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Time does not run slower or faster

  1. May 29, 2007 #1
    In another thread that was locked, Chris Hillmann told me:
    Understanding time still makes me scratch my head:frown:

    Don't we believe that the twin paradox is true, i.e. if I go on a long journey with high enough speed and come back that I am less old than the twin brother I left behind. This is not just 'times kept by observers'. We are not just talking about mechanical or other clocks. I am biologically provable younger than my brother. If I would have taken along radioactive material, it would have decayed less than the same amount of the same material left behind. Everything that went along aged less than similar things left behind.

    May I at least say that SR shows that things age slower on a speedy journey? Well, this is what I see by comparison when I come back from the journey.

    But then, how is time different from a measure of age?:rolleyes:

    (Please no arguments that GR is needed for the twin paradox, see http://www.math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html)

    Still puzzled,
    Last edited: May 29, 2007
  2. jcsd
  3. May 29, 2007 #2
    I believe the point Chris was making is that the statement in question implies a 'fact' quite seperate from the points of view of the people making the claim. It is very important in relativity to understand that there is no 'true' state of affairs and that you could conceivably observe any possible relationship in time between two events, if you were to travel in a certain direction at a certain speed relative to these events.

    As for the twins paradox - it's a paradox of special relativity, because modelling the two twins in special relativity yields a nonsensical and contradictory result - you are supposed to be confused by SR's answer because the idea is that it doesn't work for an accelerating frame. It is a means of proving that special relativity is inadequate in some real scenarios, and shows that general relativity is required.
  4. May 29, 2007 #3


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    One observer can observe a distant clock running slow. That does not imply that that clock appears to be running slowly from any other perspective. Indeed, for a person travelling with that clock, the clock will appear to run completely normally.

    If you measure time only by looking at your own wristwatch -- which moves with you -- then you will never experience time slowing down or speeding up at all. Your wristwatch will look to you as it always does, regardless of how you move.

    - Warren
  5. May 29, 2007 #4


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    I don't think it shows SR is inadequate to the physical problem since you can perfectly well use SR to predict how much the accelerating twin aged, it's just that if you want to use the basic (non-tensor) equations of SR you have to calculate this from the point of view of an inertial frame, you can't use the same equations in a non-inertial coordinate system where the accelerating twin was at rest the whole time.

    My guess is that Chris was just making the point that in relativity it only makes sense to compare the rate that two clocks are ticking at any given moment if they are right next to each other, for separated clocks there is no physical meaning to the question of which is ticking slower, since different coordinate systems give different answers. However, all coordinate systems will agree on the accumulated time on each clock between the time they depart from a common point in spacetime and the time they reunite at a different point in spacetime, so you can say that one twin "aged less" over the course of the entire trip, you just can't say that twin was "aging slower" at any particular moment during the trip.
  6. May 30, 2007 #5

    Chris Hillman

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    Not even close!

    For good reason, BTW, so everyone please be careful to avoid trying to simply start up a locked thread all over again.

    in post # 14 of https://www.physicsforums.com/showthread.php?t=171946

    That's not even remotely close what I meant, and indeed seems to directly contrary to what I was trying to tell Harald/birulami. This is discouraging, since I thought I expressed myself reasonably clearly! (JesseM seemed to understand what I wrote.)

    Sojourner, I was in fact trying to debunk the sloppy notion that "time slows down" is a useful way to think about anything in either str or gtr. Rather, in these theories, one can compute what various ideal observers will measure in specific scenarios, including elapsed times between events on their world lines. The relationship between such measurements turns out to be incompatible with the Galileo's kinematics, but is described in flat spacetime by Einstein's relativistic kinematics. (In curved spacetime things are bit more complex, but on small scales, relativistic kinematics works fine.)

    I was also trying to debunk the sloppy notion that relativity theory says "everything is relative" or that "there are no absolute facts". In fact, as I pointed out, one should rather look for statements which do not depend upon the coordinate description. These will have physical meaning and can be interpreted in terms of the results of actual measurements made by actual observers in a specified state of motion (having a specified world line) in the spacetime of interest.

    That's also wrong, as I have often pointed out in various forums on many past occasions. Rather, we can treat accelerated observers in special relativity, but we need to use a tool appropriate to treat observers who are not inertial observers. The appropriate tool is the kinematic decomposition of a vector field, which works the same way in any Lorentzian spacetime, but this concerns the mathematics of congruences, not physics at all--- in particular, this is completely independent of any theory of gravitation.

