Bell’s Spaceship Paradox. Does the string break?

[Mike_Fontenot]

Once again, the above interchange has become so contorted that I can no longer follow it.

My proof, that two separated rockets, with equal accelerometer readings, will maintain a constant separation during the acceleration, is correct.

 

[Neddy Bate]

Once again, the above interchange has become so contorted that I can no longer follow it.

My proof, that two separated rockets, with equal accelerometer readings, will maintain a constant separation during the acceleration, is correct.

Oh what a coincidence, my hypothetical person also says, "My proof is correct!"

Since you are having trouble understanding, let me explain. The hypothetical person's argument is wrong for all the same reasons your argument is wrong. AND YOU WERE ARGUING THEY WERE WRONG JUST AS I HAVE BEEN!

Hypothetical Person's Argument:
1. Their "ABSUDITY" is not something that happens to the home twin in the first place. SHE does not perceive her top to instantaneously change from pink to blue. It is the traveling twin or trailing rocket who calculates that.
2. Their solution is to make the top still be pink when she is 80 years old, even though it is given that it should be blue by the time she is 80. There is never any explanation as to how the pink top changes to blue after that. What is supposed to happen? No clue is ever given, they consider the matter settled without even a Minkowski diagram showing what they are thinking.
3. They continue to believe they are correct, even though they are not. A total lost cause to even talk to, so we might as well give up and let the person believe their fantasies. Maybe delusional, who knows.

Your Argument:
1. Your "ABSUDITY" is not something that happens to the home twin in the first place. SHE does not perceive the leading rocket to instantaneously change from co-located with her to a location far away. It is the traveling twin or trailing rocket who calculates that.
2. Your solution is to make the leading rocket still be co-located with her when she is 80 years old, even though it is given that it should have started moved away from her at v=0.866c when she was 50, and so it could not possibly be co-located with her when she was 80. There is never any explanation as to how the leading rocket ever gets far away from her. What is supposed to happen? No clue is ever given, you consider the matter settled without even a Minkowski diagram showing what you are thinking.
3. You continue to believe you are correct, even though you are not. A total lost cause to even talk to, so we might as well give up and let the person believe their fantasies. Maybe delusional, who knows.

 

[Neddy Bate]

Mike,

I will not be replying to you again in the future. Enjoy your fantasies.

 

[Mike_Fontenot]

As before, it's easiest for me to answer you in red:

1. Your "ABSURDITY" is not something that happens to the home twin in the first place. Yes, it DOES happen to her. She SEES it happen. SHE does not perceive the leading rocket to instantaneously change from co-located with her to a location far away. Yes, she does. It is the traveling twin or trailing rocket who calculates that.
2. Your solution is to make the leading rocket still be co-located with her when she is 80 years old No, that is incorrect. It (the leading rocket) instantaneously moved a finite distance from her (when she was 50), and it was left with a fixed and finite velocity after that. It will forever continue to move at that speed, in the direction opposite from where the traveling twin is coming from. But all that is unimportant: what matters for my proof is what happens, according to her, instantaneously, when she is 50.,[...]

 

[Halc]

I don't deny the Bell spaceship scenario. It's just a DIFFERENT scenario from the scenario I'm interested in.

It is the same, albeit more constrained. The scenario specifies identical construction of ships and thus identical acceleration profiles and thus identical velocity. It doesn't specify constant proper acceleration. It is allowed to vary, but does not require it to vary. The identically constructed ships will behave the same in S and will presumably run out of fuel at the same time (relative to S) and coast thereafter.
Point is, they have identical velocity at all times relative to S.

In the Bell scenario, the initial inertial observers GUARANTEE that the spacing between the two rockets is constant.

The scenario doesn't say that.
I looked at the wiki article and it is full of errors, so it is a poor source. The picture in the upper-right is wrong for instance, or misleading at best. But the original scenario quoted is spot on, so we'll work with that. I want to point out the proper use of a frame reference every time a frame dependent statement is made since each of the statements would be meaningless without the reference.

