Questions tagged [special-relativity]
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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2 Different Results For Length Contraction
Consider a frame of reference S' moving with a velocity $v$ along x-axis with respect to a frame of reference S.
Using Lorentz transformation, $x'=\gamma(x-vt)$, where $\gamma=\frac{1}{\sqrt{1-\frac{...
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2answers
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Using time-dilation to our advantage?
Assume we have a super-computer working on an important problem, and we estimate it will take about $200$ years to solve. But, we need the answer in $20$ years.
Could we ship the super-computer into ...
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62 views
Show that there exists a reference frame where the two events happen at the same time [on hold]
question
I am trying to show that if the Lorentz Invariant Interval is negative
$$c^2 \Delta t^2 - \Delta x^2<0$$
then there exists a reference frame $S^{'}$ where $\Delta t^{'}=0$.
context
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1answer
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Does a magnet moving in a uniform electric field experience torque?
Assume a uniform electric field of $E_y$ along $y$ in the lab frame of reference $(x,y,z,t)$. A simple magnet bar is set in motion at $v$ along $x$ in this electric field so that the alignment of the ...
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1answer
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Proof of forbidden free electron-photon absortion using spacetime diagram
I'm trying to solve this exercise from the book "Modern Classical Physics" by Kip Thorne:
Show, using spacetime diagrams and also using frame-independent calculations, that the law of conservation ...
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3answers
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What is the proof for the relativistic expression for kinetic energy?
In his book on relativity, Albert Einstein states in chapter 15 that we now don't write kinetic energy as $K_e = \frac{1}{2}mv^2$ but as $$K_e = \frac{mc^2}{\sqrt{1- v^2/c^2}}-mc^2.$$
How is this ...
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Astraunaut revolving earth at speed of light holdind bar
If i stand on the ground holding a very long metal bar. By long i mean thousands of kilometers. And then i start spin around my vertical axis. And lets say that the other side of the bar is held by a ...
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1answer
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Acceleration in Twin's paradox
The Twin's paradox is a well known paradox in which there is a difference in the ages of twins after one twin travels a round trip around the space and returns back while the other twin stays put. I ...
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Paradox regarding phase transitions in relativistic systems
The main question I would like to ask is whether quantities such as density are dependent on the frame of reference. I have searched several forums and the answer is somewhat controversial. Some ...
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3answers
151 views
The role of Lorentz tranformations
My questions concern the role of Lorentz transformations in Special Relativity and General Relativity, as described in the following fragment of the series of GR lectures: https://www.youtube.com/...
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Relativity thought experiment [duplicate]
I have two doors that I can close arbitrarily quickly, and I want to shoot a long rod at relativistic speed through both doors. When measured at rest relative to the doors, the rod is longer than the ...
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Adjusting Newton's laws with relativity concepts
I break my question into three parts, with increasing "guessing status". Please tell me which of them (is any) is correct.
Suppose I am an observer in an inertial reference frame, away from all other ...
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Time dilation where one person is stationary and the other is moving [on hold]
Two twins follow different journeys. One stays still, as determined by an observer xedrelative to distant stars. The other travels to a star which is 5.5 light years away and ...
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0answers
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Cosmological or Doppler redshift in distance calculations
If I want to determine the distance to a far away galxy with a high redshift,
then using relativistic doppler shift will not give the true distance as it
does not take into account the expansion of ...
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1answer
151 views
Why doesn't accelerating reference frames in QFT lead to horrible paradoxes?
Background
So I remember that in Special Relativity while one can define acceleration things can go horribly wrong has happened historically (I'm sure there many other paradoxes). The real reason of ...
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Under the constraint that the 4-acceleration is constant in each instantaneous rest frame
Suppose a particle is in a global inertial frame and moving in the $x$ direction, starting from rest at $t=0$. Under the assumption that the 4-acceleration of the particle in its each instantaneous ...
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1answer
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Stationary aether with respect to Earth? [on hold]
Michelson & Morley's experiment implies that either the aether does not exist OR that the Earth is stationary with respect to aether.
Now, one consequence of relativity is that we CAN physically ...
