Two identical twins would always compete in 100 meter and 200 meter dashes. Every time they raced the race would end up in a tie. Neither twin could beat the other twin. Now they had qualified for the Olympics and were competing in a 200 meter dash. One twin thought that they would share the gold medal. However, when the race was run the other twin beat him in the 200 meter dash.
" How could you have possibly beaten me?" asked the one twin. "Every time we race 100 meters the race ends up a tie. Every time we race 200 meters the race ends of a tie. What was different this time?"
The other twin responded, "I looked at the 200 meter course they laid out in this Olympics and used my knowledge of Einstein's theories to beat you!"
"What do you mean?"
"You picked the wrong lane to start the race in!"
The twin that lost the race said, "Both lane 1 and lane 2 have the identical lengths. I practiced running the race from lane 1 and practiced running the race from lane 2 and with a timer I carried I saw that my times were always identical in either lane. It didn't matter what lane I ran in."
The gold medal twin explained, "In this Olympics this 200 meter race was run in two separate inertial reference frames. The first 100 meters was run in frame F0, and the second 100 meters of the race was run in frame F1.. Frame F1 was moving in the positive x direction relative to frame F0. The last hundred meters of the race was setup so that one of us had to run 100 meters in the positive x direction of frame F1 and the other had to run 100 meters in the negative x direction in frame F1."
The losing twin said, "There is absolutely nothing different about running in the positive x direction of F1 versus running in the negative x direction of F1. I ran it many times, the times were always identical."
"Yes, but in frame F0, the first 100 meters of the race was perpendicular to the x-axis. We had to run 100 meters in the y-direction in frame F0, and then jump into frame F1 to finish the last 100 meters running parallel to the x-axis there. So per Einstein, while in frame F0, we both started the race simultaneously, but as soon as we crossed into frame F1, you had lagged behind me from the start of the race and therefore you lost!"
The losing twin said, "I asked my coach in frame F0 if we started the race at the same time. He said the start and run times while in F0 were identical, but I lost because he said you ran faster them me in frame F1. I asked my coach in frame F1, how much slower was my run time was compared to your runtime in F1. He said we both ran the 100 meters in identical times. I don't know who to believe."
The gold medal twin said, "Well, before the next Olympics, study Einstein's theory and pick the right lane!"
Comments would be appreciated.
David Seppala
Bastrop TX

LiarOp 03-aug.-2021 om 22:58 schreef sepp623@yahoo.com:

[snip]

> Comments would be appreciated.

Liar.
Trump.

Dirk Vdm

> David Seppala
> Bastrop TX
>
>
>
>

On Tuesday, August 3, 2021 at 3:58:08 PM UTC-5, sep...@yahoo.com wrote:
> Two identical twins would always compete in 100 meter and 200 meter dashes. Every time they raced the race would end up in a tie. Neither twin could beat the other twin. Now they had qualified for the Olympics and were competing in a 200 meter dash. One twin thought that they would share the gold medal. However, when the race was run the other twin beat him in the 200 meter dash.
> " How could you have possibly beaten me?" asked the one twin. "Every time we race 100 meters the race ends up a tie. Every time we race 200 meters the race ends of a tie. What was different this time?"
> The other twin responded, "I looked at the 200 meter course they laid out in this Olympics and used my knowledge of Einstein's theories to beat you!"
> "What do you mean?"
> "You picked the wrong lane to start the race in!"
> The twin that lost the race said, "Both lane 1 and lane 2 have the identical lengths. I practiced running the race from lane 1 and practiced running the race from lane 2 and with a timer I carried I saw that my times were always identical in either lane. It didn't matter what lane I ran in."
> The gold medal twin explained, "In this Olympics this 200 meter race was run in two separate inertial reference frames. The first 100 meters was run in frame F0, and the second 100 meters of the race was run in frame F1. Frame F1 was moving in the positive x direction relative to frame F0. The last hundred meters of the race was setup so that one of us had to run 100 meters in the positive x direction of frame F1 and the other had to run 100 meters in the negative x direction in frame F1."
> The losing twin said, "There is absolutely nothing different about running in the positive x direction of F1 versus running in the negative x direction of F1. I ran it many times, the times were always identical."
> "Yes, but in frame F0, the first 100 meters of the race was perpendicular to the x-axis. We had to run 100 meters in the y-direction in frame F0, and then jump into frame F1 to finish the last 100 meters running parallel to the x-axis there. So per Einstein, while in frame F0, we both started the race simultaneously, but as soon as we crossed into frame F1, you had lagged behind me from the start of the race and therefore you lost!"
> The losing twin said, "I asked my coach in frame F0 if we started the race at the same time. He said the start and run times while in F0 were identical, but I lost because he said you ran faster them me in frame F1. I asked my coach in frame F1, how much slower was my run time was compared to your runtime in F1. He said we both ran the 100 meters in identical times. I don't know who to believe."
> The gold medal twin said, "Well, before the next Olympics, study Einstein's theory and pick the right lane!"
> Comments would be appreciated.
> David Seppala
> Bastrop TX

I should add that when one twin jumped to frame F1, he was at x' = -100 meters in F1 running toward x'=0 and the other twin happened to jump to frame F1 at x' = 100 meters and was running toward x' = 0. This is so there is no confusion, as to how they determined who won.
David Seppala
Bastrop TX

On Tuesday, August 3, 2021 at 3:33:31 PM UTC-7, sep...@yahoo.com wrote:
> This 200 meter race was run [on tracks at rest] in two separate inertial reference
> frames. The first 100 meters was run [on a track at rest] in frame F0, and the second
> 100 meters of the race was run [on a track at rest] in frame F1. Frame F1 was moving
> in the positive x direction relative to frame F0.
>
> In frame F0, the first 100 meters of the race was perpendicular to the x-axis. We had to
> run 100 meters in the y-direction in frame F0, and then jump [to a track that is at rest in]
> frame F1 to finish the last 100 meters running parallel to the x-axis there.
>
> When one twin jumped to [the track at rest in] frame F1, he was at x' = -100 meters in F1
> [and began] running toward x'=0, and the other twin jumped [to the track at rest in] frame
> F1 at x' = 100 meters and began running toward x' = 0. [They arrive at x' =0 simultaneously.]
>
> While [on the track at rest] in frame F0, we both started the race simultaneously, but as soon
> as we [jumped to the track at rest in] frame F1, you had lagged behind me from the start of
> the race and therefore you lost!"

