express in terms of spacetime intervals whether two participants in a flat region were at rest to each other

Given a flat region of spacetime as set $\mathcal S$ of events together with values of spacetime intervals (up to a common non-zero constant) for each pair of events, $s^2 : \mathcal S \times \mathcal ...
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1answer
67 views

Dot product in index notation [closed]

This is a question about a small exercise I am trying to do in order to check if I am correct. Such type of quantities can appear in propagators in QFT. Since I am not an index expert I need some ...
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1answer
71 views

Relativistic acceleration of a rocket?

I'm trying to solve a physics brain-teaser and getting nowhere fast. My knowledge of special relativity is very basic. In the problem a rocket is flying linearly at relativistic speeds (say $v>0....
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2answers
67 views

How does SUSY avoid to create non-Lorentz interactions?

A three-legs fermion interaction or boson absorbing a fermion are things we do not see in QFT because the corresponding terms in the Lagrangian are not Lorentz invariant. But in susy, naively, such ...
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0answers
36 views

Gradient of $ct'$ axis in spacetime diagrams

This is either an unimportant piece of information or it's meant to be obvious, but I can't find anywhere what the gradient of the $ct'$ axis in a spacetime diagram should be. I know that the $ct'=1$ ...
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3answers
161 views

What's the problem with light traveling at speed higher than $c$?

I'm trying to understand how Einstein concluded that time is relative based on thought experiments such as a torch attached to the end of a rocket. Based on answers to questions like this one, this ...
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4answers
125 views

Tensor calculus in special relativity

We say that any function $f(t,x,y,z)$ is a tensor of rank {0 0} because it takes no vectors or one-forms in order to give a real number. But couldn't we have just written the same function as $f(t,x,y,...
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1answer
31 views

Multiple Objects at Constant Speed

Imagine 1 million objects travelling in space, at a constant speed, along an imaginary line. They don't deviate from that line for the sake of this argument. Now, object 1 has a velocity of $v_{1}=1$ ...
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1answer
51 views

How does time dilation occur due to velocity and gravity [duplicate]

I am trying to understand and clarify the way time dilation occurs due to general and special relativity and for which reason. In the case where an object is approaching a planet in free-fall how does ...
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1answer
78 views

Different definitions of the parity transformation for the Dirac spinors

There are two definitions of the parity transformation acting on the Dirac spinors: $\Psi_P = \eta \gamma^0 \Psi$ with $\eta = i$ ($P^2=-1$ as in Srednicki) and $\eta=1$ ($P^2=+1$ as in Peskin & ...
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3answers
235 views

How can we prove charge invariance under Lorentz Transformation?

We have gravitational force between two massive particles and we have electromagnetic force between two charged particles. When special relativity suggests that mass is not an invariant quantity why ...
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3answers
72 views

Mass and frequency of photons [duplicate]

Light is affected by gravity which means light has got mass. Quantum theory tells us that light consists of discrete quanta of energy, which we call photons. These photons have a rest mass of zero (as ...
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1answer
159 views

Can special relativity be derived from the invariance of the interval?

As far as I know, the classical approach to special relativity is to take Einstein's postulates as the starting point of the logical sequence, then to derive the Lorentz transformations from them, and ...
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3answers
165 views

Why did Einstein took speed of light unit or constant in his equation of relativity?

We can find that no object can have speed more than light from Einstein's equation of relativity because if anything have speed more than light then we get -ve value within square root. But why did ...
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2answers
66 views

Planes of Simultaneity on Minkowski diagrams

As seen from a "stationary" reference frame, Why do lines of simultaneity for fast-moving observers run parallel to distance axis instead of perpendicular to the time axis. Obviously, in a regular t ...
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2answers
377 views

How to achieve speeds faster than light? [duplicate]

So, I heard that all speed is relative. And that nothing can travel faster than light. Then I guess it is OK for a spaceship to leave Earth at 0.6c constant speed. And what if an other spaceship were ...