Age-Changes Caused By Instantaneous Velocity-Changes

[Mike_Fontenot]

When Tom makes a sharp change in velocity, his line of simultaneity "swings" to point at a different event on Sue's worldline than it did just before the velocity change; you're just calculating the "size of the swing" based on the change in velocity and the distance from Sue.

Yes, that's it.

It's interesting, but I'm not sure why Tom should care in the general case; the only time this calculation would have any meaning for him is if he comes back to meet up with Sue again [...]

I don't agree. I don't think ANYONE, who was on a long, distant space voyage, and who left someone behind on Earth that he cares about, could possibly accept being told that "the current age, of your distant loved one" is a meaningless concept. Or that he shouldn't even ASK the question "Wonder what my loved one might be doing right now?".

I think ANYONE would be convinced that his loved ones still exist (assuming that they are still alive), even though they are a long way away. And I don't think any traveler would EVER accept being told that their loved one "simply HAS no age, right now".

Of course, the above comments fall in the realm of philosophy, not physics. Physics certainly allows the view that simultaneity between separated persons is meaningless. But good luck selling that view to actual space travelers, whether they are used-car salesmen, or physicists.

For a traveler who never accelerates, the Lorentz equations unambiguously tell the traveler what the current age of a distant person is. (The Lorentz equations relate times and positions in two different inertial reference frames: the inertial frame in which the traveler is permanently stationary, and the inertial frame in which the distant person is permanently stationary). And what those equations tell the traveler is EXACTLY what his own elementary measurements and calculations tell him.

It is my contention that the same thing is also true for a traveler who accelerates ... the only difference is that the other inertial reference frame in the Lorentz equations (other than the distant person's inertial frame) is constantly changing, from each instant in the traveler's life to the next. I call that inertial frame, at any given instant, t, in the traveler's life, the "MSIRF(t)", which stands for the "Momentarily Stationary Inertial Reference Frame, at age t in the traveler's life".

Mike Fontenot

 

[PeterDonis]

I don't think ANYONE, who was on a long, distant space voyage, and who left someone behind on Earth that he cares about, could possibly accept being told that "the current age, of your distant loved one" is a meaningless concept. Or that he shouldn't even ASK the question "Wonder what my loved one might be doing right now?".

I think ANYONE would be convinced that his loved ones still exist (assuming that they are still alive), even though they are a long way away. And I don't think any traveler would EVER accept being told that their loved one "simply HAS no age, right now".

This claim is easy to falsify: there are plenty of other commenters in this thread (including me) who would evidently have no problem accepting this.

Also, the standard physics view doesn't quite say that "the current age of your distant loved one" is a *meaningless* concept; it just says there are limits on how precisely you can specify it. True, any point on the distant loved one's worldline that is spacelike separated from the "present" instant on your worldline could potentially correspond to "now", if you made the appropriate velocity change; but that still leaves plenty of points that are either in your past light cone (these are points you've already received light signals from--Sue's fourth birthday party, perhaps) or your future light cone (points you can still send light signals to--you still have time to transmit the message for Sue's eightieth birthday, say, so that she'll receive it on the day). It's certainly meaningful to say that Sue's "current age" has to be older than the latest event you saw a light signal from (she's older than 4) and younger than the earliest event you can still send a light signal to (she's younger than 80).

But, for example, if Sue got married at age 25, and that event on her worldline is spacelike separated from you, you don't (yet) know that she's married, or when she got married, so even the CADO equation can't tell you whether the statement "Sue is married *right now*" is true or false.

So I can see how separating the past and future light cones from the spacelike separated events would have direct meaning, as in the examples I just gave; and of course this separation will change as you go (more events come into the past light cone, and more events go out of the future light cone--if you don't send Sue's anniversary message in time, it can't arrive in time). But at any given point on your worldline, I don't see a meaningful distinction between different events that are both spacelike separated, since you won't yet have seen light signals from any of them, so you can't make any meaningful statements about them because you lack the information.

Of course, the above comments fall in the realm of philosophy, not physics. Physics certainly allows the view that simultaneity between separated persons is meaningless. But good luck selling that view to actual space travelers, whether they are used-car salesmen, or physicists.

Well, you're proposing to tell them things like "yesterday, before you made that quick velocity change, Sue was 72 years old, but now she's a teenager." Furthermore, as I showed above, you won't even *know* whether your velocity change also implied, by your logic, that "Sue was married yesterday but she's not married now", without Sue ever getting a divorce, annulment, being widowed, etc. anywhere along the part of her worldline that your line of simultaneity swept over during the velocity change. I'm not sure that will sell any better than the standard physics view.

 

[Mike_Fontenot]

[...]
The reason for the inconsistency is that a coordinate system (at least in physics) is supposed to assign only one value of (time, position) to an object.
[...]

I'm assuming that you intended to say "an event", rather than "an object", in your above statement.

I don't accept the necessity of that requirement.

What IS required, is that at ANY instant, t, in the traveler's life, that ANY given object (anywhere in the (assumed) flat universe of special relativity), has a well-defined (single-valued) position in the traveler's coordinate system, at that instant. The MSIRF(t) coordinate system (which I have also sometimes referred to as "the CADO coordinate system") fulfills that requirement.

