I don't see how the speed of light is measured in this gedanken experiment.
There are two inertial reference frames, F0 and F1, with relative velocity V=c*sqrt(3)/2 along the x-axis. At two points along the x-axis separated by a distance L = sqrt(3)/2 light-seconds as measured in F0 light from a source in F0 hits the first point and then one second later light from the same source hits the second point. Per the Lorentz transform, these two events occur 1/2 second apart as measured by observers in F1.
Now let's say these two points are on a very, very large diameter circle in F0. There is a traveler moving with angular velocity approximately V=c*sqrt(3)/2 as measured in F0. During that segment with the light pulses described above, that traveler and the observers in F1 have almost zero speed relative to each other, therefore that traveler's clock would also show that 1/2 second elapsed between those two pulses.
Let's say the observers in F0 placed 100,000 of these equally spaced points around the circumference of the circle, and the circumference of the circle is such that the traveler's speed takes him 100,000 seconds to travel the entire circumference of that circle. So if the traveler measures the time between each light pulse to be 1/2, and the traveler receives 100,000 light pulses during each trip around the circle , the traveler's clock shows that 50,000 seconds have elapsed during each trip around the circumference.
Now if the circle is centered at (0,0) as measured in F0, and when the traveler at that point in time is at (0,R) a light pulse is sent perpendicular (in the z direction) to the traveler's motion, and hits a mirror that is 50,000 light seconds above the circle (as measured in F0), and reflects back down to (0,R), that light pulse will arrive at (0,R) the same instant in time the traveler completes one revolution of the circle.
If the traveler measures the distance between that light pulse's starting point and return point to be greater than 50,000 light seconds, the traveler will measure the speed of light to be greater than the standard speed of light c. So how does this traveler measure that the speed of light is no greater than the speed of light measured in F0?
Thanks,
David Seppala
Bastrop TX

On Saturday, November 6, 2021 at 7:43:41 AM UTC-7, sep...@yahoo.com wrote:
> How does this traveler measure that the speed of light is no greater than the speed of light measured in F0?

Again, the assertion of special relativity is that the speed of light (in vacuum) has the speed 1 (i.e., c in conventional units) in terms of each system of inertia-based coordinates. In particular, this applies to the speed of light in terms of the inertia-based coordinates in which a given traveler (or dog, or bowling ball) is at rest at any given moment.

You have specified that the pulse in question, in terms of F0, goes outbound from (t,x,y,z) = (0,0,R,0) to (h,0,R,h), so the speed is h/h = 1. In terms of F1, which is moving in the positive x direction at speed v in terms of F0, those events have the coordinates (0,0,R,0) and (gh,-vgh,R,h) where g=1/sqrt(1-v^2), so the speed is hg/(hg) = 1. Likewise the return leg has speed 1 in terms of both F0 and F1. The same applies to the inertia-based coordinate system in which your dog is at rest at any other moment during his journey around the circle.

Needless to say, the elapsed proper time for the object moving around the circle also agrees with special relativity, and at every moment the traveler's proper time advances at the same rate as the coordinate time of the inertia-based coordinates in which he is momentarily at rest.

Special Relativity: 842 ... Barnpole Dave: 0

On Saturday, November 6, 2021 at 9:44:20 AM UTC-7, Al Coe wrote:
> On Saturday, November 6, 2021 at 7:43:41 AM UTC-7, sep...@yahoo.com wrote:
> > How does this traveler measure that the speed of light is no greater than the speed of light measured in F0?
>
> Again, the assertion of special relativity is that the speed of light (in vacuum) has the speed 1 (i.e., c in conventional units) in terms of each system of inertia-based coordinates. In particular, this applies to the speed of light in terms of the inertia-based coordinates in which a given traveler (or dog, or bowling ball) is at rest at any given moment.
>
> You have specified that the pulse in question, in terms of F0, goes outbound from (t,x,y,z) = (0,0,R,0) to (h,0,R,h), so the speed is h/h = 1. In terms of F1, which is moving in the positive x direction at speed v in terms of F0, those events have the coordinates (0,0,R,0) and (gh,-vgh,R,h) where g=1/sqrt(1-v^2), so the speed is hg/(hg) = 1. Likewise the return leg has speed 1 in terms of both F0 and F1. The same applies to the inertia-based coordinate system in which your dog is at rest at any other moment during his journey around the circle.
>
> Needless to say, the elapsed proper time for the object moving around the circle also agrees with special relativity, and at every moment the traveler's proper time advances at the same rate as the coordinate time of the inertia-based coordinates in which he is momentarily at rest.
>
> Special Relativity: 842 ... Barnpole Dave: 0

The light speed measurement is just a collective average.
Light is quantize in waves of energy.

