Special relativity Definition and 1000 Threads

Two four-vectors have the property that ##A^\mu B_\mu = 0## (a) Suppose ##A^\mu A_\mu > 0##. Show that ##B^\mu B_\mu \leq 0## (b) Suppose ##A^\mu A_\mu = 0##. Show that ##B^\mu## is either proportional to ##A^\mu## (that is, ##B^\mu = k A^\mu##) or else ##B^\mu B_\mu < 0##. Part (a) is...

Right, so I thought I'd done this correctly but clearly not because my velocity is greater than the speed of light, where have I gone wrong? P = (M, 0, 0, 0) p1 = (E1, p1x, p1y, p1z) p2 = (E2, p2x, p2y, p2z) P = p1 + p2 p2 = P - p1 square each side to get (p2)2 = P2 - 2Pp1 + p12 therefore (m2)2...

I've tried using gammamc^{2} = E1 + E2 but how do i find gamma?? If i try to use the kinetic energy then I just get gammamv^2 = 1gev but i don't know v? very confused

In A.P. French's Special Relativity, the author said the following, As I understand, photons are massless, so I don't think the last equation above applies to photons, but then, when deriving it, he used an equation proper to photons (##E=pc##). So in which context is ##m=p/c## valid?

[Note from mentor: this was originally posted in a non-homework forum, so it lacks the homework template.] Summary:: Special relativity problems. More details below The formula for speed for special relativity is V = (u-v) / (1-u*v) / (c^2) Here the book...

Happy new year, I got very far in this question. I attempted to use conservation of energy first. Ei=(Pfc)^2+mec^2 Where pf is the initial momentum of the photons Ef=(γmec^2)+(pf'c)^2 Then used conservation of momentum Pf=γmvcos(Θ) Pf'=-γmvsin(Θ). After that I added Pf and Pf'. and used...

According to the 2nd postulate of Special Relativity, speed of light in vacuum is the same in all inertial reference frames. If I take a beam of photons and see the other photons in the beam from a frame of reference of a single photon, do they look stationary or moving at the speed of light...

I'm interested in the history of thought that led to the discovery of special relativity. Of all the equations in special relativity, e.g. the equation for the invariant interval, the equation for gamma, the Lorentz transformation equations, the equation for velocity addition, etc., which one...

## \ \ \ \ \ ##In ##K##，System ##M## is composed of a spring ## N ## and four particles ## P, Q, A and B ##. The ends of spring ## N ## are fixedly connected with particles ## P and Q ## respectively. Particle ## A ## is adjacent to particle ## P ##, and particle ## B ## is adjacent to particle...

This is my first thread. I hope I do it right. I just started reading the book Special Relativity by W.Rindler. And as I was reading it, I stumbled upon a pickle. So in Lorentz theory, it says, supposedly we could measure the original to-and-fro time T2 directly with a clock, and suppose we...

[Moderator's note: Thread spun off from previous thread due to topic change.] Thanks! I am working on understanding why non-local effects violate the special theory of relativity. I am not there yet, but maybe when I finally get there I will leave the BM train.

Recently, I've been studying about Lorentz boosts and found out that two perpendicular Lorentz boosts equal to a rotation after a boost. Below is an example matrix multiplication of this happening: $$ \left( \begin{array}{cccc} \frac{2}{\sqrt{3}} & 0 & -\frac{1}{\sqrt{3}} & 0 \\ 0 & 1 & 0 & 0...

A problem of an isolated system's velocity in different inertial systems, in special relativity ##\ \ \ \ \ ## In the inertial reference frame ##K##, the velocity of each component of an isolated system in ## x## direction is zero at a certain time. ##\ \ \ \ \ ## The inertial reference frame...

[BEGINNGING NOTICE] Before I begin showing my attempted solution, I would just like to quickly mention that this is a "repost" of the same question I had around a week ago. While I would usually use the "reply" function on the same thread, I believe that thread is getting pretty messy (sometimes...

Below is the attempted solution after researching the contents available on Introduction to Electrodynamics by Griffith. To begin with, I defined the rod as having a length of ##l'## at rest in frame ##S'##. Thus, in frame ##S'##, the height of the rod is ##l' sin(\theta ')## and its horizontal...

