The case for True Length = Rest Length

[Mike_Fontenot]

[...]

Velocity is velocity. It's silly to re-define it.

Mike Fontenot

 

[Dale]

So GrayGhost are you going to answer the question I asked above? I don't think that what you described above is logically possible, but it is hard to tell without a mathematical formulation.

 

[GrayGhost]

Velocity is velocity. It's silly to re-define it.

It's not a matter of redefining velocity Mike. It's the matter of how the LTs may be applied by B from his accelerating POV, and in a way that matches the twin A experience. I was merely pointing out the problems at hand. In the LTs, velocity is < c, and light's speed is c. You have stated that twin B can use the LTs, however that he must use the velocity that A records of B, not that which B records of A. That's what I said too, I made the attempt to justify why twin B can (and should) use that velocity ... my position being that there exists a 1:1 mapping of like-A/B-worldline-slopes, the slope of the A-worldline per B matching the slope of the B-worldline per A.

The problems are these ...

(1) twin A can move thru B-space superluminally when B undergoes proper acceleration. Obviously, that velocity should not be used in the LTs by twin B.

(2) light's speed varies from c because B's own sense-of-simultaneity dynamically rotates while the light travels. However, the LTs require an invariant c.​

IMO, these problems are resolved by using the instantaneous slope of the A-worldline for v in the LTs (where v is always < c), as opposed to B determining the A-velocity from change in position over duration (which can be superluminal).

GrayGhost

 

[Dale]

these problems are resolved by using the instantaneous slope of the A-worldline for v in the LTs (where v is always < c), as opposed to B determining the A-velocity from change in position over duration (which can be superluminal).

What is "instantaneous slope" if not "change in position over duration". You are contradicting yourself. This is why working out the math is so important.

 

[ghwellsjr]

Here's something for you to think about, while you are mulling all this over:

Take the standard twin "paradox" scenario, with gamma = 2. Suppose that immediately before the turnaround, their separation according to the home-twin, is L lightyears. The traveler says their separation is L/2 lightyears then.

Half way through the turnaround (when the home-twin says their relative velocity is zero), the home twin says their separation is still L, and the traveler NOW also says their separation is L lightyears. So the traveler says that their separation has changed by L/2 lightyears, during an infinitesimal amount of his ageing, so he says that their relative velocity during that first half of the turnaround has been infinitely large.

Denote the age of the traveler at the beginning of the turnaround as t1, and the age of the traveler at the midpoint of the turnaround as t1+delta, where delta is infinitesimally small, but non-zero). Denote the MSIRF at the beginning of the turnaround as MSIRF(t1), and the MSIRF at the midpoint of the turnaround as MSIRF(t1+delta) ... they are DIFFERENT inertial frames.

Ask yourself this: what do MSIRF(t1) and MSIRF(t1+delta) say about THEIR own separation (with respect to the home-twin) during the first half of the turnaround? Do either of them agree with the traveler, that the separation changes by L/2 during the infinitesimal time delta, and thus that the velocity during the time delta is infinitely large?

Mike Fontenot

When the traveler decelerates and becomes at rest in the frame in which the home-twin has always been at rest, the home-twin has no awareness of this event until long after it has occurred. You cheat when you give him knowledge from the frame of reference that we are aware of.

The traveler also does not experience an infinite velocity when he decelerates. He does not see the home-twin suddenly fly away from him. If he remained stationary in his original rest frame for a long time, instead of accelerating back toward home, he would gradually see the home-twin moving away from him, just as he would see all other objects in the sky (at rest in his original rest frame), both in front of him and behind him start to move away from him.

What if at the "moment" (as you define NOW for both twins) when the traveler decelerates, the home-twin were to also accelerate away from the traveler with the exact same acceleration profile, would you conclude that in the MSIRF of the home-twin, the traveler has not accelerated at all but continued on his steady speed away from the home-twin? Would this actual increase in speed in the home-twin negate your conclusion that the relative infinite velocity between the two twins has gone away? And would the traveler also agree from his MSIRF that the relative velocity has not changed at all and that the separation between the two of them remains constant at L/2?

 

[GrayGhost]

this post posted by accident.

 

[GrayGhost]

What is "instantaneous slope" if not "change in position over duration". You are contradicting yourself.

For reference ...

https://www.physicsforums.com/attachm...2&d=1299884366"​

DaleSpam,

Look at the illustration in the link above. If we are to assume that velocity is nothing more than the change of position over time, then twin A moves superluminally from point 1 to point 3 thru B-space during B's own virtually-instant proper acceleration. Clearly, this velocity cannot be used in LTs, and for good reason. I don't see this as overly complicated, personally.

My position is that the slope of the A-worldline dictates A's current velocity wrt B per B, far as "what velocity B should use in the LTs" goes. If you imagine a uniform almost-virtually-instant twin B proper acceleration, it's quite easy to envision how the A-worldline progresses from vertical to the slope of 0.866c, never exceeding 0.866c, let alone c.

Now you assume I am contradicting myself. However, there are 2 processes occurring wrt the A-worldline (per B) as B accelerates ...

(1) The A-worldline rotates steadily from vertical to a slope indicative of 0.866c, never exceeding 0.866c.

(2) The intersection of "the A-worldine and B-line-of-simultaneity" moves thru B-space, and can be superluminal.​

Now if the velocity is to be determined by the receipt of light signals, and doppler shifts converted into their appropriate dilation equivalent, then superluminal motion is never detected. The established velocity will match the current slope of the A-worldline per B. The reason this works out as such, is because events move in space and time per B during his acceleration, something that does not happen classically. One such event would be the location of the A-clock upon commencement of B acceleration, ie twin B's departure event from twin A. As twin B accelerates, said event drops further and further back in B time, and further and futher away in B-space, per B. This keeps the worldline slope at sub-c, which in my illustration never exceeds 0.866c even though A must move thru B-space superluminally (if velocity is determined in the classical way change in position over time).

GrayGhost

 

[Mike_Fontenot]

[...]

In the twin "paradox" example I gave previously (with gamma = 2), IF the traveler concludes that his distance to the home twin increases by L/2 lightyears during his infinitesimal ageing during the first half of his turnaround, then he MUST conclude that their relative velocity was infinite (on average) during that section of his life. Period. Non-negotiable.

