Accelerations of Rockets

[sep...@yahoo.com]

In my post "Relativity Acceleration Question" the responses weren't clear to me for the following scenario.
Ten identical rockets are built. Four are shipped to four different inertial reference frames to be tested. In frame F0, observers at rest in F0 measure that rocket R0 accelerates from a speed of zero wrt F0 to a speed of V=c*sqrt(3)/2 wrt F0 in 10**8 seconds, with a constant acceleration rate as measured in F0 of 3*sqrt(3)/2 meters per second squared. Observers at rest in F1 measure that their identical rocket, called R1, accelerates from a speed of zero wrt F1 to a speed of V=c*sqrt(3)/2 wrt F1 in 10**8 seconds, with a constant acceleration rate as measured in F1 of 3*sqrt(3)/2 meters per second squared. Observers at rest in F2 measure that their identical rocket, called R2, accelerates from a speed of zero wrt F2 to a speed of V=c*sqrt(3)/2 wrt F2 in 10**8 seconds, with a constant acceleration rate as measured in F2 of 3*sqrt(3)/2 meters per second squared. Observers at rest in F3 measure that their identical rocket, called R3, accelerates from a speed of zero wrt F3 to a speed of V=c*sqrt(3)/2 wrt F3 in 10**8 seconds, with a constant acceleration rate as measured in F3 of 3*sqrt(3)/2 meters per second squared.
Now rockets R1, R2 and R3 are shipped to inertial reference frame F4 along with an untested identical rocket R4. All four of these rockets are pointed along the positive x-axis and all are initially positioned at x = 0. At time t = 0 as measured in F4, all of the four identical rockets start accelerating. Do they all travel side by side and accelerate a the same acceleration rate?
If rocket R0 has started its acceleration before any of those rockets at rest in F4 simultaneously started their accelerations, and R0 has zero velocity wrt to F4 just as the accelerations of the other rockets start, does rocket R0 travel side by side next to the other rockets as all the rockets accelerate?
In my previous acceleration post, the answer to these two questions seemed to be no, but no clear explanation that I understood was given as to why that occurs.
David Seppala
Bastrop TX

[Dirk Van de moortel]

Op 25-sep.-2021 om 17:20 schreef sep...@yahoo.com:

> In my post "Relativity Acceleration Question" the responses weren't clear to me for the following scenario.

Other than some kicks in the butt, you don't deserve any response.
But don't worry, they can't help it, so you're about to be amply
technically entertained anyway.

Dirk Vdm

[Rob Acraman]

From the previous discussions, it seems to me that you have still never acknowledged the main point that has been repeatedly explained.

Let's take a rocket that has been built to accelerate at a constant 9.8 metres/second^2 by the rocket - ie, the on-board rocket's accelerometer will always read 9.8 metres/second^2, and the astronaut will feel his feet pressed to the floor by 1G.

Now that rocket is launched from F0. For a while, F0's measurements will (NEARLY exactly) agree that the rocket is accelerating at 9.8 metres/second^2. This is because (like all other relativistic effects like time dilation, etc) relativistic effects are negligible at low speed. Negligible, but NOT zero.

After a while, those effects become NOT negligible. The acceleration AS MEASURED BY F0 will become markedly LESS than 9.8 metres/second^2. For example, after some time, that rocket's acceleration would drop to 7 metres/second^2 as measured by F0.

So let's be clear : at that time the rocket's acceleration AS MEASURED BY the rocket's on-board accelerometer (and the force felt by the astronaut) remains 9.8 metres/second^2, but the rocket's acceleration AS MEASURED BY frame F0 is 7 metres/second^2.

DO YOU UNDERSTAND THIS ?

[Dirk Van de moortel]

Op 25-sep.-2021 om 17:59 schreef Rob Acraman:

It doesn't matter whether he understands.
You'll entertain each other anyway.

Dirk Vdm

[Maciej Wozniak]

In the meantime in the real world, however, GPS clocks keep
MEASURING t'=t, just like all serious clocks always did.

[sep...@yahoo.com]

I understand that, yes. I have no problem with that. I'm trying to understand what takes place if the rocket is built such that the acceleration is CONSTANT as measured in F0 so that F0 observers measure the change in velocity relative to their inertial reference frame to be a constant a*t, and the distance traveled as measured by observers in their inertial reference frame to be 0.5*a*t**2 as the rocket accelerates from zero wrt to F0 to V=c*sqrt(3)/2 wrt to F0.

Thanks,
David Seppala
Bastrop TX

[mitchr...@gmail.com]

Heat can accelerate or decelerate the atom.
The interstellar space ship must slow down in order to land.

Mitchell Raemsch

[Al Coe]

On Saturday, September 25, 2021 at 8:20:54 AM UTC-7, sep...@yahoo.com wrote:
> ... rocket R0 accelerates from a speed of zero wrt F0 to a speed of V=c*sqrt(3)/2 wrt

> F0 in 10**8 seconds, with a constant acceleration rate as measured in F0 of 3*sqrt(3)/2
> meters per second squared.

This means the control system for the rocket must be programmed to continually adjust the proper thrust such that the rocket initially produces a proper acceleration (as measured by an accelerometer in the rocket) of A=3sqrt(3)/2 m/sec^2 at the beginning and gradually increasing until it is producing proper acceleration of 8A=24sqrt(3)/2 m/sec^2 by the end. In other words, the proper acceleration at the end is eight times as great as at the beginning. So, the rocket's proper thrust per unit mass must gradually increase by a factor of 8 during the acceleration from rest to speed V (in terms of F0).

> If rocket R0 has started its acceleration before [rocket R4] at rest in F4 simultaneously started
> its accelerations, and R0 has zero velocity wrt to F4 just as its accelerations [at constant rate
> A in terms of F4] starts, does rocket R0 thereafter travel side by side next to R4 as they accelerate?

No, of course not. When R4 begins its acceleration, the engine control system of rocket R4 is programmed to produce thrust to give the proper acceleration of A, but by that time R0 is moving at some speed u > 0 (which you failed to specify) in terms of F0, so the control system of rocket R0 has already increased its thrust level to produce proper acceleration of (say) 1.365*A (if u is half V), meaning rocket F0 must be producing 1.365 times as much thrust per unit mass at that moment. So the rockets have very different proper accelerations at that time (and thereafter), and hence they obviously do not remain side by side.

This was all carefully explained in the previous thread. What part don't you understand?

[sep...@yahoo.com]

If rocket R1 is at rest in F1, and rocket R2 is at rest in F2, and rocket R3 is at rest in F3 and they all start accelerating simultaneously along the x-axis when they happen to be at the same x position, do those three rockets travel side by side throughout their journey?

[Al Coe]

On Saturday, September 25, 2021 at 11:38:42 AM UTC-7, sep...@yahoo.com wrote:
> If rocket R1 is at rest in F1, and rocket R2 is at rest in F2, and rocket R3 is at rest
> in F3 and they all start accelerating simultaneously along the x-axis when they
> happen to be at the same x position, do those three rockets travel side by side
> throughout their journey?

Of course not. You are stipulating that they all have different initial trajectories (at rest in different frames), starting at the same time and place with different speeds, so by definition they diverge. Do you honestly not understand that? Honestly?

