Can the Twin Paradox be simplified?

Big surprise....I can recommend some perfectly crackpot journals that would be more than happy to accept your perfectly crackpot papers. Try Aperion, they'll definitely accept your papers. You don't need to thank me. If that fails, try Progress in Physics.

 

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I would be curious to see the specifics of such an experiment, as I claim it is impossible. Absolute age differential demands acceleration, which is also absolute. Relative velocity determines nothing.

 

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As an extension of my previous post, timewarp, the twin (and/or triplet) paradox is not possible without acceleration. The standard triplet paradox simply puts the participants under acceleration prior to the measurements of the experiment (i.e. prior to the experiment itself). The fact is, your triplets could not experience an age differential from their hospital beds without it.

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If two inertial frames are moving relative to each other, each one will say that the other's clocks are ticking slow compared to his own. So you have an apparent paradox even before acceleration is introduced.

Perhaps what you meant to say is that the solution to the paradox requires acceleration? While that may or may not be the case, it is easy to demonstrate that acceleration is certainly not the cause of time dilation in SR.

 

Correct, what I meant is that any absolute statements made regarding age differentials require involving acceleration (or gravity, of course). Perhaps you could expand on how you would introduce time dilation without acceleration??

 

I already gave one simple example: If two inertial frames are moving relative to each other, each one will say that the other's clocks are ticking slow compared to his own. This is the case regardless of which one may or may not have accelerated in the past.

Another example is to use a certain amount of acceleration to "resolve" the twin paradox. Then repeat it using the same amount of acceleration, but with a longer or shorter journey. In that case, you get a different age differential even though the acceleration is the same.

 

The paradox here only exists when we switch frames, magically, in our mind. Each observer's view of the world is self-consistent. I could equivalently say that a car appears to me to be shorter than you do because it is foreshortened due to my relative angle from it, except in this analogy we must stand together to mutually agree on whose view was illusory.

Yes this is true, but what causes a bank deposit's growth: interest rate or length of time accruing that interest? I see the interest rate as the "cause" of the value differential between the initial deposit and the final account value, and the time in the account as determining the extent of the growth. Perhaps we could agree that both interest rate and time are necessary for account growth, just as acceleration and time are necessary for age differential?

 

Yes, I think we agree there. My point was only that we don't need to know anything about acceleration histories in order to find ourselves in this situation. At this stage, we don't know which frame will be the "younger" frame, and we know it doesn't have anything to do with any acceleration in the past. I think your point is that it does depend on which frame accelerates to make the frames at rest with each other, and I can agree with that.

That's a pretty good analogy. I'd say it's more like a stock certificate instead of a bank account. I would say that the relative velocity is analogous to the effective interest rate earned. The amount of time traveled is analogous to the amount of time the stock is owned. Then, acceleration would be something like making sure you sell your stock before everyone else does, (making you the younger twin). Otherwise, if they sell before you, you lose all your investment as well as your dividends, plus you have to pay some penalties for not keeping enough money in your account, (making you the older twin). Something like that.

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Acceleration does not cause time dilation, but it is necessary to bring the two inertial frames together so that they can compare clocks in the same reference frame.

Until both twins are in the same inertail frame, there can't be any comparison of age made, and at least one of them will have to undergo acceleration in order to return 'home'. And that acceleration, while it does not in itself cause any time dilation, does differentiate the two frames, and so we see that the traveling twin is younger when we bring the frames back into synch.

 

I believe this is a distinction without a difference. There are 3 types of logical causes: necessary, sufficient and contributory. Acceleration is certainly necessary and contributory to time dilation, and if we loosely consider the non-inertial frame on the surface of a massive body to be "under acceleration" relative to a distant frame then it is sufficient.

Well I guess we need to keep "age differential" and "time dilation" distinct. Time dilation is a rate, while age differential is determined by (rate*time) after an initial syncing. From this perspective I believe my original analogy is more appropriate: acceleration is a change in interest rate (where relative velocity would be merely a consequence this rate differential) and time spent at this rate differential determines the extent of the account balance growth.

 

I think you are confused, Neddy Bate posted the nonsense you are attributing to me. As an aside, neither of you understands the way acceleration does or does not account for the age differential in the twins paradox, the short of it is that acceleration has no contribution, I explained this to ....you! in another thread . I am quite sure that will not stop you guys continuing to talk about it.

 

Tach, that thread ended with you posting a quoted reference to a "Twin Paradox" solution that did not involve twins and thus did not require the inclusion of accelleration. You never proved "your" original point. You just cited a reference that was consistent with your result, and everyone else let the subject drop.

