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. S

    Calculating T1 in an Elastic Collision with Equal Masses

    Homework Statement A particle of rest mass m0 collides elastically with a stationary particle of equal mass and scatters at angle θ. The incident particle has kinetic energy T0 before the collision and T1 after the collision. (a) Show that T12 (2m0c 2 + T0) 2 = p02 p12 c4 cos2 θ. (b) Using the...
  2. S

    How is Rest Mass Affected in the Process of Rocket Propulsion?

    Homework Statement A rocket, initially at rest, propels itself in a straight line by giving portions of its mass a constant (backward) speed vout relative to its instantaneous rest frame. (a) Is rest mass conserved in this process? (b) Show that m0du′ = −dm0 vout, where m0 is the rocket’s...
  3. D

    Acceleration & Special Relativity: Explained

    So my question arises from the whole time dilation thought experiment where one person stays on Earth the other speeds off in a rocket at near light speed. Upon return of course the one in the rocket is younger, etc. The reason I bring this up is how do we determine who is actually moving...
  4. I

    Special relativity violation using entanglement

    As I understand it, faster than light communication is not possible, but I have a specific example which concludes that it is and I'm trying to find the mistake. The scheme uses two things 1) An entangled Bell pair ## | \phi \rangle = | 0 0 \rangle + | 1 1 \rangle## ( neglecting normalization )...
  5. L

    Special Relativity: Twin Paradox Question

    I've already completed most of the question, it's an add on at the end that has stumped me. I've calculated using time dilation the difference in ages between the two twins, Joe traveled at v = 24/25 (c=1 units) to a planet for 7 years in HIS reference frame and returned at v = 12/25 The...
  6. S

    Special Relativity: Collision of a Particle and Antiparticle

    Homework Statement A particle and its anti-particle are directed toward each other, each with rest energy 1,000 MeV. We want to create a new particle with rest energy 10,000 MeV and total energy 100,000 MeV. What must the speed of the particle and antiparticle be before the collision. ERest0 =...
  7. H

    Special Relativity: Solving for τ

    I'm on my first pass through special relativity and I can't remember the math that would take me from: (∂τ/∂x') + (ν/(c2-ν2))(∂τ/∂t) = 0 To τ = φ(ν)(t - (ν/(c2 - ν2))x') Any help would be appreciated. Also, sorry for the terrible format, but I haven't taken the time to figure out how to do...
  8. H

    What do you mean, approaching the speed of light?

    If velocity is relative and dependent on an observer then how does an isolated object "approach the speed of light"? Approaching the speed of light relative to what? Does the ubiquitous constant velocity/closed compartment analogy break down at relativistic speeds? If one were traveling "near...
  9. U

    Rigidly Constantly Accelerating Frame

    We know that when a rigid frame, say a rocket undergoes constant proper acceleration, its worldline is hyperbolic. The equation is given by: x^2 - c^2t^2 = \left( \frac{c^2}{a_0} \right)^2 Suppose P is such a worldline and worldine can also be written as: I understand how these are...
  10. E

    Integration of an acceleration formula involving vectors

    Homework Statement Suppose a constant force F acts on a particle of mass m initially at rest. (a) Integrate the formula for acceleration \vec{a} = \frac{\vec F}{\gamma m} - \frac{\vec v}{\gamma mc^2}(\vec F \cdot \vec v) where \gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} to show that the speed...
  11. U

    General Relativity - Index Notation

    Homework Statement (a) Find matrix element ##M_{ij}## (b) Show that ##x^j## is an eigenvector of ##M_{ij}## (c) Show any vector orthogonal to ##x^j## is also an eigenvector of ##M_{ij}## Homework EquationsThe Attempt at a Solution Part(a) [/B] \frac{\partial^2 \Phi}{\partial x^i x^j} =...
  12. Curious&TheNon