On Saturday, November 6, 2021 at 11:44:20 AM UTC-5, Al Coe wrote:
> On Saturday, November 6, 2021 at 7:43:41 AM UTC-7, sep...@yahoo.com wrote:
> > How does this traveler measure that the speed of light is no greater than the speed of light measured in F0?
>
> Again, the assertion of special relativity is that the speed of light (in vacuum) has the speed 1 (i.e., c in conventional units) in terms of each system of inertia-based coordinates. In particular, this applies to the speed of light in terms of the inertia-based coordinates in which a given traveler (or dog, or bowling ball) is at rest at any given moment.
>
> You have specified that the pulse in question, in terms of F0, goes outbound from (t,x,y,z) = (0,0,R,0) to (h,0,R,h), so the speed is h/h = 1. In terms of F1, which is moving in the positive x direction at speed v in terms of F0, those events have the coordinates (0,0,R,0) and (gh,-vgh,R,h) where g=1/sqrt(1-v^2), so the speed is hg/(hg) = 1. Likewise the return leg has speed 1 in terms of both F0 and F1. The same applies to the inertia-based coordinate system in which your dog is at rest at any other moment during his journey around the circle.
>
> Needless to say, the elapsed proper time for the object moving around the circle also agrees with special relativity, and at every moment the traveler's proper time advances at the same rate as the coordinate time of the inertia-based coordinates in which he is momentarily at rest.
>
> Special Relativity: 842 ... Barnpole Dave: 0

When the traveler makes one complete trip around the circumference of the circle, do you agree that his clock shows an elapsed time of 50,000 seconds, or there abouts?
David Seppala
Bastrop TX

On Saturday, November 6, 2021 at 10:46:40 AM UTC-7, sep...@yahoo.com wrote:
> When the traveler makes one complete trip around the circumference of the circle, do
> you agree that his clock shows an elapsed time of 50,000 seconds, or there abouts?

There abouts? Given the stated conditions, the elapsed time on the clock to travel a distance of L at speed v is Lsqrt(1-v^2), which is exactly L/2 for the v you specified. And, yes, this is perfectly consistent with special relativity, and, no, it does not entail any contradiction. If you don't understand this, please re-read the explanation above, bearing in mind that special relativity does not assert that the speed of light is c in terms of arbitrary coordinate systems, only in terms of inertia-based coordinate systems. The coordinate system currently swimming around in your brain is not an inertia-based coordinate system. Understand?

Op 06-nov.-2021 om 19:45 schreef Al Coe:
> On Saturday, November 6, 2021 at 10:46:40 AM UTC-7, sep...@yahoo.com wrote:

[snip]

> The
> coordinate system currently swimming around in your brain

LOL!

Dirk Vdm

On Saturday, 6 November 2021 at 19:45:52 UTC+1, Al Coe wrote:
> On Saturday, November 6, 2021 at 10:46:40 AM UTC-7, sep...@yahoo.com wrote:
> > When the traveler makes one complete trip around the circumference of the circle, do
> > you agree that his clock shows an elapsed time of 50,000 seconds, or there abouts?
> There abouts? Given the stated conditions, the elapsed time on the clock to travel a distance of L at speed v is Lsqrt(1-v^2), which is exactly L/2 for the v you specified. And, yes, this is perfectly consistent with special relativity,

But in the meantime in the real world, forbidden
by your moronic religion GPS clocks keep measuring
t'=t, just like all serious clocks always did.

On Saturday, November 6, 2021 at 1:45:52 PM UTC-5, Al Coe wrote:
> On Saturday, November 6, 2021 at 10:46:40 AM UTC-7, sep...@yahoo.com wrote:
> > When the traveler makes one complete trip around the circumference of the circle, do
> > you agree that his clock shows an elapsed time of 50,000 seconds, or there abouts?
> There abouts? Given the stated conditions, the elapsed time on the clock to travel a distance of L at speed v is Lsqrt(1-v^2), which is exactly L/2 for the v you specified. And, yes, this is perfectly consistent with special relativity, and, no, it does not entail any contradiction. If you don't understand this, please re-read the explanation above, bearing in mind that special relativity does not assert that the speed of light is c in terms of arbitrary coordinate systems, only in terms of inertia-based coordinate systems. The coordinate system currently swimming around in your brain is not an inertia-based coordinate system. Understand?

So you agree that the traveler's clock shows 50,000 seconds of elapsed time per each complete trip around the circumference of the circle. How far does the traveler say the light pulse sent in the z direction at the start of the traveler's trip around the circle travels until the traveler returns to that same start point in F0 when that pulse simultaneously returns there?
David Seppala
Bastrop TX

On Saturday, November 6, 2021 at 1:15:16 PM UTC-7, sep...@yahoo.com wrote:
> How far does the traveler say the light pulse sent in the z direction at the start of
> the traveler's trip around the circle travels until the traveler returns to that same
> start point in F0 when that pulse simultaneously returns there?

Again, talking about what someone says is hopelessly ambiguous. People can say all kinds of things. A relevant question would be (for example) "What spatial distance does the outbound pulse traverse in terms of the inertia-based coordinates in which the traveler is at rest at the moment when he is at (0,0,R,0)?" As explained previously, the answer is gh, and the time for the pulse to complete that outbound leg in terms of these coordinates is also gh, so the speed of light in terms of these inertia-based coordinates is 1.