"My" Attempted Solution To begin, please note that a lot - if not all - of the "solution" is largely based off of @eranreches's solution from the following website: https://physics.stackexchange.com/questions/369352/scalar-invariance-under-lorentz-transformation. With that said, below is my...

Summary: The problem is to generalize the Lorentz transformation to two dimensions. Relevant Equations Lorentz Transformation along the positive x-axis: $$ \begin{pmatrix} \bar{x^0} \\ \bar{x^1} \\ \bar{x^2} \\ \bar{x^3} \\ \end{pmatrix} = \begin{pmatrix} \gamma & -\gamma \beta & 0 & 0 \\...

with distance between planets as 4x10^8m measured by you on the ship My attempt: t' = γ(t - ux/c^2) γ = 5/3 u = 0.8c t = 0.9s x = 4x10^8m answer is: -0.278 Therefore not possible My question is what if we traveled rightwards, from p2 to p1, would the answer change? Should my above information...

Unfortunately, I am not entirely confident of the above equations being able to do the trick and ultimately solve for the question. However, my guess is that using the equation written above for "boost", I could perhaps use ##v## and insert it into the ##x##-direction part of the matrix...

Homework Statement: Problem: The planet X is far 48 light-years from Earth. Suppose that we want to travel from Earth to planet X in a time no more than 23 years, as reckoned by clocks aboard our spaceship. At what constant speed would we have to travel? How long would the trip take as reckoned...

I have been getting back to studying physics after a long break and decided to go through the problems in Rindler. But there is something I don't quite understand in this problem. To first answer the second part, Exercise II(12), I wrote $$\frac{du_2}{dt} = \frac{du_2}{du_2^\prime}...

Clarification: The statement in the title is actually from the solution to the homework question, as given by the textbook (you can see the whole thing below under "Textbook solution"). The solution doesn't explain everything, which is where my confusion comes from. Usually in my classes we...

The Lorentz covariance of Maxwell equations was known before Einstein formulated special relativity. So what exactly special relativity brought new with respect to mere Lorentz covariance? Is special relativity just an interpretation of Lorentz invariance, in a sense in which Copenhagen...

I'm a bit lost at how to exactly start this exercise... As far as I understand we need to first determine ##d\tau_E## and ##d\tau_S##. First question: Since we can neglect the Earth's movement, can I also neglect the movement of the satellite with respect to the far away observer? If so, I...

I'm struggling in the details of this exercise. Let ##S'## be the reference frame where the acceleration of the spaceship is constant, in which case we have ##u'(t')= a' t'## (since we assume no acceleration at the beginning). The rest frame of the rocket ##S## is connected to ##S'## via a...

Homework Statement: A spaceship has two clocks: one in the front and one at the back. The clocks are synchronized in the spaceship's frame of reference. The spaceship zooms past the Earth's surface at a relativistic speed. Prove that in the Earth's frame of reference, the clock at the front...

Alice and Bob are initially in the same inertial frame. There are 2 point test masses m1 and m2. Initially m1 is at the origin and m2 is on the positive x-axis. At time zero, m1 is instantaneously accelerated to velocity Vx in the positive x-direction. After some time, m1 collides with m2...

Let m be a point test mass. Initially m has velocity Vy in the poisitive y-direction, and zero velocity in the x-direction. At time zero, m is accelerated in the positive x-direction. In the limit as the time goes to infinity, the velecity in the positive x-direction goes to the speed of...

is there a equation that links quantum gravity and special relativity?

Recently I have come into Special Relativity and specifically Lorentz transformation. Let's assume two frames A and B moving relative with speed ##v##. The position of a particle moving with respect to B is given by ##x′=f(t′)=3t′##. What is the function of position ##x=f(t)## of the particle...

Hey guys. Noob here. Question; S frame = x,y,z,t S' frame = x',y',z',t' S' is moving with a speed v relative to S and t=t'=0 when origins coincide v= 0.6c find the coordinates of x = 4 & t = 0 in S' When I use lorentz transformation, I get a negative t' and x' = 5. This doesn't make sense to...