[Maciej Wozniak]

In the meantime in the real world, however, GPS clocks

keep indicating and measuring t'=t, just like all serious
clocks always did. Do you honestly not understand
that? Honestly?

[sep...@yahoo.com]

On Saturday, September 25, 2021 at 1:26:35 PM UTC-5, Al Coe wrote:

If F0 observers measure the acceleration of rocket R0 to be a constant V=at, when the rocket reaches a velocity U that acceleration is still constant as the rocket accelerates from U to V=c*sqrt(3)/2. If the rocket has an initial velocity of U instead of zero, what acceleration rate do the observers in F0 measure that acceleration rate to be once the acceleration has started. What formula do you use to compute the velocity of the rocket relative to F0 when the initial velocity is U instead of zero wrt to F0?
David Seppala
Bastrop TX

[sep...@yahoo.com]

In response to:

>
> > If rocket R0 has started its acceleration before [rocket R4] at rest in F4 simultaneously started
> > its accelerations, and R0 has zero velocity wrt to F4 just as its accelerations [at constant rate
> > A in terms of F4] starts, does rocket R0 thereafter travel side by side next to R4 as they accelerate?
>

Al replied:

No, of course not. When R4 begins its acceleration, the engine control system of rocket R4 is programmed to produce thrust to give the proper acceleration of A, but by that time R0 is moving at some speed u > 0 (which you failed to specify) in terms of F0, so the control system of rocket R0 has already increased its thrust level to produce proper acceleration of (say) 1.365*A (if u is half V), meaning rocket F0 must be producing 1.365 times as much thrust per unit mass at that moment. So the rockets have very different proper accelerations at that time (and thereafter), and hence they obviously do not remain side by side.

Please explain the following:
If there are two rockets in F0, and the thrusters are programmed as you say they must be in this scenario what happens in the following. The two rockets are side by side at rest in F0. Simultaneously both rockets are sent signals to simultaneously start the acceleration of each rocket. The programming of the thrusters start simultaneously, but suppose there is a problem with the thrusters in one rocket such that they are not activated until T seconds after the launch time. Now both thrust programs are running identically. What is the acceleration rate of the delayed rocket now as measured by the observers in F0?
David Seppala
Bastrop TX

[Al Coe]

On Saturday, September 25, 2021 at 1:06:04 PM UTC-7, sep...@yahoo.com wrote:
> If F0 observers measure the acceleration of rocket R0 to be a constant V=at...

The symbols "V=at" do not signify an acceleration, so your sentence doesn't parse. Let A denote the constant rate of acceleration of R0 in terms of F0. If the rocket has F0 speed v=0 at t=0, then subsequently its F0 speed is v=At (although this can't be continued indefinitely, because the proper acceleration and rocket thrust go to infinity as v approaches c).

> ...when the rocket reaches a velocity U that acceleration is still constant as the

> rocket accelerates from U to V=c*sqrt(3)/2.

The coordinate acceleration is still A in terms of F0, and the proper acceleration of the rocket when it has speed U in terms of F0 is A/(1-U^2)^(3/2). By the time it reaches speed V it has the proper acceleration 8A.

> If the rocket has an initial velocity of U instead of zero, what acceleration rate do the
> observers in F0 measure that acceleration rate to be once the acceleration has started.

By your own stipulation, the coordinate acceleration rate of R0 in terms of F0 is always A, but the proper acceleration (corresponding to the thrust per unit mass produced by the rocket) when at speed U in terms of F0 is A/(1-U^2)^(3/2).

> What formula do you use to compute the velocity of the rocket relative to F0 when the
> initial velocity is U instead of zero wrt to F0?

The velocity in terms of F0 is then v = U + At. Understand?

> Two rockets are side by side at rest in F0. Simultaneously both rockets are sent signals

> to simultaneously start the acceleration of each rocket. The programming of the thrusters
> start simultaneously, but suppose there is a problem with the thrusters in one rocket such
> that they are not activated until T seconds after the launch time. Now both thrust programs
> are running identically. What is the acceleration rate of the delayed rocket now as measured
> by the observers in F0?

Since you've stipulated that each rocket (when it is accelerating) has a constant coordinate acceleration rate of A in terms of F0, each rocket (when it is accelerating) has a constant coordinate acceleration rate of A in terms of F0.

Does this clear things up for you?

[sep...@yahoo.com]

I'm trying to understand accelerations because of a different scenario. Maybe you can explain things. Let's say there are three inertial reference frames F0, F1 and F2. F1 has a relative velocity of |V| = c*sqrt(3)/2 in the negative x direction along the x-axis relative to F0 and F2 has a relative velocity of |V| =c*sqrt(3)/2 moving in the positive x direction relative to F0. There are two identical rockets at rest in F1. When these rockets are launched they each accelerate in identical acceleration patterns. We can say they have a constant acceleration rate as measured in F0, or a constant proper acceleration rate, whatever. In F1 the two identical rockets are at rest positioned with x coordinates 10 meters apart as measured in F1. Observers in F0 measure the separation of the rockets to be a length of 5 meters. At time t=0 (as measured in F0), observers in F0 start the accelerations of both rockets simultaneously. In F1 observers say one rocket started accelerating before the other rocket. The two rockets accelerate from F1 to F0 and continue until they reach F2.
As viewed in F0, the accelerations of the two rockets are identical throughout the journey. The two rockets started 5 meters apart as measured in F0 so when they simultaneously have zero velocity wrt F0, they are still 5 meters apart. When they finish their journey to F2 as measured by observers in F0 they are still 5 meters apart, but as measured by observers in F2 the two rockets end up 10 meters apart. How do observers on board each of the two rockets explain the separation of the two rockets during the journey? They say initially the two rockets were 10 meters apart. One rocket started accelerating before the other rocket, so the two rockets move closer and closer together as they approached F0. When the two rockets have zero velocity wrt F0, the rockets are only 5 meters apart. However, once they reach F0, the two rockets are no longer moving toward each other, but they start increasing their separation from 5 meters back to 10 meters as they continue toward F2. Please explain how the observers on board the two rockets explain why the rockets went from 10 meters to 5 meters back to 10 meters of separation when no change in the acceleration pattern between the two rockets occurred.

[Rob Acraman]

Great - I'm glad that you do understand that the coordinate acceleration (eg as measured by F0) will have a different value from the proper acceleration (eg, as measured by the on-board accelerometer, and felt by the astronaut).

However, that means that what you are not doing is APPLYING that understanding. Since you are never applying that understanding, you are simply spinning off multiple scenarios that would be a contradiction if coordinate-acceleration and proper-acceleration were the same.

Since, as you say you understand, coordinate-acceleration and proper-acceleration are NOT the same, but can have wildly differing values for the same rocket at the same instant, those attempted-contradctions fail.

Let's look at your latest post :

On Sunday, September 26, 2021 at 10:21:39 PM UTC+10, sep...@yahoo.com wrote:
> There are two identical rockets at rest in F1. When these rockets are launched they each accelerate in identical acceleration patterns. We can say they have a constant acceleration rate as measured in F0, or a constant proper acceleration rate, whatever.

No, it shouldn't be "whatever". You should be laying out a concisely specified scenario. It shouldn't be up to the respondents to specify YOUR scenario for you, or to guess what you mean.