Again, what your brain is dimly imagining is a system of coordinates in which the time coordinate corresponds to the proper time of the traveler, the locus of simultaneity is taken from the inertia-based coordinates in which the center of the circle is at rest, and the space coordinates are taken from a rotating system of coordinates in which the traveler is stationary. That is *not* an inertia-based coordinate system, and the speed of light is obviously not 1 in terms of those coordinates, and special relativity does not say that the speed of light is 1 in terms of those coordinates. So your 842nd attempt to find a contradiction in special relativity has failed... and it has failed for the same reason as the previous 841 attempts.

Look, this is just Relativity 101: Suppose a star is 100 light years away, and you accelerate outward and reach the star in just 10 years of proper time on your clock. Every clueless newbie says "Ahah! I traveled 100 light years in 10 years, so I exceeded the speed of light!" But of course you did not exceed the speed of light in terms of any system of inertia-based coordinates.

If you're going to show that the speed of light (or anything else) exceeds 1 in terms of some system of inertia-based coordinates, then you need to point out a system of inertia-based coordinates in which the speed of light (or something else) exceeds 1. But you cannot do this, because inertia-based coordinate systems are related by Lorentz transformations, which, by grade school algebra, preserve the speed of light. Now do you understand?

On Saturday, November 6, 2021 at 3:54:56 PM UTC-5, Al Coe wrote:
> On Saturday, November 6, 2021 at 1:15:16 PM UTC-7, sep...@yahoo.com wrote:
> > How far does the traveler say the light pulse sent in the z direction at the start of
> > the traveler's trip around the circle travels until the traveler returns to that same
> > start point in F0 when that pulse simultaneously returns there?
> Again, talking about what someone says is hopelessly ambiguous. People can say all kinds of things. A relevant question would be (for example) "What spatial distance does the outbound pulse traverse in terms of the inertia-based coordinates in which the traveler is at rest at the moment when he is at (0,0,R,0)?" As explained previously, the answer is gh, and the time for the pulse to complete that outbound leg in terms of these coordinates is also gh, so the speed of light in terms of these inertia-based coordinates is 1.
>
> Again, what your brain is dimly imagining is a system of coordinates in which the time coordinate corresponds to the proper time of the traveler, the locus of simultaneity is taken from the inertia-based coordinates in which the center of the circle is at rest, and the space coordinates are taken from a rotating system of coordinates in which the traveler is stationary. That is *not* an inertia-based coordinate system, and the speed of light is obviously not 1 in terms of those coordinates, and special relativity does not say that the speed of light is 1 in terms of those coordinates. So your 842nd attempt to find a contradiction in special relativity has failed... and it has failed for the same reason as the previous 841 attempts.
>
> Look, this is just Relativity 101: Suppose a star is 100 light years away, and you accelerate outward and reach the star in just 10 years of proper time on your clock. Every clueless newbie says "Ahah! I traveled 100 light years in 10 years, so I exceeded the speed of light!" But of course you did not exceed the speed of light in terms of any system of inertia-based coordinates.
>
> If you're going to show that the speed of light (or anything else) exceeds 1 in terms of some system of inertia-based coordinates, then you need to point out a system of inertia-based coordinates in which the speed of light (or something else) exceeds 1. But you cannot do this, because inertia-based coordinate systems are related by Lorentz transformations, which, by grade school algebra, preserve the speed of light. Now do you understand?
Answer the simple question, from a "physics" point of view and not from a "math" point of view. When the traveler is at (0,R) what does he measure as the distance to the mirror that is at (0,R, 50,000 light-seconds) as measured in F0?
David Seppala
Bastrop TX

On Saturday, November 6, 2021 at 2:15:05 PM UTC-7, sep...@yahoo.com wrote:
> Answer the simple question, from a "physics" point of view and not from a "math" point of view.

I answered the question from a physics point of view. Inertia-based coordinate systems are a physical concept, defined as the systems of coordinates in terms of which all the equations of physics take their homogeneous and isotropic form. The speed of light in vacuum always has the value 1 in terms of such systems. Do you understand this?

> When the traveler is at (0,R) what does he measure as the distance to the mirror
> that is at (0,R, 50,000 light-seconds) as measured in F0?

Again, in terms of the inertia-based coordinates (F1) in which the traveler is at rest at that moment, those events have the coordinates (0,0,R,0) and (gh,-vgh,R,h) where g=1/sqrt(1-v^2), so the distance to the mirror is hg and the speed is hg/(hg) = 1.

The distance in terms of the travelers inertia-based rest coordinates at that moment will always be hg, no matter how many times you ask. If you don't believe me, try asking the question again; the answer will still be hg. Understand?

