Age-Changes Caused By Instantaneous Velocity-Changes

[ghwellsjr]

This is what I said in post #31:

We do know that whenever any observer, clock, object, or any other thing experiences acceleration and there is a changing speed, that thing experiences a real, physical change in the rate its clocks tick and the rate it ages and it experiences a real, physical change in dimension along the direction of acceleration.

I didn't say anything about any kind of frame, inertial or accelerated, and I didn't qualify the type of clock, idealized or not. I'm talking about real, physical stuff. If you can build a so-called ideal clock, then it will change its tick rate when it is accelerated between one speed and another.

But I think the term ideal clock means one that won't be affected by an acceleration in a way other than what SR would predict. For example, a grandfather clock would not be classified as an ideal clock because even minor accelerations will throw it off.

Frames are not real, physical things. They are ideas in our minds that help us conceptualize real or imaginary things. Things don't change just because we think differently about them.

I didn't think my quote above would find any disagreement except by those people like Mike who have what appear to me to be alternative ideas about aging. Does anybody actually disagree with my quote?

 

[matheinste]

Of course every clock changes its tick rate, ideal or not, when it is accelerated, you just can't tell that it is changing because you are constantly reassigning a new frame of reference for it as you go along. But if you analyze an accelerating clock from any single frame of reference, you must conclude that it is changing its tick rate.

"because you are constantly reassigning a new frame of reference for it as you go along"

I think this statement is a little misleading in that it implies some sort of mental action or calculation on the observers part. A clock traveling with you, that is, an ideal clock at rest with respect to you does not change its "rate of ticking" as far as you are concerned. In fact the idea of a changing rate of such a clock has no meaning for an observer at rest with respect to it because even in principle it is undetectable because you have nothing in your common rest frame to compare it with. So your reality is that the clocks functioning remains the same. Or better still, the scaling of your time coordinate axis, for you, remains the same.

Of course in the case of spatially separated clocks, except for some specific acceleration profiles, there are synchronization issues, but these clocks are not at rest with respect to each other.

And of course an observer, whose relative speed with respect to yourself changes, will observe your coordinate time axis to alter or your clock rate to change but your "reality" is not the same as their "reality" but both are equally valid "realities"

I know this is basic stuff and I know that we are, or at least intend, to say the same thing, but the wording can lead to misunderstandings for beginners.

Matheinste.

 

[ghwellsjr]

I stand by my wording and I want beginners and experts alike to understand my very clear statement from post #31:

We do know that whenever any observer, clock, object, or any other thing experiences acceleration and there is a changing speed, that thing experiences a real, physical change in the rate its clocks tick and the rate it ages and it experiences a real, physical change in dimension along the direction of acceleration.

Please don't quote me from post #33 unless you are also going to provide the context from Mentz144 in post #32. What I was trying to say there and in subsequent posts is that an ideal clock is one that changes its tick rate exactly as demanded by SR when it is accelerated from one speed to another.

 

[matheinste]

I stand by my wording and I want beginners and experts alike to understand my very clear statement from post #31:

Please don't quote me from post #33 unless you are also going to provide the context from Mentz144 in post #32. What I was trying to say there and in subsequent posts is that an ideal clock is one that changes its tick rate exactly as demanded by SR when it is accelerated from one speed to another.

Mentz144 was stating the clock hypothesis and there is nothing to add. I have no problem with what you are saying as long as it is understood that an ideal clock only changes its tick rate in a coordinate dependent way. That is, only when observed by an observer at rest in a frame whose velocity, relative to the frame in which the clock is at rest, changes.

Matheinste.

 

[Dale]

We do know that whenever any observer, clock, object, or any other thing experiences acceleration and there is a changing speed, that thing experiences a real, physical change in the rate its clocks tick and the rate it ages and it experiences a real, physical change in dimension along the direction of acceleration.

Frames are not real, physical things. They are ideas in our minds that help us conceptualize real or imaginary things. Things don't change just because we think differently about them.

I don't like the words "real" or "physical", they are notoriously hard to define. However, if frames are not "real physical things" then frame-dependendent changes such as a clock's tick rate cannot be a "real, physical change".

 

[Mike_Fontenot]

If the traveler looks at an image of the home twin (holding a sign which gives her current age at the instant the image was transmitted), he should understand that the age reported on the sign is NOT the current age of the home twin when the traveler receives that image ... because of the finite velocity of light, the home twin will have aged during the transit of the image. If the traveler CORRECTLY allows for the home twin's ageing during the transit of the image, he will obtain the CORRECT current age of the home twin, at the instant when he receives the image.

