1. Three clocks A, B and O are co-located in one spot.
2. Synchronize them.
3. Physically measure a distance L from O in the opposite directions
4. Send A and B in the opposite directions at equal speed mechanically and stop them at distance L away from O.
5 Measure the one-way speed of light as follows:
-- One-way speed of light between O and A.
--One-way speed of light between O and B then
If Einstein's P2 is correct then
The one-way speed of light between OA = The one-way speed of light between OB.
If Einstein's P2 is wrong then
The one-way speed of light between OB =/ The one-way speed of light between OA..

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 10-Sept-23 5:27 am, Ken Seto wrote:

1. Three clocks A, B and O are co-located in one spot.
2. Synchronize them.
3. Physically measure a distance L from O in the opposite directions
4. Send A and B in the opposite directions at equal speed mechanically and stop them at distance L away from O.
5 Measure the one-way speed of light as follows:
-- One-way speed of light between O and A.
--One-way speed of light between O and B then
If Einstein's P2 is correct then
The one-way speed of light between OA = The one-way speed of light between OB.
If Einstein's P2 is wrong then
The one-way speed of light between OB =/ The one-way speed of light between OA..

Measuring the one way speed of light requires a model of space time, but
in your proposed experiment you can avoid that just be appealing to
symmetry instead.

I suggest you spend the required amount of money to test this. No one
else is going to do it for you.

Sylvia.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Saturday, September 9, 2023 at 12:27:06 PM UTC-7, Ken Seto wrote:

1. Three clocks A, B and O are co-located in one spot.
2. Synchronize them.
3. Physically measure a distance L from O in the opposite directions
4. Send A and B in the opposite directions at equal speed mechanically and stop them at distance L away from O.
5 Measure the one-way speed of light as follows:
-- One-way speed of light between O and A.
--One-way speed of light between O and B then
If Einstein's P2 is correct then
The one-way speed of light between OA = The one-way speed of light between OB.
If Einstein's P2 is wrong then
The one-way speed of light between OB =/ The one-way speed of light between OA..

The second postulate is not a claim the one-way speed is c. It claims the velocity is "independent of the source velocity." In your experiment, everyone agrees it would be c for both. It is only a claim the one-way speed is c regardless of source
velocity. Your source and sinks are not moving. One-way speed of light is directly observed by the Doppler shift and, in Roemer's measure, by the moon of Jupiter.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Saturday, September 9, 2023 at 8:40:10 PM UTC-7, Laurence Clark Crossen wrote:

On Saturday, September 9, 2023 at 12:27:06 PM UTC-7, Ken Seto wrote:

1. Three clocks A, B and O are co-located in one spot.
2. Synchronize them.
3. Physically measure a distance L from O in the opposite directions
4. Send A and B in the opposite directions at equal speed mechanically and stop them at distance L away from O.
5 Measure the one-way speed of light as follows:
-- One-way speed of light between O and A.
--One-way speed of light between O and B then
If Einstein's P2 is correct then
The one-way speed of light between OA = The one-way speed of light between OB.
If Einstein's P2 is wrong then
The one-way speed of light between OB =/ The one-way speed of light between OA..

The second postulate is not a claim the one-way speed is c.

Really?

https://en.wikipedia.org/wiki/Postulates_of_special_relativity

"2. Second postulate (invariance of c)

As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body. Or: the speed of light in free space has the same value c in all
inertial frames of reference."

... One-way speed of light is directly observed by the Doppler shift...

Really?

You cannot measure the speed of light using the Doppler shift, that only tells you about the change in both frequency and wavelength as you observe light from a moving source. The speed of light remains c, a constant... as proclaimed in the second
postulate.

This is high-school freshman stuff, first week in the course. Apparently you either have never taken a course in physics or you have forgotten everything that was taught to you. Read a dang textbook and quit embarrassing yourself with rank beginner
mistakes!

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Sunday, 10 September 2023 at 06:25:15 UTC+2, Paul Alsing wrote:

On Saturday, September 9, 2023 at 8:40:10 PM UTC-7, Laurence Clark Crossen wrote:

On Saturday, September 9, 2023 at 12:27:06 PM UTC-7, Ken Seto wrote:

1. Three clocks A, B and O are co-located in one spot.
2. Synchronize them.
3. Physically measure a distance L from O in the opposite directions
4. Send A and B in the opposite directions at equal speed mechanically and stop them at distance L away from O.
5 Measure the one-way speed of light as follows:
-- One-way speed of light between O and A.
--One-way speed of light between O and B then
If Einstein's P2 is correct then
The one-way speed of light between OA = The one-way speed of light between OB.
If Einstein's P2 is wrong then
The one-way speed of light between OB =/ The one-way speed of light between OA..

The second postulate is not a claim the one-way speed is c.

Really?

https://en.wikipedia.org/wiki/Postulates_of_special_relativity

"2. Second postulate (invariance of c)

As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body. Or: the speed of light in free space has the same value c in all

inertial frames of reference."

Most of your fellow idiots are denying that. Well,
nobody should expect a bunch of fanatic clowns
to be able to detemine a common version of
anything.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Saturday, September 9, 2023 at 12:27:06 PM UTC-7, Ken Seto wrote:

1. Three clocks A, B and O are co-located in one spot.
2. Synchronize them.
3. Physically measure a distance L from O in the opposite directions
4. Send A and B in the opposite directions at equal speed mechanically and stop them at distance L away from O.
5 Measure the one-way speed of light as follows:
-- One-way speed of light between O and A.
--One-way speed of light between O and B then
If Einstein's P2 is correct then
The one-way speed of light between OA = The one-way speed of light between OB.
If Einstein's P2 is wrong then
The one-way speed of light between OB =/ The one-way speed of light between OA..

