Special relativity Definition and 1000 Threads

The information I have are the following: ##p^\mu=(E, p, 0, 0)## ##p'^\mu=(E', p'\cos\beta, -p'\sin\beta,0)## ##k^\mu=\tilde{E}(1, \cos\alpha, \sin\alpha, 0)## Where: ##E=\sqrt{M^2+p^2}## ##E'=\sqrt{m^2+p'^2}## Using the conservation of the four-momentum ##p^\mu=p'^\mu+k^\mu##...

Sine-Gordon model is looking trivial 1D model: just $$\phi_{tt} = \phi_{xx}-\sin(\phi)$$ which has physical realization as lattice of coupled pendulums, e.g. nice video: Despite looking so trivial, it e.g.: has analogues of massive particles ("kinks") corresponding to complete rotation -...

Consider an observer on Earth (Neglect any effect of gravity). Call him A. Let 2 rockets be moving in opposite direction along x-axis (x-axis coincides with the x-axis of A) with uniform velocities. Call them B and C. At t=0, in A's frame, the rockets are separated by length ##l## . Let ##V_a##...

First I wrote in ##S'##, by using Gauss theorem $$ \int_{\Sigma} \underline E' \cdot \hat n d\Sigma = \frac Q {\varepsilon_0} \rightarrow E'(r)2\pi rH=\frac{\lambda'H}{\varepsilon_0} $$ $$ \underline E'(\underline r)=\frac{\lambda'}{2\pi\varepsilon_0r}\hat r $$ Its components are...

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...

The only way I know of to derive special relativity is to start with the two postulates, derive the Lorentz transformations, and rewrite the laws of physics consistent with those transformations. Are there alternative ways to derive special relativity? Thank you.

My name is Dilip (James) I am fascinated by physics and have written three books on the subject, which indicates my level of interest.. My latest book “The Electromagnetic Universe: A New Physics” is available on Amazon and describes in detail: a new theory on the propagation of light, a new...

I stumbled across a cheap copy of Synge’s Special Relativity. I know that it was an important book, but there is an undercurrent in the comments that it is now dated. Is it still worth spending time with?

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...

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...

Hi, I'm a 15-year-old high school 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...

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+...

[Mentors' note: This question was orginally assumed a train traveling at the speed of light. Further discussion shows that this assumption is not required for the question; any relativistic velocity is enought to raise the question. The post has been edited, changes in boldface, to reflect...

First, I calculated the velocity of the object with regards to earth, which is: $$v'=\frac{V-v}{1-\frac{vV}{c^2}}=0.34c$$ Now, the problem is solved if I consider the length ##l=45m##(so by calculating the ##\gamma## factor with ##v'##) to be the proper one... but since it's measured by the...

Hello Is the distortion of spacetime by gravitational waves directly related to the contraction of objects in motion predicted by special relativity ? In other words Besides the existence of the gravitational waves , did the LIGO experiment definitely confirm the contraction of the bodies in...

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...

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...

Would the second postulate (The speed of light in free space has the same value c in all inertial reference frames.)be also true if it was in some medium instead of in free space? I know the value won't be c anymore but I want to know whether the speed of light in that medium would be the same...

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)...

hello Does special relativity entail matter annihilation ?

Let us have an observer at rest at (0,0) in a coordinate plane. Another at (1,0) moving away from the first observer at 5 m/s in the x direction as seen by observer 1 and another object at (1,1) moving away from observer 2 at 0.5C in the y direction as seen by observer 2. Should observer 1 see...

Good day. I have read many books, forums, and articles, and watched many youtube videos, all in an effort to understand special relativity and time dilation. Or rather, more precisely, trying to find a valid explanation that does not result in contradictions and paradoxes, and if it does, one...

Special Relativity tells us - the faster things travel their time is slower relative to a stationary observer. Do massless particles, like photons traveling at the speed of light, experience zero time and in their frame of reference travel "instantaneously".

Assuming Einstein summation convention, suppose $$R^2=\eta_{\mu\nu}x^{\mu}x^{\nu}$$ I was able to show that $$\partial_{\mu}R=\frac{\eta_{\mu\nu} x^{\nu}}{R}$$ by explicitly doing the covariant component of the four-gradient and using the kronecker tensor. However, how do I use the equation...

Hello, I am spending time learning more about the theory of special relativity and string theory. One of the things that I have read about string theory is that it includes other dimensions in relation to space (space has 9 dimensions in string theory, supposedly). However, from what I...

Currently, the only part of the textbook question that is completely throwing me off is "an angle of ##l=\sqrt{2}c##". If I am not mistaken, how am I suppose to interpret that as an angle and calculate for the answers of (a) and (b) accordingly? As for my attempted solution process of this...

I am assuming that B is a stationary observer here. For the first part of the trip, using the formula, rocket A is approaching B at velocity $$v_A$$ =0.6 c. The length that A travels is $$L_A = v_A t_1 $$ where $$t_1 = $$ 6 hrs. For the first part of the trip, B is receiving signals at a rate...

