Bell’s Spaceship Paradox. Does the string break?

[Janus58]

The only thing you've shown is that assuming an instantaneous change of velocity returns a non-physical result when dealing with extended systems.
This stems from the fact that when dealing with scenarios like Bell's Paradox, in order to do a full analysis, you need the value of the acceleration. Acceleration is a measure of change of velocity over time. If you divide a finite velocity by zero time you get an undefined acceleration, which results in inconsistent results.

 

[DaveC426913]

How do YOU describe the twin paradox?

Sure, but you first. Cite a reputable source that supports your assertion. Because I dontvthink thats the general wisdom.

 

[billvon]

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

Not if you assume an infinite acceleration, which is what an instantaneous turnaround is.

 

[Mike_Fontenot]

The only thing you've shown is that assuming an instantaneous change of velocity returns a non-physical result when dealing with extended systems.
This stems from the fact that when dealing with scenarios like Bell's Paradox, in order to do a full analysis, you need the value of the acceleration. Acceleration is a measure of change of velocity over time. If you divide a finite velocity by zero time you get an undefined acceleration, which results in inconsistent results.

On the contrary, using instantaneous velocity changes has been extremely helpful in special relativity. For example, in the most common way of introducing the twin paradox, it is commonly said that at the instant that two twins (he and she) are born, one of them (he) instantaneously leaves on a trip at a constant speed of 0.866 lightyears per year (ly/y). And then it is immediately stated that during that outbound trip, each twin says the other twin is ageing at half their own rate of ageing. (That follows from the well-known time-dilation equation of special relativity). The same thing happens on his inbound trip ... they each say the other is ageing at half their own rate. The paradox is that, when they are reunited, both twins obviously can't say that the other twin is the younger at their reunion, because they can just look at each other, and they will obviously agree about their respective ages. The paradox is resolved by concluding that, when he instantaneously reverses his course, she instantaneously gets older by exactly the amount needed to make them agree about their ages when they are reunited.

 

[DaveC426913]

No. None of those instantaneouslys are meant to reflect reality. They are merely simplifications to the thought experiment to make the math easy.

You are taking it too literally.

It is self-evident that, if you were to assume infinite acceleration, you will get unrealistic results.

(Its not technically a paradox, a paradox is multiple conflicting solutions. This solution isnt conflicting, its merely unreal.)

The resolution is to recognize that such and idealized scenario cannot happen IRL.

 

[Halc]

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.

This is just not true. My main gripe is with the word 'must' that I bolded. One may at any time choose to use a different abstract coordinate system which makes a different arbitrary choice of which non-local events (those on the Earth worldline say) are simultaneous with a given event (the turnaround event say). Such an abstract choice makes no physical difference, hence the twin at home doesn't experience getting suddenly older, and this wording suggests.

So it isn't 'the Twin Paradox resolution'. It might be one of them, but it is a poor one since it doesn't generalize. Ditto for explanations via acceleration.

All this has little to do with Bell's spaceship which involves both ends accelerating, not just one of them.

Immediately after (rear ship's) instantaneous speed change, suppose the leading rocket is assumed to instantaneously increase its separation from the trailing rocket.

That's just an instantaneous change of choice of coordinates. Nothing physically ends up in a different place instantaneously. Acceleration of something is not needed to make this change in choice of coordinates, so no rocket needed.

So yes, an event possibly years into the front ship's journey is a greater spatial distance away from the rear ship's departure event than was the front ship's departure event. You seem to find rather ordinary geometric fact to be unbelievable.

THAT would result in her seeing the leading rocket INSTANTANEOUSLY move a finite distance away from her

Is she not on the rocket then? If she's on it, she never sees it move away from her. If she's just watching, she sees it depart as normal. No teleporting. Yes, I know you posit teleporting (your program provided shows it, backwards no less, and you've defended it), and yes, that is indeed absurd, but you don't seem bothered by faster than light travel or retro-causality. SR of course suggests no such thing.

How do YOU describe the twin paradox?

Using geometry to point out that his worldline is of shorter proper length than hers. That is a general solution, meaning it works for all scenarios (even GR) and coordinate system choices.

The paradox is that

There is no paradox. At no point is there any contradiction. It becomes paradoxical only if one drags additional premises into it like 'twins are always the same age regardless of where they've gone'.

when they are reunited, both twins obviously can't say that the other twin is the younger at their reunion

At least one of them would obviously be wrong, probably the one that doesn't know his physics. If they're educated, they'll both agree on everybody's expected age.

