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. PLAGUE

    I Why "time part" represents energy in Four-momentum?

    I was going through Spacetime Physics by Taylor and Wheeler and came to a point where they said, and I quote, This part feels too abrupt for me and I am looking for a more elaborated explanation. Here is a link to that chapter.
  2. PLAGUE

    I Proof of Invariance of Spacetime Interval

    I was going through Spacetime Physics by Taylor and Wheeler and came to a point where they showed a proof of Invariance of Spacetime Interval. You can find the proof Here and Here is the second part of that proof. They used an apparatus that flies straight "up" 3 meters to a mirror. There it...
  3. m082844

    I Why doesn't relativity of simultaneity lead to a contradiction?

    I cannot get the following out of my head. Suppose this situation. Three frames, with varying velocities, simultaneously intersect their origins at the same time and place, making this point and time x0=0 and t0=0. These frames... let's call them observers. These observers have an agreed upon...
  4. F

    Confused by Lorentz transformation equation

    TL;DR Summary: Solving a problem regarding a train going past a station using length contraction and the Lorentzian transformation. I'll dive straight in. I encountered a problem where there is a train travelling at 0.6c going past a station, length 500 m when measured by an observer at rest...
  5. lambdadandbda

    Photon emission opening angle

    I'm doing special relativity in undergrad and I have the following problem: Let a particle of mass M travelling at speed ##\beta = 1/2## (##\gamma = 2/\sqrt 3 \ \ c=1##) decay in to two photons: ##A \rightarrow 1+2## 1) Calculate energy and moment of the photons in the reference frame of the...
  6. M

    I Physical meaning of zero time metric

    I am reading Wald's General Relativity and just did problem 2.8(b). The result I get is ##\omega^2(x'^2+y'^2)-1## as the coefficient for ##dt^2##, and I am wondering about the physical significance of when ##x'^2+y'^2=\frac{1}{\omega^2}##, what would this mean? Mads
  7. Sciencemaster

    I Observational Astronomy Project Ideas to Show Special Relativity

    This semester, I'm taking a class on Observational Astronomy which requires us to perform observations for a final project over the course of roughly a month (mid-March to Mid-april, although it could be a bit longer or shorter). As we get to choose the project, I'd like to take this opportunity...
  8. J

    I Special relativity puzzle relating to motion of a body when restrictions are placed on the Doppler shift of the body

    Hello I have not posted here for a while, but just wanted to post this puzzle I devised. Was posted on Reddit, but no takers. I think the solution is interesting. The Puzzle You are flying around in space and you see your friend Steve chilling in an inertial frame in his own spaceship and you...
  9. F

    I Variation of the lightning train thought experiment

    Hi all, I've been going over some special relativity as it's a topic I never really studied during my younger years and wanted to get to grips with it, especially since it's such a fundamental part of our understanding of the cosmos. I was reading about Einsteins train lightning thought...
  10. G

    Time slows down at lower gravitational potential

    Common interpretation is that time slows down at lower potential. I wonder if people are simply saying for the time interval between two events at lower potential, it's smaller than what would be measured at greater potential ##d \tau < d t##. i.e. Clock at lower potential shows a time interval...
  11. D

    I Question about Special Relativity: Mary from planet B flys at 0.8c to Tom on planet A...

    Quite simple question. There are two planets A and B, they are 4 light years apart measured by tom on planet A. Say both A and B remain stationary. Mary flys 0.8c to tom on planet A. When she passes planet B she should see Tom or planet A 2.4 light years away, am I correct? What about tom now...
  12. jv07cs

    I 3+1 split of the Electromagnetic Tensor and Maxwell's Equations

    I'm currently studying the covariant formulation of electromagnetism for a research project I'm doing and I'm a bit a stuck on how to perform the 3+1 split of the Electromagnetic Field Tensor and Maxwell's Equations. I understand that a 3+1 split of a four-vector consists of separating the...
  13. Sciencemaster

    Misc. DIY Experiment of Special Relativistic Effects?

