Neil Ashby's https://www.researchgate.net/publication/26386594_Relativity_in_the_Global_Positioning_System gives an excellent account of the relativistic corrections made in the GPS system.
The correction for the Sagnac Effect is amusing. The design team accepted the Sagnac Effect and designed...
Read further and you will see how the third term in Eqn 28.3 evaluates to Eqn 28.6 where you see the 1/r term.
See the footnote in Vol 2, Chap 21
As an aside, I often find it useful not to worry too much if, on my first reading, I don't understand the full detail of something. I find it...
Imagine throwing a ball to a person 5 feet away. The ball rises 4 feet and the total flight time is 1 second.
Viewed in space, the ball travels in a parabola, rising 4 feet and traveling 5 feet horizontally.
But viewed in spacetime you need to add in a time axis and the distance between the...
I have long since forgotten so cannot give you a simple answer. But a hint of what to look for may help.
You need to be searching (internet, wiki etc) for far field as opposed to near field.
It is the far field which allows radio waves to propagate vast distances with enough signal strength...
The point I was trying to make with my 1 million observers is that it isn't the clock itself which ticks slower. It is the moving observer(s) who measure the clock to tick slower. If 1 million observers each measure the clock to tick at 1 million different rates then it cannot be the clock...
OK - let's remove that potential confusion.
Imagine there are 1 million observers who are all traveling at different speeds. They arrange things so that they all arrive together at the clock's location when the clock shows 12 o'clock.
Every observer is at the same place at the same time...
I really dislike the phrase "a moving clock runs slow" because I find it ambiguous and, arguable, incorrect.
Why? Because you need to specify who is observing the clock so as to remove the ambiguity. I prefer the phrasing "If a clock is moving relative to an observer that observer measures it...
In the thread Twin paradox not including accelerations, it is wrong where? Andrew Kirk, a Science Advisor, Homework Helper, Insights Author and Gold Member states something identical to my assertion, namely (my underlines):
If, as in the twin paradox, the acceleration causes a change in speed then this does does affect the clock rate.
I think therefore your statement is both incorrect and very misleading.
99% of the explanations of the twin paradox say "It is caused by the fact that the traveling twin...
Thank you.
I have discovered The Equation of Motion in Rindler Space
Consider a frame traveling at velocity v relative to a fixed frame, and at (local) acceleration a as depicted by the top pair of frames below.
We can instead consider this moving frame to be at rest relative to the...
It is one which I thought was in general use so I am very surprised by those who appear never to have heard of it or recommend it not be used. All here seems to cite wiki as their authority so I shall too. See Special relativity and go to Measurement versus visual appearance to find (my...
The key point to take away from the twin paradox is that the time difference is due to the moving twin's change of frame.
The acceleration is essentially irrelevant except for the fact that the moving twin must decelerate and accelerate so that they can change their frame.
You can easily set...
I used the word observe advisedly in distinction to see. Observe includes the calculation.
If I see a light 186,000 miles away flash at exactly noon, I observe that it flashed a second before noon.
And Doppler affects only the perceived frequency not the speed.
I am trying to learn about Rindler coordinates and would appreciate if you could point to a good introduction to them.
Are they in some way similar to rotating coordinates? By that I mean do we rewrite things like the Lorenz equations to take account of the acceleration as different rates of...
This is a translation of Einstein's 1905 paper On the electrodynamics of moving bodies.
As you see he restricted himself to inertial frames throughout. The two principles on which his theory were based are:
1. The laws by which the states of physical systems undergo change are not
affected...
See the space-time diagram below.
The Twin Paradox
One twin stays on earth.
One twin leaves Earth at high speed (0.4142c), travels for 5 Earth years, and then returns.
The stay-at-home twin says that 10 years have elapsed since the traveller left.
The traveller says only 9...
That is wrong.
Special Relativity deals with things where the observer is not accelerating. ie the observer is in an inertial frame.
Objects the observer measures can be accelerating.
Remember, paradox means apparently wrong until the explanation is given showing it is actually correct.
The...
The speed of light may be thought of as the "conversion factor between distance and time".
If we take the speed of light to be 3 x 10^8 metres/second this means that in spacetime, 3 x 10^8 metres of distance is equal to 1 second of time.
I attach below pages 5, 6 and 7 from The Los Alamos Primer which describe how the Los Alamos Project calculated an estimated yield for the weapons they were inventing based on the release of the electrostatic energy stored in the nucleus when it is assembled from its constituent protons...
I always like to think about it like this.
Do an experiment to measure some fundamental constants.
1. Measure the permittivity of free space in a vacuum (also called the electric constant) - it is epsilon-nought, 8.854 x 10^-12 F/m
2. Measure the permeability of free space in a vacuum (also...