Naked Science Forum
On the Lighter Side => New Theories => Topic started by: Mike_Fontenot on 08/12/2013 16:51:18
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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?
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Well, let us assume that a arrow of time can be related to the constant 'c', using Planck scale and treating that as a minimal configuration of a 'Planck clock', making those two (locally) equivalent. That would mean that all 'points' in a universe, locally described though, have a set constant time rate. Using that you can argue that it is possible to define someone others arrow of time, even relativistically. As we now have a set foundation for what a arrow is.
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Strange, keep jumping over words today :)
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What such a reasoning also, more or less, presumes, is that a relativistic uniform motion/speed must be treated the same way as an acceleration/deceleration, meaning that both will present you with time dilations. some like to think of the twin experiments time dilation as a result of accelerating decelerating ('turning around'), but that's not the case if you use this reasoning.
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What such a reasoning lead to (it does for me at least:) is a question of what can be defined as a 'inertial observer'. If I have a rod moving uniformly at some relativistic speed I would state that it from Earth must be both time dilated and Lorentz contracted.
A inertial observer of this rod should then ideally be a clock attached to it, 'at rest' with it. As there is different uniform speeds existing, fairly easy to prove logically, I should be forced to define any other inertial observer only by placing it 'at rest' with what it observes, should I not? And sharing that local frame of reference, being perfectly 'at rest' with what you measure on, there can be no time dilation, neither any Lorenz contraction.
So, can I define Earth as a inertial object (ignoring its spin for this) from where I measure too? Relative myself being on Earth observing the rod, Earth represent a inertial frame of reference, but relative the rod (moving uniformly, and relativistically), it can't be. That as Earth (and so me) can't be 'at rest' with it.
The point I'm arguing is that if I want to define both as belonging to a same frame of reference, I actually need to place them at rest with each other, which (to me then:) also becomes a indirect proof for a time dilation and Lorentz contraction to have to exist between two uniformly moving objects, not being at rest with each other.
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A thought (possibly heretical) that I find difficult to shake of is this: What if we were able to set up the perfect twin-paradox situation and, on completion, found that the various clocks had all behaved just as relativity says they should, but the twins are still the same age?
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A thought (possibly heretical) that I find difficult to shake of is this: What if we were able to set up the perfect twin-paradox situation and, on completion, found that the various clocks had all behaved just as relativity says they should, but the twins are still the same age?
If we send out a ship to a star 1 light year away both ourselves and the other star are at fixed distances with little variation in acceleration relatively speaking. The ship however is moving in relation to both. The times on earth and the distant star will be roughly equivalent in relativistic terms, however the acceleration of the ship would be the only reason for any dilation relative to start and end points on the journey. This is my personal point of view.
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Well, that would indeed be interesting Bill :)
But hasn't NIST already proven the validity of different clock readings? As measured over frames of reference? And then we have acceleration chambers giving us a same result. And then there are those muons, traveling further than what should be possible for them, explainable due to a Lorentz contraction from their frame (point of view), equivalent to a time dilation as described from Earths frame of reference. And those muons are 'free falling', in a gravitational field from Earths frame, equivalent to a uniform 'weightless' motion (also describable as being no 'motion' at all in a 'black box scenario'.) if instead measured in their own frame. So there is no acceleration measurable in their frame by any accelerometer, but we still have to define them as 'time dilated' for their whole journey.
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But you have a really nice point in that a different arrow, as defined by a gravitational time dilation by NIST, don't seem to do anything measurable to us macroscopically. What I mean that we still 'hang together', don't we? :). So even though, assuming that mass, motion, etc, produce time dilations, the fact is that it doesn't seem to matter for us. The communication between those time dilations is done through 'c' though, locally defined, and each frame has a set relation to that. The problem with that, to me, is to see what consist of one such 'local frame'?
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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/cadoequation/cado-reference-frame
and its derivation (as well as a good bit of additional information) are given in my previously referenced paper.
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the case where each twin is perpetually inertial (i.e., neither of them ever accelerate)
Barring Star Trek transporter technology, this one is easy to solve. If they are natural born twins and they never accelerate, then they are eternally colocated, and they each know the other's time accurately, with no debate ;)
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I assume that you mean when being 'at rest' relative each other there Evan? As we can argue them to be on Earth, loosely defined, as NIST have shown gravitational time dilations to exist at short distances too. Or do you assume that a time dilation only exist in a acceleration deceleration, making all uniform motion equivalent from the aspect of time dilations? We could use identical 'test particles' in a uniform motion (flat space), make it three so we can define different uniform speeds relative each other. Either they have no measurable time dilations/Lorentz contractions relative each other, no matter what 'speed' any of them define relative some other, or they must have.
I say they must have.
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The point with using three 'identical test particles', or rockets :) Is that, although we can define any motion as being 'non existent' in a black box scenario, when involving three we must acknowledge the existence of different uniform motions. Different uniform motions exist, and measuring a time dilation is not dependent on causality alone, meaning that for any uniform motion I must assume a preexisting acceleration/deceleration. The Big Bang does not treat the inflationary aspect as a real speed of something moving, and so accelerating in three(four) dimensions, in my definitions of it that is. If that is true then I think you also can assume particles coming into existence, finding different uniform motions, you can involve kinetic energy (collisions) too, to define the same at a later stage. On the other hand, the Big Bang is strange, and so is a inflation. Another way to argue it is to use events, or time segments. That means that I will ignore any prerequisite we might assume to a uniform motion (acceleration/deceleration), just looking at what I locally measure in a comparison between my clock, and a clock existing on a different frame of reference.
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[...] the case where each twin is perpetually inertial (i.e., neither of them ever accelerate)
[...] If they are natural born twins and they never accelerate, then they are eternally colocated, and they each know the other's time accurately, with no debate ;)
You are right, of course ... I WAS taking some liberties there, in order to try to keep my posting as short as possible. In the case where the "twins" are perpetually-inertial, the scenario actually has to consist of two separate babies, born to two separate mothers who have some constant relative velocity with respect to one another, and who happen to be momentarily co-located at the moment of the two births. And in this case of perpetual-inertial-ness of both "twins", the "twins" are never again co-located, and so it's not the complete "twin paradox" situation. The reason for initially considering that modified scenario was to construct a situation where each "twin" is obviously entitled to use the Lorentz equations in the determination of their own perspective about the current age of the other "twin". That especially simple modified scenario is important to consider initially, because it is the easiest way to show that the simultaneity results obtained via the Lorentz equations ARE meaningful, and should be taken seriously and at face-value ... they give the same result that the each inertial person can determine using only his own elementary measurements and elementary calculations. Only then is it productive to move to the standard twin "paradox", where the traveler is NOT perpetually inertial. The essence of most of the interesting controversy about the traveler's perspective involves the question of exactly WHEN the traveler is entitled to use the Lorentz equations to determine simultaneity. Some say never. Some say "if he hasn't recently accelerated in the past". Some say "If he hasn't recently accelerated in the past, OR won't accelerate too soon in the future". Others say "he can use it at any unaccelerated instant of his life, regardless of how and when he accelerates at other times". I am a member of that latter group, except that I extend it to include ALL instants, whether he is accelerating then or not.
In the case of the MSIRF solution (which I usually refer to as "the CADO reference frame") of the traveler's perspective in the standard twin "paradox" scenario, it turns out that accelerations that occur at any instant when the twins are co-located don't have any effect on the traveler's perspective. And in general, the larger the separation of the two twins, the larger is the effect of acceleration on the traveler's conclusion about the home twin's current rate of ageing.