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Time, mass and length

  1. Aug 5, 2006 #1
    In the theory of special relativity when two observers are in relative motion with each other then each observer measures an increase in mass, a slower clock rate and a contraction of length in the other observer's frame of reference.

    How are we to interpret this according to the theory of special relativity?
    Is this actually happening to both frames or is this simply an effect of the relative motion. In other words is it considered real or simply a distortion of reality?

    Edit: highlighted text to clarify the questions.
     
    Last edited: Aug 5, 2006
  2. jcsd
  3. Aug 5, 2006 #2
    You are asking two different questions in one sentence. And the question is very poorly phrased.

    1. The effect is reciprocal . All frames behave identically in SR .
    2. The effect is also measurable for:
    - time dilation (Ives-Stilwell measure time dilation thru the Transverse Doppler Effect, the muons reach the Earth due to time dilation)
    - mass increase (particle in nuclear accelerators are known to experience
    increased resistence to further speed increase as a function of their instantaneous speed)

    To my best knowledge, the effect has not been measured directly for:
    - length contraction but the effect has called upon in the explanation of MMX. See here:
    http://en.wikibooks.org/wiki/Special_Relativity:_aether
     
    Last edited: Aug 5, 2006
  4. Aug 5, 2006 #3
    Basically I am asking:

    Is the reciprocal effect actually happening to both frames or is this reciprocal effect a distortion of reality?
     
  5. Aug 5, 2006 #4
    Last edited: Aug 5, 2006
  6. Aug 5, 2006 #5

    Jorrie

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    My take on this is that it is just the way one frame observes the other, so it is obviously reciprocal and nothing is physically happening to either frame.

    In my engineering view, it is a measurement phenomenon and not a physical one. We measure the elapsed time for the muon to travel to Earth's surface as being longer than it's (statistical) lifetime, but that is because we are not present at the two events (the muon's birth and arrival at Earth's surface). For the muon, present at both events, nothing strange happens – it does not have our 'measurement problem'!:smile:
     
  7. Aug 5, 2006 #6

    Hans de Vries

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    It's a reality rather than a distortion. Still there is only one reality in
    4D space-time.

    For instance: The Lorentz contraction is the result of the non-simultaneity
    of Special Relativity. To see this we can imagine that we instantaneously
    "freeze" a bypassing traveler. Walking around him we can now see him
    "hanging in the air", indeed being contracted in the direction in which he
    was moving.

    The traveler however will complain that his front was stopped first, before
    his back was frozen in time, and argues that this is the reason of his
    compressed state. You can give him your "freezing device" and do the
    experiment the other way around. This time you'll be the one who is
    Lorentz contracted.


    Regards, Hans
     
  8. Aug 5, 2006 #7
  9. Aug 5, 2006 #8

    pervect

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    Generally speaking, what is "real" or "actual" is a philosphical question. Philosophical questions, by definition, don't have any definite answers, so one is free to assume that any particular phenomenon is "real" or "appearance" as desired.

    While philosophical questions don't make any actual difference, i.e. they don't make any experimental predictions, or else they wouldn't be philosophical, there is usually a philosophy that makes any particular theory the most understandable.

    For relativity, I would say that this philosophy is the idea that the Lorentz interval is "real" and "fundamental". Invariant mass is also in the same category. "Time" and "space" are less fundamental than the Lorentz interval.

    Of course, like any philosophy, one is not forced to this belief, it's just a matter of convenience and possibly communication.
     
  10. Aug 5, 2006 #9
    Indeed, that seems to be the crux in the theory of relativity.

    But at the same time, we postulate a fundamental speed, e.g. the speed of a light signal.
    What else is speed than a measure of distance/duration?

    If we consider time and space, and thus, speed less fundamental, then reflectively, observer A, seeing a light beam going towards observer B, must conclude that B sees this light at the same speed because of B's Lorentz distorted measurement of speed.

    If A and B are in relative motion should one not logically conclude that the identical observer speed of light is due to the Lorentz distortion, rather than that the Lorentz distortion is due to the constancy of the speed of light?
     
  11. Aug 5, 2006 #10

    jtbell

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    As Pervect noted, it depends on your definition of "reality". Do you expect "reality" to be the same in different reference frames? If not, whose reference frame do you prefer?

    I think a legitimate point of view is that length contraction itself (to use it as an example) is not "real", in the sense that the object itself doesn't "perceive" the contraction in its own reference frame. Nevertheless, length contraction has real physical consequences in other reference frames.

    As an analogy, suppose that a friend is standing in front of you, some distance away. She's holding a meter stick, oriented horizontally and perpendicular to your line of sight. There's a light behind her so all you can see is a silhouette.

    She turns the meter stick so that it's oriented at an angle to your line of sight, but still horizontal. To you, the meter stick now appears to be shorter. It's not really shorter, of course. Nevertheless, the apparent shortening has real physical consequences, because your friend can now walk towards you, through a door which is less than a meter wide, without the meter stick hitting the doorframe!
     
