Relativity Definition and 998 Threads

Hi, I've a doubt about the application of the principle of relativity as follows. Assume as principle of relativity the following statement: It is impossible by any experiment performed inside a "closed" laboratory to say whether we are moving at constant velocity or staying at rest. Consider...

What are the best books for a second exposure to Special Relativity? I can find plenty of threads on introductory books …

Time when the left beam hits the left wall in the ground frame ##vt_1-x = c t_1## ##t_1 = \frac{x}{c+v}## Time when the right beam hits the right wall in the ground frame ##ct_2 = vt_2 + y## ##t_2 = \frac{y}{c-v}##Setting the times equal to each other with the constraint x+y=L to find x and...

Assumptions 1. General Relativity is the modern and most complete widely accepted theory of gravitation, formulated in a background independent, geometric way. 2. General Relativity is formulated in a manner consistent with Special Relativity and I could imagine that it might be possible to...

We study metrics, in them, we take time as a coordinate. I mean to say that if time is a coordinate then in normal mathematical language, we can have negative coordinate values as well. This confuses me a lot as I want to see and understand the concept from the true physicist's perspective...

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 -...

If the statement above is correct, I do not understand this concept. I guess by charging my phone I am not producing matter. Does it mean in this case, energy converts to mass (not matter)? Can someone please explain this?

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.

Does $$\partial^\beta(g_{\alpha\beta}A_\mu A^\mu)$$ mean the same as $$\frac {\partial (g_{\alpha\beta}A_\mu A^\mu)}{\partial A^\beta} ?$$ If not could someone explain the differences?

a) We use the definition of speed: v = delta_L/delta_t delta_t = delta_L/v = 45000 m/(0.99540*3*10^8 m/s) = 1.55*10^-4 s b) We use the length contraction equation: delta_L = L_0*sqrt(1-v^2/c^2) L_0 = delta_L/sqrt(1-v^2/c^2) = 45000 m/sqrt(1-0.99540^2) = 469698 m However, the solution shows...

Does the law of conservation of mass fail to meet the first postulate of the special theory of relativity(the laws of physics are the same in all inertial frames of reference)?

It would be wholly exaggerative for me to say that I have this story "in the works", so "I have an idea for a story" would be far more fitting! This story involves a method of terraforming which requires manual control of robotic drones from a high-speed orbital ring, made from unobtainium and...

Where can I find numerical relativity source code?

I am doing a project where the final scope is to find an extra operator to include in the proca lagrangian. When finding the new version of this lagrangian i'll be able to use the Euler-Lagrange equation to find the laws of motion for a photon accounting for that particular extra operator. I...

How does general relativity shows the conservation of energy. Because I was reading and listening to something today that touched on this subject. It almost seems as though if you scale GR to larger sizes it stops working and turns into an incomplete law of nature like Newton's laws of gravitation.

It is an electron initially pushed by the action of the electric field. The vectors of force and velocity are parallel to each other. Here's the questionA possible expression of speed as a function of time is the following: $$v(t) = \frac{At}{\sqrt{1 + (\frac{At}{c})^2}}$$where is it $$A...

It is an electron initially pushed by the action of the electric field. The vectors of force and velocity are parallel to each other. Here's the questionA possible expression of speed as a function of time is the following: $$v(t) = \frac{At}{\sqrt{1 + (\frac{At}{c})^2}}$$where is it $$A...

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?

I have been looking through some of the threads about the twins paradox in relativity. It’s clear there’s a lot of confusion on this, and I am yet one more person very confused on this. So I was thinking about a hypothetical experiment, and I will lay out my hypothesis of what might...

Can someone give a meaningful explanation that the relative speed of two oppositely directed light beams is why only one light speeds? I understand that based on the Einstein relativity theory, the relative speed of two beams is C, because nothing can be quicker than light speed. However it is...

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...

So, i was trying to calculate, the net force between 2 point charges in their rest frame, and in a frame where they are moving. So, assume, there are 2 point charges each of charge +q. They are r distance apart from each other and moving parallel to each other with a speed v relative to a lab...

What I've done is using the TOV equations and I what I found at the end is: ##e^{[\frac{-8}{3}\pi G\rho]r^2+[\frac{16}{9}(G\pi\rho)^{2}]r^4}-\rho=P(r)## so I am sure that this is not right, if someone can help me knowing it I really apricate it :)

Suppose you have a tensor quantity called "B" referenced in a certain locally inertial frame (with four Minkowski components for instance). As far as I know, a parallel transportation of this quantity from a certain point "p" to another point "q" consists in expressing it in terms of the...