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1answer
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Relativistic rockets paradox [on hold]
The next problem is, as I understand, a spin on the ladder paradox which is extensively documented everywhere. There are two rockets ($A$ and $B$), of length $L_p=1$m which are traveling in opposite ...
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1answer
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Why the energy and momentum conservation equations do not include terms reflecting the particle nature of the photons? [on hold]
It is well known that light has a dual nature. However, the energy and momentum conservation equations embody the wave aspect of light but not the material aspect of the photon. Should there be ...
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1answer
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Casimir operator and particle worldline
I'm studying Killing vectors in 2d Minkowski space-time, with signature $(+,-)$, the usual metric given by
$ds^2=dt^2-dx^2$.
I have found these Killing vectors:
$\xi^{(1)}=(1,0)=\partial_t\equiv ...
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1answer
112 views
Can we talk about velocity field and acceleration field in 1D?
It's well know that a charged particle radiate when it is accelerated. We can rely on two different formulas. The first one it's from Jefimenkos :
$$\mathbf{E}(\mathbf{r}, t) = \frac{1}{4 \pi \...
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2answers
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Does light have mass? Why? [duplicate]
I've been wondering whether light has mass. Yet given the wave-particle duality of light, the statement seems to be affirmative. With that, how to calculate it?
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Equivalence Principle holding in Special Relativity? (let alone QFT)
Motivation
I am pretty confused of why people are hopeful to find a version of the equivalence principle ("the complete physical equivalence of a gravitational field and a corresponding acceleration ...
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1answer
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Covariant relativistic photoelectric effect
General textbooks introduce the photoelectric effect as the Einstein's formula
$$hf=hf_0+E_c(max)$$
and where $E_c=mv^2_e/2$ is the kinetic energy maximum value, the work function is $eV_0=hf_0$, and ...
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2answers
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Why is relativistic velocity addition not symmetric?
The Galilean velocity addition formula is $$u' = v + u$$ This is symmetric if one swaps $v$ and $u$.
What are the fundamental reasons why the (generalized) relativistic velocity addition formula is ...
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Twin Paradox in String Theoretical Backgrounds / Compactifications
It is a common exercise while learning special relativity to work out the resolution to the twin paradox. As an extension, I have looked at the twin paradox with compact dimensions, i.e. having an ...
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2answers
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Time difference as a result of Lorentz boost
So I am given two clocks A and B moving in $S'$ frame with a velocity $V$ relative to $S$ frame. The two clocks are separated by a distance $L$ and are synchronized in $S'$ frame. The objective is to ...
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1answer
44 views
Time dilation when moving toward or away from the earth
For a given speed, is the time dilation of a space traveler different if moving radially toward the earth as compared with moving radially away from the earth?
Is the time dilation of a space traveler ...
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1answer
98 views
Do superluminal worldlines constitute closed time-like curves under the right conditions?
A closed time-like curve is defined as a word-line that returns to its starting point, in the $x$, $y$, $z$, $t$ coordinates. So, for a chronology respecting observer, an object traversing a closed ...
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Lorentz Transformation Notation
A frame $s'$ is moving with velocity $v_1$ in the x-direction with respect to a frame $s$. $s''$ is moving with velocity $v_2$ in the y-direction with respect to $s'$. I know to multiply the matrix ...
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2answers
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How could 'rest mass' and 'invariant mass' be the same?
The terms rest mass and invariant mass are often interchanged, however i cannot reconcile these concepts:
Consider a photon ...
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1answer
198 views
Minimizing proper time
I've started studying general relativity course and now I have a question about proper time. Consider functional
$$S[x]=-\int_A^B ds,$$
where $A$, $B$ are fixed points of the space-time and $ds^2=dt^2-...
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1answer
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Could the universe as we know it still be viable if the speed of light was not independent of the observer? [closed]
It has been known for some time that the speed of light is independent of the observer and the apparent paradoxes that would have occurred applying classical rules (for example summing velocities) ...
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1answer
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An apparent contradiction combining entanglement and relativity [closed]
An elementary particle like a photon or electron can be measured in 2 possible states - spin up or down in electron, vertical or horizontal in photons. We'll call those states state 1 or 2, and the ...