It IS certainly bizarre that the question (when asked of a traveler who has undergone acceleration), "How old were you when that distant person was 40 years old?" can have more than one answer ... the traveler may well (correctly) respond "When she was 40 years old, I was 20, 23, and 30 years old". It's bizarre, maybe even unpalatable for some, but it's not inconsistent.

Mike Fontenot

 

[Mike_Fontenot]

This claim is easy to falsify: there are plenty of other commenters in this thread (including me) who would evidently have no problem accepting this.

It won't be falsified until some human has made that kind of voyage, and truly has not experienced the feelings that I described ... no one has yet.

[...]
Also, the standard physics view doesn't quite say that "the current age of your distant loved one" is a *meaningless* concept
[...]

Some physicists contend that only invariant quantities have any meaning. Simultaneity isn't invariant.

[...]
But, for example, if Sue got married at age 25, and that event on her worldline is spacelike separated from you, you don't (yet) know that she's married, or when she got married, so even the CADO equation can't tell you whether the statement "Sue is married *right now*" is true or false.
[...]

Of course not. But it may tell me, at some instant in my life, that my well-loved daughter is currently four years old, so I can probably rule out the possibility that she is currently married. At some earlier time in my life, it may have previously told me that she was then 130 years old, and I was then able to rule out much chance that she was still alive ... although I could have imagined that she might have been married at some time in her life, and maybe had a whole passel of kids. It's weird ... but sometimes that's just the way nature is, like it or not.

Mike Fontenot

 

[PeterDonis]

It won't be falsified until some human has made that kind of voyage, and truly has not experienced the feelings that I described ... no one has yet.

...

Of course not. But it may tell me, at some instant in my life, that my well-loved daughter is currently four years old, so I can probably rule out the possibility that she is currently married. At some earlier time in my life, it may have previously told me that she was then 130 years old, and I was then able to rule out much chance that she was still alive ... although I could have imagined that she might have been married at some time in her life, and maybe had a whole passel of kids. It's weird ... but sometimes that's just the way nature is, like it or not.

I could make the same kind of argument for the standard physics view: "There is no definite answer to the question, How old is my daughter *right now*? It's weird--but sometimes that's just the way nature is, like it or not."

Your reason for preferring your argument over mine is essentially emotional--you don't think that, when humans start actually traveling at relativistic speeds, they will *like* being told that there is no definite answer to the question of how old their loved ones are *right now*. But you do, apparently, think they will like (or at least prefer) being told that yesterday their loved ones were most likely dead but today they're just toddlers, and tomorrow, when the rocket changes course again, they will be most likely dead once more. In other words, your claim (in so far as it goes beyond simply calculating numbers according to your equation, and tries to say what those numbers "really mean") isn't really a claim about physics per se; it's a claim about human psychology and how humans will react in a given (currently hypothetical) situation.

As such, your claim seems highly implausible to me based on what I have experienced of human psychology; but I agree that, strictly speaking, we won't know for sure until humans actually start making such trips and having to consider such questions for real, as opposed to just discussing them abstractly.

Some physicists contend that only invariant quantities have any meaning. Simultaneity isn't invariant.

Simultaneity as such isn't invariant, but the event at which a particular spacelike geodesic (such as the "lines of simultaneity" your equation calculates) crosses a particular timelike worldline *is* invariant; your equation simply calculates the time coordinates, on Sue's worldline, of such events. I'm not saying that a number such as that is necessarily "meaningless"; I'm just saying I don't think it means what you think it means. But, as I noted above, whether "what you think it means" is reasonable is really a question about human psychology, not physics.

 

[PAllen]

Separating the question of what is seen versus the interpretation you give it, might clarify this discussion. What is seen (e.g. captured on a video camera) is a physical observable. Interpreting the movie will involve assumptions beyond observable physics.

Imagine the 'instant turnaround twin' is looking through a telescope at an image of clock with the 'stationary twin'. Before the twins separated, of course, assume they synchronized clocks and know each have the same (white) clock. Passing the point of instant turnaround the turning twin sees:

- clock changes from red to blue
- clock reads just a moment later than before
- clock's hands are suddenly moving much faster than before (but no jump in time
shown on image)
- clock appears further away
- clock has rotated

The statement that this is what is seen (or filmed) is physics. I claim essentially anything else is interpretation, and that several interpretations are equally plausible. Mike_Fontenot is focused on the idea that since the clock suddenly looks farther away, the event of its image emission must be earlier than the event of image emission of the clock received just before turnaround. This, despite the fact that the time shown on the clock has moved forward not backwards, and we can assume we 'know' we are actually observing the world line of real clock. What about the color change? Is that 'real'? If I accept the color change as an artifact of relative motion, not any indication about the real clock of the stationary twin, I can accept any or all of the other changes as being artifacts as well. For example, my twin promised he wouldn't rotate his clock. So do I believe he is a liar or that the rotation is a visual artifact of relative motion?

