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. J

    Action and reaction when fast object is pushed

    Let's say Bob floats in space. Bob's identical twin Joe moves past Bob at relativistic speed. As Joe is passing by, Bob gives him more speed by pushing him with his hand. Somehow I just happen to know that Joe will feel a smaller force pushing him than what Bob feels. So my question is: Why is...
  2. Lito

    Special relativity -- Proper time

    Homework Statement Alice is driving a race car around an essentially circular track at a constant speed of 60 m/s. Brian, who is sitting at a fixed position at the edge of the track, measures the time that Alice takes to complete a lap by starting his watch when Alice passes by his position...
  3. I

    Special Relativity - Lorentz Transformation & Matrices

    Homework Statement There are three observers, all non accelerating. Observer B is moving at velocity vBA with respect to observer A. Observer C is moving at velocity vC B with respect to observer B. All three observers and all their relative velocities are directed along the same straight line...
  4. S

    Show that a nonlinear transformation preseves velocity

    Homework Statement I have a particle moving with uniform velocity in a frame ##S##, with coordinates $$ x^\mu , \mu=0,1,2,3. $$ I need to show that the particle also has uniform velocity in a frame ## S' ##, given by $$x'^\mu=\dfrac{A_\nu^\mu x^\nu + b^\mu}{c_\nu x^\nu + d}, $$ with ##...
  5. W

    Special relativity: flashes of light

    Homework Statement In a frame of reference A lights are on the x-axis at x = D and x = -D, where D = 0.6 x109. They flash simultaneously at t = 0. There's also a frame of reference A' moving at v = 0.8c. i) Where and when do the flashes happen in A'? ii) Therefore when would observers at...
  6. kontejnjer

    How Does Fermi Transport Describe a Gyroscope's Motion on a Rotating Disk?

    Homework Statement Describe the motion of a gyroscope with center of mass fixed on a rotating disk in coordinates of an observer which is at rest on the disk in the absence of gravity. Homework Equations The hint given was to somehow use Fermi transport, so I'm guessing: \mathbb F_u X=\nabla_u...
  7. m4r35n357

    I Is it time to "retire" time dilation and length contraction?

    Considering the enormous number of questions posed on this forum and other places, the concepts seem fundamentally flawed (because both are formally and practically unobservable). The calculations themselves (together with the Lorentz Transform) are highly error-prone and the results misleading...
  8. J

    Speed of an antimuon in a pi meson decay

    Homework Statement I'm trying to confirm the speed of an antimuon in the \pi^+ \rightarrow \mu^+ \nu_{\mu} decay through the laws of conservation but it doesn't add up. Homework Equations [/B] 1.Energy-momentum relation: E^2 = (pc)^2 + (mc^2)^2 2. Rest masses: m_{\pi} = 139.6 \...
  9. J

    How Do You Calculate the Original Mass in a Relativistic Disintegration Problem?

    Homework Statement A body at rest in a frame of reference S disintegrates into two pieces moving in opposite directions. The masses of each fragment are 3.0kg and 4.0kg and their velocities 0.8c and 0.6c, respectively. Find the mass of the body before it disintegrated. (Answer: 10kg) Homework...
  10. vJames

    Visual Effects of Special Relativity

    Hi all, I've got a high school special relativity physics test coming up in a week and thought I should post here instead of under homework/coursework as I don't really have any set questions that I'm asking. My problem is that I can explain the visual effects we learned but not with enough...
  11. K

    Rotation in special relativity

    [this thread was split off from https://www.physicsforums.com/threads/confusion-in-general-relativity.840710/] I read that Einstein gave the following argument: If we look at a rotating (and hence accelerated) frame from an Inertial frame, which is supposed to be away from all gravitational...
  12. K

    Which Quintuplet Returns to Earth Last Based on Time Dilation Ranking?

    Homework Statement Five identical quintuplets leave Earth when they reach the age of 21, in the year 2121. Each quintuplet goes on a spaceship journey that takes T years, as measured by a clock in each spaceship. During the journey they travel at a constant speed v, as measured on earth, except...
  13. K

    Spring potential energy and mass

    Homework Statement One end of a vertical spring of spring constant k = 1900 N/m is attached to the floor. You compress the spring so that it is 2.50 m shorter than its relaxed length, place a 1.00-kg ball on top of the free end, and then release the system att = 0. (All values are measured in...
  14. T

    Does Length Contraction affect measured velocity?

    First, let me clarify if my understanding of length contraction is correct. Is it accurate to say that relativistic velocities not only affect the measured length of an object in the direction of motion, but also the distance to the object from an observer in the direction of motion? For...
  15. S

    Kaon Decay -- Special relativity

    Homework Statement A K0 particle is unstable and has a mass of 8.87x10-28 kg. It can decay into π+ and π- particles, each of mass 2.49x10-28 kg. Suppose that a K0 is moving in the +x direction and decays by this process, with the π+ moving off at 0.9c and the π- moving off at 0.8c. a) What was...
  16. bcrowell

    SR as Geometrical Constructions

    This is just a random thought, may be totally wrong. Euclidean geometry was originally described as a constructive theory in which the axioms state the existence (and implied uniqueness) of certain geometrical figures. These constructions are the ones that can be done with two concrete tools: a...
  17. E

    What is the difference between standard and isotropic metrics?

