Bell’s Spaceship Paradox. Does the string break?

[Neddy Bate]

I still stand by EVERYTHING I've posted. I'm certain that I am correct.

Mike,

Don't give up yet. I'll be posting a Minkowski diagram over the weekend which you will definitely want to see. I have most of it drawn, but I need some time to add all the coordinates.

 

[Halc]

Phyti, the twin paradox has NOTHING to do with light signals being sent back and forth between the twins.

I actually agree with this.

It's about the time dilation equation

No it isn't. It's about differential aging, a physical fact. Time dilation is nothing but an abstract coordinate effect. Hence it having more than one valid explanation, with the dilation equation being just one of them. It can be used without considering anybody's point of view, hence my encouragement to discard the humans altogether.

which says that any person (she) who isn't accelerating (i.e., who is inertial) must conclude that any other person (he) who is moving with respect to her is ageing more slowly than she is

This is wrong, for the reason I posted prior. No decent physics text would say that. I qualify that statement since there's probably one out there that says something like that, but I've never seen one.


Anyway, the topic wasn't about Mike being in denial of the outcome of the twins thing. It's about denial of Bell's spaceship scenario.

I did a graph showing my numbers from post 76, two ships separated by a distance of 2LY abruptly changing velocity by .866c.
I tried also to graph what Mike asserts, but no numbers have been provided, so I'm open to corrections.

 

[Mike_Fontenot]

[...]

Anyway, the topic wasn't about Mike being in denial of the outcome of the twins thing. It's about denial of Bell's spaceship scenario.

I don't deny the Bell spaceship scenario. It's just a DIFFERENT scenario from the scenario I'm interested in. In the Bell scenario, the initial inertial observers GUARANTEE that the spacing between the two rockets is constant. This is clear from the Wiki article:

"The distance between the spaceships does not undergo Lorentz contraction with respect to the distance at the start, because in S, it is effectively defined to remain the same [...]."

(In the above, "S" is the frame of the initial inertial observers).

The fact that in that scenario, the initial inertial observers guarantee that the rocket separation is constant (according to them) requires that people on the rockets will conclude that the separation is INCREASING as the acceleration progresses. For them, the separation is increasing because the acceleration of the leading rocket is greater than the acceleration of the trailing rocket, as confirmed by the two accelerometers.

In contrast, in the scenario that I'm am interested in, the scenario is DEFINED by the fact that the two accelerometers always show the same readings. In that case, the separation between the rockets in constant, as my most recent proof shows:

https://vixra.org/abs/2308.0119

"A Non-Constant Separation of the Rockets Contradicts the Resolution of the Twin Paradox"

 

[Neddy Bate]

I don't deny the Bell spaceship scenario. It's just a DIFFERENT scenario from the scenario I'm interested in. In the Bell scenario, the initial inertial observers GUARANTEE that the spacing between the two rockets is constant. This is clear from the Wiki article:

"The distance between the spaceships does not undergo Lorentz contraction with respect to the distance at the start, because in S, it is effectively defined to remain the same [...]."

(In the above, "S" is the frame of the initial inertial observers).

The fact that in that scenario, the initial inertial observers guarantee that the rocket separation is constant (according to them) requires that people on the rockets will conclude that the separation is INCREASING as the acceleration progresses.

This is great to hear. You seemed to be denying the INCREASED separation in the rocket frames for awhile there, so this is progress. However...

For them, the separation is increasing because the acceleration of the leading rocket is greater than the acceleration of the trailing rocket, as confirmed by the two accelerometers.

No. The accelerometers display the same constant acceleration on both rockets in the Bell's scenario. You should be able to see this by the fact that they remain at a constant separation distance in the initial inertial frame. And yet the separation still INCREASES in the rocket frames. See this graphic from the same wiki page, and read the caption at the bottom:

https://en.wikipedia.org/wiki/Bell's_spaceship_paradox#/media/File:Bell_observers_experiment2.png

In contrast, in the scenario that I'm am interested in, the scenario is DEFINED by the fact that the two accelerometers always show the same readings. In that case, the separation between the rockets in constant, as my most recent proof shows:

https://vixra.org/abs/2308.0119

"A Non-Constant Separation of the Rockets Contradicts the Resolution of the Twin Paradox"

There is no "in contrast" because Bell already had both accelerometers displaying the same. The only way you are going to get a constant separation distance in the rocket frames is to let the rockets get closer together in the initial inertial frame by the exact same factor as the length contraction would be for a solid rod.

