Here's a problem where the Lorentz transform gives a conflicting result. If you could explain what restriction I need to follow when applying the transform it would be appreciated.
The problem I have difficulty with is a traveler moving along the sides of a polygon. He seems to get contradictory measures of the rate of a flashing light.
Let's say the polygon is a square at rest in inertial reference frame F0. Let each side of the square equal 10*sqrt(3)/2 light-seconds in length.. Let there be a light source at the center of this square that flashes at a rate of one flash per second. Let the traveler move with a velocity of V = c*sqrt(3)/2 relative to F0 as he travels along each side of the square. Let the flashes occur such that each time he starts traveling on one side of the square he receives a flash of light.
As measured in F0, the traveler takes 10 seconds to travel the length of one side of the square. So the traveler receives 10 flashes as he travels one side of the square. As he makes a complete trip around the square he receives 40 flashes from the light source at the center of the square. The moving traveler, using the Lorentz transform, shows an elapsed time of 5 seconds as each side of the square passes him. So during each complete revolution around the square, the traveler's clock changes by 20 seconds. If he receives 10 flashes along each side of the square, he must conclude that the flash rate of the light source is 40 flashes per 20 seconds or 2 flashes per second. The Lorentz transform however gives the answer as 1 flash every 2 seconds. How does the moving traveler measure the flash rate on each side of the square to be one flash every two seconds while measuring that he receives flashes at a rate of two flashes per second?
What restrictions must be followed to give a consistent measurement of the flash rate by the moving traveler.
Thanks,
David Seppala
Bastrop TX

sepp623@yahoo.com <sepp623@yahoo.com> wrote:
> Here's a problem where the Lorentz transform gives a conflicting result.
> If you could explain what restriction I need to follow when applying the
> transform it would be appreciated.
> The problem I have difficulty with is a traveler moving along the
> sides of a polygon. He seems to get contradictory measures of the rate
> of a flashing light.
> Let's say the polygon is a square at rest in
> inertial reference frame F0. Let each side of the square equal
> 10*sqrt(3)/2 light-seconds in length. Let there be a light source at the
> center of this square that flashes at a rate of one flash per second.
> Let the traveler move with a velocity of V = c*sqrt(3)/2 relative to F0
> as he travels along each side of the square. Let the flashes occur such
> that each time he starts traveling on one side of the square he receives a flash of light.
> As measured in F0, the traveler takes 10 seconds to travel the
> length of one side of the square. So the traveler receives 10 flashes as
> he travels one side of the square. As he makes a complete trip around the
> square he receives 40 flashes from the light source at the center of the
> square. The moving traveler, using the Lorentz transform, shows an
> elapsed time of 5 seconds as each side of the square passes him. So
> during each complete revolution around the square, the traveler's clock
> changes by 20 seconds. If he receives 10 flashes along each side of the
> square, he must conclude that the flash rate of the light source is 40
> flashes per 20 seconds or 2 flashes per second. The Lorentz transform
> however gives the answer as 1 flash every 2 seconds. How does the moving
> traveler measure the flash rate on each side of the square to be one
> flash every two seconds while measuring that he receives flashes at a
> rate of two flashes per second?
> What restrictions must be followed to give a consistent measurement
> of the flash rate by the moving traveler.
> Thanks,
> David Seppala
> Bastrop TX
>

This, like many of your other scenarios, is the problem of trying to apply
time dilation formulas when you switch inertial reference frames, which is
what you do every single time the traveler turns a corner of the polygon.
The line of simultaneity changes every time.

To see this in action, look at the last section of Chapter 2 in Robert
Mills’ book Space, Time, and Quanta.

--
Odd Bodkin -- maker of fine toys, tools, tables

Odd Bodkin <bodkinodd@gmail.com> wrote:
> sepp623@yahoo.com <sepp623@yahoo.com> wrote:
>> Here's a problem where the Lorentz transform gives a conflicting result.
>> If you could explain what restriction I need to follow when applying the
>> transform it would be appreciated.
>> The problem I have difficulty with is a traveler moving along the
>> sides of a polygon. He seems to get contradictory measures of the rate
>> of a flashing light.
>> Let's say the polygon is a square at rest in
>> inertial reference frame F0. Let each side of the square equal
>> 10*sqrt(3)/2 light-seconds in length. Let there be a light source at the
>> center of this square that flashes at a rate of one flash per second.
>> Let the traveler move with a velocity of V = c*sqrt(3)/2 relative to F0
>> as he travels along each side of the square. Let the flashes occur such
>> that each time he starts traveling on one side of the square he receives a flash of light.
>> As measured in F0, the traveler takes 10 seconds to travel the
>> length of one side of the square. So the traveler receives 10 flashes as
>> he travels one side of the square. As he makes a complete trip around the
>> square he receives 40 flashes from the light source at the center of the
>> square. The moving traveler, using the Lorentz transform, shows an
>> elapsed time of 5 seconds as each side of the square passes him. So
>> during each complete revolution around the square, the traveler's clock
>> changes by 20 seconds. If he receives 10 flashes along each side of the
>> square, he must conclude that the flash rate of the light source is 40
>> flashes per 20 seconds or 2 flashes per second. The Lorentz transform
>> however gives the answer as 1 flash every 2 seconds. How does the moving
>> traveler measure the flash rate on each side of the square to be one
>> flash every two seconds while measuring that he receives flashes at a
>> rate of two flashes per second?
>> What restrictions must be followed to give a consistent measurement
>> of the flash rate by the moving traveler.
>> Thanks,
>> David Seppala
>> Bastrop TX
>>
>
> This, like many of your other scenarios, is the problem of trying to apply
> time dilation formulas when you switch inertial reference frames, which is
> what you do every single time the traveler turns a corner of the polygon.
> The line of simultaneity changes every time.
>
> To see this in action, look at the last section of Chapter 2 in Robert
> Mills’ book Space, Time, and Quanta.
>

To cue it simply, this is just another variant of the twin “paradox”, where
there is a round trip that necessitates a change in inertial reference
frames for at least one of the players. The lesson to be taught in all of
these cases is that it is a mistake to try to insist that the symmetry of
time dilation formulas should still apply. It does not. It never does in
cases where there is a change in inertial reference frames. In these cases,
it will be a reality that BOTH players note, that less time has elapsed for
one player than for the other. One twin really does come back younger than
the other.

