Bell’s Spaceship Paradox. Does the string break?

[Mike_Fontenot]

My (Mike Fontenot's) responses are in red.

Halc said:

So I notice that if you didn't run out of space at the edge of your chart, your LoS line intersects the leading ship worldlineat a separation distance of 69.28 in the S" frame in which both ships are stationary after the acceleration events, which is twice the separation distance (34.64) between the ships in frame S in which both ships were stationary before the acceleration events. So your drawing shows any string between them needing to be twice as long in order to not break.

First, let me reiterate that my proof does NOT depend on anything that happens after the time 30+ for the traveling twin. The changes between 30- and 30+ are where all the important action is. But, to try to understand your point, I DID extend the worldline of the leading rocket, starting from the point T = 50 on the T axis, and also the LOS of the leading rocket from that point. The intersection between the LOS of the traveling twin (his) when he is 30+, and the leading rocket's world line starting from the point T = 50 on the T axis, occurs a LONG way from the right edge of my paper ... several yards across my office. So I lost interest in your explanation at that point. I say again: my proof doesn't depend on anything that happens after the time 30+ for the traveling twin, and after the time 50+ for the home twin and the leading rocket. The fact that the separation between the two rockets is constant (in the non-absurd case) means that the thread DOESN'T break. The thread would break in the absurd case, but that doesn't matter, because the absurd case couldn't happen.

 

[Mike_Fontenot]

But wasn't this your surmise in the first place?

IOW, you interpreted SR to mean that he would see an instantaneous aging, despite everyone telling you that wasn't true.
Now you've proven that your surmise was wrong, and that you agree with everyone.
(Have I got that right? It's been a long thread.)

I'm sorry, I couldn't follow your post. Can you elaborate? I'll try to respond if I can understand what you're saying.

 

[Mike_Fontenot]

We all drew the same spacetime diagram, so the geometry of the events is not in dispute.

I'm sorry, I couldn't understand your point here. Could you elaborate about my post to you in #177?

 

[Neddy Bate]

So I notice that if you didn't run out of space at the edge of your chart, your LoS line intersects the leading ship worldlineat a separation distance of 69.28 in the S" frame in which both ships are stationary after the acceleration events, which is twice the separation distance (34.64) between the ships in frame S in which both ships were stationary before the acceleration events. So your drawing shows any string between them needing to be twice as long in order to not break.

You are correct. In the instant before the traveling twin accelerates toward his twin sister, he says his distance to her is 34.64 light years, which is also the distance to the leading rocket which is co-located with her. In the instant after he accelerates toward her, he says his distance to her has become 17.32 light years (length contraction of her x axis), and he also says the distance to the leading rocket has become 69.28 light years. This is due to ROS (relativity of simultaneity) and her now being 80 years old instead of 50, and of course the leading rocket cannot still be co-located with her when she is 80 because it departed from her when she was 50. All of this is clearly shown on the spacetime diagrams that pan far enough over to see the intersection of the LOS and the leading rocket's worldline.

Mike says he is okay with all of the above, but he just wants to ignore it and say that the distance between the rockets does not change. So 34.64 to 69.28 is not a change? Notice how Mike keeps saying now that his "proof" does not even need the LOS that points to her being 80 years old. He wants to ignore that, and only look at the LOS that points to her being 50 years old. Well, that is one way to make sure one's proof says what one wants it to say, just ignore the part that proves otherwise!

So that is one of the things that Mike will not acknowledge, because it shows that his claim that the string does not break is wrong. His whole non-proof is all about doubling down on his claim about the string not breaking. Trying desperately to prove himself right when he is wrong means having to ignore a whole lot of inconvenient truths.

I predict this will go on for months if we keep replying. He is not about to admit his errors or deceptions. He already has his papers printed and ready to sell. It is too late to change them now!

 

[Mike_Fontenot]

No one has found an error in my proof itself.

My proof is in https://vixra.org/pdf/2308.0119v1.pdf

Quote the sentence which is incorrect in that pdf.

 

[phyti]

;
It seems all are looking at the history of events, and describing what happened.

