[Eternal Student]

Hi.

Show me where in the above I have changed anything.

 
You said this:

The important thing to understand is that the diagram, as shown, is INCORRECT.  It does NOT show the correct viewpoint of that first set of inertial observers.

    If it doesn't show the situation you wanted to discuss, then don't show it.  Show the diagram that does show the situation you wanted to discuss.
     There is a diagram that corresponds to the situation you wanted to discuss.
A diagram like this one, for example:

Diagram from  https://math.ucr.edu/home/baez/physics/Relativity/SR/BellSpaceships/spaceship_puzzle.html 

If you had shown a diagram like that and had the rockets experience the appropriate accelerations to create that,  then exactly as you have stated:

That correct diagram shows that, according to the given inertial observers, the two rockets get closer together during the acceleration, and therefore the string does NOT break.

We're all in agreement with that.

   You seem to be suggesting that the original situation, with the original diagram you did supply was just outright impossible - it isn't, it is a possible situation but just a different one to the situation you are describing later.
1.    There is a situation (where the rockets experience a certain pattern of acceleration) where the distance between the rockets stays constant in the lab frame AND then the string must break.
2.    There is another situation (a different pattern of acceleration) where the string does not break but then the distance between the rockets would be seen to reduce in the lab frame as time progressed.

    This comment was made in a much earlier post from me:

Notice that they (ucr.edu website on Bell's spaceship paradox) do end the discussion with a diagram showing a very different pair of worldlines the objects could have traced out in the lab frame  (the one you called IRF in your posts),  where the people in the rockets now would find that the distance between the rockets remains constant - but the person in the lab frame no longer does.

    Just to be clear then, both situations are possible.   They require a different pattern of acceleration for the rockets.   The first situation is not made "impossible" just by talking about the second situation.

Best Wishes.

[MikeFontenot (OP)]

I didn't understand your reply very well, but one thing that DID catch my attention was that you are including cases for which the rockets don't produce equal thrusts.  I'm not at all interested in that.  In my analysis, both rockets are equipped with accelerometers that ALWAYS show exactly the same acceleration for each spaceship.  WHEN you do that, then the original diagram (that hung over my desk for 20 to 30 years) violates special relativity ... because the inertial observers who are stationary with the rockets immediately before the rockets are fired, claim that the separation between rockets is constant.  Special relativity (via the length contraction equation) says that any inertial observer will conclude that yardsticks that are moving (in the direction of their length) wrt himself are shorter than his own yardsticks (by the gamma factor).  I.e., if gamma = 2.0, the yardsticks are only half as long as they would be if they weren't moving relative to the inertial observer.  So the inertial observers who are stationary with the rockets immediately before the rockets are fired MUST (according to special relativity) say that the two rockets get closer together as their speed increases.  Therefore that initial diagram CAN'T be correct if special relativity is correct.  Special relativity says that as the velocity of the rockets increases, the two curves must have a vertical separation that is a factor of gamma times less than the initial separation.  (Gamma is equal to 1 when velocity is zero, and goes to +infinity as velocity approaches the speed of light).  And because the lower curve already approaches the speed of light as t goes to infinity, we can't make it curve upward any more that it already does ... so we have to lower the upper curve, so as to make their vertical separation equal to the original separation divided by gamma.  As "t" goes to infinity (where "t" is how long the trailing rocket as been accelerating), the upper curve will asymptotically approach the lower curve (from above).  (I.e.,the two spaceships ultimately will get infinitesimally close together.)

[MikeFontenot (OP)]

In light of the above, it is ironic that Halc banished my postings to the "other theories" basement.  The term "other theories" is intended by the forum to mean "NON-RELATIVITY crackpot theories".  That's ironic, because my postings take the existing diagram (which I've shown VIOLATES special relativity) and replace it with a new diagram (never before defined) which OBEYS special relativity!

[Eternal Student]

Hi.

WHEN you do that, then the original diagram (that hung over my desk for 20 to 30 years) violates special relativity ... because the inertial observers who are stationary with the rockets immediately before the rockets are fired, claim that the separation between rockets is constant.

     It doesn't violate special relativity and it's not impossible for that to be the motion and corresponding worldlines of the rockets.    Are the observers who were "stationary with the rockets immediately before the rockets were fired" going to observe those worldlines for the rockets or not?   That is a choice you have.    Decide how the rockets will move in this frame (which I'll call the lab frame).   You can make this choice - but then it will determine what happens to a piece of string that connected the two rockets.

