The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.
2
votes
1answer
96 views
Lorentz invariance of the wave equation
I want to show that the 2-d wave equation is invariant under a boost, so, the starting point is the wave equation
$$\frac{\partial^2\phi}{\partial x^2}=\frac{1}{c^2}\frac{\partial^2\phi}{\partial ...
2
votes
0answers
72 views
Fermi Walker vs. Fermi transport
A vector field $f^\mu$ is said to be Fermi-Walker transported along a curve $\gamma$ parametrized with $\tau$ if the following holds $$\frac{\mathrm{D}}{\mathrm{d}\tau}f^\mu = -(a^\mu v^\nu - a^\nu ...
0
votes
2answers
101 views
Inertial Frames of Reference - Description of an Inertial Frame of Reference
An inertial frame of reference is described as being a frame of reference in which the first law of Newton (the law of inertia) holds. This means that all events as described with respect to this ...
0
votes
1answer
77 views
Developments originating from $E=mc^2$
What kind of significant impacts have originated from $E=mc^2$.
Generally, it is regarded as the most famous equation of all time. Except for nuclear energy (fission and fusion) I do not know any ...
0
votes
1answer
92 views
Sign and Four Acceleration Special Relativity
If $ use $(+,-,-,-)$ sign convention then four position, four velocity become positive but four acceleration becomes negative!
$x_{\mu}x^{\mu}=\tau^2c^2,$
$U_{\mu}U^{\mu}=c^2,$
...
0
votes
1answer
44 views
How the effect travel's? [duplicate]
Let us assume that we placed lot's of ball touching each other in a hollow cylindrical tube, now if we push one ball at the end the ball at the other end move's instantly. So how do the information ...
2
votes
1answer
89 views
Angular velocity and the speed of light
So, accelerate a particle to just under the speed of light, then send it round a bend, technically it accelerates due to the change of direction, will its speed exceed or match $c$?
Keep it simple, ...
7
votes
1answer
246 views
What if the binding energy becomes larger than the rest mass?
Looking at the equation for binding energy and mass defect,
$$
B = m_{\text{free}} - m_{\text{bound}} \\
\Rightarrow m_{\text{bound}} = m_{\text{free}} - B,
$$
my question is the following. Suppose ...
1
vote
2answers
118 views
Lorentz boost matrix for an arbitrary direction in terms of rapidity
We have derived the Lorentz boost matrix for a boost in the x-direction in class, in terms of rapidity which from Wikipedia is:
Assume boost is along a direction $\hat{n}=n_x \hat{i}+n_y \hat{j}+n_z ...
0
votes
1answer
73 views
What's the relativistic energy of a moving strained spring as $k\to\infty$
Suppose a spring with stiffness $k$, is strained by constant forces on each end.
In a frame where the strained spring moves at a constant velocity, what's the total relativistic energy of the moving ...
6
votes
3answers
313 views
Can something travel faster than light if it has always been travelling faster than light?
I know there are zillions of questions about faster than light travel, but please hear me out. According to special relativity, it is impossible to accelerate something to the speed of light. However, ...
1
vote
2answers
121 views
what is potential energy in special relativity?
i know what is rest energyE$_o$, total energy , kinetic energy E- E$_o$ and momentum but what is potential energy in special relativity?
5
votes
2answers
207 views
Causality and Quantum Field Theory
I have a problem with proof of causality in Peskin & Schroeder, An Introduction to QFT, page 28. To avoid confusion I use three vectors notation, rewriting the Eq. (2.53) for $y=0$ as follows:
...
8
votes
2answers
365 views
Violation of Lorentz invariance (Lagrangian for particle)
I'm trying to get the relativistic action (or Lagrangian) for a free particle in the case of violation of Lorenz invariance.
Suppose we have the modified dispersion relation:
$$
...
2
votes
2answers
106 views
Why is there no time dilation for frequency of a wave?
Since frequency of a wave is a function of time, then for a particular ray of the wave, why would the frequency remain the same when observed from a moving reference frame? The frequency should change ...
0
votes
1answer
45 views
if i want action to be positive number then it require that $\tau_i$ be bigger than $\tau_f$, isn't it true? [closed]
the action is the length of the geodesic
$S=-E_o\int_i^f d\tau$
we get an action that is minimised for the correct path.
if i want action to be positive number then it require that $\tau_i$ be ...