I personally would reason as follows:

The more we separated at high speed, the less meaningful it becomes to talk about where they are 'right now'. The sudden change in apparent visual distance coincident with my sudden turnaround I would believe to be a visual artifact. I assume the distant clock I am observing is, in fact, white (not red or blue), and did not jump at infinite speed; the apparent infinite speed jump I would think has character similar to a phase velocity.

If I insist on matching image emission events to points earlier on my worldline (from when I see them), then I have several choices at turnaround, none 'objectively true':

a) Switch matching schemes after turnaround. I relabel all matching assignments I made earlier to be consistent with the new scheme; thus I treat all previously observed images to have been sent earlier than I thought a moment ago. I do not believe anything has gone back in time, I have just switched all my interpretations to a new scheme based on what I see now.

b) I can blend from my old scheme to my new scheme, such that no prior matching needs to be relabeled and after some amount of time I am matching events based completely on my new state of motion.

The arbitrary character of either of these just shows that it is arbitrary which events with spacelike separations you declare simultaneous.

 

[Dale]

I don't accept the necessity of that requirement.

This requirement is not some optional feature like a car's luggage rack. It is an essential part of the definition of a coordinate chart. If your mapping does not fulfil this requirement (one-to-one map between points in the manifold and points in R(N)) then it simply is not a coordinate chart by definition.

Btw, the whole discussion regarding how people would feel about the age of their loved ones is a ridiculous red herring that has nothing to do with the physics.

 

[Dale]

According to your proposed frame for Tom, describe (in detail) the plot of Sue's age, versus Tom's age, according to Tom. Also, describe the plot of Sue's age, versus Tom's age, according to Sue.

Attached are the plots of Sue's age vs Tom's age using Passionflower's method for Tom (which was particularly simple to calculate), and Tom's age vs Sue's age using the standard inertial frame for Sue. I slightly modified the problem to use v = 0.6 c so that the numbers would be nicer, but I thought that to be an immaterial change.

Now that I have met your challenge, it is your turn to define your terms and to show one example of any measurement which is not correctly predicted by any arbitrary coordinate system.

 

[matheinste]

But it may tell me, at some instant in my life, that my well-loved daughter is currently four years old, so I can probably rule out the possibility that she is currently married. At some earlier time in my life, it may have previously told me that she was then 130 years old, and I was then able to rule out much chance that she was still alive ... although I could have imagined that she might have been married at some time in her life, and maybe had a whole passel of kids. It's weird ... but sometimes that's just the way nature is, like it or not.

Mike Fontenot

You cannot "know" anything about an event which is not colocated (the word here is used loosely) with you, you can only predict with varying degrees of certainty. The fact that we have to define what we mean by now for such events shows this. The concept of "knowing" something about an object/person not colocated with you is completely useless for physics, although of course the predictions that the laws of physics lead us to about such objects are extremely useful and used all the time.

I cannot even conceptually grasp the meaning of the word "now" in such a context. I understand that various conventions can be used, but the fact that we have this choice is further proof of the lack of any natural definition, but of course some conventions are more "intuitively" satisfying than others.

Excuse my perhaps irrelevant ramblings, but any misconceptions related to "time at a distance", which usually rears its head and wastes enromous amounts of time in the "twin paradox" bugs me.

Matheinste.

 

[Mike_Fontenot]

[...]
Imagine the 'instant turnaround twin' is looking through a telescope at an image of clock with the 'stationary twin'. [...] Passing the point of instant turnaround the turning twin sees:
[...]
- clock appears further away
[...]

As long as the MAGNITUDE of the velocity stays the same before and after the velocity change (as it does in this example), then the apparent size of the image is exactly the same immediately after and immediately before the instantaneous velocity change. The distance to the home twin, according to the traveler, is L/gamma, where L is the distance according to the home twin. Gamma has the same value for v = +0.866 as it does for v = -0.866.

Mike Fontenot

 

[Mike_Fontenot]

I could make the same kind of argument for the standard physics view: "There is no definite answer to the question, How old is my daughter *right now*? It's weird--but sometimes that's just the way nature is, like it or not."

Your reason for preferring your argument over mine is essentially emotional [...]

I made it clear in my post that those particular comments of mine WERE philosophy, not physics. But there IS an argument that is pure physics (which I have given several times before), as to why I contend that the only valid reference frame for the traveler is the CADO frame: any other frame will contradict the traveler's own elementary measurements and calculations. And I have indicated before that those elementary measurements and calculations involve the determination by the traveler of how much the home twin ages during the transit of the images giving her age at the instants that the images are transmitted.

Mike Fontenot

 

[PeterDonis]

But there IS an argument that is pure physics (which I have given several times before), as to why I contend that the only valid reference frame for the traveler is the CADO frame: any other frame will contradict the traveler's own elementary measurements and calculations.