Consider two identically constructed rockets at rest in an inertial frame S. Let them face the same direction and be situated one behind the other. If we suppose that at a prearranged time both rockets are simultaneously (with respect to S) fired up, then their velocities with respect to S are always equal throughout the remainder of the experiment (even though they are functions of time). This means, by definition, that with respect to S the distance between the two rockets does not change even when they speed up to relativistic velocities

Note the lack of "GUARANTEE" of the constant separation in S. That is derived from the actual specification, which is simply identical acceleration profiles. Arguably, it is the identical velocity relative to S which are asserted, even though that follows from identical acceleration at any point in time in S.

According to the special theory the thread must contract with respect to S because it has a velocity with respect to S. However, since the rockets maintain a constant distance apart with respect to S, the thread (which we have assumed to be taut at the start) cannot contract: therefore a stress must form until for high enough velocities the thread finally reaches its elastic limit and breaks

Note the lack of reference to the LCE here. It just says contracted in S, but not by how much since the contracted length in S is dependent on far more variables than have been specified in this scenario.

So we have several potential places for your denial to come into play.
1) At a given time in S, if two objects with identical velocity relative to S undergo identical coordinate acceleration relative to S, they will experience identical proper acceleration.
2) At a given time in S, if two objects with identical velocity relative to S experience identical proper acceleration, they will undergo identical coordinate acceleration relative to S.
3) At a given small interval in time in S, if two objects with identical velocity in S undergo identical coordinate acceleration in S during that interval, they will continue to have identical velocity relative to S.

Given the above, it follows that identical accleration profiles in S results in identical velocity relative to S at all times in S. There's more.

4) At a given interval in time in S, any two objects with identical velocity profiles in S will remain at constant separation relative to S.
5) You said "I'm certain that I am correct.", thereby validating your choice to ignore the above.

So which is it? The above shows how identical velocity in S at all times in S follows from identical acceleration at all times in S. It is not an assumption, but rather something that follows.
The latter part shows how constant separation in S follows from identical velocity at all times in S. You must disagree with at least one of the first 4 points since you assert otherwise. You rarely post numbers, and the charts you've show clearly violate point 3, and your assertions further imply that you don't agree with 2 either. It is unclear where you stand on points 1 and 4.
So kindly defend how the points with which you disagree are in fact wrong. That or fall back to point 5 which effectively says "I'm a troll so I don't have to".

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 just color all the things I find incorrect. The first one isn't among the important ones, so I don't know why you insist on this exercise when you won't identify which specific points of mine (and not just the conclusion) you find wrong.

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 speed toward 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.

There you go. The whole thing is a train wreck, for the reasons already posted above.
The only thing with which I agree is the green part, which is actually what you assert, and thus is indeed absurd.

The bit about what see must see is particularly offensive and totally doesn't follow from the prior text.
Most of the orange statements are simply not-even-wrong since they're meaningless without frame references.


Neddy, if you are interested in any of my selected bits, I can explain what's wrong with them.
I cannot particularly explain most of it to Mike any more than I can explain it to my cat.

Once again, the above interchange has become so contorted that I can no longer follow it.

Case in point.

 

[Mike_Fontenot]

Halc, it should be clear to both of us that you and I will never agree about much of anything. So further exchanges between us would only waste both of our times. But you and Neddy might be able to have some interesting conversations. Go for it.

I still stand by everything I've stated ... and I'm certain that I'm correct.

 

[Halc]

I still stand by everything I've stated ... and I'm certain that I'm correct.

Ah, option 5. No surprise there. I'm also quite certain that your statement is a lie, not that you don't stand by your statements, but that you hold any kind of belief about them being correct.
I've done this long enough to distinguish the ignorant from the trolls, and the ignorant demonstrate a very different kind of feel.

Halc, it should be clear to both of us that you and I will never agree about much of anything.

Nothing wrong with that, but if you disagree with the entire scientific community, 120 years of physics, being in denial of all of it, then it's probably a problem with you and not with everybody else.

 

[Mike_Fontenot]

I'm also quite certain that your statement is a lie, not that you don't stand by your statements, but that you hold any kind of belief about them being correct.

You're wrong about that. I believe everything I've said I believe.