All you are doing is adding signals passed back and forth between the
players. That’s fine, and the twin “paradox” has been discussed with
signals being passed between the twins. (See reference given). The
accounting at the frame switches is what’s important.

--
Odd Bodkin -- maker of fine toys, tools, tables

On Saturday, 23 April 2022 at 15:51:21 UTC+2, bodk...@gmail.com wrote:
> Odd Bodkin <bodk...@gmail.com> wrote:
> > sep...@yahoo.com <sep...@yahoo.com> wrote:
> >> Here's a problem where the Lorentz transform gives a conflicting result.
> >> If you could explain what restriction I need to follow when applying the
> >> transform it would be appreciated.
> >> The problem I have difficulty with is a traveler moving along the
> >> sides of a polygon. He seems to get contradictory measures of the rate
> >> of a flashing light.
> >> Let's say the polygon is a square at rest in
> >> inertial reference frame F0. Let each side of the square equal
> >> 10*sqrt(3)/2 light-seconds in length. Let there be a light source at the
> >> center of this square that flashes at a rate of one flash per second.
> >> Let the traveler move with a velocity of V = c*sqrt(3)/2 relative to F0
> >> as he travels along each side of the square. Let the flashes occur such
> >> that each time he starts traveling on one side of the square he receives a flash of light.
> >> As measured in F0, the traveler takes 10 seconds to travel the
> >> length of one side of the square. So the traveler receives 10 flashes as
> >> he travels one side of the square. As he makes a complete trip around the
> >> square he receives 40 flashes from the light source at the center of the
> >> square. The moving traveler, using the Lorentz transform, shows an
> >> elapsed time of 5 seconds as each side of the square passes him. So
> >> during each complete revolution around the square, the traveler's clock
> >> changes by 20 seconds. If he receives 10 flashes along each side of the
> >> square, he must conclude that the flash rate of the light source is 40
> >> flashes per 20 seconds or 2 flashes per second. The Lorentz transform
> >> however gives the answer as 1 flash every 2 seconds. How does the moving
> >> traveler measure the flash rate on each side of the square to be one
> >> flash every two seconds while measuring that he receives flashes at a
> >> rate of two flashes per second?
> >> What restrictions must be followed to give a consistent measurement
> >> of the flash rate by the moving traveler.
> >> Thanks,
> >> David Seppala
> >> Bastrop TX
> >>
> >
> > This, like many of your other scenarios, is the problem of trying to apply
> > time dilation formulas when you switch inertial reference frames, which is
> > what you do every single time the traveler turns a corner of the polygon.
> > The line of simultaneity changes every time.
> >
> > To see this in action, look at the last section of Chapter 2 in Robert
> > Mills’ book Space, Time, and Quanta.
> >
> To cue it simply, this is just another variant of the twin “paradox”, where
> there is a round trip that necessitates a change in inertial reference
> frames for at least one of the players. The lesson to be taught in all of
> these cases is that it is a mistake to try to insist that the symmetry of
> time dilation formulas should still apply. It does not. It never does in
> cases where there is a change in inertial reference frames. In these cases,
> it will be a reality that BOTH players note, that less time has elapsed for
> one player than for the other. One twin really does come back younger than
> the other.

In the meantime in the real world, however, forbidden
by your insane Shit TAI keep measuring t'=t, just like
all serious clocks always did.

On Saturday, April 23, 2022 at 5:56:48 AM UTC-7, sep...@yahoo.com wrote:
> During each complete revolution around the square, the traveler's clock changes
> by 20 seconds.

Yes.

> If he receives 10 flashes along each side of the square, he must conclude that the
> flash rate of the light source is 40 flashes per 20 seconds or 2 flashes per second.

No, you are mixing up the flash rate of the source and the reception rate of the traveler, which are not the same because in terms of F1 (the traveler's co-moving inertial coordinate system on edge 1) the source is approaching the traveler from almost directly ahead (due to aberration), so even though, in terms of F1, the pulse rate of the source is just 0.5 pulses per second, the traveler encounters pulses arriving at 2 per second. Likewise for F2, F3, and F4 (the co-moving inertial coordinate systems in which the traveler is at rest on the other three edges).

> The Lorentz transform however gives the answer as 1 flash every 2 seconds..

Right, in terms of any of the inertial coordinate systems F1, F2, F3, and F4 the pulse rate of the source is 0.5 flashes per second.

> How does the moving traveler measure the flash rate on each side of the square
> to be one flash every two seconds while measuring that he receives flashes at a
> rate of two flashes per second?

See above. In terms of each of the inertial coordinate systems F1, the rate of the source flashes can be measured in any normal way, e.g., by a grid of standard clocks mutually at rest and inertially synchronized in F1. Again, since the source is approaching the traveler at high speed in terms of these coordinates (aberration), the reception rate at the traveler is much higher than the emission rate at the source (Doppler).

> What restrictions must be followed to give a consistent measurement of the flash rate
> by the moving traveler.

The results described above are perfectly consistent, as you can see, once you correctly account for the aberration and Doppler effects.

As usual, you're not really asking the question that would clear up your confusion. The question you should be asking is, if the rate of proper time dtau/dt of the source is 1/2 in terms of F1, F2, F3, and F4, how is it possible that the rate of the traveler's proper time in terms of F0 on each of those edges is also 1/2, so the traveler's total elapsed time around the square is 1/2 of the sources elapsed time? The answer is that the simultaneity mappings between the events of the traveler and the events of the source in terms of F1, F2, F3, and F4 are disjoint. The simultaneity mapping in terms of F1 maps 5 seconds of the traveler's proper time to 2.5 seconds of the source's proper time, and the same for F2, and F3 and F4, so you might naively think that the total elapsed time for the source is 10 seconds, but that is not true, because the F2 simultaneity mapping maps the traveler's start time at the beginning of edge 2 to an event at the source that is 30/4 seconds *after* the event that maps to the traveler at the end of edge 1. Similarly for the other edge transitions, so this disjoint mapping omits 30 seconds of the source's proper time during each trip around the square.

In summary, your mistake was three-fold: You failed to account for aberration, you failed to account for Doppler, and you failed to account for the relativity of simultaneity. This is all just Relativity 101.

