Special relativity Definition and 1000 Threads

In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
The laws of physics are invariant (that is, identical) in all inertial frames of reference (that is, frames of reference with no acceleration).
The speed of light in vacuum is the same for all observers, regardless of the motion of the light source or observer.

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  1. D

    I Why and how Dirac cones are "tilted"?

    Given a Weyl Hamiltonian, at rest, \begin{align} H = \vec \sigma \cdot \vec{p} \end{align} A Lorentz boost in the x-direction returns \begin{align} H = \vec\sigma\cdot\vec{p} - \gamma\sigma_0 p_x \end{align} The second term gives rise to a tilt in the "light" cone of graphene. My doubts...
  2. mpolo

    B Special Relativity: Time Dilation Explained

    I am trying to get this idea of Time dilation understood. If there exists only two objects in a Universe and one object is stationary and the other object is moving at 99 % the speed of light. Their clocks were both synchronized when both objects were stationary relative to each other. Then the...
  3. V

    Special relativity, gradient of velocity

    Homework Statement I have noticed that in some calculations they use $$ \vec{\nabla}\cdot\vec{u}=\frac{1}{V}\frac{dV}{d\tau}$$. I would like to derive it. Homework Equations ##\vec{u}=(\frac{dt}{d\tau},\frac{dx}{d\tau},\frac{dy}{d\tau},\frac{dz}{d\tau})## ##\vec{A}\cdot\vec{B}=A^{\mu}B_{\mu}##...
  4. T

    Special Relativity - Rocket problem (particle mechanics)

    Problem statement: A rocket propels itself rectilinearly by giving portions of its mass a constant (backward) velocity ## u ## relative to its instantaneous rest frame. It continues to do so until it attains a velocity ## v ## relative to its initial rest frame. Prove that the ratio of the...
  5. Umrao

    SR: Does observation change when changing reference frame

    Homework Statement Special relativity: A rod traveling with the relativistic velocity of 0.866c moving towards a garage. The length of the rod is L, that of the garage is L/2. From the reference frame of the garage, we find the value of Lorentz factor = 2 we say that rod would fit inside garage...
  6. R

    B Special relativity and expansion of the Universe, A paradox

    Consider two bodies A &B are moving apart with a velocity V due to the expansion of space. According to an observer in A the body B is moving away and an observer in B feels the body A is moving apart. Can some one answer in which body the time dilates and why?. ( I am specifying once again that...
  7. C

    I Deductions of Formulas for Energy

    So, I am a newbie in quantum mechanics, took modern physics last fall for my physics minor. I know that Schrodinger based his equation based on the equation K + V = E, by using non-relativistic kinematic energy (P2/2m + V = E) p becoming the operator p= -iħ∇ for the wave equation eigenfunction...
  8. T

    [SR] Relativistic runner and two relativistinc trains....

    Homework Statement A train of length L moves at speed 4c/5 eastward, and a train of length 3L moves at speed 3c/5 westward. How fast must someone run along the ground if he is to coincide with both the fronts-passing-each-other and backs-passingeach-other events? Homework Equations Velocity...
  9. Cathr

    I Frames of Reference and Time Perception in Space Travel

    Suppose I'm an observer out in space and 30 km from me there's another observer, who is static with respect to me. Let's say my name is A and the other is B. We're both far far away from all the cosmical objects that might have a gravitational influence on us. We both notice a spaceship flying...
  10. Andy_K

    I Twin Paradox - Observation at Turnaround Moment

    Dear All, I am doing the Special Relativity course at World Science U, and came across this question which I got wrong: When 100 nanoseconds have elapsed on traveling Gracie's watch, she immediately stops, turns around, and heads back toward George at the same speed of her outbound journey...
  11. A

    I Why special relativity is unsuitable to describe gravity

    I am trying to understand why the special relativity is not suitable for describing the gravity. Consider a counterexample assuming it is the suitable and the space-time containing a gravitational mass is flat. Then one could describe the acceleration of a test particle from his inertial frame...
  12. Andy_K

