Samshorn said:
Indeed, which is why you were mistaken when you claimed above that the reciprocalness of the two Doppler effects is not classically contradictory. Hopefully that's clear now.
I hope you are not purposely misrepresenting what I said. I will assume that you never understood what I said. So I will draw a diagram to show how even under classical Doppler the explanation that I offered in the second paragraph of post #3 works:
The horizontal axis is distance and the vertical axis is time.
Here is that explanation:
ghwellsjr said:
Let's say that you are looking at two observers with clocks. One of them is a fixed distance away from you so you will see his clock ticking at the same rate as your own. They may have different times on them but we don't care about that, we only care about tick rates. The second observer is traveling at a constant speed from the first one directly toward you. Therefore, you will see his clock ticking faster than yours. You also know that you are seeing time progress on the traveler's clock compared to the first observer's clock just as the traveler is seeing them but delayed in time, provided that the light from both clocks travels towards you at the same speed. Therefore the ratio of the tick rates that you see of the distant fixed clock to the traveler's clock is some ratio that we called R. But the ratio of the tick rates that you see of the traveler's clock compared to your own (which is the same as the distant fixed clock) is the inverse of R.
You are the green observer C. You are looking at the clocks of the red observer A and the blue observer B. The red observer A is stationary with respect to you but both of you are traveling in the medium at the same speed. The blue observer, B, is traveling at some unknown, arbitrary speed from observer A towards you, the green observer C. The tick of each clock is represented by a colored dot.
In this example, you see blue's clock ticking three times faster than your own as depicted by the pale blue signal lines coming from his tick dots toward you. But you receive three of his for every one of your tick dots.
You can also see the same thing that the blue observer sees when he looks at the red observer's clock compared to his own, just delayed in time, namely that blue sees red's clock ticking at 1/3 the rate of his own clock. This is depicted by the black lines coming from each of red's tick dots and impinging on blue's tick dots but only every third one.
The two Doppler effects that I was talking about are your observations of B's clock compared to your own (3, in this example) and A's clock compared to B's clock (1/3, in this example). You can pick any other example and you will get the same result that the two Doppler factors are inverses of each other. And it doesn't matter if you consider classical Doppler or Relativistic Doppler or if you consider that the observers are moving with respect to a medium or stationary in it.
OK, got that? Please do not misrepresent what I said again. Of course if you think I am mistaken, then you're going to have to offer some proof--a diagram would be good.
Samshorn said:
It isn't just me who is invoking inertial coordinate systems, you are invoking them too (albeit tacitly and with denials). The two principles that you explicitly cited as your foundation are both expressed in terms of inertial coordinate systems. For example, Einstein expresses the relativity principle by saying the laws of physics are not affected "whether they be referred to the one or the other of two systems of coordinates in uniform translatory motion". No other principle is needed for this, provided of course that you've given some operationally meaningful definition of "inertial coordinate system" (which Einstein did in the first sentence of the first paragraph of Part I of his EMB paper). Likewise the lightspeed principle (or any proposition about 'speeds') has meaning only in the context of operationally meaningful measures of space and time.
The Principle of Relativity has experimental evidence which does not require the formulation of a specific set of laws and a transformation that embodies that principle. This is what Einstein was talking about in his
1920 book on relativity. For example, in at the end of chapter 5 which is about the Principle of Relativity, he says:
However, the most careful observations have never revealed such anisotropic properties in terrestrial physical space, i.e. a physical non-equivalence of different directions. This is a very powerful argument in favour of the principle of relativity.
Or in chapter 7 where he says:
Prominent theoretical physicists were therefore more inclined to reject the principle of relativity, in spite of the fact that no empirical data had been found which were contradictory to this principle.
So I'm talking about the "careful observations" and "empirical data" that support the Principle of Relativity without considering what specific laws or transformation is involved.
When MMX was performed, did they have to establish a reference frame or a coordinate system involving spatial coordinates and an establishment of coordinate time throughout that spatial coordinate system? In the same way, my thought experiment involving three observers and their clocks, which is separate from the twin scenario, does not establish any coordinate system. It does make a lot of assumptions which are always made in any discussion of this type but are rarely enunciated, so I don't know why we have to get any more specific than just stating the normal and usual way of discussing a thought experiment.
