There are two inertial reference frames F0 and F1 with relative velocity along the x-axis of V = c*sqrt(3)/2. In F0 there is a clock at rest in F0 at x=A and another clock at rest in F0 at x=B separated a distance of 10*sqrt(3)/2 light-years. There is a clock in F1 that travels from A to B. When this F1 clock passes A, the F0 clocks read zero and the clock in F1 reads zero as it passes clock A. When the F1 clock arrives at B, clock B in F0 reads 10 years, and per Einstein the clock in F1 reads 5 years.
Now let's add an accelerating clock to this scenario. When the F1 clock is at A, a clock that is initially at rest in F0 with time shown as zero starts accelerating at a constant rate (as measured in F0) toward B. The acceleration rate is such that this clock and the F1 clock arrive at B simultaneously.
Observers in F0 say the accelerating clock was always running at a slower rate then the clocks in F0. Observers in F1 say except for one instant of time, the accelerating clock was always running slower than the F1 clock. This implies that an observer accelerating along with the accelerating clock observes that the F1 clock is running faster than the accelerating clock.
Is that correct? So if clocks have a relative velocity in two inertial frames then each frame says the other frame's clock is running at slower rate. But if a clock is accelerating then that clock's rate is slower instead of faster than an inertial frame's clock, except for one instant of time. Correct?
Thanks,
David Seppala
Bastrop Tx

On Monday, March 6, 2023 at 9:12:09 AM UTC-8, sep...@yahoo.com wrote:
> Now let's add an accelerating clock to this scenario. When the F1 clock is at A, a clock that is initially at rest in F0 with time shown as zero starts accelerating at a constant rate (as measured in F0) toward B. The acceleration rate is such that this clock and the F1 clock arrive at B simultaneously.

That's impossible, because the accelerating clock would be moving at sqrt(3)c when it reaches B. Do you understand this?

More importantly, did you understand the answer to your previous question? And the one before that? And...

On Monday, March 6, 2023 at 12:12:55 PM UTC-6, Trevor Lange wrote:
> On Monday, March 6, 2023 at 9:12:09 AM UTC-8, sep...@yahoo.com wrote:
> > Now let's add an accelerating clock to this scenario. When the F1 clock is at A, a clock that is initially at rest in F0 with time shown as zero starts accelerating at a constant rate (as measured in F0) toward B. The acceleration rate is such that this clock and the F1 clock arrive at B simultaneously.
> That's impossible, because the accelerating clock would be moving at sqrt(3)c when it reaches B. Do you understand this?
>
> More importantly, did you understand the answer to your previous question? And the one before that? And...
Okay,
Let's say the velocities are lower for the clock in F1 and the accelerating clock. When the two clocks meet, why does the accelerating clock show that less time has elapsed?
Thanks,
David Seppala
Bastrop TX

On Monday, March 6, 2023 at 3:07:20 PM UTC-8, sep...@yahoo.com wrote:
> Let's say the velocities are lower for the clock in F1 and the accelerating clock.
> When the two clocks meet, why does the accelerating clock show that less time
> has elapsed?

That's the result of what's called relativistic time dilation. Here are your actual questions:

> Observers in F1 say except for one instant of time, the accelerating clock
> was always running slower than the F1 clock.

In terms of the standard inertial coordinate system S1, the rate of the accelerating clock (except for the instant when it is at rest in S1) is less than the rate of the clock that is constantly at rest in S1.

> This implies that an observer accelerating along with the accelerating clock
> observes that the F1 clock is running faster than the accelerating clock.
> Is that correct?

That's a garbled and ambiguous statement. In terms of the standard inertial coordinate system in which the accelerating clock is momentarily at rest at any given instant, the clock at rest in S1 is running slow. However, the accelerating clock is not continuously at rest in any standard inertial coordinate system, it is continuously accelerating, and if we map its events to the events of the clock at rest in S1 along the temporal slices of the sequence of inertial coordinates in which the accelerating clock is at rest, then between two given intersecting events the clock at rest in S1 is advancing net faster than the accelerating clock. We can quantify these statement precisely. You see, talking about what "observers observe" is hopelessly ambiguous; you must be much more precise and explicit to accurately express the objective facts of the situation.

> So if clocks have a relative velocity in two inertial frames then each frame says the
> other frame's clock is running at slower rate.

Frames don't say anything. Given two relatively moving clocks, each clock runs slow in terms of the standard inertial coordinates in which the other clock is at rest.

> But if a clock is accelerating then that clock's rate is slower instead of
> faster than an inertial frame's clock, except for one instant of time. Correct?

Again, that's garbled and ambiguous. Regardless of acceleration, given two relatively moving clocks, each clock runs slow in terms of the standard inertial coordinates in which the other clock is momentarily at rest. Now, maybe you are trying to ask this: Is it true that, given two clocks in flat spacetime moving from event E1 to event E2, one along an inertial path and one along an accelerating path, the clock that follows the inertial path has the greater elapsed proper time? The answer to that question is yes. Any other qustions?

On Tuesday, 7 March 2023 at 01:55:18 UTC+1, Trevor Lange wrote:
> On Monday, March 6, 2023 at 3:07:20 PM UTC-8, sep...@yahoo.com wrote:
> > Let's say the velocities are lower for the clock in F1 and the accelerating clock.
> > When the two clocks meet, why does the accelerating clock show that less time
> > has elapsed?
> That's the result of what's called relativistic time dilation.

And is just some pure bullshit - as anyone can check in GPS.