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 of the Spinor Field

I'm reading chapter 3 of Peskin and Schroeder and am stuck on page 43 of P&S. They have defined the Lorentz generators in the spinor representation as: \begin{equation} S^{\mu \nu} = \frac{i}{4}[\...
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Do you encounter more photons (per unit time) when moving forwards at a constant velocity?

Let's say you have rain hitting you evenly on all sides (not very realistic, I know). If you were to move forwards at a constant speed, there would be more droplets of rain hitting you per second on ...
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Time travel outside of light cone without causality violation

If one is able to travel into the past but at a spatial distance that puts him outside of his own past light cone would this be considered a causality violating trip? Looking at a Minkoski diagram, it ...
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Lorentz Invariant Integration Measure [closed]

When we canonically quantize the scalar field in QFT, we use a Lorentz invariant integration measure given by $$\widetilde{dk} \equiv \frac{d^3k}{(2\pi)^3 2\omega(\textbf{k})}.$$ How can I show that ...
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Deriving the action and the Lagrangian for a free point particle in Special Relativity

My question relates to Landau & Lifshitz, Classical Theory of Field, Chapter 2: Relativistic Mechanics, Paragraph 8: The principle of least action. As stated there, to determine the action ...
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Help Me Gain an Intuitive Understanding of Lorentz Contraction

I'm having a hard time getting an intuitive understanding of Lorentz Contraction. I understand what it is by definition but I don't 'get it.' I'm not a physicist, just an amateur, so sorry if this ...
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Poincare group vs Galilean group

One can define the Poincare group as the group of isometries of the Minkowski space. Is its Lie algebra given either by the equations 2.4.12 to 2.4.14 (..as also given in this page - http://en....
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Why are usually 4x4 gamma matrices used? [duplicate]

As far as I understand gamma matrices are a representation of the Dirac algebra and there is a representation of the Lorentz group that can be expressed as $$S^{\mu \nu} = \frac{1}{4} \left[ \gamma^\...
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Is Einstein's Special Relativity completely inclusive of Newton's 3 laws of motion?

Relativity has always been explained to me (in books I've read, etc) as a superset of newton's laws - that is; it encapsulates all of Newton's mechanics in addition to other effects (observer effect, ...
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Has relativity of simultaneity been directly observed?

I know that thought experiment about trains when a flash of light in the middle reaches the both end simultaneously for a passenger but different times for the bystander. So were there (non-thought) ...
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Relativity and Current in Wire

If an observer is stationary relative to a current-carrying wire in which electrons are moving, why does the observer measure the density of moving electrons to be the same as the density of electrons ...
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Why is the stress-energy tensor symmetric?

The relativistic stress-energy tensor $T$ is important in both special and general relativity. Why is it symmetric, with $T_{\mu\nu}=T_{\nu\mu}$? As a secondary question, how does this relate to the ...
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Simple Experiment to Demonstrate Special Relativity

I am trying to think of a good experiment that can be done for under $250 or so that would demonstrate some aspect of Special Relativity. Ideally this will be done in a few years with my kids when ...
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Why Negative Energy States are Bad

The argument is often given that the early attempts of constructing a relativistic theory of quantum mechanics must not have gotten everything right because they led to the necessity of negative ...
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What spacelike, timelike and lightlike really mean?

Suppose we have two events $(x_1,y_1,z_1,t_1)$ and $(x_2,y_2,z_2,t_2)$, then we can define $$\Delta s^2 = -(c\Delta t)^2 + \Delta x^2 + \Delta y^2 + \Delta z^2$$ which is called the spacetime ...
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What axiomatizations exist for special relativity?

Einstein 1905 gives the following axiomatization of special relativity (Perrett and Jeffery's translation): The laws by which the states of physical systems undergo change are not affected, whether ...
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Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation?

In Physical Review Letters, there was a paper recently published: Masud Mansuripur, Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation, Phys. ...
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How can relativistic effects be the cause of magnetic forces when the normal speeds of carrier charges are so low?

I had read here that magnetism arises from a current because of the special relativistic effect associated with the speed of the moving charges in that current. However that speed is only on the ...
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If $v_{a \dot{b}}$ transforms like a four-vector, what does $v_{a}^{\dot{b}}$ describe?

The $( \frac{1}{2}, 0)$ representation of the Lorentz group acts on left-chiral spinors $\chi_a$, the $( 0,\frac{1}{2} )$ representation on right-chiral spinors $\chi^{\dot a}$. The $( \frac{1}{2}, \...
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How is the Photoelectric Effect affected by Blue-Shifting

I was thinking about the Photoelectric Effect and Blue-Shifting when I came up with a thought experiment that I couldn't think of an answer for. The thought experiment is as follows: A metal plate is ...
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Relativistic drift velocity of electrons in a superconductor?

Is there a formula for the effective speed of electron currents inside superconductors? The formula for normal conductors is: $$ V = \frac{I}{nAq}$$ I wonder if there are any changes to this ...
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Why can't massless particle exceed speed of light?

Why massless particle can't exceed speed of light?
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Spontaneous breaking of Lorentz invariance

Is it possible to spontaneously break Lorentz invariance, i.e., have a Lagrangian that respects LI but a vacuum which does not? If it is possible, why isn't there even the slightest hint of the ...
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Do the integral forms of Maxwell's Equations have limited applicability because of retardation?

In the usual bookwork treatment, it is easy to show that the differential and integral forms of Maxwell's equations are equivalent using Gauss's and Stokes's theorems. I have always thought that ...
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Is there a mathematical reason for the Lagrangian to be Lorentz invariant?

