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Counter intuitivity and relativity

  1. Feb 11, 2010 #1
    One of the first expressions that I came across in studying SR was that it was Counter Intuitive.

    In particular this expression was used to define the relationship between local time and the time measured by a 'moving clock'.

    It seemed to be thought that newcomers to the theory would assume that, as the travelling clock would be seen to run slowly by a stationary observer, then an observer moving with the clock, would expect see the stationary clock run fast.

    {But that would mean that the 'newcomer' would be imagining it all as a single frame of reference - (such as the clock in a moving car running fast compared to a stationary one, which would be true if that clock were, indeed, running fast)}.

    But that is not what is being compared, is it?

    Are we not comparing the measuring of a moving clock, compared with a stationary (local) one?

    And, if so, then the reciprocal is measuring exactly the same measurement, i.e. the measurement of a clock (local to the stationary observer) moving relative to an observer local to the 'moving' clock.

    So in each case it is the measurement of a clock moving relative to the observer making the measurement. So, at least to me, it is intuitive that the two measurements would show the same relationship.

    This brings one to the question; if the two clocks are identical and the moving clock runs slow, which is the real time?

    (And I suppose, the associated question; if something can be measured, is it there fore real?)

    Now, my answer would be Yes they are real and therefore that both measurements have to be real.

    But how can both measurements be 'real' if they are identical clocks showing different times?

    The answer that I give has to be that both measurements are real and correct because they are not measuring the same thing.

    It seems to be assumed that because we are dealing with clocks that are local to each of two frames of reference, and that because 'clocks' somehow define how we measure time in SR, that we are measuring the same interval.
    But in one case we are measuring a stationary (local) clock and in the other we are measuring a moving clock. i.e. we are measuring it under different conditions.

    Am I getting this right?
  2. jcsd
  3. Feb 11, 2010 #2


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    This is correct. A clock measures the proper time of the curve in spacetime that represents its motion. ("Proper time" is a coordinate independent mathematical property of a curve).
  4. Feb 11, 2010 #3


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    Hi Grimble! Hi Fredrik! :smile:
    ah, that's for a moving clock that turns round and comes back.

    Isn't the question about two clocks that stay stationary in different inertial frames … how can each's measurement of the other as slow be real and correct?

    I'd say that they are measuring the same thing (well, each other's same thing! :wink:), since each is measuring a moving clock (not one stationary and one moving).

    Grimble will have to look for another explanation as to how it can be real and correct that each measures the other as slow. :smile:
  5. Feb 11, 2010 #4


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    Here's how I'd summarize the difference: If we want to measure the rate clock B is ticking in the rest frame of clock A, we can't just measure that using clock A itself, we need multiple synchronized clocks at rest in clock A's frame to compare their times with the time on B as it passes them. For example, if clock A reads 10 seconds and B reads 10 seconds at the moment they pass, and clock A2 (which is at rest relative to A, and synchronized with A in their own rest frame) reads 20 seconds and B reads 18 seconds when they pass one another, then we can say that B is only ticking at 0.8 the rate of A and A2 in their mutual rest frame.

    On the other hand, if we want to measure the rate A is ticking in the rest frame of clock B, we have to do the reverse, using multiple clocks at rest and synchronized in B's frame, say B and B2. Then if A and B both read 10 seconds when they pass, but when A passes B2, A reads 18 seconds while B2 reads 20 seconds, then we can say that in the B rest frame it is clock A that is running slow by a factor of 0.8.

    I provided I diagram illustrating such a scenario with multiple clocks moving alongside each other in this thread, if the above is unclear you may want to take a look.
  6. Feb 11, 2010 #5


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    What I said is true for all (ideal) clocks in both SR and GR, but you're right about this:
    An explanation should mention that the definition of what it means to measure the ticking rate of a distant clock as slow is that we determine that it advances less than ε seconds between two events on its world line that are simultaneous and ε seconds apart in our co-moving inertial frame. (At least this is the definition we'd use when both clocks are moving with constant velocity forever).

    The reason why the "apparent conflict" isn't really a conflict is that my co-moving inertial frame isn't the same as yours. So if we just understand the basic definitions, it's not even an apparent conflict.
  7. Feb 11, 2010 #6
    I don't find this conter-intuitive. Within the framework of the theory it's a natural conclusion, or it seems to be. Am I missing something? (I'm serious, am I?)
  8. Feb 11, 2010 #7


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    uhh? :redface: "A is slower than B, and B is slower than A" not counter-intuitive?

    What would Euclid have said?? :wink:
  9. Feb 11, 2010 #8
    Probably something that is a bannable offense! :rofl: Then again, Euclid wasn't a Relativist! ;)

    EDIT: Ok, it would be bannable if you spoke ancient greek. Fortunately I have the rare power to curse in modern and ancient greek... a power I shall not exercise. :laugh:
  10. Feb 11, 2010 #9
    Thank you, tiny-tim and Hi!

