On Saturday, 4 March 2023 at 18:42:35 UTC+1, mitchr...@gmail.com wrote:
> On Friday, March 3, 2023 at 4:43:17 PM UTC-8, Mike Fontenot wrote:
> > On 3/3/23 12:37 PM, Tom Roberts wrote:
> > > On 3/2/23 9:51 AM, Mike Fontenot wrote:
> > >> in his 1907 paper. [Einstein] said that, according to the
> > >> accelerating observers, both clocks have the same acceleration, and
> > >> the clocks have a constant separation.
> > >
> > > Just because Einstein said something does not mean it is true. In this
> > > case, he was writing before many of the details about SR were known.
> > >
> > > TODAY we know that it is not possible for two objects separated
> > > spatially and accelerating along the line between them to have both
> > > equal proper accelerations and constant proper separation.
> > >
> > I realized this morning that I was wrong about the separation being
> > constant ... the separation increases with time. (I had a diagram
> > showing that behavior, tacked up on the wall over my desk, that I had
> > produced probably about 20 years ago.) That's good, because it still
> > results in the exponential equation being infinite for instantaneous
> > velocity changes ... i.e., it doesn't change my conclusion that the
> > exponential equation is wrong.
> >
> > Whether or not I can still derive a replacement equation is unknown, but
> > I'm cautiously optimistic. I won't have much time to work on it,
> > though, until tax-prep time is over.
> Time dilation for gravity comes from its strength

No, it comes from some imagination of
some brainwashed morons, Time is what
clocks indicate, and, as anyone can test in
GPS, what clocks indicate is t'=t.

On Tuesday, February 28, 2023 at 4:13:19 PM UTC-8, Mike Fontenot wrote:
> On 2/28/23 4:07 PM, JanPB wrote:
> >
> > It is the conclusion of observers who are undergoing the acceleration.
> > What makes you think it's not?
> >
> Because it is the conclusion of inertial observers, and inertial
> observers don't agree with accelerating observers.

They both necessarily agree whether a taut rope needs unwinding
or not. Equivalently: they both necessarily agree whether a taut rope
eventually breaks or not if it's not being unwound.

--
Jan

On Wednesday, March 1, 2023 at 10:32:25 AM UTC-8, Mike Fontenot wrote:
> On 3/1/23 11:04 AM, Tom Roberts wrote:
>
> >
> > Not true. Proper distance and proper acceleration are both invariant. So
> > the above is the conclusion of ALL observers.
> >
> > I repeat: for the case of equal proper accelerations, see the Bell
> > spaceship paradox -- it shows that the proper distance between the
> > spaceships is increasing (not constant as you fantasize).
> >
> Inertial observers and accelerating observers do NOT agree about the
> acceleration of the clocks, or about the separation of the clocks.

They agree about the actual separations (proper distances) and the
actual behaviour of, say, a rope pulled taut between the spaceships.

This is not an observer-dependent thing.

--
Jan

On Thursday, March 2, 2023 at 7:51:48 AM UTC-8, Mike Fontenot wrote:
> On 3/1/23 3:27 PM, RichD wrote:
> >
> > He doesn't understand hyperbolic motion in the Minkowski plane.
> > He believes, because they undergo identical accelerations, hence
> > identical speed profiles, they maintain constant separation.
> >
> > It's a case where common sense physics fails.
> >
> Then common sense failed for Einstein also, in his 1907 paper. HE said
> that, according to the accelerating observers, both clocks have the same
> acceleration, and the clocks have a constant separation.

The clocks do have constant separation in terms of the original
inertial system at rest. But the proper distance (which is an
observer-independent quantity) between the spaceships increases.
So a rope pulled taut between them will eventually break.
According to the original inertial system at rest this happens
because the rope Lorentz-contracts.

--
Jan

On Thursday, March 2, 2023 at 8:44:02 AM UTC-8, Mike Fontenot wrote:
> On 3/1/23 11:53 AM, Tom Roberts wrote:
> > On 3/1/23 12:22 PM, Mike Fontenot wrote:
> >> Given that every piece of mass is accelerating at exactly the same
> >> rate, there is no way that the separation between clocks can vary with
> >> time.
> >
> > While true in Newtonian physics, this is FALSE in Special Relativity.
> >
> No, it is not false in special relativity.
>
> It IS false, according to INERTIAL observers observing accelerating
> clocks (see Wiki: "Bell's spaceship paradox").

