Special relativity Definition and 1000 Threads

I had a DM with @PAllen about the notion of non-standard inertial frame. Let's consider a (global) inertial frame in the context of flat spacetime. Apply now to it a general transformation of spatial coordinates alone. Such a transformation yields a frame that is no longer inertial. Although...

Hey, I’ve been trying to understand time dilation, and I think I might be mixing some concepts. If you’re moving very close to the speed of light (say 0.99999c), your clock slows. If you then enter a strong gravitational field, that also slows clocks. From your point of view, would that mean...

I've been reviewing some introductory tensor stuff, and I've come to the realization that some of the things tensors do confuse me. For example, the notes I'm reading say that the invariant interval is both ##S=\eta_{\mu\nu} x^\mu x^nu## and ##S=x^T \eta x##. Both of which are totally fine on...

if light pulse is to the right, but moving car's velocity is to the left, we would expect c-v, but we get c instead which is greater. but if light pulse is to the right, and moving car's velocity is also to the right, we would expect c+v, but we get c instead which is smaller. how could the same...

If we don't multiply time by the speed of light C, in Lorentz transformation equatins, the invariant tensor of U.U will not be equal to c^2. So it seems the coefficient of C is an obligation for parameter t. I thought it's just for visual convenience in graphs, besides C is not dimensionless.

In what sense is the following explanation of the Twins Paradox faulty in logic: Each twin views the other as length contracted, but the twin on earth only sees the rocket in motion and thus shortened (along with the twin) while the destination planet is at rest in the earth frame and the...

import pygame # Initialize Pygame pygame.init() # Get the screen resolution info = pygame.display.Info() WIDTH, HEIGHT = info.current_w, info.current_h # Set to the current screen size # Constants WHITE = (255, 255, 255) LIGHT_COLOR = (255, 255, 100) OBJECT_COLOR = (100, 255, 100)...

The action for a free particle is $$I=-m\int{ds} = \int \left(-m\frac{ds}{dt}\right) dt \quad\quad\quad(*)$$ hence the Lagrangian is $$L=-m\frac{ds}{dt}=-\frac{m}{\gamma}=-m\sqrt{1-v^2} .$$ Dirac ("General Theory of Relativity", p. 52) infers this by checking that it gives the correct spatial...

We want to relate acceleration in two frames, an inertial frame S, and the instantaneous inertial reference frame of the particle on which it is being accelerated, S', which is moving in the ##x## direction at the moment. Let the acceleration in S be ##(a_x,a_y)## and in S' be ##(a_x',a_y')##...

Rancher, film producer, writer, AI entrepreneur, US Army veteran/paratrooper and theoretical physicist. Granted, that’s a professional Venn diagram you won’t see often, but I’ve just submitted my first paper for pre-published peer review on viXra and am hoping to contribute to the forum and...

How is the angle between two 4-vectors defined in special relativity? Consider two 4-velocity vectors: $$U^\mu=(1,0), \\ V^\mu=\gamma_{rel}(1,v_{rel})$$ Where the vectors are written in the frame of the particle with ##U^\mu##. The dot product between these is $$U^\mu V_\mu=\gamma_{rel}$$ If...

I recently had a look at some textbooks to see how they make use of the Lorentz factor. I have seen that many textbooks introduce γ purely as a mathematical shorthand. On the other hand, some books that delve a little deeper into γ use graphs to show how γ and v are related. I have found...

This is a question to school teachers (and all those who know about physics syllabus at school). Is relativity (special and or general) taught in school (pre university) in your country? If yes, at what age are students introduced to relativity? What aspects are taught? As far as I remember...

Suppose there are two reference frames. One is rotating with respect to another with rotational velocity ##\omega##. Now if in one of the reference frames the vector potential is $$(1, 0, 0, 0)$$ then in the other reference frame it will be $$(\sqrt{1-(\omega r)^2}, 0, \omega r, 0)$$. Now in...

I have a Hamiltonian $$ H = \frac{1}{2} g^{\alpha \beta}\left(p_\alpha- A_\alpha\right)\left(p_\beta- A_\beta\right) $$ I want to calculate the equation of motion. How can I calculate the equation of motions $$ \frac{dx^\mu}{d\tau} = g^{\mu\nu}(p_\nu - A_\nu) $$ This one is straight...