 

[Neddy Bate]

Mike,

Below is the Minkowski diagram of the scenario that you specified. The only difference is that when the twin reaches the turnaround point and instantly decelerates to v=0.000c with respect to the home twin, I did not let him sit there for 10 years. I just let him instantly accelerate back toward her at v=-0.866c again.

Notice how for any time after t=40 the worldline of the leading rocket is no longer co-located with the home twin (who is always located on the t axis). The lead rocket cannot be co-located with her when she is 70 years old, which is what the traveling twin says is her age as soon as he begins moving toward her at v=-0.866c. The leading rocket is long gone away from her. Now put your finger on the graph where you think it should be located, and then explain to us how that is supposed to work.

 

[Mike_Fontenot]

Their wording (in the Wiki article) DOES confirm that they are aware that the initial inertial observers MUST obey the length-contraction equation (LCE). The LCE says that the initial inertial observers must conclude that the separation measured by them is LESS than the separation measured by the people on the trailing rocket. So, given that the separation is by design equal, according to the initial inertial observers, then the LCE REQUIRES that the separation, according to the trailing observers, is increasing. But if that last requirement is true, then my recent proof, in

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

"A Non-Constant Separation of the Rockets Contradicts the Resolution of the Twin
Paradox"

REQUIRES that the accelerometers in the Bell scenario CAN'T show equal readings ... the leading accelerometer must have a higher reading than the trailing accelerometer. But in my scenario, the two accelerometers are assumed at the outset to be equal, by design. Therefore, the Bell scenario IS a different scenario than the scenario I am addressing, and I'm not interested in their scenario.

 

[Neddy Bate]

Their wording (in the Wiki article) DOES confirm that they are aware that the initial inertial observers MUST obey the length-contraction equation (LCE). The LCE says that the initial inertial observers must conclude that the separation measured by them is LESS than the separation measured by the people on the trailing rocket. So, given that the separation is by design equal, according to the initial inertial observers, then the LCE REQUIRES that the separation, according to the trailing observers, is increasing. But if that last requirement is true, then my recent proof, in

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

"A Non-Constant Separation of the Rockets Contradicts the Resolution of the Twin
Paradox"

REQUIRES that the accelerometers in the Bell scenario CAN'T show equal readings ... the leading accelerometer must have a higher reading than the trailing accelerometer. But in my scenario, the two accelerometers are assumed at the outset to be equal, by design. Therefore, the Bell scenario IS a different scenario than the scenario I am addressing, and I'm not interested in their scenario.

In Bell's scenario the accelerometers show identical readings and the rockets stay a constant distance apart in the initial inertial frame. If you "require" them to show different readings, then you are back to denying Bell's scenario. Any comment on my Minkowski diagram?

 

[Neddy Bate]

I'm not sure why this is difficult for you to understand, Mike. Bell said the rockets "will have at every moment the same velocity, and so remain displaced one from the other by a fixed distance. Now, if a fragile thread is tied between B and C, it's not long enough anymore due to length contractions, thus it will break. The artificial prevention of the natural contraction imposes intolerable stress".

 

[Neddy Bate]

Mike,

Do you see your dilemma yet?

You might want to start deleting your "paper" now, before someone sees it and thinks you've lost your mind.

 

[Mike_Fontenot]

In Bell's scenario the accelerometers show identical readings and the rockets stay a constant distance apart in the initial inertial frame.

They have no idea what the two accelerometers actually read.

If you "require" them to show different readings, then you are back to denying Bell's scenario.

In the Bell scenario, the accelerometers show different readings because the length contraction equation requires it. If the initial inertial observers conclude that the separation in their frame is constant (which was the forced situation), then the length contraction equation REQUIRES that the separation increases in the frame of the trailing rocket. And THAT requires that the thrust of the leading rocket is greater than the thrust of the trailing rocket.