No, the relevant measure of distance traveled by each runner for any incremental segment is the distance in terms of inertial coordinates in which the track for that segment is at rest, and the relevant time is in terms of the same coordinate system. Each runner has gone the same track distance in the same track time.

Special Relativity: 786
Barnpole Dave: 0

Diagnosis: Dave (for the 786th time) was confused by the relativity of simultaneity.

On Wednesday, August 4, 2021 at 12:03:05 PM UTC-5, Al Coe wrote:
> On Tuesday, August 3, 2021 at 3:33:31 PM UTC-7, sep...@yahoo.com wrote:
> > This 200 meter race was run [on tracks at rest] in two separate inertial reference
> > frames. The first 100 meters was run [on a track at rest] in frame F0, and the second
> > 100 meters of the race was run [on a track at rest] in frame F1. Frame F1 was moving
> > in the positive x direction relative to frame F0.
> >
> > In frame F0, the first 100 meters of the race was perpendicular to the x-axis. We had to
> > run 100 meters in the y-direction in frame F0, and then jump [to a track that is at rest in]
> > frame F1 to finish the last 100 meters running parallel to the x-axis there.
> >
> > When one twin jumped to [the track at rest in] frame F1, he was at x' = -100 meters in F1
> > [and began] running toward x'=0, and the other twin jumped [to the track at rest in] frame
> > F1 at x' = 100 meters and began running toward x' = 0. [They arrive at x' =0 simultaneously.]
> >
> > While [on the track at rest] in frame F0, we both started the race simultaneously, but as soon
> > as we [jumped to the track at rest in] frame F1, you had lagged behind me from the start of
> > the race and therefore you lost!"
> No, the relevant measure of distance traveled by each runner for any incremental segment is the distance in terms of inertial coordinates in which the track for that segment is at rest, and the relevant time is in terms of the same coordinate system. Each runner has gone the same track distance in the same track time.
>
> Special Relativity: 786
> Barnpole Dave: 0
>
> Diagnosis: Dave (for the 786th time) was confused by the relativity of simultaneity.
Al,
In frame F1, per Einstein, the runners did not start the last 100 meter leg simultaneously. One started before the other and hence one twin finished the last leg of the race before the other twin.
David Seppala
Bastrop TX

On Wednesday, August 4, 2021 at 11:28:05 AM UTC-7, sep...@yahoo.com wrote:
> In frame F1, per Einstein, the runners did not start the last 100 meter leg
> simultaneously. One started before the other and hence one twin finished
> the last leg of the race before the other twin.

Right, for the first leg, on the track at rest in F0, they each run 100 meters in an equal elapsed coordinate time of del-t in terms of F0, and for the second leg, on the track at rest in F1, they each run 100 meters in an equal elapsed coordinate time del-t' (= del-t) in terms of F1. Hence they both ran a total of 200 coordinate meters in the same total elapsed coordinate time, noting that the relevant coordinate system is always the one in which the track under foot is at rest. The fact that they arrive at x'=0 at different coordinate times t' is due to the fact that they started at x'=+-100 at different times t', due to the relativity of simultaneity.

You may have noticed that in actual races on spatially curved tracks the runners start in staggered positions, chosen so that the total distance to the common finish line is the same. Conversely, if they started with a common line, the end points would have to be staggered. You see, sane people understand that we must account for things like curved tracks and having part of the track in motion relative to another part, etc., leading to spatially and/or temporally staggered start or end lines. The governing principle is always to make the total track-distance and (in the latter case) track-time comensurate.

On Wednesday, August 4, 2021 at 2:26:17 PM UTC-5, Al Coe wrote:
> On Wednesday, August 4, 2021 at 11:28:05 AM UTC-7, sep...@yahoo.com wrote:
> > In frame F1, per Einstein, the runners did not start the last 100 meter leg
> > simultaneously. One started before the other and hence one twin finished
> > the last leg of the race before the other twin.
You wrote:
The fact that they arrive at x'=0 at different coordinate times t' is due to the fact that they started at x'=+-100 at different times t', due to the relativity of simultaneity.

At what point in the race did the one twin take the lead over the other other twin?
David Seppala
Bastrop TX

On Wednesday, August 4, 2021 at 1:20:22 PM UTC-7, sep...@yahoo.com wrote:
> > The fact that they arrive at x'=0 at different coordinate times t' is due to the fact that
> > they started at x'=+-100 at different times t', due to the relativity of simultaneity.
>
> At what point in the race did the one twin take the lead over the other other twin?

The phrase "take the lead" is ambiguous (because of the relativity of simultaneity), but per your specification, in terms of F1 the runner at greater x' starts running prior to the other runner, and finishes running prior to the other runner. So, in that sense, he is "in the lead" for the entire race. In terms of F0 the runners start at the same time and arrive at the conveyor belt at the same time, and then the x'=0 mark is moving toward the runner at greater x and away from the runner at lesser x, so in this sense the former is closing on the x'=0 mark more quickly beginning at that transition, so one could say he begins to "take the lead" beginning at the point.

On Wednesday, August 4, 2021 at 3:58:22 PM UTC-5, Al Coe wrote:
> On Wednesday, August 4, 2021 at 1:20:22 PM UTC-7, sep...@yahoo.com wrote:
> > > The fact that they arrive at x'=0 at different coordinate times t' is due to the fact that
> > > they started at x'=+-100 at different times t', due to the relativity of simultaneity.
> >
> > At what point in the race did the one twin take the lead over the other other twin?
> The phrase "take the lead" is ambiguous (because of the relativity of simultaneity), but per your specification, in terms of F1 the runner at greater x' starts running prior to the other runner, and finishes running prior to the other runner. So, in that sense, he is "in the lead" for the entire race. In terms of F0 the runners start at the same time and arrive at the conveyor belt at the same time, and then the x'=0 mark is moving toward the runner at greater x and away from the runner at lesser x, so in this sense the former is closing on the x'=0 mark more quickly beginning at that transition, so one could say he begins to "take the lead" beginning at the point.

