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.
5,984 questions
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Illusion that $v > c$?
I am currently studying length contraction in special relativity (and having the hardest time getting the harder exercises in my book right) and there is the following exercise in my book is driving ...
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What do I see If I move with the speed of light? [duplicate]
Will I be able to see anything or I would be blind?
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From the standpoint of a tachyonic frame of reference, is the universe perceived as a black hole? [on hold]
I am familiar with the limitations imposed by special relativity related to the existence of tachyonic observers. Still, since many experiments directed towards the detection of tachyons have been ...
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1answer
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Is there a physical observable with the same units as c/G?
Dividing the speed of light $c$ by the gravitational constant $G$
yields the dimension mass*time/area or mass/(length * speed)
Is there a physical quantity used in textbooks with this dimension? I ...
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2answers
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Why does the 'metric Lagrangian' approach appear to fail in Newtonian mechanics?
A well known derivation of the free-space Lagrangian in Special Relativity goes as follows:
The action $\mathcal{S}$ is a functional of the path taken through
configuration space, $\mathbf{q}(\lambda)...
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How are the time dilation and the relativistic Doppler shift added together in what observers “see”?
I'm using the illustration from this question:
Suppose A and B are d light years away, and at rest. Then they symmetrically start to travel toward each other (symmetric acceleration process in ...
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If an object is travelling near light speed, would it's actions seem to be in slow motion?
Hypothetically if we were observing a clock travelling near light speed relative to us, we would see the clock ticking at a much slower speed than us. If that is true, then would all actions that are ...
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Why isn't time contraction a thing?
I'm very naive about relativity, but if it could be possible that Alice ages less than Bob in a journey, doesn't it logically follow that from the point of view of Alice, Bob has, at some point, gone ...
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How does one's view of the universe change as one approaches the speed of light?
I found an interesting and fun question at worldbuilding.stackexchange.com , that to my surprise, I don't find that easy to answer. I would like to quote here that question , but with a small ...
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Nature of Experiment or Measurement tied to Special Relativity concepts
Premise: In special relativity, we come across concepts like Length Contraction and Time Dilation. Pertaining to these topics, I have come across the following diagram (or its slight variations) in ...
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A beginner's question on time dilation
I have just started understanding relativity so the question might look absurd.
I know that the faster we move through space , the slower we move through time.
But I haven't understood it fully.
I ...
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1answer
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Origin of the energy distribution of synchrotron radiation
Is there an easy explanation why synchrotron radiation from a bending magnet (e.g. in an electron storage ring) has an energy distribution? In other words, given a specific magnet with a defined ...
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Commutation relation Lorentz Algebra
Related question, which I don't understand either. I think is easier to get the Lorentz group algebra as defined by Maggiore,
$$
[J^{\mu\nu},J^{\rho\sigma}] = i(\eta^{\nu\rho}J^{\mu\sigma} - \eta^{\...
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1answer
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How to determine if a tensor is covariant or contravariant?
In special relativity, the coordenates of a event are in general written using a 4-vector: $$x^{\mu} = \binom{ct}{\textbf{x}}$$ where $\textbf{x} = (x,y,z)$ are the spacial coordenates. This is a ...
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Momentum Four-Vectors particle physics
I am studying Special Relativity, and am really struggling to get my head around four-vectors.
I am looking at the following question. You have a particle of rest mass M and total energy E, which ...
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The pure energy released from antimatter annihilation can reveal the mysteries of universe [on hold]
The pure energy released from antimatter annihilation can there be any use of this clean energy for research purposes. Like the use of light waves in LIGO for gravitational waves study. Can we use the ...
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1answer
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Why is the past also represented as a light cone in the opposite direction? (layman)
I recently heard about light cones as mentioned in Stephen Hawking's A Brief History of Time. I understand light can be seen as a cone when a flash of light is spread from an ...
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Question about pair production
Pair production can't occur in vaccum because momentum cannot be conserved because the photon does not have a rest frame of reference, that means that the produced pair has a center of mass frame of ...
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Difference between coordinate systame and frame of reference in relativity
I have taken a relativity course, and am not quite clear as to whether the notion of a frame of referene is independent of the coordinate system. At the moment, I think that any frame of reference (of ...
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2answers
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Time Dilation Special Relativity
Let's say we have an observer named Jack on a spaceship traveling at a constant velocity of 0.95c to the right, according to Bill, who is on the Earth. Then the spaceship reaches planet A and then ...
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Pair production problem, how is energy not conserved here?
The problem is asking me to find the minimum photon energy that would produce an electron-positron pair when it collides with a free electron at rest.
This is my attempt at trying to conserve both ...
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Why isn't there a quantum number associated with the Lorentz boost?
It is a re-post of this question since there is no answer.
I am doing problem 3.2 of Schwartz's QFT and figured out all previous questions, where we identified the conserved current of Lorentz ...
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Why haven't we yet tried accelerating a space station with people inside to a near light speed? [on hold]
Is that something we could do if we use ion or nuclear thrusters?
Wouldn't people in the station reach 0.99993 speed of light in just ...
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1answer
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What is the energy of a photon reflected off of a moving mirror?
In accordance with the above diagram, a photon with energy $E$ is reflected off of a moving mirror with speed $v$. I think I am supposed to use the conservation of four momentum to find the reflected ...
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1answer
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Boost as a generator of constant acceleration
In Covariant Loop Quantum Gravity by Carlo Rovelli p204, Sec 10.4, there is a paragraph which states
..., a trajectory at constant acceleration is generated by the boost
generator $K_z$ in the ...