Since you have chosen to lump us with that choice, in the interest of progressing the discussion I'll choose constant proper acceleration. Both rockets are fixed to acceleration at, say, 9.8 metres / second ^2 by the on-board accelerometer. This means that each astronaut will measure the same proper time for their trip from F1 to F0. Let's add a little extra detail - both rockets pause (ie switch off their engines) for a milli-second when they reach F0. This gives them time to exchange signals, and so confirm that each IS at rest wrt F0 for that period.

> At time t=0 (as measured in F0), observers in F0 start the accelerations of both rockets simultaneously. In F1 observers say one rocket started accelerating before the other rocket.

This is critical.

Note that "F1 observers" includes the astronauts on the rockets immediately prior to their turning on their engines. Let's give them names - Alice started her engine first, Bob started his later.

now, both Alice and Bob measured that their accelerations from F1 to F0 took a proper time of N seconds (as measured by their respective clocks), since their proper accelerations are the same 9.8 metres / second^2.

However, as we've said, Alice started her acceleration first as measured by observers "in" F1 - and that includes Alice and Bob themselves (until they started their engines). So, going from F1 to F0, although the engines were burning for the same amount of PROPER time - *** BUT *** by both Alice's and Bob's COORDINATE times, Alice's engine was burning for longer (since Alice launched first, but "arrived" at F0 "simultaneously" with Bob).

Let's forget relativity for a second, and consider everyday accelerations - say Anna driving an Amber car and Bruce driving a Blue car, both accelerating from 0 to 100kph. Let's say they both reached that 100kph simultaneously, but Alice in the Amber car started accelerating first.

What that means is that the Amber car must have been accelerating for a longer period of time than the Blue car - eg, the Amber car went from 0 to 100 in 10 seconds, but the Blue car did it in 5 seconds. ie, the Blue car must have had a higher rate of acceleration than the Amber car. Agree ?

Going back to Relativity, likewise since Alice launched first, and Bob launched second, this means that although their PROPER acceleration rates were the same 9.8 metres / second ^2, however their COORDINATE acceleration rates (both as measured by F1, and also by their own accelerating coordinate systems) must have had Bob as the higher COORDINATE acceleration rate.

Back to non-relativity Anna and Bruce for a last consideration. We've agree that Anna starts first with a smaller acceleration, and Bruce starts later with a higher acceleration. Let's also say that Bruce has an X metres head start. What happens ?

Well, Anna starts, and immediately starts getting closer to Bruce. Then Bruce starts accelerating, but for a while he is still slower than Anna - so Anna is still getting closer to him (ie, the distance between them decreases). After a period of time, Bruce's speed matches Anna's, so this is the closest that Anna gets to Bruce - Bruce will then start pulling away from her (ie, distance increases).

So to summarise: Bruce and Anna start some distance from eachother. Anna starts accelerating with a constant acceleration, then Bruce also starts accelerating with a constant acceleration. This means that the distance from Anna to Bruce decreases, then reaches a minimum, and then starts increasing .... all with neither Alice nor Bruce ever changing their acceleration rate. Hey, that sounds a little familiar - where have I heard that before ?? Oh, that's right :

> Please explain how the observers on board the two rockets explain why the rockets went from 10 meters to 5 meters back to 10 meters of separation when no change in the acceleration pattern between the two rockets occurred.

So back to our Relativity - yes, Alice and Bob both have the same PROPER acceleration of 9.8 metres / second ^2, but that doesn't change the fact that (as you state you "understand", yes? ) that their COORDINATE measurements of the other's acceleration is different (with Bob having a higher acceleration than Alice).

[Al Coe]

On Sunday, September 26, 2021 at 5:21:39 AM UTC-7, sep...@yahoo.com wrote:
> > Does this clear things up for you?
> I'm trying to understand accelerations because of a different scenario.

In this thread you described a scenario and asked for an explanation, and the explanation was provided to you. Then you asked some follow-up questions, and those questions were answered. (You're welcome.) And now you totally lose interest in that scenario and disregard it. If you really want to make progress, you need to update your thinking with what you have learned.

> Maybe you can explain things. Let's say there are three inertial reference frames F0, F1 and F2.

I already explained that scenario, in each of *seven* previous threads. Every aspect of it has been explained, and every follow-up question has been answered, multiple times. For example, see the thread you started on Sep 1, in which this scenario was (once again) fully explained in detail, and you couldn't find any fault in the explanation. Then in desperation you switched to questions about the elapsed times on the various trajectories, and all those questions were answered. Then in even greater desperation, you then tried to switch to general relativity, and your misunderstanding of the equivalence principle was patiently explained... and then you ran away. Remember?

If there is something about the explanation you still don't understand, then quote that specific part of the explanation and state what you don't understand about it. You're never going to learn if you continue to disregard the clear and complete explanation and simply re-state the original question, over and over, as if you had never been provided with the explanation many times.

[sep...@yahoo.com]

Say the two rockets have an identical proper acceleration of 9,.8 meters / second^2 once each starts accelerating. There is an accelerometer that measures a constant value throughout the journey once the acceleration of each rocket begins. Let one rocket have a 6 meter rod that is perpendicular the the x-axis. Just before the acceleration starts, an astronaut at the head of the rocket aligns the rod with the x-axis. He cannot reach the tip of the other rocket with that rod. He returns the rod perpendicular to the x-axis just as the acceleration begins. At random times the as the astronaut accelerates from F1 to F2, he aligns the rod with the x-axis. Each time he tries to touch the tip of the other rocket, but he can't reach it. However, when the two rockets are close to zero relative velocity with respect to F0, the astronaut once again aligns the rod with the x-axis. This time he can touch the tip of the other rocket with the rod. He can do this for awhile, but once the rockets both have a significant velocity beyond F0, the astronaut can no longer touch the tip of the other rocket with the rod.
No one has explained the "physics" of this scenario. Everyone says per Einstein's coordinates of course he can't touch the tip of the other rocket. What part of this don't you understand? No one tells me physically what happens. Everyone says its a math consequence of Einstein's theory so it makes perfect sense. If the astronaut sleeps during the journey, what everyone is implying is that he will have no idea when he wakes up whether or not he will be able to touch the tip of the other rocket with the rod. Why does he need to know how long he slept to know if he can touch the tip of the other rocket with the rod?
If the two rockets have an identical acceleration rate, and one starts accelerating toward the other rocket first, the two rockets keep getting closer and closer together until Einstein's coordinates result in them moving away from each other. Why does the astronaut say that happens when there is no difference in the acceleration rates?
Why does the astronaut say that the two rockets accelerate in the identical way, but if one rocket starts its acceleration first, the other rocket accelerates faster. The answer is of course, that's what Einstein's theory says, what part of that don't you understand? Explain the "logic" behind that concept.
David Seppala
Bastrop TX

[Al Coe]

On Sunday, September 26, 2021 at 10:09:06 AM UTC-7, sep...@yahoo.com wrote:
> No one has explained the "physics" of this scenario.

Sorry, but that's a lie. The physics of the scenario, and the mathematics, has been explained to you in detail many times. The physics is not really in question, because you are stipulating Lorentz invariance. You just keep getting confused by the mathematics of the situation.

> Everyone says per Einstein's coordinates of course he can't touch the tip of the other

> rocket. No one tells me physically what happens.