[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...

Hello All You may be aware of Queen's song '39 where the effects of time dilation are key to the plot. Quote: For so many years have gone though I'm older but a year Your mother's eyes, from your eyes, cry to me Presumably the lyrics were influenced by Brian May's studies in maths and...

Hello All I pivot a long rigid rod at one quarter its length and gradually accelerate the tip of the short end to close to the speed of light. An observer is standing some distance away from the mechanism, so that he/she can see the whole length of the rod. What would the shape of the rod...

In a inertial frame of reference ##S## body accelerate with constant acceleration ##a##. Can then exist inertial frame of reference ##S'## which moves with speed ##u## relative to ##S## in which body does not accelerate? And why?

In classical Hamiltonian mechanics, because of Liouville's theorem about the volume of phase space being preserved by time evolution, there are no attractors. Naively, I think of the Raychaudhuri equation in GR as showing a shrinking volume. However, I guess Raychaudhri's equation does not...

Recently, when reading an entry about Mercury's perihelion shift, someone mentioned a "hand-wavy" explanation as to why GR predicts the orbit so precisely. I was wondering if there was some elementary way to expound on what he was saying. Fundamentally, the comment said something to the effect...

I thought I'd start by writing the problem in a tensor formalism. I have identified with ##S## the Earth and ##S'## the rocket. Since the acceleration provided is in the rocket's frame of reference, I can write the following four-vector. $$ a'^\mu=(0, a, 0, 0) $$ Since we are interested in the...

The problem: Visualising the problem (My question is with regards to this): Why is the above set-up correct? In the above diagram, S would be moving at velocity -v relative to S', instead of v. Is this because the question says "speed v", and so we can set the direction as such? Why would the...

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...

In Robert M. Wald's General Relativity he writes on page ##61##: The energy of a particle as measured by an observer - present at the site of the particle - whose 4-velocity is ##v^a## is defined by $$E=-p_a v^a$$ Thus, in special relativity, energy is recognized to be the "time component" of...

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...

(1) I remember reading somewhere that in general relativity, "space" and "time" lose their metrical meanings. Is that true? And yet, we continue talking of space and time in general relativity as spacetime. (2) Moreover, as someone mentioned in this thread, what happens to the speed of light? In...

I first began to identify the various events in the problem. I call the rocket ##S'## and the Earth ##S##. Sending signal Tail signal reflection Head signal reflection Tail signal return Head signal return For the Earth I know that: ##t_4 = T## ##t_5 = T + \Delta T## Since the two events...

Hi, starting from this thread I'm a bit confused about the content of the principle of relativity from a mathematical point of view. Basically the "Galilean principle of Relativity" puts requirements on the transformation laws between Inertial Frame of Reference (IFR); thus they have to...

The International Bureau of Weights and Measures combines the readings of 450 atomic clocks around the world to obtain a time standard with sub-nanosecond accuracy. These clocks run at different rates - a clock at 1 km of altitude gains about 7 ns a day compared to one at sea level due to the...

Hi everybody I saw quite a nice Youtube vid about general relativity and how gravity bends spacetime and therefor redirects angular momentum into the center of gravity. I thought the first time I begun to understand the concept but immediatly the questions poped up. The video basically says...

In the test of General Relativity by perihelion motion of mercury, the stress-energy tensor is set to 0 in Schwarzschild solution. Then, is the curvature caused by solar mass, or by the 0 stress-energy? Or, do we consider solar mass as the gravitating mass? Or the 0 stress-energy the gravitating...

This video explains gravity in a way I haven't encountered before (regardless of how irritating the presenter may be). Nevertheless, I find it hard to believe that a squirrel falls from a tree to the ground due to gravitational time dilation between its head and its feet. The amount is so...

We are discussing the introduction to Einstein field equation, so he start talk about the linearity in Newtonian gravity and the non linearity in GR. But there is somethings I am missing: > " (...) in GR the gravitational field couples to itself (...) A nice way to think about this is provided...

In relativity, the wave function in different frames is not unitarily related, because the wave function collapses at different times. For example, in a Bell experiment, in a frame in which Alice and Bob measure simultaneously, there is no collapse. But in a frame in which Alice measures...

I want to solve this question first using the train frame, and so going to the ground frame, but the things got wrong, so i would aprpeciate to know why. I mean, there is another ways to solve it, but i want to know where is the error here. Simply, in train frame the time elapsed between the...