Others have commented (and continue to comment) on this part of your argument, so I won't say much about it. I'll only comment that, since all the events on Sue's worldline that *could* be labeled as "now" by Tom, at any given event on Tom's worldline (which particular event on Sue's worldline was "now" by your equation would depend on Tom's velocity and distance relative to Sue) are spacelike separated from Tom at the point where Tom labels them "now", the choice of labeling can make no difference to any actual physical measurement Tom makes. If you can present an actual physical measurement Tom can make that will give different results depending on which spacelike separated event on Sue's worldline Tom labels "now", then you have something much more than just an interesting equation: you have an alternate theory of physics that contradicts relativity.

 

[Dale]

But there IS an argument that is pure physics (which I have given several times before), as to why I contend that the only valid reference frame for the traveler is the CADO frame: any other frame will contradict the traveler's own elementary measurements and calculations.

Which is not a valid argument since you are unable or unwilling to define your key terms. As JesseM asserts, the only way for your statements to be true is for you to define "elementary measurements and calculations" in such a way as to make your statement a tautology. You also have failed to provide one single example of a situation where any valid coordinate system gave a wrong result for any measurement.

 

[PAllen]

As long as the MAGNITUDE of the velocity stays the same before and after the velocity change (as it does in this example), then the apparent size of the image is exactly the same immediately after and immediately before the instantaneous velocity change. The distance to the home twin, according to the traveler, is L/gamma, where L is the distance according to the home twin. Gamma has the same value for v = +0.866 as it does for v = -0.866.

Mike Fontenot

Right, thanks, for symmetric turnaround you don't see a change in distance. Even more argument that there is no plausible basis for the turnaround twin to change their simultaneity labeling unless 'they feel like it'. The apparent distance over c just before and just after turnaround will be the same in this case, so the simplest interpretation for time of emission will be that it stays the same. You have a simple, continuous, logical (though still not physically required) match up of emission events and corresponding events on the turnaround twin's worldline.

The more complex choices I described would only apply to asymmetric turnaround (return trip at different speed, relative to 'stationary' twin, than outward trip).

 

[PAllen]

Right, thanks, for symmetric turnaround you don't see a change in distance. Even more argument that there is no plausible basis for the turnaround twin to change their simultaneity labeling unless 'they feel like it'. The apparent distance over c just before and just after turnaround will be the same in this case, so the simplest interpretation for time of emission will be that it stays the same. You have a simple, continuous, logical (though still not physically required) match up of emission events and corresponding events on the turnaround twin's worldline.

The more complex choices I described would only apply to asymmetric turnaround (return trip at different speed, relative to 'stationary' twin, than outward trip).

Actually, I was right the first time. The question is, what event on the stationary twin's world line is seen at the turnaround point? It is not the halfway point of the stationary twin's world line. It is, in fact, the event (in stationary twin's coordinates):

t = T(1 - v/c)
x = 0

where T is the turnaround time in stationary twin's coordinates. This event changes from perceived (by turnaround twin) distance:

T*v (1 - v/c) / gamma

to

T*v (1 + v/c) / gamma

Thus, I stand by my original post #56 in all particulars.

 

[PAllen]

Actually, I was right the first time. The question is, what event on the stationary twin's world line is seen at the turnaround point? It is not the halfway point of the stationary twin's world line. It is, in fact, the event (in stationary twin's coordinates):

t = T(1 - v/c)
x = 0

where T is the turnaround time in stationary twin's coordinates. This event changes from perceived (by turnaround twin) distance:

T*v (1 - v/c) / gamma

to

T*v (1 + v/c) / gamma

Thus, I stand by my original post #56 in all particulars.

Note also, that the question of what event on the 'stationary twin's' world line is seen at turnaround is invariant physics (it is the time seen on the image of the stationary twin's clock, by the turnaround twin at moment of turnaround). On the other hand, what event on the turnaround twin's world line (in the past of the turnaround) corresponds to this emission event is pure convention. The distance is also interpretation (parallax distance and radar distance will differ).

 

[Mike_Fontenot]

According to your proposed frame for Tom, describe (in detail) the plot of Sue's age, versus Tom's age, according to Tom. Also, describe the plot of Sue's age, versus Tom's age, according to Sue.

Attached are the plots of Sue's age vs Tom's age using Passionflower's method for Tom (which was particularly simple to calculate), and Tom's age vs Sue's age using the standard inertial frame for Sue.
[...]

If you look at the two quotes above, you can see that you didn't provide the two plots I asked for. But it's easy enough to translate what you provided, into what I asked for.

I came to an immediate conclusion about the suitability of your reference frame for the traveler. But I'm going to delay giving my critique, because I want to see if any other forum members realize the obvious problem with it. Is anyone awake out there?

Mike Fontenot

 

[Mike_Fontenot]

If you look at the two quotes above, you can see that [Dalespam] didn't provide the two plots I asked for. But it's easy enough to translate what [Dalespam] provided, into what I asked for.

If any forum members want to construct their own rough sketches of the plots I asked for, by translating from Dalespam's plots, then to get the big picture, you should plot the entire ranges of the two twin's ages, starting from zero age, and stopping about 5 years beyond when the traveler does his second velocity change. Also, use the same scale for each axis. (And note that for both plots, the home twin's age should be plotted vertically, and the traveler's age is plotted horizontally).

