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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1answer
71 views
$\frac{dt}{d\tau}=\gamma$ in special relativity
I hope this is not too silly a question: We often see
$$\frac{dt}{d\tau}=\gamma=\frac{1}{\sqrt{1-v^2}},$$ taking $c=1$.
Problem:
I don't understand why...
In the Minkowski metric, using the ...
2
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1answer
51 views
Field Tensor and classical limits
I would be very grateful if someone would kindly explain this generalization of the Lorentz force law to the special relativity domain. Please bear with me.
Classically, the Lorentz force law is ...
2
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1answer
120 views
Retarded time Lienard Wiechert potential
In a potential which needs to be evaluated at the retarded time, is this the time which represents the actual time the "physics" occurred? So $t_{\text{ret}}=t-\frac{r}{c}$, not just because it may be ...
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0answers
54 views
Conservation of angular momentum tensor $L^{\mu\nu}$ in special relativity [duplicate]
I have edited this question because I don't think that the related post answers my question fully. It refers to Noether's theorem but I would like an explicit illustration in an easier fashion: The ...
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0answers
65 views
Relativistic interaction: gamma + proton = delta
We have a proton at rest, and there's an incident photon that is absorbed by the proton producing the excited state "delta".
Photon energy: $\hbar \omega$,
Proton rest Energy: $m_p c^2$,
Delta rest ...
4
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1answer
63 views
Relativity of simultaneity - An example
I am trying to understand the relativity of simultaneity in different frames, and I am trying to work out an example.
Suppose along the x-axis there are two points 2000m apart. Event A happens at t=0 ...
4
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2answers
116 views
Can dark matter be relativistic dust?
As far as I know the mass of an observed object increases as it approaches the speed of light.
Is it possible that the excess mass called "dark matter" is due to relativistic dust?
Surely, stars ...
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2answers
128 views
Do objects have energy because of their charge?
My gut feeling tells me things should have energy because of their charge, like they have energy because of their mass.
Is this possible? Has it been shown? If not then what is missing to make such ...
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3answers
168 views
Is there absolute proof that an object cannot exceed the speed of light?
Have any known experiments ruled out travelling faster than the speed of light?
Or is this just a widely accepted theory?
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3answers
157 views
What truly is mass, and is there a direct way to measure it?
We know a mass of an object of one kilogram as an object that weighs W = mg = 9.8 N and we reference it to that, (when it should as a fundamental parameter describe weight not the opposite). But if we ...
5
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3answers
414 views
Does entanglement not immediately contradict the theory of special relativity?
Does entanglement not immediately contradict the theory of special relativity? Why are people still so convinced nothing can travel faster than light when we are perfectly aware of something that ...
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2answers
73 views
Can acceleration feel like constant gravity for indefinitely long?
So here's the setup: I'm in a spaceship, without windows as always, and the ship is accelerating upwards at a constant rate of $1\,\text{g}$. So inside the spaceship it feels like I'm being pulled ...
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1answer
92 views
The Klein–Gordon equation
As we know that the Schrödinger equation presents basis of Quantum Mechanics and analogy with Newton second law in Classical Mechanics, I thought that relativistic interpretation of Schrödinger ...
4
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1answer
116 views
Lorentz invariance of positive energy solutions to the Klein-Gordon equation
I am reading Arthur Jaffe's Introduction to Quantum Field Theory. (You can find it here.) There is an interesting question posed in Exercise 2.5.1:
Solutions to the Klein-Gordon equation propagate ...
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2answers
167 views
Has anyone ever measured the one way speed of light perpendicular to the Earth at the Earth's surface?
1 - Has anyone ever measured the one way speed of photons traveling perpendicular to the Earth at the Earth's surface?
2 - Given our current understanding of Physics is there any way both the upward ...
2
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1answer
74 views
Properties of the Faraday tensor for constant fields
I'm doing a special relativity past exam paper and have got caught up with something that I hope someone can help me with!
I have to show that for constant fields, the magnitude of A, the ...
3
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2answers
79 views
How does the wavelength change in relativistic limit?
In the text, it reads that the momentum of a particle will change if it is moving at speed close to light speed. In the general case, the wavelength is given as
$$
\lambda = \frac{h}{p}
$$
and
$$p ...