There is no way to measure light speed because the measuring device is never at rest and we do not know its motion in the unmarked.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 11-Sept-23 11:51 am, mitchr...@gmail.com wrote:

On Saturday, September 9, 2023 at 12:27:06 PM UTC-7, Ken Seto wrote:

1. Three clocks A, B and O are co-located in one spot.
2. Synchronize them.
3. Physically measure a distance L from O in the opposite directions
4. Send A and B in the opposite directions at equal speed mechanically and stop them at distance L away from O.
5 Measure the one-way speed of light as follows:
-- One-way speed of light between O and A.
--One-way speed of light between O and B then
If Einstein's P2 is correct then
The one-way speed of light between OA = The one-way speed of light between OB.
If Einstein's P2 is wrong then
The one-way speed of light between OB =/ The one-way speed of light between OA..

There is no way to measure light speed because the measuring device is never at
rest and we do not know its motion in the unmarked.

We can measure the speed relative to the measuring device.

Sylvia

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Monday, 11 September 2023 at 08:29:04 UTC+2, Sylvia Else wrote:

On 11-Sept-23 11:51 am, mitchr...@gmail.com wrote:

On Saturday, September 9, 2023 at 12:27:06 PM UTC-7, Ken Seto wrote:

1. Three clocks A, B and O are co-located in one spot.
2. Synchronize them.
3. Physically measure a distance L from O in the opposite directions
4. Send A and B in the opposite directions at equal speed mechanically and stop them at distance L away from O.
5 Measure the one-way speed of light as follows:
-- One-way speed of light between O and A.
--One-way speed of light between O and B then
If Einstein's P2 is correct then
The one-way speed of light between OA = The one-way speed of light between OB.
If Einstein's P2 is wrong then
The one-way speed of light between OB =/ The one-way speed of light between OA..

There is no way to measure light speed because the measuring device is never at
rest and we do not know its motion in the unmarked.

We can measure the speed relative to the measuring device.

And You can't ever comprehend that Your precious
measurements are just repeaters of Your insane
postulates.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Sylvia Else <sylvia@email.invalid> wrote:

On 11-Sept-23 11:51 am, mitchr...@gmail.com wrote:

On Saturday, September 9, 2023 at 12:27:06?PM UTC-7, Ken Seto wrote:

1. Three clocks A, B and O are co-located in one spot.
2. Synchronize them.
3. Physically measure a distance L from O in the opposite directions
4. Send A and B in the opposite directions at equal speed mechanically and

stop them at distance L away from O.

5 Measure the one-way speed of light as follows:
-- One-way speed of light between O and A.
--One-way speed of light between O and B then
If Einstein's P2 is correct then
The one-way speed of light between OA = The one-way speed of light
between OB. If Einstein's P2 is wrong then The one-way speed of light
between OB =/ The one-way speed of light between OA..

There is no way to measure light speed because the measuring device is never at rest and we do not know its motion in the unmarked.

We can measure the speed relative to the measuring device.

Actually the speed of light isn't measured that way anymore.
And it wasn't, before it was fixed by definition.
Precision measurements of the speed of light were done,
when they could still be done, on standing waves,
that is, in a cavity, or between mirrors.

If you analyse what those measurements were actually doing
you'll see that what was actually done in those measurements
was to establish a ratio of units. [1]
(the second from an atomic clock, the meter from a Krypton line)

When it was found that this ratio could be measured more accurately
than the length unit could be realised in practice
the ratio c was defined, and the length unit was abolished.
(as a fundamental unit of the SI)

You should realise that all this pottering about with flashlights,
clocks and trains and rulers is for didactic purposes only.
No one ever mounted a light speed measuring apparatus
on a railway carriage.

It is make believe physics, for didactic purposes,
good only for those who feel a philosophical need
to believe that relativity can be derived from experiments. [2]
(or at least could have been derived, in principle)
It can't, a postulate of some kind is needed.
And yes, it took someone of Einstein's genius to see it,

Jan

[1] The same kind of experiments are still being done,
and they still do the same kind of thing.
(with ever increasing precision)
Only the name of those experiments has changed.
Nowadays we call it a calibration of a (secondary) meter standard,
or the determination of the (absolute) frequency of a light source.

[2] Mostly naive empirists, positivists, or worse, neo-positivists.
Maybe you should try your hand at naive Popperianism for a while.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Monday, 11 September 2023 at 11:47:51 UTC+2, J. J. Lodder wrote:

When it was found that this ratio could be measured more accurately
than the length unit could be realised in practice
the ratio c was defined, and the length unit was abolished.
(as a fundamental unit of the SI)

Noone cares about your moronic SI, unfortunately,
anyone can check GPS - their ideological madness
is useless and ignored when it comes to serious
measurements.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Sunday, September 10, 2023 at 12:25:15 AM UTC-4, Paul Alsing wrote:

On Saturday, September 9, 2023 at 8:40:10 PM UTC-7, Laurence Clark Crossen wrote:

On Saturday, September 9, 2023 at 12:27:06 PM UTC-7, Ken Seto wrote:

1. Three clocks A, B and O are co-located in one spot.
2. Synchronize them.
3. Physically measure a distance L from O in the opposite directions
4. Send A and B in the opposite directions at equal speed mechanically and stop them at distance L away from O.
5 Measure the one-way speed of light as follows:
-- One-way speed of light between O and A.
--One-way speed of light between O and B then
If Einstein's P2 is correct then
The one-way speed of light between OA = The one-way speed of light between OB.
If Einstein's P2 is wrong then
The one-way speed of light between OB =/ The one-way speed of light between OA..

The second postulate is not a claim the one-way speed is c.

Really? Does it claims that the one-way speed of of light is isotropic in all frames???

Really?

https://en.wikipedia.org/wiki/Postulates_of_special_relativity

"2. Second postulate (invariance of c)

As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body. Or: the speed of light in free space has the same value c in all

inertial frames of reference."

... One-way speed of light is directly observed by the Doppler shift...

Really?

You cannot measure the speed of light using the Doppler shift, that only tells you about the change in both frequency and wavelength as you observe light from a moving source. The speed of light remains c, a constant... as proclaimed in the second

postulate.

This is high-school freshman stuff, first week in the course. Apparently you either have never taken a course in physics or you have forgotten everything that was taught to you. Read a dang textbook and quit embarrassing yourself with rank beginner

mistakes!