Mike Fontenot

 

[Dale]

If you look at the two quotes above, you can see that you didn't provide the two plots I asked for. But it's easy enough to translate what you provided, into what I asked for.

Oops, you are right, I switched the axes on the second plot. As you say, easy enough to translate.

While you are preparing your incisive critique you should also start getting ready to address the challenge I issued.

 

[Mike_Fontenot]

If any forum members want to construct their own rough sketches of the plots I asked for, by translating from Dalespam's plots, then to get the big picture, you should plot the entire ranges of the two twin's ages, starting from zero age, and stopping about 5 years beyond when the traveler does his second velocity change. Also, use the same scale for each axis. (And note that for both plots, the home twin's age should be plotted vertically, and the traveler's age is plotted horizontally).

Actually, in order to illustrate that PassionFlower's reference frame has a problem, it is only necessary to plot the first leg of the traveler's (Tom's) journey (starting with his birth, and ending when he is 20 years old).

The age of the home twin (Sue), as a function of the age t of the traveler, is always denoted using the root acronym "CADO". Then, I add either of two "subscripts", either "_T" or "_H", to indicate WHOSE conclusion is being referred to (either the Traveler's conclusion, or the Home twin's conclusion, respectively.

So, we sketch two different curves on the same graph, with the vertical axis being the home twin's (Sue's) age, and the horizontal axis being the traveler's (Tom's) age. And we indicate which of those two curves corresponds to the traveler's (Tom's) conclusion (CADO_T), and which corresponds to the home twin's (Sue's) conclusion (CADO_H), about Sue's current age.

What is in dispute, is whether the curve CADO_T(t) should be determined using my reference frame for the traveler (I'll refer to it as "the {MSIRF(t)} frame"}, or using PassionFlower's frame (I'll refer to it as "the PF frame") ... or perhaps some other alternative (Doby & Gull (?)).

So, to do the comparison, we actually need to plot two different versions of CADO_T(t). I'll use the original label, CADO_T for my {MSIRF(t)} frame, and CADO_T_PF for PassionFlower's frame.

Use the same scale on each axis. Make the vertical axis twice as long as the horizontal axis, with the horizontal axis ranging from zero to 20 years old, and the vertical axis ranging from zero to 40 years old.

The CADO_H(t) curve is then a straight line, of slope 2. (I'm using my originally specified velocity of 0.866c, resulting in a gamma value of 2). This follows purely from the well-known time dilation result: Sue says that Tom is always half her age (since they were both born at the same instant, and (momentarily) at the same location). Or, equivalently, Sue says that she is always twice as old as Tom ... thus the slope of 2.

The CADO_T(t) curve is a straight line, of slope 1/2. This also follows from the time dilation result (since Tom is unaccelerated during his whole life, up until he is 20 years old). This result can also be obtained from the basic CADO equation, but the result is the same either way. (The CADO equation, during segments where v is constant, can be used to show that Tom will come to the same conclusion about their relative rates of ageing as he would have if he were perpetually inertial).

[ADDENDUM: Actually, the above result follows DIRECTLY from the definition of the {MSIRF(t)} frame itself: the {MSIRF(t)} frame is the collection of all the momentarily stationary inertial reference frames (one for each instant t of the traveler's life), such that the traveler, at each instant t of his life, adopts the conclusions of the inertial reference frame with which he is momentarily stationary at that instant. So, during any segment where his acceleration is zero, he agrees with the single inertial reference frame with which he is stationary during that entire segment (no matter how short or long that segment may be). I.e., anytime the traveler temporarily stops accelerating, he IMMEDIATELY becomes a full-fledged inertial observer, and remains an inertial observer up until he starts to accelerate again.]

For PassionFlower's frame, the CADO_T_PF(t) curve is a straight line, of slope 1. (This is true, for the first leg, regardless of what the constant relative velocity v is).

I encourage anyone following all this to sketch out the above three curves (all on the same graph).

Now, can anyone see what the problem is with PassionFlower's frame?

If not, here's a hint:

Add this to the original scenario: Tom's mother actually gave birth to two twins: Tom and Jerry. All three of them (mother and her two twin sons) continue along (co-located) at their constant velocity of +0.866c relative to Sue. Tom and Jerry are indistinguishable during their first 20 years of life ... neither of them has ever accelerated. Tom reverses course (with v = -0.866c) when he is 20 (as described previously), but Jerry NEVER accelerates. Question: What does Jerry conclude about Sue's current age? I.e., what does the curve CADO_TJ(t) look like? (The subscript "_TJ" denotes the additional Traveler's (Jerry's) conclusion about Sue's current age). Plot that curve along with the other three curves. Do you detect any problem with PassionFlower's frame?

Mike Fontenot

 

[PAllen]

What is in dispute, is whether the curve CADO_T(t) should be determined using my reference frame for the traveler (I'll refer to it as "the {MSIRF(t)} frame"}, or using PassionFlower's frame (I'll refer to it as "the PF frame") ... or perhaps some other alternative (Doby & Gull (?)).

Actually, what is in dispute is that virtually everyone except you claims this is not a question of physics at all; it is a question of convention, convenience, and taste.