And IF (as in the CADO reference frame) the traveler's conclusions about those two distances (at the beginning and at the midpoint of the turnaround) AGREE with the respective MSIRFs' conclusions about those distances at those two instants, then those two distances ARE L/2 and L, respectively. So the traveler MUST conclude that the distance to his home twin increases by L/2 during the first half of the his turnaround. Period. Non-negotiable.

IF the traveler ALWAYS agrees, about the instantaneous distance to his home twin, at each instant of his life, with his MSIRF at that instant, then he WILL disagree with that MSIRF about the relative velocity of the home twin at any instant during the first half of his instantaneous turnaround. Each MSIRF is an inertial frame, and NO inertial frame will EVER conclude that the home twin has an infinite relative velocity with respect to the traveler.

If you want to use a reference frame for the traveler, for which the relative velocity of the home twin during the first half of the turnaround ISN'T infinite, then that reference frame CAN'T agree with the conclusion of the traveler's MSIRF about his current distance to the home twin, at each instant during that first half of the turnaround. You just CAN'T have it both ways.

Mike Fontenot

 

[Dale]

For reference ...

https://www.physicsforums.com/attachm...2&d=1299884366"​

DaleSpam,

Look at the illustration in the link above.

The link doesn't work.

If we are to assume that velocity is nothing more than the change of position over time

It is not an assumption, it is a definition.

If you want to re-define velocity that is OK, but you will have to be very very clear and precise. No handwaving, just precise mathematical definitions. You are using non-standard terms and you are re-defining standard terms, so you cannot assume that I will understand what you mean without a rigorous treatment.

Again, say that you have an inertial unprimed frame:
$$(t,x)$$

And in that inertial frame there is an observer B with a timelike worldline:
$$(t_B(\lambda),x_B(\lambda))$$

What is the expression or operation to determine B's coordinates:
$$(t',x')$$

And now the operation to determine the velocity.
$$v_A(\lambda)=f(?)$$

 

[GrayGhost]

The link doesn't work.

Ahhh, a Cut-N-Paste problem there. Here's a repost with th correct web address ...

****************************************************************

For reference ...

https://www.physicsforums.com/attachment.php?attachmentid=32982&d=1299884366"​

DaleSpam,

Look at the illustration in the link above. If we are to assume that velocity is nothing more than the change of position over time, then twin A moves superluminally from point 1 to point 3 thru B-space during B's own virtually-instant proper acceleration. Clearly, this velocity cannot be used in LTs, and for good reason. I don't see this as overly complicated, personally.

My position is that the slope of the A-worldline dictates A's current velocity wrt B per B, far as "what velocity B should use in the LTs" goes. If you imagine a uniform almost-virtually-instant twin B proper acceleration, it's quite easy to envision how the A-worldline progresses from vertical to the slope of 0.866c, never exceeding 0.866c, let alone c.

Now you assume I am contradicting myself. However, there are 2 processes occurring wrt the A-worldline (per B) as B accelerates ...

(1) The A-worldline rotates steadily from vertical to a slope indicative of 0.866c, never exceeding 0.866c.

(2) The intersection of "the A-worldine and B-line-of-simultaneity" moves thru B-space, and can be superluminal.​

Now if the velocity is to be determined by the receipt of light signals, and doppler shifts converted into their appropriate dilation equivalent, then superluminal motion is never detected. The established velocity will match the current slope of the A-worldline per B. The reason this works out as such, is because events move in space and time per B during his acceleration, something that does not happen classically. One such event would be the location of the A-clock upon commencement of B acceleration, ie twin B's departure event from twin A. As twin B accelerates, said event drops further and further back in B time, and further and futher away in B-space, per B. This keeps the worldline slope at sub-c, which in my illustration never exceeds 0.866c even though A must move thru B-space superluminally (if velocity is determined in the classical way change in position over time).

GrayGhost

 

[GrayGhost]

In the twin "paradox" example I gave previously (with gamma = 2), IF the traveler concludes that his distance to the home twin increases by L/2 lightyears during his infinitesimal ageing during the first half of his turnaround, then he MUST conclude that their relative velocity was infinite (on average) during that section of his life. Period. Non-negotiable.

Let's see how twin B plugs that infinite twin A velocity value into the LTs, see where twin A is placed by B into twin B's own system.

And IF (as in the CADO reference frame) the traveler's conclusions about those two distances (at the beginning and at the midpoint of the turnaround) AGREE with the respective MSIRFs' conclusions about those distances at those two instants, then those two distances ARE L/2 and L, respectively. So the traveler MUST conclude that the distance to his home twin increases by L/2 during the first half of the his turnaround. Period. Non-negotiable.

In this, we agree.

IF the traveler ALWAYS agrees, about the instantaneous distance to his home twin, at each instant of his life, with his MSIRF at that instant, then he WILL disagree with that MSIRF about the relative velocity of the home twin at any instant during the first half of his instantaneous turnaround. Each MSIRF is an inertial frame, and NO inertial frame will EVER conclude that the home twin has an infinite relative velocity with respect to the traveler.

Seems to me that when twin B and the MSIRF observer are colocated, twin A must exist somewhere in spacetime and both those fellows must agree (even though they will disagree as to how twin A got there over time) ... assuming they have diligently and correctly maintained the current location of twin A. The reason they must agree Mike, is because they are momentarily of the very same frame-of-reference. All observers who are stationary wry one another, even if momentarily, must agree on where twin A then is. Maintaining the current twin A location via continuous radar tracking (and processing) is more laborious for twin B than for the momentarily colocated MSIRF-observer, but it doesn't change the fact that at that instant ... they must map where twin A is (identically) within their own (overlaid) system(s).

If you want to use a reference frame for the traveler, for which the relative velocity of the home twin during the first half of the turnaround ISN'T infinite, then that reference frame CAN'T agree with the conclusion of the traveler's MSIRF about his current distance to the home twin, at each instant during that first half of the turnaround. You just CAN'T have it both ways.

The fact that it is more difficult for twin B to (keep track and) determine the location of twin A at any instant during his own acceleration, does not lead that he should disagree with the momentarily colocated MSIRF-observer. All observers at rest with each other agree on the location and clock readout of a moving observer.

GrayGhost

 

[Dale]

If we are to assume that velocity is nothing more than the change of position over time, then twin A moves superluminally from point 1 to point 3 thru B-space during B's own virtually-instant proper acceleration.

Exactly. And again, it is not an assumption, it is a definition. If you wish to re-define velocity then you may, but you need to be completely specific about it.