Special Relativity: 843 ... Barnpole Dave: 0

On Saturday, November 6, 2021 at 4:34:54 PM UTC-5, Al Coe wrote:
> On Saturday, November 6, 2021 at 2:15:05 PM UTC-7, sep...@yahoo.com wrote:
> > Answer the simple question, from a "physics" point of view and not from a "math" point of view.
> I answered the question from a physics point of view. Inertia-based coordinate systems are a physical concept, defined as the systems of coordinates in terms of which all the equations of physics take their homogeneous and isotropic form. The speed of light in vacuum always has the value 1 in terms of such systems. Do you understand this?
> > When the traveler is at (0,R) what does he measure as the distance to the mirror
> > that is at (0,R, 50,000 light-seconds) as measured in F0?
> Again, in terms of the inertia-based coordinates (F1) in which the traveler is at rest at that moment, those events have the coordinates (0,0,R,0) and (gh,-vgh,R,h) where g=1/sqrt(1-v^2), so the distance to the mirror is hg and the speed is hg/(hg) = 1.
>
> The distance in terms of the travelers inertia-based rest coordinates at that moment will always be hg, no matter how many times you ask. If you don't believe me, try asking the question again; the answer will still be hg. Understand?
>
> Special Relativity: 843 ... Barnpole Dave: 0
What does hg stand for?
David Seppala
Bastrop TX

On Saturday, November 6, 2021 at 9:31:05 PM UTC-7, sep...@yahoo.com wrote:
> What does hg stand for?

The same thing it stood for in my first message in this thread, posted hours ago, that you ignored. It is seven sentences. Do you have the attention span to read seven sentences? Is there anything in those seven sentences that you think is wrong or unclear? Here's the message again to refresh your memory:

On Saturday, November 6, 2021 at 7:43:41 AM UTC-7, sep...@yahoo.com wrote:
> How does this traveler measure that the speed of light is no greater than the speed of light measured in F0?

Again, the assertion of special relativity is that the speed of light (in vacuum) has speed 1 (i.e., c in conventional units) in terms of each system of inertia-based coordinates. In particular, this applies to the speed of light in terms of the inertia-based coordinates in which a given traveler (or dog, or bowling ball) is at rest at any given moment.

You've specified that the pulse in question, in terms of F0, goes outbound from (t,x,y,z) = (0,0,R,0) to (h,0,R,h), so the speed is h/h = 1. In terms of F1, which is moving in the positive x direction at speed v in terms of F0, those events have the coordinates (0,0,R,0) and (gh,-vgh,R,h) where g=1/sqrt(1-v^2), so the speed is hg/(hg) = 1. Likewise the return leg has speed 1 in terms of both F0 and F1. The same applies to the inertia-based coordinate system in which your dog is at rest at any other moment during his journey around the circle.

Needless to say, the elapsed proper time for the object moving around the circle also agrees with special relativity, and at every moment the traveler's proper time advances at the same rate as the coordinate time of the inertia-based coordinates in which he's momentarily at rest.

Special relativity: 842 ..... Barnpole Dave: 0

On Sunday, 7 November 2021 at 05:48:28 UTC+1, Al Coe wrote:
> On Saturday, November 6, 2021 at 9:31:05 PM UTC-7, sep...@yahoo.com wrote:
> > What does hg stand for?
> The same thing it stood for in my first message in this thread, posted hours ago, that you ignored. It is seven sentences. Do you have the attention span to read seven sentences? Is there anything in those seven sentences that you think is wrong or unclear? Here's the message again to refresh your memory:
> On Saturday, November 6, 2021 at 7:43:41 AM UTC-7, sep...@yahoo.com wrote:
> > How does this traveler measure that the speed of light is no greater than the speed of light measured in F0?
> Again, the assertion of special relativity is that the speed of light (in vacuum) has speed 1 (i.e., c in conventional units) in terms of each system of inertia-based coordinates. In particular, this applies to the speed of light in terms of the inertia-based coordinates in which a given traveler (or dog, or bowling ball) is at rest at any given moment.

Again, in the meantime in the real world, forbidden
by your moronic religion GPS clocks keep measuring
t'=t, just like all serious clocks always did.

On Saturday, November 6, 2021 at 11:48:28 PM UTC-5, Al Coe wrote:
> On Saturday, November 6, 2021 at 9:31:05 PM UTC-7, sep...@yahoo.com wrote:
> > What does hg stand for?
> The same thing it stood for in my first message in this thread, posted hours ago, that you ignored. It is seven sentences. Do you have the attention span to read seven sentences? Is there anything in those seven sentences that you think is wrong or unclear? Here's the message again to refresh your memory:
> On Saturday, November 6, 2021 at 7:43:41 AM UTC-7, sep...@yahoo.com wrote:
> > How does this traveler measure that the speed of light is no greater than the speed of light measured in F0?
> Again, the assertion of special relativity is that the speed of light (in vacuum) has speed 1 (i.e., c in conventional units) in terms of each system of inertia-based coordinates. In particular, this applies to the speed of light in terms of the inertia-based coordinates in which a given traveler (or dog, or bowling ball) is at rest at any given moment.
>
> You've specified that the pulse in question, in terms of F0, goes outbound from (t,x,y,z) = (0,0,R,0) to (h,0,R,h), so the speed is h/h = 1. In terms of F1, which is moving in the positive x direction at speed v in terms of F0, those events have the coordinates (0,0,R,0) and (gh,-vgh,R,h) where g=1/sqrt(1-v^2), so the speed is hg/(hg) = 1. Likewise the return leg has speed 1 in terms of both F0 and F1. The same applies to the inertia-based coordinate system in which your dog is at rest at any other moment during his journey around the circle.
>
> Needless to say, the elapsed proper time for the object moving around the circle also agrees with special relativity, and at every moment the traveler's proper time advances at the same rate as the coordinate time of the inertia-based coordinates in which he's momentarily at rest.
>
> Special relativity: 842 ..... Barnpole Dave: 0

Instead of using F1 or F0 coordinates in your explanation, tell me what elapsed time is shown on the traveler's clock from the time when the pulse is emitted from the circumference at the point where the traveler is at, then reflected off the mirror and returns to the traveler when he makes one complete circumference.
Then, if you can, tell me how far the traveler measures the separation between him and the mirror.
Just give me those two measurements made by the traveler.

