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The following is a quote from the Haifa Lectures (Sachs):
“If, for example, the time change in the description of any process in nature is a physical change in aging, then when a twin sister space pilot goes on a round trip journey from her sister at home, she would age less than her sister during the journey, from the perspective of the stay-at-home sister. But from the perspective of the traveling sister, it is the stay-at-home sister who making the round trip journey and the stay-at-home sister would be younger than her pilot sister after the completion of the round trip journey! Thus, with this interpretation, it would have to be concluded that when the traveling sister returns from her round trip, she would be both older and younger than her sister. This is called the “twin paradox”. The error in this conclusion is the faulty interpretation of the time measure as an objective physical change instead of a subjective scale change, when transforming to different reference frames!”
Sachs seems to be saying that there is no physical difference in the ageing of the twins. His argument (if I interpret it correctly) that either twin can correctly regard the other as the “moving” twin ignores the fact that the pilot experiences acceleration and, therefore, must be considered as moving relative to the stay-at-home twin.
Time dilation has been experimentally tested, but could it be reasonable to argue that although the clocks used in the experiment show different times, nothing physical has happened to either clock, and that they are both the same age as they would have been if they had both stayed on the ground?
Is this what Sachs means by: “faulty interpretation of the time measure as an objective physical change instead of a subjective scale change”
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Notice the last sentence in Sach's statement. In that one Sachs clearly indicates that the idea in the first part of the paragraph is wrong. I don't really understand the explanation he gives in the final sentence. But whatever it says we can still expect the traveling twin to age less than the stay at home twin. It will take a bit of thought and investigation for me to figure out just how that works.
Bill Gill
C is not the speed of light in a vacuum.
C is the universal speed limit.
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There is a long writeup about the twin paradox on Wikipedia:Twin paradox. It seems that there are a number of different ways of addressing the twin paradox and they all come out working properly. Here is one sample that they give which shows how it works, at least in this instance. Different methods of doing the calculation work out differently, but have the same answers. Specific example
Consider a space ship traveling from Earth to the nearest star system: a distance d = 4 light years away, at a speed v = 0.8c (i.e., 80 percent of the speed of light).
(To make the numbers easy, the ship is assumed to attain its full speed immediately upon departure—actually it would take close to a year accelerating at 1 g to get up to speed.)
The parties will observe the situation as follows:
The Earth-based mission control reasons about the journey this way: the round trip will take t = 2d/v = 10 years in Earth time (i.e. everybody on Earth will be 10 years older when the ship returns). The amount of time as measured on the ship's clocks and the aging of the travelers during their trip will be reduced by the factor epsilon = sqrt{1 - v^2/c^2}, the reciprocal of the Lorentz factor. In this case ε = 0.6 and the travelers will have aged only 0.6 × 10 = 6 years when they return.
The ship's crew members also calculate the particulars of their trip from their perspective. They know that the distant star system and the Earth are moving relative to the ship at speed v during the trip. In their rest frame the distance between the Earth and the star system is εd = 0.6d = 2.4 light years (length contraction), for both the outward and return journeys. Each half of the journey takes 2.4/v = 3 years, and the round trip takes 2 × 3 = 6 years. Their calculations show that they will arrive home having aged 6 years. The travelers' final calculation is in complete agreement with the calculations of those on Earth, though they experience the trip quite differently from those who stay at home. I hope this helps. Bill Gill
C is not the speed of light in a vacuum.
C is the universal speed limit.
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Bill, I have no problem with the logic of the Wiki reasoning. What I wonder about is the conditional clause at the start of the Sachs quote:
“If, for example, the time change in the description of any process in nature is a physical change in aging...."
Is he saying that no physical change takes place?
If so, does that mean that (as in the Wiki example) one twin ages 10 years in her F of R, while the other ages 6 years in hers; or does it mean that there is no age difference when they come back together - just a descriptive factor that makes no physical difference?
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“If, for example, the time change in the description of any process in nature is a physical change in aging...."
That isn't completely clear, but I think I may have figured it out. I believe that what he is saying is that the clock being used in that particular example is the physical change associated with aging. The Wiki article mentioned that. I'm not going to go looking at the complete article but I recall it saying something about the age of the persons participating being the equivalent of clocks.
Bill Gill
C is not the speed of light in a vacuum.
C is the universal speed limit.
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