Special Relativity: 867 ... Barnpole Dave: 0

On Saturday, April 23, 2022 at 9:24:48 AM UTC-5, Al Coe wrote:
> On Saturday, April 23, 2022 at 5:56:48 AM UTC-7, sep...@yahoo.com wrote:
> > During each complete revolution around the square, the traveler's clock changes
> > by 20 seconds.
>
> Yes.
> > If he receives 10 flashes along each side of the square, he must conclude that the
> > flash rate of the light source is 40 flashes per 20 seconds or 2 flashes per second.
> No, you are mixing up the flash rate of the source and the reception rate of the traveler, which are not the same because in terms of F1 (the traveler's co-moving inertial coordinate system on edge 1) the source is approaching the traveler from almost directly ahead (due to aberration), so even though, in terms of F1, the pulse rate of the source is just 0.5 pulses per second, the traveler encounters pulses arriving at 2 per second. Likewise for F2, F3, and F4 (the co-moving inertial coordinate systems in which the traveler is at rest on the other three edges).
> > The Lorentz transform however gives the answer as 1 flash every 2 seconds.
> Right, in terms of any of the inertial coordinate systems F1, F2, F3, and F4 the pulse rate of the source is 0.5 flashes per second.
> > How does the moving traveler measure the flash rate on each side of the square
> > to be one flash every two seconds while measuring that he receives flashes at a
> > rate of two flashes per second?
> See above. In terms of each of the inertial coordinate systems F1, the rate of the source flashes can be measured in any normal way, e.g., by a grid of standard clocks mutually at rest and inertially synchronized in F1. Again, since the source is approaching the traveler at high speed in terms of these coordinates (aberration), the reception rate at the traveler is much higher than the emission rate at the source (Doppler).
> > What restrictions must be followed to give a consistent measurement of the flash rate
> > by the moving traveler.
> The results described above are perfectly consistent, as you can see, once you correctly account for the aberration and Doppler effects.
>
> As usual, you're not really asking the question that would clear up your confusion. The question you should be asking is, if the rate of proper time dtau/dt of the source is 1/2 in terms of F1, F2, F3, and F4, how is it possible that the rate of the traveler's proper time in terms of F0 on each of those edges is also 1/2, so the traveler's total elapsed time around the square is 1/2 of the sources elapsed time? The answer is that the simultaneity mappings between the events of the traveler and the events of the source in terms of F1, F2, F3, and F4 are disjoint. The simultaneity mapping in terms of F1 maps 5 seconds of the traveler's proper time to 2.5 seconds of the source's proper time, and the same for F2, and F3 and F4, so you might naively think that the total elapsed time for the source is 10 seconds, but that is not true, because the F2 simultaneity mapping maps the traveler's start time at the beginning of edge 2 to an event at the source that is 30/4 seconds *after* the event that maps to the traveler at the end of edge 1. Similarly for the other edge transitions, so this disjoint mapping omits 30 seconds of the source's proper time during each trip around the square.
>
> In summary, your mistake was three-fold: You failed to account for aberration, you failed to account for Doppler, and you failed to account for the relativity of simultaneity. This is all just Relativity 101.
>
> Special Relativity: 867 ... Barnpole Dave: 0

If the traveler receives 40 flashes from the same light source every 20 seconds, and 80 flashes every 40 seconds and 120 flashes every 60 seconds and 40*n flashes every 20*n seconds as he makes n revolutions around the polygon how does he "measure" that the light source is flashing at a rate of one flash per every two seconds instead of using the Lorentz transform?
David Seppala
Bastrop TX

On Saturday, April 23, 2022 at 9:35:40 AM UTC-7, sep...@yahoo.com wrote:
> On Saturday, April 23, 2022 at 9:24:48 AM UTC-5, Al Coe wrote:
> > On Saturday, April 23, 2022 at 5:56:48 AM UTC-7, sep...@yahoo.com wrote:
> > > During each complete revolution around the square, the traveler's clock changes
> > > by 20 seconds.
> >
> > Yes.
> > > If he receives 10 flashes along each side of the square, he must conclude that the
> > > flash rate of the light source is 40 flashes per 20 seconds or 2 flashes per second.
> > No, you are mixing up the flash rate of the source and the reception rate of the traveler, which are not the same because in terms of F1 (the traveler's co-moving inertial coordinate system on edge 1) the source is approaching the traveler from almost directly ahead (due to aberration), so even though, in terms of F1, the pulse rate of the source is just 0.5 pulses per second, the traveler encounters pulses arriving at 2 per second. Likewise for F2, F3, and F4 (the co-moving inertial coordinate systems in which the traveler is at rest on the other three edges).
> > > The Lorentz transform however gives the answer as 1 flash every 2 seconds.
> > Right, in terms of any of the inertial coordinate systems F1, F2, F3, and F4 the pulse rate of the source is 0.5 flashes per second.
> > > How does the moving traveler measure the flash rate on each side of the square
> > > to be one flash every two seconds while measuring that he receives flashes at a
> > > rate of two flashes per second?
> > See above. In terms of each of the inertial coordinate systems F1, the rate of the source flashes can be measured in any normal way, e.g., by a grid of standard clocks mutually at rest and inertially synchronized in F1. Again, since the source is approaching the traveler at high speed in terms of these coordinates (aberration), the reception rate at the traveler is much higher than the emission rate at the source (Doppler).
> > > What restrictions must be followed to give a consistent measurement of the flash rate
> > > by the moving traveler.
> > The results described above are perfectly consistent, as you can see, once you correctly account for the aberration and Doppler effects.
> >
> > As usual, you're not really asking the question that would clear up your confusion. The question you should be asking is, if the rate of proper time dtau/dt of the source is 1/2 in terms of F1, F2, F3, and F4, how is it possible that the rate of the traveler's proper time in terms of F0 on each of those edges is also 1/2, so the traveler's total elapsed time around the square is 1/2 of the sources elapsed time? The answer is that the simultaneity mappings between the events of the traveler and the events of the source in terms of F1, F2, F3, and F4 are disjoint. The simultaneity mapping in terms of F1 maps 5 seconds of the traveler's proper time to 2.5 seconds of the source's proper time, and the same for F2, and F3 and F4, so you might naively think that the total elapsed time for the source is 10 seconds, but that is not true, because the F2 simultaneity mapping maps the traveler's start time at the beginning of edge 2 to an event at the source that is 30/4 seconds *after* the event that maps to the traveler at the end of edge 1.. Similarly for the other edge transitions, so this disjoint mapping omits 30 seconds of the source's proper time during each trip around the square.
> >
> > In summary, your mistake was three-fold: You failed to account for aberration, you failed to account for Doppler, and you failed to account for the relativity of simultaneity. This is all just Relativity 101.
> >
> > Special Relativity: 867 ... Barnpole Dave: 0
> If the traveler receives 40 flashes from the same light source every 20 seconds...
> how does he "measure" that the light source is flashing at a rate of one flash per
> every two seconds...