 

[Halc]

You're wrong about that. I believe everything I've said I believe.

Again, no surprises, whereas if you actually held that belief, you'd point out exactly where my demonstration (the 1st 4 points above) of constant separation in S went wrong.

You challenged me to find the mistakes in your little 'proof', and I had to paint half of it a different color due to the density of mistakes. You've not challenged one of them, so I presume you accept each and every mistake. Somebody who actually knew he was right wouldn't do that. Every time the mistakes are identified, you change the subject or just run away. Hence my listing of point 5 (run away), which you promptly and predictably selected.

 

[Mike_Fontenot]

[...] so I presume you accept each and every mistake.

You're wrong in your presumption. I haven't made any mistakes. I believe everything that I've claimed to believe, and I'm certain that my proof is correct: separated rockets with constant equal accelerometer readings will have a constant separation.

Given that you and I disagree about everything, and that will never change (given our long history), let's quit wasting each others' time.

What I don't understand, is why you and Neddy seem to want to avoid any debate among yourselves. You both agree that I'm wrong about everything, but I doubt that y'all agree about everything.

Over and Out.

 

[phyti]

Mike;

You can't see the GPS satellites, but you can receive their em signals that your device uses to calculate your location and time.

It requires making measurements.
What makes the 'twin' scenario or Bell scenario any different?
There is no instant knowledge.

 

[phyti]

Neddy;

There is no Bx (green line of simultaneity) from At10 to Bt20 for either B. Once B1's motion ends and B2's motion starts, the Bx axis rotates to At40 to Bt20.
Establishing the Bx axis is essentially the same as the clock synch method (which Mike accepts).

The expression to plot B1 is x=vt for t range (0 to 40).
The expression to plot B2 is x=69.3-vt for t range (40 to 80).
There is no continuous expression for both lines, thus they are discontinuous or cutoff at their intersection.

The coordinate transforms for A(0, 40) is B(-69, 80). Not in agreement with the B description. If B1 continued outbound, it would have been correct, but that never happened.
An alternate and simpler method would be for each clock to emit a flash of light for each unit of time, and count them. B1 counts 5 outbound, B2 counts 75 inbound, a total of 80 vs 40 for B.

 

[Neddy Bate]

This is my corrected Minkowski diagram:

For this one, the outgoing frame moves left to right and has the positive axis on the right side of the origin. The incoming frame moves right to left and also has the positive axis on the right side of the origin.

The one I posted earlier had the positive axis on the left for the incoming frame, so some signs were backwards. The earlier one also had totally wrong coordinates for the event at the upper left corner of the diagram. This one is all correct, as far as I can tell.

 

[DaveC426913]

Mike_Fontenot, have you considered taking your concerns to physicsforums.com? The place is full of excellent physicists/mathematicians who can give you very clear, unequivocal answers.
They have a way of framing problematic scenarios in ways that make misconceptions vanish - like straightening out the kinks in a garden hose.

 

[Mike_Fontenot]

Mike_Fontenot, have you considered taking your concerns to physicsforums.com? The place is full of excellent physicists/mathematicians who can give you very clear, unequivocal answers.
They have a way of framing problematic scenarios in ways that make misconceptions vanish - like straightening out the kinks in a garden hose.

I got permanently banned from that forum about twenty or thirty years ago. They thought I was as dumb (or subversive) as Neddy and Halc do.

 

[DaveC426913]

I got permanently banned from that forum about twenty or thirty years ago. They thought I was as dumb (or subversive) as Neddy and Halc do.

Ah.

A wise woman once told me: "If someone calls you X, you can ignore them. If two people call you X, you should give it some thought. If three people call you X, you're probably X."


Not an insult, simply suggesting maybe consider if you have a blind spot about some serious misconceptions in your preferred area of study?

 

[Mike_Fontenot]

This is my corrected Minkowski diagram:

For this one, the outgoing frame moves left to right and has the positive axis on the right side of the origin. The incoming frame moves right to left and also has the positive axis on the right side of the origin.

