What is Special relativity: Definition and 1000 Discussions

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. bananabandana

    I Deriving Covariant Form of $E_{1}E_{2}|\vec{v}|$

    Given a two particle scattering problem with (initial) relative velocity $|\vec{v}|$, apparently the product $E_{1}$E_{2}|\mathb{v}|$ can be expressed in the covariant form: $$ E_{1}E_{2}|\vec{v}| = \sqrt{ (p_{1}\cdot p_{2} - m_{1}^{2}m_{2}^{2}} $$ My textbook gives no further explanation -...
  2. K

    B Quantum entanglement and special relativity

    There are a pair of entangled particles moving in opposite directions. A measurement is done on particle A, the wavefunction collapses randomly, you observe either spin up or spin down, A does an action at a distance on B, particle B instantly collapses to the opposite spin state, a measurement...
  3. Luxucs

    Special Relativity - Relativity of Simultaneity?

    Homework Statement A thin rod of proper length 4a is traveling along the x-axis of a frame S with a speed ##{\frac {\sqrt 3} 2}c## in the positive x-direction. A hollow cylinder CD of proper length 2a is placed with its axis along the x-axis, so that when the ends of the cylinder are open the...
  4. Hamza Abbasi

    Relativistic Velocity Addition

    Homework Statement Two spaceships pass each other. Spaceship A moves relative to nearby planet at velocity v1 , while spaceship B moves at velocity v2 relative to the planet . How fast does spaceship A moves relative to spaceship B. Homework Equations Velocity Transformation : v* =...
  5. E

    Is Transcending Relativism Possible?

    Greetings Folks, I expect to be interested to post profound news here in a few days. Together with trimmings, it will come in very few lines. So it probably will not take much of your time to decide whether you are interested or not. I hope you do not find such an engagement to be...
  6. F

    How Do You Calculate Proton Beam Energy in a Lab Frame?

    Homework Statement a) [Solved] What is the threshold energy in the center of mass for production of an antiproton in a proton-proton collision? Make sure quantum numbers are conserved. (This one was easy and I manage to solve it) b) In a fixed target experiment calculate the proton beam energy...
  7. T

    Position of the front of an asteroid using special relativity

    Homework Statement I'm stuck on part (d) but I've included the previous subquestions in case they're useful. The length of an asteroid is exactly 300 m = 1 µls (micro light-second) when at rest. Draw a carefully labelled space-time diagram to illustrate the following: (a) Depict the rest...
  8. G

    Ultra-Relativistic Particle Decaying to Identical Particles

    Homework Statement Show that it is impossible for an ultra-relativistic particle with ##pc>>Mc^2## to disintegrate into two identical massive particles of mass m. Homework Equations Conservation of four momentum The Attempt at a Solution The four momentum of the ultra-relativistic particle...
  9. BookWei

    I Spacetime is homogeneous and isotropic

    I read the Special Theory of Relativity in Jackson's textbook, Classical Electrodynamics 3rd edition. Consider the wave front reaches a point ##(x,y,z)## in the frame ##K## at a time t given by the equation, $$c^{2}t^{2}-(x^{2}+y^{2}+z^{2})=0 --- (1)$$ Similarly, in the frame ##K^{'}## the wave...
  10. F

    Relativistic Decay: Calculating Pion Momentum

    Homework Statement A Sigma^+ decays at rest into a neutron and a pion^+ meson, i.e. according to the reaction $$\Sigma \rightarrow n + \pi$$ The n and π masses are assumed known. The kinetic energy of the π + is measured to be 92 MeV. Determine the momentum of the pion. Homework Equations...
  11. mjda

    I What is the difference between covariance and invariance in special relativity?