    I Special Relativity Course at World Science University by Brian Greene

    Dear All, Just wanted to share this excellent free Special Relativity online course I came across by Brian Greene, which I believe is one of the best around. Not sure if it's been shared before here. Special Relativity — World Science U, by Brian Greene...
  13. Hiero

    How the surface area of a cone changes; special relativity

    Homework Statement A cone has half angle θ0 and lateral surface area S0 in the frame in which the cone is at rest. If someone moves at relative speed β=v/c along the cones symmetry axis, what surface area will they see for the cone? Homework Equations I believe the lateral surface area of a...
  14. Alfredo Tifi

    I Einstein clock syncing with one way light emission absorber

    Two spaceships with their engines shut off and identical radio receiver-amplifier-reemitting devices are in the empty space, very far from each other and from any celestial body. The lag time from absorbing to reemitting in the device is vary small compared to the return time of the signal (2t)...
  15. P

    Massive spin-s representations of the Poincare group

    Context The following is from the book "Ideas and methods in supersymmetry and supergravity" by I.L. Buchbinder and S.M Kuzenko, pg 56-60. It is about realizing the irreducible massive representations of the Poincare group as spin tensor fields which transform under certain representations of...
  16. Hiero

    B Special relativity implies the space cannot be "closed"?

    I think special relativity would disallow our universe from having the structure similar to an ant on a sphere. What I mean is that it can't be possible to travel in a constant direction and to come back to your original location. Suppose there is an observer S on a planet and an observer S'...
  17. R

    I Are special relativity rules encoded in the Dirac equation?

    This may seem like a stupid question, but i can't get my head around this so please bear with me. I just looked at the derivation of Dirac equation and my question is: do the solutions for a free particle obey special relativity? because if yes why? I mean I thought using E2=(mc2)2+(pc)2 would...
  18. Hiero

    B Special relativity; mixed up time and space due to motion

    I just want to be sure I understand this correctly: Suppose there's a long spaceship moving in uniform motion relative to me (an inertial frame). Now someone in the front* of the spaceship calls someone (on the phone) in the back of the spaceship. *(this long length of the ship is oriented...
  19. B

    I Rest Energy in special relativity

    I was reading about Rest Energy and came across this line: "In special relativity, however, the energy of a body at rest is determined to be mc2. Thus, each body of rest mass m possesses mc2 of “rest energy,” which potentially is available for conversion to other forms of energy. The...
  20. A

    I Square of the difference of four-vectors

    What is the correct way to expand (p3-p4)2 where p3 and p4 are 4-vectors, with metric gmu nu=diag[1,-1,-1,-1], p = [wp, p], where p is 3-vector, and wp= (p2+m2)(1/2)
  21. D

    Momentum of W Bosons After Collision in Particle Physics Lab

    Homework Statement In a particle physics lab, an electron e− and a positron e+ collide, annihilate, and produce a W+ boson and a W− boson. Just before the collision, the electron and positron have a total energy of E = 100 GeV each, with velocities pointing along the +x-axis and -x-axis...
  22. A

    B Muon Time Dilation: Earth vs Muon Perspective

    From the reference frame of the earth, the distance between the surface of the Earth and the muon is longer, but the muon survives because time for the muon is slowed down. From the reference frame of the muon, the time experienced by the muon is not slowed down but the muon survives because...
  23. D

    Momentum Energy and relativity question

    Homework Statement A particle of mass m is moving along the positive x direction with momentum p and energy E It collides with a particle of the same mass at rest to form a new particle of mass M. Show that M^2 = 2m/c^2 * (E + mc^2) 2. Homework Equations E^2= p^2c^2 + m^2c^4 The Attempt...
  24. A

    B Question: What Makes Light Move & Why Does It Travel at 299792458 mps?

    what makes the light moving and why it moves with this speed 299792458 mps?
  25. D

    Relativity With velocity of objects moving in different fram

    Homework Statement i)A police spaceship P is chasing another spaceship A. Both ships have velocities βP = βA = 3c/5 as measured along the x-axis in the Solar System reference frame O. The police ship is a distance L = 1 light-second (i.e. the distance traveled by light in one second) behind...
  26. Jianphys17

    How to Self-Study Special Relativity Effectively?

