The Traveler's Perspective in the Twin "Paradox"

[Mike_Fontenot]

It is remarkable that, more than 100 years after the birth of the special theory of relativity, that there remains considerable controversy and disagreement about the traveler's perspective in the traditional twin "paradox" scenario. Specifically, at each instant of his life, what does the traveler conclude about the current age of (and current distance to) any given distant object or person (in the (assumed flat) universe)?

One view is that whenever any observer (whether inertial of not) is not co-located with some other person, that there simply IS no meaning to the concept of that other person's current age. Another view is that the current age of a distant person DOES have a meaning for a (perpetually-inertial) observer, but that it has NO meaning for an observer who (sometimes) accelerates.

Among those who believe that the traveler IS entitled to his own perspective, some nevertheless believe that the current age of a distant person, for an observer who sometimes accelerates, has no DEFINITE value ... it is "discretionary". In other words, the observer is free to CHOOSE the current age of a distant person from among several different possibilities (or perhaps, from an unlimited number of possibilities).

Others believe that the the current age of a distant person, according to the traveler, is some definite value that is "non-negotiable" and non-discretionary. Among this group, some believe that that definite value can only be properly determined by using the general theory of relativity, via the equivalence principle. Conversely, others believe that, in the (assumed) absence of any significant masses within the spatial region of interest, that the special theory of relativity is all that is needed to provide that definite current age of the distant person. But, even among this latter group, there is disagreement as to WHAT that definite value of the current age IS.

Who is right?

(I'll provide my own personal "take" on the issue after some other forum members have had a chance to provide theirs).

[Mike_Fontenot]

I had planned to wait a bit longer before posting about which of the alternative groups that I listed in my previous post that I myself occupy (and what I contend the CORRECT value of the definite current age of the traveler IS). But the silence on the forum is deafening ... not very many members yet on this new forum ... hopefully that will change soon. So here's my "take":

[...]
Others believe that the the current age of a distant person, according to the traveler, is some definite value that is "non-negotiable" and non-discretionary. Among this group, some believe that that definite value can only be properly determined by using the general theory of relativity, via the equivalence principle. Conversely, others believe that, in the (assumed) absence of any significant masses within the spatial region of interest, that the special theory of relativity is all that is needed to provide that definite current age of the distant person. But, even among this latter group, there is disagreement as to WHAT that definite value of the current age IS.
[...]

I am personally in the above quoted latter group (traveler's perspective is definite and non-negotiable, and determinable purely via special relativity).

There are two reasons why I don't believe that the traveler's perspective is arbitrary, "negotiable", and/or "meaningless". The first reason is philosophical: IF the home twin (she) exists AT ALL at some given instant of the traveler's (his) life when he is distant from her, then it would seem that she must be doing SOMETHING definite at that instant of his life. And that SOMETHING defines a unique instant in HER life.

The second reason is that the simultaneity result given by the Lorentz equations isn't just some meaningless age: it is the result that the traveler can determine from his own elementary calculations, when he receives a sequence of radio messages from her, giving her current age at the time she transmits the message. If he properly allows for her ageing during the transit of the message, and adds that to her announced age in her message (when she TRANSMITTED that message), in order to get her age when he RECEIVES that message, then he will get the same result given by the Lorentz equations. I show the process that the traveler must use, to properly determine her ageing during the transit of her message, in my paper

"Accelerated Observers in Special Relativity", PHYSICS ESSAYS, December 1999, p629.