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Saturday, September 9, 2023 at 8:51:00 PM UTC-4, Sylvia Else wrote:

On 10-Sept-23 5:27 am, Ken Seto wrote:

1. Three clocks A, B and O are co-located in one spot.
2. Synchronize them.
3. Physically measure a distance L from O in the opposite directions
4. Send A and B in the opposite directions at equal speed mechanically and stop them at distance L away from O.
5 Measure the one-way speed of light as follows:
-- One-way speed of light between O and A.
--One-way speed of light between O and B then
If Einstein's P2 is correct then
The one-way speed of light between OA = The one-way speed of light between OB.
If Einstein's P2 is wrong then
The one-way speed of light between OB =/ The one-way speed of light between OA..

Measuring the one way speed of light requires a model of space time, but
in your proposed experiment you can avoid that just be appealing to
symmetry instead.

My experiment only testing the isotropy of the one-way speed of light.

I suggest you spend the required amount of money to test this. No one
else is going to do it for you.

Sylvia.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Sunday, September 10, 2023 at 11:29:04 PM UTC-7, Sylvia Else wrote:

On 11-Sept-23 11:51 am, mitchr...@gmail.com wrote:

On Saturday, September 9, 2023 at 12:27:06 PM UTC-7, Ken Seto wrote:

1. Three clocks A, B and O are co-located in one spot.
2. Synchronize them.
3. Physically measure a distance L from O in the opposite directions
4. Send A and B in the opposite directions at equal speed mechanically and stop them at distance L away from O.
5 Measure the one-way speed of light as follows:
-- One-way speed of light between O and A.
--One-way speed of light between O and B then
If Einstein's P2 is correct then
The one-way speed of light between OA = The one-way speed of light between OB.
If Einstein's P2 is wrong then
The one-way speed of light between OB =/ The one-way speed of light between OA..

There is no way to measure light speed because the measuring device is never at
rest and we do not know its motion in the unmarked.

We can measure the speed relative to the measuring device.

Sylvia

How do you measure the relative that shows it is not an absolute
order instead sylvia?

Mitchell Raemsch

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Saturday, September 9, 2023 at 11:18:15 PM UTC-7, Maciej Wozniak wrote:

On Sunday, 10 September 2023 at 06:25:15 UTC+2, Paul Alsing wrote:

On Saturday, September 9, 2023 at 8:40:10 PM UTC-7, Laurence Clark Crossen wrote:

On Saturday, September 9, 2023 at 12:27:06 PM UTC-7, Ken Seto wrote:

1. Three clocks A, B and O are co-located in one spot.
2. Synchronize them.
3. Physically measure a distance L from O in the opposite directions 4. Send A and B in the opposite directions at equal speed mechanically and stop them at distance L away from O.
5 Measure the one-way speed of light as follows:
-- One-way speed of light between O and A.
--One-way speed of light between O and B then
If Einstein's P2 is correct then
The one-way speed of light between OA = The one-way speed of light between OB.
If Einstein's P2 is wrong then
The one-way speed of light between OB =/ The one-way speed of light between OA..

The second postulate is not a claim the one-way speed is c.

Really?

https://en.wikipedia.org/wiki/Postulates_of_special_relativity

"2. Second postulate (invariance of c)

As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body. Or: the speed of light in free space has the same value c in all

inertial frames of reference."

Most of your fellow idiots are denying that. Well,
nobody should expect a bunch of fanatic clowns
to be able to detemine a common version of
anything.

Relativity is like a hydra with many heads because it is totally inconsistent nonsense.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Monday, September 11, 2023 at 2:47:51 AM UTC-7, J. J. Lodder wrote:

It is make believe physics...
to believe that relativity can be derived from experiments.
(or at least could have been derived, in principle)
It can't, a postulate of some kind is needed.

Not at all. The principles of physics, including the principle of relativity, are all derived from experience. Of course, the induction is always incomplete, e.g., in every closed system we've ever observed, momentum is conserved, but we can never
observe every closed system for all time, so when constructing a physical theory we assume the principle of momentum conservation, but this is not an arbitrary or conventional assumption, it is the most firmly of all empirically-founded propositions.
Similarly for the principle of relativity, which leaves only a single degree of freedom in the relationship between the standard inertial coordinate systems (operationally established), and that degree of freedom is fixed by any one of many empirial
facts, which unambiguously establish special relativity.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Tuesday, 12 September 2023 at 08:27:34 UTC+2, Bill wrote:

On Monday, September 11, 2023 at 2:47:51 AM UTC-7, J. J. Lodder wrote:

It is make believe physics...
to believe that relativity can be derived from experiments.
(or at least could have been derived, in principle)
It can't, a postulate of some kind is needed.

Not at all. The principles of physics, including the principle of relativity, are all derived from experience.

It's just a mad lie, and even some of your fellow idiots
are admitting it is.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 12-Sept-23 4:02 am, mitchr...@gmail.com wrote:

On Sunday, September 10, 2023 at 11:29:04 PM UTC-7, Sylvia Else wrote:

On 11-Sept-23 11:51 am, mitchr...@gmail.com wrote:

On Saturday, September 9, 2023 at 12:27:06 PM UTC-7, Ken Seto wrote:

1. Three clocks A, B and O are co-located in one spot.
2. Synchronize them.
3. Physically measure a distance L from O in the opposite directions
4. Send A and B in the opposite directions at equal speed mechanically and stop them at distance L away from O.
5 Measure the one-way speed of light as follows:
-- One-way speed of light between O and A.
--One-way speed of light between O and B then
If Einstein's P2 is correct then
The one-way speed of light between OA = The one-way speed of light between OB.
If Einstein's P2 is wrong then
The one-way speed of light between OB =/ The one-way speed of light between OA..

There is no way to measure light speed because the measuring device is never at
rest and we do not know its motion in the unmarked.

We can measure the speed relative to the measuring device.

Sylvia

How do you measure the relative that shows it is not an absolute
order instead sylvia?

Mitchell Raemsch

That's just gibberish.

