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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Velocity addition rule in special relativity

I just worked out a problem showing peculiarities of the velocity addition rule in special relativity. This was the statement for the problem: "Nefarious thieves flee the scene of their bank ...
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3answers
781 views

Is there an upper limit to temperature in thermodynamics or statistical mechanics

In many presentations of statistical mechanics where we have a system of particles having mass, such as the molecules of an ideal gas, the temperature is often equated to the average relative velocity ...
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0answers
32 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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1answer
45 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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0answers
16 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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0answers
26 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 ...
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1answer
60 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
39 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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2answers
94 views

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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1answer
32 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 ...
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1answer
49 views

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
19 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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Hole-and-nail paradox in special relativity

Yesterday we started relativity on our physics class, and my professor taught us a few concepts. We did some examples on how things changed by looking them from different reference systems, and a ...
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1answer
88 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 ...
2
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1answer
131 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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2answers
133 views

Doubts regarding Einstein's 1905 derivation of mass-energy equivalence

This is a follow up on this question. In his [paper][2] under the title:Does the inertia of a body depend upon its energy-content, Einstein drives the famous $E=mc^2$ equation. His argument can be ...
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2answers
48 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
265 views

Perfect fluid and Cauchy momentum equation

The stress-energy tensor of a perfect fluid is given by $$T^{\mu\nu}=\left(\rho+pc^{-2}\right)u^\mu u^\nu+pg^{\mu\nu}$$ The divergence of the stress-energy tensor is zero: $\nabla_\mu T^{\mu\nu}=0$. ...
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2answers
104 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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0answers
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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5answers
519 views

Speed of light as a universal speed limit

It follows from special relativity that nothing can travel faster than light. Einstein believed this would have to hold so generally that he assumed the Einstein-Podolsky-Rosen paradox to indicate a ...
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3answers
601 views

Faster than light signals and the price to be paid if we accept them : a very simple protocol

Some physicists currently understand entanglement as transferring information instantaneously, yet not violating causality. Is this really a satisfactory explanation, or should be look for something ...
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1answer
32 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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1answer
240 views

Who aobserves length contraction?

I have a homework in our nuclear physics class. The question is "An astronaut whose height in the earth is exactly 6ft is lying parallel to the axis of a spacecraft moving at a 0.9C relative to the ...
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0answers
39 views

Special Relativity and Space travel [closed]

I'm doing a science project on space travel where I have to include a part about special relativity and how time acts when you're traveling in space with high speed. I'm not really sure where to start ...
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1answer
61 views

Restrictions on the form of a function imposed by Lorentz invariance

I need help proving a couple of theorems regarding the most general form of a function with some particular Lorentz-transformation properties. By the way, the question is possibly (though not ...
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2answers
61 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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2answers
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is following alternative interpretation of total energy possible? E=m'v^2 instead of E=m'c^2 [closed]

I have read the paper, http://arxiv.org/pdf/physics/0206061.pdf "Fundamental Disagreement of Wave Mechanics with Relativity", some time ago, in which the author claims that there is another way to ...
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4answers
785 views

Special Relativistic approximation to GR

Some time ago I was talking to a professor in college about some of the fundamental aspects and origin of General Relativity. I was surprised to learn, in fact, that a pretty good approximation to GR ...
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0answers
17 views

Basic Special Relativity Problem [closed]

A cylindrical rocket 10 m long and 2 m in diameter moves at a speed $ V=0.9c $ with respect to earth, where $c$ is the speed of light in vacuum. I. Knowing that the pilot's heart beats 70 times per ...
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0answers
27 views

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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0answers
34 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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1answer
206 views

The effect of relativistic near misses

Alice and Bob are both floating in free, empty space. Alice does not like Bob very much. Thus one day, believing that there is no such thing as overkill, Alice takes her programmable hyper-energetic ...
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1answer
105 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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6answers
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If I walk along the aisle of a bus traveling at the speed of light, can I travel faster than it?

Let's say I fire a bus through space at (almost) the speed of light. If I'm inside the bus (sitting on the back seat) and I run up the aisle of the bus toward the front, does that mean I'm traveling ...
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2answers
269 views

Spacetime and uncertainty principle

I only have limited knowledge of relativity and quantumphysics but as far as I know, the uncertainty principle relates the uncertainty of space and momentum of a particle. Einstein however, explained ...
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1answer
74 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
44 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 ...
3
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1answer
79 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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2answers
123 views

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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2answers
48 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 ...
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2answers
232 views

Dimensional Paradox Demonstrated by Light Moving Between Parallel Mirrors

In a thought experiment, there are two parallel mirrors which are very long which also face each other. One has a hole in it and one flash from a strobe light shines into that hole. One observer in ...
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1answer
55 views

Special relativity and Simultaneity

I am struggling on a problem involving 2 events seen in different reference frames and could do with advice or a starting point for this question: A spaceship approaches a galaxy travelling with a ...
0
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1answer
79 views

Electron decay in high-energy accelerators

As far as I understand, electrons are infinitely stable since they are the least massive particle with non-zero electric charge. However, when accelerated to high-energies, the energy (or mass) of the ...
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1answer
61 views

Atoms traveling at the speed of light [closed]

If an atom was to travel at the speed of light (although impossible), wouldn't the nucleus break apart? I say this because the particles holding the protons together in the nucleus wouldn't be able to ...
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4answers
5k views

Deriving the Lorentz Transformation

I have been trying to understand a more or less geometric derivation of the Lorentz transformation, and I'm getting stuck at one spot. The wikipedia article for the Lorentz transformation for frames ...
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1answer
40 views

Matrices belonging to orthochronous Lorentz group

My Professor says that all members of the orthochronous Lorentz group may be written as $e^\Gamma$, where $$ \Gamma^{\mu}_{\nu}=\Lambda^{\mu \rho} \eta_{\rho \nu}$$ Here $\Lambda$ is an antisymmetric ...
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2answers
94 views

Are Lorentz transformations a fundamental law?

I've seen derivations of Lorentz transformation but are they really derivations or are we just teasing out the formula using some special cases and then assuming it to be valid for all the cases. Is ...
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2answers
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Definitions: 'locality' vs 'causality'

I'm having trouble unambiguously interpreting many answers here due to the fact that the terms locality and causality are sometimes used interchangeably, while other times seem to mean very different ...
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3answers
889 views

Special relativity and electromagnets

This Veritasium video explains how electromagnets can be explained by special relativity, and how the magnetic field surrounding a current-carrying wire can also be viewed as an electric field, if ...