Special relativity Definition and 1000 Threads

In sect. 2.3.2 "Ideal Clock", p. 33, of É. Gourgoulhon's text book on "Special Relativity in General Frames" $$ \tau_C [ \, \text{tick}_{j}, \text{tick}_{(j + N)} \, ] = K_C \, N. $$ (equation (2.11); notation adapted.) The only other reference to this "constant K" is on the following page...

This is probably a stupid question but, ## \frac{d\partial_p}{d\partial_c}=\delta^p_c ## For the notation of a 4D integral it is ##d^4x=dx^{\nu}##, so if I consider a total derivative: ##\int\limits^{x_f}_{x_i} \partial_{\mu} (\phi) d^4 x = \phi \mid^{x_f}_{x_i} ## why is there no...

In the context of the Theory of Relativity are there any spacetimes or metrics with a complete absence of symmetries? I mean, consider a type of space or metric where no symmetries would hold (at least not exactly, but approximately). A space or metric where the Poincaré invariance (including...

Einstein's two postulates of special relativity reads, according to Wikipedia: The postulates are most often formulated similarly to this. But in my opnion, the second postulate shouldn't be formulated as above, because then one misses the point. This is particular true for the second...

The constancy of the speed of light is a fundamental principle in modern physics, and it is supported by a wide range of current experimental evidence. There is no evidence to suggest that the speed of light was different in the past, and the idea that it could have been different is at odds...

I refer to the video of this page, where there is a description of Galilean relativity that is meant to be an introduction to SR, making the comprehension of the latter easier as a smooth evolution from the former. All the series is in my opinion excellent, but I think that this aspect is...

Hi every one.How can i prove the below equation? And then that it's Lorentz invariant quantitude ? Thanks for your help

Hello all you clever people, I was wondering if you guys could answer a question for me regarding special relativity and the none existence of time. At least in the sense that the block universe people believe. So I'm writing as if the block universe is the correct interpretation What does...

I have previously studied special relativity, but only at an introductory level. So I decided to explore the subject more in detail later by thinking and working things out on my own, in addition to doing research online. In particular, I seem to have noticed some intriguing patterns between...

I once read (though I don’t remember where) that in the same way that you talk about a dimensionless ratio between Y and X in ordinary space, you can conceive of c as a dimensionless ratio between T and X in spacetime. Do you know where I can find a reliable treatment of that idea? As...

If conservation of charge gets violated in future experiments, what would be the implications on relativity? I have some faint idea that this will cause photons to have non-zero rest mass, but does this affect special relativity at all? Also, does special relativity make conservation of charge...

I have been reading Wikipedia’s derivations of the Lorentz Transformations. Many of them start with the equation of a spherical wavefront and this reasoning: - We are asked to imagine two events: light is emitted at 1 and absorbed somewhere else at 2. For a given reference frame, the distance...

I have a rocket and it is moving straight from a point P with a velocity ##v##. When I say that ##x'=0## is at the place we sit in the rocket, then when the event happened outside his rocket at the point P, can I say that the coordinate of the event is for him negative, so ##x'=-vt'##, although...

Hello. This is my first post on this site. anyone here familiar with "Doubly Special Relativity"? an ARXIV paper was linked in the OP. Some follow up links or other advice would be appreciated. Kowalski-Glikman, J., "Introduction to Doubly Special Relativity", (2004). arXiv:hep-th/0405273...

In relativity, momentum of a body is given by ##p=mv/\sqrt{1-v^2/c^2}##, but if mass is exactly zero and velocity is exactly ##c##, how is the photon momentum even defined? I don't think this problem can be resolved by simply stating the other formula relating energy to momentum, since it was...

Alice measures the spin, also Bob measures. If we assume that the signals (from Alice to Bob) were sent, they had to be with the speed e.g. 10 c But in another frame of reference Bob first measures, next Alice. Measurement of Alice was cause and was sent back in time, or measurement of Bob was...

From Wikipedia article about Hyperbolic motion, I have the following coordinate equations of motion for Bob in his accelerated frame: ##t(T)=\frac{c}{g} \cdot \ln{(\sqrt{1+(\frac{g \cdot T}{c})^2}+\frac{g \cdot T}{c})} \quad (1)## ##x(T)=\frac{c^2}{g} \cdot (\sqrt{1+(\frac{g \cdot T}{c})^2}-1)...

Alice rests at ##X=L+1## in the inertial frame (T, X). Bob is at rest in the Rindler frame (t, x) at ##x=1## and has the proper acceleration ##\alpha=1##. In the rest frame of Alice, Bob moves from event ##E_1=(-T_2, L+1)## over the distance of ##L## in negative X-direction to event ##(0, 1)##...

Muons are a popular way to provide evidence for Special Relativity. But, does Muon Tomography provide evidence for SR? Can you calibrate your muon detectors without reference to SR? Is there any need to refer to SR when interpreting the data? I tutored a high school student who argued the...

How was it justified before conducting the MICHELSON–MORLEY experiment to assume that the sun was at rest with respect to the ether? Also, was the ether assumed to have the same velocity with respect to the Earth throughout space at one instant in time, or like wind, with different velocities at...

In relativity, no signal travels faster than light, and hence if something happened away from me, I will only know about it after some time. This means I cannot measure instantly the position and time of something as it happens; this would violate special relativity. I however imagine that I...

In describing the Galelian or Lorentz transformations, All books I've read keep talking about clocks and meter sticks, but I don't see how an event happening away from the observer could be instantaneously described by a set of coordinates and a point in time; information conveying the event...

