I shall attempt to teach the LTs without the use of analytic geometry. I shall use the famous barn-ladder paradox. I will also take the opportunity to demonstrate the inequality of coordinate and proper relative velocity.Dolan apprehends that the Lorentz contracted Jan & ladder just fit inside the barn, Dolan closes both doors and reads Jan's stopwatch, corrected for relativistic doppler. Dolan also reads his own stopwatch at this event.
When compared in the same inertial frame, a ladder is exactly twice as long as a barn. The barn has doors at either end, as usual. The ladder now acquires a velocity relative to the barn v such that gamma = 2.
Dolan is in charge of operating the automated & very quick barn doors. Jan rides the ladder at the front end with his stopwatch. Jan starts his stop watch just as he passed the first door. Dolan also starts his stopwatch at this event. As usual, once
Dolan calculates Jan's proper relative velocity in the barn's frame:his relative velocity in his frame or in the barn's frame where he is contracted, his watch is slow and his mind more slothful than usual.
v = length of barn / Dolan's stopwatch
Dolan also watches from the barn's frame as the Lorentz contracted, time dilated Jan calculates his velocity relative to the barn--this is Jan's coordinate relative velocity from Dolan's point of view. Because gamma = 2 Jan forms the ratio
[ Dolan's stopwatch/2 ] / [ Barn's length x 2 ] = v' = 4v = v * gamma^2
"But wait!" you scream in protest "If you apply the LTs and calculate v' in Jan's frame you get v' = v. Tru dat. But the principle of relativity states that there are no privileged frames. It doesn't matter according to Einstein, whether Jan calculates
Except it does matter! As I have just demonstrated, the only frames in which the relative velocity of two observers agree with each other is when it is calculated in each of their own inertial frames. The relative velocity of two observers is ALWAYsunequal when calculated in all other frames.
Let me hasten to add that the two barn door are sooooo fast that their openings and closings are almost instantaneous and can be considered as a single spacetime event.
Let me hasten to add that the two barn door are sooooo fast that their openings and closings are almost instantaneous and can be considered as a single spacetime event.
On Wednesday, April 26, 2023 at 2:57:58 PM UTC-5, patdolan wrote:Prokary, you dastard. Failing to print the next sentence completely changes the meaning of the first sentence. BTW, it was Dnvrfantj and not Purgy Purgatorio who primed the v on the Special relativity webpage. And only hours before I discoveries it.
Let me hasten to add that the two barn door are sooooo fast that their openings and closings are almost instantaneous and can be considered as a single spacetime event.Your statement shows that you haven't the FOGGIEST notion
of the meaning of the term "spacetime event."
I shall attempt to teach the LTs without the use of analytic geometry. I shall use the famous barn-ladder paradox. I will also take the opportunity to demonstrate the inequality of coordinate and proper relative velocity.Dolan apprehends that the Lorentz contracted Jan & ladder just fit inside the barn, Dolan closes both doors and reads Jan's stopwatch, corrected for relativistic doppler. Dolan also reads his own stopwatch at this event.
When compared in the same inertial frame, a ladder is exactly twice as long as a barn. The barn has doors at either end, as usual. The ladder now acquires a velocity relative to the barn v such that gamma = 2.
Dolan is in charge of operating the automated & very quick barn doors. Jan rides the ladder at the front end with his stopwatch. Jan starts his stop watch just as he passed the first door. Dolan also starts his stopwatch at this event. As usual, once
Dolan calculates Jan's proper relative velocity in the barn's frame:his relative velocity in his frame or in the barn's frame where he is contracted, his watch is slow and his mind more slothful than usual.
v = length of barn / Dolan's stopwatch
Dolan also watches from the barn's frame as the Lorentz contracted, time dilated Jan calculates his velocity relative to the barn--this is Jan's coordinate relative velocity from Dolan's point of view. Because gamma = 2 Jan forms the ratio
[ Dolan's stopwatch/2 ] / [ Barn's length x 2 ] = v' = 4v = v * gamma^2
"But wait!" you scream in protest "If you apply the LTs and calculate v' in Jan's frame you get v' = v. Tru dat. But the principle of relativity states that there are no privileged frames. It doesn't matter according to Einstein, whether Jan calculates
Except it does matter! As I have just demonstrated, the only frames in which the relative velocity of two observers agree with each other is when it is calculated in each of their own inertial frames. The relative velocity of two observers is ALWAYsunequal when calculated in all other frames.
