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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Lorentz-Transformation in a closed loop (Sagnac)

I have a problem transforming from one system to another when the direction of motion is changed. To demonstrate the problem I'll set up an easy example with intuitive numbers: enlarge ↵ left: ...
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185 views

What does it mean to divide space and time?

Goldstein's mechanics book, on the chapter on relativistic mechanics says that "We cannot assume that all observers make the same division into time and space in the same way." What does it mean to ...
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278 views

What does v=c in the Lorentz transformation for time tell us?

For the simpler cases as boost in the x-direction, the time dilation formula following the Lorentz transformation for time is $$\Delta t'=\gamma(\Delta t-v\frac{\Delta x}{c^2})$$Now, we observe that ...
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If I am a light travel around Earth, what relativistic phenomenons do I have?

In school, or even in university, we are only taught Lorentz transformation in one direction. It is quite easy: $$\begin{align} t' &= \gamma \left( t - \frac{vx}{c^2} \right) \\ x' &= ...
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How would I relate $\Lambda=e^{-i\omega_{\mu\nu}J^{\mu\nu}/2}$ to the Lorentz boost matrix?

$\omega_{\mu\nu}$ contains infinitesimal parameters and $J^{\mu\nu}$ contains generators of boost and rotation. Any 4-vector transforms as $p^\mu=\Lambda^\mu_\nu p^\nu$. Starting from given ...
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1answer
28 views

Definition of a symbol $s_{NN}$ appearing in particle physics

What is the meaning of $s_{NN}$ in particle physics? See e.g. here http://www4.rcf.bnl.gov/brahms/WWW/thesis/karabowicz_phd_thesis.pdf page 18 in the pdf. What is its relation to energy? I ...
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1answer
60 views

What are the effects of increased mass on persons traveling at near light speed?

It's been a long time since I studied physics (and then only very superficially), so please bear with my gross naivete. This question's been running around in my head for about two weeks now, and I ...
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1answer
47 views

light falling on a completely reflecting friction less mirror

If you had a perfectly reflective mirror whose face was perpendicular to the ground and was kept on a friction less track on the ground, and you shined a flashlight on it, what would happen? Would ...
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2answers
535 views

How do I derive the transformation law of a Weyl spinor under a Lorentz transformation?

Let $\xi$ be a spinor. If $(\theta ,\phi)$ are the parameters of a rotation and pure Lorentz transformation, then how can we prove that the transformation rule for $\xi$ can be written as $$\xi ...
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0answers
33 views

How do I prove the Lorentz-invariance of the Dirac equation? [closed]

How do I prove the invariance of the Dirac equation under Lorentz transformation? $$ \left[ \gamma^{\mu}\left( i\hbar\partial_{\mu} - \frac{e}{c}A_{\mu}(x) \right)-mc \right]\psi(x) = 0$$
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56 views

Trying to understand relativistic action of a massive point particle

I got badly lost in derivation of relativistic formulas for energy and momentum. I stumbled upon relativistic action as follows (which should explain relativistic motion of a classical particle): $$ ...
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79 views

Spacelike to timelike four vectors

First at all, let me just say that I'm not a Physicist, I study mathematics. So, I have this question. If you have a spacelike four vector, is there any transformation that could change it to be a ...
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1answer
125 views

Time dilation simple derivation

In a special theory of relativity we have a phenomenon known as time dilation. There is a simple explanation of this, with a thought experiment with a train and a flash light: We flash a light in a ...
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2answers
66 views

Causality and Simultaneity in special relativity

I am a little confused about the implications of special relativity on causality and simultaneity. Are the following two statements true? For two events A and B that are close enough in space and ...
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3answers
111 views

Does time pass slowly in water?

