# The No-Acceleration Scenario Does NOT Resolve the Twin "Paradox"

Discussion in 'Physics & Math' started by Mike_Fontenot, Dec 31, 2017.

1. ### Mike_FontenotRegistered Member

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In the standard twin "paradox" scenario, with an instantaneous turnaround (which requires an infinite acceleration by the traveling twin that lasts only an infinitesimal time), what makes it SEEM paradoxical is that the traveling twin ("he") is inertial during what SEEMS like essentially his entire trip ... inertial all except the single instant of the turnaround. And SURELY the home twin ("she") couldn't possibly age any during that single instant in the traveling twin's life, COULD she? While the traveling twin is inertial, he in entitled to use the famous time dilation result, which tells him that the home twin is ageing more slowly than he is. So it SEEMS paradoxical that, when the twins are reunited, he finds that it is the home twin who is the older.

The resolution of the "paradox" is that, according to the traveling twin, the home twin ages by a very large amount during that one instant in his life at his turnaround. The implicit assumption that nothing could happen to the home twin's age during that single instant in the traveling twin's life at the turnaround was wrong.

It is often claimed that acceleration by the traveling twin cannot be the resolution of the twin "paradox" because an equivalent scenario, one with no acceleration, can also resolve the "paradox". The revised scenario says that a third person (perpetually inertial) could just happen to be passing by (and momentarily co-located with) the traveling twin at the point where the traveler intended to do his instantaneous turnaround. (This third person has always been, and will continue to be, headed toward the home twin.) And it just coincidentally happens that that third person has exactly the same age as the traveling twin when they are momentarily co-located. So the traveling twin decides not to accelerate (and just continue moving away from the home twin), and it is just the third person who meets up later with the home twin. At the meet-up, the third person will be exactly as old as the traveling twin would have been at his reunion with the home twin, if he had instantaneously turned around as originally planned. So it is then contended that this scenario is completely equivalent to the original scenario, but without any acceleration. But that contention is not correct.

If the third person is really to be a VALID substitute for the traveling twin at the instant of his meet-up with the home twin, in the sense of fully addressing the original "paradox", the third person's total ageing, ACCORDING TO THE TRAVELING TWIN, during the ENTIRE trip (beginning with the separation of the two twins) MUST be the same as the total ageing that the traveling twin WOULD have experienced if the traveling twin had turned around as originally planned. And since the third person (by design) has the same age when he meets up with the home twin as the traveling twin would have had at the reunion (if he had done the turnaround as originally planned), it follows that the third person (if he is to be a valid substitute for the traveling twin) HAD to be age zero, according to the traveling twin, when the traveling twin started his trip. But that is not the case, which can be seen from the following numerical example.

Let the gamma factor for the two twins' relative motion be equal to 2, which implies that their relative velocity (traveling away from other) is v = 0.8660... ly/y . Let the traveling twin be 10 years old at the (originally planned) turnaround point. According to the home twin, the third person is traveling at the same speed toward her. To determine the speed W at which the traveling twin and the third person are approaching each other (according to each other), we must use the relativistic addition of velocities result:

W = 2v / (1 + v * v) = 0.98974... ly/y , which gives a gamma factor of

GAMMA = 7.

(I use capital letters for this gamma factor, to distinguish it from the gamma factor of the relative motion between the two twins.)

So what does the traveling twin say is the age of the third party at the beginning of the scenario (right when the traveling twin starts moving away from the home twin)? He says that the third person is ageing 7 times slower that he is, so while the traveling twin was ageing by 10 years getting to the turn point, the third person was ageing by 10/7 = 1.4285... years. So the third person was 10 - 1.4285 = 8.5714 years old at the beginning of the scenario. Since he was NOT zero years old then, he CANNOT (in the opinion of the traveling twin) be a valid substitute for the traveling twin for the purpose of resolving the twin "paradox". So the two scenarios are NOT equivalent, and the non-acceleration argument is a red herring ... it does not resolve the paradox.

3. ### arfa branecall me arfValued Senior Member

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What if the third person synchronises a clock with the traveling twin at the intersection point?