Special relativity (via the length contraction equation) says that any inertial observer will conclude that yardsticks that are moving (in the direction of their length) wrt himself are shorter than his own yardsticks (by the gamma factor).  I.e., if gamma = 2.0, the yardsticks are only half as long as they would be if they weren't moving relative to the inertial observer.  So the inertial observers who are stationary with the rockets immediately before the rockets are fired MUST (according to special relativity) say that the two rockets get closer together as their speed increases.

   There weren't any rigid connections like yard sticks between the rockets.  If you do put a rigid connection rod between them (e.g. the rope or piece of string in Bell's spaceship paradox) then you do find there is a problem, exactly as you have outlined.
      If the motion of the rockets was as originally described (constant separation in the lab frame), then the string must break.

      Alternatively you can start the problem the other way round.  Stipulate that a string of fixed length was attached between the two rockets and it did not break as the rockets accelerated.   Then the motion of the rockets (in the lab frame) could not have been as previously described,  it would have been different.  The motion of the rockets in the lab frame would be exactly as you have described later in the post - the observers who stay in the lab frame would see the rockets getting closer together as time progresses.   One consequence of this is that, in the lab frame, the rockets did not have the same acceleration at every moment of time.

I hope that makes some sense.   You can choose how the rockets move in the lab frame   OR   if the string will break.   However, you can't choose to have the rockets accelerate equally at every moment of time in the lab frame AND ALSO avoid the string breaking  --->   That's a combination that is not possible.

Best Wishes.

[MikeFontenot (OP)]

I'm just not able to follow you, Eternal.

Each rocket has an attached accelerometer, and those two accelerometers always show exactly the same acceleration. (That is part of the initial specification of the scenario).  The INITIAL diagram says that the inertial observers who are stationary wrt the rockets immediately before the rockets fire, say that the separation of the rockets doesn't vary.  But THAT violates special relativity:  special relativity says (via the length contraction equation) that an inertial observer MUST conclude that a yardstick moving away from himself (in the direction of its length) is shorter than his own yardsticks.  (And the faster the yardstick moves, the shorter it becomes, according to that inertial observer).  So those inertial observers must conclude that the separation of the rockets MUST decrease as the rockets accelerate away.  And the faster the rockets go, the more the separation decreases.  So that initial diagram is incorrect, because it violates special relativity.

[Eternal Student]

Hi.

I'm just not able to follow you, Eternal.

   That's ok.   It's probably my fault.   Also the entire Bells spaceship paradox is quite tricky.

Each rocket has an attached accelerometer, and those two accelerometers always show exactly the same acceleration. (That is part of the initial specification of the scenario).

    This part is ok.   It's best to assume the accelerometers show a constant acceleration at all times.   Have the acceleration shown on the accelerometer = a(t) = a = a constant, independent of how long the rocket has been in flight.

The INITIAL diagram says that the inertial observers who are stationary wrt the rockets immediately before the rockets fire, say that the separation of the rockets doesn't vary.

   Yes.  That is the space-time diagram you would have for the rockets if they follow the prescribed behaviour (both rockets have the same acceleration a, showing on their accelerometers).   In the frame of reference of those observers (which I will call the lab frame from here onwards),  the worldlines of the two rockets are exactly as you've shown in your first diagram.
   In the lab frame the separation of the two rockets would not vary with time.

But THAT violates special relativity:  special relativity says (via the length contraction equation) that an inertial observer MUST conclude that a yardstick moving away from himself (in the direction of its length) is shorter than his own yardsticks.

