Special relativity Definition and 1000 Threads

Hi, My question can result a bit odd. Consider flat spacetime. We know that inertial motions are defined by 'zero proper acceleration'. Suppose there exist just one free body in the context of SR flat spacetime (an accelerometer attached to it reads zero). We know that 'zero proper...

I can't seem to wrap my head around it: if an object is moving at speed v in frame S, and its observed to move at speed v' in S', what is the relationship?

Hello all. Recently this twin paradox variant occurred to me, and I can't wrap my head around it: Alice and Bob are in the same (roughly inertial, for our purposes) reference frame, separated by a sideral distance. Let's say Alice is on Earth and Bob on Pluto. They synchronize their clocks at...

I hear that philosophy refuse to "relativity concepts"(e.g relativity moral).Relativity theory says about the relativity of spacetime.I do not understand why special relativity does not contradict with general philosophy?(I know the theory Idea Form of Plato)

In SR, for the momentary co-moving reference frame, U (the velocity four vector) takes the form (1,0,0,0). I'm wondering whether the basis vectors associated with this velocity are zero or if the coefficients in front of the basis vectors are zero. In classical mechanics we would say that the...

Ateempt of solution: There are two key coordinates in this scenario, the leftmost tip of the rod, which in ##S'## is ##C_{0} = (t', 0, ut',0)## and the opposite tip ##C_{1} = (t', L,ut',0)## An angle ##\phi## could be found through a relationship such as ##tan(\phi) = \frac{ \Delta x}{ \Delta...

I am confused about how to find the length of a wave train emitted within a time interval T and that is moving with speed c relative to a moving frame that is itself moving with velocity v. Apparently the answer is that the wave train's length is cT - vT, but I tried to plug in variables into...

I am wondering if there is a typo in my textbook. Please see the attachment. The textbook says "...keeping only the lowest term in x = v/c." I am wondering if it should be "x = v/(nc)," as I circled in blue on the left side. It is a binomial expansion of the denominator. Shouldn't x be v/(nc)...

Hello, I try to understand how to get the last relation below ##(3)## ( from stress energy tensor in special relativity - Wikipedia ). I understand how to get equation ##(1)## but I don't grasp how to make appear the gradient operator in the dot product and the divergence operator in the...

Hi, I have no education in physics beyond the intro undergrad level. How do the clocks compare in the following scenarios? In the beginning, two clocks are placed next to each other and synchronized. Then they are moved in opposite directions, traveling an equal distance from the beginning with...

I've already made a post about this topic here, but I realized that I didn't understand the explanation on that post. in Chapter 7 of Rindler's book on relativity, in section about electromagnetic field tensor, he states that _and introducing a factor 1/c for later convenience, we can ‘guess’...

Bob is standing on Earth and Alice is on a distant planet at a constant distance from Earth. Their watches are already synchronized in the following sense: Suppose Alice's planet is a light-year away from Earth. Bob emits a light signal to Alice at time t = 0 according to Bob's watch. When Alice...

Radio wave travels at the speed of light 3x10^8 (m/s) Converting the distance to meter: 1.3 x 3.1x 10^16 = 4.03x10^16m The time it takes in our Earth frame of reference is: 4.03x10^16m/3x10^8 (m/s) = 4.26 years The answer is B But wouldn't the time in light's frame of reference be 0 and it's...

Basically I just want to work out a constant acceleration problem in relativity, of the same kind of introductory physics. Vo= 0.9999c Vf = 0 D= 50 Au Accel, Earth frame? Accel, Ship frame? Time of transit, Earth frame? Time of transit, ship frame? Motion is 1-D. All origins line up at the...

This approach is seeming intuitive to me as I can visualize what's going on at each step and there's not much complex math. But I'm not sure if I'm on the right track or if I'm making some mistakes. Here it is: ##A## has set up a space-time co-ordinate system with some arbitrary event along his...

Hey everyone, I have generated a nice little velocity vs time graph that I would love if somebody could help me put to use. I have marked data points on the x-axis for the Y-value for every second on the function. Just to be clear: X-axis = time in seconds & Y-axis = velocity in meters/second...