 

[Halc]

It is self-evident that, if you were to assume infinite acceleration, you will get unrealistic results.

I'm ok with infinite acceleration so long as one realizes that everything (ships, observers, clocks) are treated as points. Any object with nonzero volume can only accelerate its center of mass at a finite rate without distortion. Doing so is not only physically impossible, it is mathematically impossible.

Mike's errors in this topic are not made by assuming infinite acceleration. It's just done to prevent unnecessary complications in a simple scenario.

 

[Mike_Fontenot]

Halc, I'm indebted to you for discovering that my chart, for the initial inertial observers' view of the rocket separation (when the two accelerometers read the same constant value), showed the interesting negative slopes (and greater than speed of light slopes) for the larger initial separations (D = 2 and D = 3). I had never computed the leading rocket's curve for any separation greater than D = 1. I think that chart is VERY important. I'll try to attach the latest version of that chart below.

 

[phyti]

Mike;

Wiki:
"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."

Length contraction occurs in material objects because the atoms are bound by em forces which can vary due to motion just as a light clock rate can vary due to motion. In a light clock, light intercepts moving targets and the cycle rate decreases. In an atom, light intercepts moving targets and the longer transit time is equivalent to increased distance, resulting in weaker binding energy, resulting in compression of material or transformed em fields.
Space/vacuum has no known structure with elements similar to atoms that allow for such effects.
Coordinates in space are assigned to objects in space. How would you know space moved?

In the 'bell prdx.gif', two ships 2 units long are separated by a gap 2 units long. They are connected by a red taut flexible cord. Both ships accelerate simultaneously via a computer program, in the U frame (ct, x), located in space distant from any significant masses. Typically objects are tracked via their center of mass for the benefits of momentum and energy conservation factors. The centers remain 4 units apart during acceleration. During the acceleration the ships become length contracted resulting in an expanded gap, resulting in a broken cord.



#53

In the case of the instantaneous turnaround, there is an IP1 immediately before the turnaround, and an IP2 immediately after the turnaround. For each of those IP's, their line of simultaneity ("LOS") can be plotted on a Minkowski diagram. Where those two LOS's intersect the home twin's world line then give her age, according to the AP, immediately before and after the turnaround. I.e., that gives the amount by which she instantaneously ages during his turnaround, according to him.

In the 'twins-4.gif', the B velocity profile v=.5. At the reversal point Bt=8.66, the spacetime path is discontinuous, meaning there is no connection of the outbound to inbound paths. It would be a physically impossible motion by a single object. There is no acceleration.

After the 1st B observer detects the A-clock values from At=1 to At=5, a 2nd B observer could detect the A-clock values from At=5 to At=20. The experiment would be done in a passive mode.

B receives 5 red shifted signals outbound and 15 blue shifted signals inbound. There is no time jump. Notice the Bx axis for At=5 is not established until Bt=8.66. There is always a delay between an event and awareness of the event.

In an active mode, the observer makes measurements with (blue) light to establish the (green) Bx axis aka axis of simultaneity. It is constant while the direction is constant, as shown for the interval At=0 to 5 and Bt=0 to 5.77. After the reversal the light signal was emitted outbound and returns inbound, which shortens the round trip time, and rotates the Bx axis toward the orthogonal position at Bt=8.66. There is no time jump. All A-clock events are detected in the order they occur by the two B observers.

The B-clock loses more time than the A-clock since its speed relative to light was greater than that of the A-clock for the duration of the trip.

 

[Halc]

I'd like to comment on some of this

Mike;

First of all, Mike seems not to care about how to do it right. He has this LCE that he's misapplying and perhaps suggesting that the contradictions that result is some kind of evidence that Einstein is wrong. It's always Einstein with the trolls. There are whole websites that publish any fallacious paper that show this, and they hold conventions to separate the trolls from their money. Flat-Earther's are also invited, but it's less fun since Einstein isn't directly a champion of a round Earth.

Mike has posted his stuff on other sites, and I see the posts here have shows absolutely zero evidence of having learned anything from the errors pointed out on those other sites, including posting the same topic at least 6 times on this site (merged now), each time making the same mistakes despite having them pointed out.

So I'm here for clarification on your post, and not so much with any hopes of converting Mike back into a scientific mindset where empirical evidence is actually worth something.

