On Monday, September 27, 2021 at 3:09:06 AM UTC+10, sep...@yahoo.com
> Say the two rockets have an identical proper acceleration of 9,.8 meters / second^2 once each starts accelerating. There is an accelerometer that measures a constant value throughout the journey once the acceleration of each rocket begins. Let one rocket have a 6 meter rod that is perpendicular the the x-axis. Just before the acceleration starts, an astronaut at the head of the rocket aligns the rod with the x-axis.
As others have told you, the swivelling of the pole is just an irritating addition that adds nothing to the scenario. Instead, just say "The rocket has a 6 metre pole fixed to the front" - Done.
The fact that you keep on repeating this I guess means that you believe (incorrectly) that the results between swivelled vs fixed pole would be different. Such a belief would point to a deeper misunderstanding of SR, but we can look at that later.
> However, when the two rockets are close to zero relative velocity with respect to F0, the astronaut once again aligns the rod with the x-axis. This time he can touch the tip of the other rocket with the rod. He can do this for awhile, but once the rockets both have a significant velocity beyond F0, the astronaut can no longer touch the tip of the other rocket with the rod ..... If the astronaut sleeps during the journey, what everyone is implying is that he will have no idea when he wakes up whether or not he will be able to touch the tip of the other rocket with the rod. Why does he need to know how long he slept to know if he can touch the tip of the other rocket with the rod?
> No one has explained the "physics" of this scenario.
Firstly, no - the explanation has been given to you repeatedly, and what I am explaining to you about how this ties in with SR is what I have picked up from these threads (Thanks Al ).
Secondly, the details that are puzzling you above are not even strictly to do with SR. It's just the natural, inevitable result of vehicles with different (coordinate) accelerations and starting times - and let's be clear : Talking about one rocket being within 5 metres of the other is just another way of saying the x(Bruce) - x(Alice) < 5. In other words, we are talking about COORDINATES, so our interest is primarily in the COORDINATE acceleration values, rather than how much force the astronaut is feeling (ie, rather than the proper acceleration values).
Let's start by extending my earlier question :
On Sunday, September 26, 2021 at 3:24:16 AM UTC+10, sep...@yahoo.com
> On Saturday, September 25, 2021 at 10:59:07 AM UTC-5, Rob Acraman wrote:
> > So let's be clear : at that time the rocket's acceleration AS MEASURED BY the rocket's on-board accelerometer (and the force felt by the astronaut) remains 9.8 metres/second^2, but the rocket's acceleration AS MEASURED BY frame F0 is 7 metres/second^2.
> > DO YOU UNDERSTAND THIS ?
> I understand that, yes. I have no problem with that.
OK, do you also understand, as a consequence of that, that two identical rockets, both programmed to have the same identical proper acceleration, can have different coordinate accelerations as measured by Frame F0 ? For example, if one rocket launches and accelerates for some time before the second launches, then although they have the same PROPER acceleration (since both their on-board accelerometers correctly show the same value, and the astronauts both feel the same force), but will have different COORDINATE accelerations (eg as measured by Frame F0) ?
I am going to proceed on the basis that your answer to that will be "Yes" again, but I expect you to clearly say "No" in your reply if you do not.
OK, so let's go over Anna and Bruce from my previous post again, but this time we'll plug some numbers in.
So, let's say Anna is in a car preset to have a constant coordinate acceleration of 5 metres / second^2, Bruce is in one preset to have a constant coordinate acceleration of 10 metres / second^2 - but Bruce is 25 metres ahead of Anna, and set to only start moving 2 seconds after Anna.
So this will play out as :
t=0 Anna is a x=0, Bruce is at x=25. Distance between them = 25 - 0 = 25.
t=1 Anna is a x=2.5, Bruce is at x=25. Distance between them = 25 - 0 = 22.5.
t=2 Anna is a x=10, Bruce is at x=25 (but now starts moving). Distance between them = 25 - 10 = 15.
t=3 Anna is a x=22.5, Bruce is at x=30. Distance between them = 30 - 22.5 = 7.5.
t=4 Anna is a x=40, Bruce is at x=45. Distance between them = 45 - 40 = 5.
At this instant, Anna and Bruce are both going at the same speed of 20 metres/second.
We can imagine that they are overtaking a truck travelling at 20 metres / second emblazoned with the logo "F0".
t=5 Anna is a x=62.5, Bruce is at x=70. Distance between them = 70 - 62.5 = 7.5.
t=6 Anna is a x=90, Bruce is at x=105. Distance between them = 105 - 90 = 15
t=7 Anna is a x=122.5, Bruce is at x=150. Distance between them = 150 - 122.5 = 27.5.
> If the two rockets have an identical acceleration rate, and one starts accelerating toward the other rocket first, the two rockets keep getting closer and closer together until Einstein's coordinates result in them moving away from each other. Why does the astronaut say that happens when there is no difference in the acceleration rates?
Well, look at what happened with Anna and Bruce. Anna started accelerating towards Bruce first, then the two of them kept getting closer and closer together until they got within 5 metres of eachother (so if Anna had a 6 metre pole fixed to the front of her car, it would have touched Bruce), and then they start moving away from eachother.
That also means that if Anna or Bruce fell asleep at t=1 (it was a "micro-nap" :D and they were only passengers, not the drivers !), then when they woke up, they would have no idea whether that 6-metre pole can touch both cars or not. They need to know how long they slept before they can figure out whether that pole can reach or not.
There is also nothing about either vehicle having to change their acceleration, nor anything wild about one of their clocks instantly gaining time when they start accelerating.
NOTHING about this should be puzzling to you. It is simple, direct, inevitable, and obvious result of differing (coordinate) accelerations and differing start times.
That means that your misunderstanding is NOT with all these features, but instead simply with this :
For cars on earth, with low velocities and therefore negligible relativistic effects, Accelerations are just one number always - ie, Proper Acceleration = Coordinate Acceleration. That means for Anna and Bruce above, Anna's PROPER acceleration would be 5 metres / second ^2 (ie, the same as her COORDINATE acceleration), and Bruces PROPER acceleration would be 10 metres / second^2 (ie, the same as his COORDINATE acceleration).
So I bet you are going to say to me "So they have different PROPER accelerations, therefore that scenario is different from what I said".
WRONG, and therefore THAT is the cause of all your confusion about this.
You confusion is NOT about the rockets coming closer together, then apart, without changing their accelerations. That is simply the same as Anna and Bruce's coordinates above.
Your confusion is because you are still equating PROPER acceleration with COORDINATE acceleration.
You said above " I understand that, yes. I have no problem with that. " .... but here when it counts, you are totally ignoring / rejecting it. Instead, when performing the same calculations as I did for Anna and Bruce above, you want to plug in the PROPER acceleration values rather than the COORDINATE acceleration values.
THAT is why you are not taking on board all the explanations that have been given to you.
So in summary, your scenario is of two rockets Rocket-A and Rocket-B accelerating from F1 to F0 both having the same PROPER acceleration. However, as measured by F1, and also as measured by the non-inertial-coordinates of Rocket-A, and also as measured by the non-inertial-coordinates of Rocket-B :
- Rocket A takes off before Rocket B
- Rocket A has a lower COORDINATE acceleration than Rocket B (to see why, re-read my previous post, esp where I say "this is critical")
These facts mean that the COORDINATES (including how close the rockets get, and so whether the pole can reach from one to the other) WILL play out similar to how Anna and Bruce plays out above.