    It doesn't violate special relativity.   Yardsticks with some non-zero velocity in the lab frame would show contraction - but there weren't any yardsticks hanging between the two rockets, so it's not an issue.
    Hypothetically you can imagine there were yardsticks between the rockets and indeed, if those yardsticks were to move with the rockets, then as the rockets accelerate, those yardsticks have to take up less space (contract) in the lab frame.   That doesn't change the space between the rockets in the lab frame, that will be whatever is shown on the diagram (it is always measured along a straight line parallel to the x-axis and in our diagram that will be a constant).  However, it does mean that using a frame of reference that moves with the rockets will disagree about the distance that exists between the rockets.   An (instantaneous) rest frame for the rocket (i.e. a frame that moved with the rocket) shows that the space between the two rockets is bigger than that reported in the lab frame.
    I know that was complicated so let's say the same thing again but in a different way:  We have a lab frame, that's where all the rockets were at rest before the engines were started.    Yardsticks that remain at rest in the lab frame, will remain 1 yard long in the lab frame for ever.  So if you already had these yardsticks nailed up and held in the background of space, then as the two rockets race past them you could still see that at every moment of time, there were (say) 100 yard sticks between the rockets.    Meanwhile, yardsticks that aren't at rest in the lab frame do show length contraction in the lab frame.  Since these yardsticks are moving with the rockets you can't just have them nailed up on the background of what you're considering static space in the lab frame.   Instead you need some other system where they do move along with the rockets.   Do that by whatever system you care for, for example have a million other mini-rockets at your disposal, each mini-rocket precisely 1 yard long (proper length, or length measured when that rocket was stationary in the lab frame) and have them race after the two main rockets we are interested in and try to get themselves lined up nicely head-to-toe in-between the those two main rockets.    You would find that you do need more than 100 of those yard-sticks (the moving ones, the 1-yard mini-rockets) to bridge the gap between the two main rockets.  Indeed the faster the two main rockets go, the more that a yardstick or 1-yard mini-rocket undergoes contraction in the lab frame -  so you'd find that more of the mini-rockets need to move in and join the line of mini-rockets bridging the gap between the two main rockets.
      I hope that makes sense.
     There has been no violation of special relativity required so far.    The observers who remained in the lab frame were not "forced" to conclude the distance between the two main rockets was reducing.  Instead all they notice is that while the distance stays the same in their frame of reference (which they can see by looking at the stationary yard sticks nailed up in the background), it can't be staying the same in a frame of reference that moved with the rockets (because more 1-yard mini-rockets had to be used to bridge the gap).

Best Wishes.

[MikeFontenot (OP)]

Your explanation is too contorted for me.  The bottom line is that on the original diagram, the vertical and horizontal axes refer to the viewpoint of the inertial observers who are stationary wrt the rockets before they ignite.  The diagram says that those inertial observers say that the distance between the rockets is CONSTANT during the entire acceleration.  But that contradicts special relativity: special relativity says that ANY inertial frame that is moving wrt the above inertial observers will have shorter yardsticks than the above inertial observers' yardsticks, according to the above inertial observers.  Therefore, according to the above inertial observers, the distance between the rockets continually DECREASES during the acceleration.  Therefore the original diagram (which says otherwise) is INCONSISTENT with special relativity.  Go ahead and use the diagram if you want to, but if you do, you are NOT doing special relativity.

In order to be consistent with special relativity, that original diagram must be modified as I have previously described, with the lower curve remaining unchanged, but with the original upper curve (at each instant "t") being lowered so that the vertical distance between the lower curve and the new upper curve is the original constant vertical distance, divided by the factor "gamma".  "gamma" is equal to

  1 / (1 - v * v),

where "v" is the velocity of the trailing rocket, and is given by the slope of the lower curve.  "v" increases from zero at "t" = 0, and asymptotically approaches the speed of light (1.0 lightyear per year) as "t" goes to infinity.

If you disagree with any of my above statements, identify the first such statement that you disagree with, and tell me exactly why you disagree with it.

[Eternal Student]

Hi.

If you disagree with any of my above statements, identify the first such statement that you disagree with

This one:   

But that contradicts special relativity

and tell me exactly why you disagree with it.

   Because I think it's wrong.

You seem to have said much the same thing in your last 3 posts and I know I've been trying to say much the same thing, just in some slightly different ways, in a few of my last posts.    I'm not sure it's going to be very productive for me to say the same stuff again  or vice versa.
     
You said, in one of your very earliest posts, that the diagram had been hanging on your wall for the last 20 years.   I was guessing that you had studied Special Relativity at that time.   If that's not correct, that's fine - I know I learn a lot of stuff and certainly wasn't born with much knowledge of anything.   However, it suggests an alternative course of action would be sensible - perhaps we should cover some basic principles of SR  before trying to tackle the tricky example of Bell's spaceship paradox.    On the other hand, you may just have reached an alternative understanding or point of view and remain quite firmly set in that view.   That's also fine, there's no law against it.   I don't think I will easily change your opinion and equally, I don't think you'll change my opinion.   If you bring something new then I may read it  BUT on the short term I've already spent a lot of time here and I am way behind on other tasks.

   What-ever happens I wish you well.

[MikeFontenot (OP)]

Hi.

If you disagree with any of my above statements, identify the first such statement that you disagree with

This one:   

But that contradicts special relativity

and tell me exactly why you disagree with it.

   Because I think it's wrong.

What a pathetic cop-out!

[Origin]

What a cop-out!