The one I posted earlier had the positive axis on the left for the incoming frame, so some signs were backwards. The earlier one also had totally wrong coordinates for the event at the upper left corner of the diagram. This one is all correct, as far as I can tell.

That's an improvement, but you've still got the initial conditions wrong: my proof starts with the traveling twin stationary with respect to the home twin. At the beginning of the scenario, they are separated by 34.64 ly. She is 40, and he is 20. They stay that way until she is 50 and he is 30. At that instant, he instantaneously changes his speed wrt her from zero to 0.866 (directed toward her). And that is also the instant when the two separated rockets (colocated with him and her) instantaneously change speed from zero to 0.866 ly/y (by prior agreement), both directed along the line from him and through her position (but not quite hitting her!). All of the action of interest in this proof, though, happens when she is exactly 50. If you CORRECTLY assume that the leading rocket and the trailing rocket maintain the same separation during their instantaneous speed changes, then she sees nothing absurd (the rocket colocated with her doesn't spontaneously disappear from her position and re-appear a finite distance from her [in the direction away from the traveling twin] ... it just instantaneously starts moving at a fixed speed away from her). But if you INCORRECTLY assume that the leading rocket instantaneously increases its distance from the trailing rocket, then she will see the leading rocket instantaneously disappear from her position, and instantaneously re-appear a finite distance away from her (in the direction opposite to the direction from her to him). THAT would be absurd. So the assumption that the separation between the trailing rocket and the leading rocket increases when they accelerate equally is INCORRECT. Note that the usual scenario is stated in terms of a FINITE acceleration lasting a FINITE time, to effect a given speed change. But what I'm describing is a Dirac delta function acceleration, that uses an infinite acceleration lasting an infinitesimal time, and produces the same speed change as in the finite acceleration case. (The Dirac delta function acceleration is the same thing that is normally used in the twin paradox scenario ... it produces an instantaneous velocity change).

 

[Mike_Fontenot]

Ah.

A wise woman once told me: "If someone calls you X, you can ignore them. If two people call you X, you should give it some thought. If three people call you X, you're probably X."


Not an insult, simply suggesting maybe consider if you have a blind spot about some serious misconceptions in your preferred area of study?

Believe whatever you want. But I'm convinced that I'm correct. I've successfully put too many small pieces of this giant jigsaw puzzle together for it to be wrong. Prior to my doing this proof, I had already concluded that two separated rockets with equal accelerometer readings maintain a constant separation, because that's what Einstein believed in his 1907 paper, and that's what Einstein's equivalence principle maintains.

 

[DaveC426913]

Believe whatever you want.

Ok that's cool. I'm not here to troll you, and I plan to leave this thread in peace momentarily.
(I mean, you're actually conversing about science, so that's a plus in my eyes.)

I'm convinced that I'm correct.

Did they give you any wisdom about where they thought your theory might be going off the rails?
It seems to me, input from experts in the field would be invaluable.

 

[Mike_Fontenot]

[...]
Did they give you any wisdom about where they thought your theory might be going off the rails?
It seems to me, input from experts in the field would be invaluable.

It varied all over the map. For example, Neddy and I, long ago, actually agreed about a lot of things. In particular, Neddy was always good about using Einstein's description of how unaccelerated people stationary wrt each other could construct an inertial reference frame with synchronized clocks and with yardsticks to measure positions, which gave them a meaningful concept of the current age of a distant person who is moving in an arbitrary way. And I THINK Neddy always agreed with me that the resolution of the twin paradox is that the traveling twin (he) says that the home twin (she) instantaneously gets much older when he instantaneously reverses course. I don't think that Halc believes that, or at least he doesn't like to emphasize that, preferring instead to just use the spacetime interval. And Halc isn't alone in that preference ... one of the moderators on "Physics Forum" actually recommended never discussing the twin paradox at all in special relativity courses.

Most of the recent disagreement between me and others concerns the question of whether two separated rockets with equal accelerometer readings will maintain the same separation as the acceleration proceeds. This is the "Bell's Paradox". Most people (these days) say the separation increases. I say it doesn't, and I've given a proof of that, which has provoked the most recent controversy on this and other forums.