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. Wout Veltman

    I Kinetic Energy & Speed in Inertial Frames: Chris, Bob & Angelica

    From Chris' perspective Bob is traveling with 1.5*108 m/s in direction a. Angelica is also traveling with 2.4*108 m/s in direction a. From Bob's perspective Chris is traveling with 1.5*108 m/s in direction b (The opposite of x). Angelica is traveling with 1.5*108 m/s in direction a. They all...
  2. F

    I Definition and measurement of proper length

    As I understand it, the proper length, ##L## of an object is equal to the length of the space-like interval between the two space-time points labelling its endpoints, i.e. (in terms of the corresponding differentials) $$dL=\sqrt{ds^{2}}$$ (using the "mostly plus" signature). Furthermore, this is...
  3. Matternot

    I Special relativity timebomb on distant planet 'paradox'?

    I thought of this 'paradox' which is somewhat similar to the twin paradox but can't be explained by a lack of symmetry etc. It is very similar to many paradoxes I have heard before of which the resolution is known (which is why I am mostly sure this can be resolved) Bob is looking through his...
  4. ManicPIxie

    Relativistic Addition of Velocities

    This question comes from a previous years exam as practice for my upcoming. Homework Statement Two spaceships are launched from Earth, going in opposite directions. Eventually, both spaceships have a velocity of 0.75c (where c is the speed of light), each in their respective directions. A...
  5. J

    Special Relativity Forces and Energy

    Homework Statement Hi, I have this problem: For motion under a pure (rest mass preserving) inverse square law force f = −αr/r3 , where α is a constant, derive the energy equation γmc2 − α/r = constant. Homework Equations E = γmc2 dE/dt = f.u for a pure force The Attempt at a Solution I...
  6. oa8

    How Fast Must You Travel to See Light Pulses Simultaneously?

    Homework Statement In a certain inertial frame two light pulses are emitted a distance 5 km apart and separated by 5 µs. As observed from another frame, which is traveling parallel to the line joining the points where the pulses are emitted at a velocity v with respect to this frame, the pulses...
  7. Z

    A Relativistic generalization of Newton’s equation

    If say you have some scalar field, θ(x^u), where x^u represents the 4-vector coordinates of spacetime, and then the typical classical equation of motion, a = -∇θ, how would one go about 'generalizing' this to a relativistic version? Since F = ma, would you have to write it as d/dt (P^u)...
  8. P

    Lorentz Invariance of Plane Wavefront

    Homework Statement For a plane, monochromatic wave, define the width of a wavefront to be the distance between two points on a given wavefront at a given instant in time in some reference frame. Show that this width is the same in all frames using 4-vectors and in-variants. Homework...
  9. K

    I Does Special Relativity Apply to a Moving Clock?

    A Moving Clock runs slow. But, If time t has elapsed in the S frame, does SR apply to a clock moving with speed u in the x-direction in the S frame, relative to the S frame? Or does SR apply only when the clock is in another reference frame S' moving in the x'-prime direction, given that...
  10. A

    Two athletes time compensation

    Homework Statement In a reference system S two athletes are aligned at a distance d relative to each other on the Y axis to make a run parallel to the x axis. Two starters, one next to each athlete, shoot their guns out at slightly different times, offsetting the advantage of better athlete...
  11. energeticringleader

    Rest, Mass, and Kinetic Energy

    Homework Statement I really don't have a homework question just a thought. Is rest energy "maximum energy" for a particle? As to say a particle at rest has a given energy, so when it is in motion it transfers some mass energy to kinetic energy, where both the mass and kinetic energy together...
  12. EricjamesCADstudent

    B What Einstein said on faster than light travel

    Hi, I'm a CAD student, writing a research paper for my English Comp. class on interstellar travel. I wan't to quote Einstein but can't find were he stated this exactly: Because space and time are relative, the faster you move through space the slower you move through time relative to someone...
  13. Aler93

    Particle´s acceleration respect two inertial frames

    Homework Statement System S' moves with constant speed v=(vx,0,0) respect to the system S. On the S' system a particle moves with a constant acceleration a=(ax,ay,az). What is the acceleration a'=(ax',ay',az') measured from the system S?. Homework Equations Lorentz transformation The Attempt...
  14. P