Again, the correct statement is that the flash rate of the source in terms of (say) F1 is 0.5 flashes per second, and, as clearly explained above, this can be measured in any normal way, e.g., by a grid of standard clocks mutually at rest and inertially synchronized in F1. Of course, there are infinitely many other methods, all giving the same result, but this is the canonical, defining, condition. As the source passes those clocks you will find that dtau/dt = 1/2. Notice that this measurement involves a system of clocks, all mutually at rest and inertially synchronized, as required in order for the equations of physics to hold good in their simple homogeneous and isotropic form. If you still don't understand this, go ahead and explain what you don't understand about it.

On Saturday, 23 April 2022 at 19:03:39 UTC+2, Al Coe wrote:
> On Saturday, April 23, 2022 at 9:35:40 AM UTC-7, sep...@yahoo.com wrote:
> > On Saturday, April 23, 2022 at 9:24:48 AM UTC-5, Al Coe wrote:
> > > On Saturday, April 23, 2022 at 5:56:48 AM UTC-7, sep...@yahoo.com wrote:
> > > > During each complete revolution around the square, the traveler's clock changes
> > > > by 20 seconds.
> > >
> > > Yes.
> > > > If he receives 10 flashes along each side of the square, he must conclude that the
> > > > flash rate of the light source is 40 flashes per 20 seconds or 2 flashes per second.
> > > No, you are mixing up the flash rate of the source and the reception rate of the traveler, which are not the same because in terms of F1 (the traveler's co-moving inertial coordinate system on edge 1) the source is approaching the traveler from almost directly ahead (due to aberration), so even though, in terms of F1, the pulse rate of the source is just 0.5 pulses per second, the traveler encounters pulses arriving at 2 per second. Likewise for F2, F3, and F4 (the co-moving inertial coordinate systems in which the traveler is at rest on the other three edges).
> > > > The Lorentz transform however gives the answer as 1 flash every 2 seconds.
> > > Right, in terms of any of the inertial coordinate systems F1, F2, F3, and F4 the pulse rate of the source is 0.5 flashes per second.
> > > > How does the moving traveler measure the flash rate on each side of the square
> > > > to be one flash every two seconds while measuring that he receives flashes at a
> > > > rate of two flashes per second?
> > > See above. In terms of each of the inertial coordinate systems F1, the rate of the source flashes can be measured in any normal way, e.g., by a grid of standard clocks mutually at rest and inertially synchronized in F1. Again, since the source is approaching the traveler at high speed in terms of these coordinates (aberration), the reception rate at the traveler is much higher than the emission rate at the source (Doppler).
> > > > What restrictions must be followed to give a consistent measurement of the flash rate
> > > > by the moving traveler.
> > > The results described above are perfectly consistent, as you can see, once you correctly account for the aberration and Doppler effects.
> > >
> > > As usual, you're not really asking the question that would clear up your confusion. The question you should be asking is, if the rate of proper time dtau/dt of the source is 1/2 in terms of F1, F2, F3, and F4, how is it possible that the rate of the traveler's proper time in terms of F0 on each of those edges is also 1/2, so the traveler's total elapsed time around the square is 1/2 of the sources elapsed time? The answer is that the simultaneity mappings between the events of the traveler and the events of the source in terms of F1, F2, F3, and F4 are disjoint. The simultaneity mapping in terms of F1 maps 5 seconds of the traveler's proper time to 2.5 seconds of the source's proper time, and the same for F2, and F3 and F4, so you might naively think that the total elapsed time for the source is 10 seconds, but that is not true, because the F2 simultaneity mapping maps the traveler's start time at the beginning of edge 2 to an event at the source that is 30/4 seconds *after* the event that maps to the traveler at the end of edge 1. Similarly for the other edge transitions, so this disjoint mapping omits 30 seconds of the source's proper time during each trip around the square..
> > >
> > > In summary, your mistake was three-fold: You failed to account for aberration, you failed to account for Doppler, and you failed to account for the relativity of simultaneity. This is all just Relativity 101.
> > >
> > > Special Relativity: 867 ... Barnpole Dave: 0
> > If the traveler receives 40 flashes from the same light source every 20 seconds...
> > how does he "measure" that the light source is flashing at a rate of one flash per
> > every two seconds...
>
> Again, the correct statement is that the flash rate of the source in terms of (say) F1 is 0.5 flashes per second, and, as clearly explained above, this can be measured in any normal way, e.g., by a grid of standard clocks mutually at rest and inertially synchronized in F1.

Anyone can check GPS, your gedanken
idiocies have nothing in common with any
normal way of measuring. Sorry.

Le 23/04/2022 à 16:24, Al Coe a écrit :

> the relativity of simultaneity.

That's what I say.

R.H.