Hello, I have a problem with the postulate of the invariance of the speed of light. When we move away from a light source it is redshift, it is the sign that the relative velocity between us and the light source has changed. If a stationary observer observes the phenomenon, he will measure that...

Thinking about Bell's string paradox , I understand that if both spaceships maintain the same and constant proper acceleration, the string breaks because of the non-simultaneity of the acceleration effects at both ends of the string. But I want to introduce and consider a slight and subtle...

Sorry for the extra question. Just have a lot of questions lately and I know some people around here are annoyed with that.

This is a historical question regarding SR. Has any physicist before EInstein multiplied the time coordinate with the speed of light? If yes who was it? What is a good book or paper that discusses why and how Einstein (or others before him) have come up with the idea to multiply c and t? When...

In Einstein's twin paradox,the solution comes like this: The twin on the spaceship de-accelerates his spaceship first and then accelerates in the reverse direction.This means his reference frame is not inertial hence he doesn't measure greater time interval as the other twin does...

The Lagrangian for a massless particle in a potential, using the ##(-,+,+,+)## metric signature, is $$L = \frac{\dot{x}_\mu \dot{x}^\mu}{2e} - V,$$ where ##\dot{x}^\mu := \frac{dx^\mu}{d\lambda}## is the velocity, ##\lambda## is some worldline parameter, ##e## is the auxiliary einbein and...

Statement: The magnetic field around a straight wire carrying a current can be explained Relativistically by changing the inertial frame of reference to the frame of the moving electrons - i.e., a Lorentz contraction of the positive charges in the wire will give a denser concentration of the...

I would like to know the opinions on the paper that I saw about Michelson-Morley experiment. Michelson-Morley experiment was done in 1887 and had an impact on the future direction of physics. It is taught in schools as an experiment that proves the non-existence of the aether and proves the...

hi guys I am trying to learn special relativity and relativistic quantum mechanics on my own and just very confused about the different conventions used for the notation!?, e.g: the four position 4-vector some times denoted as $$ x_{\mu}=(ct,-\vec{r})\;\;or\;as\;x_{\mu}=(ict,\vec{r}) $$ or...

I'm trying to understand this paper (equation 2.16 specifically): Bini, D., Carini, P., & Jantzen, R. T. (1995). Relative observer kinematics in general relativity. Classical and Quantum Gravity. Am I correct in reading there is no way to express the relativistic relative velocity composition...

This is not a homework question, just a scenario I've come up with. Imagine I have a male and a female clock moving towards each other. If they're in sync, one will fit inside the other and they'll continue on their way. If not, they'll collide. (Apologies for the crude drawings.) I place these...

In this picture it shows a light clock. Let's use the moving light clock example. Am I essentially calculating the b component of moving clock. Assume the moving frame is the B frame. Assume the stationary frame is the A frame https://simple.wikipedia.org/wiki/Light_clock Or essentially the b...

In the space-time of special relativity considered as fiber bundle, could it be stated that the base space is time and the fibers are space ##R^3## related to each other by the Lorentz metric as a connection and in this case would there be parallelism, and in this case: how would this fiber...

Hello, My name is Dave and I'm a physics major at UIUC. It looks like I will be taking the special relativity course (phys 225) this fall. I've always been fascinated by the theory so I decided to get a head start with Lenny and Art's perspective on it. My first head-scratching moment came in...

I am taking a summer course on special relativity and I stumbled across this problem and solution which I tought look neat. However, I think the solution provided for a) there is wrong. I will here present two of my solutions for a) and one solution for b) and ask if you think mine are okay? :)...

My solution was as follows: $$\frac {d\overrightarrow p} {dt}=q \frac {\overrightarrow v} {c}\times \overrightarrow B_0$$ The movement is in the ##[yz]## plane so ##|\overrightarrow v\times \overrightarrow B_0|=vB_0##, therefore: $$\biggr |\frac {dp} {dt}\biggr |= \frac {qvB_0} {c}.$$ On the...

Obviously, a third observer who is at rest with respect to the disk will see that the clock on the outside has a much faster velocity than a clock on the interior of the disk, so clearly the outside clock will show that it has measured less time. But that's one question. What about looking at...

Hi Physics Forums, I've devised a thought experiment called the "Killer Crate Paradox" to put a spotlight on an issue I'm having, with regards to understanding length contraction, specifically in instances where multiple objects are observable and they have different velocities and directions...

Hello, I have recently come across this article by Rizzi and Ruggiero, called "The Relativistic Sagnac Effect: Two Derivations": https://arxiv.org/pdf/gr-qc/0305084.pdf In section 3, the authors derive the Sagnac proper time difference for all beams (light beams and matter beams, including...

I am looking for generalizations of special relativity for flat spacetime. Of course, most well known generlaization of SR is general relativty. There are many other generalizations of SR for curved spacetime. All what I found is for curved spacetime. Are any more or less successfull attempts to...

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...

According to @vanhees71 and his notes at https://itp.uni-frankfurt.de/~hees/pf-faq/srt.pdf under certain conditions one can choose ##\tau## as the parameter to parametrize the Lagrangian in special relativity. For instance if we have, $$A[x^{\mu}]=\int d\lambda...

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...

@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...

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...

i) The muon reaches the ground ii) To a ground observer, the decay time is dilated $$\Delta t_d=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}\Delta\tau_d>\Delta \tau_d$$ The time for the muon to reach the ground is $$\Delta t_g=\frac{10 km}{0.999c}< \Delta t_d$$ which is why it reaches the ground...

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##...

Can someone explain me difference between A^{\mu}_{\hspace{0.2cm} \nu} A^{\hspace{0.2cm} \mu}_{\nu} and A^{\mu}_{\nu}?