If you imagine a uniform almost-virtually-instant twin B proper acceleration, it's quite easy to envision how the A-worldline progresses from vertical to the slope of 0.866c, never exceeding 0.866c, let alone c.

Now you assume I am contradicting myself. However, there are 2 processes occurring wrt the A-worldline (per B) as B accelerates ...

(1) The A-worldline rotates steadily from vertical to a slope indicative of 0.866c, never exceeding 0.866c.

(2) The intersection of "the A-worldine and B-line-of-simultaneity" moves thru B-space, and can be superluminal.​

Your point (1) is clearly not true in your diagram. The slope of the A worldline clearly exceeds 0.866c, or even c. Regarding (2) "the intersection of the A-worldline and the B-line-of-simultaneity" is just a long-winded way of saying the position of A in the B frame. The velocity of A in the B frame is by definition the derivative of this. Again, if you wish to redefine velocity you will have to be very specific. More math less english. Even if B's acceleration is finite this can lead to v>c.

Now if the velocity is to be determined by the receipt of light signals, and doppler shifts converted into their appropriate dilation equivalent, then superluminal motion is never detected.

Yes, that is the Dolby and Gull approach, not the naive/CADO approach.

The established velocity will match the current slope of the A-worldline per B. The reason this works out as such, is because events move in space and time per B during his acceleration, something that does not happen classically.

What does this mean? What is the formula that describes this "motion of events"?

I think perhaps this is the key thing that you need to define, then you could possibly define your new concept of velocity as some sort of motion in addition to or relative to this motion of events. But you really need to be clear and mathematically precise here if you want to ensure a self-consistent outcome.

Honestly, rather than patching up such a strange ad-hoc concept, I think you would be much better served actually learning some differential geometry. But if you do want to pursue this the place to start seems to be this concept of the motion of events. Start by expressing that mathematically.

 

[Mike_Fontenot]

Let's see how twin B plugs that infinite twin A velocity value into the LTs, see where twin A is placed by B into twin B's own system.
[...]

That's the whole point: the traveler must NOT use HIS value of the relative velocity in the Lorentz equations, he MUST use the HOME-TWIN'S value of the relative velocity in the Lorentz equations. Or, since the MSIRF always agrees with the home-twin about their relative velocity, the traveler can use the MSIRF's value of the velocity ... it's the same number.

I think I stated that very clearly in the first part of this posting:

https://www.physicsforums.com/showpost.php?p=3223917&postcount=314 .

Here's an excerpt from that posting:

[BEGIN EXCERPT]:

"Originally Posted by GrayGhost

[...]
My position is that the LTs must apply per twin B, even during his proper acceleration.
[...]

The Lorentz equations DO apply. But the quantity "v" that appears in the Lorentz equations needs to be "the relative velocity between the home-twin and the traveler, according to the home-twin", NOT according to the traveler. Or, since the MSIRF(t) at any given instant "t" in the traveler's life, always agrees with the home-twin about their relative velocity, you can equally well specify the velocity "v" in the Lorentz equations as "the relative velocity between the home-twin and the MSIRF(t), according to the MSIRF(t)" ... it's the same number in either case."

[END EXCERPT]

I think you are perhaps overloaded, and are trying to do so many things so fast that you are missing some important things in some of the previous posts.

[...]
Seems to me that when twin B and the MSIRF observer are colocated, twin A must exist somewhere in spacetime and both those fellows must agree (even though they will disagree as to how twin A got there over time) ...
[...]
The fact that it is more difficult for twin B to (keep track and) determine the location of twin A at any instant during his own acceleration, does not lead that he should disagree with the momentarily colocated MSIRF-observer. All observers at rest with each other agree on the location and clock readout of a moving observer.

They DO agree about the current distance to the home-twin, and about the current age of the home-twin. But they DON'T agree about the home-twin's current relative velocity.

In another previous posting, I described WHY they disagree about the relative velocity:

https://www.physicsforums.com/showpost.php?p=3217917&postcount=305 .

Here's an excerpt from that posting:

[BEGIN EXCERPT]:

And since the home twin's inertial frame always agrees about relative velocity with each of those MSIRF's, I thought that the accelerating traveler must also agree. That's why I didn't feel the need to specify "according to WHOM?" when I referred to the quantity "v" or "beta" in my paper.

But I later realized that I was incorrect: the accelerating traveler does NOT agree about velocities with his current MSIRF. They agree about distances and times at that instant, but not about velocities at that instant. The reason lies in the fact that velocities always by definition are based on changes of a distance during a very small change in time. I.e., the velocity of the home twin, relative to the traveler, according to the traveler, at some instant t of his life, refers to how that distance changes for two very closely-spaced times of his life very near the instant t. And the MSIRF's at those two different times in his life AREN'T the SAME inertial reference frame. THAT'S why the traveler generally won't agree about relative velocities with his current MSIRF.

Fortunately, this omission on my part didn't affect the results in my paper, because all the results were correct when the quantity "v" and "beta" in my equations referred to the velocity of the traveler, relative to the home twin, ACCORDING TO THE HOME TWIN. I.e., it WAS necessary for me to specify "according to WHOM" when I referred to a relative velocity.

[END EXCERPT]

I KNOW you can understand the above stuff ... just slow down a little bit.

Mike Fontenot

 

[Mike_Fontenot]

Just FYI:

In a follow-up paper to my original paper on accelerating observers, I derived "the velocity of the traveler, relative to the home-twin, according to the traveler". The result is (for units where c has unity magnitude, so I'll leave c out of the equation, for simplicity):

V = v - (L*v*a)/gamma ,

where BOTH V and v are "the velocity of the traveler, with respect to the home twin", but V is "according to the traveler", and v is "according to the home-twin" (or, equivalently, "according to the MSIRF"). v is positive when the twins are moving apart.

L is the (positive) separation between traveler and home-twin, according to the home-twin.

"a" is the traveler's acceleration, as read on an accelerometer he carries. "a" is positive when in the direction of positive v.

All of the quantities in the equation are for some arbitrary, but given, instant of the traveler's life.

Mike Fontenot

 

[GrayGhost]

I think perhaps this is the key thing that you need to define, then you could possibly define your new concept of velocity as some sort of motion in addition to or relative to this motion of events. But you really need to be clear and mathematically precise here if you want to ensure a self-consistent outcome.