 

[Passionflower]

Do you detect any problem with PassionFlower's frame?

At this stage I think it is not very fruitful to argue as you appear to be too involved with the formulas you use and I fear you lost objectivity.

What is called 'Passionflower's frame' by the way is a rock solid concept worked out by Minguizzi, there are three interesting papers on this:

Differential aging from acceleration, an explicit formula (2004)
http://arxiv.org/abs/physics/0411233

Towards a closed differential aging formula in special relativity (2006)
http://arxiv.org/abs/gr-qc/0611076

Relativity principles in 1+1 dimensions and differential aging reversal (2006)
http://arxiv.org/abs/physics/0412010

 

[Mentz114]

The Minguizzi paper is great. It's a breath of fresh air that he ( and the other authors cited) uses the term 'differential ageing'. Please, can we ban the phrase 'twin paradox' forever from this forum.

 

[matheinste]

The Minguizzi paper is great. It's a breath of fresh air that he ( and the other authors cited) uses the term 'differential ageing'. Please, can we ban the phrase 'twin paradox' forever from this forum.

You have a seconder for that proposal.

Matheinste.

 

[Dale]

Actually, what is in dispute is that virtually everyone except you claims this is not a question of physics at all; it is a question of convention, convenience, and taste.

Yes, that is correct. Nobody has a real problem with CADO (particularly not in regions of spacetime where the CADO only goes forward). The only disagreement is with Mike's misunderstanding that his preference for CADO is more than merely a personal preference, but a physical requirement.

The CADO_H(t) curve is then a straight line, of slope 2. ...
The CADO_T(t) curve is a straight line, of slope 1/2. ...
For PassionFlower's frame, the CADO_T_PF(t) curve is a straight line, of slope 1.

Yes, the different synchronization conventions yield different results for which ages of Tom are synchronized with which ages of Sue. There is nothing surprising about that.

So, it is time for you to address my challenges now.

 

[Mike_Fontenot]

[CORRECTION]:
My posting below is incorrect. I failed to answer my own previous question correctly (about how the PF frame for Jerry compares to the PF frame for Tom).

I'll post my corrected version shortly.
[END CORRECTION]

I'm surprised that no one has pointed out the obvious problem with PassionFlower's reference frame for Tom ... the readers of this thread must be half asleep.

Here's the obvious problem with PasssionFlower's frame (a frame which has also been endorsed by DaleSpam):

Using PassionFlower's frame (the "PF" frame), we want to know what Tom and Jerry each conclude about Sue's current age, relative to their own. And we are focusing attention on only the first 20 years of Tom's and Jerry's lives (when they are co-located, and identical in essentially every way).

There is a PF frame for Tom, in which Tom is forever stationary at the spatial origin. There is also a PF frame for Jerry, in which Jerry is forever stationary at the spatial origin. We want to know how these two frames compare, in their description of Sue's current age, for the first 20 years of Tom's and Jerry's lives.

The PF frame for Tom says that, during the first 20 years of his life, Tom concludes that Sue is always his SAME age. In contrast, the PF frame for Jerry says that Jerry will always conclude that Sue is HALF his age. [The above sentence is incorrect ... see my next posting for the correct PF frame for Jerry]

So, even though NOTHING distinguishes Tom and Jerry during the first 20 years of their lives, the two PF frames say that Tom and Jerry come to different conclusions about Sue's current age, purely because Tom accelerates when he is 20, whereas Jerry never accelerates.

But how does anyone KNOW, when Tom is (say) 10 years old, that he actually WILL choose to accelerate when he is 20? What if, when they are 20, Tom and Jerry decide to flip a coin, to decide which of them accelerates? Maybe it will be Jerry, not Tom, that actually ends up accelerating. Or maybe neither of them will accelerate. Or maybe both of them will accelerate. Who can KNOW, when those twins are 10 years old, what they will choose to do when they are 20? Apparently, the PF frames know.

The PF frames are obviously NON-CAUSAL.

Such a situation would probably be considered quite reasonable, by a mystic. But no physicist worth his salt could possibly take such an absurd situation seriously.

Mike Fontenot

 

[Mike_Fontenot]

OK, here's my correction to my previous post:

The PF frame for Jerry, is exactly the same as the PF frame for Tom, during their first 20 years of life. (The two frames DO differ after that point in their lives.)

Both PF frames (for the first 20 years) say that Sue is the SAME age as Tom and Jerry.

So my problem with the PF frame is that, for a perpetually inertial observer (Jerry), it produces a different result that the standard Lorentz frame. I have already argued, in another thread, that any frame other than the standard Lorentz frame, for a perpetually inertial observer, is invalid. Here's the link to my post that discusses that issue:

https://www.physicsforums.com/showpost.php?p=2978931&postcount=75

Mike Fontenot

 

[Mike_Fontenot]

The incorrect statements that I recently made about Passionflower's frame (specifically, that Sue's age in his frame depends on what the observer does in the distant future), may actually be correct for the Dolby & Gull frame. I'm not knowledgeable about that frame, but Fredrik seemed to express the opinion, in a previous thread, that Dolby & Gull DOES behave as I mistakenly originally thought PassionFlower's frame behaved. Here is a link to Fredrik's post in that thread:

https://www.physicsforums.com/showpost.php?p=2811379&postcount=30 .