Length contraction occurs in material objects because the atoms are bound by em forces which can vary due to motion just as a light clock rate can vary due to motion.
...
Space/vacuum has no known structure with elements similar to atoms that allow for such effects.

This makes it sound like it only happens to material objects. This isn't so. For instance, the spatial distance to the nearest star is say 4 LY in the frame in which both us and it are reasonably stationary. But in a frame where both are moving at .866c in the direction of one to the other, that distance is just 2 LY despite the lack of a physical object spanning the distance between them. It's a property of Minkowskian geometry and works whether there are material objects involved or not.

Coordinates in space are assigned to objects in space.

Coordinates are assigned by arbitrary choice of coordinate system, and no requirement for the presence of a physical object is required for it. For instance, there's a center of gravity of our solar system, which admittedly is inside the sun almost half the time, but the other times it is not. That point in space still has coordinates even if the sun isn't there at the time.

In the 'bell prdx.gif', two ships 2 units long are separated by a gap 2 units long.

So it is. Either the ships are normal sized and are crazily close to each other and put out acceleration of billions of g's, or they're super long (like light-years long). Either way, their centers of gravity apparently manage to get up to about 4/9c before they've traveled half their own length. Pretty impressive, but not wrong in any way. It is of little use to Mike who puts his small (points) ships light years apart, a simpler model.

Typically objects are tracked via their center of mass for the benefits of momentum and energy conservation factors.

I did note the CoM thing, but energy and momentum are never conserved here since these are accelerating rockets with energy and momentum in U being zero at first, and not-zero thereafter.

During the acceleration the ships become length contracted resulting in an expanded gap, resulting in a broken cord.

This makes it sound like only the contraction of the ships is what breaks the cord, and if the ships were instead points, the cord would not break. But the cord is also accelerating (if dragged by the lead ship, then it accelerates more than either ship), and thus the cord must contract. If it cannot due to being attached to the rear ship, then it breaks.
I think in Mike's latest example, it was a tape measure with markings, attached only to the lead ship. Your length-2 ship contract to 1.8 units, but the first length-2 of the tape measure would contract down to much less than that so that the marking as seen by the nose of the trailing ship would be much higher than the 2.25-units that Mike's misapplied LCE would suggest.

In the 'twins-4.gif', the B velocity profile v=.5. At the reversal point Bt=8.66, the spacetime path is discontinuous, meaning there is no connection of the outbound to inbound paths.

No idea what you mean by this. No discontinuity is shown in the picture. The statement makes it sound like the event of the end of the outbound leg is not the same event as the beginning of the return leg, but the picture shows this to be the same event.

It would be a physically impossible motion by a single object. There is no acceleration.

If there's no acceleration, then the outbound ship keeps moving outbound. Perhaps you are suggesting a tag-team sort of scenario where two different ships meet out there, and the returning one syncs its clock with the outbound one, thus implementing the twins scenario without any actual acceleration and without any actual twins. That would be fine, but for thought experiments, an abrupt turnaround of a ship treated as a point object is not problem. None of it changes the arithmetic, and nothing in any of relativity requires an actual human observer to be present anywhere at any time. All we need is to put clocks in bullets and fire them in various directions and compare them when they pass.
That's another thing with which Mike cannot deal. He has a compulsion to put a human at every clock (a helper friend as he calls them) like the clock wouldn't be functional without a human to keep it company.

 

[Mike_Fontenot]

Halc, you don't agree with the diagram I posted above (that shows, for D = 2 and D = 3, the negative slopes and speeds greater than the speed of light), and which is my diagram for the perspective of the initial inertial observers (IIO's) who are stationary wrt the rockets before they're ignited. And you also disagree with my conclusion that from the perspective of the people on the trailing rocket (POTR), the separation between the rockets is always constant. (Those two perspectives, in my opinion, correspond to the SCENARIO where the two rockets have accelerometers that always show the same acceleration "A" after the rockets are ignited).

You don't agree with me. So what are YOUR conclusions for the scenario where the accelerometers always read the same acceleration "A" during the acceleration? I.e., what is your diagram that gives the perspective of the initial inertial observers (IIO's)? Can you describe it for me? And how would you describe the separation of the rockets, as a function of time, according to the people on the trailing rocket (POTR)? And how does the length contraction equation (LCE) fit into your solution?

 

[DaveC426913]

This makes it sound like it only happens to material objects.