During that thread that was what I had contended from the start. If you set the hypothetical up involving twins, triplets or clocks synchronized in the same FoR, there must be accelleration involved for them, to wind up in different inertial FoR. (moving relative to one another)

As an aside, accelleration does involve time dilation and can contribute to the paradox. It just complicates the problem because how it affects time is dependent upon the rate and duration of accelleration, compared to the gravitational field the stationary twin is exposed to. If the acceleration is greater than 1G (1 earth standard gravity) the clock will be running slow compared to the stationary twin. If it is less than 1G time will run somewhat faster than compared to the stationary twin. These are not issues normally stated in the paradox and are not really relavent to the issue the paradox attempts to address.

Further, when accelleration is involved, it has the same affect on time whether it is accelleration or deceleration. The net G force determines the clock rate.., slow or fast, as compared to a stationary twin.., on a planet.., in a gravity well.

 

Yes, time dilation is a rate, just like an interest rate. But time dilation is caused by relative velocity, not acceleration. So you should have relative velocity analogous to the interest rate. All acceleration does is tell you who closed out their account first.

 

It seems that 100 years discussion again renewed here – when all, rather probably, is evident – the paradox is in reality a manifestation of inherent self –contradiction of Einstein’s "special relativity theory", which appears since in the theory it is postulated globality of Lorentz transformations (LT) and equality of the IRFs.

When these postulates mean nothing else that Einstein and Minkowsky equated erroneously two fundamentally different things – fundamental essences "Space" and "Time" (the rules that govern processes in Matter) and concrete material – and rigid! - objects, i.e., clocks and scales.

Again, any material object moves in absolute spacetime with speed of light in some direction. And just after an acceleration in given IRF, a clock/ scale obtain some momentum and as a result – changes its direction (rotates) in spacetime what an observer sees as a slowing down of clock’s reading and FotzGerald- Lorentz contration;

when in the standard SRT that is interpreted as "[global, in whole Universe] spacetime rotation". Though to say, e.g., when a car turns (say to the right) on a crossroad, that in reality at that Earth turns to the left - is in fact the same and is equally absurd. However the mathematics is in both cases the same – till the case when two cars occur in the crossroad and turn in different directions – and poor Earth cannot decide – where must She rotate?

In fact all what Einstein made new to the VFL-theory – that is famous energy/mass equation, though it follows from the LT and was known for EM processes already. But when all rest physical society thought that all is possible to reduce to electromagnetism and, seems, start a competition "Who first develops corresponding "Theory of Everything" , Einstein was the first who declared that nature of material objects can be non-EM, but E=mc^2 is true…

Note besides, that there weren’t any experimental tests of the SRT – all experiments that were made are in reality testing of the VFL-theory. The experiments that really can reveal difference SRT/VFLT are real – e.g. - that is the experiment with two clocks in an orbit (see, e.g. paper "The informational model - possible tests" and a version somewhere in Net)

More – see SSDS posts above (former thread's page) and links in the posts.

Cheers

 

The fact that you don't understand that there is no difference between the term "twins" and the term "observers with clocks" constitutes just a proof that you don't even understand the problem statement.

You mean that you don't understand the problem statement?

Totally irrelevant for the triple-twin case. You are disagreeing with mainstream science.

Experiment and mainstream physics says that you are wrong. See here

 

Neddy Bate and Tach, my apologies for misattributing that quote. Anyway, Tach, I see that your oblivious douche-baggery has finally gotten you banned. Enjoy! Perhaps while you are away you can see how other members in this thread can disagree without being complete asshats.

I have a problem with the Clock Hypothesis "confirmation" for the following reasons:

They did not compare a muon under acceleration with one never having been accelerated, but rather one that had already been accelerated to an equivalent energy! Isn't it possible that the energy added to a body through acceleration is what causes time dilation?

Also, the nature of orbital acceleration is suspect to me. If they were to subject a muon to \(10^{18}g\) in perpetuity in a single direction does anyone believe that the results would be the same? If my bank's rate oscillates between 10% return and -10%, and after 20 years my account has not grown, do when then conclude that interest rate does not cause a change in account balances? In other words, cancelling out the effect of acceleration is not the same thing as being able to declare it is not necessary!

In the end, relative velocity and acceleration are married and it's impossible to separate them, so trying to declare the importance of one over the other is futile. The only attempt to do so (that I've seen) is the in the 3rd-twin paradox, and I would be happy to show why that analysis is no good.

 

First! Do you know how to read?

Twins can be treated as special clocks, the problem you seem incapable of understanding is that they cannot be resynchonized after birth. That means they are special clocks that are synchronized, at birth.., in a common frame of reference. Triplets would raise the same issue for the thought experiment. If they or any clocks are synchronized in a common frame of reference, at least one has to have experienced some acceleration, for any two or more to be in frames of reference in motion relative to one another.

The thought experiment was and is one that highlights an apparent paradox within special relativity and generally excludes, effects associated with general relativity and acceleration. This can be done with twins by "assuming" that all velocities are instantaneous and uniform. In other words, acceleration is excluded from the hypothetical. If this is the case when one presents a hypothetical the proper response when someone mentions acceleration is, "This is a hypothetical and acceleration is not a factor under consideration.".