I want to explain my thoughts longer, but since my English is terrible, I will try to keep it as short as possible. This is the Minkowski diagram for the question above. ct-axis is the worldline of the space station, and ct'-axis is the worldline of the spacecraft. What I am confused about is...

I've already got "Personal Speculation Warning" and I had a private conversation with @Nugatory, who told me, that I have to publish it in an appropriate peer-reviewed journal before it can be posted for discussion here. I replied with a question, if he is willing to believe, that...

In 2005, Robert B. Laughlin (Physics Nobel Laureate, Stanford University), wrote about the nature of space: "It is ironic that Einstein's most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity]...

There are two coordinate frames K and K'. A particle is moving. The position of the particle in K frame in (t, x, y, z) and K' frame is (t', x', y', z'). the z axis of K and K' are aligned. and K' is rotating with respect to K with an angular velocity w. Relate the equation of motion in these...

I’ve been following this recent discussion on the speed of light and its implications in special relativity, and it got me thinking about proper time along light-like curves and the use of the Lorentz factor, ##\gamma##. One point that stood out to me is the claim that proper time along a...

Im utterly confused about this video and I would like some opinions about it: "How Superposition Causes Length Contraction -- And Explains the Principle of Relativity" Approximately content: 1) Length contraction is entirely physical (shorter molecular bonds??). 2) Oliver Heaviside's retarded...

Hi, today I have asked a very similar question on the topic, however now my question is more specific and focused, therefore I wanted to ask this again. From the following thread, Nugatory's answer, I understood that some physical quantities need to be described by contravariant vectors, such...

Hi, I am very confused about the mathematics related to special relativity. I have understood, that a four-vector with an upper index has the form: $$A^\mu = (A^0 , A^1, A^2, A^3)$$ where lowering the index would make the indices other than the ##0##th negative: $$A_\mu = (A_0, -A^1, -A^2...

Even if I do not agree completely with him, I have followed some of the works of Tim Maudlin on explaining Bell's theorem which have been illuminating. He founded the John Bell Institute and he is what I would consider a Bell fundamentalist. However today I found on YouTube two very weird...

How did you find PF?: Google search Hello, I am a semi-retired management consultant specializing in procurement and supply chain. Most of my work involves collection and analysis of a company's procurement data and identification of value creation opportunities from initiatives such as...

I think that we travel to future all the time. As all intertial frame of motion is relative. We are currently travelling at very high speeds with relative to a particle accelerator's particle and time is slowing down for us with relative to the particle. I think so we are also travelling to...

So I've learned about time dilation and how getting close to the speed of light can have affects of time dilation. Looking into a bit more I see that when you are really close to the speed of light, say getting to the point of 99.9999999999% the speed of light, then it starts to become that...

Please clear any misunderstanding I have and if I am correct, kindly give me some more details and depth of SR time dilation which I am missing.

What are the supporting arguments for the assumption that space and time are homogeneous?

TL;DR Summary: problem help pls :( so i have a presentation competition on physics. and I chose the energy mass equivalency topic. while researching, I came across a video stating that if we compress a spring, it's energy increases, so it's mass also increases. same thing with a cup of coffee...

Hi everyone, I am a grade 12 high schooler(high school almost completed) who has gone through mechanics, some linear algebra, calculus and currently working through electrodynamics and EM, I would like to get an introductory view of Special Relativity, so I found this lecture course on NPTEL by...

I apologize for the simple question, but here it is. The energy momentum relation models changes in energy ##E## and 3-momentum ##\textbf{p}_3 = \{ p_1,p_2,p_3 \}## with changes in velocity given ##(\textbf{p}_4)^2 = M^2##, where ##M## denotes mass and ##\textbf{p}_4## denotes 4-momentum, where...

I was watching an explanation of why the spacetime interval is invariant in all inertial frames (even when it's not lightlike) and the author made the assertion that if we have the relationship ds'=f(ds), we can expand the function as A+B*ds+C*ds^2+... (where C is not the speed of light). That's...

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...

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...

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...

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...

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...

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...

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.

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...

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...

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.

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...

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...

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...

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...

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

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...