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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Representation theoretic constraints in SUSY algebra
Let's try to build from scratch the SUSY commutator $[Q_\alpha^I, P_\mu]$. We know that the result of this commutator must be a fermonic generator belonging to $(1/2, 0)\otimes(1/2,1/2) \simeq (1, 1/2)...
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What is the best way to build understanding of general relativity? [closed]
I am modifying my recent post to be a little bit more direct since, as commented by some smart moderators, my initial post was sprawling and asking questions that would take papers and textbooks to ...
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Thermodynamics and Special Relativity [closed]
What happens to the temperature of a body (not in the body frame) as it approaches the speed of light? My thinking is that the molecules will necessarily 'prefer' (as a natural consequence of the ...
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Understanding spinors, double cover and professor's expanation
I'm following an introductory course in QFT, and we are facing the spin group part. I think that most of the details are left apart because it would take too much time to be developd, and my profesor ...
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Seeming contradiction between Lorentz equations and length contraction
I'm currently teaching IB physics and I'm preparing to cover relativity in my class as it's recently been added to the syllabus.
I'm experimenting with different ways to explain relativity and while ...
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Relativistically, shouldn't a current loop produce an electric field that is negative perpendicular to the loop and positive in the plane of the loop?
Relativistically, the electric field of a moving charge is not purely radially directed, but is instead concentrated perpendicular to the line of motion. So, a current loop consisting of electrons as ...
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Anomaly in Photoelectric effect
Good day.
While doing a physics experiment for a university assignment, I was tasked with measuring the maximum wavelength at which a potassium cathode shined by a monochromatic light emits electrons.
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What is the time dilation due to acceleration?
what is the formula to calculate time dilation due to acceleration. I have tried to search in google to find out the answer but I couldn't find any equation to calculate the time dilation due to ...
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Cannot understand this identity between kronecker and metric tensor [closed]
I'm working on Lorentz generators and I am really not able to understand this relation:
$$\omega_{\rho \sigma} \eta^{\rho\mu} \delta^{\alpha}_{\nu} = \frac{1}{2}\omega_{\rho \sigma} \left(\eta^{\rho\...
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Unclear passage in Lorentz generators derivation
It's not clear to me a passage, in the extraction of the generators of Lorentz's group acting on the Minkowksi's space points: we have
\begin{equation*}
\begin{split}
x^{' \alpha} & = \Lambda^{\...
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In order for Sound to exist, are Spacetime, Matter & Motion required first, in that exact order?
From what I’ve read so far online, briefly reading Newton, Einstein, and Minkowski’s theories this is the order I’ve come to. I.e, for matter to exist first there has to be space and time, for motion ...
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A problem of relative time when two observers in different frame of reference try to calculate the time experienced by another object
From what I understand from special relativity the time of the one which accelerated to attain that velocity runs slower.
Let three observers be together and the three observers be A,B and C from fig ...
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What Do We Envision the Fabric of Space to Be? Physical or Immaterial? [closed]
Sorry if this question is a bit lackluster or based on mistaken proof, I’m a high school student who’s highly interested in the fields of Quantum Theory and particle physics, and I’m trying to get a ...
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Is there a mistake in this special relativity question? Partial derivative
I’m not asking for the answer or even how to solve it — I just want to know if there has been a mistake.
Given
$$U^\alpha = (1+t^2, t^2, \sqrt{2}\,t,0)$$
Show that (using the “brute force” method)
$$...
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Is this experiment a valid way to measure the one-way speed of light? [duplicate]
Ok so my proposed experiment is as follows:
A light ray is emitted from a source (like laser)
When it's emitted the timer starts (there is only 1 clock in whole setup, which is a crucial aspect for ...
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Hall voltage vs frame dependent electric field in conductor
The hall voltage is created by a current in a magnetic field.
Similarly, a non current carrying conductor in an electric and magnetic field will appear to have a voltage in a different reverence frame....
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Equivalence of inertial frames of reference and lorentz transform derivation [duplicate]
I trying to understand Lorentz transformation derivation, and confuse on a simple statement: If i have 2 frame of reference, and the second moves relative to the first with speed $V$, so relative to ...