Any comment on my Minkowski diagram?

I haven't had time to try to sort it out yet. All I need to know is that IF the (incorrect) assumption is made that the separation between the rockets increases (according to the people on the trailing rocket), the result (as shown in my paper) is that the home twin will see the leading rocket instantaneously jump away from her, which is absurd, which means the assumption that the rocket separation increases (according to the people on the trailing rocket) is incorrect, and must be rejected.

Here's your challenge: Find the FIRST statement in my paper (it's less than a page long) that you contend is incorrect, and report that statement. I'll copy that paper below, to make that easy:

A Non-Constant Separation of the Rockets Contradicts the Resolution of the Twin Paradox

The resolution of the Twin Paradox is well-known: during the traveler's (his) instantaneous
turnaround, he must conclude that his home twin's (her) age instantaneously increases.But IF
it's true that the two separated rockets in the Bell's Paradox (whose accelerometers show equal
constant readings) DON'T maintain a constant separation, that CONTRADICTS the resolution of
the Twin Paradox.

Here's how to see that contradiction:

Suppose we start out with him being separated and stationary with respect to her.

Imagine that, at the instant before he instantaneously increases his speedtoward her, he is
colocated and stationary with respect to the TRAILING rocket.And suppose that the LEADING
rocket is colocated and stationary with HER then. (The rockets are unaccelerated before and at
that instant).

When he instantaneously changes his speed with respect to her from zero to some large non-zero
value, the two rockets instantaneously do the same thing.

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! So the ASSUMPTION that the separation of the rockets isn't constant CAN’T be
correct.

 

[phyti]

Mike;

So the home twin (she), who never accelerates, must conclude that he (who is also inertial except for the one instant when he instantaneously reverses his course) is ageing only half as fast as she is ageing. So she knows that, if she is 80 years old when he returns, he will be 40 years old then.

She is assuming, IF his speed is a constant .0866, and IF they reunite, THEN (future) his accumulated time WILL BE (future) .5 of her time.
It's all prediction, conditional (if, then) statements. Your statements can only be verified (become factual evidence) at the reunion.

The ONLY answer is that, when he instantaneously reverses course, he MUST conclude that she instantaneously gets 60 years older during his course reversal. THAT is what resolves the twin paradox.

That has been shown to be false, if you can interpret spacetime graphics.

 

[phyti]

Mike;

This is the example with two observers B1 and B2.
If B1 doesn't make measurements past the reversal point (magenta), he loses the A history which includes the Bx line of simultaneity from At5 to At10.
If B2 doesn't make measurements before the reversal point (magenta), he loses the A history which includes the Bx line of simultaneity from At10 to At15.
The A history is missing from At5 to At15. That is not equivalent to an instantaneous motion between two different locations.

 

[Neddy Bate]

They have no idea what the two accelerometers actually read.

That is false. Accelerometers display a reading that tells the proper acceleration, and it is given that the proper acceleration for both rockets is the same because of the way they move identically in the initial inertial frame S. Thus, both accelerometers must read the same. What kind of physics would have an inertial frame with two identical and simultaneously moving rockets with two different accelerometer readings? Nonsense physics, that is what kind.

From the wiki article:
"The distance between the spaceships does not undergo Lorentz contraction with respect to the distance at the start, because in S, it is effectively defined to remain the same, due to the equal and simultaneous acceleration of both spaceships in S. It also turns out that the rest length between the two has increased in the frames in which they are momentarily at rest (S′), because the accelerations of the spaceships are not simultaneous here due to relativity of simultaneity."

In the Bell scenario, the accelerometers show different readings because the length contraction equation requires it. If the initial inertial observers conclude that the separation in their frame is constant (which was the forced situation), then the length contraction equation REQUIRES that the separation increases in the frame of the
trailing rocket. And THAT requires that the thrust of the leading rocket is greater than the thrust of the trailing rocket.

It does not require different accelerometer readings to have the distance between the rockets increase in the frame of the trailing rocket. In my Minkowski, diagram it is the change in the angle of the simultaneity line that causes the increase in distance, nothing to do with different accelerations. The accelerations are all the same, they all go from 0.000c to 0.866c instantaneously in the initial inertial frame.