Sorry, but that too is a lie. You have been given the clear and complete explanation of precisely what happens, and why. Each time, you just run away, without even trying to say what part of the explanation you don't understand.

> Everyone says its a math consequence of Einstein's theory so it makes perfect sense.

That's a lie. The explanation given to you does not mention any individual, and does not simply make unsupported assertions from authority; it clearly explains the scenario in detail within the context of Lorentz invariance, which you are not disputing. The applications of forces necessary to make the objects move as they do has been clearly explained to you. The Doppler effect for signals between the objects has been fully explained to you. The elapsed times on clocks has been fully explained to you. The kinematics has been fully explained to you. After all this, you've been invited to say if there is anything that is unclear to you. Instead of answering, you just revert back to re-stating your original question, and lying that no one has ever given you the explanation.

Remember, you aren't challenging the empirical foundation of special relativity, you are claiming that there is a logical contradiction in special relativity. In other words, you are saying "According to special relativity, the following happens, but this doesn't make sense because [fill in your latest idiocy]". You're explicitly talking about what happens in the context of special relativity. Obviously if special relativity were false, then special relativity would be false (duh), but it would be irrational for you to take the falseness of special relativity as an apriori assumption on which to base your proof that special relativity is false. That would be just assuming what you are trying to prove.

> If the astronaut sleeps during the journey, what everyone is implying is that
> he will have no idea when he wakes up whether or not he will be able to touch
> the tip of the other rocket with the rod.

That's a lie. I've explained to you that everyone always agrees on all the facts, and that special relativity is not a subjectivist theory, and I've explained to you in detail the relations between the twins (or BB's or clocks) and the ends of the measuring rod. You simply don't pay attention.

> If the two rockets have an identical acceleration rate...

In terms of what system of coordinates? They do not have identical coordinate acceleration rates in terms of all systems.

> and one starts accelerating toward the other rocket first...

"First" in terms of what system of coordinates? Remember, the temporal ordering is coordinate-dependent.

> the two rockets keep getting closer and closer together until Einstein's

> coordinates result in...

No, that's a lie. You've been told, over and over, that coordinates are not used to cause anything to happen, they are used to describe what happens, and the coordinates are not the property of any individual (regardless of whatever crazed fixation you have on that individual). The dynamics and kinematics of the entire scenario, in terms of every imaginable system of coordinates, have been thoroughly explained to you in detail. You've been invited to state what part of the explanation seems wrong or unclear to you, but you simply ignore it and run away.

> them moving away from each other. Why does the astronaut say that happens when
> there is no difference in the acceleration rates?

Acceleration rates in terms of what system of coordinates? The motions of all the objects in terms of every imaginable system of coordinates (both inertial and accelerating) have been described for you in full detail, along with the forces and the Doppler effects and the elapsed times and so on. Everything has been explained, and all your misconceptions have been exposed and debunked. Remember?

> Why does the astronaut say that the two rockets accelerate in the identical way,

In terms of what system of coordinates? Every description in terms of every system of coordinates has been described in detail, and they all are perfectly consistent and correct. You have not noted anything wrong in any of the explanations. Remember?

> but if one rocket starts its acceleration first, the other rocket accelerates faster.

"First" in terms of what system of coordinates? And "accelerates faster" in terms of what system of coordinates? All you are doing is mindlessly mixing verbal parts of a description in terms of one system of coordinates with verbal parts of the description in terms of other systems of coordinates, and declaring that you don't understand. Naturally you can't understand gibberish, which is what you are constructing by conflating different things.

Remember, what's confusing you is pure math. You aren't disputing physical Lorentz invariance, you are trying to show that special relativity can't be correct by showing that, if special relativity were correct, it would lead to a contradiction. To show that, you must correctly apply special relativity, and show that it leads to a contradiction. But, to the contrary, you've been shown repeatedly that all the results in your scenario are perfectly consistent and clear. Given a consistent description of events in terms of one system of coordinates (say, F0), the translation to other systems is pure math.

Do you have *any* rational and honest criticism of the explanation you've been given?

[sep...@yahoo.com]

You often ask in a reply, "In terms of what system of coordinates". Give the response in terms of the astronauts making the separation measurement with the 6 meter rod and with accelerometers on board each rocket. Granted their coordinate systems relative to any inertial system of coordinates are continually changing, but explain how if the astronauts cannot detect any change in their acceleration rate, why from the point of view of the astronauts the rod cannot touch the tip of the other rocket at the start of the acceleration, but midway the rod can, but then further down the trip the rod can't. Explain from the astronauts point of view when no change in acceleration is felt or measured why this is so. Don't give the explanation that at the start of the journey the astronauts use F1 coordinates, midway they use F0 coordinates, and at the end of the journey they use F2 coordinates. Explain why the astronauts did not detect any change in the acceleration of either rocket, and the rod was always the same length as measured by the astronauts, yet at the start and end of the journey the rod couldn't reach tip to tip of the two rockets, but at the midway point the rod could. Explain from the astronauts point of view why two identical rockets accelerating the identical way can start accelerating at different times but reach the same velocity simultaneously.
David Seppala
Bastrop TX

[sep...@yahoo.com]

On Sunday, September 26, 2021 at 1:29:15 PM UTC-5, Al Coe wrote:

If two observers have identical clocks and each of the observers along with each of their clocks always have some relative velocity with respect to each other, why do the clocks sometimes run slower and sometimes run faster than each other. I know in inertial reference frames each frame measures the other frame's clock as running slower due to the difference in relative velocities. Why isn't that true when the clocks undergo accelerations? In identical accelerations one clock can be measured to run faster than the other clock instead of slower, why is that?
David Seppala
Bastrop TX

[Al Coe]

On Sunday, September 26, 2021 at 12:03:01 PM UTC-7, sep...@yahoo.com wrote:
> You often ask in a reply, "In terms of what system of coordinates". Give the response in

> terms of...

You misunderstand. Whenever I talk about accelerations, speeds, positions, time intervals, etc., I clearly specify what system of coordinates I'm referring to. This applies to all of the statements in all of the explanations that I've given you. The person who persistently refuses to specify their coordinate systems is you. That's why I'm repeatedly asking you to specify.

> the astronauts making the separation measurement with the 6 meter rod and with
> accelerometers on board each rocket.

This has already been done for you dozens of times. The precise worldlines of the two astronauts (or BB's or clocks) have been described, along with the worldlines of the ends of the measuring rod (whose proper length you alter in each thread, first 10 meters, then 5 meters, now 6 meters...), and these world lines have been described in terms of each system of coordinates, including not just the inertial coordinate systems but also in terms of typical non-inertial systems consisting of slices of the co-moving inertial coordinate systems of the astronauts. Each time I give you the explanation, I invite you to point out anything that seems wrong or unclear to you, and each time you just run away.

> Granted their coordinate systems relative to any inertial system of coordinates
> are continually changing, but explain how if the astronauts cannot detect any change

> in their acceleration rate...

Any change in their own proper accelerate rate? Or any change in their own coordinate acceleration rate (in terms of some specified coordinate system), or any change in the *other* astronaut's proper or coordinate acceleration rates? All the acceleration rates of all the objects in terms of every specified system of coordinates are all mutually consistent and they describe exactly the same sequence of events. Do you understand this? If not, which descriptions in terms of which coordinate systems do you think are mutually inconsistent?