    Can anyone briefly explain the difference between covariance and invariance in terms of special relativity? My understanding is that an invariant quantity is a value which does not change regardless of frame of reference it is being measured in. Covariance is a value which when measured in...
  12. mjda

    I The relativistic de Broglie equation

    I'm having trouble understanding how the 4-wave vector is derived, and also how it is then used alongside the 4-momentum vector to formulate the relativistic de Broglie equation. The inner product of the 4-momentum vector with itself, is an invariant quantity. If we define the 4-momentum...
  13. stevendaryl

    Insights Rindler Motion in Special Relativity, Part 2: Rindler Coordinates - Comments

    Greg Bernhardt submitted a new PF Insights post Rindler Motion in Special Relativity, Part 2: Rindler Coordinates Continue reading the Original PF Insights Post.
  14. A

    Special relativity - angles between fields

    Homework Statement In an electromagnetic filed, the elctric field ##\vec{E}## forms an angle ##\theta## with the magnetic field ##\vec{B}##, and ##\theta## is invariant for all inertial observers. Finding the value of ##\theta##. Homework Equations Tranformations of fields perpendicular to the...
  15. A

    Electromagnetic Tensor: Calculating $\det{F^{\mu}}_\nu$

    Homework Statement Given an electromagnetic tensor ##F^{\mu\nu}##, showing that: $$\det{F^{\mu}}_\nu=-(\vec{B}\cdot\vec{E})^2$$ Homework Equations The Attempt at a Solution I had only the (stupid) idea of writing explictly the matrix associated with the electromagnetic tensor and calculating...
  16. James Chase Geary

    Special Relativity problem: Lorentz transformation and Reference Frames

    Homework Statement S and S' are in standard configuration with v=αc (0<α<1). If a rod at rest in S' makes an angle of 45o with Ox in S and 30o with O'x in S', then find α. Homework Equations We are in the world of Lorentz transformations so we have t'=(t-vx/c2)/(1-v2/c2)1/2...
  17. A

    Special relativity - Gauge invariance

    Homework Statement In an inertial reference frame ##S## is given the four-potential: $$A^\mu=(e^{-kz}, e^{-ky},0,0)$$ with ##k## a real constant. ##A^\mu## fullfills the Lorentz gauge? And the Coulomb gauge? Which is the four-potential ##A'^\mu## in a reference frame ##S'## which is moving...
  18. K

    B Distance Expansion When Moving Away from an Object?

    In a physics video on YouTube it's told that moving away from an object causes eextension of the length. (Link: from 6:00, but video is Norwegian) Imagine: From planet B to planet C, the distance is 20 light years. And from planet A to planet B the distance is 20 light years. We are on...
  19. A

    Special relativity - Transformation of angles

    Homework Statement Let's have a three-particle decay of equal mass ##m##; in the CM frame the three particles have equal energy ##E## and they form angles of ##\frac{2\pi}{3}## between each other. Which is the angle between two of the three particles in the rest frame of the other one. (The...
  20. K

    B How can the speed of light be constant for all observers?

    A rocket is in constant velocity. The velocity of the rocket is 150Mm/s (or 0.5 of the speed light, or 150 million meters per second) relative to us (we as observer). We observe two lights, one moving in parallell with the rocket, another is moving in the opposite direction. Below I have made...
  21. A

    Special relativity - kinematics

    Homework Statement A photon hits a proton at rest in the laboratory frame and there is the process: $$\gamma + p \rightarrow n+\pi^+$$ The mass of the pion is ##m_\pi## and assuming that the masses of the proton and the neutron are the same (##m##): Finding the threshold energy of the foton...
  22. stevendaryl

    Insights Rindler Motion in Special Relativity: Hyperbolic Trajectories - Comments

    Greg Bernhardt submitted a new PF Insights post Rindler Motion in Special Relativity: Hyperbolic Trajectories Continue reading the Original PF Insights Post.
  23. F

    Synchronized clocks in two moving reference frames

    Homework Statement My professor gave us a werid question which is as follows In the laboratory frame, two clocks are synchronized and measure two light sources at the same time situated at 3 years in time axis and 3 light years and 2 light years in x-axis >At what velocity is the frame ##S'##...
  24. ZapperZ

    "Classical Physics Is Wrong" Fallacy - Comments

    Greg Bernhardt submitted a new PF Insights post "Classical Physics Is Wrong" Fallacy Continue reading the Original PF Insights Post.
  25. V

    A Understanding E-Field Transformation in Feynman II_26

    I have been learning SR from various sources. Most of the time from Feyman's Lectures but that's not the only place. In II_26 he gives the transformation for the E-field of a moving charge in the x direction under a standard Lorentz configuration. In Eqn 26.11 he derives a formula for the Ex...
  26. Adgorn