    The metric $$ds^2=-R_1(r)dt^2+R_2(r)dr^2+R_3(r)r^2(d\theta^2+sin^2d\phi^2)$$ when changed to $$ds^2=-R_1(r)dt^2+R_2(r)(dr^2+r^2d\Omega^2)$$ upon setting ##R_2(r)=R_3(r)##, the later metric holds the name of isotropic metric. My question what is the difference between the first and the second...
  18. Tiggy B

    Find velocity of an accelerated proton using kinetic energy

    Homework Statement So I'm trying to find the final velocity of a proton that is being accelerated by a particle accelerator, just before it collides with a particle. All I have is its kinetic energy just before collision: 4.7066×10^(-13) J. I thought I should use KE = 1/2 mv^2 but then...
  19. SquidgyGuff

    Finding relativistic force in terms of acceleration

    Homework Statement The instantaneous force F acting on a particle, as measured in frame S, is Use the formula for the linear momentum () in and the definition of the acceleration a to show that The Attempt at a Solution The professor said that this required use of programs such...
  20. S

    Momentum in special relativity

    when studying momentum 4 vectors,i encountered the CT momentum which is MC.can some explain where has this come from?
  21. 0

    Invariance of Acceleration in Inertial Reference Frames

    Claim: The acceleration (both direction and magnitude) for any object is the same in any inertial reference frame. Is this claim true? I think it is, but someone mentioned to me that time may be an issue as it's not agreed upon in all inertial reference frames. I'd appreciate any references...
  22. E

    I What is the Principle of Equivalence and how was it determined?

    Equivalence principle says that gravitational forces are equivalent physically to inertial forces. Can someone explain what is meant by that and how was it concluded?
  23. N

    First Year Special Relativity Question

    Homework Statement Planets A and B are 10 light years apart in the reference frame of planet A. A deep-space probe is launched from A, and 5 years later (in reference frame A) a similar probe is launched from B. Does a reference frame exist in which these two events (a) are simultaneous and (b)...
  24. sunrah

    I Why is special relativity a local phenomenon?

    Where does the requirement come from that special relativity applies only locally? It is not immediately obvious from the two postulates. I'm asking because this is important for the validity of the Hubble Law.
  25. U

    I Struggling with the Special Relativity and simultaneity

    As I understand, one of the Special Relativity roots is the statement that two events SIMULTANEOUS in one inertial frame are NOT necessarily simultaneous in another inertial frame that is moving against the first one. To illustrate and PROVE this statement Einstein gave his well known example...
  26. I

    Special Relativity: Lenght contraction and a photon.

    Reading an old thread (wich is now closed or i would post the question there) there was a discussion about the size of a photon, and if it was an adequate question at all. The discussion on the other thread couldn't agree on a response. Yet there was some postulates that could work with this...
  27. kontejnjer

    Timelike and spacelike vectors

    Homework Statement Show that if x^{\mu} is timelike and x^{\mu}y_{\mu}=0, y^{\mu}\neq 0, then y^\mu is spacelike. Homework Equations ds^2=\\>0\hspace{0.5cm}\text{timelike}\\<0\hspace{0.5cm}\text{spacelike}\\0\hspace{0.5cm}\text{lightlike} metric is diag (+---) The Attempt at a Solution Don't...
  28. M

    Analyzing Relativistic Effects on Low-Flying Satellites

    Homework Statement [/B] A low flying Earth satellite travels at about 8000m/s. For the satellite, the relativistic factor $$\gamma = \frac{1}{\sqrt{1-\beta^2}}$$ where $$\beta = \frac{v}{c}$$ is close to 1 because v<<c. Estimate by how much gamma actually deviates from 1 by expanding gamma in...
  29. Anama Skout

    Is Special Relativity Correct for Observer A?

    So let's say you're sitting on the ground (observer A) and there's a car or something that moves at .99c (observer B). (Of course, this is all hypothetical) Now, my interpretation goes that when A is seeing B, the information he gets is distorted, namely due to time dilation, length contraction...
  30. C

    Electron-positron creation from colliding photons

    Homework Statement Consider two photons, one with energy ε1 = 2MeV traveling to the right, and the other with energy ε2 = 3MeV moving tot he left. The two photons collide head-on and produce a positron-electron pair. Suppose the the electron and positron move along the same axis as the photons...
  31. I

    Is There a More Comprehensive Course on Special Relativity?

    I started special relativity course at science world u website Is this course enough? Or is there is more powerful course? I need a book for special relativity from A to Z Thanks
  32. VoteSaxon

    Special Relativity derivations ....

