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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votes
3answers
509 views
Special Relativity and $E = mc^2$
I read somewhere that $E=mc^2$ shows that if something was to travel faster than the speed of light then they would have infinite mass and would have used infinite energy.
How does the equation show ...
3
votes
2answers
75 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
$$p ...
2
votes
1answer
70 views
Properties of the Faraday tensor for constant fields
I'm doing a special relativity past exam paper and have got caught up with something that I hope someone can help me with!
I have to show that for constant fields, the magnitude of A, the ...
1
vote
2answers
120 views
Lorentz boost matrix for an arbitrary direction in terms of rapidity
We have derived the Lorentz boost matrix for a boost in the x-direction in class, in terms of rapidity which from Wikipedia is:
Assume boost is along a direction $\hat{n}=n_x \hat{i}+n_y \hat{j}+n_z ...
5
votes
3answers
173 views
What's the purpose of the arbitary additive constants in Einstein's Inertia of Energy Paper?
In Einstein's paper: Does the Inertia of a Body Depend upon its Energy content? he introduces arbitary additive constants whose purpose I'm confused about.
The paper has a frame $(x,y,z)$ where a ...
7
votes
4answers
349 views
How does $E=mc^2$ put an upper limit to velocity of a body?
How does $E=mc^2$ put a upper limit to velocity of a body? I have read some articles on speed of light and they just tell me that it is the maximum velocity that can be acquired by any particle. How ...
4
votes
4answers
310 views
Relativistic mass and imaginary mass
The (relativistic) mass of an object measured by an observer in the $xyz$-frame is given by
$$m = \frac{m_{rest}}{\sqrt{1 - \left(\frac{v}{c}\right)^2}}.$$
Mathematically $v$ could be greater than the ...
0
votes
2answers
77 views
If inherent randomness exist in quantum mechanics, what then of eternalism implied by relativity?
I am nothing but a curious layman so don't go too technical on me.
First of all, I am well aware that a lot of people consider the question of determinism vs indeterminism to be unsolved and others ...
1
vote
3answers
87 views
Special Relativity - speed of light question
Just a basic question:
I know that if you are traveling at $x$ speed the time will pass for you slower than to an observer that is relatively stopped. That's all just because a photon released at the ...
0
votes
0answers
35 views
Inelastic relativistic collision [closed]
I have to solve the following problem:
A particle of rest mass, $m_1$, and velocity $v_1$ collides with a stationary particle of mass $m_2$. Find the rest mass $m$ and velocity $v$ of the resultant ...
4
votes
2answers
133 views
Relativistic Lorentz force law
If we consider the the relativistic Lorentz force law:
$$\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}$$
...
1
vote
1answer
121 views
Showing Lorenz gauge is satisfied in retarded potential - vector calculus
I am trying to show that $\nabla\cdot \vec{A}=-\mu_0 \epsilon_0 \frac{\partial V}{\partial t}$
$V=\frac{1}{4\pi\epsilon_0}\int \frac{\rho(\vec{r}',t_r)}{r}d\tau'$
$\vec{A}=\frac{\mu_0}{4\pi}\int ...
5
votes
1answer
71 views
Is there any experimental evidence to support the Terrell rotation?
The Shapiro delay was predicted in 1964 and observed by 1966, and is now a tool used to measure the mass of distant binary pulsars. The Terrell-Penrose rotation was published in 1959, but I can find ...
5
votes
2answers
242 views
What if a faster-than-light particle is found?
What will be the consequence (severe ones) on laws of physics if a particle that travels faster than light is discovered?
I am looking for a more general answer so that a high school student would be ...
3
votes
0answers
102 views
Meaning of spin
I'm pretty astounded that I did not hear about this sooner, but in my course on QFT our professor told us that the concept of spin can be used to mean three things:
Mechanical spin (apparently a ...
2
votes
2answers
96 views
Lorentz invariance of the action for free relativistic particle
I tried to check the Lorentz invariance of the standard special relativity action for free particle directly: ($c=1$)
$$
S=\int L dt=-m\int\sqrt{1-v^{2}}dt
$$
Lorentz boost:
$$ ...