    Solution of basic special relativity problem

    Homework Statement This is more of a solution check than an actual problem, but I didn't see any other fitting thread to post this on. I'm starting to learn special relativity and have received 2 starting questions on the subjects, I solved them to the best of my abilities but have no actual...
  27. A

    Change in time due to accelerated light-clock

    Homework Statement A light-clock (a photon traveling between two mirrors) has proper length l and moves longitudinally through an inertial frame with proper acceleration ##\alpha## (ignore any variation of a along the rod). By looking at the time it takes the photon to make one to-and-fro...
  28. F

    Speed and direction of b and anti-b quark

    Homework Statement A Higgs particle of mass M is moving in the z-direction with speed $\Beta_H$c compared to the lab system. It decays to a b-quark ans anti-b quark, each of mass m. What is the speed and direction of the b-quark compared to the lab-system, if the Higgs system, (a) it is emitted...
  29. P

    I Relativistic Energy Dispersion Relation: Explained

    I'm in the process of learning special relativity (SR), and I'm a bit confused as to why the relativistic energy dispersion relation ##E^{2}=m^{2}c^{4}+p^{2}c^{2}## gives the energy for a free particle? I get that it is the sum of (relativistic) kinetic energy plus the rest mass term (a...
  30. A

    Inertial frame where rods have same length

    Homework Statement I was re-reading my old Relativity book (by Rindler) and taking a look at some of the problems. He asks: Using a Minkowski diagram to establish the following result: Given two rods of rest lengths ##l_1## and ##l_2 (l_2 < l_1)##, moving along a common line with relativity...
  31. VIctor Medvil

    A SR/GRs Views on QM/QFT | Physics Forums

    This ties into this thread https://www.physicsforums.com/threads/i-want-to-know-the-exact-problems-of-merging-gr-and-qm.939509/ , I would like to know SR/GR's opinion of QM/QFT. I need both sides of the story.
  32. VIctor Medvil

    A I want to know the exact problems of Merging GR and QM

    This thread is I want a set of experts in the subject to show me the exact math of why Einstein's field Equations along with Special Relativity and Schrodinger's Equation along with deeper QM like QFT cannot be fused with GR. I want to see the exact anomalies in the equations myself from the...
  33. A

    Special relativity - Maximum mass

    Homework Statement Finding the maximum mass ##M_x## which can be made from a collision of identical particles with mass ##m##, in the laboratory frame, in which one particle is at rest and the other one has energy ##E##. The reaction is the following: ##a+b \rightarrow a+b+x##.The Attempt at a...
  34. G

    Relativistic Harmonic Oscillator Lagrangian and Four Force

    Homework Statement Consider an inertial laboratory frame S with coordinates (##\lambda##; ##x##). The Lagrangian for the relativistic harmonic oscillator in that frame is given by ##L =-mc\sqrt{\dot x^{\mu} \dot x_{\mu}} -\frac {1}{2} k(\Delta x)^2 \frac{\dot x^{0}}{c}## where ##x^0...
  35. A

    Special relativity - constant acceleration

    Homework Statement A rocket is flying away from the Earth with a costant acceleration ##a## in a frame in which the rocket is at rest. Finding the equation of motion (the relation between the distance from the Earth and the terrestrial time). Showing that there is a maximum time ##T## after the...
  36. Destroxia

    Special Relativity - Length Contraction

    1. Homework Statement Why does the non-relative simultaneous frame have an additional term of ##v \Delta t## along with the contracted length ## L ## for ## \Delta x ##? 2. Homework Equations ## L + v \Delta t = \Delta x ## ---- (1) ## \Delta x = \gamma \Delta x' = \gamma L_{\star} ## ----...
  37. A

    Special relativity - inverse Compton scattering

    Homework Statement In the inverse Compton scattering there is a particle, with energy ##E## in the laboratory frame and mass at rest ##m##, which collide head on with a photon with energy ##E_\gamma##. Finding the maximum energy the photon can have after being scattered. The Attempt at a...
  38. A