At the risk of me-tooing, you voiced my objection too. Length conteaction is not about atoms.

That's another thing with which Mike cannot deal. He has a compulsion to put a human at every clock (a helper friend as he calls them) like the clock wouldn't be functional without a human to keep it company.

I do notice a tendency for Mike to assume that what a relativistic observers sees is what they literally and naively think to be true - as if they are unaware that relativistic effects need to be applied to their observations in order in make sense of them.

I think thats why he inserts humans: to conclude what they see as real, and not what the math says.

 

[Mike_Fontenot]

I do notice a tendency for Mike to assume that what a relativistic observers sees is what they literally and naively think to be true - as if they are unaware that relativistic effects need to be applied to their observations in order in make sense of them.

I think thats why he inserts humans: to conclude what they see as real, and not what the math says.

No, that's not why I use humans in my descriptions. My human observers, AGREE with what "the math" says (although I would use the term "the physics", not "the math"). There are a lot of disagreements about "what the physics says". I use humans just to make the example more tangible, and "real" and "meaningful".

 

[Mike_Fontenot]

Halc, I still hope that you will give me your views that I asked you for in my post #71 above. And I would also like to get your critique of my latest proof that when the accelerometers have the same constant readings on each of the two rockets, the distance between the two rockets is constant, according to people on the trailing rocket. Here is that argument:

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.

Q.E.D.

 

[Halc]

Halc, you don't agree with the diagram I posted above

The only diagram of your with which I agree is the 20 year old one that you now say is wrong. It seems you know your relativity (at least SR, I see no hint of GR knowledge) well enough, as evidenced by some of the earlier threads you've posted on TNS. But then you got seduced by the dark side and decided to deliberately apply equations to inappropriate scenarios and to use the contradictions which result as some kind of proof that Einstein (the person more than the theory) is wrong. All corrections are ignored, as required by the troll handbook. You're pretty textbook now.
As a moderator, I try to limit my interaction with trolls as much as possible on TNS, but here I am totally open to rendering my opinion.

the negative slopes

Coupled with an accelerometer that says the slope is always getting more positive, a direct contradiction with a slope growing more negative. Direct contradictions don't seem to bother you at all, a big sign that you are deliberately getting things wrong for whatever jollies that gives you.

and speeds greater than the speed of light

That also seems not to bother you. You've defended it despite knowing it's impossible under SR.

You don't agree with me. So what are YOUR conclusions for the scenario where the accelerometers always read the same acceleration "A" during the acceleration?

The web is full of descriptions of this. It's only you with the different assertions, all of which lead to the absurdities listed above, not to mention retro-causality, being in multiple (at least 3) places at the same time. It's not me that disagrees with you, it's the entire physics community, and their conclusions. I don't make up my own physics.

I.e., what is your diagram that gives the perspective of the initial inertial observers (IIO's)?

The one you drew 20 years ago suffices nicely. The ones posted on wiki are also just fine.

Can you describe it for me? And how would you describe the separation of the rockets, as a function of time, according to the people on the trailing rocket (POTR)?

Depends on which coordinate system they choose to use, but using say an inertial frame in which the POTR is momentarily stationary, the lead rocket is further away, hence the breaking of the hypothetical string. I edited your old picture to add a line of simultaneity for the POTR since your picture only had one for the POLR.



That shows a separation of about 0.57 (using your tic marks) in the momentary inertial frame of POTR at time 0.5 as shown on the rear ship.

And how does the length contraction equation (LCE) fit into your solution?

It doesn't fit at all since it only describes distances between parallel inertial worldlines, of which there are none in this scenario.

 

[Halc]

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.

That is not 'the' resolution, but it is a badly worded 'a' resolution.
To word it better, the event on the home twin's worldline simultaneous (relative to the inbound inertial frame) with the turnaround event is much lower than the event on the home twin's worldline simultaneous (relative to the outbound inertial frame) with the same turnaround event.
Essentially, I will accept your wording, despite it making it sound like there is some kind of causal relationship going on, which it most definitely isn't.

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).

OK, they're both present at the respective rockets at the events where they begin their identical acceleration, stationary with respect to the rockets.

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.

OK, so no continuous acceleration, but just an abrupt change in velocity for both rockets, him, but not her I presume. Tell me if I'm getting this wrong, but so far, so good.
It isn't Bell's spaceships anymore (which involves continuous acceleration), but the string very much still breaks in it.

