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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In SR length contraction, does matter flatten because the space around it flattens or does the structure of the matter flatten?

Most people believe length contraction is a real spatial phenomenon and if so there's nothing to contract in empty space and since matter contains mostly empty space then it is only the structure of ...
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Acceleration in special relativity causing “strange” force

So, imagine an observer who is stationary on Earth. Relative to it, a rocket is moving with a constant velocity of $0.5c \overrightarrow{i} + 0.5c \overrightarrow{j}$. Their axes of coordinate systems ...
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What does it mean when we say the kinematic space of the time slice of Ads3 is ds2?

I have been going through this paper Integral Geometry and Holography the authors in page 19 demonstrate the idea of kinematic space using $Ads_3$, they start off with a hyperboloid model and show ...
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Interpretation of equal absolute values of pressure and tension in the electric or magnetic field along Cartesian axes aligned with the field

For an electric or magnetic field along the $x$ axis, the stress-energy tensor in mixed covariant-contravariant form, in $(t,x,y,z)$ coordinates, is of the form $\operatorname{diag}(1,1,-1,-1)$ (...
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Is it Valid to Derive $E = pc$ From the Energy-Momentum Relationship for Photons?

Given a particle with mass $m$ moving at velocity $v$, total energy is: $$E^2 = (pc)^2 + (mc^2)^2$$ Note I am not using the relativistic - rest mass convention, as I was taught to think in ...
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Proof that representation of proper orthochronous Poincaré group is unitary

We have defined the action of the representation of the Lorentz group on the Fock space by $U(\Lambda)a^*(k_1)\dots a^*(k_N)\Omega = a^*(\Lambda k_1)\dots a^*(\Lambda k_N)\Omega$. I am now to proof ...
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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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In the twin paradox does the returning twin also come back permanently length contracted flatter than the twin on Earth?

This video from Brian Greene suggests this is so: https://www.youtube.com/watch?v=2sZUNud6rRw&list=PLj6DWzIvBi4PFDXCCV1bNhVUgDLTwVbFc&index=60 It shows if you stop a pole in the barn (...
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On existence of other physical constants and the assumption in proof for special theory of relativity? [closed]

The only constant (that exist in the world) is speed of light in vacuum or c which is close to 3X10^8 m/s so 'all other constants should be variables (to some degree) w.r.t. this constant'. If this is ...
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What does special relativity say about the apparent versus real length contraction in regards to a large body such as Earth?

Suppose there are 2 spaceships moving perpendicular to a large body (ex. Earth) at very high speeds. According to all official educational resources I have found online ( such as Fermi Lab and many ...
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How is Newtonian Mechanics contradictory to Special Relativity at a certain parameter? [duplicate]

How is Newtonian Mechanics contradictory to Special Relativity at a certain parameter and what conditions must be met for Newtonian Mechanics to be a suitable model for describing systems?
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Very Massive Relativistic Body [duplicate]

You're observing a massive object (probably a neutron star), and it is moving at a significant fraction of the speed of light relative to you. The mass of the object is just below the mass necessary ...
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Is really there exists any kind constant that can explain expanding universe and increasing time?

I know far galaxies moving out from us I.e universe expanding I.e increasing space.There also time always growing up.From four dimensional analysis space time has covariance. I want to know is there ...
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For a perfect fluid, what does $-u_a\nabla_bT^{ab}$ represent?

Let $u_b$ be the 4-velocity of the perfect fluid and $T^{ab}$ be the stress-energy tensor of the fluid. Then, exactly what does $-u_a\nabla_bT^{ab}$ represent? I suspect it is related to some kind of ...
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Covariance of the perfect fluid's stress tensor

In Special Relativity, for a perfect fluid (i.e. without heat transference or viscosity) we have a stress tensor $T_{\mu \nu}$ $$ T_{\mu \nu} = -p\eta_{\mu \nu} + (\rho + p)u_\mu u_\nu $$ It is said ...
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Why are speeds of different EM waves in vacuum not EXACTLY equal?

It is said in my textbook (reference below) that the different waves of the Electromagnetic Spectrum have velocities almost equal to each other. (Variations are within a few m/s according to my ...
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How was it determined that the speed of light in vacuum is a constant?