    But that is exactly what I am saying!
    so you are agreeing with my explanation, (but maybe I could have phrased it better).
  11. Feb 11, 2010 #10


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    I have yet to find a good definition of "real". Do you have one? If not then I would recommend staying away from all questions about the reality of something.

    Time dilation is a frame varying measurable effect. Whether or not you want to call that real depends entirely on your definition of "real".
  12. Feb 11, 2010 #11
    Well I think you are right, because you are looking at it within the right framework.

    My point was that to say it was counter intuitive is to belittle newcomers to the theory by implying that it is beyond them to understand what is being described.
  13. Feb 11, 2010 #12
    Understood! :smile: I see your point.

    DaleSpam Well... I think I'd argue for the reality of time dilation. Gravitational lensing has been directly observed, and many other properties that would be terribly inconsistant if GR was wrong. The consintancy of the observation of the laws of physics is only maintained if effects such as time dilation are real. By real, I would say it's something you and I experience daily. Astronauts experience it, and a clock on an airplane did. That's real for me.

    If we lived in a purely GR world, I think you could make a good argument for local realism. the fact that QM is telling us that is not the whole story is valid, but outside of the purview of the intuitivite nature of Relativity.
  14. Feb 11, 2010 #13


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    I also experience dreams daily. According to that definition dreams are real. Is that what you want?
  15. Feb 11, 2010 #14
    Dreams are real, your subjective interpretation of that neurological activity during sleep or upon waking is only real as a subjective experience. However in theory each neuron's activity could be mapped, so yes, dreams are as real as sleep.

    The pink elephant you rode in the dream, is not real, that is the definition of a 'fantasy'.

    I think people have the semantic BALLS, to make distinctions between 'real' experiences, and the subjective experience of one person that is not universally observed to be consistant.

    This is the Relativity area after all, and we're not talking about [tex]\Psi = \infty [/tex] of pure SQM. (to be clear, I mean 'the wavefunction is everything' not literally psi at infinity)
  16. Feb 11, 2010 #15


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    I experience dreams nightly! :wink:
    No, sorry :redface:, I'm completely disagreeing …

    you're saying that two "inertial clocks" are different, because one is stationary and the other is moving, and that that difference explains the apparently counter-intuitiveness …

    I'm saying they're exactly the same, and you'll have to look for another explanation.
  17. Feb 11, 2010 #16


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    That is not time dilation, it's differential ageing. And it has nothing to do with lensing.

    I emphatically agree.
  18. Feb 11, 2010 #17


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    OK, I will certainly agree that neurological activity is mappable (or measurable), but that is not a part of your definition of "real".

    I certainly experienced it. According to your definition that makes it "real".

    My point is that it is notoriously difficult to come up with a good definition of "real". The definition "something you and I experience daily" has lots of holes in it. For example, what about something that is real but rare? It would not meet your definition since it may not be experienced daily. What about something like love that is immaterial but a common experience, do you want to classify that as "real" or not? What about something that is physical and can be measured but not experienced directly, what types of experiences qualify something for reality?

    I am not trying to be annoying here, it is just that I feel it is pointless to discuss of whether or not something is "real" until the term is defined clearly. There is a whole branch of philosophy, ontology, devoted to this topic. It is not trivial (although it is probably not important either).
  19. Feb 11, 2010 #18
    I was talking about situations in which confirmation of GR's predictions have been tested.
  20. Feb 11, 2010 #19
    You're not being annoying, but without getting into overly philosophical realms... you never did ride that pink elephant. You THOUGHT you did, but not even in the complete manner of a normal 'thought'. I agree that 'something you and I experience daily' can't be the only standard of 'real', but then that was not a very good expression of what I meant.

    As for discussing what is real, there is probably never going to be a point in our lives (or any others) when that is a question which can absolutely be answered. That said, when people toss 'love' and 'dreams' my way, I find that glib. Love is entirely explicable as yet another biological process, where the angst and complexity arises from the humnan interpretation. My point? When people talk to each other they always establish de facto conventions of speach, and I believe without quibbling that we don't need to discuss the potential reality of love and dreams.

    I'm talking about The Casimir Effect vs. the existence of Pions. The Lens-Thirring Effect, Gravitational lensing, Differential Aging, and all of the other notions derived from Relativity vs. The Higg's Mechanism, Photon Decay, etc.

    To be blunt, I'm talking about a simple concensus based on empirical evidence, vs just the kind of immaterial speculation of 'love'.

    You CAN try to use language in a manner consistant with math, with rigor and commonly agreed conventions at each point for a given model. The fact that most people can't and DON't isn't my damned fault.
  21. Feb 11, 2010 #20


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    The experiments with clocks on planes are not testing time dilation. Time dilation is the apparently paradoxical ( and counter-intuitive) prediction of the LT that two IFRs will see each others clocks running slower.
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