    I'd like to perform an experiment that will build intuition for Special Relativity in the real world. While I do believe that it occurs in the real world, I'd like to be able to prove it for myself, and I feel that such an experiment would help others on this forum as well. Is there an...
  14. Lotto

    B Does a hot coffee have bigger mass than a cold coffee?

    As far as I know, something like relativistic mass is just a concept, just a trick, there is nothing like the relativistic mass. When I move faster, I have higher kinetic energy, but my mass is still the same as if I was at rest. Kinetic and potential energies do not increase object's mass. A...
  15. nomadreid

    Two equations "combined" don't give the desired result

    In https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/05%3A__Relativity/5.06%3A_The_Lorentz_Transformation First, the equation (5.6.7) apparently has a typo: the x' should not be in the...
  16. PhysicsRock

    Relativistic particle moving in a potential

    Since energy is conserved and the particle is initially at rest, we can determine that ##E(0) = m_0 c^2##, so $$ m_0 c^2 = \sqrt{ c^2 p^2 + m_0^2 c^4 } + \alpha x. $$ Squaring this eqation gives $$ m_0^2 c^4 = \alpha^2 x^2 + c^2 p^2 + m_0^2 c^4 + 2 \alpha x \sqrt{ c^2 p^2 + m_0^2 c^4 }...
  17. Hak

    I Special Relativity: an ideal experiment

    Let me preface this by saying that I do not claim to dismantle relativity. That said, in reading the Feynman I came across an ideal experiment that is not entirely clear to me. The context is the usual two spacecraft moving at relatively constant speed. With the reasoning I give below Feynman...
  18. Z

    I Understanding Relativity of Simultaneity in Resnick, Part II

    In a previous post, I investigated a wrong way to synchronize clocks in a single inertial reference frame. Here is a correct way An alternative would be A few observations 1) These methods all place clocks at specific locations and synchronize them using signals (namely, light). This is a...
  19. Z

    I Understanding Relativity of Simultaneity in Resnick, Part I

    I'm going to go step-by-step through the reasoning. If there is any mistake, then it is a true mistake because I am trying to make each statement that follows as accurate as I can. Unambiguous time scale in a single frame of reference. Consider that we have two inertial frames of reference, 1...
  20. Hak

    I Not at all clear examples of special relativity (rectangle in motion and coming to rest)

    I have always had certain difficulties in correctly understanding the theory of special relativity; I often apply it to certain situations and they fall apart... Imagine there is a rectangular object placed with its long sides parallel to the ground and its short sides perpendicular to it...
  21. Feynstein100

    I Using GR to predict the shape of the entire universe?

    So I've often heard that when GR is applied to the entire observable universe to calculate its curvature, we get a value of zero, meaning that the entire universe is flat. I've got 2 problems with this. The first is that I thought GR was a local theory i.e. it only applies locally. Trying to...
  22. Z

    I How many meter sticks are there in this length contraction reasoning?

    I have a question about the concept of length contraction. The black line from (0, 0) to (1, 0) represents a meter stick in my stationary frame, call it frame A. The blue axes represent my coordinate system with coordinates x and t. The green axes represent the coordinate system of a moving...
  23. Z

    I Can we choose different functional forms for Lorentz transformation?

    Susskind's book "Special Relativity and Classical Field Theory" derived the Lorentz transformations $$x'=(x-vt)\frac{1}{\sqrt{1-v^2}}$$ $$t'=(t-vx)\frac{1}{\sqrt{1-v^2}}$$ $$x=(x'+vt')\frac{1}{\sqrt{1-v^2}}$$ $$t=(t+vx')\frac{1}{\sqrt{1-v^2}}$$ While redoing the calculations, I reached a...
  24. Z

    I ##x'=0## and ##t'=0## axes in railcar thought experiment

    I am following the book "Special Relativity and Classical Field Theory: The Theoretical Minimum" by Susskind. I want to go through a sequence of ideas to try to understand simultaneity. We have a rest frame A and a moving frame B along the x-axis. Let the coordinates be ##x## and ##t## in...
  25. S

    I Coulomb gauge Lorenz invariant?

