Very cool but the people on board that ship would still have aged the equivalent of 3 millions years wouldn't they?
Saturday, September 12, 2026
Why Does E=MC2?
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Very cool but the people on board that ship would still have aged the equivalent of 3 millions years wouldn't they?
Actually, we (physicists very broadly defined, people like me trained in theoretical chemistry) are quite confident that the people in the ship would age the same roughly fifty years as described in the text that you are disagreeing. This is very strange, granted. Indeed, it is extraordinary enough to require extraordinary evidence. As it happens, we have some extraordinary evidence...
ReplyDeleteTo me, the most convincing general evidence is how zillions of very precise measurements --- such as the precise fixed constant frequencies of spectral lines for various elements, or the endlessly varying relativistic corrections routinely performed by GPS all the time in order to make each of its zillions of very precise location calculations based on satellites travelling at several miles per second --- routinely agree with the relativistic analysis so precisely. But a more intuitively understandable line of evidence, more specifically that the 50-year enormous time distortion for the space travellers is expected, is that various elementary particles such as mesons decay with a half-life in the same general way that radioactive elements do, and they are sturdy enough that one can use cyclotrons and similar gear to speed them up to speeds approaching the speed of light (and still prevent them from escaping the laboratory). When one does, their decay slows down as predicted by relativity, even for speeds fast enough that the slowdown is not some tiny fiddly correction as appears in GPS satellite calculations but is instead a large fraction of the elapsed time. Loading a pion into a cyclotron and finding that it slows down is rather conceptually similar to loading a space traveller into a superfast spacecraft and expecting a similar slowdown, so I am pretty confident we are not just misleading ourselves with overconfident bafflegab about how physics is so tricky that the unwashed masses just misunderstand it and how because we are awesome and love patting ourselves on the back about our Sekrit Knowledge ergo this strange thing really does happens.
As a side note, it'd be difficult to build a suitable cyclotron to check the cyclotrons-and-mesons behavior at home --- few amateurs have the budget or skills to do stuff with high vacuum, and high vacuum is just one prerequisite --- but some of the spectral line evidence _could_ be checked with fairly ordinary amateur resources. One would need complicated calculations and hardcore quantum mechanics usually not mastered by undergraduates in order to calculate the results predicted by relativistic QM, but modern cheap computers and free software would help, and although computing the relativistic QM predictions is difficult, noticing that the non-relativistic models are not fitting is considerably less difficult than figuring out exactly what relativistic QM predicts. For decades hardcore amateur astronomers have done pretty sophisticated things observing and analyzing the motions of asteroids and comets, and my impression is that the difficulty of calculating basic relativistic QM effects in the hydrogen spectrum overlaps with the difficulty of some of those amateur astronomical calculations.
That's a very clear and authoritative reply, but I would say that you and Chris are both right. As I understand it, the elapsed time depends on what Einstein called the inertial frame of reference. The meson's decay speed seems longer to an observer outside the cyclotron, but is normally fast to the meson itself because it and the observer are in different frames of reference. Thus the people on the spaceship would experience only 50 years of aging, but to the people on earth the voyage would take millions of years. (I believe Heinlein used this paradox in one of his stories, _Time for the Stars_, maybe.)
DeleteJake Smith wrote "As I understand it, the elapsed time depends on what Einstein called the inertial frame of reference."
ReplyDeleteWhat I would say is related, and maybe the same thing. Einstein's relativity makes it clear that reasonable people can naturally disagree by as much as 3 million years about whether the people stepping out of the spaceship 3 million light years away are doing it at the same moment as after 3 million years have passed on Earth. (I think this relates to your "frame of reference" remark as, roughly, (1) there is no absolutely compelling reason to prefer any particular inertial frame of reference over any other inertial frame of reference and (2) with 3 million lightyears of distance difference to work with, different inertial frames of references can naturally report as much as 3 million years of time difference. It turns out that this difference is an issue of arbitrary convention like how the English and the Germans or the French could disagree about which observatory should be the center of the time zone system or the longitude system, not an issue of the physical world like whether objects fall toward the center of the Earth or upwards or sideways or whatever.)
For anyone interested in thinking very seriously about this kind of time dilation situation, I recommend tweaking the thought experiment so that the simultaneity at a distance issue (and indeed most frame of reference issues) goes away. How about thinking about a round trip, where the travellers zoom out 3 million light years, then zoom back 3 million light years, and then compare notes with the people standing outside the door of their spaceship who spent the 6-million-or-so years staying on Earth? As far as I can tell, that modified situation still captures the spirit of the thought experiment in the original post, and it contains fewer temptations to try to apply one's physical intuition to something which turns out to be surprisingly unphysical (a simultaneity concept which turns out to be as arbitrary as the zero-of-longitude concept) and which is not central to the issue. In that tweaked experiment, everyone at the return meeting should be able to agree that 100 years have passed for the travellers, and 6 million years have passed on Earth; the issue is not potentially obscured by millions of years of potential slop from third parties zooming along on some other trajectory disagreeing about whether the spaceship arrived at its distant destination at the same moment that the 3 million year calendar ticked over on Earth.
As soon as I wrote it down and stepped away and thought about it - I thought I had it backwards: that only 50 years would pass for those on the spaceship going the speed of light but that 3 million years would have passed for those still on Earth (if it's still there). The converse got me wondering if the proposed destinating in Andromeda would also e 3 million years older and if that would still be there?
ReplyDeleteThis is a confusing subject - but I'm trying. Thanks for the answers.
Assuming the problem was supposed to involve travel at 99.99999999% (ten nines) the speed of light to Andromeda (2.5 million light years away):
ReplyDeleteThe people on the ship would be about 36 years older.
The Earth would be about 2.5 million years older.
The Andromeda galaxy would be about 2.5 million years older.
Formula: Take the fractional speed of light (ten nines) and enter it into your scientific calculator. Find the arcsine (inverse operation of sine) of this number - that's an angle. Take the cosine of that angle. That's how slowly time passes for you, compared to stationary people (time = 1).
cos(asin(0.9999999999)) is about 0.0000141421. Multiply that by the distance in light years (2,500,000) and you get about 35.36 years.
Special Relativity is just trigonometry applied to space and time.
Thanks
ReplyDelete