It's easy to say at At 50 B2t was 30, at At 90 B2t was 50, etc.
In a real time account, each observer experiences a delay for the communication of an event. A simple example, A does not know that B2t=30 until At =50+34.6=84.6, getting the results of the round trip transit time for light. Measurements have to be made in order to know anything. The measurements require the observer to use his own light since he will know the local emission and return times. If he is in an inertial frame (constant velocity) he can simply divide the round trip time by 2.

As the 'A frame' shows, there is no los from B2t=30. The reason, B2 didn't make any measurements prior to B2t=30. (See post #132)

All the problems associated with the simple 'twins' triangle result from attempting to join two different discontinuous motions, outbound and inbound.

 

[Neddy Bate]

Here is my Minkowski diagram updated to include all the coordinates:

I did not bother to rotate it to Mike's preferred orientation, because he is refusing to use the correct simultaneity line. "Look at my proof that Bell was wrong! I simply refuse to use the correct simultaneity line and voila!"

 

[Neddy Bate]

It seems all are looking at the history of events, and describing what happened.

It's easy to say at At 50 B2t was 30, at At 90 B2t was 50, etc.

phyti,

When a scenario is described accurately enough, we can graph the world lines of the traveling objects on a space-time graph (with an x axis for the space coordinate and a t axis for the time coordinate). The current scenario is a simplified Twins Paradox scenario (constant velocities & instantaneous accelerations) combined with a simplified Bell's Spaceship scenario (constant velocities & instantaneous accelerations).

The lines of simultaneity come from the Lorentz Transformations (LT) of Special Relativity. The Minkowski diagram is designed to have them be of a certain slope based on the slope of the worldline. For example, on my Minkowksy diagram above, the only times the traveling twin's simultaneity lines can be horizontal is when his worldline is vertical. When his worldline is diagonal, his simultaneity lines are diagonal too, as shown in the diagram. The stay home twin's worldline is the ct axis, and her lines of simultaneity are always horizontal, so for clarity all that is left off the diagram.

The Lorentz transformations describe the simultaneity or the "now" of the events happening simultaneously with the current time in the reference frame. The traveler can know, without waiting for any light signals to be reflected back, the coordinates of hypothetical events that are happening "now" in his reference frame. It is not images of events from the past, it is the current events that are considered to be happening "now", at a certain time and place, even though the eye cannot see them yet. Different reference frames can have different simultaneities when they are in relative motion. It is all defined in the LT equations.

The speed of light being constant means we can already know the traveling twin's simultaneity lines without waiting for any signals. Yes, this does mean that the real life worldlines have to be what we planned them to be, and if they are not, then our calculations will be wrong, but we will not know about it until we see it later. But this is the hypothetical situation where the worldlines are what we planned them to be.

 

[Neddy Bate]

The slopes of lines of simultaneity are a function of the slope of the worldline:

The slopes of lines of simultaneity depend entirely and solely on the slopes of the worldline.

 

[Neddy Bate]

The LT equations convert the coordinates of an event from one reference frame to another. For example, the event (x,t)=(0.00,10,00) transforms to (x',t')=(-17.32,20.00) by these equations which transform from unprimed to primed coordinates:
x' = γ(x - vt)
t' = γ(t - vx/c²)

There are also inverse transformations for going from primed to unprimed:
x = γ(x' + vt')
t = γ(t' + vx'/c²)

And for the return half of the journey we have double primed coordinates, so unprimed to double primed:
x'' = γ(x + vt)
t'' = γ(t + vx/c²)

And the inverse from double primed to unprimed coordinates:
x = γ(x'' – vt'')
t = γ(t'' – vx''/c²)

Where gamma is this:
γ = 1 / √(1 - (v²/c²))

 

[Mike_Fontenot]

[...]
I did not bother to rotate it to Mike's preferred orientation, because he is refusing to use the correct simultaneity line.
[...]

NOTHING is needed in my proof that is not already stated there. No diagram is needed.

Exactly which statement in my proof (given in the viXra reference I provided) do you contend is incorrect?
(And if you think there is more than one incorrect statement, tell me what the first one is).