Anyone who has never done the above calculations, to determine how much the home twin has aged (according to the traveler) while the image was in transit, should do it ... it is a vary enlightening exercise. Do it for a traveler who is not accelerating, but who is moving at a velocity of 0.866c relative to the home twin (giving a gamma value of 2). For example, do it for Tom, at any instant in his life during the initial inertial leg of the scenario in the challenge I gave in one of my previous postings (#16).

The required calculations are elementary, but they are very easy to do incorrectly ... guess how I know. If you do them correctly, you will get a result (for the current age of the home twin, when the image was received by the traveler, according to the traveler) which agrees exactly with what the Lorentz equations say the result should be.

Mike Fontenot

 

[Mike_Fontenot]

No responses to my challenge (in post #16) yet? There seemed to be multiple members of this forum who felt they had a reasonable reference frame for the traveler (Tom), different from the "CADO reference frame", and at least as good. If so, the scenario I gave is about as simple as a scenario can get ... shouldn't be very hard to describe the two plots, according to your proposed frame. The solution requires only a few minutes, using the CADO equation.

Any takers?

Mike Fontenot

 

[PeterDonis]

Here's an example of the use of the equation:

Suppose the twins are 30 lightyears apart at some instant of the traveler's life, and that the traveler's velocity has been constant at v1 = -0.8 for some period of time up until that instant.

The negative sign means that the twins have been moving toward each other. (For simplicity, I'm not bothering to write the units of velocity (lightyears/year)).

Suppose that the traveler then instantaneously changes his velocity to v2 = 0.6. Then

delta(v) = v2 - v1 = (0.6) - (-0.8) = 1.4,

and so we get

delta(CADO_T) = -30 * 1.4 = -42 years.

So, with the given instantaneous velocity change, and with the given separation, the home twin gets YOUNGER by 42 years (according to the traveler), during the traveler's instantaneous change of velocity.

What event on the home twin's worldline is the new "age" value, younger by 42 years, assigned to?

 

[Mike_Fontenot]

What event on the home twin's worldline is the new "age" value, younger by 42 years, assigned to?

Suppose the traveler (Tom) has determined that, immediately BEFORE he does his velocity change, that the home twin's (Sue's) age is T1. Then the value T1 specifies a specific event on Sue's worldline.

Also, suppose that Tom has determined that, immediately AFTER he does his velocity change, that Sue's age is T2. Then the value T2 specifies another specific event on Sue's worldline.

The delta(CADO_T) equation tells us what the difference (T2 - T1) is. To get that result, all we need to know is their separation L (according to Sue) when Tom does the velocity change, and the amount of the velocity change, delta(v). We don't need to know the values of T1 and T2 themselves, in order to compute the difference between T2 and T1.

It might be easier to see what's going on, if you first understand how to use the basic CADO equation, rather than using the delta(CADO_T) equation. There is a posting that I've referenced earlier in the thread that shows a specific use of the basic CADO equation. Once you understand that, it will probably make the use of the delta(CADO) equation clearer.

Mike Fontenot

 

[PeterDonis]

Suppose the traveler (Tom) has determined that, immediately BEFORE he does his velocity change, that the home twin's (Sue's) age is T1. Then the value T1 specifies a specific event on Sue's worldline.

Also, suppose that Tom has determined that, immediately AFTER he does his velocity change, that Sue's age is T2. Then the value T2 specifies another specific event on Sue's worldline.

I'll take a look at the references you gave, but one question immediately leaps to mind: if T2 < T1 (Tom says that Sue has gotten younger after his velocity change), does that mean the event on Sue's worldline specified by T2 is *before* the event specified by T1 (meaning, "before" according to Sue)?

 

[Mike_Fontenot]

I'll take a look at the references you gave, but one question immediately leaps to mind: if T2 < T1 (Tom says that Sue has gotten younger after his velocity change), does that mean the event on Sue's worldline specified by T2 is *before* the event specified by T1 (meaning, "before" according to Sue)?

Yes.

I think you're wanting to look at all this from the perspective of a Minkowski diagram, which is always a good idea. If fact, I originally inferred the CADO equation while playing around with Minkowski diagrams. It might help you, in understanding what's going on, to take a look at this post from a previous thread:

https://www.physicsforums.com/showpost.php?p=2829903&postcount=3

Also, in my previous response to you, I probably should have pointed out that, when working through a specific traveling-twin type problem, what you do is work your way forward in the traveler's life, and determine at each stage of his life what the current age of the home twin is (according to the traveler). So, I should have answered your question by saying that, immediately BEFORE the traveler does an instantaneous velocity change, he already has determined (from previous calculations) the current age of the home twin (T1). So he can then use the delta(CADO_T) equation to calculate (T2 - T1), which then tells him the current age of the home twin (T2), immediately AFTER his velocity change.

Mike Fontenot

 

[PeterDonis]

Yes.

