Last year, Alan Alda posed a challenge to science communicators, to explain a flame in terms that an 11-year old could understand. this drew a lot of responses, and some very good winners. This year’s contest, though still called the “Flame Challenge,” asked for an answer to the question “What Is Time?”

This is a little closer to my corner of science, so I considered entering, but as previously noted, I’m crushingly busy at present. And either scripting/ shooting/ editing a video, or doing the necessary work to hack a written response down to the prescribed 300 characters was more time than I could really afford. Alas.

The finalists for 2013 have been announced, and as is sadly typical of competitions I don’t enter, I don’t really like any of them. The third of the video entries, the zero-production-value one, is probably the best, as far as I’m concerned, but I’m not very fond of any of them. So the following is an after-the-fact crack at the question, banged together very quickly at the end of a long weekend, but serving at least to illustrate the tack I would’ve taken had I had time to enter.

————

What Is Time?

Time, very simply, is what you measure with a clock.

That sounds like a complete punt, I know, the “because I said so” of science answers, but it’s true. You may have heard all sort of bizarre stuff about time– time passes at different rates if you move at high speed, time and space are the same thing, time slows down near a black hole, or that time travel into the past might actually be possible. All of that weird stuff is true, coming out of Albert Einstein’s theory of relativity, but the reason we know all that stuff comes down to this: time is what you measure with a clock.

The starting point of Einstein’s theory– and similar work by other scientists (Henri Poincaré, Hendrik Lorentz) at about the same time– is the realization that there isn’t a giant master clock at the center of the universe that everybody sets their watches by. They realized that if you want to talk about when things happen, you need to specify how you know that. If you want to know whether two events in different places happen at the same time, you need clocks at both of those places showing the same time, which turns out to be trickier than you might think.

When think carefully about how to get clocks to show the same time, weird things pop out. Two people who are moving relative to each other will each think that the other’s clock is ticking too slow. They’ll disagree about how much time passes between two events, and may even disagree about which event happened first. Our most exotic theories about time start by thinking about clocks.

So what’s a clock? A clock is anything that does a regular, repeated action. You count the number of times the action repeats, and that tells you how much time has passed. The sun rising and setting, a pendulum swinging back and forth, a light wave jiggling electrons in an atom: all of these have been used as clocks. Some clocks are more accurate than others, but they all do the same thing, which is to measure time.

And the very best clocks we know of confirm all the strange predictions of relativity. Scientists in Colorado have clocks so good they can measure the change in time from moving at walking speed, or from moving one foot higher in elevation. The Global Positioning System people use to navigate with their phones uses atomic clocks in space, and wouldn’t work without a correction for the change in time. There are even spinning stars thousands of light years away that act like clocks, whose slowing down confirms that gravity bends space and time, sending out waves that stretch and compress everything by a tiny amount.

So what is time? Time is what you measure with a clock. And when you think carefully about what that means and how to do it, you discover some pretty amazing things.

————

That’s more than the 300 word limit for a written answer, so we’ll pretend that I would’ve read this over some awesome video, with cool pictures and animations. Or maybe just staring into a webcam like the guy in the third of the video finalists (really, if I’d known that was an option, I might’ve entered for real…). Also, I cheated by throwing in a couple of hyperlinks. Sue me.

This also serves to illustrate my very-much-an-experimentalist, atomic-molecular-and-optical-physicist take on the whole question. General relativity is cool and mind-bending and all that, but at some point, you need to ground things in terms of actual physical measurements, which means time is ultimately about clocks. And I think it’s useful to remember that all the unification of space and time stuff ultimately began with scientists thinking very carefully about the extremely practical problem of synchronizing separated clocks.

Comments

  1. #1 Ori Vandewalle
    April 29, 2013

    Does that make distance what you measure with a ruler?

  2. #2 Matt Leifer
    http://mattleifer.info
    April 29, 2013

    This suffers from the same problem that all attempts at operational definitions do, namely:

    “Some clocks are more accurate than others, but they all do the same thing, which is to measure time.”

    If time is just what we measure with a clock then how can you tell that some clocks are more accurate than others? Presumably, we have to fix on some sort of standard clock, which is just what we actually do in practice, the current standard being based on atomic clocks. However, suppose then that someone comes along with a method of measuring time that they claim is more accurate than current atomic standards. How do we test that? We cannot test it using the existing standard because then no method could possibly turn out to be more accurate because time is currently defined as the existing standard. In reality, people are able to tell how accurate time measurements are, in part because we have theories of how our clocks measure time so we know what the sources of error are.

    Another problem is:

    “A clock is anything that does a regular, repeated action. You count the number of times the action repeats, and that tells you how much time has passed.”