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

The distance between them is dependent on the choice of frame (unspecified) and the time, presumably that of the rear velocity change event. In any given frame, nothing can instantaneously change its location. It is where it is. If you conclude teleporting, you've done something wrong. So relative to the original IRF (F1), the rocketss (I'll call them M and F for the genders of their observers, with F always at a higher x spatial location than M) are say 2 units apart and the abrupt velocity change is .866c (I'm making up simple numbers since you've supplied none). So still relative to F1, the rockets stay 2 units apart at all times with F in front. He rides in the M rocket, but she declines her ride. The proper-length-2 string between the rockets cannot fit between them if it is moving with them, so it cannot connect them. A extended rigid object like that string cannot be instantaneously accelerated, so it immediately detaches from the F ship even if it isn't connected to the M ship. So the string is left behind with 'her'.

Relative to the new frame (F2) in which the two rockets are eventually stationary, the distance between rockets changes over time from 1 unit to 4 units. Relative to F2, the two ships are initially moving in the negative direction at .866c at 1 unit separation with M in front (a lower x value), until the rear rocket (F) is halted, letting her continue on. The front rocket is halted about 3.46 time units later when it reaches a distance of 4 from where F halted. Now both rockets are stationary in F2. Since the M rocket in front continues after F halts, the string connecting them breaks.
If you don't agree with this, show where any of my numbers is wrong. A simple Lorentz-transform of the two acceleration events yields the 3.46 time difference and the distance values I specified. It's a super simple exercise when instant velocity change is used since no calculus is required.

THAT would result in HER seeing the leading rocket INSTANTANEOUSLY move a finite distance away from her

Nonsense. She is just sitting there and watches her rocket depart on schedule. What he does has no causal effect on her. Seriously, this is your 'proof'? What she sees is what happens according to her, and has nothing to do with what event somebody else considers simultaneous with his own. Her experiencing an instantaneous age change is indeed absurd, but that's your assumption, not that of SR. You seem to have some sort of relativistic solipsism thing going on, that one observer somehow controls which events are in the present, a sort of moving-spotlight philosophical stance, except with a wildly waving spotlight from a preferred worldline (his) instead of the usual preferred frame. If you don't know what I'm talking about, here's a link to the usual non-solipsistic moving spotlight

 

[Mike_Fontenot]

The only diagram of your with which I agree is the 20 year old one that you now say is wrong.

Yes, I now think that diagram (minus the slanted straight lines) is the correct diagram for the perspective of the people on the trailing rocket (when the accelerometers on both rockets show equal readings during the whole acceleration). And GIVEN that, the diagram that you dislike (with the negative slopes, etc.) follows directly.

It seems you know your relativity (at least SR, I see no hint of GR knowledge) well enough, as evidenced by some of the earlier threads you've posted on TNS. But then you got seduced by the dark side and decided to deliberately apply equations to inappropriate scenarios and to use the contradictions which result as some kind of proof that Einstein (the person more than the theory) is wrong.

I didn't deliberately apply equations to inappropriate scenarios. I DID show, in my first paper:

"An Inconsistency Between the Gravitational Time Dilation Equation and the Twin Paradox",
https://vixra.org/abs/2109.0076,
that Einstein's exponential equation in his 1907 paper is wrong.

And I gave the corrected equation in my second paper:

"A New Gravitational Time Dilation Equation", https://vixra.org/abs/2201.0015 .

All corrections are ignored, as required by the troll handbook.

I never ignore your comments. I just don't always agree with them.

Coupled with an accelerometer that says the slope is always getting more positive, a direct contradiction with a slope growing more negative.

It's not a contradiction. The accelerometers faithfully report what the rockets are doing, according to the rockets. The negative slopes are according to the initial inertial observers.

Direct contradictions don't seem to bother you at all, a big sign that you are deliberately getting things wrong for whatever jollies that gives you. That also seems not to bother you. You've defended it despite knowing it's impossible under SR.

I never deliberately get anything wrong. And I never espouse something that I know to be impossible under SR.

It's only you with the different assertions, all of which lead to the absurdities listed above, not to mention retro-causality, being in multiple (at least 3) places at the same time.

Where have I talked about being in multiple places at the same time? I really don'y know what you're talking about, there.

It's not me that disagrees with you, it's the entire physics community, and their conclusions.

It doesn't matter to me how many people disagree with me. I feel obligated to make, what I believe to be true, known.