5. ### Mike_FontenotRegistered Member

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In effect, that's already been done. In the "No-Acceleration" scenario, part of the specification of the scenario is that the third party just coincidentally happens to be the same age (10 years old) as the traveling twin is when they are momentarily co-located at the (originally planned) turnaround point. And since the third party has the same velocity on his trip to the home twin as the traveling twin would have had, he will thus be the same age (20 years old) when he meets up with the home twin as the traveling twin would have been at the reunion. But what prevents the third party from being a valid substitute for the traveling twin, in the sense of being able to resolve the twin "paradox", is that he was NOT the same age as the traveling twin was when the traveling twin left the home twin, according to the traveling twin.

7. ### Neddy BateValued Senior Member

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I disagree.

In the no-acceleration scenario, the third person is only meant to be a substitute for the second half of the original out-and-back journey. As such, the only requirement is that the third person meet up with the traveling twin at the would-be turnaround point, sharing the same time on his clock, and the same velocity which the traveling twin would have had after the instantaneous turnaround.

In the no-acceleration scenario, the original traveling twin still represents the first half of the original out-and-back journey. As such, he and the home twin are the only two required to have the same time on their clocks at the very start.

Last edited: Jan 1, 2018
8. ### NotEinsteinValued Senior Member

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I haven't checked the details of your situation (other members appear to have done that), but your conclusion at least is correct: the theory of special relativity handles accelerations just fine, so doing away with the acceleration has no bearing on the twin paradox. (Which, if you do all derivations carefully, actually doesn't exist in special relativity in the first place.)

9. ### Neddy BateValued Senior Member

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I think Mike_Fontenot is saying that removing acceleration from the scenario makes it invalid, which seems to be the opposite of what you are interpreting his words to mean.

10. ### NotEinsteinValued Senior Member

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You may be right, and I may be mis-interpreting it. I'm only making the point that with or without acceleration, there is no contradiction in this scenario when using the theory of special relativity; both scenario's are handled without any problems.

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I agree.

12. ### arfa branecall me arfValued Senior Member

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I think if the outgoing twin synchronises a clock with the ingoing third party, it doesn't matter what the outgoing twin knows about the age of the third party. What matters is what the clocks measure, and the outgoing twin's clock becomes irrelevant to the "paradox" after the synchronisation.

13. ### Confused2Registered Senior Member

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Could we call the turn-around point 0 (zero)? Where the home twin lives at -x. The traveling twin starts at -x/2 in his frame and the extra twin starts at x in the home twin frame, x/2 in the extra twin frame and x/7 in the traveling twin frame. With luck all these x's will turn out to be numerically equal. The twin and the extra twin will cross at zero and everybody will be happy.

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15. ### Neddy BateValued Senior Member

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That's right. And just as the outgoing twin's clock is irrelevant after the synchronisation, the third party's clock before the synchronisation is also irrelevant. This is contrary to Mike_Fontnont's claim that the third party's clock must say zero at a time that is well before the syncrhonisation, (at the start of the experiment when the home twin and traveling twin's clock both say zero.)

Last edited: Jan 2, 2018
16. ### Neddy BateValued Senior Member

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No, you are overlooking the possibility that the apparent paradox can still come from the instantaneous acceleration scenario, while the non-accelerated scenario can be useful to resolve that apparent paradox by letting the third party represent the second half of the instantaneous acceleration scenario, just without any actual acceleration.

Think of it this way: Would you have any objection to the original traveling twin being replaced at the very start by an inertial one who never accelerated, but just happened to be passing the home twin when both their clocks say zero? I would hope not.

17. ### Xelasnave.1947Valued Senior Member

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Pity we can not conduct an experiment to observe actual results.
Alex

18. ### Confused2Registered Senior Member

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The Muon experiment is close... ( http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html )
the muons travel down through the atmosphere at high velocity between two clocks separated by 10km in the Earth frame. Time dilation is as predicted by SR. I see no reason to claim the same effect would not be observed if the muons were traveling up through the atmosphere, or if by some means the muons were reflected back up the way they came. The physical interpretation of the Minkowski spacetime diagram

19. ### Neddy BateValued Senior Member

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Okay, after thinking about this some more, I think I understand your concern a little better. You want the resolution offered by the non-accelerating scenario to specifically show that the traveling twin should realize that the home twin would suddenly age by a large amount during his instantaneous turnaround. I agree that is the key information that is needed, not just the time-dilated aging rates given by the time dilation formula.