So in my three-observer/clock thought experiment, I stated that if the Principle of Relativity is assumed to be true, then whatever Doppler effect each observer determines for any other observer has a symmetrical relationship. This is the part that I said does not work under classical Doppler but that because classical Doppler does not conform to the Principle of Relativity in the way that we are concerned about here.
Samshorn said:
Again, those two principles are expressed in terms of inertial coordinate systems. So you can't claim to be invoking these principles while denying that you are treating with inertial coordinate systems. Also, even if we overlook the logical inconsistency of your analysis, it doesn't allow you to conclude the traveling twin ages less, because it fails to quantity Q, which could be 1.
Once again, you are misrepresenting what I said. What I said was:
ghwellsjr said:
If I can correctly determine that A sees B's clock accumulate Q times the amount of time on his own clock, then there can be no other answer than B sees A's clock accumulate 1/Q times the time on his own clock. Why is this controversial?
This is true even if Q = 1, isn't it? And it's true when Q ≠ 1, isn't it. It's not controversial, is it?
Samshorn said:
Special relativity is not incoherent, whereas the "explanation" that you propose as an alternative to special relativity is incoherent, for the reasons I've explained. Again, you invoke principles whose meanings are explicitly given in terms of inertial coordinates, and yet you claim to do without any reference to inertial coordinates. That isn't logically consistent. Also, you yourself admit that your approach can never be quantitative, and for the same reason, i.e., inability to connect with any operationally defined measures of space and time.
Again, a misrepresentation of what I said. I didn't say or imply that SR was incoherent. Why do you imply things like this? And if you properly understood my approach, you would see that it is perfectly coherent and logically consistent and has nothing to do with the fact that it has limitations.
Samshorn said:
No, you simply assumed your result, i.e., you assumed that the age ratios of the twins are reciprocal, and from this assumption you backed out what value F would need to have in order for your assumption to be true. That is backwards from what's needed to demonstrate why the twins get reciprocal results.
You make it sound like my assumption is invalid. How can it not be valid? You objection doesn't make any sense at all.
Samshorn said:
Well, it's certainly possible to correctly determine the result according to special relativity, but one of my points is that you haven't correctly determined anything. Again, without providing any operational meaning to the concepts of speed (as in the 'speed' of light and the motions of the twins) you have no warrant to even expect any Doppler shift at all (e.g., your unquantified Q could always be 1), not to mention that you can't apply either of the principles you claim to be applying, which are based on the same operational meanings. All you've done is appropriated a result from special relativity and forfeited its quantitative content and claimed to be able to explain it qualitatively by some fuzzy hand-waving (with the mistaken notion that classical Doppler is all that's required) with no logical coherence. For example, you claim time dilation is not observable, which of course is false, and in fact time dilation is a necessary consequence of your premises, as explained previously.
Another misrepresentation of what I said. I never said "that classical Doppler is all that's required". You need to read carefully all that I have written and understand it instead of misrepresenting it and accusing me of having mistake notions and characterizing my posts as "fuzzy hand-waving" and having "no logical coherence".
Samshorn said:
It's called the twins "paradox" precisely because beginning students suspect that if we worked out the result from the other twin's perspective, applying the same principles, we would get the symmetrical (not reciprocal) result, typically because they think of relativity in purely kinematical terms, without understanding the dynamical foundations in the principle of inertia. Hence they suspect that special relativity is logically inconsistent. To explain why special relativity is logically consistent, and why the other twin sees 1/Q, it makes no sense to simply assume that special relativity is logically consistent and that therefore the twin must see 1/Q. This is the very thing that we need to show, by carrying out the analysis from the other twin's point of view. This requires us to explain why the two points of view are dynamically asymmetrical, even though they are kinematically symmetrical, and this requires us to define operationally meaningful measures of space and time - the very thing you fail to do.
I made very clear that I was not talking about Special Relativity. I was talking about the Principle of Relativity. The OP did not ask about Special Relativity, he asked:
Moris526 said:
In the twin's paradox, why one of the brothers is older when they meet again?. if movement is relative. What determines which of them ends up older?
Movement being relative is an issue of the Principle of Relativity and I wanted to show that it's not because of any particular theory about relativity, but just because of that Principle and that light propagates independently of it the motion of its source, that we can determine which twin ends up older, just like he asked.
By the way, none of the ideas that I presented in this thread are unique to me. They have come up on this forum and in other references by other people in the past.