It of course it is not a 'cop out' since ES has patiently pointed out your errors in multiple posts.  I think it's disingenuous for you to imply that was their only reply was that you are wrong. 
It appears to me that you came up with an idea that you think shows a flaw in Einstein's relativity and this is such an exciting prospect that you are refusing to consider any of the errors pointed out to you.

[MikeFontenot (OP)]

[...]
It appears to me that you came up with an idea that you think shows a flaw in Einstein's relativity [...]
[...]

You've got that exactly backwards!  I think Einstein is the greatest physicist that ever lived.  And I am the strongest of believers in the truth (and MEANINGFULNESS) of special relativity.  But Einstein himself said he got a few things wrong: he regretted adding a cosmological constant to his theory of general relativity.  And the fact that his exponential equation in gravitational time dilation was wrong (as I've proven) WOULD have been accepted by him if he had known about it while he was alive ... it had gotten past him only because he never applied gravitational time dilation (in its special relativity equivalent) to the case of near-instantaneous speed changes.  Apparently no one else (besides me) has ever done that either.

You have also misunderstood what I've said about the original diagram in this thread.  That original diagram (which is the basis of the contention that the thread breaks in Bell's spaceship scenario) is INCONSISTENT with special relativity ... i.e., that diagram VIOLATES special relativity.  I've shown how to correct that diagram so that the new diagram IS consistent with special relativity.  And that new diagram says that the inertial observers who are stationary with the rockets immediately before the rockets are fired, will conclude that the rockets get CLOSER TOGETHER during the acceleration.  Therefore the thread does NOT break in Bell's spaceship scenario.

 

[Origin]

And the fact that his exponential equation in gravitational time dilation was wrong (as I've proven)

No physicists believe that you have proven time dilation as expressed in relativity as wrong.
This is evident since time dilation is still taught in universities and I have not noticed any headlines proclaiming that "Mike has fixed Relativity.
Like I said before you seem to be caught up in the excitement in the belief that you have found a flaw in relativity and that is preventing you from seeing your own errors.

[Halc]

If you disagree with any of my above statements, identify the first such statement that you disagree with, and tell me exactly why you disagree with it.

It doesn't work that way.  We disagree with several of your statements, and the first one is perhaps not the source of your confusion.
I thought at first (years ago when the whole CADO thing was going on) that you had a basic grasp of at least special relativity, which is simple enough to be taught in high school. This seems to have degraded over time, and you've now descended into full purveyor of, how did you put it?  Oh yea:

crackpot theories

as evidenced by a total refusal to consider the possibility that all the other posters have a point and that these assertions you hold so tight might in fact be mistaken. We're giving up because you refuse to actually listen to having your errors pointed out. I'll give it one more try, and then let you 'win the argument' as you put it, if that's what your goal is.

So lets try to point out the core errors. I'll put the important ones in bold. First I'm going to name some frames. We have the initial inertial frame in which all ships are initially stationary and relative to which they all simultaneously commence identical (and unending) proper acceleration. That is frame F.
Then there is the inertial frame in which a given ship is momentarily stationary after one year as measured on the ship clock. This is S0 for the ship staring at F's origin, S0.5 for the ship starting at x=0.5, S3 for the ship starting at 3, and S-5 for the ship staring at x=-5.  One can have an entire array of ships, each with its own frame. For the record, your diagram shows the line of simultaneity for S0.5.

The idea, I think, was that the two curves must have exactly the same shape because of "the Principle of Relativity" ... i.e., it shouldn't matter where in space you start the curve, the curves should always have the same shape.

This is correct, but indirectly so.
The PoR just says that physics is the same for everybody doing the same thing, making local measurements. But this conclusion (that the curves in Minkowski spacetime are identical relative to the initial IRF)
So suppose we populate F with stationary mile posts, 100 per light year. Given that, each ship can look out the window and see his progress relative to F. Per the PoR, each ship is going to see the exact same number of posts go by during that year. From that one can demonstrate that indeed, the curves are identical relative to F, and that the separation between the ships relative to F must remain constant. This latter point is one you deny, but we'll get to that. Your chart from 20 years ago (presumably the one entered twice in post 6) is entirely correct. It depicts the scenario with identical proper acceleration, one of the two scenarios carefully distinguished by ES. The other one is rigid motion where the string doesn't break, which doesn't involve identical proper acceleration. This all was carefully explained by ES, but then dismissed because you 'know better'.

But the length contraction equation (LCE) of special relativity says that an inertial observer should conclude that a moving yardstick should get shorter and shorter as its speed wrt the inertial observer increases.

