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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How does one incorporate moving frames in the model of universe as an 4 dimensional affine space?
From what I understand, in relativistic and non-relativistic mechanics, we model the universe as an affine space $(E,\vec{E},-)$ where $E=\vec{E}=\mathbb{R}^4$. An orthogonal cartesian coordinate ...
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Question about the relation between Einstein's point-coincidence argument, the lorentz transformation and the principle of relativity
Is the reasoning below correct?
According to Einstein's point-coincidence argument, measurements correspond to the contact or intersection of world lines of objects or particles.
Lorentz ...
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What is the physical meaning of the metric coefficient in special relativity?
When I read Dirac's general theory of relativity, I have some questions.
The author assume $c=1$ and
$$
t=x^0, x=x^1, y=x^2, z=x^3
\tag{1}
$$
Therefore,
$$
( x^0)^2 -(x^1)^2 -(x^2)^2 -(x^3)^2
\tag{2}
...
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Special relativity elastic collision [closed]
I have to solve a problem of relativistic elastic collisions: a particle with velocity v collides with a stationary particle. The collision is linear and elastic, both particles have mass m. I need to ...
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Michelson Morley Experiment Arbitrary Ether Angle Special Relativity 2-8
Im trying to learn the material but also not get bogged down on everything I can't do. I've spent an obscene amount of time on this over the last few days. Good advice on navigating that middle ...
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Physical Significance of Relative Quantities [closed]
One of the tenets of relativity lies in the fact that the form of any physical equation must not depend on a particular choice of a coordinate system
I was wondering if this implies the fact that some ...
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Should a scalar field transform under Lorentz or Poincaré transformations?
I tried to check whether the usual plane-wave expansion for a Klein-Gordon Hermitian field is a scalar, meaning it transforms correctly under Poincaré transformations:
$$\hat{U}(\Lambda,a)\hat{\phi}(x)...
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Question on the plausibility of a time-travel-related energy paradox [closed]
if an object or person were to travel back in time, their mass-energy would disappear from the present and reappear in the past. This would imply:
A net creation of energy at the moment of ...
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Imagined spacecraft acc/decelerating at 1g to/from near $c$: Does the destination star not move faster than $c$?
Motivated by Andy Weir's novel Hail Mary, I was just reading an answer regarding the time needed to travel between stars with a constant acceleration (and deceleration after the mid-way point). Due to ...
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Interpretation of the Lorentz transformation property of quantum fields
When concerning the Lorentz transformation property of an local operator $O_a(x)$ (say, a quantum field) with Lorentz index $a$, we usually write
$$
U(\Lambda) O_a(x) U(\Lambda)^{-1} = \sum_b D_{ab}(\...
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Intuitive explanation of inductive kickback viewed from special relativity
I am trying to find an intuitive explanation to the phenomenon if inductive kickback, where if you disconnect suddenly an inductor that has it's magnetic field charged, the voltage of it's terminals ...
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Emergence of gauge invariance in QFT
This question is related to different motivations for the need of gauge invariance in QFT. I was introduced to gauge invariance in the following way.
Consider a vector field $A^\mu(x)$, with $x\equiv ...
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Dimension of Lorentz Group (as a Lie Group/Manifold)
The restricted Lorentz subgroup, $SO^{+}(1,3)$ is a subgroup of Lorentz Group, which has a real dimension 6. What then is the manifold dimension of $SO(1,3)$, the full Lorentz Group?
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In the Solution of Raychaudhuri's equation
I am new to Tensors and the math of Special Relativity. I need to solve the Realtivistic Raychaudhuri's eqaution but unable to proceed. I got the Raychaudhuri's equation from Dr.Joseph Samuel's paper ...
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When deriving length contraction, why we can only transform from reference frame S to reference frame S'?
When deriving length contraction, we assume that a rod with length $L$ in rest frame lies on x axis.To simplify, we assume that in frame S, it only has a velocity in direction of x axis. To derive ...
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Object perceived to be traveling faster then light [duplicate]
Consider an object with a worldline $$x = -vt+x_0$$ and an observer at $$x=0$$ such that the object is moving towards the observer with velocity $v$. From each point $(x,\frac{x_0-x}{v})$ in the ...
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Proving that the order of the events is invariant [closed]
Text of the exercise:
Event B is a consequence of event A. Using Lorentz transformations, prove that there is no inertial frame for which Event B happens before event A.
I wanted for someone to say ...
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Apparent Discrepancy in Lorentz Force on a Proton from Moving Reference Frames (Classical Electromagnetism)
I am grappling with a consistency issue when analyzing the force on a charged particle from different inertial reference frames, strictly within the realm of classical (pre-relativistic) ...
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Can Einstein's light clock be tested?
Has anyone ever performed, or proposed, a real experiment to directly test Einstein's light clock thought experiment? Is this realistic?
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Special relativity travel duration
I am slightly confused about the way one would compute the travel duration of an object as seen in two different inertial frames. I have an inertial frame $S$ and another frame $S^\prime$ that moves ...
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Action when a classical particle coupled to external scalar field
In the textbook classical mechanics written by Professor Liu Chuan(刘川) in Peking University, in chapter 2.8, the author directly writes down the action of a classical relativistic particle coupled to ...
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Wilson’s renormalization group: Euclidean versus Lorentzian signature
I spent all of last semester learning all about Wilson’s RG, but a few days ago I realized an incredibly basic and mildly disturbing fact.
Nature is Lorentzian, not Euclidean.
I have been Wick rotated ...
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Constant 4-force vs constant 3-force vs constant proper acceleration
This question inquires about motion under a constant 4-force in 1D.
My confusion lies in what constant 4-force actually means.
Does it mean:
A constant 4-vector over proper or coordinate time (as a ...
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Are space and time separate? [closed]
According to special relativity, two events can be a cause and effect of each other if those two events can be found in any lightcone. This contrasts with Galilean relativity, where two events can be ...
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A Relativity Paradox on Length Contraction
Relativistic “Cover-Up” Paradox
Two identical plates A and B (same rest length , same breadth) are initially parallel, one behind the other. In lab frame :
Plate A is at rest.
Plate B moves along +x ...
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