From the wiki article:
"It also turns out that the rest length between the two has increased in the frames in which they are momentarily at rest (S′), because the accelerations of the spaceships are not simultaneous here due to relativity of simultaneity."

All I need to know is that IF the (incorrect) assumption is made that the separation between the rockets increases (according to the people on the trailing rocket), the result (as shown in my paper) is that the home twin will see the leading rocket instantaneously jump away from her

That is not true. She never sees the leading rocket instantaneously jump away from her, as you well know. It is the trailing rocket who calculates that jump in its own frame, not in her frame. And to think your entire "proof" relies on this blatant misapplication of SR, and mixing frames incorrectly. Astounding.

Just look at my Minkowski diagram and tell me where the leading rocket is located at t=40 and where it is located at t=70. If it is not in the same place, then of course the trailing rocket is going to say it instantaneously jumped locations when it said the distant time jumped from t=40 to t=70. If you think it is in the same place, then you must explain how it failed to move for 30 years when you said it started moving away from her at v=0.866c at t=40. Nonsense is all you have, Mike.

 

[Mike_Fontenot]

Neddy, your post above, and your Minkowski diagram, are full of errors. I'll elaborate about that later if you want, but for now, do the challenge I gave you. And Halc, feel free to respond to the challenge too.

 

[Neddy Bate]

Neddy, your post above, and your Minkowski diagram, are full of errors. I'll elaborate about that later if you want, but for now, do the challenge I gave you. And Halc, feel free to respond to the challenge too.

I look forward to you telling me what you think is wrong with them. As for the challenge, I have told you many times that the following is not true:

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

It is the trailing rocket that calculates that instantaneous movement of the leading rocket, when he instantaneously changes the angle of his simultaneity line. It does not follow that she would be affected by his change in simultaneity. You are either deliberately falsifying what SR says, or you don't understand it. There, done.

 

[Neddy Bate]

Oh, and this is also incorrect:

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

Your error (or deception) here is that you do not state a reference frame. It is the trailing rocket's frame that has the leading rocket instantaneously change position, but you don't say that. And the instantaneous change in position in the trailing rocket's frame is not assumed, it is calculated by the Lorentz Transforms and it shows up in a Minkowski diagram also. But it still does not affect anything in her frame. Her time passes normally.

 

[Mike_Fontenot]

When the two separated rockets have a constant separation, with constant thrust and equal accelerometer readings (according to the people on those rockets), which is my view, the scenario can be explained more easily, so I'll start with that, and then later in this posting I'll address the alternative view that the separation of the rockets increases during the equal accelerations.

First, omit the trailing and leading rockets entirely.

The traveler (he) starts out (in this scenario) motionless wrt his home twin (she). They each say that their separation is 34.64 ly. She is 40 years old, and he is 20 years old. Ten years passes (for them) with no speed changes, so she is then 50, and he is 30. He then instantaneously changes his speed relative to her to 0.866 ly/y, moving toward her. He says she instantaneously got 30 years older during his instantaneous speed change, so she is then 80. He says that his distance from her instantaneously changed from 34.64 ly to 17.32 ly. She says their separation didn't change ... it's still 34.64 ly. For the present purposes, that's the end of the scenario ... we're not concerned about what happens during his trip back home.

Now, we add the two rockets to the scenario. Before he instantaneously changed his speed from zero to 0.866 ly/y toward her, he had acquired another rocket (in addition to his own), called the trailing rocket, and it was stationary (and un-fired), at his side, perpendicular to the direction between him and her. And there was another rocket beside her, called the leading rocket, which also hadn't been fired yet, and which was stationary wrt her.

When he instantaneously changed his speed from zero to 0.866 ly/y, directed toward her, he also instantaneously changed the speed of the trailing rocket from zero to 0.866 ly/y. And by prior agreement, the leading rocket next to her instantaneously changed its speed from zero to 0.866 ly/y, directed away from her, in the direction opposite to him. Even though the leading rocket has instantaneously changed its speed, it hasn't yet moved away from her (but it will begin to do that). I.e., she will see the leading rocket start to move away from her, at a constant speed. There is nothing absurd about that at all. End of story for the above scenario.