    Calculating the Time Difference in Special Relativity: Alphonse's Joy Ride

    Homework Statement Alphonse decides to go for a joy ride in his Astro-Scooter. He maintains a speed of 0.604 c and is gone for 6.53 years according to his ship's clock. His twin brother Carl says he is full of beans. According to Carl, how long has Alphonse been gone? To=? T=6.53 years...
  13. I

    Special Relativity Simple Problem

    Homework Statement Consider the usual two inertial frames S and S' in standard configuration. In 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 (de-Broglie-) speed...
  14. Quarlep

    The reality of Relative Velocities in Special Relativity

    Lets suppose we have a observer O and two objects A and B a speed is 0.5c and B speed is 0.3c than we can calculate other relative speed acoording to these informations.We know that (according this info B sees A going to 4/17c but we can pretty sure that's true because we can't ask. him How...
  15. Nicholas moore

    Need feedback for an experiment involving Geiger tubes

    I hypothesize that I can measure an increase in background radiation due to cosmic rays from ground level in Utah to 10,000 ft altitude with a Geiger Muller set-up. I feel that I have enough information to order equipment now (a working knowledge of gm tubes, energy levels of & the special...
  16. PWiz

    Special relativity and general relativity

    I have studied most of the concepts of Newtonian mechanics and understood the calculations and derivations involving the concerned formulae. I have a basic knowledge of calculus (differentiation of products along with differentiation of trigonometric, logarithmic, exponential and implicit...
  17. Einstein Devotee

    Time dilation why or how, Special Relativity causes

    I understand the theory of special relativity and the mathematics which support it. I even understand that the time dilation has been proven. Therefore I am going to ask a question which on first blush may appear that I disagree with it but that is not the case. The question I can not seem to...
  18. T

    Time in QM vs SR: Energy, Frequency & Motion

    In QM, the energy operator is proportional to the time derivative E ~ d/dt So higher energy particles have higher frequencies, i.e. their wave functions change more often per time than when at rest But in SR, higher energy particles seem to exist in slow motion, appearing to age little How...
  19. arpon

    Calculating Rocket Velocity to Sun

    Homework Statement An astronaut went to sun from Earth by a rocket. According to the clock in the rocket, the traveling time was 5 minute. What was the velocity of the rocket? ( Earth is 8 light minute away from sun) Homework Equations t = \frac {t_0}{\sqrt {1 - \frac{v^2}{c^2}}}The Attempt at...
  20. N

    Time Dilation and Relative Time

    I was reading in Clifford M.Will's book "Was Einstein right? Putting General Relativity to the Test" that there was an experiment done where in October 1971 an experiment was done with radioactive clocks, and plane trips taken going with the spin of the earth, and against it. He reports: "The...
  21. B

    Special Relativity rocket’s speed

    Homework Statement A rocket flies between two planets that are one light-year apart. What should the rocket’s speed be so that the time elapsed on the captain’s watch is one year? Homework Equations I have v = d'/t' d'=d/ϒ t'=1 year d=1 light year The Attempt at a Solution Will the equations...
  22. M

    Time Difference between two inertial frames of reference

    Homework Statement Let S and S' be two inertial frames of reference where S' is moving at a velocity of 0.6c relative to S. When x = x' = 0, t = t' = 0, where t and t' are time of the clocks on S and S' respectively and x and x' are the x-coordinates of the S and S' frames respectively. An...
  23. S

    General relativity vs special relativity

    Hello, Everybody! I'm new to the board, and am happy to have found you! I have six questions I can't seem to find the answers to, either in books or online -- yet I know the answers are out there! I'll post each question in a separate thread, and hope that someone who knows far more than I do...
  24. U

    Compton Scattering Angle - CM FRAME

    Homework Statement Given incoming photon has energy 10Mev and scatters at angle 25 degrees, find the scattering angle in CM frame. Homework EquationsThe Attempt at a Solution [/B] In lab frame, let the energy of incoming photon be ##E##. Total 4-vector would be ##P + Q =...
  25. U

