The Traveler's Perspective in the Twin "Paradox"

I am not aware of any disagreement about something as mundane as twin paradox, it certainly was not mentioned in my physics courses. It kind of sounds like you are spamming your site.
I have a deal for you. If you can supply some of the names of these professional physicist that think there is disagreement about the ages of the twins in the twin paradox, I will go to your site so you can increase your visitor count.

 

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'Two groups" for those who don't understand relativistic physics. People who understand how to use the theory choose coordinates and solve it.

 

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Your question is answered in the following, by a physicist.

 

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I'm not aware of any disagreement. To the extent there's any ambiguity, it's simply because accelerating observers and reference frames don't have the same status as their inertial counterparts. The relativity principle of special relativity guarantees that all inertial reference frames will have the same basic properties and will basically be interchangeable with one another. Relativity does not make the same promise about accelerating reference frames. That doesn't mean accelerating frames can't be defined and used, but it does mean that the results you get will depend on how you chose to define/construct them. This is true even for many "predictions" about inertial reference frames. For instance, the well-known relativistic time dilation formula strictly only gives the time dilation factor of a moving object according to a particular way of defining simultaneity that we've adopted. (One can argue that the way we define simultaneity in relativity is very natural, convenient, practical, etc. That doesn't change the fact it's still a definition.)

That said, there's a fairly standard way of defining the reference frame associated with an accelerating observer based on all the instantaneous rest frames the observer passes through. The construction goes something like this: at any given point along an accelerating observer's trajectory, there's an inertial reference frame that the observer is, at that instant, at rest in. At that instant, use the instantaneous rest frame's spatial axis (distance measure and simultaneity convention) as the accelerating frame's spatial axis, and use the observer's accumulated proper time as the accelerating frame's time coordinate. (For the special case of uniform proper acceleration and up to translation and rotation of the spatial axes, this construction gets you the same thing as the Rindler coordinate chart.)

As it happens, I discussed some properties of this construction in [POST=3051585]a post[/POST] on this forum several months ago (starting from "I've saved this comment for last [...]"). Based on certain comments in the abstract of your Physics Essays article, it sounds like you've either rederived this construction or found something similar to it.

 

Very good post.

Yes, the "CADO reference frame" is identical to the collection of what are usually called "the co-moving inertial reference frames" ... I prefer to call them the collection of inertial reference frames with which the traveler is momentarily stationary at each instant of his life, which I abbreviate as "the MSIRF's". At each instant of his life, the traveler's conclusion about the current age of the distant home twin is the same as the conclusion of the particular MSIRF with which he is momentarily stationary at that instant. A perpetually-inertial observer in that particular MSIRF who happens to be co-located with the traveler at that instant can use the Lorentz equations to determine the home twin's current age at that instant, and the traveler adopts that same conclusion. My "CADO equation" gives the same current age for the home twin as the result given by Lorentz equations (as it must, since it was derived from the Lorentz equations). The utility of the CADO equation is that it is easier and faster to use than the Lorentz equations, and is less likely to be applied incorrectly.

Although the MSIRF approach is widely used to determine the traveler's viewpoint, there is considerable resistance to it, primarily (I believe) because many people find some of its consequences so abhorrent that ANY alternative is considered preferable. For example, in the standard (idealized) instantaneous-turnaround twin paradox, the MSIRF solution says that, according to the traveler, the home twin instantaneously gets much older during the traveler's turnaround. That bothers many people, but much MORE abhorrent to them is the fact that, if the traveler accelerates in the opposite direction, the home twin rapidly gets YOUNGER. The result is that, according to the MSIRF solution, the home twin can have the same age at multiple different instants of the traveler's life (according to the traveler), so the traveler's reference frame thus defined cannot be a GR "chart". But that is actually of no consequence to the traveler: all he wants his reference frame to do is to tell him, at each instant of his life, the home twin's current age (and her current distance from him) ... and the MSIRF solution does exactly that.

One fairly popular alternative to the MSIRF method is Dolby and Gull's "Radar Method". It does not suffer from the sudden age changes of the home twin, and the home twin never gets younger, no matter how the traveler accelerates. But the radar method is NON-CAUSAL: the traveler's conclusion about the current age of the home twin depends on whether or not he decides to accelerate IN THE FUTURE.

My (admittedly unusual) view is that there IS only one correct solution to the accelerating traveler's perspective of the home twin's current age. I base that on a proof I gave in my paper, that (I contend) shows that the MSIRF solution agrees with the observations and elementary calculations that the traveler can himself make. His observations involve receiving messages from the home twin, giving her age at the time of message transmission. His elementary calculations involve properly determining by how much the home twin ages during the message transit, which he can then use to determine her current age when the message was received.

 

Why should this result trouble you or anyone else if you just take it for what it is? It's just a consequence of an accelerating observer's definition of simultaneity changing rapidly as they accelerate, and is something that (as I'm sure you know) is very easy to visualise on a Minkowski diagram.

