On Mon, Dec 24, 2018 at 12:30 AM Bruce Kellett <[email protected]> wrote:
> 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. > > As seen by someone who perceives the rocket to be length contracted, the clocks will not appear to be in sync. Jason -- 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.