For over a hundred years now we have accepted that the speed of light is the same in all frames of reference. What I'm wondering is - how was this determined? I'm aware of the Michelson and Morley ...
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Relativistic energy density (dust, presureless gas or number of particles)

The basic question on the relativistic energy density of the dust (pressureless gas or some number of moving particles). I assume that for some group of particles it is intuitively obvious to write ...
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Maxwell's equations in relativistic notation

We define $$x^\alpha=(ct,x,y,z)$$ $$\partial_\alpha=\frac\partial {\partial x^\alpha}=\biggl(\frac 1 {c^2} \frac\partial {\partial t} ,\nabla \biggr)$$ $$F_{\alpha \beta}=\begin{pmatrix} 0 & -\...
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Invariant quantities? [duplicate]

Every phisical quantity is tensor quantity (special cases of tensors are vectors and scalars). There are transformation rules for tensors. For example for scalar quantity F transformation rule is F'(x'...
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Resolution between off-shell and on-shell views of particle interactions in popular writing

This question is based on this blog post 'Is Dark Matter Lurking in Neutron Decays?' and a following comment I re-read recently. It has something I have seen often in popular writing, which I believe ...
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Is The Third Time Derivative of Position Relative, and if it is, Can it be represented in 6 Dimensions?

Einstein’s Theory of Special Relativity only applied to objects at constant velocities. This could be represented in a four dimensional Minkowski Space. From what I understand, Einstein compared ...
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Perpendicular velocities (special relativity)

Imagine that you are traveling in a spaceship that passes by Earth at a velocity of $v$ (Lorentz factor = $\gamma$), and you fire an escape pod from your spaceship pointed straight up (in the $y$ or $...
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Is the phase velocity of plane wave solutions of the Klein-Gordon equation larger than $c$?

The phase velocity is given by $$ v= \frac{\omega}{k} \, .$$ Using the usual dispersion relation $$ E^2 = p^2c^2+ m^2c^4 \leftrightarrow \omega^2 \hbar^2= k^2\hbar^2 c^2 + m^2c^4$$ yields $$ v= \frac{\...
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How does $p\cdot u$ relate to observed energy and momentum for a massive particle?

Gravitation by Charles W. Misner, Kip Throne and John Wheeler page 65 Exercise 2.5. The book defined "energy" for a photon $E=-\mathbf p\cdot \mathbf u$ for subsection 2.8, which later explained as a ...
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Coordinate-free representation of invariant interval [closed]

Suppose event B is at the origin of space-time diagram. Let A and C be arbitrary events (A is in the backward light cone and C is on the forward light cone with B at the origin). The world line ...
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How can a proton travel the milky-way in 296 seconds? [closed]

In the Introductory Special Relativity book, by W. G. V. Rosser, the author presented an example about Lorentz Length contraction. In this example, a proton is crossing the milky-way galaxy and he is ...
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What does it mean to SQUARE the speed of light? [closed]

$E=mc^2$ But what exactly does it MEAN to square the speed of light? Like, what is happening in the universe at that point in the equation?
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Lorentz transformation of hamiltonian

I'm really rusty on LT and hope to get soem clarification. How would the loretnz transformation of the following quantity turn out? $$\Lambda_\mu^\nu \int d^3ka^\dagger(k)a(k)$$
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Tensor acting on another tensor

On page 22 of Sean Carroll's Spacetime and Geometry, he says that tensors can act on other tensors and gives the following example: $$ U^{\mu}_{\nu} = T^{\mu \rho}_{\sigma} S^{\sigma}_{\rho \nu}$$ ...
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Michelson-Morley Experiment as evidence for Special Relativity

Context: Our state (NSW, Australia) recently got a new syllabus for the year 12 physics course, and as such we are the first year going through with the new course. One of the things we need to learn ...
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Relativistic trajectory in a constant electric field

I'm trying to write the trajectory ($y^i = y^i(t),\ i \in \{1, 2, 3\},\ y^0 = t$) of a particle seen from an inertial reference frame, ${\cal O\ '}$, that moves along $y^2$ axis with constant speed $(...
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Shared link between non-relativistic QM and Special Relativity: Proper time? [closed]

So in the path integral formulation of QM, each path gets weighted by a phase factor of $e^{iS/ \hbar}$, where S indicates the classical action of the path. For a small displacement in space and time (...
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How can I think of the flat space metric tensor as a multilinear function?