Al,
Let's say a twin carries a clock with him and whenever he runs 100 meters in frame F0 that clock shows an elapsed time of 10 seconds. Whenever that twin runs 100 meters in frame F1, that same clock shows an elapsed time of 10 seconds. Whenever that twin runs 200 meters in either lane 1 of this Olympic event or runs 200 meters in land 2 of this Olympic event his clock always shows an elapsed time of 20 seconds. I understand that Einstein's concepts say you cannot used the elapsed time shown on the clock to determine who won the race, but I don't understand the logic behind that concept. Please explain why the twin can always use the elapsed time shown on his clock to determine the race result if the race is only run in one inertial frame, but the twin cannot use the elapsed time shown on his clock if the event takes place in two inertial reference frames. If one twin jumps on a train or conveyor belt and his clock read T seconds and he as at x = -100 meters in that inertial reference frame, and the other twin jumps on a train at location x = 100 meters and his clock reads T seconds, don't both clocks read T+10 seconds if it takes each of them 10 seconds to run a hundred meters in frame F1?
Thanks,
David Seppala
Bastrop TX
David Seppala
Bastrop TX

On Thursday, August 5, 2021 at 1:17:46 PM UTC-7, sep...@yahoo.com wrote:
> > > > The fact that they arrive at x'=0 at different coordinate times t' is due to the fact that
> > > > they started at x'=+-100 at different times t', due to the relativity of simultaneity.
> > >
> > > At what point in the race did the one twin take the lead over the other other twin?
> > The phrase "take the lead" is ambiguous (because of the relativity of simultaneity), but per your specification, in terms of F1 the runner at greater x' starts running prior to the other runner, and finishes running prior to the other runner. So, in that sense, he is "in the lead" for the entire race. In terms of F0 the runners start at the same time and arrive at the conveyor belt at the same time, and then the x'=0 mark is moving toward the runner at greater x and away from the runner at lesser x, so in this sense the former is closing on the x'=0 mark more quickly beginning at that transition, so one could say he begins to "take the lead" beginning at the point.

> > Special relativity: 787
> > Barnpole Dave: 0

> If one twin jumps on a conveyor belt and his clock read T seconds and he
> as at x = -100 meters in that inertial reference frame, and the other twin
> jumps the conveyor belt at location x = 100 meters and his clock reads T
> seconds, don't both clocks read T+10 seconds if it takes each of them 10
> seconds to run a hundred meters in frame F1?

Of course they do (i.e., they each read T+10 when they respectively complete the 100 meter leg at the stipulated speed). You were already told this in a prior message. The reason for your confusion is that you are failing to take the relativity of simultaneity into account.

Special relativity: 788
Barnpole Dave: 0

> Please explain why the twin can always use the elapsed time shown on his clock
> to determine the race result if the race is only run in one inertial frame...

That's doesn't make any sense. The elapsed proper time for one runner doesn't tell us anything about the elapsed proper time of the other runner. The same misconception is present in your second clause as well.

> but the twin cannot use the elapsed time shown on his clock if the event takes
> place in two inertial reference frames.

Again, the relevant measure of performance for a segmented race conducted on track segments at rest in S1, S2, ..., Sn is dt1+dt2+...+dtn where dtj is the coordinate time in terms of Sj to traverse the coordinate distance dxj, where dx1+dx2+...+dxn = 200 meters. The elapsed proper time for each segment is sqrt[dtj^2 - (dxj/c)^2]. Hence the sum of the coordinate times is not simply proportional to the sum of the proper times.

Special relativity: 789
Barnpole Dave: 0

On Thursday, August 5, 2021 at 5:36:20 PM UTC-5, Al Coe wrote:
> On Thursday, August 5, 2021 at 1:17:46 PM UTC-7, sep...@yahoo.com wrote:
> > > > > The fact that they arrive at x'=0 at different coordinate times t' is due to the fact that
> > > > > they started at x'=+-100 at different times t', due to the relativity of simultaneity.
> > > >
> > > > At what point in the race did the one twin take the lead over the other other twin?
> > > The phrase "take the lead" is ambiguous (because of the relativity of simultaneity), but per your specification, in terms of F1 the runner at greater x' starts running prior to the other runner, and finishes running prior to the other runner. So, in that sense, he is "in the lead" for the entire race. In terms of F0 the runners start at the same time and arrive at the conveyor belt at the same time, and then the x'=0 mark is moving toward the runner at greater x and away from the runner at lesser x, so in this sense the former is closing on the x'=0 mark more quickly beginning at that transition, so one could say he begins to "take the lead" beginning at the point.
> > > Special relativity: 787
> > > Barnpole Dave: 0
>
> > If one twin jumps on a conveyor belt and his clock read T seconds and he
> > as at x = -100 meters in that inertial reference frame, and the other twin
> > jumps the conveyor belt at location x = 100 meters and his clock reads T
> > seconds, don't both clocks read T+10 seconds if it takes each of them 10
> > seconds to run a hundred meters in frame F1?
> Of course they do (i.e., they each read T+10 when they respectively complete the 100 meter leg at the stipulated speed). You were already told this in a prior message. The reason for your confusion is that you are failing to take the relativity of simultaneity into account.
>
> Special relativity: 788
> Barnpole Dave: 0
> > Please explain why the twin can always use the elapsed time shown on his clock
> > to determine the race result if the race is only run in one inertial frame...
>
> That's doesn't make any sense. The elapsed proper time for one runner doesn't tell us anything about the elapsed proper time of the other runner. The same misconception is present in your second clause as well.
> > but the twin cannot use the elapsed time shown on his clock if the event takes
> > place in two inertial reference frames.
> Again, the relevant measure of performance for a segmented race conducted on track segments at rest in S1, S2, ..., Sn is dt1+dt2+...+dtn where dtj is the coordinate time in terms of Sj to traverse the coordinate distance dxj, where dx1+dx2+...+dxn = 200 meters. The elapsed proper time for each segment is sqrt[dtj^2 - (dxj/c)^2]. Hence the sum of the coordinate times is not simply proportional to the sum of the proper times.
>
> Special relativity: 789
> Barnpole Dave: 0
Please explain the rules for events to be simultaneous. For example, if the two twins are at rest in frame F1, with one twin at x' = 100 meters and the other twin is at x' = -100 meters, and a pulse of light is sent from x' = 0 to start running, from each of the twin's point of view did they start running simultaneously? If not, then the difference depends on the speed at which the twins run. If the twins accelerate in an identical fashion as measured in F1, do they say that the difference in the times they started accelerating continually changes?
Thanks,
David Seppala
Bastrop TX