Depends on which coordinate system they choose to use, but using say an inertial frame in which the POTR is momentarily stationary, the lead rocket is further away,

I believe the perspective of the people on the trailing rocket is THEIR OWN perspective, not the perspective of any collection of inertial observers. Merely knowing that both accelerometers show the same constant readings is enough for the people on the trailing rocket to conclude that the separation is constant.

(And then I asked
And how does the length contraction equation (LCE) fit into your solution?

It doesn't fit at all since it only describes distances between parallel inertial worldlines, of which there are none in this scenario.

I don't understand that at all. I don't believe there are any such restrictions on the length contraction equation (LCE) The LCE says that in any inertial frame, a moving yardstick (moving along the direction of its length) will be shorter than the inertial frame's own yardsticks.

 

[Mike_Fontenot]

Essentially, I will accept your wording, despite it making it sound like there is some kind of causal relationship going on, which it most definitely isn't.

I've never said that the traveler's (his) belief that the home twin's (her) age instantaneously increases has any affect on her life, according to her (or according to other inertial observers). But he MUST believe that she ages instantaneously, because otherwise he can't explain how they agree at the reunion (because he KNOWS that she was otherwise ageing more slowly than he was during the parts of his trip when he was inertial).

OK, they're both present at the respective rockets at the events where they begin their identical acceleration, stationary with respect to the rockets.

I'm putting the primary emphasis on the traveling twin (he) and on the home twin (her), as given in the twin paradox. It is the two rockets that are "add-0ns".

And I said:
"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."

OK, so no continuous acceleration, but just an abrupt change in velocity for both rockets, him, but not her I presume. Tell me if I'm getting this wrong, but so far, so good.

Yes, you've got it right.

It isn't Bell's spaceships anymore (which involves continuous acceleration) ...

Yes, it's a completely different thing. It is just the twin paradox scenario, but with the rockets added on (but not affecting the twins [except that the home twin observes the leading rocket instantaneously jumping from being co-located with her to being separated from her by a finite distance (which is absurd)]. That's what this example is saying: that non-constant separation of the rockets results in an absurdity, and so the rockets must have a constant separation (according to the people on the trailing rocket).

(Your comments that followed this point were based on your misunderstandings about my scenario, and hopefully that has been corrected now).

This material is based on my latest viXra article (just a one-pager):

https://vixra.org/abs/2308.0119

Basically, the resolution of the twin paradox MANDATES that the separation of the two rockets (with equal accelerometer readings) must be constant, according to the people on the trailing rocket.

 

[phyti]

Halc;

I have posted on about 6 different forums within a 15 yr period, and Mike has appeared on most of them. I don't understand why he is fixated on this particular 'twins' example.
Whenever he makes an appearance, I still try to shine a light to help him navigate.

1. This makes it sound like it only happens to material objects. This isn't so. For instance, the spatial distance to the nearest star is say 4 LY in the frame in which both us and it are reasonably stationary. But in a frame where both are moving at .866c in the direction of one to the other, that distance is just 2 LY despite the lack of a physical object spanning the distance between them. It's a property of Minkowskian geometry and works whether there are material objects involved or not.
2. Coordinates are assigned by arbitrary choice of coordinate system, and no requirement for the presence of a physical object is required for it.
3. This makes it sound like only the contraction of the ships is what breaks the cord, and if the ships were instead points, the cord would not break.
4. No discontinuity is shown in the picture. The statement makes it sound like the event of the end of the outbound leg is not the same event as the beginning of the return leg, but the picture shows this to be the same event.
If there's no acceleration, then the outbound ship keeps moving outbound. Perhaps you are suggesting a tag-team sort of scenario where two different ships meet out there, and the returning one syncs its clock with the outbound one, thus implementing the twins scenario without any actual acceleration and without any actual twins.