This is also correct, but all your objects are point objects (the ships). You've not depicted any rigid extended objects like rulers. The string represents such a ruler. You could color the string red and green, switching every thousandth of a light year and write numbers on it. If it's pre-stressed, it won't stretch further and it would make a wonderful ruler. We can tow it behind the lead ship and not attach it at all to the trailing one so it can pull away from the trailing ship as it accelerates.

The above diagram (without the diagonal straight lines) shows the perspective of the two accelerating observers.

This is wrong. The one chart you've posted shows F, the perspective of somebody who doesn't accelerate at all. You put out no pictures other than that one.

One thing that diagram DOESN'T show is how the ages of those two observers compare, as time progresses.

It does show it, but since it depicts F, it shows their ages relative to F. Both curves have little age marks on them, showing their ages to always be identical relative to each other in frame F, even if they're both younger than the non-accelerating clocks.

The inertial observers who are stationary wrt the rockets immediately before the acceleration begins ...

There doesn't need to be a mess of them. One observer (or none) will do. The frame defines the coordinates of all the events, not the observers. Any observer with any motion can still use frame F

... will say that the rockets get closer together as the acceleration progresses.

This is very wrong. SR does not posit this nor does it conclude this. I think this is one of the most important assertions you erroneously believe. Unlearn this. It cannot be true.
Take the rocket starting at x=0. After a year it moves to F coordinate of about x=0.54 and is moving at ~.76c relative to F, for a dilation factor of 1.56 or so.
That means that a ship starting at x=-3 would have to move to x = 0.54 - (3/1.56) = 1.38 which is moving 1.62 in a year, which is over light speed.
A ship starting at x=5 would need to be at x=0.54 + (5/1.56) = 3.74, or moving backwards at over light speed despite accelerating forward. This is what results from the assertion you make. It cannot be. It would be evident if you ran some example numbers, but you repeatedly refuse to do so. Feel free to correct my arithmetic if you find it in error.
Looking at it from the S0 frame makes it even worse since the ship at x=-3 hasn't even pulled out of the parking lot yet when the ship defining S0 is a year into its trip. Or do you also deny relativity of simultaneity?

I don't believe that SR predicts that.

Science isn't a religion. Belief hasn't a role to play. It's all about the mathematics working out or not, and your 'beliefs' mathematically lead to direct contradictions with the premises of SR.


After this you mostly just keep repeating the same assertions over and over without addressing any of the corrections provided. You do say this:

To obtain the correct diagram, at each instant of the given inertial observers' time, it is necessary to compute the gamma factor (where "v" is the speed of the rockets at that instant), and divide the constant separation "L" of the rockets (according to the observers on the rockets) by gamma.  The result is then added to the location of the trailing rocket, to get the location of the leading rocket.

But you never do this. You don't run any numbers. You don't provide a 'corrected diagram'. If you did, it would run into the contradiction demonstrated just above with things needing to move faster than light to get to where you insist they should be.

"If you're loosing an argument, change the subject."

You feel the need to quote some anonymous crybaby.  Are you implying that you channel this sentiment. You may notice that I'm not nearly so polite in my dealing with a stubborn crank as is ES, who seems to have not made a single mistake in his posts. I tend to walk away from conversations such as this.

Never argue with a fool; onlookers may not be able to tell the difference.

That quote is not so anonymous.

That's ironic, because my postings take the existing diagram (which I've shown VIOLATES special relativity) and replace it with a new diagram (never before defined) which OBEYS special relativity!

This is wrong, but also a lie. There has been no replacement diagram.

If you reject all this due to it contradicting your personal belief system about what SR says, then as ES says, I wish you all the best. If you're actually interested in correcting your knowledge of the theory, then I'll respond to questions.

And the fact that his exponential equation in gravitational time dilation was wrong (as I've proven)

This is another error. You've yet to demonstrate even the beginnings of an understanding of what the equation in question calculates, let alone whether it is correct or not.

The rest is repetition.  From other threads:

NOTE: My use of the phrase "Proper Separation" in the title of this submission means that it is the separation of the two people undergoing the acceleration, ACCORDING TO THOSE TWO PEOPLE THEMSELVES.

Proper separation only applies between two objects that are relatively stationary. This is the same scenario in this topic, and at no time after commencement of acceleration (assuming we never cease acceleration) is either observer stationary relative to the other.