    Lorentz Transformation of relative velocity

    Homework Statement If two particles have velocities u and v in frame S, find their relative speed in frame S'. Homework EquationsThe Attempt at a Solution Isn't it strange that the relative speed doesn't depend on the velocity of the frame, ##\vec s##? Since the two particles have velocities...
  26. U

    Two particle collision - One in excited state

    Homework Statement (a)Find energy of photon emitted (b)Show that relative velocities after de-excitation are reversed (c)Find an expression for CM frame energy and find momentum of either particle in CM frame (d)Consider now, for a nuclear process and describe the initial and final conditions...
  27. S

    Relativistic relative velocity of particles

    Homework Statement In a given inertial frame two particles are shot out simultaneously from a given point with equal speeds u at an angle of 60 degrees with respect to each other. Using the concept of 4-velocity or otherwise, show that the relative speed of the particles is given by ##u_R =...
  28. C

    Lorentz Transformation - Clock

    Homework Statement Use the Lorentz Transformation equations to derive the formula relating the time period of a moving clock to that of a stationary clock Homework Equations X'=y(X-vt) Y'=Y Z'=Z t'=y(t-vx/c^2) The Attempt at a Solution t'=1/sqrt(1-(v/c)^2) . (t-vx/c^2)
  29. T

    Special relativity and the speed of light constant

    Hi guys. I know that light does not travel through time. Is that because its speed is constant for all observer?
  30. D

    Fizeau's Experiment interpretation

    Hi all,In Einstein's book, "Relativity: The Special and General Theory", he uses the Fizeau experiment to show how the Lorentz Transform correctly predicts the addition of velocities. I have some difficulty understanding the interpretation of the results, however. Suppose that liquid M is in...
  31. D

    Understand Relativity & Lorentz Transformation - Aaron

    Hi all,I am trying to understand relativity and Lorentz Transformation more clearly but I have some problems. Assume that we have frame F' which is moving at velocity v with respect to F. Now assume we have an object, O, moving at velocity, w, with respect to F. Frame F has its own time, t, and...
  32. LachyP

    Who wants a chat? Preferably about Physics

    Hello, I'm Lachlan Pearce and love physics (mostly special relativity, astrophysics, and a little of quantum physics). If anyone wants to discuss any of this I'd be happy to.. :)
  33. Amaterasu21

    Question about time in QM vs. special relativity?

    This question is about both quantum mechanics and special relativity, so I wasn't sure which forum to post it in. If mods think it's in the wrong forum then please move it as you see fit! My understanding is that in special relativity, we live in a four-dimensional "block universe" of...
  34. Alettix

    Relativistic Work: Deriving Formula & Application to Electrons

    Hello, I have tried to derive a relativistic formula for work using the E = ϒmc^2 equation and that work is equivalent to change in energy. But I have not gotten especially far and everything is messy. However, when looking at solutions to some harder problems I encountered the formula...
  35. V

    Special relativity help - force

    Homework Statement A claim is made that a new force field F(x) (independent of the four-velocity) is discovered which induces on a mass m a 4-acceleration a = du/dτ = F(x)/m at position x. Would this be consistent with special relativity? Why or why not? Homework EquationsThe Attempt at a...
  36. QuantumCurt

    Special Relativity: Trip to Andromeda by rocket

    Homework Statement This is from chapter 1 (2nd edition) of Taylor and Wheeler's 'Spacetime Physics.' It's a four part problem, and I didn't have any troubles with parts a, b, or c. I'm stuck on part d. I'm supposed to determine if we could make it to Andromeda within a lifetime. Assume that...
  37. Gravity

    Does Penrose's Andromeda paradox prove determinism?