 

[Neddy Bate]

 

[Mike_Fontenot]

[...]

In my proof, I needed no diagrams at all ... it's just text. So what is the first thing in that text that you think is incorrect? Here's the link again, in case you need it:

https://vixra.org/pdf/2308.0119v1.pdf

 

[Neddy Bate]

I did that in posts 135, 136, 138...

 

[Mike_Fontenot]

I did that in posts 135, 136, 138...

I looked all that way back, but it's too contorted for me.
Just quote the first sentence in my proof that you maintain is incorrect. Here is the viXra link again:

https://vixra.org/pdf/2308.0119v1.pdf

(You still have a mistake in your latest diagram, and I can tell you what that is, but I want to first see what you think is the first incorrect sentence in my proof).

 

[Neddy Bate]

THAT would result in HER seeing the leading rocket INSTANTANEOUSLY move a finite distance away from her, WHICH IS ABSURD!

That would not occur in her own reference frame. It is a completely false claim, similar to someone saying, "THAT would result in HER seeing her own age change INSTANTANEOSLY from 50 years old to 80 years old, WHICH IS ABSURD!" Or the one you argued against for awhile: "THAT would result in HER seeing her own blouse change INSTANTANEOSLY from a pink one to a blue one WHICH IS ABSURD!"

There is no difference, they are all equally false and preposterous claims. You cannot make a valid "proof" using a false premise.

You wanted it, you got it. Now address it properly. Do not just repeat your baseless assertion. Show me where that occurs on the Minkowski diagram I posted, for example.

 

[Halc]

My (Mike Fontenot's) responses are in red.
First, let me reiterate that my proof does NOT depend on anything that happens after the time 30+ for the traveling twin.

Is OK. It's when he turns 30 that the separation distance becomes 69 in S". It wasn't before that.

But, to try to understand your point, I DID extend the worldline of the leading rocket, starting from the point T = 50 on the T axis

You didn't draw the lead rocket worldline at all, so I don't know how it could be extended. But if you draw a line from that t=50 event parallel to the trailing rocket line, it would match our drawings.

The intersection between the LOS of the traveling twin (his) when he is 30+, and the leading rocket's world line starting from the point T = 50 on the T axis, occurs a LONG way from the right edge of my paper ... several yards across my office.

Your paper is about 85 years wide. One more sheet would have been enough, barely.
If you claim it is yards away, then you are incorrectly computing that the proper separation distance between the two rockets is far larger than 69 LY, a funny claim to make for somebody who insists that the original 34.6 LY string is enough.

So I lost interest in your explanation at that point.

As is your reaction to any critique that falsifies your claims. I notice you conveniently lose interest or otherwise run away whenever your mistakes are made clear, making one wonder why you keep asking what's wrong with your 'proof', but then ignore the repeated answers.

No one has found an error in my proof itself.

Your refusal to read/address any of the errors identified does not constitute a lack of them having been pointed out. Neddy gives some of his list:

I did that in posts 135, 136, 138...

Among others of mine:
84 identified several. Your reply was a request to identify the first one (not the important ones). The important ones were ignored.
109 was very explicit: Your reply was to directly deny the first premise of SR and then ignore the most important points.
145 highlighted about a dozen errors. Your reaction was to run away. I even listed that as one of the options, and you selected it.

I looked all that way back, but it's too contorted for me.

Then ask questions for clarification. Running away or otherwise refusing to engage just shows a complete lack of ability to defend one's pet assertions.

I did not bother to rotate it to Mike's preferred orientation, because he is refusing to use the correct simultaneity line.

He did draw the S" LoS correctly, even if he doesn't know how to use it. He completely neglected to draw the lead rocket worldline, which seems strange since what that rocket does (or more to the point, what Alice sees it doing) seems critical to the "proof".

That would not occur in her own reference frame

That would not occur in any reference frame. What an observer sees is objective fact and not frame dependent in any way. Mike seems not to realize this.

 

[Neddy Bate]

He did draw the S" LoS correctly, even if he doesn't know how to use it. He completely neglected to draw the lead rocket worldline, which seems strange since what that rocket does (or more to the point, what Alice sees it doing) seems critical to the "proof".