    That is correct. I don't understand why you think this is incompatible with anything I said. Have you read Geroch, General Relativity from A to B? This is also a nice introduction to str which should clarify your confusion.

    That's why you are confused, Harald--- "things age slower"? Slower with respect to what?! A clock? If not a clock, then what? "A speedy journey"? Speedy in what sense? (Recall that "distance in the large" is tricky. Recall also that in the conventional twin paradox, one twin suffers an impulsive blow and has nonconstant velocity.)

    As you just said yourself, ideal clocks are assumed not to be affected by accelerations. Thus, ideal clocks all run at the same rate everywhere and everywhen, by definition. The elapsed time between events A, B as measured by clock C is the distance measured along the world line of C from A to B. Note that the events A, B are on the world line of C, by definition, as JesseM pointed out--- any other scenario involving timing of events distant from C requires carefully defining a notion of "distance in the large"; there is no unique choice, so whatever conclusion you draw in such a scenario may only be valid for a specific notion of "distance in the large".

    As is so often the case, the basic confusion here is between local and global structure. The twin paradox involves a global comparison. I think JesseM understands this--- at a guess, because he has a stronger background in manifold theory than Sojourner or Harald. None of us can do anything about the fact that understanding relativistic physics requires grappling with a bunch of subtle points from manifold theory. The best thing I can do, I think, is to try to recommend some good books which address some of these issues, such as Geroch, The Geometry of Physics.
    Last edited: May 30, 2007
  7. May 30, 2007 #6


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    Consider the statement: distances (specifically E-W distances) on the Earth are shorter at higher lattitudes (closer to the North pole) than at lower lattiutdes (closer to the equator).

    Would you agree with this statement, or would you say "distances are the same, no matter where you are on Earth"?
  8. May 30, 2007 #7
    I said
    and Chris Hillman answered

    Ok, that makes sense. Without reference, the comparative "slower" has no meaning. In the twin paradox setup, the acceleration singles out the reference frame of the observer who stays at home for comparison.

    Aside from all physical theory I find it disturbing to imagine the process that causes me and the stuff I take along to age less over the journey as compared to home. If the lag is a few years it would be truly shocking to get back. Something happens during the journey, something works different on the journey than at home. And I wouldn't mind getting a bit more insight in how the mental picture of the process could be. There is more here to understand than how to apply the Lorentz transformation. But sometimes I have the impression that there is a ban on thinking in that direction. Maybe it is to philosophical and beyond physics?

    Thanks for your input,
  9. May 30, 2007 #8
    Looks like I should have taken the book more seriously. It is dusting on the bookshelf. I'll try it again then.:redface:

  10. May 30, 2007 #9

    Chris Hillman

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    Yes. Do you see what it was? (Answer below).

    No! We keep trying to tell you that physics is based on the premise that physical law works the same everywhere and everywhen.

    Instead of muttering darkly about conspiracy theories, go back to the first bit I quoted above and see if you can take it further.

    What changed? Model the scenario using two world lines which are intially and finally coincident. One represents the world line of an inertial observer, so it is a straight line. The other bends away then bends back. Note that there are at least three places where acceleration is needed since path curvature nonzero: first, the traveling twin needs to start moving away from his brother, second he has to slow down and then start approaching his brother, third he has to slow down again so that his world line is coincident with his brother's world line. Now it should be easy to see that the Lorentzian distance measured along the traveler's world line is smaller (don't forget the sign in the line element!).

  11. May 30, 2007 #10


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    Conceptually, I think the best approach is to ditch the idea that time "flow" in any real sense, and accept the spacetime viewpoint where the universe is a 4D spacetime manifold with various worldlines embedded in it like pieces of string frozen in a block of ice. Then the fact that one twin ages less can be understood in a "geometric" sense, in terms of the lengths of different paths through spacetime which are determined by the spacetime geometry. Just as the distance between two points on a 2D piece of paper (the length of a straight line connecting them) is given by the 2D pythagorean theorme [tex]\sqrt{dx^2 + dy^2}[/tex], and the distance between two points in 3D space is given by the 3D pythagorean theorem [tex]\sqrt{dx^2 + dy^2 + dz^2}[/tex], so the "distance" in spacetime between points in 4D spacetime (the 'proper time' along a straight worldline connecting them, where 'proper time' is the time interval measured by a clock which has that worldline) is given by [tex]\sqrt{c^2 dt^2 - dx^2 - dy^2 - dz^2}[/tex]. And just as you can find the length of a non-straight path in space by approximating the path as a bunch of line segments and using the pythagorean theorem to find the length of each (and taking the limit as the number of segments approaches infinity in the case of a smooth curve), so you can find the proper time along a non-straight worldline by approximating it as a bunch of straight (inertial) segments and using the above formula to find the proper time along each. Just as it is always true that a straight path between points in 2D or 3D space is always shorter than a non-straight path between the same two points, so it is always true that a straight worldline between two events in the flat spacetime of SR will always have a greater amount of proper time than a non-inertial worldline which goes between the same two events; this is why the twin that accelerates will always have aged less than the inertial twin.