    Hey, What is meant by Coulomb gauge not being Lorenz invariant? The Coulomb gauge is just a constraint on \mathbf{A} and \phi and thus it is independent of inertial frame. I posted the question in the wrong section. This question is in the context of QFT. The notes says: A disadvantage of...
  26. P

    B Is the Speed of Light Consistent Across Rotating Reference Frames?

    Does it violate the postulate of special relativity in any sense?
  27. Hak

    B Does Time Move Slower for Travelers in Special Relativity Experiments?

    In the mental experiment of special relativity (which has been experimentally proven anyway), in which it is shown that for the traveler on the spaceship, time passes more slowly because the clock (the tick-tock of light beams) goes slower... What is the correlation between the traveler's...
  28. BadgerBadger92

    B Difference between special relativity and redshift?

    For quite a while I thought that time dilation was the effect of bodies moving close to the speed of light dilates the passage of time. I also have read about red shift, which seems to be the same thing, though I’m sure they are totally different. I learned in special relativity (the time...
  29. Hak

    I Time intervals measured by stationary and moving observers

    [Moderator's note: Thread moved to relativity forum as it is not a specific homework problem but a general question about SR.] Homework Statement: While studying relativity, a question arose for me about time intervals measured by stationary and moving observers. In particular, one of the...
  30. M

    B Can Dark Flow Be measured, based on Special Relativity?

    Let's assume Dark Flow is real. If so can't we measure it based on 2 atomic clocks. Dark Flow occurs presumely in a southerly direction. One atomic clock must start at the time the earth's rotation begins to bring the first atomic clock in a slightly southerly direction, (due to the earth's 23.4...
  31. Leureka

    I Magnetic field as result of length contraction

    Hi all, Recently I've tried to wrap my head around a common explanation of magnetic fields that you see online, especially among science educators like veritasium or minute physics. The setup is as follows: there is a wire, composed of the same number of negative charges (electrons) and...
  32. Lotto

    What will the final velocity of the particles be?

    So I would get ##u=\frac{vc}{\sqrt{4c^2-3v^2}}=0.996c##. But the right answer is ##0.956c##. Where is my mistake?
  33. M

    B How to measure time in reference frame with clock?

    I considered example of time dilation with light clock. I have a question about measuring time in reference frame with clock. If we know that clock move from A to B in the reference frame with clock then what time of motion is measured in this reference frame? (In non-moving reference frame...
  34. Sciencemaster

    I Is an accelerating frame the same as an inertial frame at a point?

    If we have an observer that is accelerating in one direction (perhaps a rocket ship accelerating towards the sun), would its reference frame be identical to an observer at the same point that is not accelerating, but has the same instantaneous velocity? In other words, is an accelerating...
  35. M

    A Electrodynamics of moving bodies - §2: On the relativity of... (again)

    Here is a screenshot from Einstein's 1905 ELECTRODYNAMICS OF MOVING BODIES:My understanding is that here Einstein says that the rod, the 2 observers and the 2 clocks are in the moving system, one observer & clock at each end of the rod. From their point of view they are not moving. They can very...
  36. S

    B Another special relativity related "paradox"

    Full disclosure: I have asked this question on stackexchange too, but I think I didn't frame my question properly there, which probably led to misunderstandings and complicated answers. Plus some comments there led me to refine the question a bit so I hope it's in a good state now. I am new to...
  37. R

    I A Hidden Zero in Einstein's Simple Derivation

    I was reading Einstein's Simple Derivation of the Lorentz Transformation which is Appendix I in his book Relativity: the Special & the General Theory. (Online copies can be found at Bartleby's and the Gutenberg Project websites.) I came across an interesting but confusing result by using the...
  38. sergiokapone

    I Special Relativity Paradox "Terrorist and Spaceship"