David Seppala
Bastrop TX

On Sunday, November 7, 2021 at 5:33:18 AM UTC-8, sep...@yahoo.com wrote:
> Instead of using F1 or F0 coordinates in your explanation...

I didn't just give you the answer in terms of F0 and F1, I gave you the answer for *every* system of inertia-based coordinates, and showed that, in every case, the distance divided by the time for the pulse of light is 1. This is what you are challenging, remember? You claimed that there is an inertia-based coordinate system in which the speed of light is not equal to 1, and your claim has been thoroughly debunked.

You've also been informed that it is trivial to define systems of coordinates in which the speed of light is not equal to 1, such as by mixing the distance measurement of one system with the time measurement of another, which is what you are trying to do. You keep trying to use the distance in terms of the inertial coordinates in which the circle is at rest and the proper time of the traveler moving along the circumference of the circle at high speed. By mixing up two different systems of reference, you do not have an inertia-based system of coordinates.

> Just give me those two measurements made by the traveler.

Again, I have done that repeatedly and explicitly. Remember, in special relativity when adults talk about something "as measured by X" they are just using this as sloppy shorthand for "in terms of the inertia-based coordinates in which X is at rest". Thus your question is asking for the distances and durations of the light pulse in terms of the inertial coordinates in which the traveler is at rest, at each moment during his journey, and I have given you all of those explicitly (you're welcome), and shown that in each case the speed of the pulse is 1.

> tell me what elapsed time is shown on the traveler's clock...[and] how far the traveler
> measures the separation between him and the mirror.

Again, the phrase "as measured by the traveler" means "in terms of inertial coordinates in which the traveler is at rest", which of course is changing as the traveler accelerates around the circle, progressing from being at rest in a sequence of inertial coordinate systems. As an example, when the traveler is at (t,x,y,z)=(0,0,R,0) he is at rest in an inertial coordinate system in which the spatial distance between emission and reflection events is gh and the duration of the pulse travel is gh so the speed of the pulse in terms of this coordinate system (in which the traveler is at rest) is 1. We can do the same thing for any other point on the traveler's journey, and show that the speed of the pulse is 1 in terms of his inertial rest frame at that point.

Now do you understand? If not, what part of the explanation and the answer do you think is wrong or unclear?

On Sunday, 7 November 2021 at 16:28:57 UTC+1, Al Coe wrote:
> On Sunday, November 7, 2021 at 5:33:18 AM UTC-8, sep...@yahoo.com wrote:
> > Instead of using F1 or F0 coordinates in your explanation...
>
> I didn't just give you the answer in terms of F0 and F1, I gave you the answer for *every* system of inertia-based coordinates, and showed that, in every case, the distance divided by the time for the pulse of light is 1. This is what you are challenging, remember? You claimed that there is an inertia-based coordinate system in which the speed of light is not equal to 1, and your claim has been thoroughly debunked.
>
> You've also been informed that it is trivial to define systems of coordinates in which the speed of light is not equal to 1, such as by mixing the distance measurement of one system with the time measurement of another, which is what you are trying to do. You keep trying to use the distance in terms of the inertial coordinates in which the circle is at rest and the proper time of the traveler moving along the circumference of the circle at high speed. By mixing up two different systems of reference, you do not have an inertia-based system of coordinates.

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

On Sunday, November 7, 2021 at 9:28:57 AM UTC-6, Al Coe wrote:
> On Sunday, November 7, 2021 at 5:33:18 AM UTC-8, sep...@yahoo.com wrote:
> > Instead of using F1 or F0 coordinates in your explanation...
>
> I didn't just give you the answer in terms of F0 and F1, I gave you the answer for *every* system of inertia-based coordinates, and showed that, in every case, the distance divided by the time for the pulse of light is 1. This is what you are challenging, remember? You claimed that there is an inertia-based coordinate system in which the speed of light is not equal to 1, and your claim has been thoroughly debunked.
>
> You've also been informed that it is trivial to define systems of coordinates in which the speed of light is not equal to 1, such as by mixing the distance measurement of one system with the time measurement of another, which is what you are trying to do. You keep trying to use the distance in terms of the inertial coordinates in which the circle is at rest and the proper time of the traveler moving along the circumference of the circle at high speed. By mixing up two different systems of reference, you do not have an inertia-based system of coordinates.
> > Just give me those two measurements made by the traveler.
> Again, I have done that repeatedly and explicitly. Remember, in special relativity when adults talk about something "as measured by X" they are just using this as sloppy shorthand for "in terms of the inertia-based coordinates in which X is at rest". Thus your question is asking for the distances and durations of the light pulse in terms of the inertial coordinates in which the traveler is at rest, at each moment during his journey, and I have given you all of those explicitly (you're welcome), and shown that in each case the speed of the pulse is 1.
>
> > tell me what elapsed time is shown on the traveler's clock...[and] how far the traveler
> > measures the separation between him and the mirror.
> Again, the phrase "as measured by the traveler" means "in terms of inertial coordinates in which the traveler is at rest", which of course is changing as the traveler accelerates around the circle, progressing from being at rest in a sequence of inertial coordinate systems. As an example, when the traveler is at (t,x,y,z)=(0,0,R,0) he is at rest in an inertial coordinate system in which the spatial distance between emission and reflection events is gh and the duration of the pulse travel is gh so the speed of the pulse in terms of this coordinate system (in which the traveler is at rest) is 1. We can do the same thing for any other point on the traveler's journey, and show that the speed of the pulse is 1 in terms of his inertial rest frame at that point.
>
> Now do you understand? If not, what part of the explanation and the answer do you think is wrong or unclear?