sepp623@yahoo.com <sepp623@yahoo.com> wrote:
> On Thursday, August 5, 2021 at 5:36:20 PM UTC-5, Al Coe wrote:
>> On Thursday, August 5, 2021 at 1:17:46 PM UTC-7, sep...@yahoo.com wrote:
>>>>>> The fact that they arrive at x'=0 at different coordinate times t'
>>>>>> is due to the fact that
>>>>>> they started at x'=+-100 at different times t', due to the
>>>>>> relativity of simultaneity.
>>>>>
>>>>> At what point in the race did the one twin take the lead over the other other twin?
>>>> The phrase "take the lead" is ambiguous (because of the relativity of
>>>> simultaneity), but per your specification, in terms of F1 the runner
>>>> at greater x' starts running prior to the other runner, and finishes
>>>> running prior to the other runner. So, in that sense, he is "in the
>>>> lead" for the entire race. In terms of F0 the runners start at the
>>>> same time and arrive at the conveyor belt at the same time, and then
>>>> the x'=0 mark is moving toward the runner at greater x and away from
>>>> the runner at lesser x, so in this sense the former is closing on the
>>>> x'=0 mark more quickly beginning at that transition, so one could say
>>>> he begins to "take the lead" beginning at the point.
>>>> Special relativity: 787
>>>> Barnpole Dave: 0
>>
>>> If one twin jumps on a conveyor belt and his clock read T seconds and he
>>> as at x = -100 meters in that inertial reference frame, and the other twin
>>> jumps the conveyor belt at location x = 100 meters and his clock reads T
>>> seconds, don't both clocks read T+10 seconds if it takes each of them 10
>>> seconds to run a hundred meters in frame F1?
>> Of course they do (i.e., they each read T+10 when they respectively
>> complete the 100 meter leg at the stipulated speed). You were already
>> told this in a prior message. The reason for your confusion is that you
>> are failing to take the relativity of simultaneity into account.
>>
>> Special relativity: 788
>> Barnpole Dave: 0
>>> Please explain why the twin can always use the elapsed time shown on his clock
>>> to determine the race result if the race is only run in one inertial frame...
>>
>> That's doesn't make any sense. The elapsed proper time for one runner
>> doesn't tell us anything about the elapsed proper time of the other
>> runner. The same misconception is present in your second clause as well.
>>> but the twin cannot use the elapsed time shown on his clock if the event takes
>>> place in two inertial reference frames.
>> Again, the relevant measure of performance for a segmented race
>> conducted on track segments at rest in S1, S2, ..., Sn is
>> dt1+dt2+...+dtn where dtj is the coordinate time in terms of Sj to
>> traverse the coordinate distance dxj, where dx1+dx2+...+dxn = 200
>> meters. The elapsed proper time for each segment is sqrt[dtj^2 -
>> (dxj/c)^2]. Hence the sum of the coordinate times is not simply
>> proportional to the sum of the proper times.
>>
>> Special relativity: 789
>> Barnpole Dave: 0
> Please explain the rules for events to be simultaneous. For example, if
> the two twins are at rest in frame F1, with one twin at x' = 100 meters
> and the other twin is at x' = -100 meters, and a pulse of light is sent
> from x' = 0 to start running, from each of the twin's point of view did
> they start running simultaneously? If not, then the difference depends
> on the speed at which the twins run. If the twins accelerate in an
> identical fashion as measured in F1, do they say that the difference in
> the times they started accelerating continually changes?
> Thanks,
> David Seppala
> Bastrop TX
>

David, the rules for simultaneity are pretty simple.
Let’s say you have two events, A and B, and you don’t know whether they are
simultaneous or not, but they are separated from each other and from you.
But suppose you can determine the following facts:

1. Signals from the two events were received where you are at the same
time.
2. Signals traveled at the same speed to you from each of the two
events.
3. The distance between you and each of the events is the same.

Then the two events have to be simultaneous. The reason is that 2 and 3
together imply that the propagation time of the signal has to be the same
for both events — equal distances, equal speeds. Then this and 1 tell you
that the two events A and B happened at the same time prior to the receipt
of the signal — common arrival time, equal propagation times.

Likewise, suppose 2 and 3 were true but 1 was not. Then this unambiguously
tells you that A and B are not simultaneous.

Likewise, suppose 1 and 2 were true but 3 was not. Then this also
unambiguously tells you that A and B are not simultaneous.

Likewise, suppose 1 and 3 were true but 2 was not. Then this also
unambiguously tells you that A and B are not simultaneous.

Now, the really interesting thing is that for two different observers
looking at the same two events A and B and applying the same rules as
above, they will come to different conclusions about whether A and B are
simultaneous or not. And you can quickly figure out why just by sorting out
which of the three conditions does not hold true for one of the observers.

This is called the relativity of simultaneity. It is an observational fact.
It is also the underlying basis for time dilation and length contraction.

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

On Friday, August 6, 2021 at 8:17:59 AM UTC-7, sep...@yahoo.com wrote:
> Please explain the rules for events to be simultaneous.

Simultaneous means at the same time, which means at equal values of the t coordinate of a given system of coordinates. There are infinitely many different systems of coordinates, with different temporal foliations, so two spatially separate events that are simultaneous in terms of one system of coordinates are generally not simultaneous in terms of another. This is the relativity of simultaneity.

> If the two twins are at rest in frame F1, with one twin at x' = 100 meters and the other
> twin is at x' = -100 meters, and a pulse of light is sent from x' = 0 to start running, from
> each of the twin's point of view did they start running simultaneously?

The arrivals of the pulses at the twins are simultaneous in terms of the inertial coordinate system in which they are at rest, though not in terms of any other system of inertial coordinates, let alone any more general coordinate systems.

> If not...

See above. Again, they are simultaneous (same value of t) in terms of the inertial coordinates in which they are at rest, but not in terms of other coordinate systems.

> ...then the difference depends on the speed at which the twins run.

No, you specified that the twins are both at rest in F1, at least until the pulses reach them, so their subsequent speeds are irrelevant. In fact, their current and prior speeds are also irrelevant, because you are specifying two events at equal distances from the source of the isotropic signal in terms of F1, and hence the arrivals are at equal t values in terms of F1.

> If the twins accelerate in an identical fashion as measured in F1, do they say that
> the difference in the times they started accelerating continually changes?

No, the things you are typing make no sense at all. You specified two events that are simultaneous in terms of F1, and not in terms of other systems. That is all. The rest of what you are typing is gibberish.