On Saturday, April 23, 2022 at 12:03:39 PM UTC-5, Al Coe wrote:
> On Saturday, April 23, 2022 at 9:35:40 AM UTC-7, sep...@yahoo.com wrote:
> > On Saturday, April 23, 2022 at 9:24:48 AM UTC-5, Al Coe wrote:
> > > On Saturday, April 23, 2022 at 5:56:48 AM UTC-7, sep...@yahoo.com wrote:
> > > > During each complete revolution around the square, the traveler's clock changes
> > > > by 20 seconds.
> > >
> > > Yes.
> > > > If he receives 10 flashes along each side of the square, he must conclude that the
> > > > flash rate of the light source is 40 flashes per 20 seconds or 2 flashes per second.
> > > No, you are mixing up the flash rate of the source and the reception rate of the traveler, which are not the same because in terms of F1 (the traveler's co-moving inertial coordinate system on edge 1) the source is approaching the traveler from almost directly ahead (due to aberration), so even though, in terms of F1, the pulse rate of the source is just 0.5 pulses per second, the traveler encounters pulses arriving at 2 per second. Likewise for F2, F3, and F4 (the co-moving inertial coordinate systems in which the traveler is at rest on the other three edges).
> > > > The Lorentz transform however gives the answer as 1 flash every 2 seconds.
> > > Right, in terms of any of the inertial coordinate systems F1, F2, F3, and F4 the pulse rate of the source is 0.5 flashes per second.
> > > > How does the moving traveler measure the flash rate on each side of the square
> > > > to be one flash every two seconds while measuring that he receives flashes at a
> > > > rate of two flashes per second?
> > > See above. In terms of each of the inertial coordinate systems F1, the rate of the source flashes can be measured in any normal way, e.g., by a grid of standard clocks mutually at rest and inertially synchronized in F1. Again, since the source is approaching the traveler at high speed in terms of these coordinates (aberration), the reception rate at the traveler is much higher than the emission rate at the source (Doppler).
> > > > What restrictions must be followed to give a consistent measurement of the flash rate
> > > > by the moving traveler.
> > > The results described above are perfectly consistent, as you can see, once you correctly account for the aberration and Doppler effects.
> > >
> > > As usual, you're not really asking the question that would clear up your confusion. The question you should be asking is, if the rate of proper time dtau/dt of the source is 1/2 in terms of F1, F2, F3, and F4, how is it possible that the rate of the traveler's proper time in terms of F0 on each of those edges is also 1/2, so the traveler's total elapsed time around the square is 1/2 of the sources elapsed time? The answer is that the simultaneity mappings between the events of the traveler and the events of the source in terms of F1, F2, F3, and F4 are disjoint. The simultaneity mapping in terms of F1 maps 5 seconds of the traveler's proper time to 2.5 seconds of the source's proper time, and the same for F2, and F3 and F4, so you might naively think that the total elapsed time for the source is 10 seconds, but that is not true, because the F2 simultaneity mapping maps the traveler's start time at the beginning of edge 2 to an event at the source that is 30/4 seconds *after* the event that maps to the traveler at the end of edge 1. Similarly for the other edge transitions, so this disjoint mapping omits 30 seconds of the source's proper time during each trip around the square..
> > >
> > > In summary, your mistake was three-fold: You failed to account for aberration, you failed to account for Doppler, and you failed to account for the relativity of simultaneity. This is all just Relativity 101.
> > >
> > > Special Relativity: 867 ... Barnpole Dave: 0
> > If the traveler receives 40 flashes from the same light source every 20 seconds...
> > how does he "measure" that the light source is flashing at a rate of one flash per
> > every two seconds...
>
> Again, the correct statement is that the flash rate of the source in terms of (say) F1 is 0.5 flashes per second, and, as clearly explained above, this can be measured in any normal way, e.g., by a grid of standard clocks mutually at rest and inertially synchronized in F1. Of course, there are infinitely many other methods, all giving the same result, but this is the canonical, defining, condition. As the source passes those clocks you will find that dtau/dt = 1/2. Notice that this measurement involves a system of clocks, all mutually at rest and inertially synchronized, as required in order for the equations of physics to hold good in their simple homogeneous and isotropic form. If you still don't understand this, go ahead and explain what you don't understand about it.

As the moving traveler goes around the polygon do you agree that he measures his clock to run slower than the clock at rest in the inertial reference frame that is at the center of the polygon?
David Seppala
Bastrop TX

On Sunday, April 24, 2022 at 9:00:15 AM UTC-7, sep...@yahoo.com wrote:
> As the moving traveler goes around the polygon do you agree that he measures
> his clock to run slower than the clock at rest in the inertial reference frame that
> is at the center of the polygon?

Anyone can measure any specified quantities, such as

dtau_traveler/dt_F0
dtau_traveler/dt_F1 (or F2, or F3, or F4)
dtau_source/dt_F0
dtau_source/dt_F1 (or F2, or F3, or F4)
.... and so on.

These are all measurable quantities. For example, we have dtau_traveler/dt_F0 = 1/2. In words, this signifies that, in terms of the standard inertial coordinate system x,t in which the source is at rest, the proper time tau of the traveler satisfies the relation dtau/dt = 1/2. For another example, we have dtau_source/dt_F1 = 1/2. And so on. Now do you understand? You began by alluding to a "contradiction", but can you actually point out any contradiction?

On Sunday, April 24, 2022 at 11:27:30 AM UTC-5, Al Coe wrote:
> On Sunday, April 24, 2022 at 9:00:15 AM UTC-7, sep...@yahoo.com wrote:
> > As the moving traveler goes around the polygon do you agree that he measures
> > his clock to run slower than the clock at rest in the inertial reference frame that
> > is at the center of the polygon?
> Anyone can measure any specified quantities, such as
>
> dtau_traveler/dt_F0
> dtau_traveler/dt_F1 (or F2, or F3, or F4)
> dtau_source/dt_F0
> dtau_source/dt_F1 (or F2, or F3, or F4)
> ... and so on.
>
> These are all measurable quantities. For example, we have dtau_traveler/dt_F0 = 1/2. In words, this signifies that, in terms of the standard inertial coordinate system x,t in which the source is at rest, the proper time tau of the traveler satisfies the relation dtau/dt = 1/2. For another example, we have dtau_source/dt_F1 = 1/2. And so on. Now do you understand? You began by alluding to a "contradiction", but can you actually point out any contradiction?

If a traveler is moving around the circumference of a circle and there is a clock at rest in the center of the circle, and there is an array of clocks at rest all along the circumference of the circle as the moving traveler passes each clock again and again and compares the time shown on his clock to the time shown on each clock he passes again and again, does his clock show that less time has elapsed compared to all the clocks at rest around and at the center of the circle? See if you can do the science "measurement", and instead of the math.
David Seppala
Bastrop TX

On Sunday, April 24, 2022 at 10:23:10 AM UTC-7, sep...@yahoo.com wrote:
>> we have dtau_traveler/dt_F0 = 1/2. In words, this signifies that, in terms of the
>> standard inertial coordinate system x,t in which the source is at rest, the proper
>> time tau of the traveler satisfies the relation dtau/dt = 1/2.
>
> If a traveler is moving around the circumference of a circle and ... there is an
> array of clocks at rest all along the circumference of the circle, as the moving
> traveler passes each clock, does his clock show that less time has elapsed
> compared to all the clocks at rest around and at the center of the circle?