In water the speed of light is slower than it is in vacuum. By special relativity the speed of light is constant. Typically, for the basic explanation of special relativity a clock which has a mirror ...
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1answer
3k views

How Special Relativity causes magnetism

So my physics teacher assigned us an article about how special relativity causes magnetism in a wire with a current, even with the low drift velocities of electrons in a current. It seemed that the ...
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25 views

Time dilation: different clocks [duplicate]

The plane is flying with a speed u=300m/s. How much time Δt′ would have to pass for a passanger on that plane for time difference 1s to occur between the time Δt′ on the plane and the time Δt on the ...
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1answer
766 views

Explanation of a proper time (an add)

I have read on web that: Proper time $\tau$ is a time interval measured by a clock which at rest relative to the observer. But lets consider this problem: The plane is flying with a speed ...
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59 views

Why is my understanding of the second postulate of special relativity incorrect?

SR postulate 2 states that light propagates in free space at a defined velocity that is independent of the motion of the emitting source. Since velocity is a vector quantity, it is directional. In ...
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89 views

Which is proper time $(t_0)$ and improper time $(t')$?

A lighthouse has two blinking spotlights 0.4 meters apart. The spotlight on the right blinks 5 seconds after the one on the left. How much time elapses between the blinkings of the spotlights as ...
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2answers
96 views

Beat Frequency for Police Radar with Special Relativity

"A radar speed trap operates on a frequency $v_o = 109 Hz$. What is the beat frequency between the transmitted signal and one received after reflection from a car moving at v = 30 m/s toward the ...
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1answer
52 views

Every Relativistic Field Satifies the Klein-Gordon Equation?

I've read that every relativistic scalar field (and in some sense, any field) satisfies the Klein-Gordon equation. Is the reasoning for this just based on the quantum mechanical substitution of $E\to ...
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7answers
355 views

What does the statement “the laws of physics are invariant” mean?

In the first paragraph of Wikipedia's article on special relativity, it states one of the assumptions of special relativity is the laws of physics are invariant (i.e., identical) in all inertial ...
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What happens when a photon hits a mirror?

When a photon of light hits a mirror does the exact same photon of light bounce back or is it absorbed then one with the same properties emitted? If the same one is bounced back does it's velocity ...
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1answer
46 views

Electric field, special relativity, and charged particle

Given a uniform electric field in the $z$ direction and an observer moving at constant $v$ in the $y$ direction, how you would describe the motion of a charged particle that start at rest in the ...
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129 views

How does light actually behave?

Senario: I am walking 5 meters/second and have a laser pointer that I shoot a burst of light from perpendicular to to the path I am walking on. Would the light travel perpendicular to the path from ...
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26 views

Fermi's understanding of the Doppler effect

I am now reading the classic paper by Dicke, The Effect of Collisions upon the Doppler Width of Spectral Lines At the very beginning of the paper, Dicke said ''Quantum mechanically, the Doppler ...
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78 views

Calculating length contraction at speed $c$ (not near it)

Is the Lorentz transform applicable to speeds that are lower than light only?Because I'm trying to calculate length contraction of objects moving at speed $c$ (not near it) and it turns always 0. Is ...
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1answer
56 views

Why is the Poincaré group non-abelian?

Based on what I've learned, I gather the Poincaré group is the group of isometries of Minkowski spacetime and it is a non-abelian Lie group. Why is it non-abelian? Or perhaps rather, does the fact ...
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325 views

Vector spaces for the irreducible representations of the Lorentz Group

EDIT: The vector space for the $(\frac{1}{2},0)$ Representation is $\mathbb{C}^2$ as mentioned by Qmechanic in the comments to his answer below! The vector spaces for the other representations remain ...
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3answers
71 views

Twin paradox - a further variant

I am still troubled by the "twin" paradox (thanks to those who have answered my previous question and suggested some reading which I will follow up). I have however thought of a variation on the ...
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1answer
86 views

Energy for acceleration towards speed of light is relative?

This seems a very simple question - and I guess it will turn out to be so. It's a given that accelerating particles with mass towards the speed of light takes more and more energy (ultimately an an ...
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3answers
216 views

Are some events simultaneous in all reference frames? (Einstein goes drinkin')

If simultaneity is not a universal characteristic (eg. events are not simultaneous in all reference frames), then why do some events seem to be simultaneous in all reference frames as in the following ...
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182 views

Can we derive the Schrödinger equation from the Klein-Gordon equation?