    The ship left Earth at a speed of 0.5c . When the distance between the ship and Earth was 0.25 light year, a terrorist was caught on Earth who said that he had planted a bomb at the time of departure and activated it for 10 months. At that moment, a warning signal was sent from Earth. The...
  39. Z

    I Condition for centering starlight in a water filled telescope (Airy's experiment to reveal the motion of the Earth through the Ether)

    I'd like to understand how to obtain equation (2) below. **My question is how to obtain (2)?** **Here is my attempt to answer this question (which runs into an obstacle)** Suppose we have a telescope on earth with air inside the tube (instead of water) and around the telescope. Consider...
  40. Immer Tzaddi

    I Lorentz Transformation: Premises + Derivation

    Recollections of a late Spring semester's lesson describing the derivation of Lorentz's Transformation often solicit many unanswered questions. The textbook used has been secured; however, it is unknown. Whether, that secondary school instructor provided the premises used for the derivation from...
  41. RafaPhysics

    Aberration and Doppler shift in Special Relativity

    A large disk rotates at uniform angular speed ##\Omega## in an inertial frame ##S##. Two observers, ##O_1## and ##O_2##, ride on the disk at radial distances ##r_1## and ##r_2##, respectively, from the center (not necessarily on the same radial line). They carry clocks, ##C_1## and ##C_2##...
  42. Trysse

    I Three inertial particles: Separating the twins from the paradox

    This is a response to a recent insight article regarding the twin paradox. The idea is to model the most basic scenario in a way, that the paradox disappears. This basic scenario and its kinematic effects are then modeled using only a straightedge and a compass. The best way to read this post...
  43. D

    I Observer on Earth watching a spaceship traveling at c/2

    i have just started on relativity, so be simple. you are going to travel 1 lightyear at half the speed of light. therefore, it would take 2 years to travel 1 lightyear. on Earth, you would see me going half the speed of light, so it should take two years as well? i calculated gamma as being...
  44. Sophrosyne

    B A scenario to help understand the twin paradox in SR

    I am looking at some of the threads on the twin paradox, and getting even more confused. I have been trying to run through the details of what each twin is seeing, and was wondering if I could get some help. I am just trying to imagine how each twin is “seeing” the other twin at each step as the...
  45. P

    I Forces and gravitational time dilation

    The following is more of an interesting example and observation than a question that I am presenting for public comment. It's somewhat related to a recently thread, which was closed for moderation, but I think it's different enough not to fall under the ban of reposting threads that have been...
  46. RafaPhysics

    Speed of a star in Special Relativity

    Hey, I have this problem from the Special Relativity by AP. French . Exercise 3.3, Chapter 3. The figure shows a double-star system with two stars, A and B, in circular orbits of the same period T about their center of mass. The earth is in the plane definied by these orbits at a distance R of...
  47. T

    I Why is there nothing faster than light?

    Hi guys! Is there a simple explanation to describe why light owns the faster speed at the universe ?
  48. AronYstad

    Special Relativity: What are the events in the question?

    This was part of a test we did a while back, so I forgot how exactly I solved it, but I think I basically solved the question by putting the values into equations and hoping for the best, since I didn't have a good understanding back then. Since then, I have learnt that it's a good idea to break...
  49. phinds

    B LIGO Back Online: Upgraded Detector to Spot Fainter Gravitational Waves

    From this morning's Economist briefing: The Laser Interferometer Gravitational-Wave Observatory—the world’s most sensitive device for spotting gravitational waves—starts up again on Wednesday after a three-year hiatus for upgrades. LIGO is designed to detect subtle ripples in space and time...
  50. joshuadeepak

    B Time Dilation in Non-Stationary Reference Frame: A, B, C

    Let's consider three observers A, B and C. The experiment starts at t = 0. A is 'absolutely' stationary. B immediately (please imagine it) starts moving at speed v1 with respect to A. C immediately starts moving at speed v2 with respect to A in the same direction as B. Let's say A measures a...
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