    I Detecting Earth in an Elevator: Thought Experiment

    I have in mind thought experiment where physicist is in elevator falling towards the Earth. Question would be if he is not allowed to look outside, how would he detect the presence of the planet? Let's not take in consideration tidal forces and assume he is taking local measurements during small...
  15. J

    I Time dilation (something seemingly paradoxical)

    Hello. Consider the following case: Two observers, A and B, moving relative to each other with velocity v. For B, it's A that moves (with v) and so DTb=g*DTa (where DT denotes finite time difference and g is/the Lorentz factor gamma). So, (following the same logic as in Morin's Classical...
  16. adamaero

    Light hours special relativity time dilation

    Homework Statement http://phy240.ahepl.org/Chp1-Relativity-Serway.pdf#page=39 #32 Planet R is 25 lighthours away from Earth. It takes 25 h (according to an Earth observer) for a spacecraft to reach this planet. The clocks are synchronized at the beginning. What is the spacecraft 's time...
  17. adamaero

    Special relativity ~ show that....given this

    Homework Statement A rod of length L0 moves with a speed v along the horizontal direction. The rod makes an angle of θ0 with respect to the x'-axis. (a) Show that the length of the rod as measured by a stationary observer is given by L = L0*√[1-(v2/c2)cos2θ0] (b) Show that the angle that the...
  18. Elvis 123456789

    Photon beam is incident on a proton target produces a particle

    Homework Statement A photon beam is incident on a proton target (at rest). Particle X (and nothing else) with rest mass M=1.232GeV/c2 is then produced. Use m_p =0.938GeV/c2 as the proton mass. a) What is the energy of the photon beam, in terms of GeV? b) What is the momentum of the moving...
  19. Elvis 123456789

    Determining beta as a function of relativistic momentum

    Homework Statement For a fast moving particle, its momentum and energy are frequently easier to measure than its velocity. a) Show that the factor of beta (as defined by β=v/c), can also be determined by measuring the ratio of relativistic momentum (p) and total energy (E). b) Sketch...
  20. P

    Special Relativity simultaniety

    Homework Statement Two events occur in an inertial system K as follows. Event 1: x1 = a, t1 = 2a/c, y1 = 0, z1 = 0 Event 2: x2 = 2.6a, t2 = 1.9a/c, y2 = 0, z2 = 0 What is the velocity of the frame K' in which these events appear to occur at the same time? Express the velocity vector using...
  21. RJLiberator

    Special Relativity Question (Lorentz)

    Homework Statement Synchronized clocks A and B are at rest in our frame of reference a distance 2 light minutes apart. Clock C passes A at a speed of c*4/5 bound for B, when both A and C read t =0 in our frame. a) What time does C read when it reaches B? b) How far apart are A and B in C's...
  22. X

    Lorentz boost to obtain parallel E and B fields?

    Homework Statement Suppose given an electric field \vec{E} and a magnetic field \vec{B} in some inertial frame. Determine the conditions under which there exists a Lorentz transformation to another inertial frame in which \vec{E} || \vec{B} Homework Equations If we give a Lorentz boost along...
  23. F

    Ball hitting a wall with relativistic effects

    Homework Statement I have encountered a problem in Sean Carroll's GR book, exercise 1.1 Consider an inertial frame S with coordinates ##~x^μ = (t, x, y ,z)~##, and a frame S' with coordinates ##x^{μ'}## related to S by a boost with velocity parameter ##v## along the y-axis. Imagine we have a...
  24. tomdodd4598

    I Special Relativity Approximation of Gravitation

    Hey there, I have two questions - the first is about an approximation of a central gravitational force on a particle (of small mass) based on special relativity, and the second is about the legitimacy of a Lagrangian I'm using to calculate the motion of a particle in the Schwarzschild metric...
  25. H

