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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Behaviour of Dirac Bilinears

Dirac bilinears transform in the Lorentz indices as, $\bar{\psi}\psi$ scalar $\bar{\psi}\gamma^\mu\psi$ vector $\bar{\psi}\sigma^{\mu\nu}\psi$ 2nd rank (antisymmetric) tensor $\bar{\psi}\gamma^{\mu}\...
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25 views

How to express in terms of spacetime intervals the average speed of one participant having moved between two suitable others

Given a flat region of spacetime as set $\mathcal S$ of events together with values of spacetime intervals (up to a common non-zero constant) for each pair of events, $s^2 : \mathcal S \times \mathcal ...
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1answer
16 views

How to express in terms of spacetime intervals whether two participants in a flat region were at rest to each other

Given a flat region of spacetime as set $\mathcal S$ of events together with values of spacetime intervals (up to a common non-zero constant) for each pair of events, $s^2 : \mathcal S \times \mathcal ...
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1answer
67 views

Dot product in index notation [closed]

This is a question about a small exercise I am trying to do in order to check if I am correct. Such type of quantities can appear in propagators in QFT. Since I am not an index expert I need some ...
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1answer
73 views

Relativistic acceleration of a rocket?

I'm trying to solve a physics brain-teaser and getting nowhere fast. My knowledge of special relativity is very basic. In the problem a rocket is flying linearly at relativistic speeds (say $v>0....
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2answers
68 views

How does SUSY avoid to create non-Lorentz interactions?

A three-legs fermion interaction or boson absorbing a fermion are things we do not see in QFT because the corresponding terms in the Lagrangian are not Lorentz invariant. But in susy, naively, such ...
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36 views

Gradient of $ct'$ axis in spacetime diagrams

This is either an unimportant piece of information or it's meant to be obvious, but I can't find anywhere what the gradient of the $ct'$ axis in a spacetime diagram should be. I know that the $ct'=1$ ...
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3answers
162 views

What's the problem with light traveling at speed higher than $c$?

I'm trying to understand how Einstein concluded that time is relative based on thought experiments such as a torch attached to the end of a rocket. Based on answers to questions like this one, this ...
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4answers
125 views

Tensor calculus in special relativity

We say that any function $f(t,x,y,z)$ is a tensor of rank {0 0} because it takes no vectors or one-forms in order to give a real number. But couldn't we have just written the same function as $f(t,x,y,...
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1answer
31 views

Multiple Objects at Constant Speed

Imagine 1 million objects travelling in space, at a constant speed, along an imaginary line. They don't deviate from that line for the sake of this argument. Now, object 1 has a velocity of $v_{1}=1$ ...
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1answer
51 views

How does time dilation occur due to velocity and gravity [duplicate]

I am trying to understand and clarify the way time dilation occurs due to general and special relativity and for which reason. In the case where an object is approaching a planet in free-fall how does ...
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1answer
78 views

Different definitions of the parity transformation for the Dirac spinors

There are two definitions of the parity transformation acting on the Dirac spinors: $\Psi_P = \eta \gamma^0 \Psi$ with $\eta = i$ ($P^2=-1$ as in Srednicki) and $\eta=1$ ($P^2=+1$ as in Peskin & ...
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252 views

How can we prove charge invariance under Lorentz Transformation?

We have gravitational force between two massive particles and we have electromagnetic force between two charged particles. When special relativity suggests that mass is not an invariant quantity why ...
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3answers
74 views

Mass and frequency of photons [duplicate]

Light is affected by gravity which means light has got mass. Quantum theory tells us that light consists of discrete quanta of energy, which we call photons. These photons have a rest mass of zero (as ...
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1answer
160 views

Can special relativity be derived from the invariance of the interval?

As far as I know, the classical approach to special relativity is to take Einstein's postulates as the starting point of the logical sequence, then to derive the Lorentz transformations from them, and ...
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3answers
167 views

Why did Einstein took speed of light unit or constant in his equation of relativity?