    Homework Statement Using the special relativity formulae p = mv / [1 - (v/c)2] E2 = p2c2 + m2c4 derive linear relations between: (i) momentum and mass; (ii) energy and mass; (iii) energy and momentum, which involve only c, c2, β = v/c, and γ (= 1/sqrt(1 - β2)) The attempt at a solution I am...
  33. S

    The Mysterious Synchronization of Clocks in Special Relativity

    Let's say we have a clock that work like this , districts beam of lights are sent in constant time gaps (created by a crystal or some other radioactive process) to a sensor. the sensor is connected to a counter that counts the number of beams, and here we have our clock. Now if we put 2 clocks...
  34. B

    What is the Time Interval Between Arrival of Wave Fronts at C' in S?

    Homework Statement Assume that the train shown in the figure below is 1.9 km long as measured by the observer at C' and is moving at 170 km/h. (The point C' is midway along this train.) What time interval between the arrival of the wave fronts at C' is measured by the observer at C in S...
  35. bcrowell

    Cauchy-Schwarz for two spacelike vectors

    In Euclidean geometry, the Cauchy-Schwarz inequality is ##|e\cdot f| \le |e||f|##. In a Minkowskian signature, the inequality is reversed for timelike vectors. Apparently for spacelike vectors it depends on whether the two vectors span the light cone...
  36. J

    Quantum Problems books in various topics in Physics

    I want college-level problems books on the following physics topics: 1)Quantum Mechanics 2)Electromagnetism 3)Classical Mechanics 4)Thermodynamics (and Statistical Mechanics) 5)Waves 6)Special Relativity
  37. vanhees71

    A Bell spaceship paradox quantitatively

    Yesterday, I found the time to write a bit further on my SRT FAQ and wanted to give a quantitative analysis of the Bell space-ship paradox on the example of the two rockets accelerating with constant proper acceleration, and I found a problem, I cannot solve. So I took this section out from my...
  38. T

    ?Understanding Special Relativity: Speed Addition & Subtraction

    special relativity says speed can be additive and subtractive ,our motion influences the speed , i did not get this part .how can our motion influence the speed of other object ?and how can speed be additive and subtractive
  39. J

    Special relativity -- 2 parallel space ships & time perception....

    If two people are in in space ships traveling next to each other at the same speed and they are going close to the speed of light they see each other expiriencing time more slowly. Why does this happen?
  40. Cosmology2015

    A First Course in String Theory/Invariant Interval/Metric

    Hello, Before starting, I would like to apologize for any errors in the use of symbols. This is my first time :sorry:. I am studying the wonderful book of Barton Zwiebach, "A First Course in StringTheory". In chapter 02, I am experiencing for the first time with the mathematics of special...
  41. Devin

    Derive Lorentz Transformations w/ Special Relativity

    Hope this derivation helps someone!
  42. Devin

    Lorentz Transformations with Special Relativity Derivation

    Any advice on my derivation layout?
  43. F

    B Travel at 3,000,001 m/s: Time Travel Explained

    would that person go into the future?why? also if i travel 1,000,000 m/s on Earth and my friend travels 20m/s per second on Earth would we experience 2 different time frame? so basically the second question is if someone travels a different speed than me on Earth whether the difference of speed...
  44. D

    Lorentz scalars - transformation of a scalar field

    When one considers a Lorentz transformation between two frames ##S## and ##S'##, such that the coordinates in ##S## are given by ##x^{\mu}## and the coordinates in ##S'## are given by ##x'^{\mu}##, with the two related by x'^{\mu}=\Lambda^{\mu}_{\;\;\nu}x^{\nu} then a scalar field ##\phi (x)##...
  45. Pyrus

    Observer is moving &charge is stationary,magnetic field acts

    CASE I - Do magnetic field is felt by observer which is moving and charge is stationary? CASE II- Do magnetic field is felt by observer which is moving with same velocity as that of charge? Does it has some experimental proofs and explanations...
  46. K

    Special Relativity Train Scenario

    Assume there is an engineer who built a tunnel, tunnel length is 10m, and we have a train its length is also 10m...so the tunnel can encompasses the entire length of the train. But if we assume that train is a light express train, it always comes through the tunnel at relativistic speed, let's...
  47. D

    Consequences of space-/time-/light-like separations

    I'm trying to prove the following statements relating to space-like, time-like and light-like space-time intervals: 1. There exists a reference frame in which two space-time events are simultaneous if and only if the two events are space-like separated. 2. There exists a reference frame in...
  48. D

    Coincidence of spacetime events & frame independence

    I have been reading these notes: http://isites.harvard.edu/fs/docs/icb.topic455971.files/l10.pdf in which they claim that if two spacetime events are coincident in one frame of reference then they are coincident in all inertial frames of reference, thus spacetime events are absolute i.e. they...
  49. Noctisdark

    Relativity Special Relativity Problem Textbook ,

    Hi PF, I'm trying to learn both special and general relativity, I have read all about them, learned the basic math needed, but that was all without "enough" exercices to completely understand the theory, so I need problem books that are purely or mostly about problems about special relativity...
  50. G

    What is the cause of time dilation in Special Relativity?

    One of the basic foundation of special relativity is that the speed of light is a constant, hence time is relative to the inertial framework reference. Usually GPS is also mentioned as a modern experimental evidence. My questions: if Maxwell's equations describe EM fields, how can we derive a...
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