The question is in reference to calculating relativity of simultaneity. I am on the step where I take the time in Alice's frame from the front and from the rear clock and minus it to the get the total time. I end up with gamma squared etc (For more details see the picture below) I have...

hello all : looking for books to read in this times ,undergraduate level mostly , but i have some problem finding good ones for introductory elementary particle physics other than griffths and for special relativity any recommendations

I am more confused by the theory of relativity as I start thinking about it. I have a question and it might sound silly but please, correct me if I am wrong. Suppose, A and B are twins where A is at the Earth, and B is moving on a spacecraft at a speed near to the speed of light. In this...

In Jackson, (3rd edition p. 545), there are equations they are given as, $$A = e^L $$ $$det A = det(e^L) = e^{Tr L}$$ $$g\widetilde{A}g = A^{-1} $$ $$ A = e^L , g\widetilde{A}g = e^{{g\widetilde{L}g}} , A^{-1} = e^{-L}$$ $$ g\widetilde{L}g = -L $$ I have several doubts. 1) $$det(e^L) =...

If anybody has studied the book: A First course in String Theory - Barton Zweibach - 2nd edition This statement is present in 6th chapter of book on pg 110

Well I became interested in String theory before my high school. Now I am in ginal year of my BS in Physics. I am working on a project in string theory.

I think this should be t'= Lorentz factor* (1+v/c)t, but that doesn't make sense to me.

Momentum ##\vec{p}## before collision is momentum of proton of the energy ##E=76.4\mbox{GeV}##. Law of conservation of energy is E+mc^2=E_1+E_2+...+E_n mc^2=0.94\mbox{GeV} We could generate only even number of particles after collision because of law of conservation of electric charge. Also...

Okay, so, while discussing Rindler space with my professor, I was asked to prove that for a free-falling observer, proper time for passing through the Rindler horizon is finite. That is at least how the question is phrased. So, the professor obviously assumes that it is clear and trivial to me...

https://scholar.harvard.edu/files/david-morin/files/relativity_chap_1.pdf The questions start at page 44 Whenever I refer to y, y = gamma. 1.1 This question is primarily deriving LV/C^2? How does 2LV / c^2-v^2 becomes 2Lv / c^2(1-v^2/c^2)1.4 On the solution page it shows fig 1.61 and fig...

I kinda know how to do this problem, it is just that I hit a sign problem. If I take the partial derivative of the coordinate transformation with respect to ##x'^\mu##, I get writing it first in the inverse form, ##x^\alpha = x'^\alpha - \epsilon^\alpha## ##\frac{\partial x^\alpha}{\partial...

Hi, I read various threads in PF about the concept of invariant speed and the speed of light in vacuum that in our universe happens to be the same as the 'invariant speed'. My doubt is about the speed of the light in vacuum as measured from a non-inertial frame (basically in the context of SR...

Hello everyone! Let's say that you were to attempt to go as fast as possible on a spaceship with the mass of an average car in an absolute perfect vacuum. What I am wondering is, that if you were to reach a certain speed, and stop applying energy to this imagined spaceship, would the spaceship...

Einstein's synchrony convention (ESC) defines the one-way speed of light as equal to the roundtrip speed IN A VACUUM, at least, the discussions and papers I read on it (even Einstein's 1905 paper) always seem to set the context as in space (a near vacuum) or in a (theoretical) vacuum. I'm...

Generally speaking, when a simple contraction occurs there is a contraction point. Length contraction in special relativity appears to be a simple contraction, and hence there should be a contraction point. Where is this contraction point located?

As per special theory of relativity, no inertial reference frame is special! If a spaceship is moving at 100 m/s, no one can conduct an experiment to determine whether it is moving at 100 m/s or the rest of the universe is moving to the opposite direction at -100 m/s, if I understand the...

I am trying to answer exercise 5 but I am not sure I understand what the hint is implying, differentiate with respect to ##p_\alpha## and ##p_\beta##, I have done this but nothing is clicking. Also, what is the relevance of the hint "the constraint ##p^\alpha p_\alpha = m^2c^2## can be ignored...

