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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Failure of Central Limit Theorem for Juttner Distribution?

So I've heard the claim Central Limit Theorem can give the Maxwell Boltzmann distribution. However, it fails to reproduce the Juttner distribution. Why is this so?
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Rindler's criterion and definition of linearity of the Lorentz and Poincaré transformations

In Wolfgang Rindler's "Introduction to Special Relativity", 2.ed. 1991, on p.11 his derivation of the special Lorentz transformation $ x'=f(x) $ starts with the proposition that this ...
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Understanding where equation $2.3$ comes from?

I'm trying to understand this paper (equation $2.3$ specifically): Bini, D., Carini, P., & Jantzen, R. T. ($1995$). Relative observer kinematics in general relativity. Classical and Quantum ...
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Speed of light problem [duplicate]

This question totally hypothetical and I'm aware we can't travel at speed of light but IF .... If you were to travel at the speed of light according to Einsteins theory of relativity you would gain ...
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Time Dilation Explanation [closed]

This might be a dumb question but I'm still going to ask it. So basically I've been trying to learn Special Relativity through this lecture by Brian Greene, and the way he justifies time dilation is ...
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Logistics of Recreating the Michaelson-Morley Experiment

I want to recreate the Michaelson-Morley Experiment and am wondering how technically challenging it would be. I'm not looking for it to be super precise, just good enough to provide reasonable ...
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Can space proper-time (SPT) diagrams as used by Lewis Epstein in Relativity Visualized be used to explain the twins paradox of special relativity?

Space proper-time (SPT) diagrams are perhaps easier for the layman to understand than Minkowski diagrams, although I don't much about them. I have been, so far, unable to understand fully the latter, ...
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Why using incorrect formula results in a correct formula? [duplicate]

I know that the mass of a photon is zero. However, others say no it is just the rest mass which is zero, the relativistic mass isn't, but I say that no it is also zero because the rest mass $m$ is ...
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Can we interpret timelike, rest frame motion as velocity in the time direction? If so, does it cause charge to generate a ''$B$ field'' perp. to time?

For background: I've had courses on SR/GR from Hartle, E&M from Griffiths/Purcell, and know E/B fields are unified/transform with lorentz boost. My question is less about 'does SR account for E/B ...
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$t$ and $t'$ in Lorentz transformations

I don't really understand what the primed and unprimed coordinates imply in Lorentz transformations. In all of the books, they simply derive the coordinates, assuming that an inertial frame $ S$ is at ...
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Velocity addition and Thomas precession

In Goldstein’s classical mechanics, section 7.3, there's an approximation (7.19) that I do not understand, in particular $\beta''_y=\beta'_y/\gamma $. Worse, even if I accept the approximation, it ...
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What will happen if one used $[\phi (x), \frac{\partial L}{\partial (\partial _x\phi(x))}]=i\hbar$ to get a Quantum Field Theory?

Classical field theory does not discriminate between space and time, but canonical quantisation does. We use the relation $$[\phi (x), \frac{\partial L}{\partial (\partial _t\phi(x))}]=i\hbar$$ to get ...
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Moving spaceship problem in Special Theory of Relativity [closed]

Answer is (a). I am thinking like this way. According to passengers in moving spaceship, they take 1 hr to reach the Pegasus. Or we can say that as they will find themselves at rest, so the Pegasus ...
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Lorentz transformations in Minkowski space including invariants

Let's assume the reference frame of a still observer with the 2 axes: the x-axis and time axis t. Let's say there's another observer within that frame moving with a constant velocity v with respect to ...
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Are there things with different physical attributes that serve exact same purpose in a system? [closed]

I’ve been puzzling about this cross-disciplinary concept for the last week. Can you think of any two things that have different physical make up that serve the exact same purpose? For instance, ...
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Proof that conservation of momentum is Lorentz invariant

In classical mechanics, if $$\frac{\mathrm d}{\mathrm d t}\sum_i m_i\vec{v_i}=0$$is true for one frame of reference, then it is easy to prove that this is true for all frames (since different frames ...
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Try this method to calculate the speed of light [duplicate]