    Hi, I was wondering, as in the Bachelor's degree curriculum there is no SR course, for one who is interested in theoretical physics (as me), would do it alone, perhaps with texts such as Rindler or Synge ...? Thank you in advance !
  27. Peter Martin

    I Special Relativity vs Newtonian Gravity: Understanding Their Compatibility

    In his little book for the layman, Seven Brief Lessons on Physics author Carlo Rovelli states: What is it about SR which is incompatible with gravity-as-a-force?
  28. C

    Which light turned on first and how much later did the second one turn on?

    Its been a few years since I have done any special relativity so I am a bit rusty, need help with either my working/understanding or if correct, making sense of my answer. This is not CW, just a question from a past exam paper that I am using as preparation. 1. Homework Statement Street light...
  29. Curtis Cleary

    Calculating Momentum in an Observer's Frame of Reference

    Homework Statement Hi all, I'm given an electron with momentum 2.0*10-20kgm/s and was asked to convert the momentum into units of Mev/c then calculate the total energy of the electron, the lorentz factor and the speed of the electron, I did this successfully but then the question got confusing...
  30. T

    I Can Born Rigid Motions Occur in Curved Spacetime?

    Can a sphere or disk rotating with uniform speed follow born condition of rigidity?
  31. Bob Walance

    I Two Clocks Orbiting a Non-Rotating Planet: Questions Answered

    Two clocks A and B are orbiting a non-rotating planet. Each clock periodically transmits its current time value via a radio signal and the other can receive that value. Their orbits are in closely-spaced parallel planes and both orbits are the same distance from the planet. The two clocks are...
  32. T

    I Derive Relativistic Beaming Equation: Learn Physics Easily

    While studying about some physics things, I came to know a term Relativistic beaming. I looked up in wiki and found a pretty decent article which gives you an equation where the real and apparent luminosity are related by a factor of (Doppler factor)^3-a where a is spectral index. But where's...
  33. JulianMau

    I Clocks ON a rotating disk: What happens?

    I was reading about the Ehrenfest Paradox and it got me thinking about something (that I think is) similar: Suppose we take a large, flat, and rigid disk, and we attach to various parts of it a number of clocks (some very close to the center of the disk, some along the edge, others in between)...
  34. L

    I How to understand the derivation for this process in QFT?

    I'm reading the book "Quantum Field Theory and the Standard Model" by Matthew Schwartz and I'm finding it quite hard to understand one derivation he does. It is actually short - two pages - so I find it instructive to post the pages here: The point is that the author is doing this derivation...
  35. D

    Special Relativity Conceptual Question

    Homework Statement Einstein developed much of his understanding of relativity through the use of gedanken, or thought, experiments. In a gedanken experiment, Einstein would imagine an experiment that could not be performed because of technological limitations, and so he would perform the...
  36. L

    Decay rate of a particle into three particles

    Homework Statement Consider the process of decay of a muon into one electron, one electron antineutrino and one muon neutrino using the Fermi theory. Assume the matrix element is, ignoring the electron's and the two neturino's masses, |\mathcal{M}|^2 = 32G_F^2(m^2-2mE)mE being E the electron...
  37. R

    The minimum KE required for muons to travel a given distance

    Homework Statement Muons of Kinetic energy 'E' are produced in collision with a target in a laboratory. The mass of a muon is ##106MeV/c^2## and its half life in it's rest frame is ## 1.4 * 10^{-6}## in its rest frame. what should be the minimum KE such that more than half of the muons...
  38. Grisha

    I Confusion with relativity of simultaneity

    I know variations of these have probably been asked numerous times before, but I'm having trouble with this specific scenario. Imagine the classic Train Paradox, except instead of lighting strikes we have an observer at the centre of the train shooting laser pulses towards the rear (Event E1)...
  39. peroAlex

    Special Relativity: Length Contraction Problem

    Hello! I have a small problem with a task professor gave us. I tried many options (you will see below) but I cannot seem to get the right solution. Any advice or guideline how to solve this would be really helpful. In advance I thank you for helping me. Homework Statement Our professor of...
  40. P

    Special Relativity - Is damage absolute?