5
votes
2answers
200 views
Is the curvature of spacetime invariant? Could it be characterized as the ether?
I'm writing a paper for a Philosophy of Science course about GR/SR and I'm wondering if I can (1) characterize the curvature of spacetime as invariant and (2) argue that this is what Einstein referred ...
-2
votes
1answer
62 views
How would time duration and space distance change when we move in the speed of light? [closed]
It is possible to figure out how time duration and space distance change when we are close to the speed of light - but I am not sure what happens to them if we travel in the speed of light.
1
vote
0answers
28 views
Why can't we accelerate to the speed of light? [duplicate]
Why can't we accelerate to the speed of light? It's just a speed and nothing else. Universe also crossed the speed of light at the time of big bang. Is this is just a interpretation or there is any ...
4
votes
2answers
87 views
What are the uses of proper length as a parameter?
Proper time is used to parameterize the world line of a moving particle in a way which is Lorentz invariant, which is elegant and powerful. Since space and time are usually treated on the same ...
1
vote
2answers
81 views
What is the highest speed time dilation has been tested?
What is the highest speed time dilation has been tested?
How close to the Special Relativity prediction did it get?
0
votes
0answers
34 views
Special relativity: Related speed [closed]
If a sheep is moving in a velocity of 2mph related to a train, and the train is moving in a velocity of 2mph related to the ground what is the velocity of the SHEEP related to the ground.Is there an ...
2
votes
1answer
112 views
Life of a photon [duplicate]
I am a student of class 12th and as far as i know when anything reaches about 99.99% of the speed of light it starts traveling in time or time for it slows down so that it don't breaks the speed ...
2
votes
3answers
94 views
Please explain this statement about Lorentz transformations
I'm reading Sternberg's Group Theory and Physics. I have a question about chapter 1.2 Homeomorphisms.
Background:
A Lorentz Metric is defined as $||{\bf x}||^2=x_0^2-x_1^2-x_2^2-x_3^2$
And a ...
9
votes
3answers
338 views
How does a photon experience space and time?
To an an external observer it appears that time has stopped for photon. But this relation is reflexive, so for an observer travelling with the photon it appears the universe has stopped everywhere.
...
1
vote
1answer
90 views
Faraday's Law and Galilean Invariance
In Jackson's text he says that Faraday law is actually:
$$
\oint_{\partial \Sigma} \mathbf{E} \cdot \mathrm{d}\boldsymbol{\ell} = -k\iint_{\Sigma} \frac{\partial \mathbf B}{\partial t} \cdot ...
0
votes
1answer
77 views
Senior High School work on Doppler measurements
Sorry this question is really vague- as a result I'm very confused. Perhaps you can help me make sense of it.
"Radar measurements: Construct a space-time diagram of the radar tracking of an asteroid ...
0
votes
1answer
114 views
Lorentz transformation problem
In the equation (1.18) they omitted the translation vector $a^\mu$, but why?
4
votes
4answers
313 views
Can a photon get emitted without a receiver?
It is generally agreed upon that electromagnetic waves from an emitter does not have to connect to a receiver, but how can we be sure this is a fact? The problem is that we can never observe non ...
0
votes
1answer
24 views
Measuring life through radiation
Dramatic title, I know. But it's shorter than Measuring a person's effective mass through radiation and comparing it to their weighed mass and I figured this would get people's attention.
I just ...
2
votes
3answers
182 views
If time slows down when you move faster, does this give you an “effective speed” different from your proper speed?
Suppose you're travelling at 0.9c toward the sun, and you tag past the Earth and start a clock. Would Lorentz contraction/time dilation cause you to get to the sun faster than (about) 9 minutes ...
3
votes
2answers
125 views
Metric coefficients in rotating coordinates
Let $(t,x,y,z)$ be the standard coordinates on $\mathbb{R}^4$ and consider the Minkowski metric
$$ds^2 = -dt^2+dx^2+dy^2+dz^2.$$
I am trying to compute the metric coefficients under the change of ...
4
votes
1answer
110 views
Mass of a compressed spring
I was wondering if:
The mass of a compressed spring is greater than that of an uncompressed spring
The mass of a body on the surface of the Moon is greater than that on Earth
according to the ...