The above comments apply to the case where each "twin" is perpetually inertial (i.e., neither of them ever accelerate), so that there is no doubt that each "twin" is entitled to use the Lorentz equations (and the time-dilation result). But I also show, in the above paper, that regardless of how the traveler accelerates, that his conclusions (at each instant of his life) about the current age of the home twin, is ALWAYS exactly the same as the conclusion of a perpetually-inertial person who happens to be momentarily co-located and mutually-stationary with the traveler at that instant. That means that the traveler himself is entitled to use the Lorentz equations to determine simultaneity at each instant of his life, whether he is accelerating then or not. I call that momentarily-stationary inertial reference frame the "MSIRF". (It is usually referred to by others as "the co-moving inertial frame", but I prefer my term). This same method of obtaining the traveler's perspective, of the current age of the home twin, has been used by others. For example, Taylor and Wheeler used the same approach in their example (Example 49) in their "Spacetime Physics" book, pp. 94-95. And Brian Greene in his NOVA series (and in his book) on the "Fabric of the Cosmos" also used the same approach.

The simultaneity result given by the Lorentz equations can also be determined by an equation I derived long ago that I call "the CADO equation". I originally coined the acronym "CADO" just to save time having to repeatedly write the phrase " the Current Age of a Distant Object". The CADO equation gives exactly the same answer as is given by the Lorentz equations (as it must, since it was derived from the Lorentz equations) ... it's just easier and faster than using the Lorentz equations, and it is less likely to be miss-used in applications. The CADO equation is especially simple and quick to use when all the velocity changes are the idealized instantaneous changes, but it is also fairly easy to use for piecewise-constant finite accelerations (perhaps alternating with "coasting" segments with no acceleration). It is even valid for any acceleration profile whatsoever, although in continuously-varying-acceleration scenarios, numerical integration will generally be required. The CADO equation is fully explained and illustrated on the webpage

https://sites.google.com/site/cadoequat ... ence-frame

and its derivation (as well as a good bit of additional information) are given in my previously referenced paper.

When the CADO equation has determined the home twin's current age (according to the traveler), for all of the instants of the traveler's life, I call the result "the CADO reference frame". It is essentially a "montage" of all of the MSIRF's from each instant of the traveler's life. But it is important to understand that the CADO reference frame is a SINGLE (non-inertial) reference frame that covers the entirety of the traveler's life. The traveler DOESN'T "jump around" in inertial frames ... he has his OWN reference frame ... it is his OWN "perspective".

[Mike_Fontenot]

When the CADO equation has determined the home twin's current age (according to the traveler), for all of the instants of the traveler's life, I call the result "the CADO reference frame". It is essentially a "montage" of all of the MSIRF's from each instant of the traveler's life. But it is important to understand that the CADO reference frame is a SINGLE (non-inertial) reference frame that covers the entirety of the traveler's life. The traveler DOESN'T "jump around" in inertial frames ... he has his OWN reference frame ... it is his OWN "perspective".

I think I could have worded the above paragraph a bit better, but the forum software won't let me edit it now, so I'll try again here:

The "montage" of "momentarily-stationary inertial reference frames" (the "MSIRFs", or "co-moving inertial frames"), combined into a whole, form a single (non-inertial) reference frame that constitutes the traveler's own "perspective" of the (assumed flat) universe. The MSIRF at each instant "t" of the traveler's life can determine the current age of, and the current distance (and direction) to, each object or person in the entire universe. Generally, for a given MSIRF(t), the perspective of that particular MSIRF for times before and after that particular instant "t" is of no interest or relevance for the traveler ... for that particular MSIRF, it is only that MSIRF's perspective at that particular instant "t" that has any importance for the traveler. The montage of all those MSIRFs, forming one single (non-inertial) frame, then provides him with his own perspective for his entire life. I call that single non-inertial frame the "CADO reference frame". The commonly-used description of the accelerating traveler "changing frames" or "frame-jumping" is misleading ... he has his OWN single reference frame during his entire life, and that single frame provides him with his "perspective" ... it tells him everything he needs or wants to know about the (assumed flat) universe; there is no other requirement for his own reference frame, provided that it agrees with his own elementary measurements, and his own elementary calculations (and the CADO reference frame does that).

[gill1109]

This statement seems to me to be circular: "There are two reasons ... . The first reason is philosophical: IF the home twin (she) exists AT ALL at some given instant of the traveler's (his) life when he is distant from her, then it would seem that she must be doing SOMETHING definite at that instant of his life. And that SOMETHING defines a unique instant in HER life."