If Fredrik's interpretation of Dolby & Gull's frame is correct, then my original (incorrect) objections about PassionFlower's frame DO apply to Dolby & Gull's frame ... i.e., that Dolby & Gull's frame is NON-CAUSAL.

(DaleSpam originally planned to provide a description of the simultaneity plots for both PassionFlower's frame and for Dolby & Gull's frame, for the specific example I described earlier in this thread. I saw DaleSpam's description for PassionFlower's frame, but if he ever posted it for Dolby & Gull's frame, I must have missed it.)

Mike Fontenot

 

[Passionflower]

I'm surprised that no one has pointed out the obvious problem with PassionFlower's reference frame for Tom ... the readers of this thread must be half asleep.

Frankly I am no longer interested in arguing, since as I wrote before I fear you lost objectivity. Based on this I suggest you attempt to remove yourself a bit from 'your' CADO equations and try to find some more objectivity.

A topic on differential aging as described by Minguzzi would be very interesting and helpful but if every other posting has the acronym CADO more than three times I for one will not be interested in participating.

 

[Dale]

The PF frames are obviously NON-CAUSAL.

Such a situation would probably be considered quite reasonable, by a mystic. But no physicist worth his salt could possibly take such an absurd situation seriously.

I have never heard the term "non-causal" applied to a reference frame. You will have to define it clearly and unambiguously (not your strong point) and demonstrate why a "non-causal" reference frame is invalid (i.e. makes incorrect predictions about physical experiments). You can call something a nasty-sounding name like "non-causal" and imply some sort of guilt by association by linking it with mystics, but any "physicist worth his salt" would avoid falling for your logical fallacies and ask you to define your terms and demonstrate your claim.

In addition, once you fix the origin of the "PF" frame the lines of simultaneity are fixed regardless of any future or past accelerations, and the D&G method only assigns coordinates to events in the past light cone of the observer, so it is hard for me to imagine any definition of "non-causal" that would make sense. If anything the CADO seems more likely to be "non-causal" since it assigns new coordinates to events outside of the past light-cone as the observer accelerates.

In any case, I see that you are still trying to change the subject from the fact that you have failed to answer my repeated challenge. It makes me wonder what you are trying to hide. I suspect that you know full well either that your position is wrong or that you are incapable of doing the math required to prove your position right.

 

[Mike_Fontenot]

In my response to PAllen's post,

https://www.physicsforums.com/showpost.php?p=2962578&postcount=56 ,

specifically the quote I gave from his posting:

> [...]
> Imagine the 'instant turnaround twin' is looking through a telescope at an
> image of clock with the 'stationary twin'.
> [...]
> Passing the point of instant turnaround the turning twin sees:
> [...]
> - clock appears further away
> [...] ,

I said:

As long as the MAGNITUDE of the velocity stays the same before and after the velocity change (as it does in this example), then the apparent size of the image is exactly the same immediately after and immediately before the instantaneous velocity change. The distance to the home twin, according to the traveler, is L/gamma, where L is the distance according to the home twin. Gamma has the same value for v = +0.866 as it does for v = -0.866.

My last two sentences were correct, but my first sentence may well be incorrect ... my apologies to PAllen. I have never investigated how the two-dimensional image of some distant object (when viewed through a telescope) would APPEAR to an accelerating observer ... it's a question that I consider to be a distraction from more important issues, and of minor importance. It is the TRUE current distance (according to the traveler) to the distant object, that I think is of fundamental importance, not the APPARENT distance.

The image being viewed through a telescope is an OLD image, and the solid angle subtended by the object gives an incorrect indication of the CURRENT distance to the object.

This issue came up in another thread. Here are two postings of mine from that thread:

https://www.physicsforums.com/showpost.php?p=2987503&postcount=24

and

https://www.physicsforums.com/showpost.php?p=2988591&postcount=30 .

Mike Fontenot

 

[PAllen]

In my response to PAllen's post,

https://www.physicsforums.com/showpost.php?p=2962578&postcount=56 ,

specifically the quote I gave from his posting:

> [...]
> Imagine the 'instant turnaround twin' is looking through a telescope at an
> image of clock with the 'stationary twin'.
> [...]
> Passing the point of instant turnaround the turning twin sees:
> [...]
> - clock appears further away
> [...] ,

I said:



My last two sentences were correct, but my first sentence may well be incorrect ... my apologies to PAllen. I have never investigated how the two-dimensional image of some distant object (when viewed through a telescope) would APPEAR to an accelerating observer ... it's a question that I consider to be a distraction from more important issues, and of minor importance. It is the TRUE current distance (according to the traveler) to the distant object, that I think is of fundamental importance, not the APPARENT distance.

The image being viewed through a telescope is an OLD image, and the solid angle subtended by the object gives an incorrect indication of the CURRENT distance to the object.