The traveler is never "at rest". So start with something simple. If his clock shows t=0 when the light pulse is emitted, in this scenario, what does the traveler's clock show when he completes one trip around the circumference of the circle just as the light pulse returns?
Just give me a number in seconds, if you can.
David Seppala
Bastrop TX

On Sunday, November 7, 2021 at 8:18:42 AM UTC-8, sep...@yahoo.com wrote:
> The traveler is never "at rest".

As always, you are mistaken. The traveler (and everything else) is *always* at rest in terms of some system of inertial coordinates. If an object is unaccelerated, then it is continually at rest in a single system of inertial coordinates, whereas if it is accelerating it is at rest in a sequence of inertial coordinate systems. It is vitally important for you to understand this. This is basic physics, not unique to special relativity. The same is true in Newtonian physics.

> If his clock shows t=0 when the light pulse is emitted, in this scenario, what does the
> traveler's clock show when he completes one trip around the circumference of the
> circle just as the light pulse returns?

What is wrong with you? How many times does the same question need to be answered? If you scroll up to the previous messages you can see the answer to this trivial question has been given multiple times... and you can also see that the elapsed time on an accelerating clock between two events does not equal the elapsed time in terms of any system of inertial coordinates. Remember, your claim is that the speed of light is not 1 in terms of some system of inertial coordinates, but your claim has been thoroughly debunked..

You've also been informed that it is trivial to mix and match space and time coordinates from different systems such that the speed of light is not 1 in terms of those mixed coordinates, and this is what you are doing. Remember the space traveler going to a star 100 light years away in just 10 years of elapsed time on his clock. You see, the 100 lightyear distance is in terms of one frame, and the elapsed proper time on the clock is the time of a different frame. This is exactly what you are doing by trying to combine the elapsed time on the traveler's clock with the distance in terms of the stationary circle's frame (in which the traveler is moving at high speed). Now do you understand the fallacy of your reasoning?

On Sunday, November 7, 2021 at 11:16:13 AM UTC-6, Al Coe wrote:
> On Sunday, November 7, 2021 at 8:18:42 AM UTC-8, sep...@yahoo.com wrote:
> > The traveler is never "at rest".
> As always, you are mistaken. The traveler (and everything else) is *always* at rest in terms of some system of inertial coordinates. If an object is unaccelerated, then it is continually at rest in a single system of inertial coordinates, whereas if it is accelerating it is at rest in a sequence of inertial coordinate systems. It is vitally important for you to understand this. This is basic physics, not unique to special relativity. The same is true in Newtonian physics.
> > If his clock shows t=0 when the light pulse is emitted, in this scenario, what does the
> > traveler's clock show when he completes one trip around the circumference of the
> > circle just as the light pulse returns?
> What is wrong with you? How many times does the same question need to be answered? If you scroll up to the previous messages you can see the answer to this trivial question has been given multiple times... and you can also see that the elapsed time on an accelerating clock between two events does not equal the elapsed time in terms of any system of inertial coordinates. Remember, your claim is that the speed of light is not 1 in terms of some system of inertial coordinates, but your claim has been thoroughly debunked.
>
> You've also been informed that it is trivial to mix and match space and time coordinates from different systems such that the speed of light is not 1 in terms of those mixed coordinates, and this is what you are doing. Remember the space traveler going to a star 100 light years away in just 10 years of elapsed time on his clock. You see, the 100 lightyear distance is in terms of one frame, and the elapsed proper time on the clock is the time of a different frame. This is exactly what you are doing by trying to combine the elapsed time on the traveler's clock with the distance in terms of the stationary circle's frame (in which the traveler is moving at high speed). Now do you understand the fallacy of your reasoning?