> why from the point of view of the astronauts the rod cannot touch the tip of the
> other rocket at the start of the acceleration, but midway the rod can, but then
> further down the trip the rod can't.

This is exactly what has been explained to you, in excruciating detail, a dozen times before. For the most recent, see your thread started Sep 1. If you can't even say what part of the explanation seems wrong or unclear to you, then it's difficult to know how to clarify it further.

> Explain from the astronauts point of view when no change in acceleration is felt
> or measured why this is so.

This has already been explained to you, in detail, a dozen times before. The paths of the two astronauts (not in mechanical equilibrium with each other), and the positions of the ends of the rod (in mechanical equilibrium with each other, so following Born rigid motion) have been fully explained.

> Don't give the explanation that at the start of the journey the astronauts use F1
> coordinates, midway they use F0 coordinates, and at the end of the journey they
> use F2 coordinates.

What you've stated there is tautologically true, i.e., they are both initially at rest in F1, and then later at rest in F0, and then still later at rest in F2. This is the specification of the scenario. For you to deny this is insane. You yourself specified it.

> Explain why the astronauts did not detect any change in the acceleration of

> either rocket...

Acceleration in terms of what system of coordinates? The fact that two separate objects have the same proper acceleration does not imply that the distance between them is constant in terms of every system of inertial coordinates, let alone in terms of the non-inertial coordinates in which one or the other of these accelerating objects is continually at rest. This has all been carefully explained to you repeatedly, and you always just run away.

> and the rod was always the same length as measured by the astronauts...

Again, this has all been explained to you in full detail in several previous threads, most recently in the thread you started on Sep 1. If you can't point to anything in the explanation that seems wrong or unclear, you clearly have no valid criticism. I invite you again to point out anything in the explanation that seems wrong or unclear to you.

> If two observers have identical clocks and each of the observers along with each

> of their clocks always have some relative velocity with respect to each other...

Relative velocity in terms of what system of coordinates? You see, if we are confining ourselves to inertial coordinate systems, then the term "relative velocity" has an unambiguous conventional meaning of "the velocity of one object in terms of the inertial coordinates in which the other object is continually at rest", but in your scenario you are imagining accelerating coordinate systems, i.e., systems in which accelerating objects are continually at rest, and this is ambiguous because there are many different such coordinate systems. So you have to specify what system of coordinates you have in mind.

> why do the clocks sometimes run slower and sometimes run faster than each other.

In terms of what system of coordinates? You see, when talking about separate clocks running faster or slower than each other, it depends on the mapping between their worldlines, so you can't say one clock is absolutely running faster than the other, it depends on the coordinate system that provides the mapping of comparison. Now, the elapsed times on clocks in your scenario have been thoroughly described and explained to you a dozen times before. I've invited you to point out anything that seems wrong or unclear to you, and you can never point anything out. So that settles it, right?

> I know in inertial reference frames each frame measures the other frame's
> clock as running slower due to the difference in relative velocities.

Right.

> Why isn't that true when the clocks undergo accelerations?

Why isn't what true? In every case, for any given system of coordinates X=x^1, Y=x^2, Z=x^3, T=x^0 (accelerating or not) the elapsed proper time on a clock as it goes a coordinate distance dx^1, dx^2, dx^3 in coordinate time dx^0 is the integral of sqrt(g_mn dx^m dx^n) along the path, where g_mn are the metric tensor components for the given system of coordinates.

> In identical accelerations one clock can be measured to run faster than the
> other clock instead of slower, why is that?

Huh? Again, the elapsed proper time on a clock as it goes a distance dx^1, dx^2, dx^3 in time dx^0 is the integral of sqrt(g_mn dx^m dx^n) along the path. Accordingly, the elapsed times on the clocks in your scenario were described explicitly in the previous threads. Remember, with accelerating coordinate systems, the mapping from one worldline to another is continually tilting. If there was something about those explanations that seem wrong or unclear to you, go ahead and point it out.

[sep...@yahoo.com]

If two astronauts are in rockets in F1 separated by a distance L and one rocket starts accelerating first moving toward the other rocket before the second rocket starts to accelerate (like in the scenario we've been discussing), at what point does the astronaut in the first rocket say that the other astronaut's clock ran faster than his own clock? Does the second astronaut's clock instantly gain time as determined by the astronaut that started accelerating first?
David Seppala
Bastrop TX

[Al Coe]

On Sunday, September 26, 2021 at 1:23:11 PM UTC-7, sep...@yahoo.com wrote:
> If two astronauts are in rockets in F1 separated by a distance L and one rocket
> starts accelerating first moving toward the other rocket before the second rocket
> starts to accelerate (like in the scenario we've been discussing), at what point does
> the astronaut in the first rocket say that the other astronaut's clock ran faster than
> his own clock?

In terms of what system of coordinates? Again, this has nothing to do with "what people say". Specifying an astronaut does not suffice to specify a coordinate system. To compare the readings of separate clocks, we need to compare them "at the same time", but simultaneity is relative, so the meaning of "at the same time" (same value of the t coordinate) depends on the system of coordinates.

> Does the second astronaut's clock instantly gain time as determined by the
> astronaut that started accelerating first?

Of course not. Don't be absurd. The elapsed times for the clocks were all explained to you in detail in the previous threads, including the one you started on Sep 1. If something about those elapsed times seems wrong or unclear to you, please point it out.

[Maciej Wozniak]

On Sunday, 26 September 2021 at 22:49:32 UTC+2, Al Coe wrote:
> On Sunday, September 26, 2021 at 1:23:11 PM UTC-7, sep...@yahoo.com wrote:
> > If two astronauts are in rockets in F1 separated by a distance L and one rocket
> > starts accelerating first moving toward the other rocket before the second rocket
> > starts to accelerate (like in the scenario we've been discussing), at what point does
> > the astronaut in the first rocket say that the other astronaut's clock ran faster than
> > his own clock?
> In terms of what system of coordinates? Again, this has nothing to do with "what people say". Specifying an astronaut does not suffice to specify a coordinate system. To compare the readings of separate clocks, we need to compare them "at the same time", but simultaneity is relative, so the meaning of "at the same time" (same value of the t coordinate) depends on the system of coordinates.
> > Does the second astronaut's clock instantly gain time as determined by the
> > astronaut that started accelerating first?
> Of course not. Don't be absurd. The elapsed times for the clocks were all explained to you in detail

In the meantime in the real world, the clocks of GPS
elapse t'=t, just like all serious clocks always did.

[Rob Acraman]

On Monday, September 27, 2021 at 3:09:06 AM UTC+10, sep...@yahoo.com wrote:

> Say the two rockets have an identical proper acceleration of 9,.8 meters / second^2 once each starts accelerating. There is an accelerometer that measures a constant value throughout the journey once the acceleration of each rocket begins. Let one rocket have a 6 meter rod that is perpendicular the the x-axis. Just before the acceleration starts, an astronaut at the head of the rocket aligns the rod with the x-axis.

As others have told you, the swivelling of the pole is just an irritating addition that adds nothing to the scenario. Instead, just say "The rocket has a 6 metre pole fixed to the front" - Done.

The fact that you keep on repeating this I guess means that you believe (incorrectly) that the results between swivelled vs fixed pole would be different. Such a belief would point to a deeper misunderstanding of SR, but we can look at that later.

