thought experiment about time dilation

nonnonenon

In theory, their clocks tick slower to their partners because of time dilation.
But in reality, you have to take Relativistic Doppler effect into consideration if you want to simulate how they see other's clocks. And this makes their clocks tick faster to their partners.

Is this version correct?

PeterDonis

I would put it the other way around. What each observer actually sees--meaning, the images that actually reach each observer from the other, containing the actual images of clock readings--is what is directly observed. (It is not "simulated".) The relativistic doppler effect tells you about that without having to bring in time dilation at all; all you need to know is the relative velocity of the two observers. And, as you say (and as ghwellsjr explained in detail), each observer in this scenario actually sees images of the other observer's clock running faster than his own.

However, each observer knows that the images he is seeing at a given instant took some time to get to him (at least, that's true until the two observers meet up at 4:00 pm, by both their clocks, at which point they are at the same spatial location). When each observer corrects for that, he finds that the other observer's clock is running slower than his own while they are in relative motion, by a factor equal to the time dilation factor based on their relative velocity. This is not "in theory"--it's what each observer will actually conclude when he corrects for light travel time.

The above is, I believe, a sufficient answer to your question; but I feel compelled to say some more, though it might only add confusion. If you find that the above is enough, feel free to ignore the rest of this post.

Which answer is correct "in reality"? IMO, if you feel you have to ask that question, you're thinking about it wrong. If two observers are spatially separated, there is no single answer to the question of whether either one's clock is "running slower" or "running faster"; it depends on how you want to define your terms. The only questions that have definite, unique answers are questions about invariants.

Things that are directly observed are invariants: for example, "what clock reading on B's clock is contained in the image of B that observer A receives, at the instant when A's clock reads 3:30 pm?" Also, when two observers are *not* spatially separated (as A and B are not at 4:00 pm), they can directly observe each other's clock with no light travel time delay, so those observations have to be invariant--for example, the fact that A's and B's clocks both read 4:00 pm when they meet.

But for example, if A asks himself, at the instant when his clock reads 3:30 pm, "what time is B's clock reading *right now*?" the answer will depend on how he wants to define "right now". The image he is receiving from B at that instant will show a clock reading; that, as above, is a direct observable. A can adjust that clock reading for the light travel time if he wants, and the result of that computation will be "B's clock reading right now" for A, according to the usual convention for constructing A's frame of reference while he is moving. But there is no principle of physics that *requires* A to adopt the result of that computation as "B's clock reading right now".

Does that mean that time dilation is "not real"? Of course not. Consider the standard "twin paradox" scenario: observer T sits at rest in his spaceship, floating freely, while observer S flies away at relativistic speed, then turns around and comes back. S's clock will have less time elapsed than T's; that's an invariant physical fact, and the usual explanation is time dilation. (There's a lot lurking beneath the "usual explanation", of course; but it's still essentially correct.) So yes, time dilation is "real". But notice that, to show that it was "real" here, I gave a scenario where it's a direct observable--T and S both pass through the same pair of events, at the start and end of the trip, so the difference in elapsed times on their clocks is directly observed by both of them.

I hope this didn't muddy the waters too much.

Vandam

Thanks for the link to Einstein's 1905 paper. The english translation. I hope you ever read the original german paper:
http://nausikaa2.mpiwg-berlin.mpg.de...905&step=thumb
I did it for you. I speak flemish which is close to german. That helps a lot.

Let me first show you the verbs in the english and german versions:

>>>>>>>>>>>
It is known that Maxwell's electrodynamics—as usually understood at the present time—when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena.

Daß die Elektrodynamik Maxwells -- wie dieselbe gengen-
wärtig aufgefaßt zu werden pflegt -- in ihrer Anwendung auf
bewegte Körper zu Asymmetrien führt, welche den Phänomenen
nicht anzuhaften scheinen, ist bekannt.
-------
It might appear possible to overcome all the difficulties attending the definition of “time” by substituting “the position of the small hand of my watch” for “time.”

Es könnte scheinen, daß alle die Definition der ,,Zeit“ be-
treffenden Schwierigkeiten dadurch überwunden werden könnten,
------
Thus, whereas the Y and Z dimensions of the sphere (and therefore of every rigid body of no matter what form) do not appear modified by the motion, the X dimension appears shortened in the ratio ...