The circle has 100,000 equally spaced marks (as viewed in F0) along the circle's circumference. The marks and circle size are such that when the traveler moves with velocity V the F0 observers measure that it takes one second for the traveler to go from mark to mark. When the traveler starts at the first mark and travels to the second mark, the traveler has virtually zero velocity with respect to F1. F1 observers and hence the traveler see that a half second elapses on the travelers clock from the first mark to the second. Now F1 observers measure that the elapsed time for the traveler to go from mark to mark varies as he travels around the circumference of the circle (or oval as viewed in F1). However, the traveler observes nothing different in the elapsed time readings of his clock as a he travels from mark to mark, so the elapsed time shown on his clock upon reaching the first mark is 0.5 seconds, at the 2nd mark it reads 1 second, at the third mark it reads 1.5 seconds, etc, and when he finally travels the complete circumference of the circle at mark 100,000 the traveler's clock reads 50,000 seconds.
Now when he completes one trip around the circumference, observers in F0 measure that the trip took 100,000 seconds, observers in F1 measure that the trip took 200,000 seconds, and the elapsed time shown on the traveler's clock shows 50,000 seconds have elapsed.
Is there anything wrong with that logic?
David Seppala
Bastrop TX

On Sunday, November 7, 2021 at 11:54:29 AM UTC-8, sep...@yahoo.com wrote:
> When he completes one trip around the circumference, observers in F0 measure
> that the trip took 100,000 seconds, observers in F1 measure that the trip took 200,000
> seconds, and the elapsed time shown on the traveler's clock shows 50,000 seconds
> have elapsed. Is there anything wrong with that logic?

What you've stated isn't "logic", you are merely making some assertions which are garbled in your habitual fashion, but an adult familiar with your antics can see that what your brain is struggling to express is that between the departure and arrival events the F0 coordinate time is 100,000 sec, the F1 coordinate time is 200,000 sec, and the elapsed proper time on the circling clock is 50,000 sec. This has all been explained repeatedly, so why your brain feels compelled to keep repeating it is a mystery of psychiatry.

And these trivial facts are all in perfect accord with special relativity (indeed, special relativity is how we know these figures), and this is perfectly consistent with the fact that the speed of the pulse is 1 in terms of each of the traveler's inertial rest frames during his journey... and every other system of inertial coordinates. This debunks your claim that there is an inertial coordinate system in terms of which the speed of light is not 1. Your fallacy - combining the time of one system with the distance of another - has been explained clearly and repeatedly. Do you finally understand this?

On Sunday, November 7, 2021 at 2:36:50 PM UTC-6, Al Coe wrote:
> On Sunday, November 7, 2021 at 11:54:29 AM UTC-8, sep...@yahoo.com wrote:
> > When he completes one trip around the circumference, observers in F0 measure
> > that the trip took 100,000 seconds, observers in F1 measure that the trip took 200,000
> > seconds, and the elapsed time shown on the traveler's clock shows 50,000 seconds
> > have elapsed. Is there anything wrong with that logic?
> What you've stated isn't "logic", you are merely making some assertions which are garbled in your habitual fashion, but an adult familiar with your antics can see that what your brain is struggling to express is that between the departure and arrival events the F0 coordinate time is 100,000 sec, the F1 coordinate time is 200,000 sec, and the elapsed proper time on the circling clock is 50,000 sec. This has all been explained repeatedly, so why your brain feels compelled to keep repeating it is a mystery of psychiatry.
>
> And these trivial facts are all in perfect accord with special relativity (indeed, special relativity is how we know these figures), and this is perfectly consistent with the fact that the speed of the pulse is 1 in terms of each of the traveler's inertial rest frames during his journey... and every other system of inertial coordinates. This debunks your claim that there is an inertial coordinate system in terms of which the speed of light is not 1. Your fallacy - combining the time of one system with the distance of another - has been explained clearly and repeatedly. Do you finally understand this?

You say my fallacy is "combining the time of one system with the distance of another".
So please explain the distance from the traveler to the mirror as measured by the traveler moving around the circumference of the circle. Observers in both F0 and F1 measure the distance from the plane of the circle to the mirror above the circumference of the circle to be 15*10**12 meters, if the speed of light is 3*10**8 meters/second. What does the traveling observer measure as the distance between him and the mirror? Just give me a number, if you can.
David Seppala
Bastrop TX

On Sunday, November 7, 2021 at 1:39:34 PM UTC-8, sep...@yahoo.com wrote:
> Please explain the distance from the traveler to the mirror as measured by the
> traveler moving around the circumference of the circle.

The distance from the traveler to the mirror? What on earth does that have to do with anything? Remember, what you are trying to understand is the speed of the pulse of light as it goes from the emission event (0,0,R,0) to (0,0,R,h) in terms of F0. As has been explained many times, in every system of inertial coordinates the speed of the pulse between those events is 1. This debunks your claim. The distance between the traveler as he moves around the circle and the mirror is irrelevant.

> Observers in both F0 and F1 measure the distance from the plane of the circle to
> the mirror...

Again, that is not the relevant distance for F1. Try to concentrate: The speed of the pulse in terms of any specified system of inertial coordinates x,y,z,t is sqrt(dx^2 + dy^2 + dz^2)/dt where dx,dy,dz,dt are the coordinate differences between the emission and reception events. In terms of F0 the speed is h/h = 1, and in terms of F1 the speed is hg/(hg) = 1. And in terms of any other system of inertial coordinates (including those in which the traveler is at rest at any given moment) the speed is 1. This debunks your claim. Understand?