In the above, we assumed at the outset that the separation of the two rockets would be CONSTANT during their instantaneous speed change. But what if their separation INCREASES by a finite (and large) amount during their instantaneous speed change? The ONLY difference between the outcomes of those two assumptions would be that she would see the leading rocket instantaneously change its DISTANCE from her (from zero distance to some large finite distance). THAT is ABSURD. An instantaneous change in speed is allowable (because it is just a limiting process of finite acceleration and finite duration). But an instantaneous change in distance is not allowable ... it would be like some object disappearing at some position, and instantly reappearing at some finite distance away, which is absurd. So the assumption that the separation of the two rockets increases when they accelerate is INCORRECT.

 

[Neddy Bate]

Hi Mike,

Thanks for typing all that out. I believe it will help us reach an agreement. Since you say this first part can be explained more easily, let's just start with that. Then we can move on once we have reached some kind of understanding.

The traveler (he) starts out (in this scenario) motionless wrt his home twin (she). They each say that their separation is 34.64 ly. She is 40 years old, and he is 20 years old. Ten years passes (for them) with no speed changes, so she is then 50, and he is 30. He then instantaneously changes his speed relative to her to 0.866 ly/y, moving toward her. He says she instantaneously got 30 years older during his instantaneous speed change, so she is then 80. He says that his distance from her instantaneously changed from 34.64 ly to 17.32 ly. She says their separation didn't change

Suppose someone replies to that with, "If he says she instantaneously got 30 years older, then she must see herself immediately get older. She could have been wearing a pink top when she was 50, and then all of a sudden she finds herself wearing a blue top and she is 80. The new clothes must have appeared out of nowhere in an instant. THIS IS AN ABSURDITY!"

Please carefully rebut that, telling me exactly why that is not a valid argument.

 

[Mike_Fontenot]

For context, I (Mike Fontenot) had previously said:

"The traveler (he) starts out (in this scenario) motionless wrt his home twin (she). They each say that their separation is 34.64 ly. She is 40 years old, and he is 20 years old. Ten years passes (for them) with no speed changes, so she is then 50, and he is 30. He then instantaneously changes his speed relative to her to 0.866 ly/y, moving toward her. He says she instantaneously got 30 years older during his instantaneous speed change, so she is then 80. He says that his distance from her instantaneously changed from 34.64 ly to 17.32 ly. She says their separation didn't change."

Suppose someone replies to that with, "If he says she instantaneously got 30 years older, then she must see herself immediately get older.

No, she never sees herself instantaneously get older. The progression of her age ALWAYS seems completely normal to her.

She could have been wearing a pink top when she was 50, and then all of a sudden she finds herself wearing a blue top and she is 80.

She perceives her age at 50 with the pink top progressing normally, with 30 normally perceived years passing until her birthday at 80, and today she is wearing the blue top to celebrate that birthday. She remembers when she bought the blue top, about a week ago. She vaguely remembers having a pink top many years ago, but she can't remember much about it.

 

[Neddy Bate]

No, she never sees herself instantaneously get older. The progression of her age ALWAYS seems completely normal to her.

To which that person replies, "Of course her age progression always seems normal to her, it could not be otherwise."

She perceives her age at 50 with the pink top progressing normally, with 30 normally perceived years passing until her birthday at 80, and today she is wearing the blue top to celebrate that birthday. She remembers when she bought the blue top, about a week ago. She vaguely remembers having a pink top many years ago, but she can't remember much about it.

To which the person replies:

"The assumption is that when the traveling twin or the trailing rocket accelerate toward her, the pink top instantaneously changes to the blue top, which results in an ABSURDITY when she notices that happen to her own clothes that she is wearing next to her skin. She can't help but notice it since she is co-located with it. This proves that the assumption is not correct and must be discarded. So, what must happen instead is that when the traveling twin or the trailing rocket accelerate toward her, she must still be wearing the pink top."

How do you persuade them that there is a flaw in their argument? Notice they still seem to be making the same mistake, even though you have tried to explain to them what they did wrong.