1. The typical anaut cartoon has him in a ship moving from Earth to the nearest star 4 ly distant. He accelerates in a large orbit until reaching his target speed of .6c prior to departure. Without any SR effects, his trip should take 6.67 yr. Moving at a constant velocity, SR allows him to assume a pseudo rest frame. The star arrives at ship time 5.34 yr, which he reports to Earth. He verified his velocity while leaving Earth. To reconcile the time difference, he assumes the universe outside his ship was moving in the opposite direction at .6c (the reciprocity of the principle of relativity), and was length contracted, relying on visual cues for his conclusion.
If a 2nd anaut used the same method, and simultaneously departed in the opposite direction at .6c, his report sent at 5.34 yr (predicted by SR) should arrive at Earth simultaneously with the other report.
The Earth monitor would conclude, if the universe moved at .6c in opposite directions simultaneously, it didn't move!
Why/how can the motion of a tiny ship modify the motion of the universe?
Why is the anaut the only person who experiences this, while anyone not moving with him observes his ship length contracted to different degrees depending on their relative velocity?
Why are there no astronomical observations of the specified star changing its motion?
The answer is motion, which results in time dilation, which includes his biological clock with his ship clock. Unable to detect either, he interprets his td for lc. His perception is altered by his motion. The length contraction of material objects is a physical process.
The length contraction of space is perception, physical processes modified by human analysis.
2.
In this example, the objects are the ship and the star and the distance is measured with light.
When NASA wants to land a probe on an asteroid or Mars, etc., they need to know its location.
Spatial position is relative to a reference object. Center of mass is an abstract calculation and has no physical location. There may not even be mass at that point. Space is invisible.
3.
If the cord contracts, it would shorten the time to failure. It was omitted to emphasize the lc of the ships affects the length of the gap. To graphically show lc requires the ships have dimensions.
4. The motion outbound ends at At=10 with instantaneous deceleration to 0.
The motion inbound begins at At=10 with instantaneous acceleration to .5. There is no simple equation to describe both line segments.
Yes, there are two ships to complete the B round trip. The essence of the problem is the accumulated time on the A-clock and B-clock, for a closed course. There is no requirement for people or even synchronization. Einstein's 1905 paper, par.4 described 1 of 2 clocks departing on a closed course and returning to the 2nd, indicating less elapsed time.
I think it was Paul Langevin who proposed twin life forms, for the purpose of emphasizing biological clocks.

The effects from SR only have meaning to humans, thus requiring human verification somewhere in the process of experimentation.

 

[Halc]

Yes, I now think that diagram (minus the slanted straight lines) is the correct diagram for the perspective of the people on the trailing rocket (when the accelerometers on both rockets show equal readings during the whole acceleration)

1) 'perspective' and 'frame' (or 'coordinate system') mean different things. A perspective is what somebody sees, so the perspective of a person on one of the rockets would be a an unchanging view of the interior of the rocket, and the changing view of what the instruments read, and perhaps a view out the window. It would be a video.

So I think you mean 'relative to the frame of the trailing rocket', except that is also wrong since it depicts the inertial frame in which both rockets were initially stationary.

2) The worldlines depicted maintain constant separation in the depicted inertial frame, so you agreeing with it contradicts this whole thread asserting otherwise.

3) Two of the slanted straight lines are yours, accurately depicting the lines of simultaneity of lead-ship times 0.5 and 1.3. I added a third line for the rear ship time 0.5 since it was relevant to the question asked.

I never ignore your comments. I just don't always agree with them.

Oh, but you do. You illustrate it excellently with this:

I DID show, in my first paper:

"An Inconsistency Between the Gravitational Time Dilation Equation and the Twin Paradox",
...

that Einstein's exponential equation in his 1907 paper is wrong.

I submitted a peer review of that paper which pointed out 6 errors, which were essentially ignored since most/all the errors were still present in the 2nd. You didn't reply with a refutation to any of the errors found.
Having ignored my points, I suspect you don't even know what they are since you never considered them.

One of them: The part I bold above still (in both papers) identifies the equation as 'the Gravitational Time Dilation Equation' and yet nowhere the paper is it ever implied that the equation in question has any application to a gravity. If you disagreed with that, the simple response would have been to demonstrate where in the paper Einstein suggested that the equation in question had any applicability to gravity. But no, you chose instead to just ignore the comment.

In this (merged) topic, you're making quite a joke of ignoring the blatant inconsistencies that have been pointed out by several members, instead just choosing to reassert the same things over and over, never resolving the critiques supplied. That's ignoring feedback, not just disagreeing.

It's not a contradiction. The accelerometers faithfully report what the rockets are doing

An accelerometer reports the proper change in velocity. You have a ship whose velocity relative to x is decreasing over time, and the accelerometer is asserted to lie and report that the velocity relative to x is increasing over time. That, my friend, is very much a direct contradiction. This error is made for both ships, not just the front one.

I never espouse something that I know to be impossible under SR.