Honestly, rather than patching up such a strange ad-hoc concept, I think you would be much better served actually learning some differential geometry. But if you do want to pursue this the place to start seems to be this concept of the motion of events. Start by expressing that mathematically.

Dale Dale DaleSpam. It's quite interesting you know. The theory demands that no material body can accelerate to speed c, because of energy considerations. Add, speed c represents a cosmic speed limit. Yet per twin B, twin A could move superluminally thru B-space. So what does it all mean? Hmmm.

Conceptually, it's quite clear in my mind, personally. Events move in B-space per B while B continues his own proper acceleration. Such an event is the B-departure-from-A. This is what keeps the velocity < 0.866c in my example (let alone < c), even though A moves superluminally per B from a standpoint of the-change-in-position-over-time.

You know ... this reminds me of the problem whereby many folks remain stuck, because they generally tend to ignore the time dilation while focusing only on spatial changes. Neither can be ignored, and they always exist in unison. In this case, IMO, twin A moves superluminally (per B) only if B focuses only on the spatial contraction while ignoring the time dilation component altogether. If the time dilation component is not ignored, then the cosmic speed limit is not violated. Add, it's referred to as time dilation ... however really, its a dilation of spacetime.

Indeed, what needs to be done is to math-model the twin B experience as the-collection-of-momentary-colocated-inertial-frames-of-reference that B co-occupies. Yes, differential geometry should get the job done. I haven't seen it anywhere, but I find it very difficult to believe no one has done this as yet. Now, Mike Fontenot believes he has done this. Where Mike simply states that twin B cannot use his own recorded A-velocity in the LTs (he must use an A-framer's recorded v), I merely made the attempt to explain WHY twin B must do so, and why it works. Wrt that matter, I figure I'm saying the same fundamental thing as Mike, but I'm not sure he realizes it yet.

Also, I never looked at it as though I was changing the definition of relative velocity. However, maybe I am now that you mention it? I suppose it'd be a rather presumptuous thing to do, assuming it hasn't yet been done. As I said though, I doubt I'm the first to suggest this, and I'd be very very surprised if no one has modeled it as yet. It's not a change to the classical velocity definition far as non-luminal speeds go ... it applies only to the case of luminal (and superluminal) motion from a non-inertial POV, in the relativistic case.

Wrt another comment you made ... it seems to me that if the Dolby and Gull approach converts doppler shift to the appropriate spatial offset, it should be equivalent to what I've been saying. Yes? I mean, the relativistic doppler shift is the result of dilation in space and time both, so said conversion must account for both the time component and the space component.

GrayGhost

 

[Mike_Fontenot]

[...]
[...] The result is (for units where c has unity magnitude, so I'll leave c out of the equation, for simplicity):

V = v - (L*v*a)/gamma ,
[...]

Note that this equation says that the ONLY instants (of the traveler's life) where V and v are equal, are when any of the following three things are true:

(1) The twins are (at least momentarily) co-located (L = 0),

OR

(2) The traveler is (at least momentarily) not accelerating (a = 0),

OR

(3) Their relative velocity, according to the home-twin, is (at least momentarily) zero (v = 0).

In all other cases, v and V are different ... sometimes QUITE different. Sometimes v and V even have opposite signs ... i.e., sometimes one twin will conclude that (at some given instant in the traveler's life), that their separation is decreasing, whereas the other twin will conclude that their separation is increasing.

Mike Fontenot

 

[GrayGhost]

Mike_Fontenot,

I'm curious, could you please show your derivation for how you arrived at ...

V = v - (L*v*a)/gamma​

GrayGhost

 

[Mike_Fontenot]

Mike_Fontenot,

I'm curious, could you please show your derivation for how you arrived at ...

V = v - (L*v*a)/gamma​

It's not too hard ... give it a try. Here's a roadmap:

You start with the fact that their separation, at any given instant "t" in the traveler's life, according to the traveler, is L/gamma (where L is their separation, according to the home-twin, and both L and gamma are taken as functions of "t", the traveler's age).

Their relative velocity, at the given instant "t", according to the traveler, is then just the derivative of the quantity L/gamma, with respect to "t". If you carry out that differentiation properly, you'll get the result I gave. Along the way, to evaluate the derivatives of L and gamma wrt t, you'll need to express L and gamma as functions of T (the home-twin's age), and make use of the time-dilation result to relate dt and dT.

Mike Fontenot

 

[Dale]

Dale Dale DaleSpam. It's quite interesting you know. The theory demands that no material body can accelerate to speed c, because of energy considerations. Add, speed c represents a cosmic speed limit.

That is only true in inertial reference frames. In non-inertial coordinate systems you can easily have v>c. For example, in the rotating reference frame attached to and co-rotating with the Earth even the nearest star travels an orbit of more than 12 ly/day which is >>c.

Btw, I have not adopted a patronizing tone with you, please do not adopt one with me.

Conceptually, it's quite clear in my mind, personally. Events move in B-space per B while B continues his own proper acceleration.

Then write down the conceptually clear equations so that others may benefit. I suspect that in the process of doing so you will find that it only seems conceptually clear now because you have not actually thought through the details.

A moves superluminally per B from a standpoint of the-change-in-position-over-time.

Which is the definition of velocity.

In this case, IMO, twin A moves superluminally (per B) only if B focuses only on the spatial contraction while ignoring the time dilation component altogether.

What do you mean here? Are you talking about the change in position wrt the change in proper time for A? That would be the spatial component of the four-velocity, which would indeed be useful. The nice thing about the four-velocity is that the spatial component is not limited to <c, and regardless of its value you are guaranteed to not exceed a speed of c.

Indeed, what needs to be done is to math-model the twin B experience as the-collection-of-momentary-colocated-inertial-frames-of-reference that B co-occupies.

I agree completely. This is exactly what you should do if you wish to use this idea.

Wrt another comment you made ... it seems to me that if the Dolby and Gull approach converts doppler shift to the appropriate spatial offset, it should be equivalent to what I've been saying. Yes?

No. It is quite different. See figures 5 and 9 in the link below. Note particularly in figure 9 that the inertial twin's worldline never has v>c in the non-inertial twin's frame (using the standard definition of velocity).

http://arxiv.org/abs/gr-qc/0104077

 

[GrayGhost]

DaleSpam,

There was no intent to offend you in my prior post. I realize that you likely occasionally get folks who post with puns intended, and that posts (as emails) are black-and-white and completely open to interpretation. I will make the attempt to keep my posts cut and dry, de-fun the flavor of the wording.