    Inertial frame where plane waves have the same frequency

    Homework Statement Plane harmonic waves of 1/p, 1/q, 1/r and 1/s are travelling, respectively, in the directions of the (non-unit) vectors (1,1,1), (1,-1,-1), (-1,1,-1) and (-1,-1,1). Show that there exists an inertial coordinate system in which they have the same frequency if and only if...
  26. Elvis 123456789

    Perpendicular relativistic velocities

    Homework Statement Imagine two motorcycle gang leaders racing at relativistic speeds along perpendicular paths from the local pool hall, as shown in Figure 1.21. How fast does pack leader Beta recede over Alpha’s right shoulder as seen by Alpha? Solution Figure 1.21 shows the situation as seen...
  27. Elvis 123456789

    Another relativistic particle decay question

    Homework Statement Unstable particles cannot live very long. Their mean life time t is defined by N(t) = N0e−t/τ , i.e., after a time of t, the number of particles left is N0/e. (For muons, τ=2.2µs.) Due to time dilation and length contraction, unstable particles can still travel far if their...
  28. Elvis 123456789

    Relativistic particle decay

    Homework Statement Unstable particles cannot live very long. Their mean life time t is defined by N(t) = N0e−t/τ , i.e., after a time of t, the number of particles left is N0/e. (For muons, τ=2.2µs.) Due to time dilation and length contraction, unstable particles can still travel far if their...
  29. Tazerfish

    B Derivation of time dilation without light clocks

    In the way I was taught about special relativity, time dilation is like the fundamental building block from which you derive things like relativistic mass and length contraction. So it has always struck me as quite odd, that the derivation of time dilation (in some sense the basis of special...
  30. T

    Special Relativity: time for light to traverse a rocket

    Homework Statement A 35 m long rocket is receding at 0.6c. From the point of view of a stationary observer, how long does it take for light to travel (a) from the bottom of the rocket to the top and (b) from the top to the bottom? Homework Equations t = d/v L = L0 / gamma The Attempt at a...
  31. T

    Special Relativity -- elapsed time while traveling at 0.95c

    Homework Statement A particle moving at 0.95c travels 10 m, as measured by a stationary observer, and then disappears. How long did the particle live (a) from the point of view of the observer and (b) from the point of view of the particle? Homework Equations t = d/v d = d0/gamma The Attempt...
  32. Destroxia

    Special Relativity: Super-Novae light on earth

    Homework Statement A nova is the sudden, brief brightening of a star. Suppose Earth astronomers see two novas occur simultaneously, one in the constellation Lyra. Both nova are the same distance from Earth, ## 2.5 \times 10^3 [cy]##, and are in exactly opposite direction from Earth. Observers...
  33. L

    I How to bridge the gap between these approaches to SR?

    For quite a long time now I'm having some trouble to bridge the gap between two different approaches to Special Relativity. The first approach is the traditional one. It is the approach that Einstein presented in his paper and that is taught in most of the basic textbooks. In this approach...
  34. Elvis 123456789

    Spaceship voyage at close to light speeds

    Homework Statement The last of the human race are leaving the earth, after a total nuclear destruction, to reach the only known planet suitable for lives, 2 million light years away from earth. They are traveling on the spaceship ARK, capable of close to speed of light. There is only enough...
  35. Amara

    Taylor expansion of the relativistic Doppler effect?

    [Note from mentor: this thread was originally posted in a non-homework forum, therefore it does not use the homework template.] I have been given an equation for the relativistic doppler effect but I'm struggling to see this as a function and then give a first order Taylor expansion. Any help...
  36. F

    Maxwell's eqs. & unification of electric & magnetic fields

    Maxwell's equations reveal an interdependency between electric and magnetic fields, inasmuch as a time varying magnetic field generates a rotating electric field and vice versa. Furthermore, the equations predict that even in the absence of any sources one can have self propagating electric and...
  37. A

    B How Does Time Dilation Influence Perceived Velocity?