Sylvia.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Monday, September 11, 2023 at 12:23:08 PM UTC-6, Laurence Clark Crossen wrote:

Relativity is like a hydra with many heads because it is totally inconsistent nonsense.

Larry-boy's version of relativity is inconsistent nonsense because he doesn't understand
the most basic things about it. Larry-boy's version of the Doppler effect is also
inconsistent nonsense because he doesn't understand it either.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Tuesday, September 12, 2023 at 2:27:34 AM UTC-4, Bill wrote:

On Monday, September 11, 2023 at 2:47:51 AM UTC-7, J. J. Lodder wrote:

It is make believe physics...
to believe that relativity can be derived from experiments.
(or at least could have been derived, in principle)
It can't, a postulate of some kind is needed.

Not at all. The principles of physics, including the principle of relativity, are all derived from experience

Not at all, The principles of physics are derived from postulates and postulates are assumed statements.
For example: P2 is an assumed statement, No one-way speed of light ever been measured.
. .>https://acrobat.adobe.com/link/track?uri=urn:aaid:scds:US:25556228-4404-3c67-b0cb-3d04d2636aaeOf course, the induction is always incomplete, e.g., in every closed system we've ever observed, momentum is conserved, but we can never observe every closed
system for all time, so when constructing a physical theory we assume the principle of momentum conservation, but this is not an arbitrary or conventional assumption, it is the most firmly of all empirically-founded propositions. Similarly for the
principle of relativity, which leaves only a single degree of freedom in the relationship between the standard inertial coordinate systems (operationally established), and that degree of freedom is fixed by any one of many empirial facts, which
unambiguously establish special relativity.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Tuesday, 12 September 2023 at 18:48:24 UTC+2, Tom Roberts wrote:

On 9/12/23 10:48 AM, Ken Seto wrote:

The principles of physics are derived from postulates and postulates
are assumed statements.

Those postulates are used for mathematical derivations of useful
equations.

It's you saying they're useful. Well, anyone can check
GPS: you're mistaken.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 9/12/23 10:48 AM, Ken Seto wrote:

The principles of physics are derived from postulates and postulates
are assumed statements.

Those postulates are used for mathematical derivations of useful
equations. The postulates are based on experience in observations and experiments. So the PHYSICS is based on experience, the MATH is based on idealizations of experience codified as postulates.

In the case of SR, we have a rich and useful theory that has been tested explicitly hundreds of times, and implicitly billions of times; it has
never been found wanting.

No one-way speed of light ever been measured.

NONSENSE! The one-way speed of light has been measured zillions of
times, subject of course to the condition of how the clocks were
synchronized, or assuming isotropy in cables. It is frequently performed
in undergraduate physics labs.

[This is no different in principle from measuring the
one-way speed of runners in a track meet. But the
errorbars are quite different.]

I could walk down to our optics lab today, and within an hour or two
perform a measurement of the 1-way speed of light in air or in optical
fiber or in coaxial cable. As I am a physicist, I first estimate the
accuracy I could expect, and that is at best ~ 0.1%, making it not
useful for much of anything, so not worth the bother.

[To be useful, such a measurement must be at the few
parts per billion level, and in vacuum -- that is
very challenging.]

Tom Roberts

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Bill <davos2329@gmail.com> wrote:

On Monday, September 11, 2023 at 2:47:51?AM UTC-7, J. J. Lodder wrote:

It is make believe physics...
to believe that relativity can be derived from experiments.
(or at least could have been derived, in principle)
It can't, a postulate of some kind is needed.

Not at all. The principles of physics, including the principle of relativity, are all derived from experience.

Yes, and so what? (if you replace 'derived' by based on')

Of course, the induction is
always incomplete, e.g., in every closed system we've ever observed,
momentum is conserved, but we can never observe every closed system for
all time, so when constructing a physical theory we assume the principle
of momentum conservation, but this is not an arbitrary or conventional assumption, it is the most firmly of all empirically-founded propositions.

So you need to postulate it. (or derive it from a deeper postulate)

Similarly for the principle of relativity, which leaves only a single
degree of freedom in the relationship between the standard inertial coordinate systems (operationally established), and that degree of freedom

And a postulate is needed there too.
There just is no way in which you can -derive-
the geometry of spacetime from experience.
(or any other geometry, for that matter)

Nothing new of course, Euclid and Plato already knew that,

Jan

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Tuesday, September 12, 2023 at 1:54:02 PM UTC-7, J. J. Lodder wrote:

It is make believe physics...
to believe that relativity can be derived from experiments.
(or at least could have been derived, in principle)
It can't, a postulate of some kind is needed.

Not at all. The principles of physics, including the principle of relativity, are all derived from experience.

Yes, and so what?

You said relativity couldn't be derived from experiments, and I pointed out that you were mistaken, and explained why. You're welcome.

Of course, the induction is always incomplete, e.g., in every closed system
we've ever observed, momentum is conserved, but we can never observe
every closed system for all time, so when constructing a physical theory we
assume the principle of momentum conservation, but this is not an arbitrary
or conventional assumption, it is the most firmly of all empirically-founded
propositions.

So you need to postulate it.

If by "postulate" you are referring to the fundamental process of incomplete induction on which all empiricism and indeed all rational thought is based, then your assertion is self-contradictory, because you are saying principles of physics can't be
derived from experiment, whereas the very meaning of "derived from experiment" is the process of incomplete induction. We always observe that momentum is conserved, and from this we infer the principle of conservation of momentum, which we have thereby
derived from experience. If, on the other hand, you are just saying solipsism can't be disproven, well, grow up.

Similarly for the principle of relativity, which leaves only a single degree of freedom in the relationship between the standard inertial coordinate systems (operationally established), and that degree of freedom

And a postulate is needed there too.

Nope, not in any grown-up meaningful sense. You just don't understand special relativity.

There just is no way in which you can -derive-
the geometry of spacetime from experience.
(or any other geometry, for that matter)

I've not asserted anything about "geometry". I've pointed out that we can operationally construct a grid of standard rulers and clocks mutually at rest and inertially synchronized, and then by direct observation we can determine that the readings on two
such grids are related by a Lorentz transformation. This is an operational procedure with specific operational results.