Your terminology is vague. Here is how SR models the situation:

1. according to the original inertial system at rest (call it S1), the
distance between the spaceships remains constant and a rope
between them eventually breaks because it Lorentz-contracts,

2. according to BOTH the rear/trailing (say) accelerated observer
sitting inside the spaceship (S2) AND an inertial observer momentarily
co-moving with him (S3), the rope breaks eventually,

3. According to S1, S2, and S3, the proper distance between the
spaceships increases and the rope breaks.

> But it is TRUE, according to observers accelerating with the clocks (see
> Einstein's 1907 paper:
> https://einsteinpapers.press.princeton.edu/vol2-trans/319 ).

Let's say nobody cares about papers about unfinished theories.

> Inertial observers and accelerating observers disagree about a lot of
> things. This is one of them.

If by this you mean the proper distance between the spaceships
(and not some coordinate distance which is merely a convention and
can be cooked up to be any number you want), then you are wrong.

--
Jan

On Saturday, March 4, 2023 at 11:23:16 AM UTC-8, JanPB wrote:
> On Thursday, March 2, 2023 at 8:44:02 AM UTC-8, Mike Fontenot wrote:
> > On 3/1/23 11:53 AM, Tom Roberts wrote:
> > > On 3/1/23 12:22 PM, Mike Fontenot wrote:
> > >> Given that every piece of mass is accelerating at exactly the same
> > >> rate, there is no way that the separation between clocks can vary with
> > >> time.
> > >
> > > While true in Newtonian physics, this is FALSE in Special Relativity.
> > >
> > No, it is not false in special relativity.
> >
> > It IS false, according to INERTIAL observers observing accelerating
> > clocks (see Wiki: "Bell's spaceship paradox").
> Your terminology is vague. Here is how SR models the situation:
>
> 1. according to the original inertial system at rest (call it S1), the
> distance between the spaceships remains constant and a rope
> between them eventually breaks because it Lorentz-contracts,
>
> 2. according to BOTH the rear/trailing (say) accelerated observer
> sitting inside the spaceship (S2) AND an inertial observer momentarily
> co-moving with him (S3), the rope breaks eventually,
>
> 3. According to S1, S2, and S3, the proper distance between the
> spaceships increases and the rope breaks.
> > But it is TRUE, according to observers accelerating with the clocks (see
> > Einstein's 1907 paper:
> > https://einsteinpapers.press.princeton.edu/vol2-trans/319 ).
> Let's say nobody cares about papers about unfinished theories.
> > Inertial observers and accelerating observers disagree about a lot of
> > things. This is one of them.
> If by this you mean the proper distance between the spaceships
> (and not some coordinate distance which is merely a convention and
> can be cooked up to be any number you want), then you are wrong.
>
> --
> Jan

SR is speed while GR is speed increase.
Their duality comes together through speed.
They are not mutually exclusive. They come
together as they are both based on speed.

On March 3, Tom Roberts wrote:
> No observers disagree that with equal proper accelerations the PROPER
> separation is not constant but increasing. For the simple reason that
> such proper quantities are invariant

How would the trailer measure the distance to the leader?

He could try radar echo ranging, but this is complicated by the fact
that he's in a state of acceleration. Thus the light waves are
effectively falling through a G field, hence the locality condition isn't
satisfied, and the usual presumption of a known constant speed
isn't reliable.

Furthermore, he's moving toward the leader during the light
transmission. That is, we're told he's accelerating; but he doesn't
know that, he figures he might be stationary in a constant G field.

So it's complicated -

--
Rich

On Sunday, March 5, 2023 at 3:11:20 PM UTC-8, RichD wrote:
> the usual presumption of a known constant speed isn't reliable.
>

You don't know what you are talking about, proper speed of light is c in a gravitational field. in an accelerated frame, etc. Always.

> Furthermore, he's moving toward the leader during the light
> transmission. That is, we're told he's accelerating; but he doesn't
> know that, he figures he might be stationary in a constant G field.
>
> So it's complicated -
>
Only for cranks

On Sunday, March 5, 2023 at 3:11:20 PM UTC-8, RichD wrote:
> On March 3, Tom Roberts wrote:
> > No observers disagree that with equal proper accelerations the PROPER
> > separation is not constant but increasing. For the simple reason that
> > such proper quantities are invariant
> How would the trailer measure the distance to the leader?

By pulling a rope taut between them.

--
Jan

On Monday, 6 March 2023 at 04:51:36 UTC+1, JanPB wrote:
> On Sunday, March 5, 2023 at 3:11:20 PM UTC-8, RichD wrote:
> > On March 3, Tom Roberts wrote:
> > > No observers disagree that with equal proper accelerations the PROPER
> > > separation is not constant but increasing. For the simple reason that
> > > such proper quantities are invariant
> > How would the trailer measure the distance to the leader?
> By pulling a rope taut between them.

Which century do you live, poor halfbrain?