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New Theories / Split: Bell's paradox: Does the string break?
« on: 31/07/2020 17:46:57 »
[Mod note: This topic was split from the "Is angular momentum frame dependent?" thread,
https://www.thenakedscientists.com/forum/index.php?topic=80177.msg611143 ]
You failed to quote the important part of Einstein’s paper.
“So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.”
Are the two space ships in motion relative to each other? In fact, yes.
Assume they start off with synchronized clocks and turn on their engines at an agreed time and begin to accelerate.
Spaceship 1 (in the lead) sees Spaceship 2 start up its engine a little bit later because it took a little time for the light from SP2 to reach SP1. As a result, as long as the engines are on SP1 will always see SP2 going slower, having started acceleration later. This implies that the distance between them is getting longer. A string connecting them should be under increasing tension.
However, SP2 sees SP1 start up its engine later than SP2 because of the lightspeed delay. That is, SP2 will always see SP1 going slower because SP2 started its engine first. The implies that the distance between them is getting shorter. A string connecting them should go increasingly slack.
The two spaceships are not in the same reference frame and their clocks are not synchronized. They will not agree on what they see.
Now what about that string?
SP1 thinks the string is under tension. That means that a force is being transmitted down the string at the speed of sound in the string, lightspeed at most. Assuming identical strength for the string all along its length, the string will not snap until the force wave hits the end of the string and cannot be passed on to the next segment.
SP2 thinks the string is slack, and will not snap at all. We might imagine SP1’s force wave meeting SP2’s slack somewhere in the middle, resulting in a string with neither slack nor tension. But that is assigning absolute reality to perceptions.
How can SP1 and SP2 agree on what is happening to the string? By turning off their engines at an agreed time by their originally synchronized clocks and getting back into an inertial frame of reference. SP1 will see SP2 turn off its engine a little late and catch up in speed, restoring the distance gap. SP2 will also see SP1 turn off its engines a little late and take up the slack. Once they are in a common inertial frame of reference again, they will discover that they are separated by the original length of the string, which suffered no harm.
A side note: SP1 thinks SP2 is going slower and therefore has a faster clock. SP2 thinks SP1 is going slower and has a faster clock. The perceived time difference between engine shutoffs will be the same on each side.
But what about Lorentz contraction on the string?
If SP1 and SP2 each look straight along the length of the string, they will be unable to judge its length. If each looks at the string from enough to the side to judge its length, they will observe the string to be curved because of the aforementioned perceived speed differences and the time it takes for the light to reach them from different points along the length of the string.
Once they are in a common inertial frame of reference, an outside observer in inertial motion relative to them will observe Lorentz contraction of the entire system, SP1 and SP2 and the string. No broken string, no slack string.
Lorentz contraction is relative. It is not real.
https://www.thenakedscientists.com/forum/index.php?topic=80177.msg611143 ]
Halc,
that's the answer I expected.
Mamalute Lover,
if you deny Bell's spaceship 'paradox' then you are going against Einstein and his original 1905 paper.
He starts his paper with a definition of simultaneity:
http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1905_relativity.pdf
If you deny the simultaneity then you have nothing to back up your statements.
You cannot argue this is like this because the relativity says so. You denied the relativity.
Do you have your own math? Do you have your own hypothesis?
Jano
You failed to quote the important part of Einstein’s paper.
“So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.”
Are the two space ships in motion relative to each other? In fact, yes.
Assume they start off with synchronized clocks and turn on their engines at an agreed time and begin to accelerate.
Spaceship 1 (in the lead) sees Spaceship 2 start up its engine a little bit later because it took a little time for the light from SP2 to reach SP1. As a result, as long as the engines are on SP1 will always see SP2 going slower, having started acceleration later. This implies that the distance between them is getting longer. A string connecting them should be under increasing tension.
However, SP2 sees SP1 start up its engine later than SP2 because of the lightspeed delay. That is, SP2 will always see SP1 going slower because SP2 started its engine first. The implies that the distance between them is getting shorter. A string connecting them should go increasingly slack.
The two spaceships are not in the same reference frame and their clocks are not synchronized. They will not agree on what they see.
Now what about that string?
SP1 thinks the string is under tension. That means that a force is being transmitted down the string at the speed of sound in the string, lightspeed at most. Assuming identical strength for the string all along its length, the string will not snap until the force wave hits the end of the string and cannot be passed on to the next segment.
SP2 thinks the string is slack, and will not snap at all. We might imagine SP1’s force wave meeting SP2’s slack somewhere in the middle, resulting in a string with neither slack nor tension. But that is assigning absolute reality to perceptions.
How can SP1 and SP2 agree on what is happening to the string? By turning off their engines at an agreed time by their originally synchronized clocks and getting back into an inertial frame of reference. SP1 will see SP2 turn off its engine a little late and catch up in speed, restoring the distance gap. SP2 will also see SP1 turn off its engines a little late and take up the slack. Once they are in a common inertial frame of reference again, they will discover that they are separated by the original length of the string, which suffered no harm.
A side note: SP1 thinks SP2 is going slower and therefore has a faster clock. SP2 thinks SP1 is going slower and has a faster clock. The perceived time difference between engine shutoffs will be the same on each side.
But what about Lorentz contraction on the string?
If SP1 and SP2 each look straight along the length of the string, they will be unable to judge its length. If each looks at the string from enough to the side to judge its length, they will observe the string to be curved because of the aforementioned perceived speed differences and the time it takes for the light to reach them from different points along the length of the string.
Once they are in a common inertial frame of reference, an outside observer in inertial motion relative to them will observe Lorentz contraction of the entire system, SP1 and SP2 and the string. No broken string, no slack string.
Lorentz contraction is relative. It is not real.