Just to summarize here, there is the classical velocity definition being the change in position over time, which can be superluminal (eg A per B when B is non-inertial in my illustration). Then there is the velocity as used in the LTs to map spacetime coordinates between systems, and this velocity must be v < c (ie luminal). Therefore, there must be a relationship between the instantaneous "superluminal and luminal" velocity of any body, such that the LTs may be used for transformations. My position is that non-inertial POVs must also use the LTs to map spacetime cooridnates between systems (although there's more to the process than in the all-inertial case), and that "events" are the reference for said relationship. Events do not move in inertial systems, but IMO do move in non-inertial systems. I submit that events move "to the precise tune" that allows B's LT solns (wrt A) to precisely match how A maps locations, events, and clock readouts in his own system, and vice versa.

I'll leave it at that, and take my time to attempt a math model. I'll first search about to see who else has already done so, because I have little doubt many qualified folks have argued my position before me. The conventions you mentioned seem insufficient IMO. Mike Fontenot's approach seems a good one, but I'll need to verify whether his statement regarding "disagreement in current momentary velocity" is warranted. On the surface, that's the one sticking point I have wrt his approach.

Thanx for your time DaleSpam.

Just for reference .,.

https://www.physicsforums.com/attachment.php?attachmentid=32982&d=1299884366"​

GrayGhost

 

[GrayGhost]

Mike_Fontenot,

Thanx Mike. Your approach sounds good. When I'm able to, I'll see what I can come up with model-wise.

GrayGhost

 

[ghwellsjr]

I'll leave it at that, and take my time to attempt a math model. I'll first search about to see who else has already done so, because I have little doubt many qualified folks have argued my position before me.

Is this math model the same one I was asking about here?

Here's another thing I don't understand. You keep talking about an observer using Lorentz Transforms to solve for something involving summing but you have not made it clear what the starting inertial frame is that he is working with, nor the set of events (1 time and 3 spatial coordinates) in that frame, nor the relative speed between that first FOR and the FOR he wants to convert the events in to. And after doing that for one FOR and he does it again for the next FOR, what is it that he sums and what is the significance of the sum? I just have no idea what you are thinking. Please elaborate instead of just repeating the same general recipe.

 

[GrayGhost]

Is this math model the same one I was asking about here?

Indeed it is ghwells. I have never modeled the classic twins scenario. I understand the special theory well enough. Far as the twins scenario goes, I am rather confident in how the LTs apply. My position is quite simple. In flat spacetime, the LTs map spacetime coordinates between 2 systems, inertial or not. Clearly, the non-inertial POV requires more effort than the all-inertial case, because the non-inertial POV has added relativistic effects to deal with (in real-time) that inertial POVs do not.

I'm not certain as yet, however I suspect that Mike Fontenot's approach is the same as my reasoning. Our differences are likely the result of looking at the same thing in 2 different ways. In particular, the issue as to whether twin B and the momentarily co-located MSIRF observer "agree on the twin A velocity at that instant".

DaleSpam sounds rather sure of himself that I will find problems exist in my reasoning if I attempt to model it. Given DaleSpam's knowledge on the subject, I suspect he may well be correct. However, I won't believe it until I prove it to myself.

I appreciate your comments as well ghwells, and I regret not being able to keep up in responding to all your posts. Between DaleSpam and Mike's posts I became somewhat inendated, as I don't have the time to put in like I used to. And I've had some setbacks outside of the forum here that has slowed me down substantially. The case of acceleration is quite interesting, and always quite the challenge.

GrayGhost

 

[Dale]

Just to summarize here, there is the classical velocity definition being the change in position over time, which can be superluminal (eg A per B when B is non-inertial in my illustration). Then there is the velocity as used in the LTs to map spacetime coordinates between systems, and this velocity must be v < c (ie luminal).

The Lorentz transform transforms between different inertial frames where v<c. There is no requirement that v<c in non-inertial reference frames as I have already demonstrated. Again, you can re-define velocity, but you need to be clear that you are doing so. Alternatively, you can leave velocity unchanged and define some other parameter that allows you to select the correct Lorentz transform.

I'll leave it at that, and take my time to attempt a math model.

I think that is a good idea. You will learn a lot in the process regardless of the eventual outcome.

 

[ghwellsjr]

I'm not certain as yet, however I suspect that Mike Fontenot's approach is the same as my reasoning. Our differences are likely the result of looking at the same thing in 2 different ways. In particular, the issue as to whether twin B and the momentarily co-located MSIRF observer "agree on the twin A velocity at that instant".

Do you realize that Mike believes his approach is the only valid way? And that is the argument that we all have with him? Not that his approach is wrong, it's just not preferred, but he thinks it is in some fundamental way. I doubt that you are going to understand his approach unless you get a copy of his paper because he never explains it fully on this forum. He leaves important definitions out of his explanations because he wants everyone to buy his paper for $15. If he explained what is contained in his paper on this forum, why would anyone want to buy his paper?

I have a copy of his paper but it is copywrited. I'd like to discuss his ideas but if I give away all his secrets or quote from his paper, am I violating his copywrite? Is if fair for me to be discussing his ideas on this forum when only he and I (and anyone else with his paper) will know what we are talking about? The last person that was promoting a book he wrote for $8 got instantly banned. Why is Mike still able to promote his $15 paper and not get banned? Huh?

 

[GrayGhost]

The Lorentz transform transforms between different inertial frames where v<c. There is no requirement that v<c in non-inertial reference frames as I have already demonstrated.

Indeed. I do not disagree, assuming one assumes the LTs cannot be used by non-inertial observers, because v must be v < c in the LTs. IMO, there exists a luminal A-velocity that relates to the super-luminal A-velocity noted by twin B, and the luminal v allows twin B to use the LTs to correctly transform between the A and B systems at any B-instant. I just need to prove it :)

Again, you can re-define velocity, but you need to be clear that you are doing so. Alternatively, you can leave velocity unchanged and define some other parameter that allows you to select the correct Lorentz transform.

Wrt your 1st sentence here ... Yes.

Wrt your 2nd sentence here ... Not sure what you mean there. If v>c, no LT transform can be adequately selected for use, because the results will not be correct.

I think that is a good idea. You will learn a lot in the process regardless of the eventual outcome.