Of course, we can't do this infinitely many times in infinitely many places, etc., but we can do it enough times in enough places to become as convinced as it is possible to be of anything that this is a general result, which is what grown-ups call
deriving Lorentz invariance from experience. If you do not call this deriving from experience, then you are denying that deriving from experience has any meaning, and you just are a juvenile solipsist.

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On Saturday, September 9, 2023 at 12:27:06 PM UTC-7, Ken Seto wrote:

1. Three clocks A, B and O are co-located in one spot.
2. Synchronize them.
3. Physically measure a distance L from O in the opposite directions
4. Send A and B in the opposite directions at equal speed mechanically and stop them at distance L away from O.
5 Measure the one-way speed of light as follows:
-- One-way speed of light between O and A.
--One-way speed of light between O and B then
If Einstein's P2 is correct then
The one-way speed of light between OA = The one-way speed of light between OB.
If Einstein's P2 is wrong then
The one-way speed of light between OB =/ The one-way speed of light between OA..

Most people here don't know that special relativity does not
require any clock synchronisation for its definition. The synchronisation
is merely a convenience (in relativity there is no such thing as simultaneity at a distance, there is only a useful convention for that). This is probably worth posting about in more detail sometime soon.

--
Jan

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On Tuesday, September 12, 2023 at 8:48:44 AM UTC-7, Ken Seto wrote:

On Tuesday, September 12, 2023 at 2:27:34 AM UTC-4, Bill wrote:

On Monday, September 11, 2023 at 2:47:51 AM UTC-7, J. J. Lodder wrote:

It is make believe physics...
to believe that relativity can be derived from experiments.
(or at least could have been derived, in principle)
It can't, a postulate of some kind is needed.

Not at all. The principles of physics, including the principle of relativity, are all derived from experience

Not at all, The principles of physics are derived from postulates and postulates are assumed statements.
For example: P2 is an assumed statement, No one-way speed of light ever been measured.
. .>https://acrobat.adobe.com/link/track?uri=urn:aaid:scds:US:25556228-4404-3c67-b0cb-3d04d2636aaeOf course, the induction is always incomplete, e.g., in every closed system we've ever observed, momentum is conserved, but we can never observe every

closed system for all time, so when constructing a physical theory we assume the principle of momentum conservation, but this is not an arbitrary or conventional assumption, it is the most firmly of all empirically-founded propositions. Similarly for the
principle of relativity, which leaves only a single degree of freedom in the relationship between the standard inertial coordinate systems (operationally established), and that degree of freedom is fixed by any one of many empirial facts, which
unambiguously establish special relativity.
That is a good point. That light speed is always just c can only be proved by measuring one-way speed. That is not admitted.

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On Tuesday, September 12, 2023 at 9:01:51 PM UTC-6, JanPB wrote:

Most people here don't know that special relativity does not
require any clock synchronisation for its definition. The synchronisation
is merely a convenience (in relativity there is no such thing as simultaneity
at a distance, there is only a useful convention for that). This is probably worth posting about in more detail sometime soon.

--
Jan

Although there's no such thing as general simultaneity between inertial frames, events that are common to points in different inertial frames exist. Two points
in different frames momentarily adjacent can have their times synchronized, but that means two other points some distance away will not be synchronized. This seems to indicate that nonsimultaneity is a basic property of spacetime. However, all points in any given inertial frame seem to have a built-in simultaneity
which we humans can determine only after the fact (because simultaneity cannot be determined instantaneously by an observer). And, of course, such points aren't
(or don't remain) synchronous when observed from a different frame.

Gary

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On Tuesday, September 12, 2023 at 3:54:02 PM UTC-5, J. J. Lodder wrote:

There just is no way in which you can -derive-
the geometry of spacetime from experience.
(or any other geometry, for that matter)

Nothing new of course, Euclid and Plato already knew that,

Unless I am misreading his paper, the derivation of the geometry of
spacetime from experiment is precisely what Robertson (1949) claims to
have done.
https://cds.cern.ch/record/1061896/files/RevModPhys.21.378.pdf

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On Tuesday, 12 September 2023 at 22:54:02 UTC+2, J. J. Lodder wrote:

And a postulate is needed there too.
There just is no way in which you can -derive-
the geometry of spacetime from experience.
(or any other geometry, for that matter)

Right. It's just a word of your idiot guru and his indoctrinated
minions against Euclid's math, the wielder of about a quarter
of the whole math's authority.

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On Wednesday, 13 September 2023 at 09:54:36 UTC+2, Prokaryotic Capase Homolog wrote:

On Tuesday, September 12, 2023 at 3:54:02 PM UTC-5, J. J. Lodder wrote:

There just is no way in which you can -derive-
the geometry of spacetime from experience.
(or any other geometry, for that matter)

Nothing new of course, Euclid and Plato already knew that,

Unless I am misreading his paper, the derivation of the geometry of spacetime from experiment is precisely what Robertson (1949) claims to
have done.

Oh, a fanatic idiot claims! He claims he has falsified
basic [Euclidean] math! Must be true.

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Prokaryotic Capase Homolog <prokaryotic.caspase.homolog@gmail.com>
wrote:

On Tuesday, September 12, 2023 at 3:54:02?PM UTC-5, J. J. Lodder wrote:

There just is no way in which you can -derive-
the geometry of spacetime from experience.
(or any other geometry, for that matter)

Nothing new of course, Euclid and Plato already knew that,

Unless I am misreading his paper, the derivation of the geometry of
spacetime from experiment is precisely what Robertson (1949) claims to
have done.
https://cds.cern.ch/record/1061896/files/RevModPhys.21.378.pdf

Huh? You must indeed be misreading. Robertson starts out with: ======================================================================
KINEMATICAL PRELIMINARIES
We --postulate-- [emp. Robertson] that there exists a reference frame \Sigma--Einstein's "rest system"-- [again, emp. Robertson]
in which light is propagated rectilinearly and isotropically
in free space with constant speed c. ======================================================================