Of course. That's just dtau_traveler/dt_F0, which I just told you was 1/2. Do you understand this?

I ask again: Where is the contradiction you alluded to?

On Sunday, April 24, 2022 at 12:37:51 PM UTC-5, Al Coe wrote:
> On Sunday, April 24, 2022 at 10:23:10 AM UTC-7, sep...@yahoo.com wrote:
> >> we have dtau_traveler/dt_F0 = 1/2. In words, this signifies that, in terms of the
> >> standard inertial coordinate system x,t in which the source is at rest, the proper
> >> time tau of the traveler satisfies the relation dtau/dt = 1/2.
> >
> > If a traveler is moving around the circumference of a circle and ... there is an
> > array of clocks at rest all along the circumference of the circle, as the moving
> > traveler passes each clock, does his clock show that less time has elapsed
> > compared to all the clocks at rest around and at the center of the circle?
> Of course. That's just dtau_traveler/dt_F0, which I just told you was 1/2. Do you understand this?
>
> I ask again: Where is the contradiction you alluded

So during any leg of the polygon or arc segment of the circle, does the moving traveler ever say that his clock is running faster than the clocks at rest in the inertial reference frame?
David Seppala
Bastrop TX

On Sunday, April 24, 2022 at 10:49:58 AM UTC-7, sep...@yahoo.com wrote:
> So during any leg of the polygon or arc segment of the circle, does the moving
> traveler ever say that his clock is running faster than the clocks at rest in the
> inertial reference frame?

As has been explained to you clearly a dozen times before, the clocks at rest in F0 are running at half speed in terms of the inertial coordinate system Fi in which the traveler is at rest at any given instant. In other words, we have dtau_(objects at rest in F0)/dt_Fi = 1/2 for each Fi. All these objective facts are measureable, and they are what everyone would "say". Do you understand this?

I ask again: Where is the contradiction you alluded to?

On Sunday, April 24, 2022 at 1:08:03 PM UTC-5, Al Coe wrote:
> On Sunday, April 24, 2022 at 10:49:58 AM UTC-7, sep...@yahoo.com wrote:
> > So during any leg of the polygon or arc segment of the circle, does the moving
> > traveler ever say that his clock is running faster than the clocks at rest in the
> > inertial reference frame?
> As has been explained to you clearly a dozen times before, the clocks at rest in F0 are running at half speed in terms of the inertial coordinate system Fi in which the traveler is at rest at any given instant. In other words, we have dtau_(objects at rest in F0)/dt_Fi = 1/2 for each Fi. All these objective facts are measureable, and they are what everyone would "say". Do you understand this?
>
> I ask again: Where is the contradiction you alluded to?
The clocks are not running at half the rate of the clocks of the moving traveler. If so, as the moving traveler makes each trip around the polygon or circle, he would not encounter clocks that always showed more elapsed time then his shows in each passing of a clock.
David Seppala
Bastrop TX

On Sunday, April 24, 2022 at 11:12:10 AM UTC-7, sep...@yahoo.com wrote:
> > > So during any leg of the polygon or arc segment of the circle, does the moving
> > > traveler ever say that his clock is running faster than the clocks at rest in the
> > > inertial reference frame?
> >
> > The clocks at rest in F0 are running at half speed in terms of the inertial coordinate
> > system Fi in which the traveler is at rest at any given instant. In other words, we have
> > dtau_(objects at rest in F0)/dt_Fi = 1/2 for each Fi. All these objective facts are
> > measureable, and they are what everyone would "say". Do you understand this?
> >
> The clocks are not running at half the rate of the clocks of the moving traveler.

Your brain is malfunctioning. Notice that you referred to the clocks (plural) of the traveler, but the traveler is following a single world line, i.e.., representing just one "clock, and when you talk about clocks (plural) you may be talking about the fact that at any given instant he is at rest in terms of a system of inertial coordinates Fi, and we can have an inertial grid of clocks all at rest and inertially synchronized in Fi, and in terms of those clocks each of the clocks at rest in F0 are running slow by the factor 1/2. Likewise each clock at rest in Fi is running slow by the factor 1/2 in terms of the system of clocks at rest and inertially synchronized in F0. Do you understand this?

Look, given two rows of clocks, sliding past each other in opposite directions, and with the clocks in each row inertially synchronized in their respective rest frames, the elapsed time on each clock is less than the difference in times on the clocks of the other row as it passes them. This is perfectly measurable and entirely reciprocal. Do you understand this?

> If so, as the moving traveler makes each trip around the polygon or circle, he
> would not encounter clocks that always showed more elapsed time then his
> shows in each passing of a clock.

Again, your brain is malfunctioning. See above. There is nothing contradictory about the fact that the clocks at rest in F0 run at half speed in terms of each Fi in which the traveler is (sequentially) at rest, and the fact that the clocks at rest in each Fi (and the traveler's clock) run at half speed in terms of F0. Again, see above. Do you understand this now?

