Relativity Definition and 998 Threads

(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...

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...

My attempt: ##E^2 = p^2c^2 + m_0^2c^4## ##2E dE = 2pc^2 dp ## ##\frac{dE}{E} = \frac{pc^2}{E^2}dp=\frac{p^2c^2}{E^2}## % (dp/p = 1%) ##=\frac{E^2-m_0^2c^4}{E^2}## % ##=1-\frac{m_0^2c^4}{E^2}## % ##=1-\frac{m_0^2c^4}{m^2c^4}## % ##=1-\frac{1}{\gamma ^2}## % ##=\frac{v^2}{c^2} ##% =0.81...

This is very much, a ... what's wrong with this approach... Consider a large mass with no atmosphere, i.e. the moon. On it, construct a tower of arbitrary height. On the tower build an energy to mass machine, to convert energy to mass via E=mc^2. Once the mass is created, drop it from the...

I started from: $$\frac{d}{dt}(m\gamma v_x)=qE\ \ \ \rightarrow \ \ \ m\gamma v_x - p_{0x}=qE(t-0)\ \ \ \rightarrow \ \ \ m\gamma v_x=qEt+p_{0x} $$$$\frac{d}{dt}(m\gamma v_y)=0\ \ \ \rightarrow \ \ \ m\gamma v_y -p_{0y}=0\ \ \ \rightarrow \ \ \ m\gamma v_y = p_{0y}$$$$\frac{d}{dt}(m\gamma...

I set up this problem this way: ##p_a^{\mu}=(E, \sqrt{E^2-m^2}, 0, 0)## ##p_b^{\mu}=(m, 0, 0, 0)## ##p_c^{\mu}=(2E_\gamma, 2E_\gamma, 0, 0)## I have chosen to consider the two photons as a single particle of energy equal to ##2E_\gamma##. At this point I applied conservation of the...

Hello. I have almost finished Kleppner's Newtonian mechanics book except the part discussing special relativity. I plan to read Purcell's EM book after finishing it. I've heard some people saying that Purcell presents some of the EM concepts in a relativistic way, so I am a bit worried that I...

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...

The popular account of Einstein's train-and-lightening thought experiment doesn't demonstrate "the relativity of simultaneity" as it is always claimed. In fact, it does the opposite: By describing the embankment observer as "at rest" relative to the strike locations and the train passenger as...

I have a doubt about the first request: I suppose to find the minimum energy of ##\gamma## in the situation where ##p## is stationary, there is no reason to say that the proton is stationary if I were to calculate it in the CM, right?. So I have to consider che LAB-frame to find ##E_\gamma##...

I know that general relativity fails in singularities like the center of a black hole or the big bang. GR also fails at fundamental particle levels like electrons, protons and neutrons etc. I.e. GR cannot explain interactions of various fundamental particles?? (Am I correct?) But these does...

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...

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...

A stationary observer sees a particle moving north at velocity v very close to the speed of light. Then the observer accelerates eastward to velocity v. What is its new total velocity of the particle toward the north-west relative to the observer? I ask because while the particles total...

I was going over the Einstein-Hilbert action derivation of the Einstein field equations and came across a term that does not seem to be explicitly defined. That term is the Langragian for the matter fields. What exactly is matter in General relativity in the context of the Lagrangian? Here is...

Hello. I have a question about the law of energy conservation in GR. As time is inhmogeneous, we don't have energy-momentum 4-vector which would be preserved during system's dynamical change. It is only possible to define 4-vector locally. And next, the problem regarding how to sum this vectors...

Summary:: I am looking for a good introductory book about general relativity at undergraduate level. I am looking for a good introductory book about general relativity at undergraduate level.

I just finished multivariate calculus (without any linear algebra experience yet) and I am seeking out a path to understanding General Relativity. I am wondering what are the mathematical fields after multivariate calculus that I need to master before beginning to understand GR, and what...

I have studied in high school that all chemical reactions obey conservation of mass, as the atoms are merely re-arranged, but when I read through special relativity, I was reading that you can show an infinitesimal change in mass (based on E=mc2) in combustion that's not noticeable that's being...

I am trying to understand a thought experiment I just posed, which is: if an observer is traveling near the speed of light, and sends out two photons; one in the direction of travel and one in the opposite direction, how does general relativity account for time dilation? The photon "in front"...

Trying to understand how Einstein predicted the appearance of stars during the solar eclipse around the turn of the 20th century (the first experimental confirmation of General Relativity, I believe). My impression, which is not physically correct, is that the sun attracts the photons as they...

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?

Special Relativity: For the Enthusiastic Beginner on page 49 1.8 Exercises I can't find the answers to the questions? I apologize if this is a dumb question.

General relativity. Curvature of spacetime: ok. time dilation: ok. What about space? Curvature is intrinsic and given by complex equations. But could we definitely say is there more space between 2 points along curved space through the star than would be through flat space (no star there) or...

In contributing to the thread https://www.physicsforums.com/threads/i-need-recommendations-to-read-about-physics.996304/ , I see that the video that greatly influenced me to study relativity is now available online on YouTube (made available by the film distributor). In 7th-grade, after...

(I hope my English is understood). Hello, I have a question regarding the relativity of simultaneity. The mean temperature of the cosmic microwave background tells us how big the universe is with respect to the recombination epoch. If I now measure that the mean temperature of the cosmic...

Is there a relationship between the Lagrangian ‘hill diagram’ and the spacetime curvature embedment graphs? The Lagrangian map shows effective potential, which deals with centrifugal force. As centrifugal force is a fictitious force (and gravity is as well), I would assume the underlying...

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...

Einstein's theory describes gravity as a curvature of spacetime. As such, everything is affected by it. This includes light, which has no mass, as was made clear for the first time during the famous 1919 solar eclipse. In the standard model, the cause of gravity is supposed to be gravitons...

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...

I don't know if I did this correctly. ##\int Fdx = \int dE## ##F \Delta x = \Delta E## ##Fx = Mc^2 - (mc^2 + mc^2)## ##M = \frac{Fx + 2mc^2}{c^2}## ##M## is the mass of the resulting particle. ##2mc^2## is the total energy before the collision. The issue is I'm assuming that the resulting...

Checking my understanding. Can it be said that it is the overlap of the reach and effect of each of the 4 forces, from each respective point of origin possible within the universe, that gives us universal general relativity? Like the most intricate gear set ever? Could it then also be said...

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...

Hello! I do not understand how to prove the exercise. I have searched all over but I have found no hints on how to get started. Can anybody help me?

"(a) How much time does this take in the ground frame? (b) What is the person’s speed with respect to the ground? (c) How much time elapses on the person’s watch?" I solved it, but i am with a doubt yet wrt to the letter b. We can find that the train length in the ground frame is 4L/5, so, why...