Well, that key information is exactly what the non-accelerating scenario is designed to provide, but its purpose is to do so without invoking acceleration. So if you demand acceleration be part of it, then just use the instantaneous acceleration scenario and forget about the other scenario.

But for those who would like to see the exact same information provided without acceleration being part of it, all that is required is a careful comparison of the inertial frame of the third party to the inertial frame of traveling twin, in the moment the traveling twin and third party are both in the same place, with their clocks reading the same time.

By analysing both reference frames in detail (including use of Einstein synchronised clocks at rest in both frames), we can compare what those two inertial frames would say about the time on the home twin's clock in that instant of time. Compared to what the traveling twin's inertial frame would say, the third party's inertial frame would say that the time on the home twin's clock would be a ahead by a large amount. And that large amount precisely matches the large amount obtained in the acceleration scenario, in the instantaneous turnaround.

Last edited: Jan 2, 2018
20. ### Xelasnave.1947Valued Senior Member

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I really think there is sufficient difference between a particle and a twin to leave the prediction of a result open.

Now if we could do an experiment with twins that would be the way to go.

It just seems unproductive to speculate upon something that can never be verified and to rely upon a theory that has not been tested within parameters matching the reality of human twins experiencing the senerio laid out in the paradox.

Thanks again.

Alex

21. ### Neddy BateValued Senior Member

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The issue is in no way restricted to twins or human aging. The issue is simply the natural passage of time, as recorded by an ideal clock, and naturally-decaying muons are a perfectly good example.

Twins were originally used in thought experiments because they were supposed to be an easy example, because everyone would understand that they would start off at the same age. And then if they end up different ages at the end, that would indicate that time itself had passed at different rates for each of them.

22. ### Xelasnave.1947Valued Senior Member

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Firstly thank you for replying to my post.

I assumed the issue extended past the twins but the discussion seemed to be about twins so hence my comment somewhat focused upon the prospect of an experiment specifically involving twins.

From my very limited knowledge of time dialation I gather experiments showing time dialation demonstrate the principal however the observations are of very small sections of time in the order of observed differences of less than a second and I think if we are to extrapolate we perhaps should rely upon something in addition to what clearly the theory indicates.

I suppose I have a problem generally with extrapolation without supporting observation.

Consider this.
An observer comes to this planet and determines the growth rate of a tree to be one foot per year and based on that observation determines that if the observer returns in two thousand years the trees will be then over two thousand feet tall.

It would seem the calculations predict via extrapolation trees of over two thousand feet in height.

Presumably the trees wont obey the extrapolation.

Alex

23. ### Neddy BateValued Senior Member

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You seem to think that the way relativity theory was developed was that first someone noticed that a tiny particle's lifespan lasted a few fractions of a second longer than what would normally be expected, and from that it was "extrapolated" that human-scale beings could live many years longer under similar circumstances, or something like that. Nothing could be farther from the truth.

What actually happened was that a number of different theoretical physicists were working independently to explain how the speed of light could be a physical constant as was being demonstrated in that time. Einstein happened to be the first to put it all together as a fully coherent physical theory, but Lorentz and others were on a similar path, and the equations which Einstein's theory ended up using are still to this day named after Lorentz who developed them first. However, Einstein's approach was the first completely self-consistent physics theory which was set to build upon and revolutionize the physics of Isaac Newton, and Galileo Galilei before him.

Other than speed of light experiments, at that time there was not really any experimental verification for the predictions of relativity theory. It was only after the theory was published that experiments started being proposed to test its predictions, and every test was found to support the theory. No one had ever observed such a bizarre thing as time dilation before, but relativity predicted it, and then later it was observed. Think about that. Of course no scientific theory is ever proven by experiments, but rather, it only takes one experiment to disprove a scientific theory. And to date not one has been found to disprove relativity.

The notion of 'time' discussed in physics is that of the actual passage of time on ideal clocks. It is not blind-sided by using only sand through an hourglass, or the rate of growth of human twins or trees. The clocks used in physics need to be accurate enough to measure the speed of light, (some 300,000 km per second).

Sorry for the long post, but I thought you should know the territory you are venturing into when you enter a physics thread and say something to the effect that you have not really studied it, but you suspect that perhaps someone along the way might not have considered that humans are bigger than muons, or that trees can only grow so tall before they fall over.

Last edited: Jan 2, 2018