    I took the analogy between paths on paper and worldlines in spacetime a bit further in post #9 on this thread in an effort to explain why there needn't be an objective truth about which of the two twins is aging slower at a given moment even if there is an objective truth about which of the twins aged less in total when they reunite; you may or may not find it helpful too:
  12. May 31, 2007 #11


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    You can also look at it like this: When the traveling twin A looks at the twin B and sees that B looks older, that means that in A's frame the event that B turns 50 (for example) is simultaneous to the event that A turned 10. It's not that time "moved slower" for A, but rather when A suddenly changed frame when he turned around to come home his "line of simultaneity" flipped around (making B look older) even though A sees B;s clock running slower than his. So in his frame, the two events mentioned above happen at the same time. And in A's frame B is also younger due to time dilation (which can be explained in a similar way) . That's how they can both agree on the age without "time slowing down".
  13. Jun 1, 2007 #12
    Thanks for the extensive answers. Both, Martin Hillman and JesseM, suggest that looking at worldlines helps best to understand the issue. It comes down to the simple rule to remember: "When two worldlines connecting two events are compared, the longer worldline will show the slower clock".

    While this "the longer the slower" rule is easy to remember, easy to apply and is a perfect device to predict outcomes of experiments, it explains nothing. In a bit harsh of a comparison it is like describing a TV by saying: "When you push the ON button, you will see moving pictures on the screen". This provides for nice predictions. But it does not help to understand how a TV works. In the same sense the worldlines describe what happens, but not how.

    Isn't it a fair question too ask what is going differently in two clocks on differently long worldlines such that at the end they show different times?

    One answer to my original question was that the physical laws are the same on both worldlines. Of course they are, but nevertheless the outcome is different, so something is different. Ok, the difference is the length of the worldlines. But hey, how can I phrase it properly to say that this is not an explanation. Maybe the different length of the worldlines is the cause of the different clock readings. Still this leaves the question how the cause causes the effect.

  14. Jun 1, 2007 #13


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    Give my page http://www.phy.syr.edu/courses/modules/LIGHTCONE/LightClock/ [Broken] a try. It's purpose is to give a physical explanation [a "physics first!" explanation] (consistent with more mathematical approaches) of why the lightclocks tick the way they do. In other words, WHERE are the ticks marked off on each worldline, and WHY are they where we claim they are? (For more technical details, consult the papers and the posters near the bottom of the page.)
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  15. Jun 1, 2007 #14

    Chris Hillman

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    This is growing tiresome

    I think you mean me, Chris Hillman :rolleyes: (I would have thought that my transparent choice of PF username would have prevented any possibility of confusing me with anyone else, but apparently not...)

    Say rather:

    "When two clocks whose worldlines are mutually tangent at two distinct common events A,B, but follow different paths in between those two events, the clock with the longer worldline (meaning, arc length integrated as per the metric structure, which is part of the definition of a Lorentzian manifold) will show the greater elapsed time."

    Note two critical additions: first, I specifically said the two world lines must share the same unit tangent vector at two points where they coincide, and second, I specifically said we are comparing the "elapsed proper time" recorded by the two clocks. I avoided saying either clock "runs slower"; they are both ideal clocks, so by definition they run at the same rate under all circumstances.

    Take it up with Issac Newton.

    (Newton's greatest contribution to math/sci may have been his insight that rather than trying to answer such imponderables as "what causes gravity?", one should focus on simply trying to mathematically describe gravitational interactions. IOW, one should focus on constructing mathematical models within some mathematically formulated physical theory. If you want to argue that physics should not conform to this Newtonian vision, you should probably move discussion to another forum at PF.)

    Nothing is "going differently". That's the whole point. That's why several posters have made specific corrections to what you wrote, emphasizing that ideal clocks have identical properties and function the same way under all circumstances.