    1. The problem statement, all variables, and given/known data A car of proper length 12m is being driven at 0.9c through a garage of proper length 6m. The garage has a front and back door. The garage owner, Joe, says that the car will fit inside the garage with no damage to it, albeit for a tiny...
  41. terryds

    What is the speed of the rocket relative to the Earth?

    Homework Statement Plane A flies with speed 0.6c chasing plane B which speed is 0.4c . Both speed is measured by observer on Earth. Then, plane B fires a small rocket which rest mass is 10 kg towards plane A. Rocket speed is 0.2c relative to plane B where c equals the speed of light in vacuum...
  42. Kara386

    Special relativity where am I going wrong?

    Homework Statement A spaceship moves away from Earth at 0.9c and fires a probe in the same direction as its motion at 0.7c. What is the probe's velocity relative to Earth? Homework EquationsThe Attempt at a Solution The Lorentz velocity transformation is ##v_x' = \frac{v_x -...
  43. N

    I Why is time dilation not symmetric for satellites and Earth?

    Hello, I read that satellites is effected by the time dilation caused by gravity and also by that one from special relativity. And so there is a need to prepare the onboard clock to ensure that the time is synchronized with a clock on Earth. But why is this effect not symmetric? The...
  44. F

    I Derivative of Lorentz factor and four-acceleration

    As far as I understand it, the Lorentz factor ##\gamma(\mathbf{v})## is constant when one transforms between two inertial reference frames, since the relative velocity ##\mathbf{v}## between them is constant. However, I'm slightly confused when one considers four acceleration. What is the...
  45. L

    Special Relativity -- two ships moving in one dimension

    Homework Statement You approach an enemy ship at a speed of 0.5c measured by you, and the ship fires a missile toward your ship at a speed of 0.7c relative to the enemy ship. What speed of the missile do you measure, and how much time do you have measured by you and the enemy ship before the...
  46. LarryS

    I Is the Phase Velocity of a Massive Particle Representing Anything Physical?

    Given a massive particle traveling freely. Also assume that it is in a momentum eigenstate - a pure unmodulated sine wave in position space. In non-relativistic quantum mechanics, the phase velocity for that particle would be greater than the velocity of light. Does the phase velocity for...
  47. L

    Find the energy of a photon after this annihilation process

    Homework Statement [/B] The problem is as follows: in a reference frame there is one electron at rest and one incoming positron which annihilates with the electron. The positron energy is E and two gamma rays are produced. Find first the energy of the photons in the center of mass frame as...
  48. Cathr

    B Special Relativity Q: Choosing Light as Ref

    Special relativity states that the speed of light is constant for all the references, as long as they are not accelerating. For example, the speed of light would be c for a train moving linearly with a constant speed and would also be c for an observer who's not moving at all (I took the Earth...
  49. E

    Relativistic Collision - Momentum and Energy

    Two chunks of rock, each having a mass of 1.00 kg, collide in space. Just before the collision, an observer at rest in the reference frame of a nearby star determines that rock A is moving toward the star at 0.800 c and rock B is moving away from the star at 0.750 c . If the rocks stick...
  50. F

    I Index Notation for Lorentz Transformation

    The Lorentz transformation matrix may be written in index form as Λμ ν. The transpose may be written (ΛT)μ ν=Λν μ. I want to apply this to convert the defining relation for a Lorentz transformation η=ΛTηΛ into index form. We have ηρσ=(ΛT)ρ μημνΛν σ The next step to obtain the correct...
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