On Mon, Dec 24, 2018 at 4:03 PM Jason Resch <[email protected]> wrote:
> On Sun, Dec 23, 2018 at 11:06 PM Brent Meeker <[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. 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.
