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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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 ...
3
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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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1answer
129 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
104 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: ...
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0answers
37 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
74 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
129 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 = ...
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2answers
425 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
93 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
47 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
88 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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0answers
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?
3
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1answer
60 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 ...
5
votes
5answers
397 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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0answers
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 ...
1
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0answers
22 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 ...
0
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1answer
81 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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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
47 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 ...
-1
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1answer
68 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
44 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
35 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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2answers
95 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
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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1answer
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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
95 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
54 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?
3
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1answer
149 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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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 ...
0
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1answer
34 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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2answers
107 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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2answers
162 views

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
131 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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0answers
44 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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2answers
70 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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0answers
18 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
28 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
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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1answer
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 ...
1
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1answer
184 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 ...
3
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1answer
103 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
129 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
50 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 ...
1
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1answer
66 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 ...
-1
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1answer
69 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 ...
0
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1answer
89 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 ...
4
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2answers
281 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 ...
0
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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 ...