Special Relativity: 789 Barnpole Dave: 0
Diagnosis: For the 789th time, Dave was confused by the relativity of simultaneity.

On Friday, August 6, 2021 at 11:03:27 AM UTC-5, Al Coe wrote:
> On Friday, August 6, 2021 at 8:17:59 AM UTC-7, sep...@yahoo.com wrote:
> > Please explain the rules for events to be simultaneous.
> Simultaneous means at the same time, which means at equal values of the t coordinate of a given system of coordinates. There are infinitely many different systems of coordinates, with different temporal foliations, so two spatially separate events that are simultaneous in terms of one system of coordinates are generally not simultaneous in terms of another. This is the relativity of simultaneity.
>
> > If the two twins are at rest in frame F1, with one twin at x' = 100 meters and the other
> > twin is at x' = -100 meters, and a pulse of light is sent from x' = 0 to start running, from
> > each of the twin's point of view did they start running simultaneously?
> The arrivals of the pulses at the twins are simultaneous in terms of the inertial coordinate system in which they are at rest, though not in terms of any other system of inertial coordinates, let alone any more general coordinate systems.
>
> > If not...
>
> See above. Again, they are simultaneous (same value of t) in terms of the inertial coordinates in which they are at rest, but not in terms of other coordinate systems.
>
> > ...then the difference depends on the speed at which the twins run.
>
> No, you specified that the twins are both at rest in F1, at least until the pulses reach them, so their subsequent speeds are irrelevant. In fact, their current and prior speeds are also irrelevant, because you are specifying two events at equal distances from the source of the isotropic signal in terms of F1, and hence the arrivals are at equal t values in terms of F1.
> > If the twins accelerate in an identical fashion as measured in F1, do they say that
> > the difference in the times they started accelerating continually changes?
> No, the things you are typing make no sense at all. You specified two events that are simultaneous in terms of F1, and not in terms of other systems.. That is all. The rest of what you are typing is gibberish.
>
> Special Relativity: 789 Barnpole Dave: 0
> Diagnosis: For the 789th time, Dave was confused by the relativity of simultaneity.

Okay, so your answer is self contradictory. You said they don't say the difference in their acceleration start times continually change as they accelerate, but yet as they accelerate they continually change reference frames which measure differing start times between the accelerations of the two twins. Interesting.
David Seppala
Bastrop TX

On Friday, August 6, 2021 at 9:30:21 AM UTC-7, sep...@yahoo.com wrote:
> Okay, so your answer is self contradictory.

Nope.

> You said they don't say the difference in their acceleration start times
> continually change as they accelerate...

No, I said that the events you specified with coordinates x'=-100, t'=t0 and x'=+100, t'=t0 in terms of F1 are simultaneous in terms of F1, regardless of the trajectory (speed, acceleration) of objects that pass through those events.

> but yet as they accelerate they continually change reference frames...

Stated correctly, as they accelerate, they are at rest in terms of successive systems of inertial coordinates. That is both true and irrelevant. See above.

> which measure differing start times between the accelerations of the two twins.

Again, the entire scenario of the races in two segments was fully explained previously. Since then you have asked a serious of rather pointless questions, none of which contradict the explanation of the race scenario. The answer to your most recent questions is that the events you specified with coordinates x'=-100, t'=t0 and x'=+100, t'=t0 in terms of F1 are simultaneous in terms of F1, regardless of the trajectory (speed, acceleration) of objects that pass through those events.

Special Relativity: 790 ..... Barnpole Dave: 0
Diagnosis: For the 790th time, Dave was confused by the relativity of simultaneity.

On Friday, August 6, 2021 at 11:39:19 AM UTC-5, Al Coe wrote:
> On Friday, August 6, 2021 at 9:30:21 AM UTC-7, sep...@yahoo.com wrote:
> > Okay, so your answer is self contradictory.
> Nope.
> > You said they don't say the difference in their acceleration start times
> > continually change as they accelerate...
>
> No, I said that the events you specified with coordinates x'=-100, t'=t0 and x'=+100, t'=t0 in terms of F1 are simultaneous in terms of F1, regardless of the trajectory (speed, acceleration) of objects that pass through those events.
>
> > but yet as they accelerate they continually change reference frames...
>
> Stated correctly, as they accelerate, they are at rest in terms of successive systems of inertial coordinates. That is both true and irrelevant. See above.
> > which measure differing start times between the accelerations of the two twins.
> Again, the entire scenario of the races in two segments was fully explained previously. Since then you have asked a serious of rather pointless questions, none of which contradict the explanation of the race scenario. The answer to your most recent questions is that the events you specified with coordinates x'=-100, t'=t0 and x'=+100, t'=t0 in terms of F1 are simultaneous in terms of F1, regardless of the trajectory (speed, acceleration) of objects that pass through those events.
>
> Special Relativity: 790 ..... Barnpole Dave: 0
> Diagnosis: For the 790th time, Dave was confused by the relativity of simultaneity.
Al,
Again and again, I am not asking what the events are in terms of F1. I am asking what the twins say about the starting times of their accelerations as they continue to accelerate. Answer that question.
David Seppala
Bastrop TX

On Friday, August 6, 2021 at 11:15:57 AM UTC-7, sep...@yahoo.com wrote:
> Again and again, I am not asking what the events are in terms of F1.

That is a lie. Here is the question you asked, quoted verbatim: "If the two twins are at rest in frame F1, with one twin at x' = 100 meters and the other twin is at x' = -100 meters, and a pulse of light is sent from x' = 0 to start running, from each of the twin's point of view did they start running simultaneously?" Once again, simultaneity is relativity, but you have specified that you are talking about two runners at rest in inertial coordinates F1, and the answer is yes, the receiver the start signals simultaneously in terms of F1, which is their rest frame. Now, if you want to change your question so that the runners are at rest in frames F3 and F4 at the events when they receive the signals, then those signal receptions are not simultaneous in terms of F3 or F4, but they are nevertheless simultaneous in terms of F1, regardless of the runners' states of motion.

Special Relativity: 791 ..... Barnpole Dave: 0
Diagnosis: For the 791st time, Dave was confused by the relativity of simultaneity.

> [What do] the twins say about the starting times of their accelerations as they
> continue to accelerate.