On Sunday, April 24, 2022 at 1:40:15 PM UTC-5, Al Coe wrote:
> On Sunday, April 24, 2022 at 11:12:10 AM UTC-7, sep...@yahoo.com wrote:
> > > > So during any leg of the polygon or arc segment of the circle, does the moving
> > > > traveler ever say that his clock is running faster than the clocks at rest in the
> > > > inertial reference frame?
> > >
> > > The clocks at rest in F0 are running at half speed in terms of the inertial coordinate
> > > system Fi in which the traveler is at rest at any given instant. In other words, we have
> > > dtau_(objects at rest in F0)/dt_Fi = 1/2 for each Fi. All these objective facts are
> > > measureable, and they are what everyone would "say". Do you understand this?
> > >
> > The clocks are not running at half the rate of the clocks of the moving traveler.
> Your brain is malfunctioning. Notice that you referred to the clocks (plural) of the traveler, but the traveler is following a single world line, i.e., representing just one "clock, and when you talk about clocks (plural) you may be talking about the fact that at any given instant he is at rest in terms of a system of inertial coordinates Fi, and we can have an inertial grid of clocks all at rest and inertially synchronized in Fi, and in terms of those clocks each of the clocks at rest in F0 are running slow by the factor 1/2. Likewise each clock at rest in Fi is running slow by the factor 1/2 in terms of the system of clocks at rest and inertially synchronized in F0. Do you understand this?
>
> Look, given two rows of clocks, sliding past each other in opposite directions, and with the clocks in each row inertially synchronized in their respective rest frames, the elapsed time on each clock is less than the difference in times on the clocks of the other row as it passes them. This is perfectly measurable and entirely reciprocal. Do you understand this?
> > If so, as the moving traveler makes each trip around the polygon or circle, he
> > would not encounter clocks that always showed more elapsed time then his
> > shows in each passing of a clock.
> Again, your brain is malfunctioning. See above. There is nothing contradictory about the fact that the clocks at rest in F0 run at half speed in terms of each Fi in which the traveler is (sequentially) at rest, and the fact that the clocks at rest in each Fi (and the traveler's clock) run at half speed in terms of F0. Again, see above. Do you understand this now?

I did not say the traveler has multiple clocks - that's what you say is needed. Let the traveler have only one clock. As he completes each trip around the polygon or circumference of a circle he passes the same F0 clock at a given location. Each time time he passes that clock, he sees that the elapsed time on his clock is less than the elapsed time on that clock that he passes. Comprendo?
David Seppala
Bastrop TX

On Sunday, April 24, 2022 at 12:24:48 PM UTC-7, sep...@yahoo.com wrote:
> I did not say the traveler has multiple clocks

Yes you did. Specifically, you said "The clocks are not running at half the rate of the clocks of the moving traveler."

> Let the traveler have only one clock. As he completes each trip around the polygon
> or circumference of a circle he passes the same F0 clock at a given location. Each
> time time he passes that clock, he sees that the elapsed time on his clock is less than
> the elapsed time on that clock that he passes.

Right, that's what I've told you repeatedly, and I've explained in detail. See all my previous posts. And still you fail to point out any contradiction, or any disagreement with any of the facts that I've explained to you. So, are you now in complete agreement with special relativity, or do you have any remaining questions?

On Sunday, April 24, 2022 at 2:38:44 PM UTC-5, Al Coe wrote:
> On Sunday, April 24, 2022 at 12:24:48 PM UTC-7, sep...@yahoo.com wrote:
> > I did not say the traveler has multiple clocks
> Yes you did. Specifically, you said "The clocks are not running at half the rate of the clocks of the moving traveler."
> > Let the traveler have only one clock. As he completes each trip around the polygon
> > or circumference of a circle he passes the same F0 clock at a given location. Each
> > time time he passes that clock, he sees that the elapsed time on his clock is less than
> > the elapsed time on that clock that he passes.
> Right, that's what I've told you repeatedly, and I've explained in detail.. See all my previous posts. And still you fail to point out any contradiction, or any disagreement with any of the facts that I've explained to you. So, are you now in complete agreement with special relativity, or do you have any remaining questions?
So you agree that the traveler's clock is running at a slower rate than the clocks in the inertial reference frame of the polygon or circle.
So show me how this is perfectly reciprocal when the traveler is moving at a constant speed around the circumference of a circle. How does he ever determine that his clock is running faster?
David Seppala
Bastrop TX

On Sunday, April 24, 2022 at 12:54:11 PM UTC-7, sep...@yahoo.com wrote:
> So you agree that the traveler's clock is running at a slower rate than the clocks
> in the inertial reference frame of the polygon or circle.

As already explained, that's an imprecise and unclear statement (at best). To help you understand this, I gave you the example of two linear rows of clocks, moving in opposite directions, and explained that each clock shows less elapsed time between passing consecutive clocks of the other row than the difference between the readings of those other clocks as it passes them.. This is entirely reciprocal, and hence it is imprecise and unclear (at best) to say the clocks in one row run slower (or faster) than clocks in the other row. This just illustrates that you have to be clear and precise in your statements. It is correct to say that each clock runs slow in terms of the inertial coordinates in which the other row is at rest. Likewise for the polygon and circle case, it is correct to say that the traveling clock runs slow in terms of the inertial coordinates in which the source and circumferential clocks are at rest, and of course the latter clocks advance at the normal rate in terms of those coordinates. This is all basic Relativity 101.

> So show me how this is perfectly reciprocal when the traveler is moving at a
> constant speed around the circumference of a circle.

Huh? It is not reciprocal. The two linear rows of clocks are perfectly reciprocal, and these were described to help you understand why you can't just make statements like "these clocks are running slower than those clocks", you have to be very clear and precise. Now, the relations between F0 and Fi for each of the momentarily co-moving inertial coordinate systems of the traveler are perfectly reciprocal, but the traveler is not remaining at rest in terms of any of those frame during his journey, and his shifting from being at rest in one to being at rest in another, etc., breaks the symmetry. The traveler is not inertial.

> How does he ever determine that his clock is running faster?

Already asked and answered a dozen times. Yet again, you cannot be so sloppy and imprecise, you have to ask a precise question such as "Is the source clock running slow in terms of the inertial coordinates Fi in which the traveling clock is at rest at a particular moment?" And the answer is yes, the source is running at 1/2 rate in terms of those coordinates. If you then ask, "How would we measure this?", the answer, as given to you a dozen times, is we have a grid of clocks at rest and inertially synchronized in Fi, and we measure that the source clock shows dtau/dt = 1/2.

Now do you finally understand?