    But Harald, you know what is different! The length of the two world lines between A,B!

    See, you do know that. Although the restrictions I mentioned are required to make your "principle" valid.

    Imagine two people who start walking at point A and take different paths to point B, and compare their odometer readings and find that one odometer shows a greater change. Your complaint is exactly analogous to insisting that the fact that one path is longer fails to explain the discrepancy in odometer readings. This is why the notion of Lorentzian manifolds is so valuable, conceptually speaking--- it offers a vivid geometric picture which makes it thousands of times easier to think about relativistic kinematics, as (after some initial resistance) Einstein himself recognized.

    Maybe your real question is: why should we "believe" that Lorentzian manifolds offer the best way to think about relativistic kinematics. (Not the same thing at all as "offer the best way to think about time in all circumstances and all scales".) If so, your question should definitely move elsewhere.

    I can't help noticing that even casual inspection suggests considerable similarity between your views and those of one "Harold Ellis Ensle" who was known to me years ago as a relativity denier over at the unmoderated UseNet newsgroup sci.physics.relativity, a place my own world line has avoided for many years by my clock. :wink:
    Last edited: Jun 1, 2007
  16. Jun 3, 2007 #15
    Sorry for that. And thanks for your continued patience with my stubborn questions.

    I see where I went wrong. The usual graphical depiction of worldlines makes worldlines with the smaller elapsed time look longer, because their graphical length is euclidean. But the length of the worldline is in fact defined to be the elapsed time on the clock (times c) if you want.

    Maybe I should. Not that I want to prove old Isaac wrong, but my question may indeed be more philosophical than physical.

    Except that the odometer measures euclidian and is therefore much more intuitive, whereas length of a worldline, defined by means of ds=sqrt(c2dt^2-dx^2-dy^2-dz^2), has these hard to imagine opposite signs in it. Of course I know that "easier to imagine" is not the best criterium for scientific results, but without a mental picture, progress in understanding hard. The strange thing is, that after rearranging into ds^2+dx^2+dy^2+dz^2=c^2dt^2, imagination snaps back and I see a simple tradeoff between "moving through space" (dxyz) and "experiencing time" (ds), where ds is the time I feel and measure with my clock while I move along space dxyz.

    I am not this person, honestly. But writing down ds^2+dx^2+dy^2+dz^2=c^2dt^2 certainly makes me look like a heretic, because from there it seems to be easy to arrive at a view of relativity where relativity is an emergent property of an absolute background on which the magnitude of v=(ds,dx,dy,dz)/dt is constant, i.e. |v(t)|=c for all t (and yes, t is the flywheel that keeps this this absolute theater running:wink:).

    I am not trying to tell you that this is the right way to look at it. Rather I am trying to understand why it is wrong. One argument I heard elsewhere was that Occams Razor favors getting rid of the absolute background, because it is not necessary for any reasoning. In a way this was an implicit concession that the math does not give any different results. But I think there should be a stronger argument than Occams Razor, given the fact that the euclidian view is so much easier to imagine.

    Feel free to ignore my musings. You gave already some great advice and I keep reading Geroch.

  17. Jun 3, 2007 #16

    Chris Hillman

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    Required intuition for str: visualizing Minkowski geometry

    Well, it's been wearing thin.

    However, I do appreciate this information.

    Right, and books like Taylor & Wheeler should help you fix your intuition so that when you look at curves, you can visualize either Euclid geometry (shouldn't be a problem from the sound of it) or Minkowski geometry as needed.

    Thousands if not tens of thousands of students master this every year, so it is by no means impossible to obtain the neccessary intuition. When I was learning str (from Taylor & Wheeler), I found it very helpful to make two column tables comparing in detail E^2 and E^(1,1) trigonometry, path curvature, and so on.

    OK, but that's your problem, since tens of thousands of physicists around the world use the correct intuition on a regular basis. Minkowski geometry is a tried and true way to think about relativistic physics. Indeed, a hundred years of experience (well, ninety nine) shows that it is the best way. In any case, it is the universal standard, so if you want to discuss relativistic physics you must master this geometric intuition.

    Well, that's completely incorrect as I think you realize, but in any case, this is not the appropriate place to propose new ideas which you yourself suspect may be "heretical". Please take to the "Original Research" subforum.