> However, when the two rockets are close to zero relative velocity with respect to F0, the astronaut once again aligns the rod with the x-axis. This time he can touch the tip of the other rocket with the rod. He can do this for awhile, but once the rockets both have a significant velocity beyond F0, the astronaut can no longer touch the tip of the other rocket with the rod ..... If the astronaut sleeps during the journey, what everyone is implying is that he will have no idea when he wakes up whether or not he will be able to touch the tip of the other rocket with the rod. Why does he need to know how long he slept to know if he can touch the tip of the other rocket with the rod?

> No one has explained the "physics" of this scenario.

Firstly, no - the explanation has been given to you repeatedly, and what I am explaining to you about how this ties in with SR is what I have picked up from these threads (Thanks Al ).

Secondly, the details that are puzzling you above are not even strictly to do with SR. It's just the natural, inevitable result of vehicles with different (coordinate) accelerations and starting times - and let's be clear : Talking about one rocket being within 5 metres of the other is just another way of saying the x(Bruce) - x(Alice) < 5. In other words, we are talking about COORDINATES, so our interest is primarily in the COORDINATE acceleration values, rather than how much force the astronaut is feeling (ie, rather than the proper acceleration values).

Let's start by extending my earlier question :

On Sunday, September 26, 2021 at 3:24:16 AM UTC+10, sep...@yahoo.com wrote:
> On Saturday, September 25, 2021 at 10:59:07 AM UTC-5, Rob Acraman wrote:

> > So let's be clear : at that time the rocket's acceleration AS MEASURED BY the rocket's on-board accelerometer (and the force felt by the astronaut) remains 9.8 metres/second^2, but the rocket's acceleration AS MEASURED BY frame F0 is 7 metres/second^2.
> >
> > DO YOU UNDERSTAND THIS ?
> I understand that, yes. I have no problem with that.

OK, do you also understand, as a consequence of that, that two identical rockets, both programmed to have the same identical proper acceleration, can have different coordinate accelerations as measured by Frame F0 ? For example, if one rocket launches and accelerates for some time before the second launches, then although they have the same PROPER acceleration (since both their on-board accelerometers correctly show the same value, and the astronauts both feel the same force), but will have different COORDINATE accelerations (eg as measured by Frame F0) ?

I am going to proceed on the basis that your answer to that will be "Yes" again, but I expect you to clearly say "No" in your reply if you do not.

OK, so let's go over Anna and Bruce from my previous post again, but this time we'll plug some numbers in.
So, let's say Anna is in a car preset to have a constant coordinate acceleration of 5 metres / second^2, Bruce is in one preset to have a constant coordinate acceleration of 10 metres / second^2 - but Bruce is 25 metres ahead of Anna, and set to only start moving 2 seconds after Anna.

So this will play out as :
t=0 Anna is a x=0, Bruce is at x=25. Distance between them = 25 - 0 = 25.

t=1 Anna is a x=2.5, Bruce is at x=25. Distance between them = 25 - 0 = 22.5.

t=2 Anna is a x=10, Bruce is at x=25 (but now starts moving). Distance between them = 25 - 10 = 15.

t=3 Anna is a x=22.5, Bruce is at x=30. Distance between them = 30 - 22.5 = 7.5.

t=4 Anna is a x=40, Bruce is at x=45. Distance between them = 45 - 40 = 5.
At this instant, Anna and Bruce are both going at the same speed of 20 metres/second.
We can imagine that they are overtaking a truck travelling at 20 metres / second emblazoned with the logo "F0".

t=5 Anna is a x=62.5, Bruce is at x=70. Distance between them = 70 - 62.5 = 7.5.

t=6 Anna is a x=90, Bruce is at x=105. Distance between them = 105 - 90 = 15
.
t=7 Anna is a x=122.5, Bruce is at x=150. Distance between them = 150 - 122.5 = 27.5.

.>

> If the two rockets have an identical acceleration rate, and one starts accelerating toward the other rocket first, the two rockets keep getting closer and closer together until Einstein's coordinates result in them moving away from each other. Why does the astronaut say that happens when there is no difference in the acceleration rates?

Well, look at what happened with Anna and Bruce. Anna started accelerating towards Bruce first, then the two of them kept getting closer and closer together until they got within 5 metres of eachother (so if Anna had a 6 metre pole fixed to the front of her car, it would have touched Bruce), and then they start moving away from eachother.

That also means that if Anna or Bruce fell asleep at t=1 (it was a "micro-nap" :D and they were only passengers, not the drivers !), then when they woke up, they would have no idea whether that 6-metre pole can touch both cars or not. They need to know how long they slept before they can figure out whether that pole can reach or not.

There is also nothing about either vehicle having to change their acceleration, nor anything wild about one of their clocks instantly gaining time when they start accelerating.

NOTHING about this should be puzzling to you. It is simple, direct, inevitable, and obvious result of differing (coordinate) accelerations and differing start times.

That means that your misunderstanding is NOT with all these features, but instead simply with this :

For cars on earth, with low velocities and therefore negligible relativistic effects, Accelerations are just one number always - ie, Proper Acceleration = Coordinate Acceleration. That means for Anna and Bruce above, Anna's PROPER acceleration would be 5 metres / second ^2 (ie, the same as her COORDINATE acceleration), and Bruces PROPER acceleration would be 10 metres / second^2 (ie, the same as his COORDINATE acceleration).

So I bet you are going to say to me "So they have different PROPER accelerations, therefore that scenario is different from what I said".

WRONG, and therefore THAT is the cause of all your confusion about this.

You confusion is NOT about the rockets coming closer together, then apart, without changing their accelerations. That is simply the same as Anna and Bruce's coordinates above.

Your confusion is because you are still equating PROPER acceleration with COORDINATE acceleration.

You said above " I understand that, yes. I have no problem with that. " .... but here when it counts, you are totally ignoring / rejecting it. Instead, when performing the same calculations as I did for Anna and Bruce above, you want to plug in the PROPER acceleration values rather than the COORDINATE acceleration values.

THAT is why you are not taking on board all the explanations that have been given to you.

So in summary, your scenario is of two rockets Rocket-A and Rocket-B accelerating from F1 to F0 both having the same PROPER acceleration. However, as measured by F1, and also as measured by the non-inertial-coordinates of Rocket-A, and also as measured by the non-inertial-coordinates of Rocket-B :
- Rocket A takes off before Rocket B
- Rocket A has a lower COORDINATE acceleration than Rocket B (to see why, re-read my previous post, esp where I say "this is critical")

These facts mean that the COORDINATES (including how close the rockets get, and so whether the pole can reach from one to the other) WILL play out similar to how Anna and Bruce plays out above.

[sep...@yahoo.com]

Can you clarify this statement in your post:

"For cars on earth, with low velocities and therefore negligible relativistic effects, Accelerations are just one number always - ie, Proper Acceleration = Coordinate Acceleration. That means for Anna and Bruce above, Anna's PROPER acceleration would be 5 metres / second ^2 (ie, the same as her COORDINATE acceleration), and Bruces PROPER acceleration would be 10 metres / second^2 (ie, the same as his COORDINATE acceleration).

So I bet you are going to say to me "So they have different PROPER accelerations, therefore that scenario is different from what I said".

WRONG, and therefore THAT is the cause of all your confusion about this."