> What does the traveling observer measure as the distance between him and the mirror?

First, the relevant distance for determining the speed of the pulse has nothing to do with the distance between the traveler and the mirror (or the pulse) as the traveler moves around the circle. The relevant distance is the distance that the pulse traverses. Duh. Second, I remind you that the sloppy colloquial phrase "the distance an observer measures" actually means "the distance in terms of inertial coordinates in which the observer is (momentarily) at rest".

So, a sane (though dull-witted) question for you to ask would be "What is the distance traversed by the pulse of light in terms of the inertial coordinates in which the traveler is at rest?" The answer is that the traveler is accelerating, so he is successively at rest in a succession of inertial coordinate systems. The distance traversed by the pulse is different in terms of each of these systems, as is the propagation time, but the ratio of distance over time in every case is 1. That means the speed of light is always 1 in terms of the inertial coordinates in which the traveler is at rest at any given moment. Understand?

On Sunday, November 7, 2021 at 5:22:08 PM UTC-6, Al Coe wrote:
> On Sunday, November 7, 2021 at 1:39:34 PM UTC-8, sep...@yahoo.com wrote:
> > Please explain the distance from the traveler to the mirror as measured by the
> > traveler moving around the circumference of the circle.
> The distance from the traveler to the mirror? What on earth does that have to do with anything? Remember, what you are trying to understand is the speed of the pulse of light as it goes from the emission event (0,0,R,0) to (0,0,R,h) in terms of F0. As has been explained many times, in every system of inertial coordinates the speed of the pulse between those events is 1. This debunks your claim. The distance between the traveler as he moves around the circle and the mirror is irrelevant.
> > Observers in both F0 and F1 measure the distance from the plane of the circle to
> > the mirror...
>
> Again, that is not the relevant distance for F1. Try to concentrate: The speed of the pulse in terms of any specified system of inertial coordinates x,y,z,t is sqrt(dx^2 + dy^2 + dz^2)/dt where dx,dy,dz,dt are the coordinate differences between the emission and reception events. In terms of F0 the speed is h/h = 1, and in terms of F1 the speed is hg/(hg) = 1. And in terms of any other system of inertial coordinates (including those in which the traveler is at rest at any given moment) the speed is 1. This debunks your claim. Understand?
> > What does the traveling observer measure as the distance between him and the mirror?
> First, the relevant distance for determining the speed of the pulse has nothing to do with the distance between the traveler and the mirror (or the pulse) as the traveler moves around the circle. The relevant distance is the distance that the pulse traverses. Duh. Second, I remind you that the sloppy colloquial phrase "the distance an observer measures" actually means "the distance in terms of inertial coordinates in which the observer is (momentarily) at rest".
>
> So, a sane (though dull-witted) question for you to ask would be "What is the distance traversed by the pulse of light in terms of the inertial coordinates in which the traveler is at rest?" The answer is that the traveler is accelerating, so he is successively at rest in a succession of inertial coordinate systems. The distance traversed by the pulse is different in terms of each of these systems, as is the propagation time, but the ratio of distance over time in every case is 1. That means the speed of light is always 1 in terms of the inertial coordinates in which the traveler is at rest at any given moment. Understand?

Why is it so difficult for you to tell me what the distance is between the traveler and the mirror as measured by the traveler? F0 and F1 measure the distance as 15*10**12 meters. Can't you explain what the traveler measures that distance to be?
David Seppala
Bastrop TX

On Sunday, November 7, 2021 at 3:36:19 PM UTC-8, sep...@yahoo.com wrote:
> Why is it so difficult for you to tell me what the distance is between the traveler and
> the mirror as measured by the traveler?

It isn't difficult, it's irrelevant... and it isn't a single value, but rather a continuous sequence of values as the traveler moves around the circle, and, of all those infinitely many values, exactly zero of them are relevant to the determination of the speed of the pulse. Do you understand this?

> F0 and F1 measure the distance as 15*10**12 meters.

No, as always, you are mistaken. This was explained in each of the previous posts. Once again, to determine the speed of the pulse, the relevant distance is between the emission event and the reception event, and in terms of F1 the mirror is moving at high speed and it has changed its position from the emission to reception, so the distance in terms of F0 is h and the distance in terms of F1 is gh. You keep saying the distance that the pulse travels is the same in terms of these two coordinate systems, but it is clearly not. The values of h and gh are not the same. Understand?

> Can't you explain what the traveler measures that distance to be?

Ah, you see, now you've asked a different question. Up above you were asking for the distance between the traveler and the mirror as the traveler moves around the circle (which is totally irrelevant), but now you are asking for the distance from emission to reception in terms of the inertial coordinates in which the traveler is at rest. The answer to that has already been given a dozen times: The distance and time of the pulse's journey is different in terms of each of the inertial coordinate systems in which the traveler is successively at rest, but the ratio of distance over time is always 1 in each of those systems. For example, when the traveler begins at (0,0,R,0) the distance to be traversed by the pulse in terms of the traveler's rest frame is gh, as is the time the pulse will take. Now do you understand?