It was your idea. The only reason I hadn't pursued a math-model in the past, is because I felt certain it had already been done by many others since 1905. So, we'll see :)

GrayGhost

 

[ghwellsjr]

The only reason I hadn't pursued a math-model in the past, is because I felt certain it had already been done by many others since 1905.

This shows that you lack a basic understanding of Einstein's theory presented in his 1905 paper. He didn't talk about non-inertial frames and he didn't talk about each observer in a scenario being stationary in their own frame or having their own rest frame. His original version of the Twin Paradox had the traveler going in a big circle with the inertial observer located at one point on the circle, not at its center. The traveler is never inertial and yet Einstein analyzes him using a frame in which the inertial observer is stationary. Get it? One inertial frame to analyze all observers. That was Einstein's theory.

 

[GrayGhost]

Do you realize that Mike believes his approach is the only valid way? And that is the argument that we all have with him? Not that his approach is wrong, it's just not preferred, but he thinks it is in some fundamental way.

Yes and yes, I realize that.

I doubt that you are going to understand his approach unless you get a copy of his paper because he never explains it fully on this forum. He leaves important definitions out of his explanations because he wants everyone to buy his paper for $15. If he explained what is contained in his paper on this forum, why would anyone want to buy his paper?

I think I understand Mike's approach, since it's similar to what I myself have long envisioned, if not the very same thing. Although ...

I do have a disagreement with Mike on one particular matter (ie instantaneous A-velocity per B), however I'm not sure it matters far as his spacetime solutions are concerned. The way I see it, he's making correct assumptions w/o knowing WHY they are correct. I believe I have the soln to that matter, and it not only validates his assumptions but also explains WHY superluminal A-motion arises per the non-inertial B POV ... and also how a superluminal motion equates to an equivalent LT luminal velocity. So, I kill 2 (or 3) birds with 1 stone there, and possible w/o changing Mike's model's solns at all.

I have a copy of his paper but it is copywrited. I'd like to discuss his ideas but if I give away all his secrets or quote from his paper, am I violating his copywrite? Is if fair for me to be discussing his ideas on this forum when only he and I (and anyone else with his paper) will know what we are talking about? The last person that was promoting a book he wrote for $8 got instantly banned. Why is Mike still able to promote his $15 paper and not get banned? Huh?

If I cannot discuss his work after having bought it, then I see no reason to buy it in the first place.

I wouldn't ban any fellow for periodically mentioning his published paper is available for purchase, if it relates to the discussion at hand. If the posts become "too often, or chronic-sales-pitch-in-flavor", then maybe so. I don't think Mike falls into that category from what I've seen here, personally.

What sounds promissing is that you and DaleSpam seem to agree his paper is valid. I've read many papers that weren't worth a penny, and in fact I should have been paid for the time I wasted reading it. Some journals will publish almost anything, and I'll never know why they keep their reviewers.

Did buying Mike's paper help you in any respect?

GrayGhost

 

[GrayGhost]

This shows that you lack a basic understanding of Einstein's theory presented in his 1905 paper.

I understand the special theory as well as you do, probably better.

He didn't talk about non-inertial frames ...

OEMB section 3: It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide. If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the traveled clock on its arrival at A will be ½tv²/c² seconds slow.​

In a theory devoid of gravity, it seems to me that a clock moving in a continuously curved line is non-inertial. Therefore, even though Einstein's SR was a theory of uniform translatory motion, he extrapolated what the effect of acceleration would be based upon the all-inertial theory.

All I've been doing here in this thread ghwells, is hypothesizing by extrapolation (of the special theory) how twin B might apply the LTs to accurately transform his spacetime coordinates into the twin A system. Clearly, twin B cannot apply the LTs as easily as one would in the all-inertial scenario. That point was made way back yonder, and it's not as though anyone didn't already know it.

... and he didn't talk about each observer in a scenario being stationary in their own frame ...

OEMB section 1: We might, of course, content ourselves with time values determined by an observer stationed together with the watch at the origin of the co-ordinates, and ...​

and that statement allows us to imagine the same anywhere else in the OEMB paper, including section 3 where the LTs are derived. Although it does not have to be, said coordinate system may well be assigned by the observer to himself, as his own frame of reference.

His original version of the Twin Paradox had the traveler going in a big circle with the inertial observer located at one point on the circle, not at its center. The traveler is never inertial and yet Einstein analyzes him using a frame in which the inertial observer is stationary. Get it? One inertial frame to analyze all observers. That was Einstein's theory.

Get it? You're kidding, yes?

So now I must ask you, why did you feel the need to tell me all this in the first place? What's your motive here?

GrayGhost

 

[Dale]

It was your idea.

Hehe, yes, I do tend to think my own ideas are good ideas

What sounds promissing is that you and DaleSpam seem to agree his paper is valid.

I have not read his paper, since I am unwilling to pay for it. However, I have no objection to what he has described of his CADO equation on this forum. My objection is limited to his occasional incorrect claims that his CADO convention is the only correct simultaneity convention for a non-inertial observer and all other conventions are wrong. He has avoided making that claim in this thread, so I am OK with what he has said here.

 

[ghwellsjr]

I think I understand Mike's approach, since it's similar to what I myself have long envisioned, if not the very same thing.

Good, here is a post that Mike linked to in his first post on this thread (page 11, post #167)

I would say that there IS a valid frame for an accelerating observer.

That frame consists of the (infinite) collection of inertial frames (the MSIRFs), one for each instant of the accelerating observer's life, each of which being momentarily stationary wrt the accelerating observer at that given instant in his life.

This frame is a well-defined...there is no ambiguity or inconsistency at all. And it is NOT a "convention": there are no other reasonable alternatives, because it is the ONLY possible frame for the accelerating observer which doesn't contradict his own elementary measurements and elementary calculations.

Maybe you could tell us what he means by "elementary measurements and elementary calculations", because he won't tell us:

Those elementary observations and elementary calculations are given, in detail, in my paper. I'm not willing to reproduce them here.

Oh, now he calls them "elementary observations and elementary calculations". I guess "observations" is the same as "measurements". In any case, since you think you understand his approach, and it is similar, if not identical to what you have long envisioned, what exactly does he and would you mean by these terms?

What sounds promissing is that you and DaleSpam seem to agree his paper is valid.

I wonder why you think that. Can you provide the link that gave you this idea?

Did buying Mike's paper help you in any respect?

Help me? You mean help me understand his position? Yes, I believe I understand exactly what his fatal mistake is.