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4answers
369 views
How does $E=mc^2$ put an upper limit to velocity of a body?
How does $E=mc^2$ put a upper limit to velocity of a body? I have read some articles on speed of light and they just tell me that it is the maximum velocity that can be acquired by any particle. How ...
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2answers
83 views
If inherent randomness exist in quantum mechanics, what then of eternalism implied by relativity?
I am nothing but a curious layman so don't go too technical on me.
First of all, I am well aware that a lot of people consider the question of determinism vs indeterminism to be unsolved and others ...
5
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0answers
193 views
What is the difference between the properties of Electron spin and Photon polarization/helicity?
What is the difference between a photon's polarization/helicity and an electrons spin half? I know that the photon is spin 1 but isn't its polarization analogous to spin half?
This question stems ...
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3answers
104 views
Special Relativity - speed of light question
Just a basic question:
I know that if you are traveling at $x$ speed the time will pass for you slower than to an observer that is relatively stopped. That's all just because a photon released at the ...
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0answers
44 views
Inelastic relativistic collision [closed]
I have to solve the following problem:
A particle of rest mass, $m_1$, and velocity $v_1$ collides with a stationary particle of mass $m_2$. Find the rest mass $m$ and velocity $v$ of the resultant ...
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2answers
172 views
Relativity of Simultaneity
Relativity of Simultaneity seems to be about OBSERVING two events simultaneously (please correct me if I am wrong).
However, as long as the two events are separated by a distance (any distance) then ...
1
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1answer
136 views
Showing Lorenz gauge is satisfied in retarded potential - vector calculus
I am trying to show that $\nabla\cdot \vec{A}=-\mu_0 \epsilon_0 \frac{\partial V}{\partial t}$
$V=\frac{1}{4\pi\epsilon_0}\int \frac{\rho(\vec{r}',t_r)}{r}d\tau'$
$\vec{A}=\frac{\mu_0}{4\pi}\int ...
4
votes
2answers
143 views
Relativistic Lorentz force law
If we consider the the relativistic Lorentz force law:
$$\frac{d}{dt} (m\gamma \vec{u})=e(\vec{E}+\vec{u} \times \vec{B})$$
How can we deduce:
$$\frac{d}{dt} (m\gamma c^2)=e \vec{E} \cdot \vec{u}$$
...
4
votes
2answers
154 views
How do Doppler Effect and Time Dilation differ?
Above, I have drawn a diagram showing Doppler Effect (here we are using space-time but in a non-relativistic sense. Time and distance are the same for A and B).
Edit: I am adding a relativistic ...
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3answers
97 views
Special Theory of relativity on electromagnetic waves
Since time slows down and length contracts, when we travel almost at speed of light, if the speed of light (or EM waves) remains same and the wavelength of light remains same, do we measure the ...
5
votes
1answer
76 views
Is there any experimental evidence to support the Terrell rotation?
The Shapiro delay was predicted in 1964 and observed by 1966, and is now a tool used to measure the mass of distant binary pulsars. The Terrell-Penrose rotation was published in 1959, but I can find ...
5
votes
2answers
256 views
What if a faster-than-light particle is found?
What will be the consequence (severe ones) on laws of physics if a particle that travels faster than light is discovered?
I am looking for a more general answer so that a high school student would be ...
5
votes
1answer
146 views
Meaning of spin
I'm pretty astounded that I did not hear about this sooner, but in my course on QFT our professor told us that the concept of spin can be used to mean three things:
Mechanical spin (apparently a ...
2
votes
2answers
113 views
Lorentz invariance of the action for free relativistic particle
I tried to check the Lorentz invariance of the standard special relativity action for free particle directly: ($c=1$)
$$
S=\int L dt=-m\int\sqrt{1-v^{2}}dt
$$
Lorentz boost:
$$ ...
2
votes
1answer
87 views
Difference between proper and comoving frames
I'm reading this book "Introduction to Quantum Fields in Classical Backgrounds" by Mukhanov & Winitzki, and there in the chapter 8 "The Unruh Effect" they introduce 3 reference frames.
Laboratory ...