If she (distantly) exists at some instant of *his* life ... But the question is precisely, whether or not it makes sense to say that she exists *at* some instant of his life. You are assuming what you want to deduce.

(I am a complete amateur regarding relativity)

[Mike_Fontenot]

This statement seems to me to be circular:

[...]
IF the home twin (she) exists AT ALL at some given instant of the traveler's (his) life when he is distant from her,
[...]

But the question is precisely, whether or not it makes sense to say that she exists *at* some instant of his life. You are assuming what you want to deduce.

In my list (in my original post) of alternative beliefs about the traveler's perspective, I didn't include the extreme belief that the home twin doesn't even exist at all whenever she is not co-located with the traveler. I didn't include that group, because I doubt that any physicists have that belief. Perhaps some philosophers do. So for me, I'm taking her existence as "an axiom" ... I'm not even trying to give an argument for why I believe it is true. My intent was to give a philosophical argument (and much more importantly, an additional argument based on what the traveler can measure and calculate himself) that the current age of the home twin is a precise, definite, non-negotiable, non-discretionary age.

[gill1109]

I think the additional argument is the powerful thing, here. There is something which can be fairly objectively measured, and it can be used in a meaningful way.

[gris]

The twin paradox entails a thought experiment based on the assumption that length contraction isn't a simple Doppler effect and that time deletion isn't actually observing an atom-clock slowing down in a way that you can set the atom clock by. It is like stating that a five steps long bus when riding past only taking one step has length contracted the bus. The mathematics remains the same. if you drop a sand-clock from the table the time measurement will stop, and that doesn't mean that the time has stopped.

Solve these problems like you - must scientifically seen - solve crime-scenes: take the essence of all observations and arrange in verbal logic all the pieces of the puzzle in such a way that it only requires filling in via the least assumptions the missing pieces of the puzzle (= Occam & Bayes) on a "close is close enough for testing way. And subsequently accurately test. Verbal logic for the same reason why we use verbal logic as a rule in courts of law. Lex parsimony and Bayes dictate this. Otherwise you are measuring on the nano meter with a deviation in many light-years. Infinite cosmos or not? Bayes dictates you answer this question that inherently involves non complete evidence. You have to guess yes or no pressure in the system. Probably pressure, the more so that assuming that as circumstantial evidence based on an integral view of all the evidence makes for a very elegant simple solution that is also testable, and thus unique yet taboo as any probable solution will inevitably be. (Mind you this is only probably true: i.e. a prime suspect requiring further investigation.)

Assuming pressure in the system via moving un-slitable mass then assuming that mass is added to all matter acting as little black holes will accelerate this matter via added momentum (= DE) through the field of moving mass. If the field of mass is an orderly field of a dynamic crystal (= testable!) then you have waves, and an under-pressure in the field per-sieved as curved space gravity. The more acceleration the more gravity = DM & slowing down of atom clocks. DM can be tested in this way as well.

Moving mass is not at odds with GR and or QM when assuming the testable dynamic crystal acting like a hologram. That solves the interference problem and explains the double slit experiment. (Entanglement is also a non problem when seen as a superconductive split gearbox where one toothed wheel moves the one and the corresponding one keeps on moving the other way until measurement disturbs the symmetry.)

The only problem with this is that photons then must have mass and not exert gravity contrary to GR. Yet these GR photons are only a mathematical extrapolation and have never been observed i.e. they are galloping unicorns. Solving the riddle why QM and GR can't be married. This way they are: it is all Newton. Replace these unicorns with two assumed with which you can form strings then you can build the SM (a Pool has done that already.)

Elegantly thus consistent also mathematically (I don't touch GR / QM predictions at all with exception of mass-less particles and provide something better in stead.)

Thus the travelers perspective is only a problem derived by a genius not knowing about black holes, DM, DE, super conductivity. The more relevant evidence is known the easier it should become to solve these problems. The issue is testing an not arguing.