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Momentum transfer due to Thompson scattering
This is an interesting problem regarding on momentum transfer of electromagnetic waves at a relativistic limit. Here we consider Thompson scattering, but the results could be well applicable to other ...
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1answer
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Accelerated frame vs gravity frame
Can accelerated frame change curvature of space as gravity does?
Can there accelerated frame be pure inertial frame?
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Doppler Shift in Michelson-Interferometer
I've used a michelson interferometer with a moveable mirror in order to verify the doppler effect for light waves. But whilst writing the theory for my lab report I encounterd an issue I'm not able to ...
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Distance to Proxima Centauri according to SIMBAD [closed]
What is distance to Proxima Centauri measured up to 4th decimal?
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What is the Lenz reaction due to Radial EMF generated by a rotating cylindrical magnet with a steady magnetic field?
Per the top answer to the question "What is the electric field generated by a spinning magnet?", a rotating magnet can generate an electric field even if it does so on its axis of cylindrical-symmetry....
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Relativity of Simultaneous Events
I'm used to relativity of simultaneity situations that are like the Einstein lightning train thought experiment. This problem is different. Say an observer on the space station observes lamps 1 and 2 ...
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1answer
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Does Sagnac effect imply anisotropy of speed of light in this inertial frame of reference?
There seems to be a consensus that the one - way speed of light is anisotropic in a rotating frame of reference (Sagnac Effect).
Imagine a rotating ring of infinitely large diameter. In accordance ...
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1answer
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How do u get Eq3 from Eq2&Eq1 [closed]
I keep getting the wrong results by subbing eq1 into eq2
It’s from Kleppner’s an introduction to mechanics 2nd edition
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Why is electric field $E^i = E_i$ instead of $E^i = - E_i$?
Let us consider the Minkowski spacetim.
Generally, we know that when we lower or raise the index of the convariant or contravairant tensor, we need to use the metric $\eta^{\mu \nu}=\eta_{\mu \nu}=(+,...
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1answer
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Tangent space of pseudo-Euclidean manifold
My textbook says (without any justification that I can see) that
"since Minkowski spacetime is pseudo-Euclidean, the tangent space $T_P$ at any point $P$ coincides with the manifold itself".
My ...
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Question about Relativity and Proper Reference Frames [duplicate]
If your in a space ship moving at relativistic speeds in reference to an observer on Earth, time would have to be going slower on the space ship and faster on Earth. However, wouldn't the Earth be ...
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1answer
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Conservation of Energy and Momentum - Special Relativity
I am confused as to how we can assert that energy and momentum are conserved in special relativity. I was attempting a problem on the elastic collision of two particles and came across this.
I have ...
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1answer
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What does the line of constant space time (interval) represent?
In this diagram, what do the hyperbola represent. I understand that for a given hyperbola t^2-(x/c)^2 is constant, but in an answer given to this question: What spacelike, timelike and lightlike ...
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1answer
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Minkowski diagram
I have not well understood the picture of geogebra regarding the angle of time (t') that is inclined compared to (t) of 26.57°angle .
In the picture we see that the velocity is setted at 0.5c, for ...
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Does the fact that we can only measure the two-way speed of light undermine the axiom of invariance?
When we measure the speed of light we get the same answer in all directions. This is taken to undermine the aether or absolute motion hypothesis and give support to the proposal that the speed of ...
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A charge moving relativistically in electric field [closed]
I need help in the following question:
At $t=0$ a charged particle is moving at some speed $u$ in the X direction,and enters a constant electric field E in the direction of Y (all measured in lab ...
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Flux through a ball of a moving relativistic particle [closed]
I have been struggling with the following question for so long that I decided to give up and ask you, the professionals. It seems that the relativistic idea of the question is not the problem, but the ...
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2answers
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Lorentz-transformation
I don't understand how to derive the matrix representing the Lorentz-transformation given two systems S and S':
$$x' = \Lambda x$$
these transformations do not leave the differences $\Delta x^\mu$ ...
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How can a vertical beam of light move sideways with an interferometer? [duplicate]
The picture is of the Michelson Morley Interferometer.
How can the upward, vertical beam of light move sideways with the interferometer? This brings me to the conclusion that "Aether are attracted ...
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1answer
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Voyager spacecrafts life span and theory of relativity
The Voyager spacecrafts are moving with an approximate constant speed of 16 to 17 km/s. As per Einstein's theory of relativity, time passes more slowly for them compared to us. Then, is it possible ...
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0answers
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Antiparticles travelling backward through time [duplicate]
Could someone please explain to me Feynman and Wheeler's theory of waves acting forward and backward in time?
I have read about their idea of an antiparticle behaving as a particle travelling ...
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1answer
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From relativistic equation to find Dirac matrices
Is this possible and then how?
$$((\gamma \otimes \mathbf\sigma)\bullet\mathbf p)(\gamma^\prime\otimes\mathbf 1_2) = \gamma\gamma^\prime\otimes\sigma \bullet \mathbf p $$
where $\gamma$ and $\gamma^\...
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Why can't we rule out other synchronization procedures?
According to what I've read, it is generally regarded that Einstein's choice to have the speed of light equal in every direction is only a convention, and since there is no way to measure the one-way ...
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Four-velocity vector of light
Please note that my question is not a duplicate, it is not about the speed of light, my question is only technical about the four velocity vector for light, its definedeness, value and constantness.
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Combining two Lorentz boosts
Is it possible to express two Lorentz boosts $A_x(\beta)$ and $A_y(\beta)$ along the x/y-axis as one boost described by $A(\overrightarrow \delta)$?
To answer this, I start by defining $\theta \equiv ...
