# Special relativity Definition and 610 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. ### I Cat chasing the red dot moving faster than c

This topic assumes special relativity only, so no gravity is involved. I wanted to know how a superluminal thing would appear to an observer, and two of the 'things' I thought of were a moiré pattern and the red dot projected by a laser pointer. The former can be discussed, but this post will...
2. ### Galilean transform and Lorentz transform questions

I have a quick question about the Galilean transform. If I have Alice running and Bob stationary. The Galilean transform will tell me the position of Alice from Bob's stationary position. Also if I have Alice's position which is moving it will tell me Bob's stationary position. If I want Bob...
3. ### I Comparing clock rates in accelerated vs constant velocity frames

@PeroK sent me here based on a discussion starting at https://www.physicsforums.com/threads/some-ideas-on-interstellar-space-travel.1006562/post-6550265. Summary: Someone claimed that an accelerated observer's clock (observer at 1g from Earth to halfway to Alpha Centauri, then -1g the rest of...
4. ### I Time dilation paradoxes near c

I'm struggling to wrap my head around the twin paradox in special relativity especially when dealing with multiple vectors. In my thought experiment say I have a set of twins. Both set out in opposite directions and intend to sling shot around two different black holes(luckily equidistant from...
5. ### I Deriving Lorentz Transformation Equation using Hyperbolic Functions

While deriving Lorentz transformation equations, my professor assumes the following: As ##\beta \rightarrow 1,## $$-c^2t^2 + x^2 = k$$ approaches 0. That is, ##-c^2t^2 + x^2 = 0.## But the equation of the hyperbola is preserved in all inertial frames of reference. Why would ##-c^2t^2 + x^2##...
6. ### B Special Relativity violation via Quantum Mechanics?

We know that both momentum and position can not be known precisely simultaneously. The more precisely momentum is known means position is more uncertain. In fact, as I understand quantum mechanics, position probability never extends to 0% anywhere in the universe (except at infinity) for any...
7. ### B Help me determine whether this proof of time dilation formula is valid

I recently trying to learn General Relativity by first scraping the surface on ScienceClic's general relativity playlist, and then I stumbled upon a video where it said that we actually move through spacetime on a constant speed of c, and then I remember about time dilation because how speed on...
8. ### Special relativity - measure of a rod and simultaneity

Hi, I´m trying to solve a special relativity problem, and I think I need some help. There are two inertial frames of reference, ##O## and ##O'##, the last one moving with relative velocity ##v## in the ##x## direction. There's a rod with length ##L'## fixed to frame ##O'##, such that front end...
9. ### Find second object's velocity in relativity

> A particle of mass M at rest decays into two particles of masses m1 and m2 travelling in opposite directions at velocity v1 and v2 respectively. Express v2 in terms of v1, m1, m2, and M. Since both objects are from a single object that's why I took relativistic mass of both objects are same...
10. ### Special relativity and Lorentz Transformation Exercise

Summary:: Special relativity and Lorentz Transformations - I got this problem from a first-semester course at university. I have been struggling for a few days and decided to get some help. A rocket sets out from x = x' = 0 at t = t' = 0 and moves with speed u in the negative x'-direction, as...
11. ### B Why can't we rule out Lorentz Ether Theory?

I am reading pretty much everywhere that LET (Lorentz Ether Theory, or call it Neo-Lorentzian Relativity, or whatever theory that involves a preferred undetectable frame with some yet unknown properties that make all the moving objects with respect to this frame length contact and time dilate)...
12. ### B Any plausible explanation for dynamical length contraction?

I am new here, so pardon my ignorance. First of all, I am aware of the impossibility to distinguish experimentally between SR (Special Relativity) and LET (Lorentz Ether Theory). I know there is a PF policy article on LET and the Block Universe. I must admit though that LET is more appealing...
13. ### I Time and Gravity if rotating faster than a critical frequency

If a person was rotating on a verticle axis from head to toe like the earth or quasar. If nothing can go faster than light, from the person's perspective looking at the stars traveling across the night sky, if you increase the rotation of the earth, stars further than a certain critical distance...
14. ### I Time dilation at the event horizon of a black hole that is moving

Hello everyone, I have a hard time to conceptualize the case of a moving black hole. We know from SR that time slows down for moving objects; but time dilation at the event horizon is already equal (tends) to zero. It seems that it can create some sort of conflict for the black hole movement...
15. ### B Energy loss of muon moving though a medium

Hello everyone. I have just complete an experiment calculating the speed of a muon. I got it to 2.6E8 m/s, however I know that they are created at close to speed of light to be able to get down to earths surface in their short lifespan. This speed could not have been its initial speed, as it...
16. ### Relativity Special relativity in Lagrangian and Hamiltonian language

Some introduction books on Lagrangian and Hamiltonian mechanics use classical mechanics as the theoretical framework, and when it come to special relativity it goes back to the basics and force language again. I would like to ask for some recommendations on good books that introduces Lagrangian...
17. ### I Understanding of special relativity and coordinates

I'd like to get some help on checking my understanding of special relativity, specifically I'm trying to clarify the idea of coordinates. Any comment is really appreciated! The spacetime is an affine space ##M^4##, which is associated with a 4 dimensional real vector space ##\mathbb{R}^4##...
18. ### Why is time = ct and not t in special relativty?