Once you accept that any accelleration is involved, or may be involved.., you no longer have that option. Twins or Triplets as clocks tie the hypothetical to experience and to an inclusion of accelleration.

Though when speaking from a perspective of special relativitiy and the paradox, accelleration is not a factor that one must consider, that is not the same as attempting to say that accelleration has no effect on a clock's rate. The Equivalence Principle associates acceleration with gravitation as indistinguishable from one another. Now think......, GPS and general relativistic effects on satellite clocks. (don't get confused here. The general relativistic effect here is not primarily accelleration, it is the clock's position within the Earth's gravitational field? Which can be associated with acceleration via the Equivalence Principle.)

Acceleration does have an effect on clocks and thus once it is included in the hypothetical it must be accounted for. A difficult task! since though it is sometimes raised as an issue, there is seldom sufficient information to determine its affect.

So, to some things up. There is a difference between observers and clocks and twins as clocks. The clocks that observer's hold can be synchronized in a number of different ways. Twins are synchronized only once.., at birth.., in a common frame of reference. To be certain you understand, twins cannot be resynchonized.

 

Since you have referenced the above link before, I felt it deserves specific attention.

There are two papers cited in the link, the Bailey et al. paper, "Measurements of relativistic time dilation for positive and negative muons in a circular orbit", is publiclly unavailable, except as an abstract. The other, seems to have involved stringing together two experiments unrelated to the introduction, for the sole purpose of presenting the introduction...

In both cases the experiments involved, were experiments in particle physics that cannot be directly associated with macroscopic experience.

The best case, from the abstract only, is the Bailey reference. However, since it does not involve any general relativistic conditions it says nothing about general relativistic effects on time and clocks.

To understand this compare the muon storage ring situation to a satellite in orbit around the earth. In the case of the satellite there is a general relativistic time dilation associated with the satellite's location in the Earth's gravitational field. The same does not apply to the muons in the "magnetic" storage ring.

Turning back to the satellite... The satellite can be said to be undergoing a constant and uniform acceleration in its orbit around the earth. However, though via the equivalence principle uniform acceleration and gravitation should be equivalent, an orbit is a special case of acceleration where the ficticiuos centrifugal force associated with an object's acceleration around or toward a central point, is canceled by the gravitational interaction between the satellite and the, in this case earth. The satellite is in free fall. This leaves the only general relativistic effect on the satellite its location in the Earth's gravitational field and not any involved acceleration.

In the case of the muons in the magnetic containment ring, the magnetic field of the containment ring plays the same role, with respect to any centrifugal effect that the Earth's gravitational interaction with the satellite does. The general relativistic effects that might be associated with acceleration are canceled out. This eliminates acceleration from time dilation effects in both situations and reduces them to effects described under special relativity and velocity.

Neither the moun in a magnetic containment ring or the satellite in orbit, "feel" as if they are accelerating centripedally... They are both essentially traveling in a straight line, the satellite following the curvature of space and the muon following a curvature induced by the magnetic containment field. And while the satellite does experience the change in its location within the Earth's gravitational field, the muons do not, they remain in the same relative location within the Earth's gravitational field.

Neither the satellite or mouns in the above situations can be used to say anything about general relativistic time dilation involving acceleration.

 

This is all well put, OnlyMe. One thing that I might add is that we must be careful not to switch between frames magically in our mind, while granting divine knowledge to the participants. If we declare that two observers are in relative motion "and have been for eternity", to avoid the acceleration issue, there arises another problem: even if they adjust their clocks as they pass each other, they cannot know that their clocks are keeping the same time! The observers must be both co-located and inertial for a certain duration in order to be truly synced and mutually agree on this.

This is the problem with the "3rd Twin" paradox. We jump from frame to frame under the presumption that each observer can know what we do. In reality, there is no absolute conclusion to be drawn from the "3rd Twin" paradox, despite popular belief. Twin C meets up with Twin A and both conclude that Twin B is younger...so what? It's still relative knowledge without acceleration to make any absolute declarations.

 

Imagine an army of observers, all wearing blue, and lined up along the x axis of an inertial frame. Let the observers wear standardized wristwatches built to some exact specification, and synchronized to each other. Now imagine an identical army, except wearing red, and lined up along the x' axis of a relatively moving inertial frame. For convenience, let's say that the observers are passing close enough that they can see the time on each wristwatch as it passes by.

After the two armies have passed each other, the entire blue army gathers together to share all of their information with each other. Each observer had kept kept a written log recording the time displayed on each wristwatch as it passed by them, as well as the time displayed on his own wristwatch at the same time.

The blue army concludes that the red watches were running slower than their own, even though all of the wristwatches were built to the exact same standard. And if the red army gathers together to share their information with each other, they conclude that the blue watches were running slower than their own. Do you agree that they can determine this without accelerating to the other frame?