Homework Statement:: There are plenty of special relativity problems on Time dilation, length constraction, and Lorentz Transformation. But, I can't solve anyone, even the simplest problem. Relevant Equations:: Time dilation, length constraction, Lorentz Transformation What should I do to...

This example is worked out in the book, and at the beginning, they make the assumption that the muon is traveling at c, and then find the change in time from the Earth reference frame using delta t=100km/c. Then delta t is plugged into the time dilation equation on the left side and we solve for...

In this case, γ = 1/√(1-v^2/c^2) = √(1-0.6^2) = 0.8 However, I'm not sure if time observed by Earth is proper time or moving time. The definition of proper time in my textbook states that it is 'the time measured in a frame of reference where the events occur at the same points in space. I'm...

Lv = Lo / γ 1/γ =√(1-v^2/c^2) = √(1-0.8^2) = 0.6 Therefore Lv = Lo x 0.6 = 150 x 0.6 = 90m Therefore electron travels 90m in its own frame of reference (answer key solution) However, shouldn't the electron be assigned rest length, Lo, as its frame of reference is at rest with itself instead...

Summary:: Is it possible to publish a paper contradicting Einstein's special relativity in any high-ranked Journal? Which Journal is the best, i.e. open minded, for such a paper? I plan to publish a new theory of electromagnetics in a Journal. The findings are purely through strict...

I am curious about time traveling. According to Einstein's special relativity, the easiest way to travel into the future is by approaching the speed of light or faster. Now assume this setup: Sunlight travels to Earth at c (speed of light). We have the technology to reach speeds faster than...

Hello. Questions: How can special relativity describe four dimensions when we only see three spatial dimensions and we experience time?Why time is the fourth dimension and not another physical quantity? Is this only a generalisation that was needed to describe more physical phenomena and the...

I'm trying to understand the Energy-Momentum relativistic relationships for a light particles. It is commonly said that the Energy of a photon depends on the observer by the relationship ## E = - \mathbf{p} \cdot \mathbf{u}## where p is the 4-momentum of the source emitting light particles and u...

Summary:: Special relativity - 2 astronauts syncronize their clocks and moves in different paths at different velocities, which clocks is left behind? and why? Hi everyone, i have the following problem and I'm not understanding if my strategy to solve it is correct: Two astronauts synchronize...

Hey! I'm and undergrad in the third year of my applied physics program. I'm taking a course in Special Relativity, and due to Corona the exam has been replaced by a pretty free project where we delve deeply into a topic related to the course. I'm interested in music, so my professor suggested I...

A few years ago, a nuclear engineering professor explained to the class that the widely accepted theory between the relationship between space, time, and velocity may be wrong. At the time, I didn't think much about it since he had a lot of out-there beliefs and he seemed to be a bit of a...

1.8 Exercises page 49 I can't find the solutions to the questions. Where are they?

I am a little confused with the text above. Actually, all is ok until 2.51, i think i am missing something. What is this? Another way to define gamma? (The doubt is not about the raising indices, neither about "n00 = -1", is just where does the equation came from. That is, the equation is easy...

Is there a general method to determine what geometry some line element is describing? I realize that you can tell whether a space is flat or not (by diagonalising the matrix, rescaling etc), but given some arbitrary line element, how does one determine the shape of the space? Thanks

Are there any known instances of heat transfer via conduction or convection happening at relativistic speeds? Is this even possible or is there a non-relativistic limit to how fast heat can transfer in these ways, like how sound can only move so fast?

Hi, I'm taking an introduction course to Special Relativity and encountered a fairly simple problem: Dirac travels to alfa centauri, which is 4.37 lightyears away. He stays there one Earth year and then travels back, and when he comes back he has aged 5 years. At what speed did he travel...

In special relativity (especially relativistic collisions), is the center of mass frame as useful as Newtonian mechanics?

Hi, I'm stucked in this exercise. I don't know how to proceed. Any hints I appreciate it.Two bars of the same proper length L, moves in the same way on the x axis. In the referential of one of the bars the time interval between the events, when the extremity right of one bar and the extremity...

In classical mechanics, the gravitational force is described by the equation: F = Gm1m2/r^2 What would this equation - or other similar equations - look like in special relativity? This equation cannot be correct because it implies that the force acts instantaneously.

In special relativity, observers can disagree on the order of events - if Alice thinks events A, B and C are simultaneous, Bob can think A happened before B which happened before C, and Carlos thinks C happened before B which happened before A - provided A, B and C are not causally connected, of...

Can special relativity handle acceleration? I believe the answer is yes, but I don’t recall dealing with any acceleration problems when I took SR. I remember using the time dilation, length contraction and Lorentz transformation equations. These equations all assume constant motion iirc.

Hi, I've read a number of posts here on PF about Einstein's clock synchronization convention. In the context of SR we know the transformation law between inertial frame's coordinates is actually the Lorentz one. The invariant speed for Lorentz transformation is c (actually it coincides with...