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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Why do we need 3 variables to parametrize $\scr{I}^\pm$ in a Penrose diagram?
In the figure we can see the Penrose diagram for Minkowski space
If I understand correctly, $i^-$ and $\scr{I}^-$ have coordinates $r=\infty$ and $t=-\infty$ while $i^+$ and $\scr{I}^+$ have ...
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How the relativistic mass gain prob is overcome in synchrotron by adjusting the frequency of electric field to accelerate particles to high KE?
Cyclotron cannot accelerate particles beyond certain KE due to relativistic mass gain. I am from Chemistry background.
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What is the value of $W_\mu W^\mu$ for massless particles?
What is the value of the quantity $W_\mu W^\mu$ for massless particles where $W^\mu$ is called Pauli-Lubanski vector defined as $W^\mu=\frac{1}{2}\epsilon^{\mu\nu\alpha\beta}P_\nu J_{\alpha\beta}$.
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Confused about Feynman Lectures on attraction between two charges or wire as relativistic phenomenon
I am confused on one of the earlier sections of Feynman Lectures Vol 2. I've posted the relevant snippet below. Since it's in the public domain (http://www.feynmanlectures.caltech.edu/) I think I can ...
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Confusing time dilation - proper time is higher?
The problem states that 2 rockets of proper length 100m are going in opposite directions. From the system of rocket A, the tip of B took 5 microseconds to pass the rocket A. If a clock on the tip of B ...
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Would time freeze if you could travel at the speed of light?
I read with interest about Einstein's Theory of Relativity and his proposition about the speed of light being the universal speed limit.
So, if I were to travel in a spacecraft at (practically) the ...
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Constant $g$ acceleration from astronaut's frame of reference
When a spaceship is experiencing a constant acceleration of $10m/s^2$, the astronauts will be moving at nearly the speed of light after about a year in the earth's reference frame. This means the ...
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Lorentz transformation length contraction contradiction
We have a rod moving at relativistic speed. If $l_0$ is the actual length from the rods perspective. $ x_1'$ and $x_2'$ are positions of ends of the rod from the perspective of the rod.
I get a result ...
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In relativity, what is the difference between a rod that is perpendicular to direction of motion and a rod parallel to the direction of motion?
In Feynman's Lectures on Physics , chapter 15, page 6 he writes about 2 identical, synchronized light signal clocks. These are clocks that consist of a rod (meter stick) with a mirror at each end, and ...
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how to create a kinetic energy kugelblitz in theory? [duplicate]
Black holes form when enough mass gets packed so close together that its gravity gets so strong that even light cannot escape it. Mass and energy are equivalent, so theoretically it is possible to ...
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Checking the Lorentz Invariance
This seemed at first glance very easy. But there appeared some confusion.
$A$ is moving to the right with velocity $v$ with respect to $B$. The proper time for $A$ is
$$t_a=t_b\sqrt{1-v^2/c^2}$$
...
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Chaining together two successive time dilations through two Lorentz transformations [duplicate]
The three clocks $A, B, C$ at the same position in spacetime at the beginning of the measurement. $A$ starts moving to the right with the velocity $v$ with respect to $B$ and $B$ starts tracing $A$ ...
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Misconception in partial derivatives of Lorentz transformation
Let us consider a Lorentz transformation of four vectors from frame S to S' where S' is moving with relative velocity $\textbf{v}$ with respect to S. The boost is given by
$$t'=\gamma(t-vx), \quad x'=\...
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How would faster-than-light object traveling through space look like to us on Earth? [closed]
Inspired by this question on Worldbuilding, I'm intrigued by a question : How would an object, traveling faster than light through Solar System, appear to us on Earth? Lets assume that object is a ...
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Does the Lorentz transformation only apply to corresponding observers?
Let $S$ and $S'$ be inertial frames moving at a relative velocity $v$ in the $x$-direction. Imagine sending observers to all points in each reference frame. The following rules hold:
(1) In a given ...
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Rearrangement of length contraction formula
I have just learnt that an object appears shorter in length when viewed by an observer in relative motion with respect to the object. We can derive this with Lorentz transformation formulas, and that'...
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Which observer can detect the Gravitational Time Dilation?
We say clocks tick slowly in the strong gravitational fields. Is this stated from the perspective view of the one located in a weaker field or the one who is standing in that strong gravitational ...
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The path that a light beam takes in empty space
First excuse me if this question is very simple for you but for me and for my friend is not. Recently we were discussing what path a light beam will follow in a box moving at a constant velocity in ...
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Relativity theory and time [closed]
In relativity theory it is accepted that speed of light is invariant and even time is flexible. Can the mathematics of relativity be interpreted in such a way that time is invariant and everything ...
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Does having a minimum length in space violate Lorentz invariance? [duplicate]
I’m trying to understand different approaches to quantum gravity. One involves quantising space and time themselves, which i believe can result in there being a minimum possible length and time ...
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Does angular momentum affect the mass of an object in SR?
The mass of an object is given by the square root of the norm of the four momentum, which is equivalent to the energy the object has in the centre of momentum frame.
However in the centre of ...
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Jefimenko's Relativity approach [closed]
I read some books by Oleg Jefimenko (the author of "Jefimenko's equations" in electrodynamics).
In particular, in his book "Electromagnetic retardation and Theory of Relativity" he presents an ...