So whatever he does, it is not a postulate-free 'derivation'
of space-time geometry from experiment,

Jan
(Who holds that you cannot 'derive' anything at all from experiment.
The best you can do is to build theories that are empirically adequate)

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On Wednesday, 13 September 2023 at 11:29:33 UTC+2, J. J. Lodder wrote:

Prokaryotic Capase Homolog <prokaryotic.c...@gmail.com>
wrote:

On Tuesday, September 12, 2023 at 3:54:02?PM UTC-5, J. J. Lodder wrote:

There just is no way in which you can -derive-
the geometry of spacetime from experience.
(or any other geometry, for that matter)

Nothing new of course, Euclid and Plato already knew that,

Unless I am misreading his paper, the derivation of the geometry of spacetime from experiment is precisely what Robertson (1949) claims to
have done.
https://cds.cern.ch/record/1061896/files/RevModPhys.21.378.pdf

Huh? You must indeed be misreading. Robertson starts out with: ====================================================================== KINEMATICAL PRELIMINARIES
We --postulate-- [emp. Robertson] that there exists a reference frame \Sigma--Einstein's "rest system"-- [again, emp. Robertson]
in which light is propagated rectilinearly and isotropically
in free space with constant speed c. ======================================================================

So whatever he does, it is not a postulate-free 'derivation'
of space-time geometry from experiment,

That's right: iit's just POSTULATES of your bunch of
idiots against basic math (also postulate based, true).

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On Wednesday, September 13, 2023 at 4:29:33 AM UTC-5, J. J. Lodder wrote:

Prokaryotic Capase Homolog <prokaryotic.c...@gmail.com>
wrote:

On Tuesday, September 12, 2023 at 3:54:02?PM UTC-5, J. J. Lodder wrote:

There just is no way in which you can -derive-
the geometry of spacetime from experience.
(or any other geometry, for that matter)

Nothing new of course, Euclid and Plato already knew that,

Unless I am misreading his paper, the derivation of the geometry of spacetime from experiment is precisely what Robertson (1949) claims to have done.
https://cds.cern.ch/record/1061896/files/RevModPhys.21.378.pdf

Huh? You must indeed be misreading. Robertson starts out with: ====================================================================== KINEMATICAL PRELIMINARIES
We --postulate-- [emp. Robertson] that there exists a reference frame \Sigma--Einstein's "rest system"-- [again, emp. Robertson]
in which light is propagated rectilinearly and isotropically
in free space with constant speed c. ======================================================================

So whatever he does, it is not a postulate-free 'derivation'
of space-time geometry from experiment,

Jan
(Who holds that you cannot 'derive' anything at all from experiment.
The best you can do is to build theories that are empirically adequate)

You are misreading what I wrote. I did -not- write that Robertson
was "postulate-free". Robertson's initial postulate is insufficient to
derive the geometry of spacetime or the Lorentz transformation.
Starting from this minimal framework, he uses MMX, KTX and ISX
to establish that the relationship between moving frames and rest
frames, i.e. what he terms "the kinematics im kleinen of physical
space-time", is governed by the Minkowski metric.

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Prokaryotic Capase Homolog <prokaryotic.caspase.homolog@gmail.com>
wrote:

On Wednesday, September 13, 2023 at 4:29:33?AM UTC-5, J. J. Lodder wrote:

Prokaryotic Capase Homolog <prokaryotic.c...@gmail.com>
wrote:

On Tuesday, September 12, 2023 at 3:54:02?PM UTC-5, J. J. Lodder wrote:

There just is no way in which you can -derive-
the geometry of spacetime from experience.
(or any other geometry, for that matter)

Nothing new of course, Euclid and Plato already knew that,

Unless I am misreading his paper, the derivation of the geometry of spacetime from experiment is precisely what Robertson (1949) claims to have done.
https://cds.cern.ch/record/1061896/files/RevModPhys.21.378.pdf

Huh? You must indeed be misreading. Robertson starts out with: ====================================================================== KINEMATICAL PRELIMINARIES
We --postulate-- [emp. Robertson] that there exists a reference frame \Sigma--Einstein's "rest system"-- [again, emp. Robertson]
in which light is propagated rectilinearly and isotropically
in free space with constant speed c. ======================================================================

So whatever he does, it is not a postulate-free 'derivation'
of space-time geometry from experiment,

Jan
(Who holds that you cannot 'derive' anything at all from experiment.
The best you can do is to build theories that are empirically adequate)

You are misreading what I wrote. I did -not- write that Robertson
was "postulate-free".

You claimed worse, on behalf of Robinson:
====
....., the derivation of the geometry of spacetime from experiment is
precisely what Robertson (1949) claims to have done.
====
See above, still there.

AFAICS Robinson claimed no such thing.

Jan

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Bill <davos2329@gmail.com> wrote:

On Tuesday, September 12, 2023 at 1:54:02?PM UTC-7, J. J. Lodder wrote:

It is make believe physics...
to believe that relativity can be derived from experiments.
(or at least could have been derived, in principle)
It can't, a postulate of some kind is needed.

Not at all. The principles of physics, including the principle of relativity, are all derived from experience.

Yes, and so what?

You said relativity couldn't be derived from experiments, and I pointed
out that you were mistaken, and explained why. You're welcome.

You are playing false.
What you said was 'derived from experience'.

Of course, the induction is always incomplete, e.g., in every closed system we've ever observed, momentum is conserved, but we can never observe every closed system for all time, so when constructing a
physical theory we assume the principle of momentum conservation, but this is not an arbitrary or conventional assumption, it is the most firmly of all empirically-founded propositions.

So you need to postulate it.

If by "postulate" you are referring to the fundamental process of
incomplete induction on which all empiricism and indeed all rational
thought is based, then your assertion is self-contradictory, because you
are saying principles of physics can't be derived from experiment, whereas the very meaning of "derived from experiment" is the process of incomplete induction.

So you -are- a naive empiricist. A very naive one even.

We always observe that momentum is conserved, and from this we
infer the principle of conservation of momentum, which we have thereby derived from experience. If, on the other hand, you are just saying solipsism can't be disproven, well, grow up.

