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 travelling 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...
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...
This example is worked out in the book, and at the beginning, they make the assumption that the muon is travelling 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...
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...
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...
Is there a general method to determine what geometry some line element is describing? I realise 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, 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...
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...
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...
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'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...
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...
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) =...