There's a close analogy here, by the way, with rotation in Euclidean space. For instance, if you stand looking at the moon in front of you, and then quickly turn 180 degrees on the spot, you could just as well say that the moon has rapidly moved from being over 380,000 km in front of you to 380,000 km behind you in maybe about a second. I don't know about you, but I don't find this particularly troubling or noteworthy, and I don't see why rapid (and even negative) changes in what you call the 'CADO' should be any more surprising or taken any more seriously than the rapid "motion" of distant objects in rotating reference frames.

There's also an argument that I'm not sure any unique answer for the perspective of an accelerating (or any noninertial) observer really strictly makes sense. The reason for this is that, intuitively, I'd approach the problem by considering the experience or point of view of an inertial observer or measuring apparatus, and then ask what an equivalent accelerating (but otherwise "identical") system or observer would experience or measure when accelerating. The problem with this that, generally speaking, there is no such "equivalent" accelerating system. If there were, it would mean that there was some coordinate mapping between inertial and accelerating reference frames that was a symmetry of physics, which we already know isn't the case. Reasonably rigid accelerating observers and systems experience pseudo-gravitational forces and stresses which are always going to alter their structure to some degree. (For an extreme example, consider your point of view if you were accelerating at 20g. The reality is that you wouldn't have much of a point of view at all, because the extreme g-force would quickly kill you.) So if you consider your point of view while accelerating, it isn't really a meaningful comparison with the inertial case because, strictly speaking, you wouldn't be the same "you" as you would have been if you'd remained inertial. This isn't just a technicality -- perfectly rigid bodies are well known to be incompatible with special relativity. So, to my mind, when attaching a reference frame to an accelerating observer, there's always some degree of approximation and idealisation going on.

This also extends to some common "predictions" about accelerating bodies from the perspective of inertial reference frames. For instance, in some thought experiments it is common to assume that an accelerating clock would continue to measure time at a rate given by the Lorentz time dilation formula. But there's actually no fundamental reason this should happen nor any way to strictly predict this from special relativity, and in reality an accelerating clock could behave differently depending on how the act of accelerating affects it. Any clock accelerating sufficiently rapidly would at some point break and cease to usefully measure anything altogether. This extends to general relativity as well. Gravitational time dilation for instance, even for some given simultaneity convention, is generally strictly only an approximate idea (except, possibly, in the case of a uniform pseudo-gravitational field). Complications like these -- that I don't think can really be sensibly ignored -- are the reason I said that accelerating frames shouldn't be regarded to have the same status and physical significance as inertial frames in special relativity, even if there are more or less "natural" ways of constructing and defining them.

I don't doubt that an accelerating observer, given enough information, could 'measure' (say) the Rindler coordinates of events occurring in spacetime, including the age of an Earthbound twin in the twin paradox at some particular Rindler coordinate time. Even the effect of acceleration on measuring instruments I described above could conceivably be controlled or corrected for if necessary. But how is that different from any other coordinate system? In Euclidean space for instance, given enough measurement data you could determine the Cartesian (x, y, z) coordinates of some object in space. But you could just as well 'measure' its polar or spherical or hyperbolic coordinates, or any other coordinates of your own invention, and very often given the same information. Is it really worth having a debate about which of these answers should be regarded as the "correct" one?

 

I'm with them two.

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The simple act of the travelling twin, accelerating and decellerating phases in turning around, rids the whole scenario of any perceived paradox.

 

I find it strange that after 100 yr SR is debated at all, given that it's supported by so much experimental evidence.
That motivated my research and after a few years of forums and study, I see the reason as interpretation, misconception, and explanation. Too much in theoretical terms and short in terms of physics. If an inquiring mind asked "why does the anauts watch tick at the same rate in his spaceship as it does on earth?", "because the rules of physics are the same in all frames" is not an answer. It just replaces one question with another.

All observations rely on light. Since light propagates in space at a constant finite speed, all observations are historical.
1. The observer sees what the remote moving clock indicated a while ago.
2. The observer pings the clock with a light signal, and calculates the distance using the SR convention of assigning a position equal to c times half the time for the round trip, according to his clock.
Couple 1 and 2, and the observer cannot know the current time or location of the clock.

When two persons separate with relative motion, and observe each others clock to be running slower/faster than their own, how can there be a time difference when they reunite?
This is a misconception. Since each clock has a constant frequency while in inertial motion, the change is in the moving observers perception of the frequency, i.e. doppler shift. This provides no information about the accumulation of time for a clock. The aging question requires a comparison at a common location.

Todays automated answering service, with its matching of numbers to your (anticipated) request, too many times omits the one you want. For that reason I decline to join a preconceived classification and let you draw your own conclusion.

 

What if the stay at home twin accelerates to meet the returning twin? Acceleration does not decide the outcome. It only identifies which twin returns in the simplest of cases, i.e. the one who departs from the totally inertial path. The lost time is due to speed, not acceleration.

 

Nice point....Naturally, there would then be some variation, but I don't believe it invalidates what I did say.
I would also say the lost time is due to the fact of the finite speed of light and there being no Universal "NOW"

 

You are correct for that special case, but only because only one changes course. In the general case with both paths changing, each path must be analyzed and compared. The observer who separates from an inertial path and returns (as in the simple twin case) will move slower than the other twin on one segment and faster on the other segment. The loss is not linear but is a function of (v/c)^2, thus the time gained (relative to the other twin) is less than the time lost.