Während also die Y - und Z-Dimension der Kugel (also
auch jedes starren Körpers von beliebiger Gestalt) durch die Be-
wegung nicht modifiziert erscheinen, erscheint die X-Dimension
im Verhältnis ...
------
We still have to find the amplitude of the waves, as it appears in the moving system. If we call the amplitude of the electric or magnetic force A or A' respectively, accordingly as it is measured in the stationary system or in the moving system, we obtain ...

Wir haben nun noch die Amplitude der Wellen, wie
dieselbe im bewegten System erscheint, zu suchen. Nennt
man A bez. A' die Amplitude der elektrischen oder magne-
tischen Kraft im ruhenden bez. im bewegten System gemessen,
so erhält man ...
-----
It follows from these results that to an observer approaching a source of light with the velocity c, this source of light must appear of infinite intensity.

Es folgt aus den entwickelten Gleichungen, daß für einen
Beobachter, der sich mit der Geschwindigkeit V einer Licht-
quelle näherte, diese Lichtquelle unendlich intensiv erscheinen
müßte.
<<<<<<<<<

You noticed that Einstein used two different verbs: 'scheinen' and 'erscheinen'. He doesn't mix these at random. They have different meanings:

'Sheinen' means: illusion - an appearance that does not correspond to reality - it appears so, but it may not be true - what you see is mere appearance - only outward show, things are not what they seem to be, etc. (Anschein= farce, sham, make-believe, pretence etc...)

'Erscheinen' is more: as it shows, come to light, as it is, etc.

In the english version 'sheinen' and 'erscheinen' are translated by one verb only: 'appear'. Strictly speaking the translation is not wrong (ask google to translate the english words and somehow you will find 'appear'), but the very important difference in meaning in german disappears in the english translation. Or at least 'might very well' get lost. I suppose that in english one can use the verb 'appear' in both meanings as long as the context makes clear what the semantics are. In the english 1905 paper translation that's not so obvious as in the original german text. Prove is that in thousands of texts dealing with SR the english 'appears' is often replaced by 'seems', which is a synonym of 'appears', but not the correct one to match the german significance. 'Seems' refers to 'scheins' (= illusion). Dalespam's use of 'apparent' (= seeming, not proven real, illusive, illusory, likely, ostensible) is also prove of this, otherwise there would be no need to add that adjective. And his 'sense' of simultaneity is superb poetry, but no physics.
(The same mistake occurs in other translations, because a lot of them are translations of the/an english text. I will not go into that.)
Worse is that authors of those ambiguous texts (because of the use of 'appear' without proper explanation, or the word 'seem'), are probably not aware of the real significance of SR: trains ARE shorter, events ARE not simultaneous for one observer and ARE simultaneous for the other, meaning both observers ARE in different 3D worlds. etc. Those authors (not unlike many PF members) hide themselves in a type of Lorentz Ether Theory interpretation of the Lorentz Transformations as illusionary abstract calculations, because it matches perfectly the incorrect 'seems' interpretation of the german 'erscheins'. Unfortunately all those hundreds of thousands of people over the last 100 years are wrong. That's the most dreadfull and horrible scenario Einstein could ever imagine.
I hope I made my point clear why I get extremely nervous, with a sense of (to say the least) acute desperation, when I am confronted with a text using 'appear' vocabulary. (There is a tree in front of you. Nobody says that a tree appears in front of you. And for me a moving train is shorter, not appear shorter. A blitz of 10.000 volt shivers through my body. And make it a 20.000 volt when I read that the train 'seems' shorter. And over the last 20 years it was (and still is) flabbergasting to read how people try to defend that false, erroneous approach of SR.
.

harrylin

That looks interesting but not here: please don't hijack this thread - thanks! (it's even against the forum rules).

PeterDonis

I don't want to hijack the thread either, but I think it's important to say that I am uncomfortable with using "appear" in this connection too. It's unfortunate that English doesn't have a good pair of verbs that respect the distinction that the German verbs do; it makes it hard to describe scenarios with the "erscheinen" meaning without having yourself misunderstood as intending the "scheinen" meaning. I think you are making this (understandable) misunderstanding yourself in reference to at least some people here on PF (including me). If this really bothers you, a fuller discussion of it, as harrylin suggests, should have its own thread.

nonnonenon

In the calculation, time dilation is not needed when using the relativistic doppler effect, is that because the relativistic doppler effect have already considered the effect of time dilation?

jtbell

Yes.

Vandam

Correct.
See new thread:
http://www.physicsforums.com/showthr...=1#post4046189