I also seem to remember that you've incorrectly asserted that opposite ends of an accelerating rigid object (a ship, a ruler, whatever) must experience identical proper acceleration. If I remember that incorrectly, I apologize. If you still assert that, that would be another important thing that SR neither posits nor concludes.

[MikeFontenot (OP)]

And the fact that his exponential equation in gravitational time dilation was wrong (as I've proven)

No physicists believe that you have proven time dilation as expressed in relativity as wrong.

Einstein's exponential time dilation equation has only been tested for very small values of its argument L*A, where the exponential is essentially linear.  It works fine in that linear range.  It fails miserably for large values of "A" ... in particular, it disagrees with the outcome of the twin paradox, as I show in https://vixra.org/abs/2109.0076 .

[Origin]

Einstein's exponential time dilation equation has only been tested for very small values of its argument L*A, where the exponential is essentially linear.  It works fine in that linear range.  It fails miserably for large values of "A" ... in particular, it disagrees with the outcome of the twin paradox,

Millions of physicists over the past 100+ never noticed this obvious error?  Does that make any sort of sense to you? 
I know that you can't, for some reason, allow yourself to admit you are wrong on this.  I personally think this is a sad situation since you appear intelligent, but in reality if this makes you happy then have fun fighting this battle. 

[MikeFontenot (OP)]

(extra posting deleted)

[MikeFontenot (OP)]

Millions of physicists over the past 100+ never noticed this obvious error?

Have YOU ever applied the (special relativity version of the) gravitational time dilation equation to the twin paradox turnaround?  Apparently no one has but me.  It's not hard to do.  See what you get when YOU do it.  I do it in

  https://vixra.org/abs/2109.0076

Your silence is deafening!  Did you do the calculation?  Did you get the same answer I got, or a different answer?  Why the silence?

[MikeFontenot (OP)]

Scan 2023-4-23 17.01.18.jpg (243.13 kB . 1700x2338 - viewed 2769 times)

The above diagram (which I produced many years ago, and until very recently believed to be correct) is INCONSISTENT with special relativity.  That fact is still being ignored by people who should now know better.

In the above diagram, the vertical and horizontal axes refer to the viewpoint of the initial inertial observers who are stationary wrt the rockets immediately before they ignite.  The two curves show the progress of each of the two rockets.

The two sloped straight lines refer to inertial observers momentarily stationary wrt the leading rocket at two times later in the acceleration.  They say that the two rockets get farther apart during the acceleration, and so they say that the thread will break in Bell's Spaceship Paradox.

The diagram says that, according to those initial inertial observers, the distance between the rockets is CONSTANT during the entire acceleration.  BUT THAT CONTRADICTS SPECIAL RELATIVITY: special relativity says that ANY inertial frame that is moving wrt the initial inertial observers will have SHORTER yardsticks than the inertial observers' yardsticks, according to the initial inertial observers.  Therefore, according to the initial inertial observers, the distance between the rockets continually DECREASES during the acceleration.  Therefore the above diagram (which says otherwise) is INCONSISTENT with special relativity.
 
In order to be consistent with special relativity, the above diagram must be modified, with the lower curve remaining unchanged, but with the upper curve (at each instant "t") being lowered so that the vertical distance between the lower curve and the new upper curve is the original constant vertical distance, divided by the factor "gamma".  "gamma" is equal to

  1 / sqrt(1 - v * v),

where "v" is the velocity of the trailing rocket, and is given by the slope of the lower curve.  "v" increases from zero at "t" = 0, and asymptotically approaches the speed of light (1.0 lightyear per year) as "t" goes to infinity.

For example, when v = 0.866 ly/y,  gamma = 2.0 .  So when v = 0.866 ly/y, the distance between the rockets is half of what the above diagram incorrectly says it is.

[Origin]

The above diagram (which I produced many years ago, and until very recently believed to be correct) is INCONSISTENT with special relativity.

Then stop bringing it up since wrong and move on.

[MikeFontenot (OP)]

The above diagram (which I produced many years ago, and until very recently believed to be correct) is INCONSISTENT with special relativity.

Then stop bringing it up since wrong and move on.

I bring it up because most people still believe that the thread will break in Bell's Paradox (which is what that original diagram implies). The corrected diagram, which I describe, shows that the thread in Bell's Paradox does NOT break.  Most people still believe I'm wrong about that.

And, after I had shown that the original diagram is incorrect and violates special relativity (and after I had described the corrected diagram which agrees with special relativity), Halc moved this discussion from the main section (which is supposed to be "the special relativity section") to the "basement" non-relativity-theories section.  Halc has it exactly backwards!