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Find angle from two perpendicular relativistic Lorentz boosts
I have a frame $s'$ moving with velocity $v_1$ along the x-direction with respect to a frame $s$. A frame $s''$ is moving with velocity $v_2$ along the y-direction with respect to $s'$.
I want to ...
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Double Relativistic Speed of light [duplicate]
If two light photons are emitted from a point source and moving in opposite directions in space, how can global speed limit $c$ be maintained, as speed of one photon relative to other can be easily ...
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1answer
324 views
Lorentz transformation boosts as matrices
I have seen Lorentz transformation boosts (say, along the x-direction) written as (in $c=1$ units):
$$ \left[\begin{array}{cccc}{\gamma} & {-v \gamma} & {0} & {0} \\ {-v \gamma} & {\...
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3answers
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Lorentz transformations for time co-ordinates (STR)
I am little bit confused with the implication of Lorentz transformations for time co-ordinates or atleast how to apply those!
Consider 2 frames of reference $O$ and $O'$ in which $O'$ is moving with $...
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3answers
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As $SL(2,\mathbb{C})$ is a double cover of the Lorentz group, is $SL(2,\mathbb{Z})$ a discrete subgroup of the Lorentz group?
The group $SL(2,\mathbb{C})$, the group of $2 \times 2$ complex matrices with determinent $1$, is a double cover of the Lorentz group. (These transformations can be understood as Mobius ...
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Can a particle turn into a black hole through acceleration? [duplicate]
If we accelerate a particle fast enough, could it turn into a black hole from our reference frame, due to the relativistic mass and dilation? If so, would it then shed some speed through Hawking ...
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1answer
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$E = mc^2$ derivation thought experiment seems to not have conserved energy
There is an interesting derivation of $E=mc^2$ given here which I have updated to use relativistic momentum and relativistic kinetic energy. I find when doing the derivation that it doesn't appear ...
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1answer
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Law of reflection of a moving mirror in special relativity (velocity perpendicular to the normal)
I have seen this question about the law of reflection in special relativity, and it is shown that, if you have a mirror moving in the opposite direction to the mirror's surface normal, the law of ...
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3answers
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On existence of mass in different form [closed]
(I'm a mathematician actually. This is my first question on this site. So please go easy on me if it's a trivial matter or mistake)
Lately I've been thinking about special relativity.
The thought ...
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3answers
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How an ultra-relativistic electron near the speed of light keeps its spin velocity without becoming partially superluminal?
If an electron has spin and volume than the point on the surface is rotating at constant speed according to Planck constant defined angular momentum.If this electron accelerates then this point on the ...
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4answers
179 views
Why can't we define absolute rest?
If, according to the theory of relativity, as objects gain velocity and approach the speed of light then time for them slows down, why can't we define absolute rest as the inertial frame in which time ...
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1answer
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Is the equivalence of mass and energy a direct consequence of SR or not?
Special relativity gives us the invariance of four-vectors. Consistency with Newtonian physics implies the conservation of four-momentum.
The spatial part of four-momentum is
$P^0=m\gamma(v)$
...
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Traveling down a highway at near light speed
I’ve read that while traveling in space closer and closer to the speed of light everything I would be observing and I would see other people or things moving more slowly.
I’m having a hard time ...
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0answers
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$A^t\eta A=\lambda\eta $ then $\lambda$ is positive [migrated]
Let $A$ be any real $4$ by $4$ invertible matrix such that $A^t\eta A=\lambda\eta$.
Here $\eta=diag(-1,1,1,1)$. Then I have to show that $\lambda$ is positve.
I tried the determinant but it gives $\...
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1answer
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Spacing in indices, and relation to matrices, in special relativity notation
I have some general confusion regarding notation on tensors in special relativity, and how indices correspond to the matrix representation of second-rank tensors.
When one has a second-rank tensor $...
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1answer
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Relativistic muons traveling in a circle
I know the rest mass of a muon (106 MeV) and rest frame lifetime (2.2 $\mu s$).
Suppose we accelerate muons that travel through a circular ring. At a specific energy, I want to know how many times a ...