I'm reading the online version of a book that says Rindler observer comes right into my mind when I read this. So I think the book is wrong. What do you all think? On a second guess, perhaps the author takes the view that SR is only for constant speeds in the same sense that one could say that...

Since ##\nu## is contracted, we form the scalar product of the metric and inverse metric, ##g_{\mu\nu}g^{\nu\lambda} = (\vec{e_\mu} \cdot \vec{e_\nu}) \cdot (\vec{e^\nu} \cdot \vec{e^\lambda}) = \vec{e_\mu} \cdot (\vec{e_\nu} \cdot \vec{e^\nu}) \cdot \vec{e^\lambda} = \delta^\lambda_\mu## I...

If time slows as an object increases velocity wouldn't that indicate that time is object specific? And if the speed of light is a constant and does not change regardless of the velocity of an object wouldn't that indicate that time used to measure the speed of light changes? The video I have...

first off hi all. Just joined, i was looking for someone to help me understand time dilation and spatial contraction in relativity. its not homework just something i was watching, very good btw, but left me with some contradictory information as i see it. if anyone with any level of expertise at...

Ok, I hope someone can help me see how to sort this out. Alice has a full-frame (no rolling shutter) video camera that records exactly 30 frames per second. It's mounted to a telescope looking far out into space. Bob is out there in space with a digital clock that reads out to the millisecond...

I have read many GR books and many posts regarding the title of this post, but despite that, I still feel the need to clarify some things. Based on my understanding, the contravariant component of a vector transforms as, ##A'^\mu = [L]^\mu~ _\nu A^\nu## the covariant component of a vector...

What is the difference between special relativity and the Lorentz transformation? Aren't they basically the same thing? Also, I was wondering what about matter makes spacetime curve?

Since it is stated that ##E'_x = E_x##, I am going to set a special case where ##z' = z = 0##, ##E_x## in (5.10) reduces to, ##E_x = \frac{1}{4 \pi \epsilon_0}\frac{Q}{x^2}## However, ##E'_x## in (5.13) reduces to, ##E'_x = \frac{1}{4 \pi \epsilon_0}\frac{Q}{\gamma^2 x'^2}## There is an...

So, here's an attempted solution: With ##r_{min}##, $$r_{min} = \frac{1}{B + \frac{\beta}{\alpha^2}}$$ With ##r_{max}##, I get: $$r_{max} = \frac{1}{B - \frac{\beta}{\alpha^2}}$$ or $$r_{max} = \frac{1}{\frac{\beta}{\alpha^2}}$$ Other than this, I and the team have absolutely no idea on how...

Show that, according to relativistic physics, the final velocity ##v## of a rocket accelerated by its rocket motor in empty space is given by ##\frac{M_i}{M} = \Big ( \frac{c+v}{c-v} \Big) ^ \frac{c}{2 v_{ex}}## where ##M_i## is the initial mass of the rocket at launch (including the fuel)...

Below, I have already solved - I assume - correctly for question 1. Question 2, I am nearing to what I believe is the solution. Question 3, I simply have no idea where I should begin considering that it is interconnected with question 2. With that said, below is the lengthy and somewhat tedious...

Hey guys, My question is a bit confusing: When we observe a train moving close to the speed of light, passing by the platform, according to the frame of reference in the platform, the clocks in the train are ticking slower than the clocks in the platform itself. According to the frame of...

I'm struggling to get the hang of killing vectors. I ran across a statement that said energy in special relativity with respect to a time translation Killing field ##\xi^{a}## is: $$E = -P_a\xi^{a}$$ What exactly does that mean? Can someone clarify to me?

To begin with, I posted this thread ahead of time simply because I thought it may provide me some insight on how to solve for another problem that I have previously posted here: https://www.physicsforums.com/threads/special-relativity-test-particle-inside-suns-gravitational-field.983171/unread...

Below is an attempted solution based off of another user's work on StackExchange: Source: [https://physics.stackexchange.com/questions/525169/special-relativity-test-particle-inside-the-suns-gravitational-field/525212#525212] To begin with, I will be using the following equation mentioned in...

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...