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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Poincare group representation and complete set

In Weinberg's book of Qft, chapter 2 of volume 1, he uses the eigenstates of the four-momentum to construct the unitary irreducible representations of the Poincare group. My question is, since $P^\mu,...
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1answer
88 views

Is this argument valid as to why we can (not can't) reach the speed of light?Please do explain [closed]

I have already asked this question on quora, with difficulty but I have not yet obtained a "works for me" answer. Please discuss with me about this.:) Q:Why can we not touch the speed of light? F=ma;...
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2answers
109 views

Stripped twin paradox [closed]

Consider an empty space, except for Alice and Bob. Suppose Alice sees Bob move away and then come back again. Suppose Bob sees Alice move away and then come back again. Suppose either of them will ...
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2answers
74 views

Can the single object accelerate? (Relativity theory) [closed]

Suppose space is empty except for one single object. According to relativity theory it doesn't matter whether we assign a constant velocity to it or not; in both scenarios the same is predicted. The ...
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27 views

Generation of back emf with relativistic approach to EM Waves

I learnt that Magnetic force around a current carrying conductor is nothing but relativistic electrostatic force observed by a charge particle from its frame of reference. But I am not able to ...
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199 views

Covariant and contravariant 4-vector in special relativity

I've just learned about contra- and covariant vector in the context of special relativity (in electrodynamic) and I'm struggling with some concept. From what I found, an intuitive definition of ...
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2answers
57 views

Is all of a black hole's mass situated arbitrarily close to the event horizon?

Forgive me if I'm thinking about black holes in completely the wrong way, but since time dilation increases to arbitrarily large amounts the closer you get to the event horizon of a black hole, wouldn'...
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2answers
274 views

Does hotter radioactive substance have longer half life?

Sorry to have a newbie question! But I want to ask, if it is possible to change the half life of radioactive substance by heating it, my hypothesis is: When substance becomes hotter, the kinetic ...
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1answer
86 views

Why is $|\Lambda^0_0| \ge 1$ for a Lorentz transformation?

I'm taking a course of QFT and in the notes that the professor gave us he says that for a Lorentz transformation $\Lambda^\mu_\nu$ we have $|\Lambda^0_0| \ge 1$. He doesn't give further information ...
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134 views

Minkowski space-time

Suppose we have the vector space $\mathbb{R}^4$ and the Lorentz's transformation $f:\mathbb{R}^4\to\mathbb{R}^4$. Consider a inner product $g$ given by: $$g(x,y)=x^1y^1+x^2y^2+x^3y^3-c^2t^1t^2$$ for ...
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2answers
111 views

Killing field in Minkowski space-time

If we look at the killing equation for a vector field $X$ in $\mathbb{R}^{(p,q)}$ (or on an open subset thereof) in coordinates with constant diagonal pseudo-metric we get: $$X_{\mu,\nu}+X_{\nu,\mu}=...
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41 views

Can an event occur before or after the other one depending on what frame of reference we are in?

Two buses moving relative to each other with 30% the speed of light (4 light-min apart). Now by some mysterious way bus 1 comes to the knowledge that after 3 min-bus 2 time bus 2 is going to explode. ...
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1answer
79 views

Magnetic field felt by an observer “orbiting” a proton

Classically, if one has an electron orbiting a proton, how can the magnetic field felt by an observer with the same instantaneous velocity as the electron be calculated? It seems that I may find the ...
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2answers
138 views

Understanding Tensor-operations, covariance, contravariance, … in the context of Special Relativity

I'm currently learning about special relativity but I'm having a really hard time grasping the Tensor-operations. Let's take the Minkowski scalar product of 2 four-vectors: $$\pmb U . \pmb V = U^0V^...
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2answers
427 views

How do I describe the order of events in spacetime?