Once again, what people "say about" things is irrelevant. Also, the only "accelerations" in the scenario you described occur abruptly when each runner steps onto the conveyor belt. You might ask a sane questions such as "What are the start times of the runners in terms of F0, and what are their start times in terms of F1, and what are their start times in terms of the Sun's inertial rest frame, and what are the start times in terms of their own rest frames, and in terms of any other specific system of inertial coordinates that you can name. Here's the answer you were given before for the two-segment race:

Per your specification, in terms of inertial coordinate system F1 the runner at greater x starts running prior to the other runner, and finishes running prior to the other runner. In terms of inertial coordinate system F0 the runners start at the same time and arrive at the conveyor belt at the same time, and the x'=0 mark is moving toward the runner at greater x and away from the runner at lesser x, so in this sense the former is closing on the x'=0 mark more quickly beginning at that transition.

Now do you understand?

On Friday, August 6, 2021 at 1:56:18 PM UTC-5, Al Coe wrote:
> On Friday, August 6, 2021 at 11:15:57 AM UTC-7, sep...@yahoo.com wrote:
> > Again and again, I am not asking what the events are in terms of F1.
> That is a lie. Here is the question you asked, quoted verbatim: "If the two twins are at rest in frame F1, with one twin at x' = 100 meters and the other twin is at x' = -100 meters, and a pulse of light is sent from x' = 0 to start running, from each of the twin's point of view did they start running simultaneously?" Once again, simultaneity is relativity, but you have specified that you are talking about two runners at rest in inertial coordinates F1, and the answer is yes, the receiver the start signals simultaneously in terms of F1, which is their rest frame. Now, if you want to change your question so that the runners are at rest in frames F3 and F4 at the events when they receive the signals, then those signal receptions are not simultaneous in terms of F3 or F4, but they are nevertheless simultaneous in terms of F1, regardless of the runners' states of motion.
>
> Special Relativity: 791 ..... Barnpole Dave: 0
> Diagnosis: For the 791st time, Dave was confused by the relativity of simultaneity.
>
> > [What do] the twins say about the starting times of their accelerations as they
> > continue to accelerate.
>
> Once again, what people "say about" things is irrelevant. Also, the only "accelerations" in the scenario you described occur abruptly when each runner steps onto the conveyor belt. You might ask a sane questions such as "What are the start times of the runners in terms of F0, and what are their start times in terms of F1, and what are their start times in terms of the Sun's inertial rest frame, and what are the start times in terms of their own rest frames, and in terms of any other specific system of inertial coordinates that you can name. Here's the answer you were given before for the two-segment race:
>
> Per your specification, in terms of inertial coordinate system F1 the runner at greater x starts running prior to the other runner, and finishes running prior to the other runner. In terms of inertial coordinate system F0 the runners start at the same time and arrive at the conveyor belt at the same time, and the x'=0 mark is moving toward the runner at greater x and away from the runner at lesser x, so in this sense the former is closing on the x'=0 mark more quickly beginning at that transition.
>
> Now do you understand?
Al, If the twins are initially at rest in frame F1, and they start accelerating simultaneously in F1, say in opposite directions, the twins initially say the accelerations of each of them started simultaneously. What does a twin say after he has accelerated for some time t. Does THAT TWIN still say he and the other twin started their accelerations simultaneously?
David Seppala
Bastrop TX

On Friday, August 6, 2021 at 12:06:26 PM UTC-7, sep...@yahoo.com wrote:
> If the twins are initially at rest in frame F1, and they start accelerating simultaneously in F1,
> say in opposite directions, the twins initially say the accelerations of each of them started
> simultaneously.

Once again, what various people "say" is irrelevant. One twin may recite the Gettysburg Address, and the other may recite the alphabet backwards. What your brain is trying (unsuccessfully) to ask about is the coordinates of various specified events in terms of various specified systems of coordinates. Let me help you take some small baby-steps... Here's one of the (infinitely many) statements that you might have been groping to express with your willfully clueless verbiage above:

If two spatially separate twins are initially at rest in inertial coordinate systems S1, and they start accelerating simultaneously in terms of S1 in opposite directions, then they started accelerating simultaneously in terms of S1. This is tautological.

> What does a twin say after he has accelerated for some time t?

He recites the Gettysburg Address again, but this time in German. Now, suppose you were not mentally ill, and you had typed this meaningful (though still stupid) question: In terms of a different system S2 of inertial coordinates in which one of the twins is momentarily at rest after it has accelerated, are the starting events simultaneous? Answer: Obviously not, as has been explained to you in my first post, and half a dozen times more in subsequent posts.

> Does THAT TWIN still say he and the other twin started their accelerations simultaneously?

That twin has a sore tooth and isn't saying anything, but suppose you had asked, are the starting events simultaneous in terms of S2? The answer (again), as explained above (again), is obviously no. The entire race scenario, in terms of both S1 and S0, has been given to you explicitly multiple times.

Special Relativity: 792 ..... Barnpole Dave: 0
Diagnosis: For the 792nd time, Dave was confused by the relativity of simultaneity.

On Friday, 6 August 2021 at 18:03:27 UTC+2, Al Coe wrote:
> On Friday, August 6, 2021 at 8:17:59 AM UTC-7, sep...@yahoo.com wrote:
> > Please explain the rules for events to be simultaneous.
> Simultaneous means at the same time, which means at equal values of the t coordinate of a given system of coordinates. There are infinitely many different systems of coordinates,

Stop fucking, you don't have any.

On Friday, August 6, 2021 at 3:15:57 PM UTC-5, Al Coe wrote:
> On Friday, August 6, 2021 at 12:06:26 PM UTC-7, sep...@yahoo.com wrote:
> > If the twins are initially at rest in frame F1, and they start accelerating simultaneously in F1,
> > say in opposite directions, the twins initially say the accelerations of each of them started
> > simultaneously.
> Once again, what various people "say" is irrelevant. One twin may recite the Gettysburg Address, and the other may recite the alphabet backwards. What your brain is trying (unsuccessfully) to ask about is the coordinates of various specified events in terms of various specified systems of coordinates. Let me help you take some small baby-steps... Here's one of the (infinitely many) statements that you might have been groping to express with your willfully clueless verbiage above:
>
> If two spatially separate twins are initially at rest in inertial coordinate systems S1, and they start accelerating simultaneously in terms of S1 in opposite directions, then they started accelerating simultaneously in terms of S1. This is tautological.
>
> > What does a twin say after he has accelerated for some time t?
>
> He recites the Gettysburg Address again, but this time in German. Now, suppose you were not mentally ill, and you had typed this meaningful (though still stupid) question: In terms of a different system S2 of inertial coordinates in which one of the twins is momentarily at rest after it has accelerated, are the starting events simultaneous? Answer: Obviously not, as has been explained to you in my first post, and half a dozen times more in subsequent posts.
> > Does THAT TWIN still say he and the other twin started their accelerations simultaneously?
> That twin has a sore tooth and isn't saying anything, but suppose you had asked, are the starting events simultaneous in terms of S2? The answer (again), as explained above (again), is obviously no. The entire race scenario, in terms of both S1 and S0, has been given to you explicitly multiple times.
>
> Special Relativity: 792 ..... Barnpole Dave: 0
> Diagnosis: For the 792nd time, Dave was confused by the relativity of simultaneity.