2
votes
1answer
68 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 ...
6
votes
7answers
1k views
How does Newtonian gravitation conflict with special relativity?
In the Wikipedia article Classical Field Theory (Gravitation), it says
After Newtonian gravitation was found to be inconsistent with special relativity, . . .
I don't see how Newtonian ...
2
votes
1answer
98 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 ...
0
votes
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 ...
0
votes
0answers
103 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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vote
2answers
55 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
votes
2answers
37 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.
7
votes
1answer
271 views
Classical vs. Quantum use of the spin 4-vector
I have a few basic questions about the Pauli-Lubanski spin 4-vector S.
I've used it in quantum mechanical calculations as an operator, that is to say each of the components of S is a matrix operator ...
0
votes
1answer
54 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 ...
3
votes
2answers
3k views
Do light and sound waves have mass
I have been reading Hawking's 'A Brief History of Time' and it has gotten me thinking about Einstein's theory of relativity, in that it assumes that an object must have infinite mass if it is to be ...
0
votes
2answers
104 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 ...
7
votes
1answer
249 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
183 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
86 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?
2
votes
1answer
118 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 ...
1
vote
1answer
78 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 ...
0
votes
2answers
282 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
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 ...
2
votes
1answer
70 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
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
$$\frac{\partial^2\phi}{\partial x^2}=\frac{1}{c^2}\frac{\partial^2\phi}{\partial ...
4
votes
1answer
105 views
What kinds of inconsistencies would one get if one starts with Lorentz noninvariant Lagrangian of QFT?
What kinds of inconsistencies would one get if one starts with Lorentz noninvariant Lagrangian of QFT? The question is motivated by this preprint arXiv:1203.0609 by Murayama and Watanabe.
Also, what ...
0
votes
1answer
78 views
Senior High School work on Doppler measurements
Sorry this question is really vague- as a result I'm very confused. Perhaps you can help me make sense of it.
"Radar measurements: Construct a space-time diagram of the radar tracking of an asteroid ...
2
votes
0answers
74 views
Fermi Walker vs. Fermi transport
A vector field $f^\mu$ is said to be Fermi-Walker transported along a curve $\gamma$ parametrized with $\tau$ if the following holds $$\frac{\mathrm{D}}{\mathrm{d}\tau}f^\mu = -(a^\mu v^\nu - a^\nu ...
4
votes
1answer
374 views
Criticism of the Thomas precession literature
From an earlier version of the Wikipedia article on Thomas precession concerning TP and LP=Larmor precession, regarding the paper: G B Malykin, "Thomas precession: correct and incorrect solutions", ...
3
votes
3answers
3k views
Ion Drive Propulsion Top Speed
I would like to know if there is some formula / graph which would provide / show the efficiency of a certain type of propeller in space. Specifically, I'm interested in the acceleration attainable at ...
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 ...
5
votes
1answer
209 views
Is there any uncertainty between mass and proper length or time?
I was trying to naively draw a parallel between special relativity and the Heisenberg uncertainty principle. I try to understand uncertainty principle as a consequence of 4-position and 4-momentum ...
4
votes
2answers
199 views
What do massive photons have to do with superconductivity?
I keep reading that the idea of massive photons leads to an explanation of the Meissner effect but I fail to see how photons are involved with the repulsion of fields inside a superconductor.
How ...
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
90 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, ...
0
votes
1answer
123 views
Why does weak equivalence principle say gravity is equivalent to acceleration?
I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
8
votes
2answers
366 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:
$$
...
8
votes
3answers
322 views
Where's the energy in a boosted capacitor?
Suppose I look at a parallel plate capacitor in its rest frame and calculate the electrostatic energy, $E$.
Next, I look at the same capacitor in a primed frame boosted in the direction perpendicular ...
19
votes
5answers
2k views
Do photons gain mass when they travel through glass?
Please correct me if I'm wrong, but I believe that photons slow down when travelling through glass. Does this mean they gain mass? Otherwise, what happens to extra kinetic energy?
I understand now ...