As we know that the Schrödinger equation presents basis of Quantum Mechanics and analogy with Newton second law in Classical Mechanics, I thought that relativistic interpretation of Schrödinger ...
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539 views

Orthochronous Lorentz transformations are time-preserving and $SL(2,\mathbb{R})$

Let's consider the psuedosphere/hyperboloid in $\mathbb{R}^{1,2}$ given by $$x^2+y^2-z^2=-R^2.$$ We know that the Lorentz group $$O(1,2)=\{ A \in Mat(3,\mathbb{R}): A^tGA=G \},$$ where ...
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What does memorylessness mean as a postulate of special relativity?

I was reading the wiki page on special relativity postulates. And wiki says, The two-postulate basis for special relativity is the one historically used by Einstein, and it remains the starting ...
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1answer
121 views

Field of moving charge / Lorentz;Lienard-Wiechert

First question here. I'm really confused at the moment. An electron moves at constant velocity, no acceleration Wikipedia says here Lorentz: Which yields something like this: Wheras here, ...
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1answer
64 views

Is there a general theorem stating why the restricted Lorentz group's exponential map is surjective?

The exponential map for the restricted Lorentz group is surjective. An outline of why is shown on the wiki page Representation Theory of the Lorentz Group. Is there a more general theorem that states ...
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36 views

Forward and Behind Frames of Reference

It's my understanding that light travels at the same speed in all inertial frames of reference. Suppose there's a small train car 5 feet long (at our rest point of view) traveling at a constant speed ...
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1answer
64 views

Can photons “stop time”?

If traveling past the speed of light causes time to reverse than does traveling in time make time "stop"? If not then how do photons/mass-less particles experience time, if at all.
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58 views

Basic Relativistic Question - length measurement

A while ago we did an easy, introductory exercise on length measurement. Back then it seemed pretty straightforward but now when I look at it I have trouble understanding the assumption which led to ...
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2answers
126 views

Lorentz transformation paradox

I got to solve a simple exercise about special relativity when I kinda came to the conclusion it doesn't stroke with my intuition. The homework-problem The problem was about two people Sam and ...
2
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1answer
34 views

Space-like pion electromagnetic form factor

The 1986's publication "A measurement of the space-like pion electromagnetic form factor" (http://dx.doi.org/10.1016/0550-3213(86)90437-2) starts with: The pion form factor has been measured in ...
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2answers
151 views

Metric tensor in SRT

I just read on this webpage that we have (click me) $g_{\alpha \beta} = g_{\alpha}^{\beta} = g^{\alpha \beta}.$ Now, although I understand that the first and the last one are equal, I don't think ...
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1answer
37 views

Is anything without mass an EM wave?

For the longest time I thought the distinction between matter wave and other types of wave is the non-relativist mass of the "thing" under discussion. Photons are EM wave, electrons are matter waves. ...
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1answer
44 views

Why photons are having energy when they are massless? [duplicate]

As per the Einstein equation $E=mc^2$, the energy of the particle is depends on the mass of the particle. Or else in other terms the energy is proportional to the mass. If the photons are having zero ...
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2answers
61 views

Times at relativistic speeds

Consider an observer $A$ moving in a spaceship at a speed close to $c$, relative to an observer $B$. The $B$ knows that the time on $A$ runs slower, but in the inertial frame of $A$, $B$ is moving ...
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Does coordinate time have physical meaning?

I have always been a little confused by the meaning of the "$t$" which appears in spacetime intervals or metrics in general relativity. I concluded that $t$ was just a mathematical thing which allow ...
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1answer
48 views

Special Relativity - three body problem

I have a problem with solving three-body problem in special relativity. I know that in general this problem doesn't have good solution, but I have a specific case when it should be good answer. ...
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1answer
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Uniqueness of the equivalence class of inertial frames

Let us define an inertial frame as a frame of reference where the laws of physics take their usual form, as opposed to non intertial frames where one has to introduce pseudo-forces. We can further ...