We can find that no object can have speed more than light from Einstein's equation of relativity because if anything have speed more than light then we get -ve value within square root. But why did ...
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2answers
66 views

Planes of Simultaneity on Minkowski diagrams

As seen from a "stationary" reference frame, Why do lines of simultaneity for fast-moving observers run parallel to distance axis instead of perpendicular to the time axis. Obviously, in a regular t ...
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2answers
377 views

How to achieve speeds faster than light? [duplicate]

So, I heard that all speed is relative. And that nothing can travel faster than light. Then I guess it is OK for a spaceship to leave Earth at 0.6c constant speed. And what if an other spaceship were ...
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32 views

Helicity of massive particle at high enengy

We know that massless spin-1 particle like photon only has two helicity state (-1,1), what about the helicity of massive spin-1 particle (W boson) at very high energy? Does it have helicity 0 state ...
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35 views

How do I make a slowly rotating neutron star using fortran code?

I make a slowly rotating neutron star code but I am little bit confuse, when I solved the coupled differential equation using runga-kutta 4th order method. These coupled differential equations as ...
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0answers
74 views

Derive Galilean transformation. (The meaning of the relativity)

In the book The meaning of the relativity Einstein says that in classic mechanics two postulates are previously supposed: 1.- The time is absolute. 2.- The longitude is absolute. And this implies ...
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1answer
92 views

Does there exist finite dimensional irreducible rep. of Poincare group where translations act nontrivially?

I read several textbooks of QFT and find that there are two ways to classify the particles or fields. The first one is to study the irreducible representation of Lorentz group (or exactly the ...
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3answers
92 views

Confusion on relativistic electromagnetism of two charge particles

When I was introduced to the relativistic nature of electromagnetism, the following scenario is introduced: Two protons are fired such that they travel at the same velocity in parallel directions ...
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How can I do a nested lightcone integral?

I want to do an integral of the form $I(x-y)=\int d^{D+1}z_1...d^{D+1}z_n f(x-z_1)...f(z_n-y)$ where $x,z_1,...z_n,y$ are all (D+1) vectors and $f$ depends only on the proper times between them. $z_i$...
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77 views

Signification of “finite but unbounded universe”?

I recently read Einstein's book about relativity and he says that his theory predicts the shape of the universe. It would be finite but unbounded. But how is this possible? What's the difference ...
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Compressed length of a moving body [closed]

This question is on behalf of someone else without access to a computer so any further clarification or responses may be delayed. The question comes in the form of photos of the original questions as ...
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1answer
42 views

Speed of light in vacuum in special relativity

In special relativity, the speed of visible light is defined as a constant. But visible light is only a small part of the electromagnetism field. So why?
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42 views

Thought experiment on special relativity

If we were travelling in a spaceship, accelerating (arbitrary value) from a velocity 0, and we assumed that times and distances outside of the spaceship remained the same as that of ours, would we be ...
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1answer
63 views

Can information be sent faster than speed of light [duplicate]

I just had this idea one day and I decided upon a thought experiment to verify it. Imagine 2 people A & B sitting on two sides of a pipe which is stretched to a length of 3x10^8 m. The pipe is ...
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1answer
68 views

Are Coulomb's Law and Lorentz force always true for all phenomenon in physics?

I saw two equation about charge: Coulomb's law $$\mathbf F=k \frac{q_1q_2}{ r_{12}^{2} }\, \mathbf{\hat r} $$ and magnetic Force $$ \mathbf F=q \, \mathbf v\times \mathbf B$$ My question is:...
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1answer
52 views

Stacked motors thought experiment

first of all, I'm not a mathematician, just curious about something that came up to my mind and maybe you can help me out. Scenario: I have a motor that spins let's say at 20K revolutions per minutes....
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2answers
119 views

Where do I begin in order to study relativity? [duplicate]

I am in high school now and I want to get the basic idea of what relativity. Can anyone suggest me a book or website for it? I am also curious about the mathematics behind it. Is it possible for me to ...
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Why is there a minus in the Gauge Field Lagrangian kinetic term? [duplicate]

For vector Gauge fields we usually write the kinetic term: $$ \mathcal{L} ~=~ - \frac{1}{4} F_{\mu \nu} F^{\mu \nu}$$ while for matter fields e.g. for a real scalar: $$ \mathcal{L} ~=~ \frac{1}{2} ...
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What is wrong with this derivation of the lorentz factor

in attempting to derive the lorentz contraction, I assumed that light speed is measured the same from all inertial reference frames. The situation set up is object A is standing still, whilst object B ...
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2answers
263 views

Is there a limit to how hot an object can get?