In Newtonian mechanics, we have 3-space and time. Time allows us to order events. For example, I hold a ball in the air at time $t_0$. Then I drop it at some later time $t_1 > t_0$. Finally it hits ...
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2answers
99 views

Rest mass energy of electron

For electron's energy why we some time use the word "REST MASS ENERGY" why we use this word as electron is always spinning?
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1answer
50 views

Clarification for the mutual time dilation for two observers in their inertial frame of reference

I am trying to understand the idea under the theory of special relativity recently. The time dilation predicted by special relativity baffles me. I used to think that I understand the idea underlies ...
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2answers
91 views

Special Relativity and symmetry of time dilation

I stumbled across a paradox in special relativity for which I have found no answer. In the twin paradox, the loss of symmetry in time dilation is usually explained by the reversal of movement of the ...
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20 views

relativity, light, transformations [duplicate]

is the light itself a reference frame in special relativity? Can we write the special relativity transformations between a photon and other reference frames? If we can't then what other transformation ...
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0answers
23 views

Is photon massless? [duplicate]

if photon is massless then in E2=m2c4+p2c2 is m=0 ? and p=mv1-mv2 shouldnt be zero too. if both the statements are true then does photon has no energy?
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1answer
62 views

Relativity of simultaneity subtle example [closed]

imagine three persons, Person A is standing next to a device these device is an AND gate if two photons(one from right and one from left) reaches the AND gate at the same time the device explodes and ...
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5answers
579 views

Why is rapidity additive?

With the rapidity $\phi$ defined so that $\frac{v}{c}=\tanh{\phi}$, say you have 3 parallel moving reference frames $S$, $S'$ and $S''$ with a constant but different velocity/rapidity. If the ...
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35 views

Highest temperature [duplicate]

The temperature of a body varies with the KE of its particles. The maximum KE can be obtained by making the atoms move about near the speed of light. Let us take the body as a gas so that the body can ...
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0answers
25 views

Observed gravity of a fast moving particle relative to observer [duplicate]

Special relativity tells us that a fast-moving object with sufficient speed will appear more massive that it would at rest relative to an observer. Since the strength of an object's gravitational ...
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1answer
88 views

How to calculate the thrust of a rocket with relativistic exhaust

The general thrust equation is $F = \frac{dm}{dt}\cdot v$, where $m$ is propellant's mass and $v$ is the exhaust velocity, is the equation right? What if the propellant is highly relativistic? One ...
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29 views

Relativity collision problem [closed]

Here is the problem: A body of mass m (I assumed this is rest mass, but not 100%), and momentum p(subscript m) collides with a stationary particle of mass M. Find the available energy in the CM frame....
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48 views

determining electrostatic field using only symmetries

As an exercise, I'm trying to (rigorously) determine as much as possible about the electrostatic field due to a infinite line of charge (along the z-axis) without using Maxwell's equations or any of ...
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1answer
70 views

Annihilation process and photons [closed]

Why should two photons produced by the annihilation process move in opposite direction? I know you would say for the conservation of momentum but why can't they move in the same direction, I want to ...
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0answers
45 views

Spacetime as a coset of a symmetry group

In the introduction to his nice PNAS paper on symmetry, David Gross said Einstein’s great advance in 1905 was to put symmetry first, to regard the symmetry principle as the primary feature of ...
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1answer
38 views

Deduction of four-acceleration vector

Consider an Euclidean metric. The four-accelation vector can be obtained from the time derivative of four-velocity: $$a^k=\frac{du^k}{d\tau}=\gamma \frac{du^k}{dt}$$ We have that $u^k=(\gamma \vec{u}...
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Two different formulas

My problem is simple : given a particle of mass $m$, charge $q$ and velocity $\bf{v}$. If $\bf{A}$ denotes the magnetic potential satisfying $\bf{B}= \nabla \times \bf{A}$. I want to etablish the ...
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24 views

Demonstration of non orthogonality of time-like vectors on Minkowski space

I want to demonstrate that if two 4-vectors, $A^k$ and $B^k$ are orthogonal, then they aren't time-like. So, if we suppose that $A^k$ and $B^k$ are time-like, we have that: $$\sum_k A^k A_k <0, \...
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Question 17 in section 2.9 in Schutz's A First Course in General Relativity [closed]

The question is as follows: Prove that any timelike vector for which $U^0>0$ and $\vec{U}\cdot \vec{U} = -1$ is the 4-velocity of some world line. I need to show that there exists a 4-vector $\...
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1answer
97 views

Does a spaceship travelling at near lightspeed see the universe aging slow or fast?