Al,
Whenever the twins see which one of them can run 100 meters the fastest in frame F0, they do not have to start simultaneously, and they don't have to start at the same x. All they they have to do is carry a clock with them and set the clock to zero when they start running and check the time on the clock when they reach x+100 (or at x-100 if they ran in the opposite direction). Then after each of them has run the 100 meters they just have to compare the elapsed times. They can run the 100 meters days apart - makes no difference. The same is true when they see who can run the fastest in frame F1. Please clarify why they cannot use their clocks and this method of determining the winner when the race is run in two frames.
I understand that Einstein says they cannot, but I don't understand what happens with the clocks that prevent that method of determining who is fastest.
David Seppala
Bastrop TX

On Saturday, August 7, 2021 at 10:19:01 AM UTC-7, sep...@yahoo.com wrote:
> Whenever the twins see which one of them can run 100 meters the fastest in frame F0,
> they do not have to start simultaneously, and they don't have to start at the same x.

Right, they could run on completely different days, in different countries.

> All they they have to do is carry a clock with them and set the clock to zero when
> they start running and check the time on the clock when they reach x+100 (or at x-100
> if they ran in the opposite direction).

To correctly quantify the performance of the runners, the relevant measure of distance and time is in terms of inertial coordinates in which the track is at rest. A clock carried by a runner does not in general match that coordinate time, because the runner is moving in terms of those coordinates.

The total spatial distance traveled (100 meters) is defined in terms of the system(s) of inertial coordinates in which the track(s) is/are at rest, and the relevant running time is expressed in terms of the same system(s). The elapsed time showing on a clock carried by the runner would not equal the sum of the elapsed relevant coordinate times. Rather it would be the integral of dtau = dt * sqrt(1 - v(t)^2/c^2) where v(t) is the velocity of the runner at coordinate time t.

> Then after each of them has run the 100 meters they just have to compare the elapsed times.

You need to clarify what assertion you are making. After the runners have run, potentially at different velocity histories on conveyor belted tracks with different states of motion, the relevant run time for each runner is the sum of the elapsed coordinate times for each segment in terms of the respective inertial coordinates in which the track for that segment was at rest. This gives a total quantity dt. The runner might also carry a clock, giving a total elapsed time of dtau. The value of dtau is not related in a simple proportional way to dt, since the runners can have different velocity histories.

> Please clarify why they cannot use their clocks and this method of determining the
> winner when the race is run in two frames. I understand that [special relativity] says
> they cannot...

You need to clarify what you're asking me to clarify: When you say that special relativity implies that we cannot infer the winner by comparing their elapsed proper times, this means you claiming that it's possible, according to special relativity, to have dtau2 > dtau1 and dt2 < dt1. Is that what you are asserting?

On Saturday, August 7, 2021 at 1:27:29 PM UTC-5, Al Coe wrote:
> On Saturday, August 7, 2021 at 10:19:01 AM UTC-7, sep...@yahoo.com wrote:
> > Whenever the twins see which one of them can run 100 meters the fastest in frame F0,
> > they do not have to start simultaneously, and they don't have to start at the same x.
> Right, they could run on completely different days, in different countries.
> > All they they have to do is carry a clock with them and set the clock to zero when
> > they start running and check the time on the clock when they reach x+100 (or at x-100
> > if they ran in the opposite direction).
> To correctly quantify the performance of the runners, the relevant measure of distance and time is in terms of inertial coordinates in which the track is at rest. A clock carried by a runner does not in general match that coordinate time, because the runner is moving in terms of those coordinates.
>
> The total spatial distance traveled (100 meters) is defined in terms of the system(s) of inertial coordinates in which the track(s) is/are at rest, and the relevant running time is expressed in terms of the same system(s). The elapsed time showing on a clock carried by the runner would not equal the sum of the elapsed relevant coordinate times. Rather it would be the integral of dtau = dt * sqrt(1 - v(t)^2/c^2) where v(t) is the velocity of the runner at coordinate time t.
> > Then after each of them has run the 100 meters they just have to compare the elapsed times.
> You need to clarify what assertion you are making. After the runners have run, potentially at different velocity histories on conveyor belted tracks with different states of motion, the relevant run time for each runner is the sum of the elapsed coordinate times for each segment in terms of the respective inertial coordinates in which the track for that segment was at rest. This gives a total quantity dt. The runner might also carry a clock, giving a total elapsed time of dtau. The value of dtau is not related in a simple proportional way to dt, since the runners can have different velocity histories.
> > Please clarify why they cannot use their clocks and this method of determining the
> > winner when the race is run in two frames. I understand that [special relativity] says
> > they cannot...
>
> You need to clarify what you're asking me to clarify: When you say that special relativity implies that we cannot infer the winner by comparing their elapsed proper times, this means you claiming that it's possible, according to special relativity, to have dtau2 > dtau1 and dt2 < dt1. Is that what you are asserting?
Let's say a Twin 1 runs 100 meters in frame F0. He has an elapsed time of 10 seconds as measured by a clock he carries. Twin 2 runs 100 meters in frame F0. He has an elapsed time of 10 seconds as measured by the clock he carries. Although, the frame F0 clocks show a different run time for the 100 meters than the 10 seconds shown on each of the two clocks, everyone in F0 concludes that the two twins took the same amount of time to run the 100 meters. Same when the 100 meters is run in frame F1. The elapsed time on each twin's clock is T' seconds, so everyone in frame F1 agrees that the elapsed time shown on the two clocks shows that the twins took the same amount of time to run the 100 meters.
Now I am trying to understand why the twins just can't add up the elapsed time shown on their respective clocks to determine who wins. If twin 1 runs 100 meters in 10 seconds F0 on Monday, and runs 100 meters in 10 seconds in F1 on Tuesday and twin 2 runs 100 meters in 10 seconds on F0 on Wednesday, and 100 meters in 10 seconds in F1 on Thursday, with Einstein's concepts that is not enough information to determine who will win if they race 200 meters in the two frames (100 meters in each frame). But if one twin runs 100 meters in 10 seconds as measured in frame F0 and the other twin runs 10 meters in 10 seconds as measure in frame F1, does anyone doubt whether the race will be a tie if they both race in any other inertial reference frame. It will always be a tie in any inertial reference frame they race together in. So I'm trying to understand when you can use the elapsed time in a given frame to determine who will win in some other frame and when you need more information to figure out who is going to win or tie.
David Seppala
Bastrop TX