 

[ghwellsjr]

This shows that you lack a basic understanding of Einstein's theory presented in his 1905 paper.

I understand the special theory as well as you do, probably better.

I'm sure you do, but I was talking about Einstein's theory presented in his 1905 paper which you alluded to in a previous post. Special Relativity has evolved since then in all kinds of directions which I have never seen the need to investigate and I don't claim to understand these additions to what Einstein first presented.

He didn't talk about non-inertial frames ...

OEMB section 3: It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide. If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the traveled clock on its arrival at A will be ½tv²/c² seconds slow.​

In a theory devoid of gravity, it seems to me that a clock moving in a continuously curved line is non-inertial. Therefore, even though Einstein's SR was a theory of uniform translatory motion, he extrapolated what the effect of acceleration would be based upon the all-inertial theory.

(Please note, you are quoting from the end of section 4, not 3.)

Your comments show that you don't understand the difference between a non-inertial object/observer and a non-inertial frame of reference. This indicates to me that you have this erroneous concept that Special Relativity requires you to assign each object/observer to its own frame. This is completely wrong.

Einstein's SR is a theory about a single inertial frame of reference in which all objects/observers are described and analyzed, and each object/observer can have its own velocities and/or accelerations but still described by that one single frame. In this example, he talks about two clocks, one at rest at location A and the other traveling in a circle starting at A, moving away from A, and then returning to A, accelerating all the time. In other words, this clock is non-inertial. But he doesn't assign a non-inertial frame of reference to it in which it is continuously at rest nor does he assign a series of inertial frames to it in which the clock is at rest in all of them. He wasn't extrapolating SR from an all-inertial theory to include accleration. In fact, if you read the paragraph immediately before the one you quoted, you will see:

From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by ½tv²/c²(up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.​

Now, after you describe and analyze all the stationary, moving, and accelerating objects and observers in a scenario according to one inertial frame of reference, you can switch to a different inertial frame of reference which is described as having a motion with respect to the first frame of reference. And then by looking at the space-time coordinates of different events in the first frame, you can use the Lorentz Transform to see what the space-time coordinates are in the second inertial frame. That's what SR is all about.

All I've been doing here in this thread ghwells, is hypothesizing by extrapolation (of the special theory) how twin B might apply the LTs to accurately transform his spacetime coordinates into the twin A system. Clearly, twin B cannot apply the LTs as easily as one would in the all-inertial scenario. That point was made way back yonder, and it's not as though anyone didn't already know it.

I always wonder why anyone would want to go from one inertial frame to another inertial frame, I can't image why you would want to try to go from an inertial frame to a non-inertial frame. What's the point? Suppose you can find someone who has done this somewhere during the last century or suppose you figure out how to do it on your own. What do you learn by doing this?

Take for example the Twin Paradox. It is most easily described and analyzed using a frame of reference in which both twins start out at rest. You get your answer, the traveling twin has aged less upon his return. You know that any other frame will yield the same answer, so why do it? Even if you knew how to use a non-inertial frame (or a series of inertial frames) in which the traveler was always at rest to describe the scenario, why do it? You're going to get the same answer.

... and he didn't talk about each observer in a scenario being stationary in their own frame ...

OEMB section 1: We might, of course, content ourselves with time values determined by an observer stationed together with the watch at the origin of the co-ordinates, and ...​

and that statement allows us to imagine the same anywhere else in the OEMB paper, including section 3 where the LTs are derived. Although it does not have to be, said coordinate system may well be assigned by the observer to himself, as his own frame of reference.

Here's the whole quote:

We might, of course, content ourselves with time values determined by an observer stationed together with the watch at the origin of the co-ordinates, and co-ordinating the corresponding positions of the hands with light signals, given out by every event to be timed, and reaching him through empty space. But this co-ordination has the disadvantage that it is not independent of the standpoint of the observer with the watch or clock, as we know from experience. We arrive at a much more practical determination along the following line of thought.​

Einstein was rejecting this idea because it doesn't work and he proceeded to describe a method that does work. And he wasn't describing a frame of reference here. He was describing what happens when you separate time from space and treat them as independent absolutes.

His original version of the Twin Paradox had the traveler going in a big circle with the inertial observer located at one point on the circle, not at its center. The traveler is never inertial and yet Einstein analyzes him using a frame in which the inertial observer is stationary. Get it? One inertial frame to analyze all observers. That was Einstein's theory.

Get it? You're kidding, yes?

So now I must ask you, why did you feel the need to tell me all this in the first place? What's your motive here?

GrayGhost

My motive is to help you learn, and I hope you get it this time.

 

[GrayGhost]

Good, here is a post that Mike linked to in his first post on this thread (page 11, post #167)

Maybe you could tell us what he means by "elementary measurements and elementary calculations", because he won't tell us:

Oh, now he calls them "elementary observations and elementary calculations". I guess "observations" is the same as "measurements". In any case, since you think you understand his approach, and it is similar, if not identical to what you have long envisioned, what exactly does he and would you mean by these terms?

Observations = measurements, per most folks.

Wrt Mike Fontenot's "elementary observations and elementary calculations", I can only guess what he means. There are 2 issues at hand here ...

First ... to correctly map spacetime cooridnates between systems, one must first determine where the other fellow is in your own system, and the method you use must match mother nature. One thing's for certain, while non-inertial, B cannot assume A sits at half the EM's roundtrip length. Twin B must keep track of his proper acceleration every inch the way, and incorporate that into the estimated location of twin A. Or, B may also use the receipt of light signals "of known proper frequency upon transmission" to determine (via doppler shift) the relative range to A, although that may be more difficult and less accurate. In either case, the latest known location of A corresponds to the prior reflection event contained in the latest received EM signal, not anytime thereafter (which would be a guess). In any case, once B knows where A was at the reflection event, then ...

Second ... if the LT calculation (that B runs for A) is correct, then the results must precisely match what twin A then observes (measures) and calculates ... Twin B has his LT calculated A-clock readout and the associated B-range per A at that time. When twin A "observes" his current clock readout at that B estimated time value, twin A then possesses a calculated B-range at that instant based on (what Mike says) his own observations, measurements, and calculations. Twin A's calculated B-range at said A-time must precisely match the twin B LT space-transform result, or someone screwed up somewhere.