If Anna and Bruce have accelerometers in their cars, the accelerometers would show different values. Please give the Anna and Bruce example where accelerometers in their cars have the identical reading in your acceleration scenario.

[Al Coe]

On Monday, September 27, 2021 at 7:12:02 AM UTC-7, sep...@yahoo.com wrote:
> If Anna and Bruce have accelerometers in their cars, the accelerometers would
> show different values. Please give the Anna and Bruce example where accelerometers
> in their cars have the identical reading in your acceleration scenario.

The clear and complete explanation for two objects with the same proper acceleration was provided to you in seven previous threads, including the thread you started on Sep 1. Again, the two twins (or astronauts or BB's) have the same proper acceleration, as does one end of the measuring rod, but the locus of points of the other end of the measuring rod (when aligned with the motion) has slightly less proper acceleration, because the rod is in mechanical equilibrium (Born rigid motion) whereas the two astronauts are not. If there is something you don't understand about this, just ask. Ignoring the answer is not going to help you understand it.

> If two astronauts are in rockets in F1 separated by a distance L and one rocket
> starts accelerating first moving toward the other rocket before the second rocket
> starts to accelerate (like in the scenario we've been discussing), at what point does
> the astronaut in the first rocket say that the other astronaut's clock ran faster than
> his own clock?

In terms of what system of coordinates? Specifying an astronaut does not suffice to specify a coordinate system. To compare the readings of separate clocks, we need to compare them "at the same time", but simultaneity is relative, so the meaning of "at the same time" (same value of the t coordinate) depends on the system of coordinates.

> Does the second astronaut's clock instantly gain time as determined by the
> astronaut that started accelerating first?

Of course not. The elapsed times for the clocks were all explained to you in detail in the previous threads, including the one you started on Sep 1. If something about those elapsed times seems wrong or unclear to you, please point it out.

[Maciej Wozniak]

On Monday, 27 September 2021 at 18:04:48 UTC+2, Al Coe wrote:

> Of course not. The elapsed times for the clocks were all explained to you in detail in the previous threads, including the one you started on Sep 1. If something about those elapsed times seems wrong or unclear to you, please point it out.

In the meantime in the real world, however, GPS clocks

[Odd Bodkin]

I’ll remind you, David, that there is no such thing as a rigid body. A
rigid body violates laws of physics.
If you would like to hold a rod aligned in the x direction, and then
accelerate in the y direction, the rod will not, and in fact cannot, stay
straight and rigid. You could test this with a coiled spring if you like.
It’s the little things like this — the little assumptions you make — that
trip up your thinking persistently.

--
Odd Bodkin -- maker of fine toys, tools, tables

[Kye Fox]

Odd Bodkin wrote:

>> Of course not. The elapsed times for the clocks were all explained to
>> you in detail in the previous threads, including the one you started on
>> Sep 1. If something about those elapsed times seems wrong or unclear to
>> you, please point it out.
>
> I’ll remind you, David, that there is no such thing as a rigid body. A
> rigid body violates laws of physics.
> If you would like to hold a rod aligned in the x direction, and then
> accelerate in the y direction, the rod will not, and in fact cannot,
> stay straight and rigid. You could test this with a coiled spring if you
> like. It’s the little things like this — the little assumptions you make
> — that trip up your thinking persistently.

absolutely. Finally a post, in the middle of corona, making sense. People
thing the world is been modeled by Relativity in physics, meanwhile it's
all about *Fluid_Dynamics*, vortexes, turbulence etc etc.

[Al Coe]

On Monday, September 27, 2021 at 11:14:01 AM UTC-7, bodk...@gmail.com wrote:
> I’ll remind you, David, that there is no such thing as a rigid body. A
> rigid body violates laws of physics. If you would like to hold a rod
> aligned in the x direction, and then accelerate in the y direction, the rod
> will not, and in fact cannot, stay straight and rigid.

That isn't the issue. The OP has specified that the acceleration occurs at 0.00001 m/sec^2, so it takes about a million years (literally) to carry out the scenario, and with this virtually zero acceleration the rod is always in essentially mechanical equilibrium (regardless of any brain-dead re-orientations), and therefore it is in Born rigid motion (constant proper length), which is why the locus of the leading end of the rod (when aligned with the x axis) has slightly less proper acceleration than the trailing, whereas the two twins are constrained to equal accelerations (not in mechanical equilibrium), and this accounts precisely for the divergences and convergences of the relevant worldlines in the scenario. This has been explained to the OP numerous times, in explicit detail, in terms of every relevant (and some not so relevant) system of coordinates.

[mitchr...@gmail.com]

Man's orbits are unstable.
God creates gravity.
Man participates...
But he cannot do what God does...

Mitchell Raemsch

[sep...@yahoo.com]

On Monday, September 27, 2021 at 11:04:48 AM UTC-5, Al Coe wrote:
> On Monday, September 27, 2021 at 7:12:02 AM UTC-7, sep...@yahoo.com wrote:
> > If Anna and Bruce have accelerometers in their cars, the accelerometers would
> > show different values. Please give the Anna and Bruce example where accelerometers
> > in their cars have the identical reading in your acceleration scenario.
> The clear and complete explanation for two objects with the same proper acceleration was provided to you in seven previous threads, including the thread you started on Sep 1. Again, the two twins (or astronauts or BB's) have the same proper acceleration, as does one end of the measuring rod, but the locus of points of the other end of the measuring rod (when aligned with the motion) has slightly less proper acceleration, because the rod is in mechanical equilibrium (Born rigid motion) whereas the two astronauts are not. If there is something you don't understand about this, just ask. Ignoring the answer is not going to help you understand it.

Al,
The Bruce and Anna posting had simple numbers that were easy to follow, but the accelerations of the two isn't identical. Why can't you use those simple numbers and show me how two objects with IDENTICAL accelerations can come closer and closer to each other and then start moving further and further apart without their accelerations changing. Use the simple numbers. Can't you do that to help me understand the concept that was provided to me.
David Seppala
Bastrop TX

[Kye Fox]

Dirk Van de moortel wrote:

> Op 25-sep.-2021 om 17:20 schreef sep...@yahoo.com:
>> In my post "Relativity Acceleration Question" the responses weren't
>> clear to me for the following scenario.
>
> Other than some kicks in the butt, you don't deserve any response.
> But don't worry, they can't help it, so you're about to be amply
> technically entertained anyway.

Biden gets Covid-19 booster live on air, says US will have a ‘problem’
until 98% of Americans are vaccinated https://on.rt.com/bhk8

[Al Coe]

On Monday, September 27, 2021 at 1:43:20 PM UTC-7, sep...@yahoo.com wrote:
> The Bruce and Anna posting had simple numbers that were easy to follow,
> but the accelerations of the two isn't identical. Why can't you use those

> simple numbers...

That posting did not describe the scenario you are asking about... as you yourself just noted.

> Show me how two objects with IDENTICAL accelerations can come closer and closer

> to each other and then start moving further and further apart without their accelerations
> changing. Use the simple numbers.