The Hamiltonian is the energy, which is just one component of a four-vector and therefore not Lorentz invariant. The Lagrangian is the Legendre transform of the Hamiltonian and I was wondering if ...
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Why Lorentz group for fields and Poincaré group for particles?

Wigner treatment associates to particles the irreps of the universal covering of the Poincaré group $$\mathbb{R}(1,3)\rtimes SL(2,\mathbb{C}).$$ Why don't we consider finite dimensional ...
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Why do we identify symmetric 2nd rank tensors with spin-2 particles in string theory?

I am going through Tong's lecture notes on String Theory and came across the following irrep decomposition (Chap 2, p.43) of the bosonic string first excited states: $$\text{traceless symmetric} \...
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Violation of Lorentz invariance (Lagrangian for particle)

I'm trying to get the relativistic action (or Lagrangian) for a free particle in the case of violation of Lorenz invariance. Suppose we have the modified dispersion relation: $$ E^{2}=\Omega^{2}(p^{2}...
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Does the “Andromeda Paradox” (Rietdijk–Putnam-Penrose) imply a completely deterministic universe?

Wikipedia article: http://en.wikipedia.org/wiki/Rietdijk–Putnam_argument Abstract of 1966 Rietdijk paper: A proof is given that there does not exist an event, that is not already in the past for ...
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Trajectories in Rindler space with zero net time dilation

I've discovered a family of curves in Rindler space that have zero net time dilation. However I struggle to see why this should be so, i.e. what the physical significance of these curves is. My ...
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Is there a maximum energy for a relativistic particle?

So I was told today that the Standard Model breaks down at really, really high energies. The lecturer mentioned particles such as electrons hypothetically having energies equivalent to that of entire ...
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Time Dilation - How does it know which Frame of Reference to age slower?

Okay, I'm asking a question similar to this one here: Time Dilation - what happens when you bring the observers back together?. Specifically, I am curious about a specific angle on the second part of ...
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What's the difference between space and time?

I'm having a hard time understanding how changing space means changing time. In books I've read people are saying "space and time" or "space-time" but never explain what the difference is between the ...
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Would it be possible to develop special relativity without knowing about light?

My understanding of special relativity is that it is fundamentally based on the constancy of the speed of electromagnetic radiation - that this speed is a physical law (or derivable from physical laws ...
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Why is the speed of light arbitrarily the limit? [duplicate]

I know Einstein was great and all. Why is it that exactly at the speed of light is where infinite energy is required to accelerate any object with mass? Is it simply because the math of relativity ...
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Is there always a frame in which spatially separated events are simultaneous?

In relativity, if two events are simultaneous in a specified frame, they cannot be simultaneous in any other frame. My question is this: given any two events, is there always a frame in which these ...
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How to derive $E=mc^{2}$?

Is there some way to derive $E=mc^{2}$? I can understand that energy in something is proportional to its mass, but the $c^{2}$ part. I have no idea. It seems like the way the units are going it would ...
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Is Einstein's characterization of “time” as “the position of the little hand of my watch” definitive and binding in the RT?

In Einstein's very first publication dealing with the Theory of Relativity, effectively as a preamble to all subsequent thought-experimental considerations and descriptions, Einsteín put the ...
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Do photons age in a medium?

According to special relativity, time starts to slow down as we increase our speed and eventually stops once we get to the speed of light. By that logic, photons don't age in a vacuum state as, to us, ...
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Is (rest) mass conserved in special relativity?

I don't understand why it is said that the (rest) mass of a system is not conserved in relativity. I mean, the momentum of a system is conserved (i.e.: it remains constant in a frame of reference ...
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A question about $E=pc$ for massless particles

Since photon has no (rest)mass and $$E^2=(pc)^2+(mc^2)^2$$ we derive that $E=pc$ for particle with no (rest)mass. However, if we transform the non-relativistic formula for kinetic energy $$E_k=\...
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Is the speed of light in vacuum always the same value?

The escape velocity of different planets and stars vary. If they vary, the velocities of bodies escaping from the respective stars or planets should also vary. Like, if I want a ball to reach 10 ...
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Why proper acceleration is $du/dt$ and not $du/d\tau$?

Wikipedia says: In relativity theory, proper acceleration[1] is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. and says: In the ...
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Does a muon detector on Earth's surface correctly measure the mean lifetime of a muon?

Just a simple question. Does a muon detector on Earth's surface correctly measure the mean lifetime of a muon? I would think the answer is no because most muons detected are created about 15 km above ...
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Tachyon and Photons

Is there a particle called "tachyons" that can travel faster than light? If so, would Einstein's relativity be wrong? According to Einstein no particle can travel faster than light.
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How do I develop an intuitive model of spacetime?

I am your nightmare poster - a layman trying to learn special relativity. (I'm also a refugee from stackoverflow.com: trust me, it's only going to get worse). Apologies in advance if my question is ...
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Why are objects at rest in motion through spacetime at the speed of light?

I read that an object at rest has such a stupendous amount of energy, $E=mc^2$ because it's effectively in motion through space-time at the speed of light and it's traveling through the time dimension ...
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If a neutrino has a rest frame, why can't a photon have a rest frame as well?

Concerning Rest Frame Wikipedia states: For example, in the rest frame of a neutrino particle travelling from the Crab Nebula supernova to Earth the supernova occurred in the 11th Century AD ...
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Does entanglement not immediately contradict the theory of special relativity?

Does entanglement not immediately contradict the theory of special relativity? Why are people still so convinced nothing can travel faster than light when we are perfectly aware of something that does?...
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Can one deduce absolute motion through magnetism? [closed]

I am trying to understand forces in relativity: Suppose there are two electrons A , B travelling side by side at 1 cm distance at .99 c (in space or at lHC, ignoring all other factors). I know that ...