The idea is this ... we already have a special theory that maps spacetime cooridnates between inertial systems. The goal is to apply the LTs in the non-inertial case, and in a way that is completely consistent with the special theory, even if the process is not identical. If it is inconsistent with the special theory, then it's no good. Also, all observers must concur on all results, including their expected disagreements due to relative simultaneity (as in the special theory).

I wonder why you think that. Can you provide the link that gave you this idea?

Well, DaleSpam had just stated here that he's had no problem with Mike's approach. He and you both have stated that you are not arguing about his model, but rather only that he believes it's the only correct approach. I'm pretty sure you had just stated that recently here.

Help me? You mean help me understand his position? Yes, I believe I understand exactly what his fatal mistake is.

Pray tell :) I'd like to hear this !

GrayGhost

 

[GrayGhost]

I'm sure you do, but I was talking about Einstein's theory presented in his 1905 paper which you alluded to in a previous post. Special Relativity has evolved since then in all kinds of directions which I have never seen the need to investigate and I don't claim to understand these additions to what Einstein first presented.

Well, I too learned SR straight from the 1905 paper as well. IMO, it's by far the best way. Minkowski evolved Einstein's SR graphically w/o changing it, and added much to its meaning. Others did as well, eg (say) Terrell, Penrose, and Loedel. Others, extended the SR to the case of acceleration, eg Rindler for example. I do not see that anyone has since altered the original 1905 OEMB. It's still correct as written under the scope for which it was considered.

Please note, you are quoting from the end of section 4, not 3.

Indeed, good eye. Section 4 it was.

Your comments show that you don't understand the difference between a non-inertial object/observer and a non-inertial frame of reference...

Now now. You should consider that you may be reading something into my statements that are not there.

This indicates to me that you have this erroneous concept that Special Relativity requires you to assign each object/observer to its own frame. This is completely wrong...

If it does indicate to you as such, then you're mis interpreting what I said. There is no requirement to assign coordinate systems to anything including oneself, however one may also always imagine it is done so even if it was not. There's no harm in it.

Einstein's SR is a theory about a single inertial frame of reference in which all objects/observers are described and analyzed, and each object/observer can have its own velocities and/or accelerations but still described by that one single frame.

Of course. I just can't figure out why you feel the need to tell me? I could tell you the same thing, but what good does it do?

In this example, he (Einstein) talks about two clocks, one at rest at location A and the other traveling in a circle starting at A, moving away from A, and then returning to A, accelerating all the time. In other words, this clock is non-inertial. But he doesn't assign a non-inertial frame of reference to it in which it is continuously at rest nor does he assign a series of inertial frames to it in which the clock is at rest in all of them. He wasn't extrapolating SR from an all-inertial theory to include accleration.

Indeed, he did not assign any coordinate system to the accelerating clock. This doesn't mean that one cannot imagine an observer carrying the clock, who assigns himself the origin of a coordinate system he calls his own. Bottom line, it was an extrapolation of the LTs by Einstein to the accelerational case. Here's what he did ...

As you pointed out, said OEMB scenario presented an accelerating clock from the POV of an inertial clock. Of course, because the LTs are based upon the POV of a stationary observer. However, the LTs were also designed for moving inertial bodies of constant v. Einstein tactically specified that his accelerating clock move at a constant velocity v, while it moved in curvilinear motion. As you know, gamma does not depend upon the direction of motion, but rather only the relative speed. Therefore, since his accelerating clock is always the same specific v in any instant, the value of gamma must remain constant as well, since it depends on v (ie speed) and not x or t. So per the stationary POV, the accelerating clock must tick slower by the same rate an always inertial clock of the same velocity would.

Equally tactical, Einstein begins and ends the interval with the 2 clocks colocated, and so no observer in the cosmos may disagree on the outcome. The accelerating clock must tick slower per the stationary clock, and thus must age less over the common interval. However, although the accelerating clock must agree that it ages less, Einstein makes no conjecture as to the relative rate of that always-inertial clock per the accelerating clock. However, just the fact that the accelerating clock must age less over the defined interval, was an extrapolation of the special case to the more general case. My opinion is that the LTs also apply from the non-inertial POV, although the process of their application is not so easy.

From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by ½tv²/c²(up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.​

Now, after you describe and analyze all the stationary, moving, and accelerating objects and observers in a scenario according to one inertial frame of reference, you can switch to a different inertial frame of reference which is described as having a motion with respect to the first frame of reference. And then by looking at the space-time coordinates of different events in the first frame, you can use the Lorentz Transform to see what the space-time coordinates are in the second inertial frame. That's what SR is all about.

Indeed. Again, I have no idea why you are telling me this as though I do not know?

I always wonder why anyone would want to go from one inertial frame to another inertial frame, ...

Well, amonst other things, it does explain why the muon decays (as it does) as it transcends the atmosphere to earth. If folks could fly at luminal speeds from here to there, it would be nice to know in advance how much you'll age relative to others over the interval. Another way of looking at it, let's say you have intel that Darth Vader will emit a particle beam that destroys Earth at 11:24pm by his own clock. You can predict the last moment you can destroy him before he destroys the earth, assuming he flies inertially over the interval and you knew his clock readout at some prior point :)

... I can't image why you would want to try to go from an inertial frame to a non-inertial frame. What's the point? Suppose you can find someone who has done this somewhere during the last century or suppose you figure out how to do it on your own. What do you learn by doing this?

The point would be for the same reasons I mentioned above for the all-inertial case.

What you would learn is how mother nature really works. The LTs show how the dimensions are related by velocity under an invariant c. That's a great advancement in physics, and cosmology as well. The LTs explain the nature of spacetime in the special case. If our understanding of the nature of spacetime can be extended to the more general case (devoid of gravity), I see it as no less important than the advancement under the special case.

Add, folks are generally very interested in answering the questions that remain unanswered. Often, there are many different opinions as to how to answer a yet unanswered question. That usually suggests that all those competing theories are wrong. Usually, when the correct theory arises, everyone knows it and agrees, although it may take some time to be accepted. Beyond SR, if there is a correct transformation between any 2 frames in flat spacetime, then I for one want to know what it is.

... My motive is to help you learn, and I hope you get it this time.

I'll give you an A for persistence :) I hope you feel like you helped me get whatever it is that you believed I need.

GrayGhost

 

[Dale]

One thing's for certain, while non-inertial, B cannot assume A sits at half the EM's roundtrip length.

Sure he can. See the Dolby and Gull figure 9 that I pointed out earlier.