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What is the displacement of an accelerated and relativistic object?
Displacement in an accelerated classical object is:
$$s=ut+\frac {at^2}{2}$$
What is the displacement of an accelerated relativistic object?
In Newtonian mechanics there are two types of displacement....
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Special Relativity - How to Tell a New Boost's Magnitude, Direction, and Rotation about the Z-Axis After Matrix Multiplication?
Perhaps not a very bright question (and more of a personal after-thought), but how is one able to interpret or figure out the boost's magnitude (i.e. speed), direction, and rotation (about the z-axis) ...
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Why is the proper time of an unaccelerated clock maximal?
I have read that "Under all possible proper times between two events, the proper time of the unaccelerated clock is maximal, which is the solution to the twin paradox."
I got that for a clock in it's ...
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Is time dilation geometrically symmetrical?
My understanding is that length dilation is not symmetrical in all geometric directions. The contraction only happens in the direction of travel. Likewise it seems that light would appear to a ...
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In space, if 2 free electrons are brought together and then released from external forces, do they eventually reach half $c$? [closed]
I did a number of simulations of particles in motion based on Coulomb potential and the like. One constant consequence of establishing a repulsion between particles of same sign even at far distance, ...
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Why does spin determine particle statistics?
I understand that "spin" refers to the intrinsic angular momentum of a particle, which relates to the magnetic moment of a particle. I mostly follow the "Background" section of the spin-statistics ...
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Lorentz Transformation vs Special Relativity
If in the Lorentz transformation the invariance of the speed of light is not presumed (as it was assumed later with special relativity), then what was the usage and meaning of the Lorentz ...
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Which quantity is mass (tensor, vector or scalar)? [closed]
Mass and spin are fundamental characteristics of particle. Those quantities are eigenvalues of the Casimir operators of the Poincaré group. My book then writes that
$$
p^\mu p_\mu = m_0^2,
$$
where $...
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Extending Coordinate Transformation in Relativity
I have been trying to teach myself general relativity, and I come from a background in mathematics, but I am having a difficult time understanding a particular math fact my book is using. The author ...
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Find the Scalar Invariant under a Lorentz-transformation [closed]
[Question]
Given the components of two vector fields, $u^\alpha$, $v^\beta$, show that $u^\alpha v^\alpha = u^0 v^0 + u^1 v^1 + u^2 v^2 + u^3 v^3$ is not a scalar invariant under a Lorentz-...
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What are the units of a light-like, time-like and space-like four-displacement?
In Euclidean space, three-vectors can be rotated into one another, making it obvious to me that the units for the basis vectors are the same as one another. But in Minkowski geometry, space-like, time-...
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Special Relativity - Perpendicular Boosts Equaling to a Rotation after a Boost
[Question]
I recently read that two perpendicular Lorentz boosts equal to a rotation after a boost. Can anyone here show me an example of this happening? Thank you for your time and assistance!
...
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The spinor metric, basic spinor calculations and spinor indices
I'm currently reading the textbook "Finite Quantum Electrodynamics" by Günter Scharf, but I find myself stuck already on page 24.
Background
Scharf introduces the index-raising symbol (spinor metric)...
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Derivation of Lorentz Contraction WITHOUT light roundtrip
A typical Lorentz Contraction proof relies on the axiom that "the speed of light is constant" and goes as follows. Given:
Frame $F_1$ moves at speed $v$ relative to frame $F_0$. In frame $F_1$ sit 2 ...
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Special Relativity [closed]
Does special relativity require faster than light information transfer to verify length contraction and time dilation?
How does the "outside observer" measure these variables? I guess the outside ...
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Properties of space-time intervals derived by symmetry principles
In many books about special relativity I found the following arguments:
1) because the transformations between two inertial reference frames $K$ and $K'$ are linear and because if $\Delta s^2 = 0 $ ...
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Correlation between velocity and homogeneity of spacetime and isotropy of space
Considering only inertial frames of reference and constant velocities, does the fact that any velocity, with the exception for the speed of light in a vacuum, can be transformed, via an accurate ...
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Loss of simultaneity in special relativity
I was recently reading Introduction to Classical Mechanics by David Morin and while reading special relativity I came up with a paradox I am not able to resolve. It is basically related to the loss in ...
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How to interpret negative time in Lorentz transformation?
I am somewhat confused about how to interpret negative time in Lorentz transformation. In the usual case of two reference systems S and S' where the distance X (the one that measures S) to an event, ...
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What's the difference between spinor and spin?
Some related information might be found here: What is the difference between a spinor and a vector or a tensor? and Wikipedia seemed to have an explanation but was not very clear.
From what I read, ...
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Why does the conversion of mass to energy have anything to do with the speed of light? [duplicate]
Not looking for derivation, that is self explanatory. But why the speed of light, not some other constant like avagadros number or number of stars or anything else? Seems like lightspeed is special. ...
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Special Relativity problem - proper time interval
The supernova 1987A explosion in the Large Magellanic Cloud 170 000 light years from Earth produced a burst of anti-neutrinos $\overline{v}_e$ which were observed in terrestrial detectors. If the ...
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Effect of star's binding energy due to general relativity?
Due to the curvature of space-time the distances near the star are length contracted. So if that's the case then doesn't that mean that the binding energy of star should be more since the distance ...
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