On Sunday, April 24, 2022 at 3:16:55 PM UTC-5, Al Coe wrote:
> On Sunday, April 24, 2022 at 12:54:11 PM UTC-7, sep...@yahoo.com wrote:
> > So you agree that the traveler's clock is running at a slower rate than the clocks
> > in the inertial reference frame of the polygon or circle.
> As already explained, that's an imprecise and unclear statement (at best).. To help you understand this, I gave you the example of two linear rows of clocks, moving in opposite directions, and explained that each clock shows less elapsed time between passing consecutive clocks of the other row than the difference between the readings of those other clocks as it passes them. This is entirely reciprocal, and hence it is imprecise and unclear (at best) to say the clocks in one row run slower (or faster) than clocks in the other row. This just illustrates that you have to be clear and precise in your statements. It is correct to say that each clock runs slow in terms of the inertial coordinates in which the other row is at rest. Likewise for the polygon and circle case, it is correct to say that the traveling clock runs slow in terms of the inertial coordinates in which the source and circumferential clocks are at rest, and of course the latter clocks advance at the normal rate in terms of those coordinates. This is all basic Relativity 101.
> > So show me how this is perfectly reciprocal when the traveler is moving at a
> > constant speed around the circumference of a circle.
> Huh? It is not reciprocal. The two linear rows of clocks are perfectly reciprocal, and these were described to help you understand why you can't just make statements like "these clocks are running slower than those clocks", you have to be very clear and precise. Now, the relations between F0 and Fi for each of the momentarily co-moving inertial coordinate systems of the traveler are perfectly reciprocal, but the traveler is not remaining at rest in terms of any of those frame during his journey, and his shifting from being at rest in one to being at rest in another, etc., breaks the symmetry.. The traveler is not inertial.
> > How does he ever determine that his clock is running faster?
> Already asked and answered a dozen times. Yet again, you cannot be so sloppy and imprecise, you have to ask a precise question such as "Is the source clock running slow in terms of the inertial coordinates Fi in which the traveling clock is at rest at a particular moment?" And the answer is yes, the source is running at 1/2 rate in terms of those coordinates. If you then ask, "How would we measure this?", the answer, as given to you a dozen times, is we have a grid of clocks at rest and inertially synchronized in Fi, and we measure that the source clock shows dtau/dt = 1/2.
> > Now do you finally understand?
If there is a clock at rest on a leg of a polygon or on the circumference of a circle in an inertial reference frame, and there is a traveler moving along the legs of the polygon or the circumference of the circle, and when those two clocks first meet, each as a time of t=t' =0.
If these are the readings of each of those two clocks when they meet:
Clock At Rest Traveler's clock
0 0
40 20
80 40
120 60
N*40 N*20
Please explain how the traveler concludes that his clock is running at a faster rate than the clock at rest?
David Seppala
Bastrop TX

On Sunday, April 24, 2022 at 1:47:13 PM UTC-7, sep...@yahoo.com wrote:
> If there is a clock at rest on a leg of a polygon or on the circumference of a circle
> in an inertial reference frame, and there is a traveler moving along the legs of the
> polygon or the circumference of the circle, and when those two clocks first meet,
> each as a time of t=t' =0... Please explain how the traveler concludes that his clock
> is running at a faster rate than the clock at rest?

Your brain has malfunctioned again. In the previous message I carefully explained why statements like "this clock is running faster than that clock" are imprecise and unclear, and why it is necessary to very precisely and clearly state the objective facts, all of which you ignored and re-asserted your brain-dead muddle. Also, you can't say "clock at rest", you have to say "clock at rest in frame Fxyz".

Again (please try to concentrate), a clock at rest in terms of F0 is running slow in terms of the inertial coordinates Fi in which the traveling clock is at rest at the moment when they pass, and likewise the traveling clock at rest in Fi at that moment is running slow in terms of F0. The system F0 and Fi are reciprocal. This is exactly like the two reciprocal rows of clocks that you ignored. These objective facts can be measured and verified by grids of clocks at rest and inertially synchronized in the respective frames.

Now, suppose you asked a different (less stupid) question, such as: "For the circular loop, what is the rate of the clock at rest in F0 in terms of a system of accelerating coordinates C_accel, T,X, in which the traveler is continuously stationary (constant space coordinates) during his transit around the loop?" The answer to that is dtau/dT = 2, which arises from two countervailing effects, namely, the factor of 1/2 relating the instantaneous inertial coordinate systems, and the factor of 4 arising from the continual shift in the simultaneity mapping between the sequence of inertial systems. This does not contradict any of the facts about inertial coordinate systems, because C_accel is not an inertial coordinate system.

Now do you understand?

On Sunday, April 24, 2022 at 4:47:13 PM UTC-4, sep...@yahoo.com wrote:

> Clock At Rest Traveler's clock
> 0 0
> 40 20
> 80 40
> 120 60
> N*40 N*20
> Please explain how the traveler concludes that his clock is running at a faster rate than the clock at rest?

The traveler does not conclude that.

What he says, or concludes is that as his clock coincides with the "at rest clock(s)" his clock indicates a lesser value.
A lesser value does not mean "slower". In fact, "slower" here is an unnecessary word; 20<40 suffices; 20N < 40N suffices and is clear. So he notes experimentally that 20N < 40N. He also calculates that 20N < 40N. He thus says, or concludes that 20N < 40N.

Can you understand that?

On Sunday, April 24, 2022 at 9:59:31 PM UTC-5, rotchm wrote:
> On Sunday, April 24, 2022 at 4:47:13 PM UTC-4, sep...@yahoo.com wrote:
>
> > Clock At Rest Traveler's clock
> > 0 0
> > 40 20
> > 80 40
> > 120 60
> > N*40 N*20
> > Please explain how the traveler concludes that his clock is running at a faster rate than the clock at rest?
> The traveler does not conclude that.
>
> What he says, or concludes is that as his clock coincides with the "at rest clock(s)" his clock indicates a lesser value.
> A lesser value does not mean "slower". In fact, "slower" here is an unnecessary word; 20<40 suffices; 20N < 40N suffices and is clear. So he notes experimentally that 20N < 40N. He also calculates that 20N < 40N. He thus says, or concludes that 20N < 40N.
> > Can you understand that?

If a clock always shows a lesser value than another clock, and that difference in times between the two clocks keeps getting greater and greater with every reading of the clocks, doesn't that mean than one clock is running at a slower rate than the other clock?

So if the traveler is moving along one leg of a polygon (say a square) with velocity V relative to the inertial frame the polygon is in, and there is a clock at rest at the center of the polygon, what does the traveler say the readings of his clock relative to the clock at the center of the polygon is? The Lorentz transform gives the result that the clock at rest in the center of the polygon is running at a slower rate than the traveler's clock.
David Seppala
Bastrop TX