You really should learn to avoid those straw men of yours.

Similarly for the principle of relativity, which leaves only a single degree of freedom in the relationship between the standard inertial coordinate systems (operationally established), and that degree of freedom

And a postulate is needed there too.

Nope, not in any grown-up meaningful sense. You just don't understand special relativity.

You need a mirror. Your problem seems to be
that you think that you understand relativity
because you can do the excercises in the textbooks.

There just is no way in which you can -derive-
the geometry of spacetime from experience.
(or any other geometry, for that matter)

I've not asserted anything about "geometry". I've pointed out that we can operationally construct a grid of standard rulers and clocks mutually at
rest and inertially synchronized, and then by direct observation we can determine that the readings on two such grids are related by a Lorentz transformation. This is an operational procedure with specific
operational results.

How are you going to do that without postulating something?

Of course, we can't do this infinitely many times in infinitely many
places, etc., but we can do it enough times in enough places to become as convinced as it is possible to be of anything that this is a general
result, which is what grown-ups call deriving Lorentz invariance from experience.

I have no doubt at all about your ability to convince yourself about
anything you want to convince yourself of,
as convinced as it is possible to be even.

If you do not call this deriving from experience, then you
are denying that deriving from experience has any meaning, and you just
are a juvenile solipsist.

I don't mind, being in good company, such as Einstein 1905,

Jan

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JanPB <filmart@gmail.com> wrote:

On Saturday, September 9, 2023 at 12:27:06?PM UTC-7, Ken Seto wrote:

1. Three clocks A, B and O are co-located in one spot.
2. Synchronize them.
3. Physically measure a distance L from O in the opposite directions
4. Send A and B in the opposite directions at equal speed mechanically and s
top them at distance L away from O.
5 Measure the one-way speed of light as follows:
-- One-way speed of light between O and A.
--One-way speed of light between O and B then
If Einstein's P2 is correct then
The one-way speed of light between OA = The one-way speed of light between OB.
If Einstein's P2 is wrong then
The one-way speed of light between OB =/ The one-way speed of light between OA..

Most people here don't know that special relativity does not
require any clock synchronisation for its definition. The synchronisation
is merely a convenience (in relativity there is no such thing as simultaneity at a distance, there is only a useful convention for that). This is probably worth posting about in more detail sometime soon.

Indeed. That is part of the didactics.
My take on it:
One can wonder what the flash of insight was
that seems to have hit Einstein, sometime in spring 1905.
(after worrying about it all for about ten years)

My personal guess is that Einstein's flash of insight was
that the answer to the question:
In which inertial system are Maxwell's equations valid?
must be:
All of them!
(and hence an entirely new and original view of space-time)

From there on it is development, and didactic exposition,
(clocks, rulers, etc.) to get back to the starting point.
Einstein wrote the relativity paper in a very short time.

There were some bonus points along the way, such as velocity addition,
time dilation, transverse Doppler shift, and somewhat later,
mass-energy equivalence.

It is 'On the electrodynamics of moving bodies' with good reason,
(and not 'On laying out rulers and synchronising clocks')

Jan

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On 9/13/23 3:51 PM, J. J. Lodder wrote:

JanPB <filmart@gmail.com> wrote:

Most people here don't know that special relativity does not
require any clock synchronisation for its definition. The
synchronisation is merely a convenience (in relativity there is no
such thing as simultaneity at a distance, there is only a useful
convention for that). This is probably worth posting about in more
detail sometime soon.

Indeed. That is part of the didactics.

I think it goes deeper than that -- without clock synchronization, what
does 'moves in the “stationary” system of co-ordinates with the
determined velocity c' mean without being able to measure it (which
requires synchronized clocks)?

On the other hand, that quote is from Einstein's second postulate, and a
modern derivation of the theory replaces the second postulate with any
one of many experimental results.

My take on it: One can wonder what the flash of insight was that
seems to have hit Einstein, sometime in spring 1905. (after worrying
about it all for about ten years)

My personal guess is that Einstein's flash of insight was that the
answer to the question: In which inertial system are Maxwell's
equations valid? must be: All of them! (and hence an entirely new
and original view of space-time)

Yes, Stated differently, his insight was that Maxwell's equations are a
law of physics, and thus subject to the PoR. And his genius was that
this requires a complete revision of how we view space and time.

It is 'On the electrodynamics of moving bodies' with good reason,
(and not 'On laying out rulers and synchronising clocks')

Yes.

Tom Roberts

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On Wednesday, September 13, 2023 at 4:37:19 PM UTC-7, Tom Roberts wrote:

On 9/13/23 3:51 PM, J. J. Lodder wrote:

JanPB <fil...@gmail.com> wrote:

Most people here don't know that special relativity does not
require any clock synchronisation for its definition. The
synchronisation is merely a convenience (in relativity there is no
such thing as simultaneity at a distance, there is only a useful
convention for that). This is probably worth posting about in more
detail sometime soon.

Indeed. That is part of the didactics.

I think it goes deeper than that -- without clock synchronization, what
does 'moves in the “stationary” system of co-ordinates with the determined velocity c' mean without being able to measure it (which
requires synchronized clocks)?

I think it's sufficient to observe that certain clock proper time relationships hold, with no clock sync required for that.

My take on it: One can wonder what the flash of insight was that
seems to have hit Einstein, sometime in spring 1905. (after worrying
about it all for about ten years)

My personal guess is that Einstein's flash of insight was that the
answer to the question: In which inertial system are Maxwell's
equations valid? must be: All of them! (and hence an entirely new
and original view of space-time)

Yes, Stated differently, his insight was that Maxwell's equations are a
law of physics, and thus subject to the PoR.

This probably wasn't enough for him because it's "just" a convenient requirement. If only left at that, nobody would pay any attention to the
theory because there appeared no shred of evidence otherwise that
e.g. Lorentz's "abstract time coordinate" was in any way physical.

And his genius was that
this requires a complete revision of how we view space and time.