    Last edited: Aug 5, 2006
  12. Aug 5, 2006 #11

    pervect

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    Speed can also be regarded geometrically as a measure of the angle that two world lines form where they meet.

    As the ratio of two intervals ("lengths"), speed becomes dimensionless.

    However, you make a good point in that time is different from space, and the Lorentz interval does not in and of itself distinguish them, except by the sign of the interval.

    We find it convenient in relativity to use the same units to measure time and space. Furthermore, time and space "mix together" in the Lorentz transform - an interval that one observer sees as having only time components will appear to have both time and space components when viewed by another observer, for example.

    However, I would stop short of suggesting that time and space are actually the same thing. Closely related and intertwined, yes, but (according to my philosophy, anyway) not quite identical.
     
  13. Aug 5, 2006 #12
    True. Apparently time or space but not both is imaginary in SR's mathematics.

    But are we actually measuring time here?
    Can we univocally conclude that just because a clock runs slower in motion or in a curved area, that time slows down there?
     
  14. Aug 5, 2006 #13

    jtbell

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    How would you define "time," if not by the ticking of a (suitably idealized) clock?
     
  15. Aug 6, 2006 #14
    Well, obviously the number of ticks a clock gives per unit of time depends on its relative speed and the influence of space-time curvature. :smile:

    I suppose the best we can do at the moment is measuring against a clock at rest relative to the CMB and not influenced by a gravitational field.
     
    Last edited: Aug 6, 2006
  16. Aug 6, 2006 #15

    pervect

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    In general we can't, and probably don't want to, conclude that "time slows down" at all.

    Rather, in most approaches, we regard clocks as always keeping time, i.e. time is what clocks keep, just as space is what rulers measure.

    We regard time dilation as being relative, i.e. "this clock runs slower than that clock". Operationally, we also usually require that there be some sort of stationary (not changing with time) path between the clocks in order to make the comparison.

    Also note that curvature doesn't directly cause time dilation. Clock A, at a hollowed out spot at the center of the Earth, runs slower than clock B at infinity (when compared as above) - but (ignoring the sun, planets, and the rest of the universe for this example) space-time is flat both for clock A and for clock B.
     
  17. Aug 6, 2006 #16
    If you want clarity on the subject, you can go back to Eddington's enlightening statement: "Length contraction is true, but its not really true."

    Measurements between frames in relative motion are distorted - they are real only to the extent the measurments are real. As Pervect observes - its more of a philosophical viewpoint as to what is real - the difficultly is provoked by trying to reconcile the observed slowing of clocks in relatively moving frames (each apparently running slower than the other) and the actuality of a resultant real time difference that comes about in some experiments. (e.g., the proverbeal twin paradox).
     
  18. Aug 6, 2006 #17

    Hans de Vries

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    In SR, all physical processes (including clocks) proceed slower when moving.

    Now what is the REASON? Consider the following clock:

    A photon bounces back and forward between two mirrors.

    It ticks and gives you a way to measure it's proper time. Let the photon
    bounce on the x-axis and then let the clock move in the y-direction.
    (the simplest case). The clock will now tick slower because the photon
    has to follow a longer (zigzag) path. Remember? The more space is
    covered the less "proper time" proceeds: [itex]ds^2=dt^2-dx^2-dy^2-dz^2[/itex]

    Here you have the basic reason:

    All physical, chemical and biological processes go slower because more
    time is required to exchange information between the constituents of
    the process (the elementary particles).


    Regards, Hans
     
    Last edited: Aug 6, 2006
  19. Aug 6, 2006 #18
    The complete statement is:

    In SR, all physical processes (including clocks) proceed slower when moving when viewed from another frames of reference

    In your light clock example, the slowdown is as viewed from a frame of reference wrt the clock is moving with speed v. From the point of view of the frame of the clock, the time still pases at the rate of 1 second per second.
     
  20. Aug 6, 2006 #19

    jcsd

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    Well if soemthign is moving then it's another refernce frame to the person who sees it moving, that's a given.

    To tell the truth though it's not strictly true either as accelerated movement can make things proceed faster.
     
  21. Aug 6, 2006 #20
    I do not disagree with you that that is what is factually happening.

    However that does not seem to be the assumption in the theory of special relativity. In SR it seems that the question as to who is moving is not relevant, since the movement is considered relative.

    Regardless of the assumption if movement is relative, it is clear that there must be some sort of "uncertainty" principle at works with regard to knowing if something is moving or not.

    But when we consider the "twin" thought experiment, we are confronted with an asymmetrical situation.

    Is there a paradox? No, but only if one assumes that the movement was not relative.


    Well what you write here is confusing to me.

    To me it seems that one either assumes that time is just that what clocks register or one assumes that clocks are influenced by movement and thus not always are able to accurately represent time.
    So what is the position from the perspective of SR?

    For instance, in SR, with regards to the "twin" thought experiment, do any of the clocks slow down and does time slow down anywere?

    So how is this resolved in the special theory of relativity. Since it asserts that the movement is relative.
     
    Last edited: Aug 6, 2006
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