Like faster than light travel? Being in multiple places simultaneously? Retro-causality? Existence of a preferred frame? OK, you seem to have deliberately forgotten that all these things are impossible under SR, as evidenced by you rationalizing such things rather than deny that they're happening in your diagrams.

Where have I talked about being in multiple places at the same time?

You didn't, but I can take one of your pictures depicting the usual inertial frame and draw a line of simultaneity for a different inertial frame (or just do a Lorentz-transform to that different inertial frame) and the lead ship worldline will be in 3 places simultaneously. Of course you can now deny the validity of these frames (denying one of the premises of SR in doing so). I do very much notice that you never consider your speculations from a different inertial frame.

I feel obligated to make, what I believe to be true, known.

I don't think you're sufficiently stupid to actually believe what you're posting. That's just my opinion. I think you're smarter than how you present yourself.

[/QUOTE](And then I asked
And how does the length contraction equation (LCE) fit into your solution?

It doesn't fit at all since it only describes distances between parallel inertial worldlines, of which there are none in this scenario.

I don't believe there are any such restrictions on the length contraction equation (LCE)[/QUOTE]Then find any valid reference that says it is applicable in a non-inertial situation, because using it in a non-inertial context results in immediate contradictions.

The LCE says that in any inertial frame, a moving yardstick (moving along the direction of its length) will be shorter than the inertial frame's own yardsticks.

I imagine there is some pop site that actually words it that horribly. First, yes, it will be shorter in a frame that it is moving, but the LCE is supposed to be a way to compute how short it is, and it only does that for inertial motion. Your statement doesn't say anything about what length it is, only that it's shorter, which is true, but not what the LCE is about.

Notably, for a yardstick exhibiting rigid motion (it is stationary along its entire length in its own frame), relative to a different inertial frame, an accelerating yardstick is necessarily moving at different velocities at different points along its length, hence it not having any one velocity in that frame, and hence the LCE not being valid since there's no v to input.
The fact that it moves at different speeds along its length is trivial to see if you have even a nodding acquaintance with relativity of simultaneity, but I suspect you're going to need it spelled out since working it out yourself would wreck the image you're trying to portray.

I've never said that the traveler's (his) belief that the home twin's (her) age instantaneously increases has any affect on her life, according to her

You very much did say that:

THAT would result in HER seeing the leading rocket INSTANTANEOUSLY move a finite distance away from her

How else is this to be interpreted? You're talking about what she sees, not what he computes. She sees her ship teleporting away, which sounds an awful lot to me like what he is doing (not what he is believing) directly affecting her life.
This is very much what you assert anyway. Take your funny picture with the forward accelerating ship actually moving backwards, but increase the acceleration from 1g on up and up. You have a couple ships 5 light years apart, and if the continuous acceleration of both ships is high enough, they'll both have to teleport almost immeidately (one forward, one backwards) to within a meter or less of each other to keep the string from breaking. So you very much are asserting that what one of them does (decides to leave) has a profound effect on the other (faster than light causality). If the observers are left behind instead of being passengers, they'll just see the ship teleport away to 2.5 LY distant in negligible time.

But he MUST believe that she ages instantaneously

If he's chooses to use his own CMIF frame, then yes, he can believe that. There's no contradiction in it since there's no law that says such stuff can't happen in accelerated frames, or that there are say speed limits.

because otherwise he can't explain how they agree at the reunion

This part is wrong. There are plenty of other ways to explain it, many of them better.

It is just the twin paradox scenario, but with the rockets added on (but not affecting the twins [except that the home twin observes the leading rocket instantaneously jumping from being co-located with her to being separated from her by a finite distance (which is absurd)].

It is indeed absurd, but it's your assertion, not mine. Somehow you're sticking with a speculation that you admit to being absurd.

That's what this example is saying: that non-constant separation of the rockets results in an absurdity

The separation is frame dependent. It is constant only in the one inertial frame, something which you apparently deny.
I notice that you ignored (not just diagreed) with the numbers I provided about how far apart the rockets are from various frames, and why the string breaks no matter which frame is used to analyze the situtation. You've found no mistakes in my numbers, so I presume you agree with them.

Your speculation that the distance between rockets remains constant in the rocket frame results in the absurdity (your admission) of any observer at either launch pad observing the rocket teleport to light-years away in an instant, as verified by your little program you sent me that computes it. All you have to do is increase the acceleration constant to arbitrarily high values and run it for not 3 years, but a single second.