On Saturday, August 7, 2021 at 1:22:18 PM UTC-7, sep...@yahoo.com wrote:
> I am trying to understand why the twins just can't add up the elapsed time shown on
> their respective clocks to determine who wins.

Again, you are asserting that this is true, and then saying that you are trying to understand why it is true. If you don't understand why it's true, then why are you asserting it is true?

Remember, in the original scenario you described, clocks carried by the runners would show equal elapsed times, and they each go equal elapsed coordinate times in terms of the relevant systems. You have not given any example in which the elapsed time on the co-moving clocks would give a different outcome (winner/loser) than the total elapsed relevant coordinate times.

> If
> twin 1 runs 100 meters in 10 seconds in F0, and runs 100 meters in 10 seconds in F1,
> and
> twin 2 runs 100 meters in 10 seconds on F0, and 100 meters in 10 seconds in F1,
> then
> [according to special relativity] that is not enough information to determine who will win...

Well, that's overly elaborate, since it isn't even enough for the first 100 meters. Suppose one runner keeps a constant speed v for the whole 100 meters, and the other runs at speed u1 for the first 5 seconds of proper time and u2 for the second 5 seconds of proper time. The elapsed coordinate time for the first runner is 10/sqrt(1-v^2/c^2) where 10v/sqrt(1-v^2/c^2) = 100, and the elapsed coordinate time for the second runner is 5/sqrt(1+u1^2/c^2) + 5/sqrt(1-u2^2/c^2), where 5u1/sqrt(1+u1^2/c^2) + 5u2/sqrt(1-u2^2/c^2) = 100. Are you saying you don't understand how those two elapsed coordinate times could be different? Of course, for the slow speeds you are talking about, the differences would be incredibly small.

> But if one twin runs 100 meters in 10 seconds as measured in frame F0 and the other twin
> runs 10 meters in 10 seconds as measure in frame F1, does anyone doubt whether the race
> will be a tie if they both race in any other inertial reference frame.

Anyone who understands special relativity will know that those could take different amounts of coordinate time, because you haven't specified their speed histories. So it's ambiguous even for a single segment, per above. Of course, if you stipulate that each runner runs at constant speed all the time, then the proper times are sufficient to determine the winner, regardless of how many segments you consider.

Special Relativity: 793 ..... Barnpole Dave: 0

On Saturday, August 7, 2021 at 4:50:08 PM UTC-5, Al Coe wrote:
> On Saturday, August 7, 2021 at 1:22:18 PM UTC-7, sep...@yahoo.com wrote:
> > I am trying to understand why the twins just can't add up the elapsed time shown on
> > their respective clocks to determine who wins.
> Again, you are asserting that this is true, and then saying that you are trying to understand why it is true. If you don't understand why it's true, then why are you asserting it is true?
>
> Remember, in the original scenario you described, clocks carried by the runners would show equal elapsed times, and they each go equal elapsed coordinate times in terms of the relevant systems. You have not given any example in which the elapsed time on the co-moving clocks would give a different outcome (winner/loser) than the total elapsed relevant coordinate times.
>
> > If
> > twin 1 runs 100 meters in 10 seconds in F0, and runs 100 meters in 10 seconds in F1,
> > and
> > twin 2 runs 100 meters in 10 seconds on F0, and 100 meters in 10 seconds in F1,
> > then
> > [according to special relativity] that is not enough information to determine who will win...
>
> Well, that's overly elaborate, since it isn't even enough for the first 100 meters. Suppose one runner keeps a constant speed v for the whole 100 meters, and the other runs at speed u1 for the first 5 seconds of proper time and u2 for the second 5 seconds of proper time. The elapsed coordinate time for the first runner is 10/sqrt(1-v^2/c^2) where 10v/sqrt(1-v^2/c^2) = 100, and the elapsed coordinate time for the second runner is 5/sqrt(1+u1^2/c^2) + 5/sqrt(1-u2^2/c^2), where 5u1/sqrt(1+u1^2/c^2) + 5u2/sqrt(1-u2^2/c^2) = 100. Are you saying you don't understand how those two elapsed coordinate times could be different? Of course, for the slow speeds you are talking about, the differences would be incredibly small.
> > But if one twin runs 100 meters in 10 seconds as measured in frame F0 and the other twin
> > runs 10 meters in 10 seconds as measure in frame F1, does anyone doubt whether the race
> > will be a tie if they both race in any other inertial reference frame.
> Anyone who understands special relativity will know that those could take different amounts of coordinate time, because you haven't specified their speed histories. So it's ambiguous even for a single segment, per above. Of course, if you stipulate that each runner runs at constant speed all the time, then the proper times are sufficient to determine the winner, regardless of how many segments you consider.
>
> Special Relativity: 793 ..... Barnpole Dave: 0
Al I should have been clearer, I just assumed that since they are identical twins you would have assumed they run identically as I wanted to imply.
Let's say each twin runs a constant V for the 100 meters and finishes with an elapsed time on his clock of 10 seconds every time he runs, no matter what inertial frame he is in or what direction he runs in that inertial reference frame. If a twin does that in F0, and the other twin does that in F1, and then they decide to race 100 meters in inertial frame F3, the race will be a tie. Why can't they use the elapsed time shown on their clocks to determine who's going to win a 200 meter race if the race is run 100 meters in one inertial reference frame, and the other 100 meters in some other inertial reference frame? The elapsed time on their clocks are identical, and they each ran the same distance in each frame but that is not sufficient info per Einstein's concepts to determine the winner. Why not?
David Seppala
Bastrop TX
David Seppala
Bastrop TX