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. Probability distribution of outgoing energy of particle

So from particle 1 scattering in all directions with equal probability in the CM frame, I believe that that means probability of finding particle 1 in an angular range ##d\theta## is just ##\frac{d \theta}{2 \pi}##. Let P(E') be the probability density of E', so from the probability of finding...
2. I Muon travel distance vs Atmosphere Thickness?

I'm having a discussion with a friend/family member about a paper by Radwan Kassir in which he calculates the distance traveled by a muon (atmosphere thickness) in a non-standard way that shows the atmosphere thickness in the muons frame (L') is γ times the atmosphere thickness in the Earth...
3. Special Relativity: spaceships heading toward each other

In the left point of view the bar is approaching at 0.8c and the other space ship at something very near c (Einsteins velocity addition rule). To reach the left ship the other ship has to bridge double the distance of the bar with less than double the speed of the bar. Therefore they meet right...
4. I EM Faraday tensor transformation for conductor carrying current

Hi, starting from a recent thread, I'd like to discuss a point related to the Lorentz transformation of EM Faraday tensor field between inertial reference frame. As explained in this video at minute 11:20, in the Lab inertial frame there is only a magnetic field B in the region surrounding the...
5. I Is time dilation a real effect?

In the context of SR we know time dilation is basically the rate of change of moving clock's proper time w.r.t. the inertial frame coordinate time. It does mean that in principle the "tick events" of moving clock are compared against the time measurement of clocks Einstein's synchronizated in...
6. A How do we interpret measurements of Mercury's position?

When scientists measured the position of Mercury in the 18th century, they interpreted the results assuming a Euclidean background, because they did not know general relativity. So they measured r and φ in fuction of time attributing to these coordinates an Euclidean meaning, that is, assuming...
7. Relativistic elastic proton collision

How should I approach this problem? My first thought was to subtract the velocity of the second proton from the velocity of proton going upwards. However, the velocity vectors are perpendicular to each other, therefore I cannot use the SR velocity addition formula.
8. I On the physical meaning of Minkowski's spacetime model

Hi, I was thinking about the following. Suppose we have a geometric mathematical model of spacetime such that there exists a global map ##(t,x_1,x_2,x_3)## in which the metric tensor is in the form $$ds^2 = c^2dt^2 - (dx_1)^2 + (dx_2)^2 + (dx_3)^2$$ i.e. the metric is in Minkowski form...
9. "Retired" but still active

I am a long-retired physics lecturer, with the bulk of my lecturing focused on quantum and relativity. I am still active in research. I have completely lost contact with the challenge of explaining this stuff to students, and was curious to see how these challenges are met on this forum, not...
10. 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.
11. 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...
12. 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...
13. 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...
14. How Does Special Relativity Affect Photon Emission Angles?

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...
15. 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
16. 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...
17. I How Can You Approach Steve Without Being Doppler-Shifted?

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...
18. 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...
19. 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...
20. I How Does Special Relativity Affect Perceived Distances Between Planets?

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...
21. 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...
22. 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...
23. 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...
24. 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...

33. 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...
34. 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...
35. B Is the Speed of Light Consistent Across Rotating Reference Frames?

Does it violate the postulate of special relativity in any sense?
36. 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...
37. 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...
38. 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...
39. 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...
40. 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...
41. 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?
42. 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...
43. 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...
44. 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...
45. 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...
46. 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...
47. 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...
48. I Condition for Centering Starlight in a Water-Filled Telescope?

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...
49. 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...
50. 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##...