On Wednesday, April 26, 2023 at 12:37:27 PM UTC-7, patdolan wrote:Dolan apprehends that the Lorentz contracted Jan & ladder just fit inside the barn, Dolan closes both doors and reads Jan's stopwatch, corrected for relativistic doppler. Dolan also reads his own stopwatch at this event.
I shall attempt to teach the LTs without the use of analytic geometry. I shall use the famous barn-ladder paradox. I will also take the opportunity to demonstrate the inequality of coordinate and proper relative velocity.
When compared in the same inertial frame, a ladder is exactly twice as long as a barn. The barn has doors at either end, as usual. The ladder now acquires a velocity relative to the barn v such that gamma = 2.
Dolan is in charge of operating the automated & very quick barn doors. Jan rides the ladder at the front end with his stopwatch. Jan starts his stop watch just as he passed the first door. Dolan also starts his stopwatch at this event. As usual, once
calculates his relative velocity in his frame or in the barn's frame where he is contracted, his watch is slow and his mind more slothful than usual.Dolan calculates Jan's proper relative velocity in the barn's frame:
v = length of barn / Dolan's stopwatch
Dolan also watches from the barn's frame as the Lorentz contracted, time dilated Jan calculates his velocity relative to the barn--this is Jan's coordinate relative velocity from Dolan's point of view. Because gamma = 2 Jan forms the ratio
[ Dolan's stopwatch/2 ] / [ Barn's length x 2 ] = v' = 4v = v * gamma^2
"But wait!" you scream in protest "If you apply the LTs and calculate v' in Jan's frame you get v' = v. Tru dat. But the principle of relativity states that there are no privileged frames. It doesn't matter according to Einstein, whether Jan
unequal when calculated in all other frames.Except it does matter! As I have just demonstrated, the only frames in which the relative velocity of two observers agree with each other is when it is calculated in each of their own inertial frames. The relative velocity of two observers is ALWAYs
Coda:precisely the identical relative velocity between them. Galilean space and time are marvelously consistent, and so homogeneous and isotropic.
When it comes to Galilean relativity, both Dolan and Jan can uses each others clocks and meter sticks, or any other inertial frame's clocks & meter sticks, or any combination of multiple inertial frames clocks & meter sticks, to ALWAYS arrive at
Homogeneity and isotropy are impossible in the case of special relativity. In addition to the inequality of relative velocity, we also find these pathologies: violation of Kepler's third law, unlimited superluminal Lorentz contraction velocities andReitdijk-Putnam undecidability. All due to the inherent inconsistency of LT algebra when it is mapped onto the real world.
On Wednesday, April 26, 2023 at 1:45:30 PM UTC-7, Prokaryotic Capase Homolog wrote:
On Wednesday, April 26, 2023 at 2:57:58 PM UTC-5, patdolan wrote:
Prokary, you dastard. Failing to print the next sentence completely changes the meaning of the first sentence.Let me hasten to add that the two barn door are sooooo fast that their openings and closings are almost instantaneous and can be considered as a single spacetime event.Your statement shows that you haven't the FOGGIEST notion
of the meaning of the term "spacetime event."
BTW, it was Dnvrfantj and not Purgy Purgatorio who primed the v on the Special relativity webpage. And only hours before I discoveries it. See for yourself.
https://en.wikipedia.org/w/index.php?title=Special_relativity&diff=1151203352&oldid=1150777470
| Sysop: | Keyop |
|---|---|
| Location: | Huddersfield, West Yorkshire, UK |
| Users: | 307 |
| Nodes: | 16 (2 / 14) |
| Uptime: | 61:04:55 |
| Calls: | 6,915 |
| Files: | 12,379 |
| Messages: | 5,431,358 |