    OK, good, you know it's wrong. All you need to do is become comfortable with Minkowski geometry. Then you will at least be able to understand what str says, which will be good progress towards resolving whatever philosophical issues might be troubling you.
  18. Aug 27, 2007 #17


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    Imagine two people (or two clocks) traveling the same path
    between points A and B, but moving at different speeds.
    The paradox: Even though they take equal paths, they end
    up having different ages (or recording different times).

    The odometer analogy no longer applies.

    So what is it about being in different frames that causes
    people to age differently (and clocks to record different
    amounts of time over the same path)?

    Aren't all inertial frames supposed to be equivlent?

  19. Aug 27, 2007 #18


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    You're misunderstanding the analogy I think, I believe Chris was comparing distance along paths through space with proper time along paths through spacetime (worldlines). Even if two people travel the same spatial path between spatial positions A and B as defined by a particular coordinate system (other coordinate systems will not agree that they both stop at the same position in space B), their paths through spacetime, as seen on a spacetime diagram, would be different, and the paths would not even end at the same point in spacetime. Just as the geometry of space is such that a straight path will always be the shortest distance between two points, so the geometry of flat spacetime is such that if you have multiple worldlines between two events in spacetime, a straight worldline (corresponding to inertial motion) will always have the maximum proper time.
    Last edited: Aug 27, 2007
  20. Aug 28, 2007 #19


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    (to JeeseM)

    Thanks for the response, JesseM. (But where's Chris? ;-))
    Re your "straight worldline" comment, didn't both of my people have such lines?
    If there is no acceleration, then why would people in different (inertial) frame age

    (Also, I could have said that I am not using worldlines, but am simply using equal (meaning fully equivalent - same direction, no acceleration)
    distances through space. This may sound like I am using absolutes, but consider
    this: If two people travel between the same points A and B of a given inertial
    frame's x axis, then they must have traveled equal distances through space.
    And since our people and clocks do not actually travel along worldlines, but
    float in space, I have indeed shown that the odometer example is invalid.
    And think about this: Clocks and people in space do not have roads to
    "rub against" as do a car's tires in the odometer case.)

    In SR, it is given that all inertial frames are equivalent. There is no preferred
    frame. There are no preferred frames. However, experiment tell us that people
    in different inertial frames age differently. (All acceleration can be eliminated by
    simply adding a third person to the Twin Paradox case.) Forget about worldlines,
    odometers, and Minkowskian geometry; all I want to know is

    Why do people in different inertial frames age differently?

    Here I am floating around in inertial Frame A, and there you are floating
    around in (a supposedly equivalent) inertial Frame B, but we are aging
    differently! What's up wid dat?

    Last edited: Aug 28, 2007
  21. Aug 28, 2007 #20


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    Yes, but your two people don't meet at a single point in spacetime, you just had them end up at the same point in space (in one coordinate system). So you're not comparing the proper time on two worldlines which go between the same two points in spacetime, so the analogy between two paths between points in Euclidean space doesn't work. This would be more analogous to two straight paths in space which start from the same point but go in different directions, and both end at positions that have the same x-coordinate as viewed in some coordinate system. One of these paths can be longer than the other, just as one wordline had a greater proper time in your example.
    But then you're missing the point of the analogy, which was to relate the notion of lengths of two paths between a pair of points in Euclidean space to the notion of proper times of two worldlines between a pair of events in spacetime.
    Only in that frame's coordinate system. In other frames they traveled different distances through space.
    This is meaningless, a worldline is just a set of points in spacetime, and all it means to "travel along a worldline" is to occupy each of those points.
    The odometer was an analogy, and it's a perfectly valid one. Just as the length of a path in space is independent of your spatial coordinate system, and just as the length of a straight-line path between two points in space is always shorter than the length of a non-straight paths between those points, so the proper time of a worldline is independent of your inertial coordinate system in relativity, and the proper time of a straight worldline between two events in spacetime is always greater than the proper time of a non-straight wordline between those same two events.
    No, but they have clocks. Again, it's an analogy where features of one case are mapped to features of the second, with the length of paths in space (as measured by an odometer) mapped to the proper time of worldlines in spacetime (as measured by a clock).
    If you use only inertial clocks, there is no objective frame-independent truth about which of any pair of clocks was ticking faster--disagreements over simultaneity mean different frames disagree about what time is showing one a given clock "at the same time" that a clock at a different location is showing a certain reading.
    Again, not aging differently in any objective sense. In my frame you're aging slower, in your frame I'm aging slower, and in a frame where our speeds are equal we're both aging at the same rate.
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