Why is time = ct and not t in special relativity? I just started reading the book I was recommended. Maybe I missed it but as stated in the title why is time = ct and not t in special relativity? I understand they want distance/space = time. Just how do they go about doing that...
19. ### B Seeking an easy way to prove special relativity

Hello everyone, Im preparing to write an exam project in college about special relativity, however i am missing the critical experiment to prove that it is true. I thought about using the life time of muons, but i dont have a scintillator to detect them, so unless a standard geiger counter works...
20. ### I What do physicists think when they say, "we move through time"?

I recently had a discussion with my brother, about what it means to "move through time". His opinion is, that physicists cannot take this literally. His opinion is, that time is just an expression for change that takes place at different rates for different observers depending on their speed...
21. ### Minkowski diagram, where to put an event

I drew the Minkowski diagram, but I'm not sure if this is correct. From what I drew the angle between x and ct ##\approx 0## then the event is "inside" the light ray and will eventually reach A.
22. ### Relativity I want to learn special relativity. More details below

I want to learn special relativity.I have read a tiny bit of 2nd edition of Spacetime Physics: Introduction to Special Relativity and am liking it. Is it a good book? I also want problems to solve. I tried Special Relativity: For the Enthusiastic Beginner but found it to difficult. Does anyone...
23. ### Two observers viewed from different sources

I builded the translated lorentz transform, at t=0 t'=-22.5 and x'(x=0)=67.5 after that I just didn't the question
24. ### I Hafele-Keating experiment

I have seen the "Hafele-Keating with the plane as reference frame?" thread (https://www.physicsforums.com/threads/hafele-keating-with-the-plane-as-reference-frame.767913/ ), but the replies do not seem to explain (to me anyway) what when taking a plane as a reference frame, balances the slowing...
25. ### B What does this spacetime diagram mean?

I'm reading a book called "Reality is not what it seems: the journey to quantum gravity" by Carlo Rovelli and I'm struggling to understand this diagram that is part of the chapter about special relativity. https://i.stack.imgur.com/JgBDJ.jpg Before this image Rovelli writes: "It's not...
26. ### Some help in understanding energy conservation

While I am working through proving the homework statement, I encountered a problem. The problem is as follows: From the energy equation above, one can see that the minimum value of ##p## is ##m_T##. However, how does one explain why when ##p=m_T##, ##\sqrt{m^2_B+m^2_T}>m_A##?

41. ### A question on proper time in special relativity

Homework Statement:: This isn't a homework but more of a conceptual question. Relevant Equations:: Proper time, ##\tau## Simply put, the proper time between two events as observed in an unprimed frame is calculated along the timelike worldline between the two events. This implies that the...
42. ### The rising railway coach

As widely separated particles within a large enclosed space are differently affected by the nonuniform gravitational field of Earth, to use the Newtonian way of speaking, two particles released side by side are both attracted toward the center of Earth, so they move closer together as measured...
43. ### Calculation Involving Projection Tensor in Minkowski Spacetime

In Minkowski spacetime, calculate ##P^{\gamma}_{\alpha}U^{\beta}\partial_{\beta}U^{\alpha}##. I had calculated previously that ##P^{\gamma}_{\alpha}=\delta^{\gamma}_{\alpha}+U_{\alpha}U^{\gamma}## When I subsitute it back into the expression...
44. ### Best (or at least good) GR and SR textbook for a 15-year-old highschool student

Hi, I'm a 15-year-old highschool student and I was wondering what textbook you guys recommend for Special- and General Relativity. I'm familiar with the concept of the Metric Tensor and Christoffel Symbols, but I wanted a good textbook where I can really learn derive it all and gain a deeper...
45. ### Deriving length contraction using spacetime

Deriving time dilation was easy: Imagine two events in frame O' at the same location. ##ds^2 = -c^2 dt'^2## The same viewed in O frame is: ##ds^2 = dx^2+dy^2 + dz^2 - c^2 dt^2## ##\Rightarrow dx^2+dy^2 + dz^2 - c^2 dt^2 = -c^2 dt'^2## ##\Rightarrow (\frac{dx}{dt})^2+(\frac{dy}{dt})^2+...
46. ### Trying to understand electric and magnetic fields as 4-vectors

I was trying to show that the field transformation equations do hold when considering electric and magnetic fields as 4-vectors. To start off, I obtained the temporal and spatial components of ##E^{\alpha}## and ##B^{\alpha}##. The expressions are obtained from the following equations...
47. ### B Why Aren’t ALL SR Effects Cumulative?

Why aren’t all the SR effects cumulative like Time Dilation? Why should the Space dimensional effect become null when v—>0 while the Time dimension does not revert back to the 2 frames being in sync if Space and Time are treated on an equal footing. Clearly, Space and Time are not treated on an...
48. ### I Reference frame vs coordinate chart

Hello, here on PF I've seen many threads about the concepts of 'reference frame' and 'coordinate system'. In the context of SR my 'envision' about the concept of 'frame of reference' is basically the 'rods & clocks latticework' as introduced in the book Spacetime physics (Taylor, Wheeler)...
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