2
votes
0answers
75 views
Car parking special-relavity puzzle
Hi I read the following puzzle from an old text book long time ago. However it doesn't provide the answer. So what is the solution?
Let's suppose a car is going to park to a garage and the garage is ...
1
vote
1answer
51 views
What is movement through time? [duplicate]
In general, when I think of movement through space, I think of this:
$$\frac{dx}{dt}$$
But in special relativity, we also have a concept of relative duration, which means that $t$ must have a rate ...
3
votes
1answer
139 views
Lorentz transformation of classical Klein–Gordon field
I'm trying to see that the invariance of the Klein–Gordon field implies that the Fourier coefficients $a(\mathbf{k})$ transform like scalars:
$a'(\Lambda\mathbf{k})=a(\mathbf{k}).$
Starting from the ...
5
votes
1answer
145 views
Impulse from absorbing a photon? Is there an increase in rest mass?
I'm going through A P French's special relativity. In one chapter (6) the following is set up:
Suppose that a stationary particle of mass $M_0$ is struck by a photon of energy $Q$, which is ...
3
votes
3answers
307 views
Why do clocks measure arc-length?
Apologies in advance for the long question.
My understanding is that in GR, massive observers move along timelike curves $x^\mu(\lambda)$, and if an observer moves from point $x^\mu(\lambda_a)$ to ...
5
votes
2answers
155 views
Relativistic equivalent of a spring-force?
Usually what helps me understand a concept better in physics is to write a simulation of it. I've got to the point where I'm competent in the basics of special relativity, but, I can't figure out how ...
0
votes
1answer
99 views
Photons, no energy? [duplicate]
I am only 14, so I don't know much about physics, and I would appreciate help on this topic.
A photon, is said to have 0 mass. However, they carry energy, as electromagnetic radiation. Albert ...
1
vote
1answer
93 views
The status / acceptance of block time?
What is the current status or acceptance of block time as it relates to Einstein's theory of relativity? Has quantum mechanics ruled it out or is it still the favored view of the world? Perhaps there ...
0
votes
1answer
150 views
The real meaning of time dilation
Is this true or false: If A and B have clocks and are traveling at relative velocity to each other, then to B it APPEARS that A's clock moving slower, but A sees his own clock moving at normal speed.
...
1
vote
1answer
100 views
Why does only one twin travel in the twin paradox?
The wikipedia page repeatedly says that the twin travelling in space is the only one which travels, and also is the only one which faces acceleration and deceleration. So it does not age, while the ...
1
vote
1answer
83 views
Special relativity, acceleration and being in two places at once (How to resolve this paradox?):
Imagine I am on Earth I have a clock which measures time $t$. When my Earth clock reads time $t$, then when I look at a moving spacecraft's clock I see the time $t'$. Let us assume time is measured ...
-2
votes
2answers
105 views
If we are travelling with the speed of light, can we see what's behind us? [closed]
If we are travelling with the speed of light, can we see whats behind us(like if we are moving away from earth can we able see the earth)? And how we see the things that we are approaching with speed ...
8
votes
2answers
239 views
In QFT, why does a vanishing commutator ensure causality?
In relativistic quantum field theories (QFT),
$$[\phi(x),\phi^\dagger(y)] = 0 \;\;\mathrm{if}\;\; (x-y)^2<0$$
On the other hand, even for space-like separation
$$\phi(x)\phi^\dagger(y)\ne0.$$
...
3
votes
1answer
78 views
How would I perceive a purple ball when traveling at relativistic speeds
I have a 'thought experiment' which I'd like to ask about.
I was thinking what speed I would have to drive towards a crossing to see a red light as a green light - pretty easy, using the doppler ...
-4
votes
1answer
87 views
A riddle: What is the inertial frame of a clock? [closed]
Parts of the clock must be moving for the clock to tick.
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vote
0answers
148 views
Does Mansuripur's Paradox involve fictitious charges?
Mansuripur's Paradox involves a magnet moving at relativistic speeds in an external electric field.
Additional: thanks to Retarded Potential, who found the original paper.
If I understand correctly, ...
13
votes
4answers
451 views
Thought experiment regarding an object approaching a mirror
Here's a thought experiment I came up with in class today when my mind drifted (I however highly doubt I'm the first to think about this since it is pretty rudimentary) :
Let's say superman ...