If heat is the measure of how fast the atoms are moving in an object, than isn't there a limit to how hot that object can get as nothing can go as faster than the speed of light. So because the atoms ...
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0answers
26 views

Value of $E_x$ through an $X-\textrm{boost}$

Suppose I'm standing at the (0,0,0) point of a coordinate system and I see an electric field where $E_x=f(t,x,y,z)=\sin(x\cdot y\cdot z\cdot t)$ and at time $t_0=0$ I start moving on the x-axis at ...
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Electromagnetic Tensor under Lorentz transformation, $F'(\Lambda x)= \Lambda F(x) \Lambda^T$?)

Suppose we have a configuration of electric and magnetic fields $E(x1,x2,x3,x4)$ and $B(x1,x2,x3,x4)$, they depend of position and time for a fixed coordinate system. And I want to know how someone in ...
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Presentism: doesn't everything exist at the same moment? [closed]

The Help Center recommends I 'fix' this question: (original question) "It seems self-evident that everything exist in the Now. Notwithstanding time-dilation and different rates of the passage of ...
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1answer
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“Spacetime tells matter how to move; matter tells spacetime how to curve” and acceleration in flat space-time? [closed]

John Wheeler stated "Spacetime tells matter how to move; matter tells spacetime how to curve." Does this contradict with the assumption that mass can be accelerated in flat space-time (see i.e. this ...
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0answers
41 views

Lorentz invariance of the Heaviside function [duplicate]

Consider the Heaviside function $\Theta(k^{0})$. This function is Lorentz invariant if $\text{sign}\ (k^{0})$ is invariant under a Lorentz transformation. I have been told that only orthochronous ...
3
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1answer
71 views

Rest Mass Clarification

I would like to know about the Rest Mass? Why we need the phrase "rest mass"? Because, mass is a constant quantity? Or Is the Mass varying with velocity? How can we understand that mass varying with ...
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2answers
965 views

Does rest exist?

I initially thought that the concept of rest depended on an inertial frame of reference. So for example, if the Earth and everything on it were the only things in the universe, and the Earth was ...
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33 views

question dealing with time dilation and length contraction

In Einstein's theory of relativity and reference frames, It states that an observer on earth watching a spaceship fly at close to the speed of light heading away going towards a distance star that the ...
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0answers
32 views

How does length contraction map from a macro size object to its individual sub-atomic parts?

If an object consisting of many atoms is traveling close to the speed of light, explanations of length contraction seem to indicate the whole structure contracts. It seems easy to imagine an electron,...
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4answers
229 views

Rapid acceleration does what to inertial frame clocks?

I'm 10 light years from Earth and see Earth's clock/calendar reading 2000, including light travel time. In other words, I assume it's 2010 on Earth, but what I actually see is the year 2000 due to ...
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53 views

Finding an explicit expression for inverse of Lorentz transformation ${\Lambda^\mu}_{\nu}$

I'm studying in a module titled "Symmetries and Action Principles in Physics." I'm having a small trouble with the notation, I think, of special relativity. We have in the text In fact we may ...
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107 views

What do observers in relative motion agree on?

What are the measurements on which two observer in relative motion will agree? Other than the speed of light.
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Is there a relation between time dilation and (relativistic) mass increase?

I noticed that what once called relativistic mass increase and now is called energy increase is ruled by the same formula the Lorenz factor of time dilation? The formula is too particular to suggest ...
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1answer
48 views

Help with relativistic notation (Derivative of Lagrangian)

I am trying to learn QFT, but I haven't taken a course in general relativity so the relativistic notation stuff is taking me a bit to get used to. I do not understand how to do the following. For a ...
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1answer
190 views

Spin state after boost

I am working through Weinberg's QFT book, and in problem 1 in chapter 2 I ran into copious amounts of algebra, so I am trying to "cheat" a little by using some assumptions, but am unsure of their ...