I think you're wanting to look at all this from the perspective of a Minkowski diagram, which is always a good idea.

Yes, I am; basically, what you're calculating is where on Sue's worldline Tom's instantaneous "line of simultaneity" points. 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. 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, since then, as has already been noted in this thread, the equation tells him how old Sue will be when he sees her.

 

[Dale]

I see you are still trying to dodge JesseM's question.

I will take you up on your challenge in post 16 (probably on Wednesday or Thursday when my work and volunteer activities should permit) since it will be fairly straightforward to do. I will use both Doby and Gull's method and PassionFlower's method.

Then I would like for you to meet JesseM's challenge to define your terms and my challenge to show one example where two different coordinate systems predict different results for the traveling twin's measurements.

 

[kamenjar]

It doesn't look to me like the aging is a function distance and acceleration.
I would rather say that aging is function of:
f (Vo, Lo)
where:
We define ORIGIN as a starting point of travel for accelerated subject.
We define ORIGIN as not experiencing any acceleration during measurement.
Vs is "velocity of a subject that as seen by ORIGIN".
Lo is "projected distance of travel by accelerated subject" as seen by ORIGIN and compensated for the light delay of the position of the subject.

Generalized formula would be the integral of v/c over traveled distance as seen by the observer. That way you can possibly also account for non-instantaneous acceleration.

I didn't spend much time thinking about this, so I hope it is reasonable and correct.

 

[pervect]

One of the problems with CADO, is that it tries to do too much. I'm going by the description of how the frame is set up, rather than the detailed mathematics, which I am assuming for the time being are done correctly.

The problem is that if you have an observer who undergoes velocity changes, lines of constant time originating at different points on the observers worldlines will cross. This has a number of unpleasant consequences.

The general approach to this problem in physics is to say that the extent of the coordinate system of an accelerating observer is limited in its size, to the regions where the coordinate lines don't cross. (I'm not quite sure what the mathemeticans do, if they do the same thing or not, but I can describe what physicists do).

Here's a longish quote from MTW on the issue:

Constraints on the size onf an accerlated frame

IT is very easy to put together the words "the coordinate system of an accelerated observer", but it is much harder to find a concept these words might refer to. The most useful first remark one can make about these words is that, if taken seriously, they are self-contradictory.

...

"Difficulties also occur when one considers an observer who begins at rest in one frame, is accelerated for a time, and maintains thereafter a constant velocity, at rest in some other inertial coodrinate system. Do his motions define in any natural way a coordinate system? Then this coordinate system (1) should be the inertial frame (t,x) for times t<0 in which he was at rest in that other frame and (2) should be the other inertial frame (t',x') for times t' > T in which he was at rest in the other frame.

[ed-small notational notiational differences from the original here].

Evidently some further thinking would be required to decide how to define the coordinates in the regions not defined [ed t<0 or t>0]

More serious, however, is the fact that these two conditions are inconsistent for a region of space-time that satissfies simultaneously t<0 and t'>T.

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. The hybrid coordinate system will assign two different values of time and position to the same event in space-time. This is more obvious in the picture that's included in the text.

Assuming that CADO does the math properly, it will run into the same fundamental problem. It will be assigning one event in space-time two different time coordinates (and correspondingly, too different locations to go with the differing times). This is bad behavior for a coordinate system, and the usual solution is to restrict the size of "the" coordinate system of an accelerated observer. If you have to use a coordinate system that covers all of space-time, you use some different coordinate system - there are various possibilities, in GR coordinates are arbitrary so you aren't required to specify an observer to specify a coordinate system.

Though there is one other possibiltiy worth mentioning. One could resolve the inconsistency by "throwing out" one set of coordinates, by preferring one observer over the other, thus introducing a preferred observer. But this isn't within the spirit of relativity.

So to sum up:1) Any cado-like approach must either prefer one of the two observers over the other (i.e. when the worldlines cross, it throws out the inconsistent coordinates) or it must assign the same event in space-time two different time coordinates.

2) the issue of setting up coordinates for an accelerating observer is discussed in the literature and textbooks - and the standard textbook result requires one to limit the size of the coordinate system to insure that only one pair of coordinates is assigned to a point, so that it does not given two different coordinates.

3) restricting the size of the coordinate system in this manner avoid the pathologies of clocks running backwards - and a few other pathologies (like singularities in the resulting metric).

Since one _can_ do physics without coordinates, the fact that one coordinate system can't have all the features one really would want it to have everywhere in space-time isn't a problem. In fact, that's one of the reasons that GR was developed - because it isn't possible to have one ideal coordinate system that has all the properties one would like, it becomes worthwhile to go through the extra effort to learn how to do physics in arbitrary coordinates.

 

[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