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The effects of light needing to reach observers from observed objects
I know some special relativity, but the material that I've learned has always treated observers as being able to instantly view objects. In reality, the light from an object first needs to travel to ...
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"Pure Energy" in special relativity and why does the rest energy follow from a derivation at the speed of light?
I'm currently studying special relativity by reading through the lecture notes of M. Fowler from the University of Virginia.
The famous equation $E=mc^2$ is derived by analyzing the work done by a ...
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Is time not perceivable without motion or change? [duplicate]
As kind of a chicken or the egg question, does motion come before time?
Doesn’t motion allow time to exist and no motion negate time from existing?
If everything in the universe were completely frozen ...
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Lorentz transform causes Faster than light motion for Spacelike-separated object?
Consider a 5-meter rod which exists on the x-axis of a frame of reference:
Now consider an observer moving at a velocity $0.1c$ relative to this reference frame, from right to left. Their frame of ...
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Have the Predictions in the Twin 'Paradox' Problem Been Confirmed Experimentally?
I can imagine a relatively simple experimental setup whose resulting data could easily be compared with theoretical predictions:
Send two identical atomic clocks into orbit and settle them at rest ...
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Continuity equation as a four-divergence. Possible misunderstanding of contravariance, covariance, or metric signature
Context
I am studying electromagnetic quantities through the framework of special relativity. I find it notation heavy and the issue of tensors is something I am still not fully grasping. The ...
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Special Relaticity and Uniform Circular Motion, a (Seemingly) Elementary Problem?
Suppose somewhere in the abyss of space, person X is in a free-float frame. X observes spaceship Y travelling in a uniform circular path centered at X. X measures Y's constant speed to be V and Y's ...
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Positive-frequency modes in an ideal cavity
For a quantum scalar field in Minkowski spacetime, a set of preferred modes is generally introduced as
$$
f_k\propto e^{i \left(kx-\omega_k t\right)},
$$
which is said to be positive-frequency since ...
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Time Dilation According to Stationary Object [duplicate]
Hello I am learning time dilation and I'm getting confused with some concepts:
Consider the given scenario, in the frame of reference of the Earth an event takes 2 seconds to occur. In the frame of ...
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Explaining Faraday's Law With Lorentz Transformations of $E$ and $B$ Fields
I've searched around for this but haven't come across a totally satisfying explanation yet. I'm trying to build a relatively simple model of how the Lorentz Transformations of the $E$ and $B$ fields ...
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Commutation of the Hamiltonian with the generator of boost
Consider the Hamiltonian $H = (\textbf{P}^2+m^2)^{1/2}$ the generators of rotation and and boost given by $$M^{0i} = tP^i-x^iH \\ M^{ij} = x^iP^j-x^jP^i$$ where $x^i$ and $P^j$ satisfy $\{x^i, P^j\} = ...
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One-Way Speed of Light and the Big Bang
Variations on this question have been asked a few times (e.g. here, here, and a few YouTube videos here and here). The claim seems to be that because we can only measure the round-trip speed of light, ...
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From Faraday's Paradox to the design of a One Piece Axial Flux Motor
My question is introduced through the following picture:
In the thought experiment a) a Faraday copper Disc with a magnetic field attached to it (out of page) is rotated clockwise. A Lorenz force ...
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Which experimental setup replicating Michelson-Morley experiment had the longest path of light?
After the Michelson-Morley (MM) experiment many scientists performed similar experiments using the original MM experimental setup, or different derivative experimental setups employing lasers and ...
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Can I find $\frac{dm}{dt}$ where $m$ is the relativistic mass of a particle?
So, recently I learned the basics of Special Relativity, and I found out that the mass of a body increases with the increase in its velocity as given by the Relativistic Mass equation:
$m=\frac{m_0}{\...
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Can we regard metric as the Higgs field of gravity?
The longer version of the question is: should we regard special relativity just as a spontaneous symmetry breaking phase of general relativity, driven by the non-zero vacuum expectation value (VEV) of ...
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Character of group elements of the Lorentz group
I am looking for a reference for the character of the element of the Lorentz group. If the generator the Lorentz transformations is given by $$\Lambda = e^{i\alpha\cdot J-\beta\cdot K}$$, then I wish ...