    Article: https://en.wikipedia.org/wiki/Rietdijk–Putnam_argument
  38. U

    Deriving Equation 4.8 in Special Relativity: Tips and Tricks

    Taken from Steane's "Relativity made relatively easy" equation 4.8 I have been trying to show (4.8) using these relations earlier on in the book: Tried most means (rearranging, taking dot products) but can't seem to make it work. Is there an easy method I'm missing out?
  39. M

    Special Relativity and time dilation

    Homework Statement Two spaceships are traveling with a relative velocity of 1.2x10^8 m/s, both carrying clocks. According to the captain of each ship, the other captains clock ticks more slowly than his own. By what factor do the clocks disagree? Homework Equations 1/(1-(v^2/c^2))^1/2The...
  40. kq6up

    A Book that Clearly Explains Special Relativity w / Tensors?

    My professor gave us a book that is still in production to use for special relativity. I am having a hard time grasping the notation and operations with Einstein upper and lower notation. Can anyone recommend a good textbook on this topic? Chris
  41. A

    Special Relativity and the Relativity of Simultaneity.

    The position of the rocket is not specific. We just know that it is at the left of the galaxy. We know that R will explode first in the rocket's frame. Maybe the galaxy could be moving fast enough so that the time it takes for L to explode is enough for the rocket to see R's light first. In...
  42. B

    How Does Time Dilation Affect Communication and Aging in Space Travel?

    Hello, I am doing my special relativity homework and since the ideas are quite counter-intuitive it's hard to know if I'm doing the right things. So i'd like to post some work here and see if it is correct. Also, I am stuck on the final part of the question. 1. Homework Statement A space...
  43. M

    Geometry of Time Dilation

    I was recently exploring time dilation from Gravity and from velocity and I came up with an interesting derivation that I have not seen before. I was wondering if there is a paper published showing these relationships like this before and where I could find it? First you start with the...
  44. MiladP

    Does the weight of a relativistic mass change when measured on a moving scale?

    Consider two equal masses, m, are placed on two identical scales in a uniform gravitational field. If one of the masses moves with relativistic speed, does the moving scale read mg or γmg? Why? It seams that people used to call γm the relativistic mass where m is the rest mass. However, more...
  45. StonedPhysicist

    Muon special relativity problem,

    Here is the question: If 1000 muons are incident from a height of 10 km above the Earth's surface, how much slower than the velocity of light must they be traveling in the rest frame of the Earths surface for 990 of them to be expected to arrive at the ground undecayed? The mean life of a muon...
  46. N

    Calculating Time for a Swimmer to Cross a River Using Pythagorean Theorem

    Homework Statement A river is 400 feet wide and flows at 1 ft/s. A swimmer swims at 2 ft/second, straight across the river and back to where he started on the original shore. Find the time required to complete his trip. To clarify, the turn around point is straight across the river. (I have...
  47. F

    Special Relativity - "Simultaneity"

    Homework Statement An experimenter triggers two lights simultaneously, which produces a large flash located at the origin of his reference frame and a small one at x = 23.8 km. An observer, who moves with speed 0.374c in the positive x direction, also views the flashes. What is the time...
  48. F

    How Fast and Slow Does Time Flow on a Speeding Spaceship?

    I was not too sure if this was the correct forum, so feel free to move if needed. 1. Homework Statement A spaceship is measured to be exactly 1/3 of its proper length. (a) What is the speed parameter β of the spaceship relative to the observer's frame? (b) By what integer factor do the...
  49. dbmorpher

    Velocity of an Electron from Momentum

    Homework Statement If I know the momentum and mass of a particle how do I determine/differentiate the Lorentz Factor and velocity? Electron rest mass: 9.10938215e-31kg c=299792458m/s y=Lorentz Factor m=mass p=momentum e=energy Calculated momentum: 2.019006271e+14kg m/s Homework Equations...
  50. Strilanc

    Distinguishing Special Relativity from Classical Mechanics

    I was recently reading the strange world of classical mechanics. It prompted me to calculate some round trip times for things moving near the speed of light (classically, with an aether). I found that the predictions it makes are awfully similar to relativity, and I can't think of an experiment...
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