    Special relativity - scattering angle

    Homework Statement Finding the maximum scattering angle of a particle whose mass in ##m_1## which hits with relativistic velocity ##v## a particle at rest with mass ##m_2<m_1##. The Attempt at a Solution I've written the 4-momenta (p before the collision, k after the collision and the z-axis...
  39. A

    Special relativity - transformation of electromagnetic fields

    Homework Statement In a reference frame ##S## there is a particle with mass ##m## and charge ##q## which is moving with velocity ##\vec{u}## in an electric field ##\vec{E}## and in a magnetic field ##\vec{B}##. Knowing the relativisitc laws of motion for a particle in an EM field, find the...
  40. ZapperZ

    B MinutePhysics Special Relativity Series

    MinutePhysics is attempting to produce a series of video lessons on Special Relativity, using an approach, according to the video, that will be different and "simpler" than the traditional method that SR has been taught in schools. Since we often get questions on here about this topic...
  41. F

    Abstract Special Relativity, particle at rest and one moving

    Homework Statement In frame S particle 1 is at rest and particle 2 is moving to the right with velocity u. Now consider a frame S 0 which, relative to S, is moving to the right with velocity v. Determine the value of v such that the two particles appear in S' to be approaching each other with...
  42. P J Strydom

    I Can I be taught general and special Relativity on this forum

    If I am wasting anyone's time, please advise so I can leave and find another source to assist me in my quest. I have been thinking about the theory of General and Special Relativity for most of my life. When I was 16 years old, I saw a documentary about Einstein and how he used his thoughts as...
  43. nomadreid

    I Understanding Special & General Relativity: Inertial vs. Gravitational Frames

    I know this is a naive question that has almost certainly been brought up numerous times before, but my search abilities seem not to be sufficient for finding a good answer, so if anyone just refers me, that would be fine. The question: Special relativity concerns comparisons between pairs of...
  44. J

    Special Relativity Problem from Rindler

    Homework Statement In the inertial frame ##S'## the standard lattice clocks all emit a 'flash' at noon. Prove that in ##S##, this flash occurs on a plane orthogonal to the ##x##-axis and traveling in the positive ##x##-direction at speed ##\frac{c^2}{v}##. Homework Equations Lorentz...
  45. Hypercube

    B I cannot grasp simultaneity in Special Relativity

    Hi everyone, I'm struggling to grasp simultaneity in Special Relativity. Since I am struggling conceptually, I have posted my question here. But if you think this problem I made up modified should go to homework, I apologise (and feel free to move it). Suppose we have two light sources...
  46. S

    Invariant mass problem, elastic collision

    fHomework Statement Question b: Homework Equations E2=c2p2+m2c4 The Attempt at a Solution We have c2pinitial2=E02-m2c4, and Ef2=c2p2+m2c4 for each outgoing proton. Combining those equations we get c2p2=Ef2-E02+c2pinitial2. I don't know where to go from here.
  47. S

    I Energy-momentum formula and deBroglie wavelength

    Hi everyone, Im a little bit confused about deBroglies procedure on introducing his famous Matterwave formula. People already knew that the wavelength of the light was equal to Lambda = h/p. The term p comes from the energy-momentum formula; for the light the restmass = 0 so E =pc etc. As...
  48. I

    Finding the relativistic speed of a spacecraft

    Homework Statement If a spacecraft is traveling to a star which is located at a distance of 1 lightyear and it would take the spacecraft 1 year to reach the star in its own frame, how fast would the spacecraft actually fly? Also, how long would the journey take for an observer on Earth...
  49. F

    I Is the Wavefunction Speed in Quantum Mechanics Wrong?

    This problem bothered me many years ago when I was taking a university course in quantum mechanics, but I assumed it was due to an error on my part which I, however, couldn’t locate, and I didn’t ask my course instructor about it. Recently, when researching a q.m. question on the Internet...
  50. Q

    B Does this connect Quantum Theory and Special Relativity?

    This is probably extremely wrong I just want to know how. If photons don't experience time doesn't that mean they are every where at once, and if that is true doesn't part of quantum physics say before a particle is observed its in all the states it can be in? So doesn't that apply in that sense...
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