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Relativistic Light Velocity
I'm lay about relativity and I want to understand how does $c$ does not change between frames of reference.
Imagine a train of length $L_0$ at a relativistic speed and a light beam inside it. For an ...
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Does Einstein's Relativity contradict the Arrow of Time?
If according to Einstein spacetime is relative & not absolute, and the order of events can change depending on the observer's frame of reference, does this contradict the idea of the Arrow of Time/...
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Why doesn't stationary charge feel force from a current carrying infinite wire? [duplicate]
If a stationary charge is kept in front of current carrying wire , from charge's perspective the protons are at rest with it and electrons are moving , so shouldnt there be a lenght contraction in ...
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Questions about Lorentz Matrices and Lorentz Metric
(I use the abstract index notation convention in this post)
In $\mathbb{R}^4$, denote the Lorentz Metric as $g_{\mu\nu}=$diag$(-1,1,1,1)$, then we can define the Lorentz Matrices to be all $4\times 4$ ...
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Is power through a surface Lorentz invariant?
I am trying to solve this problem from Griffiths, but my point is not really to ask the answer of this problem :
A point charge $q$ is moving velocity $v$ parallel to $x$ axis. determine the total ...
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Lorentz Transformations and Angular Momentum unclear derivation
How do we get rid of $\omega^{\rho}_{\;\;\nu}$ and howt do we derive the last equation form the previous one. Here is URL for the source where I found this text page 17 (marked at bottom).
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Sending photons in opposite directions in a closed universe leads to different proper time before we see them again?
Consider a closed universe that's a 1D circle with circumference of $30$ light years in an inertial reference frame that we'll call $C_1$.
This universe has an observer who is travelling at a ...
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Unsure about the proper use of Lorentz transform
I'm not very comfortable with handling Lorentz transformations and I often have doubts...
Consider for example the following situation, illustrated by the diagram below:
A rod of length $L$ is placed ...
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Causality in formulas in general physics
Follow-up on this question about causality for Newton's second law.
In $F=ma$, the $=$ sign signifies proportionality, not causality. It makes sense, as the equal sign is invertible, whereas causality ...
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Definition of four-velocity: why define it with proper time of the object?
The four-velocity(world-velocty) is defined by : $u^μ=\frac{dx^μ}{dτ}$ ,where $τ$ is the proper time of the object.
I don't understand why it's defined with respect to the proper time but not the time ...
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On the derivation of Dirac matrices
Is it possible to retrieve the matrix elements of the $\gamma$s by simply knowing their anti-commutation relation:
$$
\{\gamma^\mu, \gamma^\nu\}=2\,g^{\mu\nu}\,\mathbb{I}_{4}
$$
I'm just trying to ...
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How would you reparametrize a worldline in terms of proper time in 2-dimensional Minkowski spacetime?
In a 2-dimensional Minkowski spacetime i.e. $x^\mu=(t,x)$, you can define the metric simply by the Minkowski metric, $ds^2=-dt^2+dx^2$, and the Christoffel symbols vanish. If you have a worldline ...
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Relation between proper acceleration and 4-acceleration
A rocket with 4-coordinate $(X^\alpha)$ is accelerating and $\tau$ is its proper time.
4-velocity $V^\alpha=\frac{d X^\alpha}{d\tau}$ and its 4-acceleration $A^\alpha = {V^\alpha}_{;\beta}V^\beta$.
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A hypothetical question about a fan/blade spinning near the speed of light in a vacuum
This question I find difficult to propose in a way that doesn't sound like it is a stupid question, but I will give it a try.
Suppose I place a fan suspended above the ground in a vacuum. The fan is ...
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Two rods of different proper lengths, questionable condition
I was solving problem 3.4 from Rindler's "Relativity - Special, General and Cosmological" (2006), which reads :
Use a Minkowski diagram to establish the following result: Given two rods of
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Why do we need to consider the full Poincare group to get unitary representations?
I am trying to study and understand QFT from the perspective of symmetries. I was referred to this super helpful answer by @ACuriousMind : https://physics.stackexchange.com/a/174908/50583. I still ...