Hello, I have a couple of questions related to reference frames in Special Relativity. Let's consider a rocket that is inertially moving towards a star with a relative velocity 0.9c. I'd like to look at this example from both the rocket's and the star's perspectives. In the reference frame of...

I would like to apply a General Lorentz Boost to some Multi-partite Quantum State. I have read several papers (like this) on the theory of boosting quantum states, but I have a hard time applying this theory to concrete examples. Let us take a ##|\Phi^+\rangle## Bell State as an example, and...

Hi. Im looking into special relativity and everything i found about time dilation on internet seems to say that moving clock appear to tick slower than the stationary one. However what I found about this is following, in § 4. (Physical Meaning of the Equations Obtained in Respect to Moving Rigid...

I find this subject fascinating. Einstein said the distinctions between past, present and future is just a persistent illusion. I was watching a special with Brian Greene and other Physicist who think we do live in a Block Universe and they explained it very well. Here's my question. Say there...

So I was reading a book on special relativity and it was explaining how, if we were to go very near the speed of light, time (relative to us traveling) would slow and space itself would condense. It used the example that if we were to try and travel to a galaxy 1 million light years away, Yet we...

Suppose we have two observers A and B and they are at rest. Observer A observes two objects falling from height H (A has same distance between the two objects). Does observer B will measure different times for the duration of falling of the two objects ? (because the two object are not in the...

I have to find pμ(τ) of a particle of mass m and charge q with v(0) = (vx(0), vy(0), vz(0)) in a electric field E parallel to the y-axis and a magnetic field B parallel to z axis, both constant and uniform, with E = B. Here follows what I have done (see pictures below): I wrote 4 differential...

I can't find an answer on my dilettante question about how we attribute reference frame to complex objects, where different parts move with different velocity or where different parts experience different influence of gravitation. For example, we can take a human's body. If we take the full...

In an accelerator when you're pushing/pulling a charged particle with a field that travels at the speed of light why should we expect to the particle to exceed the speed of light.

The mass of an object moving at speed v increases such that $$\frac{m'}{m}=\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$$ and its apparent frequency decreases such that $$\frac{\nu'}{\nu}=\sqrt{1-\frac{v^{2}}{c^{2}}}$$ so $$\frac{\nu'}{\nu}=\frac{m}{m'}$$ but equating the energies $$ h\nu= mc^{2}$$...

Sadly, that's what all I could do.

Attempt at solution: By conservation of momentum: $$P = (M,0,0,0) = p_1 + p_2 = (E_1 + E_2, 0, 0,0)$$ thus $$ M = E_1 + E_2 = 2k^2 + m_1^2 + m_2^2$$ Now $$E_1^2 - E_2^2 = m_1^2 - m_2^2 = (m_1 + m_2)(m_1-m_2)$$ $$ = M(m_1-m_2) = (2k^2+m_1^2+m_2^2)(m_1-m_2)$$ Isolating k: $$ k =...

Hello, I was wondering if anyone could set up and solve a classic train in a tunnel paradox from special relativity with unique values for multiple observers including time space diagrams. Thanks

I just stumbled over the following book on SRT Michael Tsamparlis, Special Relativity, Springer (2010) It's a gem! On the beginning-graduate level it explains the special theory of relativity from ground up, starting with a chapter on the math of Minkowski space and then providing a complete...

Starting from this post, we are able to define the concept of (proper) acceleration or rotation without any reference to something else About this definition which is the physical meaning of gyroscopes axes pointing in three mutually orthogonal spacelike directions ? In other words, from a...

I understand x' = λ(x - vt) but why does t' = λ(t - vx/c^2)? where does the vx/c^2 come from? and honestly I don't understand what t' is. because from what I understand is that t' is the length of time t as observed from the reference frame S'. which means t' = t*λ?

So I worked out the first part and obtained ##E_1 = 478.8MeV##, ##E_2 = 459.4MeV## and ##p = 0.49 MeV/c## but I can't quite wrap my head around the second part. Normally, I'd use the equation for s but I'm confused since I don't know the angle between the gamma rays.

N.A

I'm doing some exercises about special relativity and one of them asks to find the speed in an arbitrary frame of reference (1) in such a way that it perceives two events at the same time that didn't happen simultaneously in other frame of reference(2). Is it correct to state that if the...