I have no way of knowing, of course, but I suspect the big breakthrough
moment for Einstein was noticing that the Lorentz transform could be
derived just from the simple "tB - tA = tA' - tB" condition and not really
much more. This is what provided the needed "physicality" to
Lorentz's "time parameter".

It is 'On the electrodynamics of moving bodies' with good reason,
(and not 'On laying out rulers and synchronising clocks')

Yes.

When Einstein wrote his paper, he (again, I have no way of knowing for sure) considered the key result of the paper to be the physical reality of the transformed E and B fields and the time coordinate.

The full import of the kinematics part probably hit him very quickly but AFTER the paper was printed (probably within a couple of weeks or so), that's why
it didn't occur to him at first that there was a contradiction
in the way the paper selected the "stationary" system originally
(fixed in later reprints by that footnote "that is, to the first order").

--
Jan

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On Wednesday, September 13, 2023 at 1:51:11 PM UTC-7, J. J. Lodder wrote:

The principles of physics, including the principle of relativity,
are all derived from experience.

Yes, and so what?

You said relativity couldn't be derived from experiments, and I pointed out that you were mistaken, and explained why. You're welcome.

You are playing false.
What you said was 'derived from experience'.

What falseness are you referring to? Are you struggling with the fact that experiments are experience? Or with the English meanings of "derive"?

If by "postulate" you are referring to the fundamental process of incomplete induction on which all empiricism and indeed all rational thought is based, then your assertion is self-contradictory, because you are saying principles of physics can't be derived from experiment, whereas the very meaning of "derived from experiment" is the process of incomplete induction.

So you -are- a naive empiricist. A very naive one even.

Again, the very meaning of "derived from experiment" is the process of incomplete induction, and, as you agreed above, the principles of physics, including the principle of relativity, are all derived from experience. Then you deny it, then you agree
with it, then you deny it... Clearly you aren't able to articulate a coherent poisition, and you have no idea what you are talking about. Agreed?

We always observe that momentum is conserved, and from this we
infer the principle of conservation of momentum, which we have thereby derived from experience. If, on the other hand, you are just saying solipsism can't be disproven, well, grow up.

You really should learn to avoid those straw men of yours.

Again, if you are just saying solipsism can't be disproven, well, grow up. If that isn't what you are saying, and if you are not retracting your agreement that the principles of physics are derived from experience, and you ARE retracting your denials of
this, then we're now in agreement that, indeed, special relativity is derived from experience.

There just is no way in which you can -derive-
the geometry of spacetime from experience.
(or any other geometry, for that matter)

I've not asserted anything about "geometry". I've pointed out that we can operationally construct a grid of standard rulers and clocks mutually at rest and inertially synchronized, and then by direct observation we can determine that the readings on two such grids are related by a Lorentz transformation. This is an operational procedure with specific
operational results.

How are you going to do that without postulating something?

How am I going to construct a grid of standard rulers? Remember, you assured me you aren't engaging in juvenile solipsism, you are approaching this like a grown-up who knows what is meant by rulers and clocks. If the unfounded postulate you are saying
is necessary is the postulate that the world exists, etc., then you are just invoking a crude solipsism. Again, scientific induction is always incomplete, so after a trillion demonstrations of some regularity, we adopt it as a principle, so if this kind
of adoption is what you are referring to as "postulating something", then you're just referring to the normal process of incomplete induction on which all science (and indeed all rational thought) is based. This is not what grown-ups are referring to
when they make a statement like "we need to postulate something, we can't base our conclusion on experience". There are cases where that is true, but not the deriving of fundamental physical principles... which you already agreed.

To put this another way, it is misleading for you to say "special relativity can't be derived from experience, it relies on a postulate", if in fact your thesis has nothing in particular to do with special relativity, and what you mean is that NOTHING
can be derived from experience, and everything relies on a postulate, and you are NOT talking about the postulate that the world exists, etc., in which case you are sliding back toward juvenile solipsism.

To clarify your position, go ahead and state what you think must be postulated (NOT in the sense of incomplete induction, which underlies everything) in order to arrive at special relativity in particular.

Of course, we can't do this infinitely many times in infinitely many places, etc., but we can do it enough times in enough places to become as convinced as it is possible to be of anything that this is a general result, which is what grown-ups call deriving Lorentz invariance from experience. If you do not call this deriving from experience, then you are denying that deriving from experience has any meaning, and you just are a juvenile solipsist.

I don't mind, being in good company, such as Einstein 1905,

Please don't attribute your misunderstandings to Einstein. As he said, the transition to special relativity "is by no means merely a conventional step, but implies certain hypotheses concerning the actual behavior of moving measuring rods and clocks
which can be experimentally confirmed or disproved".

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On Thursday, 14 September 2023 at 06:06:41 UTC+2, Bill wrote:

On Wednesday, September 13, 2023 at 1:51:11 PM UTC-7, J. J. Lodder wrote:

The principles of physics, including the principle of relativity,
are all derived from experience.

Yes, and so what?

You said relativity couldn't be derived from experiments, and I pointed out that you were mistaken, and explained why. You're welcome.

You are playing false.
What you said was 'derived from experience'.

What falseness are you referring to? Are you struggling with the fact that experiments are experience? Or with the English meanings of "derive"?

Kookfight!
Sorry, trash, if the postulate of your idiot guru was derived
from experiments - it wouldn't be a postulate. Even
such an idiot should understand that. But, well, he doesn't.

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On 9/11/23 1:23 PM, Laurence Clark Crossen wrote:

Relativity is like a hydra with many heads because it is totally
inconsistent nonsense.

Not true.

Crossen is like a hydra with many heads because he repeats his nonsense
without understanding.

Tom Roberts

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On Friday, 15 September 2023 at 17:08:29 UTC+2, Tom Roberts wrote:

On 9/11/23 1:23 PM, Laurence Clark Crossen wrote:

Relativity is like a hydra with many heads because it is totally inconsistent nonsense.

Not true.

True, true, trash, it's been proven here many times and
the only yhing you can do about is is - pretending you
haven't noticed.
Not that inconsistency is making The Shit similiar
somehow to a hydra, of course.

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