The speed of light as we know by today is 299,792,458m\s. But that is a two-way speed of light. Light first striking a mirror and then reflected back. No one has actually ever measured a one-way speed ...
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Prove that Majorana mass term is Lorentz invariance

I have a homework to prove that using one kind of chirality, let's say left-handed, we can construct a mass term. The argument is to show that this term $\psi^TCP_L\psi$ is satisfy the dimensionality ...
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Mass definition

One definition of mass is 'a measure of the quantity of matter in an object at rest relative to the observer'. What do 'at rest' and 'relative to the observer' mean here? I know it has to do with mass ...
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How to know if one-way speed of light is different from other? [duplicate]

I'll be using Veritasium's idea of Mars and Earth, so if you know, you know. We start by measuring the time it will take light to travel from Earth to Mars and for that we will use the simple formula, ...
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How do quantum probabilities transform under Lorentz transformations?

I think I get how scattering probabilities transform under Lorentz transforms. Once the interaction phase is over, the final probabilities become time independent. Hence, every observer could describe ...
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Does the notion of an universal clock really contradict special relativity? [closed]

Special relativity says that different observers qualify two events as simultaneous based on their velocities. But isn't that a statement about information they can measure rather than about reality? ...
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Is the speed of light accurate? [duplicate]

Speed of Light As we know by today that the speed of light is exactly 299,792,458m\s. French physicist Hippolyte Fizeau is credited with making the first ...
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Lorentz transformations (Maths) vs "reality" (Phyiscs) [closed]

Let (O) be the place of emission of a light signal (event) and (M) a point moving in a rectilinear motion (observer) uniform with a speed $\vec{u}$ and which is at time $ t=\frac{||\vec{OM}||}{c}=r$ ...
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Proof that a Lorentz-invariant scalar function can only depend on scalar products

If we have a Lorentz-invariant scalar function $f$ of a single four-vector $x^{\mu}$ we can show that $f$ can only depend on $x^2$ (see Argument of a scalar function to be invariant under Lorentz ...
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What is the relativistic velocity composition law? [closed]

In Galilean relativity we have the following relative velocity composition law: $$ \vec v_{DE} + \vec v_{EF} = \vec v_{DF} $$ Where the relative velocity between $i$ and $j$ for any $i$ and $j$ is ...
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Confused about tensor notations of how vector and covectors act on each other

I'm learning/playing around with tensors and somehow got this contradiction, suppose $\{v_i\}$ and $\{w_i\}$ are basis for a vector space $V$ and $\{ v^i \}$ and $\{w^i\}$ are basis for the dual space ...
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Clarification on clock synchronization passage from Kleppner and Kolenkow

I have a question about the following passage from An Introduction to Mechanics by Kleppner and Kolenkow. The passage reads as follows: The Newtonian procedure would work if the speed of light were ...
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What is the average recessional velocity of an object in the universe?

I’m trying to get a better grasp on cosmological horizons and have a question regarding recessional velocity. In particular: What is the average recessional velocity of a cosmological object (...
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The Same Origin Requirement of Reference Frames

Currently learning special relativity: My understanding is that Lorentz Transformations are the motions of Minkowski space that preserve the spacetime interval - and the same origin point. That is two ...
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Will light be travelling faster than the speed of light? [duplicate]

If a photon is emitted from a light source travelling with some velocity, then surely the photon emitted in the direction of travel would have a velocity equal to the speed of light plus the velocity ...
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Lorentz transformations in relativity [closed]

I'm trying to solve a particular problem given in Introduction to Special Relativity by R. Resnick, which goes like this: Two observers in the S frame, $A$ and $B$, are separated by a distance of 60 ...
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Is there only one convention to define the electromagnetic field tensor?

I know that the electromagnetic field tensor depends on which metric is used. For example wikipedia uses the $(+---)$ sign convention, but in the Griffiths we have the $(-+++)$ sign convention. That's ...
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How can I calculate length contraction using hyperbolic functions?