    How do you intend to define “regular” and “repeated” other than in terms of time, i.e. regular means something like “rate of change in time is constant” and repeated means something like “recurs after a certain time interval”. I don’t see how you can really get at these concepts without referring to a more primitive concept of time. To verify if something is a good clock in the sense of being “regular” and “repeated” we are either going to have to compare it to another clock, and hence get an infinite regress, or we are going to have to make use of our current best theories of space and time, which implies a more primitive concept of time.

    Yet another problem with this definition of time is that it renders revisions of our concept of time problematic. For example, if you want to follow Julian Barbour’s idea that time is emergent then this makes no sense if time exists so long as clocks do and no one is denying that clocks exist. However, whether or not you like the idea, it is clear that there is some sense to it. It leads to a particular programme of deriving GR and quantum gravity in which time plays no fundamental role and, regardless of whether it is correct, it at least seems to make sense.

    In view of all this, I think it makes more sense to be realist about time. There is something that exists out there in the real world that roughly corresponds to our experience of time. We then use our current best theories in combination with our experimental and technological knowhow to figure out the most accurate ways to measure that thing. Assuming for the moment that time is not emergent, asking what time is beyond this is probably no more meaningful than asking what any other fundamental concept is. It attains its meaning from the role it plays in our theories and from the way those theories hook up to experimental observations.

  3. #3 Tom Singer
    April 29, 2013

    The text entry limit of 300 words seems ridiculously short compared to a 6 minute video, which allows for diagrams. They seem to all be competing against each other – the 2012 challenge only names one winner. But even allowing for that limitation, the text answers seems pretty horrible, and they waste a lot of their 300 word allotment on “engaging” bullshit. But the videos aren’t much better.

    Even your answer isn’t very satisfying, which may be a product of asking questions about something as fundamental as time. (I imagine that it’s tough to answer “What is length”, as well.) The problem with your response is, it’s circular. “What is time? Time is what we measure with a clock. What is a clock? A clock is anything that does a regular, repeated action.” But you left unaddressed, “What is regular? A regular event always happens in the same time.” And then we’re back to, what is time?

  4. #4 timo
    April 29, 2013

    Time is an abstraction of change, and neither of those can be meaningfully defined without circularity. The best we can do is point to certain aspects of our experience and say this is change and time is it’s measure.

    No definition would ever be able to explain those concepts to those who never experienced them (and not only because those who never experience change can never learn or understand anything new).

  5. #5 Chad Orzel
    April 29, 2013

    Ori: Does that make distance what you measure with a ruler?

    Yes. In the same basic way that time can’t be completely separated from measurement, neither can space. If you’re going to talk about space, you’re talking about the distance between objects, and that ultimately comes back conceptually to measuring things with a ruler. Again, this goes back to Einstein and Poincare and the rest: if you want to talk about the location of objects in both space and time, you need to specify how you plan to measure that, which is why formal treatments of relativity often start with universe-spanning grinds of clocks and meter sticks and the rest.

    Matt: If time is just what we measure with a clock then how can you tell that some clocks are more accurate than others? Presumably, we have to fix on some sort of standard clock, which is just what we actually do in practice, the current standard being based on atomic clocks. However, suppose then that someone comes along with a method of measuring time that they claim is more accurate than current atomic standards. How do we test that?

    You do the same bootstrapping process that was done the last several times we changed the definition of the second from one standard to another. You set up the proposed new standard, verify that it matches the existing one over some reasonable period, but allows a better understanding of its variability and uncertainty, then change the definition over. After all, if you were going to set up a system of units completely from scratch, you wouldn’t generally pick 9,192,631,770 as the relevant multiplier.

    I don’t really disagree with the issues you raise– those are good and subtle points, and I spent a bit of time on them when I taught a class on time a few years ago. I’m not sure I would put those in the foreground of an explanation aimed at 11-year-olds, though. (I’d be happy to have a kid go there as a follow-up, of course…) And I went in a very emphatically experimental direction with this in part as a reaction what struck me as excessively metaphysical piffle in some of the actual finalists. I’d be happy to sign on to the following, though:

    Assuming for the moment that time is not emergent, asking what time is beyond this is probably no more meaningful than asking what any other fundamental concept is. It attains its meaning from the role it plays in our theories and from the way those theories hook up to experimental observations.

  6. #6 wolfgang
    April 29, 2013

    >> how can you tell that some clocks are more accurate than others?

    you use more than one clock of the same design. The variance after n ticks tells you how accurate this clock design is.

    >> How do you intend to define “regular” and “repeated” other than in terms of time

    this just means that the physical configuration for tick n is the same (or as similar as possible) as for tick n+1.

    e.g. if you use a pendulum you make sure the length stays the same.
    nowadays it means taht clocks are isolated as much as possible from the environment …

  7. #7 LogicallySpeaking
    May 1, 2013

    Overall, nice write up. It’s for 11-year olds, so I certainly wouldn’t include much (or any) of the relevant metaphysics, but I do think the philosophy is relevant.