I'm using *your* numbers. You specified that the BBs are constantly 5 meters apart in terms of F0, and (once they have begun accelerating) they are both accelerating at a constant proper rate of A m/sec^2, which you have said is some extremely small number. (Fill in any number you like.) The BB's are initially moving in the negative x direction at sqrt(3)c/2 (at rest in F1) and eventually are moving at sqrt(3)c/2 in the positive x direction (at rest in F2). A solid measuring rod is 5 meters long (proper length), and we can place one end of the rod at the left BB, and it originally extends only half way to the right BB. The right end of the rod is accelerating at a constant proper rate of 1/[5 + c^2/A], and it has a correspondingly lesser initial velocity to match the other end of the rod in Born rigid motion. Consequently it is initially converging on the right BB, and they converge until the right end of the rod touches the right BB (when all are at rest in F0), and then the greater acceleration of the right BB causes them to diverge again.

Now do you finally understand?

[Odd Bodkin]

By “objects”, I assume you mean extended objects, things that have distance
between endpoints. Then the point has been made several times that you
cannot talk about “identical accelerations” of objects as an innately true
statement. You can talk about specific locations on two objects having
identical accelerations, but that will then not hold for other locations on
the two objects.

You and I have talked many times about bodies not being rigid, and that a
force applied at one point will not produce the same acceleration at that
point that it will a different point on the same object. The object will
stretch or compress or bend, as it must.

Now you say, ok, then apply the force in little pieces at a bunch of
different locations at the same time. That’s fine, but again, “at the same
time” is not an unambiguous statement for spatially separated points in
different frames. What will be “at the same time” for a whole bunch of
points on the body in one frame will not at all be “at the same time” for
those points on the same body in a different frame. In other words, what
appears to be “relaxed” and “unstressed” acceleration in one frame will not
be “relaxed and unstressed” in any other frame. Where there is no
stretching, compression or bending in one frame, there will be stretching,
compression or bending in another frame. This isn’t because there are
additional forces being applied in the latter case. It’s all because the
*same* forces are not being applied at the same time in all frames.

You can learn about this in Wolfgang Rindler’s explanation for a puzzle he
called a “man falling into a grate”. In one frame, all parts of the man
accelerate at the same time down into the grate. In another frame, the
front part of the man accelerates downward earlier than the rear part of
the man, and so the man bends into the hole. This is not due to any new
force. It has to do with a distributed force being applied at different
times in different frames.

You struggle with this idea mightily, and are looking for some NEW force
being applied to one body, when that’s not it at all.

[sep...@yahoo.com]

If each rocket has a 3 rods, each of 5 meters proper length, if one rod is aligned along the x-axis, and the other two are aligned perpendicular to the x-axis but rotated to be momentarily aligned along the x-axis every time a measurement is made, and one is rotated clockwise and the other is rotated counter clockwise, its not clear to me how you describe the acceleration of "one end" of the rod. In one rocket, the rods are being pushed by the acceleration of the rocket, and on the other they are being pulled by the acceleration of the rocket. So when all six of these rods are simultaneously aligned side by side are their lengths equal?
David Seppala
Bastrop TX

[Al Coe]

On Monday, September 27, 2021 at 2:56:17 PM UTC-7, bodk...@gmail.com wrote:
> By “objects”, I assume you mean extended objects, things that have distance
> between endpoints.

No, the "objects" he is referring to are point-like objects, with equal constant proper accelerations, commencing and ceasing at the same times in terms of F0. Originally he called the two objects BB's, meaning tiny metal pellets. The only extended solid object in the scenario is the ruler. Again, the acceleration is specified to be so low that the ruler is always in virtually perfect mechanical equilibrium, so it is undergoing Born rigid motion during the approximately two million years requires to carry out the acceleration from F1 to F2.

[sep...@yahoo.com]

Let me ask a simple question about proper acceleration. If there are two identical rockets accelerating in the same direction with the identical proper acceleration, if an astronaut on board one of the rockets has a 6 meter rod that is perpendicular to the direction of acceleration, and he turns it momentarily so that it is aligned with the direction of acceleration, and the rod now extends from tip to tip of the two rockets, with just that measurement he cannot tell whether the rockets will be moving closer together the next time he makes a measurement, or moving further and further apart, or if the next time he makes a measurement whether the two rockets will have the same separation. Is that correct? The astronaut in some cases must make three measurements to determine how the two identical rockets are moving relative to each other, correct?

[Al Coe]

On Monday, September 27, 2021 at 3:32:58 PM UTC-7, sep...@yahoo.com wrote:
> If ... a 6 meter rod ... extends from tip to tip of two rockets, with just
> that measurement he cannot tell whether the rockets will be ... closer
> together the next time he makes a measurement, or ... further ... apart,
> or ... will have the same separation. Is that correct?

The fact that two objects are separated by a certain distance in terms of a certain reference system at a certain time does not imply how that distance may change in the future.

> The astronaut in some cases must make three measurements to determine
> how the two identical rockets are moving relative to each other, correct?

To determine how objects are moving, in terms of a given system of reference, the necessary and sufficient condition is to measure how the objects are moving in terms of that system of reference. Position is not the same as velocity, and velocity is not the same as acceleration, and in every case we must specify the system of coordinates.

> If each rocket has a 3 rods, each of 5 meters proper length, if one rod is
> aligned along the x-axis, and the other two are aligned perpendicular to
> the x-axis but rotated to be momentarily aligned along the x-axis every time
> a measurement is made, and one is rotated clockwise and the other is rotated

> counter clockwise...

It is senseless to have multiple rods, all akimbo. As has been explained multiple times, re-orienting the rods is completely pointless and superfluous. Obviously we can have one rod with the left end aligned with the left BB, and another rod with the right end aligned with right BB, but that makes no appreciable difference. In either case the other end of the rod will originally extend only half way to the other BB, and then later it will touch the other BB, and then they will diverge again. It doesn't matter which side you align, it works the same. Obviously. Duh.

> , its not clear to me how you describe the acceleration of "one end" of the rod.

Whenever you align the rod along the x axis with one end at one BB, the other end of the rod has a unique position, 5 meters of proper distance away. The locus of those positions comprises a continuous worldline, that is 5 meters of proper distance to the other BB. That worldline has the constant proper acceleration required for Born rigid motion of the rod. Initially (when aligned) the rod extends only half way to the other BB, then it touches the other BB, and then later it reaches only half way again, for the reason explained.

> So when all six of these rods are simultaneously aligned side by side are their lengths equal?

If you align several solid objects with the same proper lengths, they do indeed have the same proper lengths. Duh.

Do you finally understand?

[Maciej Wozniak]

On Tuesday, 28 September 2021 at 03:01:31 UTC+2, Al Coe wrote:
> On Monday, September 27, 2021 at 3:32:58 PM UTC-7, sep...@yahoo.com wrote:
> > If ... a 6 meter rod ... extends from tip to tip of two rockets, with just
> > that measurement he cannot tell whether the rockets will be ... closer
> > together the next time he makes a measurement, or ... further ... apart,
> > or ... will have the same separation. Is that correct?
>
> The fact that two objects are separated by a certain distance in terms of a certain reference system at a certain time does not imply how that distance may change in the future.
> > The astronaut in some cases must make three measurements to determine
> > how the two identical rockets are moving relative to each other, correct?
> To determine how objects are moving, in terms of a given system of reference

And to determine how they are used in the real world we have to measure
it with clocks; very unfortunately, the clocks of real world (all of them - GPS,
UTC,TAI) keep indicating t'=t, just like always.