From: *Jason Resch* <[email protected] <mailto:[email protected]>>
On Mon, Dec 24, 2018 at 4:24 PM Bruce Kellett <[email protected] <mailto:[email protected]>> wrote:On Tue, Dec 25, 2018 at 4:59 AM Jason Resch <[email protected] <mailto:[email protected]>> wrote: On Mon, Dec 24, 2018 at 12:30 AM Bruce Kellett <[email protected] <mailto:[email protected]>> wrote: On Mon, Dec 24, 2018 at 4:03 PM Jason Resch <[email protected] <mailto:[email protected]>> wrote: On Sun, Dec 23, 2018 at 11:06 PM Brent Meeker <[email protected] <mailto:[email protected]>> wrote: On 12/23/2018 7:17 PM, Jason Resch wrote: > > How can this be? The rocket is a rigid structure, the front and rear > clocks accelerate at the same rate. First, there are no rigid objects in relativity theory. Otherwise they could be used for FTL signaling. Second, there is no simultaneity at different places, like the front and rear of the rocket. So it is frame dependent whether the two ends of the rocket begin to accelerate at the same time. The level of clock desynchronization is proportional to the speed and the length of the rocket. That it is one rocket doesn't even matter, it could be two rockets, which both separately accelerate at the same time given by a signal initiated from immediately between them. This is just showing that length contraction is only a spatial length contraction. The length through space time is constant, but when moving through space, an object's length will partially extend through space and partially extend through time. To the extent that an object's length contracts you will see a corresponding increase in the reach through time. (this is unrelated to acceleration effects, or rigidness). If it were related to rigidness, then the effect would disappear with the two separate rockets, but it doesn't. Similarly, if it were related to acceleration rates, rather than absolute velocity, it would be unrelated to the distance separating the clocks but it's not. Here is an example of what I am talking about, just to be clear. If a 100 meter rocket accelerates to 80% of c, then it will length contract to 60 meters, but will also extend 80 meters through the dimension of time. The total length remains 100 meters (0.6^2 + 0.8^2 = 1). However, clocks that were initially synchronized between the fore and aft parts of the rocket are separated by (80 meters / c) = 266.85 nanoseconds. If you take the clock from the front to the back you will see it speed up and resynchronize with the clock in the back when brought into proximity with the clock in the rear, likewise if you bring the clock from the rear towards the front it will slow until it resynchronizes with the clock in the front by the time it is brought into proximity with it. You are carrying the clock through the time dimension as you move it towards the front or back of the ship. I don't understand this. If the two clocks are moving at the same velocity there is no difference in clock rate between them. That's why I thought you were talking about the acceleration phase -- clock rates can differ then, but if the two clocks are at either end of the rocket moving inertially, and at rest wrt each other, then their rates are the same, regardless of the distance apart. As seen by someone who perceives the rocket to be length contracted, the clocks will not appear to be in sync. That is factually wrong. The special relativistic apparent change in clock rates depends only on the relative motion, so from the point of view of someone at rest on the ground, the clocks at the front and rear of the coasting rocket will be travelling at the same velocity relative to him. So they will both appear to be going either faster or slower at exactly the same rate, depending on the direction of the relative motion.Then what is the meaning of this problem on page 42: https://www.relativity.li/uploads/pdf/English/Epstein_en.pdfTwo rockets fly past each other at 0.6 • c. A measures the length of the other rocket B to be 40 m. What is the rest length of the rocket B, and how much are the clocks at the tip and at the end of rocket B for A desynchronized, given that they are synchronized for B? And which of the two clocks is running fast for A?More details: http://galileoandeinstein.physics.virginia.edu/lectures/synchronizing.html
I have not read Epstein. I know that some people think highly of this book as a teaching aid, but Epstein's diagrammatic methods are good only in so far as they agree with the correct Lorentz transformations. For your example of clocks as the front and rear of the rocket, the Lorentz formulae for time dilation depend only on the relative velocity of clock and observer, not on the distance to the clock So the clocks at the front and rear of the rocket run at the same rate relative to the ground observer -- both run more slowly if the rocket is receding. The problem posed in the example you give relates to the desynchronization of the clocks as seen from the ground when they are synchronized on the moving rocket. The clocks will always run (and appear to run) at the same rate, but their synchronization will depend on the method used.
So, to go back to your earlier point, from the point of view inside the rocket, the clocks will not appear to slow down or speed up as they are brought together -- they will always keep the same rate. If they are synchronized by a signal from the centre of the moving rocket, they will remain synchronized as they are brought together. However, from the point of view of the ground based observer, they were never synchronized, even though they run at the same rate. To bring them together requires moving the clocks at greater (or less) than the velocity of the rocket, and that will induce a differential clock rate, so they ultimately agree when together.
Your second reference explains this quite well. Bruce -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