    Wolfgang: None of those escape the challenge of conventionalism (that time is purely a convention). For example, if you use 10 clocks of the same design, you can determine their variance, but you can’t say which is more accurate without some pre-determined convention.

  8. #8 wolfgang
    May 1, 2013

    >> you can’t say which is more accurate

    you can say which *design* is more accurate – e.g. you will see that pendulum clocks are less accurate than atomic clocks (because the later have less variance among each other)

  9. #9 G
    May 2, 2013

    I would say that time is the axis of measurement of motion and thermodynamic entropy. Either the presence of motion or the process of thermodynamic entropy can define the existence of time.

    We measure time along that axis, by seeking examples of motion and examples of entropy that appear to be regular, in the sense that the motion or the entropy can be described by equations that produce predictable results. We also apply the logic of parsimony here, by way of assuming that, for example, an oscillator oscillates at a fixed frequency, but the observer who observes the oscillator does not oscillate in a manner that conveniently screws up his/her measurement of the oscillation.

    (Example: on an oldschool touchtone phone, press the 1 and 2 buttons at the same time, and you hear an oscillator producing a tone of 697 Hz. You can parsimoniously assume that the oscillator is stable at 697 Hz, rather than assuming that both the oscillator and yourself are being modulated at some other frequency that creates an illusion of hearing a stable 697 Hz. tone.)

    Was that any good, or did I just make an ass of myself in public? ;-)

    —-

    So I have two dumb questions:

    One:

    You have two standard clocks that you’ve observed as being synchronized to an adequate degree for your experiment. Now you put each clock on a space ship, and the two space ships fly off in whatever directions, in straight lines at the same velocity and for the same distance.

    Under those conditions, won’t the clocks remain synchronized? I assume they will, because the time contraction aboard each space ship is the same, and it is being applied for the same duration and distance.

    Two:

    If time is equivalent to measurable motion or thermodynamic entropy, what happens when the universe reaches its “heat death” stage, at which it is in a state of maximum entropy and in which no further measurable motion occurs? Here I assume that any residual Brownian motion doesn’t count because it can’t be parsed into anything regular or otherwise meaningful.

    It seems to me that, at that point, the time dimension becomes meaningless or ceases to exist.

    And if that’s the case, then, what happens to the 4-axis system of spacetime when you remove one of its axes?

    It seems to me that what happens is, what you have then is actually a point. Even if that point is as “large” as the entirety of the universe, it’s still a point. But what are the implications of that? (Or did I just do a huge foot-in-mouth maneuver?;-)

  10. #10 Frank Wappler
    http://SAT.analogies.are.to.Pierre.Bernard--as.duration.ratios.are.to.indications.of.my.follicle.clock
    May 2, 2013

    wolfgang wrote (April 29, 2013):
    > you use more than one clock of the same design.

    Considering two distinguishable clocks, how should be determined whether they are both (physically) constituted according to the same “design” specifications (and/or “environmental” specifications) and are thus equal, or to which extend they are not?;
    especially if they are distinguishable due to being separate from each other.

    wolfgang wrote (May 1, 2013):
    > you can say which *design* is more accurate

    In order to allow such a determination, which notions ought to be used in the corresponding “design” specifications? (Surely none which are in turn themselves subject to varying accuracy, such as “physical constitution” or “operating conditions”.)

    > – e.g. you will see that pendulum clocks are less accurate than atomic clocks (because the later have less variance among each other)

    Does there exist any upper limit to the variance which different atomic clocks may conceivably have among each other at all, especially if they are (pairwise) separate from each other?
    (If so, perhaps there’s some bias in the sample being considered; if not, the variances don’t differ between different “designs“.)

  11. #11 Eric Lund
    May 2, 2013

    you can say which *design* is more accurate – e.g. you will see that pendulum clocks are less accurate than atomic clocks (because the later have less variance among each other)

    You can say that pendulum clocks are less precise than atomic clocks. That does not guarantee that atomic clocks are more accurate: there could be a systematic issue with the atomic clocks.

    To take an extreme example: Archbishop Ussher calculated that the Earth was created at 0900 local (Garden of Eden) time on a specific date in 4004 BCE. That is a very precise estimate of when the Earth was created (an uncertainty of about 20 parts per billion, dominated by our not knowing exactly where in the Middle East the Garden of Eden was), but not an accurate estimate (the Earth actually formed about 4.5 billion years ago). Abp. Ussher’s estimate was consistent with what was scientifically known at the time, but he didn’t know about radioactivity or fusion.

  12. #12 alex p
    May 2, 2013

    If you are speaking from the perspective of someone who measures things for a living, you could say that time and length are the only two things that exist (i.e. they are directly measurable.) Everything else is inferred from repeated, careful, clever measurements.