This issue came up in another thread. Here are two postings of mine from that thread:

https://www.physicsforums.com/showpost.php?p=2987503&postcount=24

and

https://www.physicsforums.com/showpost.php?p=2988591&postcount=30 .

Mike Fontenot

May I ask how you propose to know the true current distance? Since what you see now, the other twin may have blown up, or started moving rapidly in a random direction. The length that has the property you claim (doesn't change before and after turnaround) would have to be defined as follows:
---
assuming the other twin continues to move at that same speed as I last saw (measured e.g. by their redshift), continuing until my 'now', then I can claim this distance doesn't change before and after turnaround (noting that my definition of 'now' for distant points just changed a lot as I shifted frames).
---

To me, that's not physics, it's just an exercise in "let's pretend".

 

[terrence777]

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[Mike_Fontenot]

[...]
In my response to PAllen's post,

https://www.physicsforums.com/showpost.php?p=2962578&postcount=56 ,

I said:

[...]
As long as the MAGNITUDE of the velocity stays the same before and after the velocity change (as it does in this example), then the apparent size of the image is exactly the same immediately after and immediately before the instantaneous velocity change. The distance to the home twin, according to the traveler, is L/gamma, where L is the distance according to the home twin. Gamma has the same value for v = +0.866 as it does for v = -0.866.
[...]

My last two sentences were correct, but my first sentence may well be incorrect ... my apologies to PAllen. I have never investigated how the two-dimensional image of some distant object (when viewed through a telescope) would APPEAR to an accelerating observer ... it's a question that I consider to be a distraction from more important issues, and of minor importance. It is the TRUE current distance (according to the traveler) to the distant object, that I think is of fundamental importance, not the APPARENT distance.

The image being viewed through a telescope is an OLD image, and the solid angle subtended by the object gives an incorrect indication of the CURRENT distance to the object.
[...]

I decided to do an analysis of the angle subtended by the diameter of the (assumed inertial) earth, at some instant when two perpetually inertial observers (with velocities of beta = +0.866 and beta = -0.866, with respect to the earth) happen to be momentarily co-located, far from the earth. In particular, I wanted to determine that subtended angle, according to each of the three inertial frames (the Earth frame, and the two "traveling" observers' frames). Those three frames disagree about the angle. The analysis is elementary, but a bit tricky. Like most calculations in special relativity, it is easy to get wrong.

Here's a specific result from the equation I derived (which relates the subtended angles, according to the three reference frames):

Suppose the subtended angle, according to the Earth frame, is 10 degrees.

Specifically, we draw a diagram (in the Earth frame) with a straight line between the center of the Earth and the point of co-location of the two traveling observers. That straight line lies along the direction of relative motion of the travelers with respect to the earth. We arbitrarily choose any Earth diameter that is perpendicular to the above straight line. Then, we draw a straight line between each end of that Earth diameter, to the point of co-location. The angle between those latter two lines is taken to be 10 degrees.)

The inertial traveler, moving AWAY from the Earth at speed 0.866c, will measure the angle subtended by the Earth diameter to be about 33 degrees. The inertial traveler, moving TOWARD the Earth at speed 0.866c, will measure a subtended angle of about 2.7 degrees.

So I definitely WAS wrong when I said that the outbound and inbound inertial observers would see the SAME size telescopic image at the instant when they are co-located. (If they receive a TV image, at the instant of co-location, giving the home twin's age at the time of image transmission, they each WILL receive exactly the same TV image. I had originally thought that the image through a telescope would likewise be the same for both travelers, but that's not the case.)

But even though the travelers see different images through the telescope at the instant of co-location, the CURRENT separation of the travelers, from the earth, at that instant of co-location, WILL be the same distance, according to both travelers' inertial reference frames: they will each agree that the separation is HALF what the Earth inertial reference frame says it is (because gamma = 2 for v = +-0.866). This result follows from the Lorentz equations, or (much easier and quicker) from either the length-contraction result, or else the time-dilation result combined with "velocity reciprocity".

If the two travelers try to DIRECTLY infer their CURRENT distance to the Earth from the angle subtended by the image of the Earth in their telescopes, they will be badly mislead. The image that each of them sees through the telescope is an old, out-of-date image ... it shows them what the Earth WOULD have looked like at some earlier time in their pasts, if light speed were infinite. For the outbound traveler, he was CLOSER to the Earth in his past, so he sees an image that is LARGER than it would be if he could see the Earth as it currently is. The inbound traveler was FARTHER from the Earth in his past, and so he sees an image which is SMALLER than it would be if he could see the Earth as it currently is.

If the travelers want to deduce the separation from the telescopic image, the old, out-of-date, directly deduced separation CAN be ADJUSTED to give the correct CURRENT separation. If they do that adjustment correctly, they will get a separation which agrees with the Lorentz equations (or with the length-contraction result). But that's a very tortuous way to get the same result that can be obtained much easier and quicker using length-contraction.

Mike Fontenot

 

[Mike_Fontenot]

CORRECTION: The angle I computed in my previous posting was the angle subtended by the RADIUS of the earth, NOT the DIAMETER of the earth. Sorry for the confusion.

Mike Fontenot