2
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1answer
103 views
Clarification regarding Special Relativity
Empty the universe of all matter. Place the Earth in that universe sitting in an inertial frame. Take a pair of twins. One twin gets into a space ship and takes off from Earth (t=a). He ...
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2answers
56 views
Minimum $E$ of $p\bar{p}$-collision for $q\bar{q}$ pair with mass $m_q$
I am currently working out the energy required to create a particle anti-particle pair from a collision of a proton travelling along the x-direction with an anti-proton which is at rest. The particle ...
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0answers
105 views
About the theory of relativity
Why is speed of light constant in every non inertial frame of reference? Is there any theoretical explanation behind this postulate Since we cannot completely depend upon the experimental results?
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1answer
72 views
Understanding bending light beam perpendicular to motion
I'm just reading a book about gravity. An example it gives is a spaceship accelerating. A beam of light travelling at right angles to the direction of movement of the spaceship enters it via a small ...
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2answers
60 views
Bondi's k factor
Consider two observers, travelling away from each other, after meeting (at which time they sync their clocks). $O$ sends a photon towards $O'$ at times $t$, received by $O'$ at time $t'=kt$, where we ...
0
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2answers
40 views
Why does the inertial mass of an object rise when a force is exerted on it in a particle accelerator? [closed]
A particle in a cyclotron requires more and more force to maintain the same acceleration as it accelerates.
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1answer
62 views
Time Dilation in relation to Acceleration
What I am looking for is a layman's explanation on the equations required to work out Time Dilation at high speeds including acceleration and deceleration of velocity. Or I would greatly appreciate it ...
1
vote
3answers
177 views
Integration by parts to derive relativistic kinetic energy
I have come across a weird integration during derivation of relativistic kinetic energy. Our professor states that i can get RHS out of LHS using integration by parts:
$$
\int\limits_0^x \! ...
0
votes
2answers
106 views
How big is an inertial frame?
How big is an inertial frame?
Consider a huge rod which is rotating about a fixed point in a plane, its length is 1 light year.
Thus light from its end closer to the fixed point to the end farther ...
1
vote
2answers
188 views
Will observers moving on a sphere experience time dilation?
A single source of light exists at a fixed point in space relative to two observers. The two observers move on the surface of a shell with a fixed radius with the light source at its centre. They move ...
2
votes
2answers
90 views
Sign convention for basic Dirac equation
The dirac equation;$$(i\gamma^\mu\partial_{\mu} - m)\psi=0 $$ is just; $$(i\gamma^{0}\partial_{0} - i\gamma^{i}\partial_{i} - m)\psi=0 $$ in a (+,---) metric right?
1
vote
1answer
84 views
Where to read about Minkowski space [duplicate]
When I learned Special Relativity, it was taught in terms of basic linear algebra, without any mention of the Minkowski space, proper time as integration on the metric, etc.
However, when I am trying ...
2
votes
1answer
126 views
Relativistic kinematics of particle decay
Suppose a particle decays to three other particles. The masses of all particles are assumed to be known and we work in the rest frame of the parent particle.
So there are 12 parameters for this ...
0
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2answers
286 views
Generating artificial gravity by using rotation
If I want to design for futuristic space stations and I want to use rotation to produce
artificial gravity. One of such designs consists of a giant ring that is rotated about its centre. If it were ...
0
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1answer
55 views
Wavefront emitted by bodies at traveling near the velocity of light
I studied that no body can travel with the velocity of light. But, assuming that when a body moves nearly velocity of light, will it obey length contraction law of Einstein or will it emit the same ...
2
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1answer
78 views
Point charge 4-current derivation
How do I derive that the 4-current of a point charge is
$$j^{\mu}(x)=ec\int_{-\infty}^{+\infty}\dot{z}^{\mu}(s)\delta(x-z(s))ds$$
where $\dot{z}^{\mu}(s)$ is the 4-velocity of the charge and $s$ is ...
2
votes
1answer
98 views
Lorentz invariance of the wave equation
I want to show that the 2-d wave equation is invariant under a boost, so, the starting point is the wave equation
$$\frac{\partial^2\phi}{\partial x^2}=\frac{1}{c^2}\frac{\partial^2\phi}{\partial ...
2
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0answers
82 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 ...