I'm pretty new to the idea of tensors, and I'm having a bit of confusion with how to think about the flat space metric tensor in special relativity. I understand that a good way to think about ...
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Finding the inverse metric of a metric close to Minkowski metric [closed]

Let $g_{uv}=\eta_{uv}+h_{uv}$ be a metric with $\mid h_{uv} \mid$ very small so that the metric is close to the Minkowski metric. Then we can write the inverse metric $g^{uv}=\eta^{uv}+k^{uv}$ with $\...
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How do time reversal and parity inversion act on a Majorana spinor in QFT?

Dirac particles are not the same Majorana particles. However, in the simple Lorentz group (boost and rotations, but no parity or time flips), they transform the same way. Particles in QFT were defined ...
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1answer
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Possible error in textbook (Lorentz transformation)

I'm concerned about the last line of this page. I believe it should be: "With the help of a friend in $S'$, the $S$ observer also measures the distance from the event to the origin of $S'$ and finds ...
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Does Einstein velocity addition rule work only for speeds, or for velocity vectors as well?

Einstein's Velocity addition rule (https://en.wikipedia.org/wiki/Velocity-addition_formula#Special_relativity) was used to describe to replace galileo's in account for relativity. However, in many ...
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Virtual rigid body in Special Relativity

Mischievous but non-trivial: Can I use a virtual rigid body in a thought experiment? For instance four equidistant rockets in tetrahedral formation, variously accelerating in such a way that every ...
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Imaginary term solution in the limit $v\ll c$ of relativistic Lagrangian

The relativistic action is $$ S=- m \int_a^b d s. $$ With metric $ds^2=dx^2 - dt^2$, we get: $$ \begin{align} S&=\pm m \int_a^b \sqrt{dx^2-dt^2}\\ &=\pm mc\int_a^b dt\sqrt{\left(\frac{dx}{...
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What does the first postulate of Special Relativity mean?

Physical laws are invariant regardless. It can be an inertial frame and also a non inertial frame. Now it is the case you cannot do any experiment in an inertial frame of reference to test if you are ...
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Is expansion an exception to the postulate that the relative velocity between two objects cannot exceed the speed of light? [duplicate]

If expansion is not an exception to this rule, then how to explain the idea that the speed of light limits the portion of the universe that we can observe? Both we and all of the rest of the matter ...
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Mass reduction due to emission of photons

when a torchlight emits a photon of energy E, will its mass reduce by (E/C^2) according to mass energy equivalance? if no what will be the reduced mass?
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Is the “spacetime” the same thing as the mathematical 4th dimension?

Is the "spacetime" the same thing as the mathematical 4th dimension? We often say that time is the fourth dimension, but I am wondering if it's means that time is like the fourth geometrical axis, or ...
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1answer
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Correct transformation of left-handed Weyl spinor

In the book "Matthew D. Schwartz, Quantum Field Theory and the Standard Model", page 164, it says that a left-handed spinor transforms as $$\psi_L \rightarrow e^{\frac{1}{2}(i\vec{\theta} - \vec{\...
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Should LIGO have been impacted by Lorentz contraction?

What bearing would or could Lorentz-Fitzgerald length contraction have on Ligo detections? Was this accounted for?
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Does charge conjugation symmetry sit in the Lorentz group?

We know the Lorentz group is $O(3,1)$ in 4 dimensional spacetime. We know that there are 4 disconnected components in Lorentz group $O(3,1)$, and https://math.stackexchange.com/q/2204349/ $$\pi_0(\...
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2answers
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Why is it necessary that different observers agree on the value of the spacetime interval $ds^2$?

What's the physical reason that all (inertial) observers agree on the value of the spacetime interval $$ds^2 = (c dt)^2 - dx^2 - dy^2 -dz^2 \, ?$$ What would be the physical implications if different ...
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1answer
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Simulteneity & Irrelevance of Frame Choice [duplicate]

Let’s assume I measure time t in my rest frame - thus in a moving frame I have t’ corrected according to the Lorentz factor. I have a moving primed frame such that t’= 0.5t for example. I measure 1 ...
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How to beat speed of light using graphene pulley motor? [duplicate]

A 10 meter graphene pulley with 10,000 teeth, attached to a second graphene pulley of 10mm with 10 teeth both in a low temperature vacuum chamber. The first graphene pulley is being rotated by a ...