Now I know this probably is well trodden territory, but this question has bugged me for some time, and I couldn't find a similar question in the archives (although plenty about relativistic time ...
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2answers
55 views

what happens to a magnetic field when it moves relative to an observer at relativistic velocities?

what happens to a magnetic field when it moves relative to an observer at relativistic velocities? Does it become an electrical field?
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1answer
155 views

What is the deep reason of length contractions and time dilations? [duplicate]

In the theory of relativity, a spacetime can have length contractions or length expansions and time can have time dilations or expansions. In theory of special relativity, any physical object with ...
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27 views

Length Contraction and Acceleration [duplicate]

Say that I have a spaceship that needs to travel 490 lightyears to the exoplanet Kepler 186f. Half the way of the trip the spaceship accelerates with a constant acceleration of 1G and on the other ...
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1answer
35 views

How to calculate relativistic mass versus time?

I know that relativistic mass is calculated as: But when mass m0 gets bigger, also mass of the accelerating body mass m gets bigger so m0 gets bigger and so on. So if body accelerates with ...
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113 views

What is the basic concept of four-dimensions in physics?

I have been reading a few books lately and browsing the internet for an explanation on the concept of "four-dimensional" space (or, space-time, as some of them have been calling it). But, what those ...
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What am I missing about the interaction between electromagnetism and Lorentz length contraction?

I was recently reading this short article: http://galileo.phys.virginia.edu/classes/252/rel_el_mag.html It explains how magnetic and electric fields are related because in one frame of reference where ...
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1answer
136 views

Why are one-particle states called representations of Poincaré group?

The one-particle states in the Hilbert space of a quantized relativistic field theory are said to form representations of the Poincaré group. Why is that? I mean, popular texts in QFT do not ...
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71 views

At what speed is the conservation of angular momentum carried out?

If the sun suddenly slowed down would pluto's orbit immediately speed up? If so, then isn't the information pertaining to the sun's angular momentum change being carried to Pluto faster than light? ...
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Real and relative velocity formula

What i need is a thing more complicated than the usual relative velocity formula. Imagine a radar. You are at the center, moving at some angle, but lets make it clear, you are always at the center. ...
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35 views

Why do we sum relativistic intervals in relativistic action of a massive point-particle, and not a function from it?

Relativistic action as follows (which should explain relativistic motion of a classical particle): $$ S = C \Delta s=C\int ds $$ Where $C$ is some constant and $\Delta s$ is relativistic interval. ...
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78 views

How is time dilation invariant of observer?

From one observer's perspective, on all moving objects time will run slower. But from the perspective of one of those objects, it's the observer who's slow. And the answer seems to be that both are ...
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1answer
45 views

Can we see ourselves slower due to time relativity?

Please bear with me because I'm noob at physics. Numbers don't have to be calculated, these are just examples, I'm just asking conceptual stuff. Just double check: Objects traveling at $0.99c$ in ...
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218 views

How can I prove that D'Alembert operator is invariant under Lorentz transformations?

I'm currently taking a course on Classical Electrodynamics and I'm trying to prove that the D'Alembert operator ($\square=\eta^{\mu \nu} \partial_{\mu} \partial_{\nu}$) is invariant under Lorentz-like ...
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1answer
108 views

What is the difference between scalar and vector mesons?

My understanding is that vectors and pseudooscalars change sign under parity operation and pseudovectors and scalars do not. However, I don't understand what the difference between a vector and ...
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Classical physics in curved space

I'm trying to learn General Relativity. As a stepping-stone between classic (Newtonian) physics and complete relativity, imagine a universe where space is curved, but time is perfectly flat. Also, the ...
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51 views

Travel by Earth rotation [closed]

why we can't go outside the atmosphere and travel with earth rotation .. and can we travel in the opposite direction of atmosphere by the same speed of atmosphere it’s moving at about 1,000 miles an ...