    Hello I have a question about how time effects velocity:So we have a car on Earth traveling 200m with 5 seconds we get that car moves 40m/s and 40x3600=144000 and 144000:1000=144km/h so car on Earth travels 144km/h now let's consider a that there is observer on spacecraft traveling 0.5c...
  38. J

    Courses Prerequisite to General Relativity/Cosmology Undergad course

    Hello, If anyone could help me with the prerequitisetes for an undergraduate General Relativity and Cosmology course I will enroll into, It will be much appreciated. The syllabus is the following(sorry for the rough translation): -Review of Special Relativity -Spacetime in GR -Geodesics...
  39. Diego Berdeja

    I Lorentz Transformations in the context of tensor analysis

    Hello everyone, There is something that has been bugging me for a long time about the meaning of Lorentz Transformations when looked at in the context of tensor analysis. I will try to be as clear as possible while at the same time remaining faithful to the train of thought that brought me...
  40. V

    I Active vs Passive Lorentz transformation

    Hi. First, excuse my English. In my lecture notes on classical electrodynamics, we are introduced to the Lorentz transformations: a system S' moves relative to a system S with positive veloticy v in the x-axis (meassured in S), spatial axis are parallel, origin of times t and t' coincide...
  41. Wise Owl

    A Solution to the wave equation in Rindler coordinates

    I have been reading these notes on Rindler coordinates for an accelerated observer. In Rindler coordinates, the hyperbolic motion of the observer is expressed through the coordinate transformation $$t=a^{-1}e^{a{{\xi}}}\sinh a{\eta}\\ {}x=a^{-1}e^{a{{\xi}}}\cosh a{\eta}.$$On a space-time...
  42. Zahidur

    I Subbing Planck length into length contraction equation?

    I was wondering if it is possible to work out the maximum amount of energy an object with mass can have using the length contraction equation (i.e. "actual" length divided by Lorentz factor). The way I thought of doing this was by rearranging e = mc^2 to get c^2 = e/m. Then, substitute e/m into...
  43. S

    B Help Understanding special relativity

    I'm trying to understand something about relativity that doesn't seem to add up. I will extend Einstein's carriage example to incorporate 4 clocks. At the beginning all these clocks are running at the same time when they are together. I put two of the clocks far away from each other (100 km...
  44. B

    Insights Precession in Special and General Relativity - Comments

    Bill_K submitted a new PF Insights post https://www.physicsforums.com/insights/precession-special-general-relativity/ https://www.physicsforums.com/insights/precession-special-general-relativity/
  45. F

    I Why is energy not Lorentz invariant?

    As I understand it, since space-time is modeled as a four dimensional manifold it is natural to consider 4 vectors to describe physical quantities that have a direction associated with them, since we require that physics should be independent of inertial frame and so we should describe it in...
  46. P

    I 'If a photon were trapped between two perfect mirrors....'

    If a photon were trapped between two perfect mirrors perpendicular to its axis of motion, and they were gradually brought together until they were touching, so that the distance between their faces was 0m, would the photon be "trapped" between the mirrors? Without space in which to move, how...
  47. P

    I Can one determine the velocity of a photon in the fourth dimension using limits?

    Can one shed light on the velocity of the photon through the fourth dimension x4 using limits? To begin with, please study the mathematics from Brian Greene’s book An Elegant Universe. The upshot is that the faster an object moves through space, the slower it moves through the fourth...
  48. Sebastiaan

    I Effect of Special Relativity on Spacecraft Thrust & Isp

    Let's say I have a Space craft traveling at 1% of speed of light and at rest speed it has an thrust of 600 kN with Specific impulse at 1.000.000s. We know we can calculate the relatavistic mass of the vessel with Einstein Special Relativity : γ = 1 / (1 - v2 / c2 )0.5 = 1.00005. Now the...
  49. A

    I What Actually Happens vs What You See in SR

    My impression always was that when you describe a problem in special relativity, you are already implicitly taking into account the light that would need to travel for some person to theoretically "see" a special relativistic phenomenon. I was confronted recently in another thread that this...
  50. A

    I What is the velocity of the photon through the fourth dimension x4?

    What is the velocity of the photon through the fourth dimension x4? Photons are real, physical entities. The fourth dimension is a real, physical entity. Therefore, photons must have a relationship with the fourth dimension. They must have some velocity relative to it. What is the velocity...
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