In the image below, the pink line on the $x$ axis is the length contracted measurement correspondent to the $x'$ measurement in the primed reference system. This length (let's call it $l$) equals $x'/...
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Creating The Sun [duplicate]

I am a high school student and just came to know about Einstein famous formula for relativity $$ E = mc^2 $$ I was wondering if somehow I was able to throw a considerably heavy object with a speed ...
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Ruling out dependence of y and z coordinates in Lorentz transformation

Let us assume that motion is in the $x$ direction, axes of both coordinate systems are aligned and their origins meet at $t=t'=0$. The most general relation between $x$ and $x'$ then becomes (ruling ...
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Invariance of lightspeed [closed]

Is there experimental evidence (not proof by mathematical deduction based on special relativity) of the invariance of light speed in two different frames of reference? For example, is it possible to ...
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Is there also relativistic length contraction caused by gravitational Lorentz transformation?

When objects move at relativistic speeds, their length as observed from outside gets scaled inversely proportional to the Lorentz factor in direction of the velocity: https://en.wikipedia.org/wiki/...
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How do I calculate the mass of a moving proton?

When a proton moves it's no longer its rest mass, it now has more mass because of the Kinetic Energy. So if we're to find the new protons mass if it was moving at some speed, how would we find it? ...
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Why is it difficult to make the Juttner distribution account for anisotropies?

Wiki states While the classic Maxwell-Juttner distribution generalizes for the case of special relativity, it fails to consider the anisotropic description. What are the challenges when one tries to ...
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Name of "coordinate representation" of spacetime symmetries

I would like to know the name of the following "natural" representation for symmetry groups that can be realized as spacetime symmetries. The easiest example is for instance the translations ...
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Does atomic time slow down at faster speeds? [duplicate]

Continuing with my questioning regarding two different "times", (but hopefully within the scope inquiry this time), if two asteroids are in an orbit around the solar system, one at 10,000kph ...
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Derivation of the transformation law for spinors

I'm reading the book Quantum Field Theory: An Integrated Approach by Eduardo Fradkin, and I got stuck where the transformation law for spinors $$ \psi'(x') = S(\Lambda) \psi(x) $$ is derived. In ...
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How can we derive the four-wavevector from first principles?

Context From [1], I understand that, "The four-wavevector is a wave four-vector that is defined, in Minkowski coordinates, as $$\mathbf{K}^\mu = \left(\frac{\omega}{c}, \mathbf{k}\right).\tag{1}"$...
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Twin Paradox: Fewer Seconds or Shorter Seconds?

In Einstein's Twin Paradox thought experiment, the travel time is shorter for the traveling brother than for the stationary brother. Since the SI unit of time in physics is the second, is the travel ...
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How important is the concept of rapidity in relativity?

After studying the concept of rapidity and the associated formulation of special relativity in terms of hyperbolic trigonometric functions of rapidity, I've come to understand the elegance of this ...
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What does an area represent in a spacetime diagram?

If I have a spacetime diagram with $t$ on the vertical axis and $x$ on the horizontal axis, does calculating an area in this diagram have any physical significance? The reason I ask is because I'm ...
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How can you calculate how long life will last with a regular run in terms of special relativity?

Imagine, John run everyday 10 km with speed 12 km/h towards the east along the equator. If he had not run, he would have died at 70 from the point of view of a motionless observer. How long will John ...
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On the Feynman's proof of Lorentz transformations

In this video he explains Feynman way of deriving the Lorentz transformations. First he considers the invariance, $$ x^{2}-(ct)^{2}=(x')^{2}-(ct')^{2}$$ He then invokes a bit of complex analysis by ...
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If the speed of light is the maximum speed anything can travel, and temperature describes vibration or motion, is there a maximum temperature? [duplicate]

Apologies for everything. This is my first question. Basically the title. If the speed of light is the maximum speed anything can travel, and temperature describes vibration or motion, is there a ...
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