Yes he drew the S'' LoS, but incorrectly wrote "not of importance to this proof" next to it. That and the lack of the rocket worldline are very serious blunders for someone trying to prove where the rocket would be located AFTER the acceleration to frame S''.

 

[Mike_Fontenot]

The text in red is by me (Mike Fontenot):

The sentence from my proof that you have decided was the first incorrect sentence needs the sentence that preceded it in order to be understood, so I have added that first:

"During his instantaneous speed change, suppose that the leading rocket is ASSUMED to
instantaneously INCREASE its separation from the trailing rocket."

"THAT would result in HER seeing the leading rocket INSTANTANEOUSLY move a finite distance away from her, WHICH IS ABSURD!

To that, you (Neddy) said:

That would not occur in her own reference frame.

Sure it would! She is at that position, at rest. Immediately before that rocket fires, she can look at that rocket ... it's right next to her, and stationary. She's been looking at it for a while. That's when she is 50-. Then, in the next instant (when she is 50+), the rocket fires, and undergoes an instantaneous speed change to 0.866 ly/y (directed in the direction away from the traveling twin). But MORE important is that, by assumption, that rocket is not ONLY instantaneously changing it's speed, it also INSTANTANEOUSLY gets farther from the trailing rocket. If it actually did that, she would certainly be able to SEE it do that. If it just instantaneously moves a short distance, she would see it suddenly disappear from where it's been by her side, and instantaneously reappear a short distance away. If it moves farther away (out of sight), she would just see it disappear instantly. Either way, that is obviously absurd, and so we must reject the assumption that the separation between the two rockets instantaneously increases during their instantaneous speed change.

Show me where that occurs on the Minkowski diagram I posted, for example.

I'll show you the remaining error in your diagram, but not until you've understood the above explanation.

 

[Neddy Bate]

Sure it would! She is at that position, at rest. Immediately before that rocket fires, she can look at that rocket ... it's right next to her, and stationary. She's been looking at it for a while. That's when she is 50-. Then, in the next instant (when she is 50+), the rocket fires, and undergoes an instantaneous speed change to 0.866 ly/y (directed in the direction away from the traveling twin). But MORE important is that, by assumption, that rocket is not ONLY instantaneously changing it's speed, it also INSTANTANEOUSLY gets farther from the trailing rocket. If it actually did that, she would certainly be able to SEE it do that. If it just instantaneously moves a short distance, she would see it suddenly disappear from where it's been by her side, and instantaneously reappear a short distance away. If it moves farther away (out of sight), she would just see it disappear instantly. Either way, that is obviously absurd, and so we must reject the assumption that the separation between the two rockets instantaneously increases during their instantaneous speed change.

Are you seriously thinking that when the traveling twin changes his LoS it will instantaneously affect the home twin and cause her to see illusions? He changes his LoS and she changes from 50 to 80 years old in an instant and you have no problem with that because you know it is just his LoS and does not affect her own inertial frame. Her blouse instantly changes from pink to blue, and you have no problem with that because you know it is just his LoS and does not affect her own inertial frame. What is different about the leading rocket that makes you think it would move at infinite speed in her own frame? Is it because it moves location? Her blouse moves location also, it jumps out of from her dresser and INSTANTANEOUSLY lands on her body! What are you worried about the leading rocket for? It is just the same as her blouse. That is a mistake that an SR beginner would make.

If you look at my Minkowski diagram, or Halc's, you can calculate how far the rocket moves when the twin shifts his LoS. Before the acceleration the traveling twin is located at x=34.64 and the leading rocket is located at x=0.00 so the distance between them is 34.64-0.00=34.64. After the acceleration, the traveling twin says he is located at x''=155.88 and he says the leading rocket is located at x''=86.61, so he calculates the distance between them as 155.88-86.61=69.27. Yet the worldline of the leading rocket does not move instantaneously away from the home twin! IT MOVES AT 0.866c AWAY FROM HER in her own frame, just as shown on the diagram.