  13. #13 Sean T
    May 2, 2013

    It seems to me that relativity, at least in prinicple, provides a “standard clock” that is physically realizable. If you have a light beam bouncing back and forth between two mirrors, and there’s a detector on each mirror, that would be as regular a repeating phenomenon as is possible, and would therefore be the standard against which all other clocks could be compared.

    Because the speed of light is constant, the time required for the light beam to travel from one mirror to the other would be a constant so long as the relative separation of the mirrors remains unchanged. This system, so long as it’s assembled in a vacuum, is a perfect clock.

    The objection that you cannot define regular or repeated without reference to time is therefore overcome. This system is regular and repeated, regardless of how you define time so long as the mirrors are not moved.

  14. #14 Chad Orzel
    May 2, 2013

    If you are speaking from the perspective of someone who measures things for a living, you could say that time and length are the only two things that exist (i.e. they are directly measurable.) Everything else is inferred from repeated, careful, clever measurements.

    Really, these days, it’s all just time measurements plus knowledge of relativity. That is, if you want to do a really good length measurement, what you actually do is a really good measurement of the time required to travel that length, and multiply by the speed of light.

  15. #15 Eric Lund
    May 2, 2013

    Because the speed of light is constant, the time required for the light beam to travel from one mirror to the other would be a constant so long as the relative separation of the mirrors remains unchanged.

    This is why your scheme breaks down. The separation of the mirrors depends on your reference frame. You, who are in the rest frame of the mirrors, see the distance between them as L, while I, who am moving at velocity v with respect to the mirrors, see that distance as L * sqrt(1 – v^2/c^2). My unit of time also differs from yours by that same factor.

    A better scheme would be to define the length in terms of a certain number of wavelengths of a certain atomic transition. That allows you to measure the apparent length in the rest frame of the reference atom even if you are not in that reference frame. Prior to 1984, the meter was defined in exactly such a fashion.

    The present time standard operates under a similar principle. The second is defined as a certain number of oscillations of a certain atomic transition. That gives you a measurement of time as seen in the rest frame of the reference atom, even if you are in a different frame. This technique has been used to measure some of the predictions of general relativity, including gravitational time dilatation.

  16. #16 RM
    May 2, 2013

    Frank Wappler:
    > Considering two distinguishable clocks, how should be determined whether they are both (physically) constituted according to the same “design” specifications

    We’re talking practical constructions here. In a nebulous spherical-cow model of reality, a idealized pendulum clock is as accurate as an atomic clock is. It’s only those nasty un-idealized practicalities of air resistance, gravitational field variations, thermal fluctuations, etc. that prevent it from be as accurate in practice.

    So the way you make two clock designs “the same”, is you write down all the ways you think relevant parameters would affect the results, build the clocks to control for all of those parameters to the best of your ability, and if the clocks match in all of the listed criteria, they’re considered to be “the same”.

    Eric Lund:
    >there could be a systematic issue with the atomic clocks.

    Given that we’re talking strictly about a difference interval in a system that repeats to a self-similar state, I’m not sure what “systematic issue” you would be talking about. Imagine your biased clock as compared to a “true” clock. There can’t be a constant shift in the number of true ticks per biased tick – that would just mean that the clock is slower/faster, not that it was biased. All constant biases fall out, so the distinction between accuracy and precision disappears – especially as we don’t have a true clock to compare things to, and so tick conversions are taken to the current mean.

    Besides, the concept of “precision” with respect to clocks is more useful when applied to tick length – i.e. what’s the precision to which one can measure a duration, given a particular tick size.

  17. #17 Rossa MacManamon
    Dublin
    May 3, 2013

    Time is what prevents everything from happening at once

  18. #18 Frank Wappler
    http://this.proves.that.you're.sharp.as.Pauli--now.cut.to.the.details
    May 3, 2013

    RM wrote (#16, May 2, 2013):
    > We’re talking practical constructions here.

    Of course; at least as practical as, say, the constructions of MTW §16.4 (which in turn are

    built on those of §10.2).

    So we don’t have to engage in any nebulous assumptions; and if we do engage in concrete,

    practical assumptions (e.g. for economy’s sake) then at least we can quantify some real range

    of (systematic) uncertainty of our estimate relative to the value we would have obtained by

    carrying out the required construction or method in practise.

    > So the way you make two clock designs “the same”, is you write down all the ways you

    think relevant parameters would affect the results

    Surely distances (or at least, distance ratios) between certain pairs of elements of setups to

    be compared, such as the distance ratios between different pairs of mirrors (cmp. #13), should

    be relevant, for instance.

    (I even wonder whether there are any other parameters I should be concerned with at all.

    Refractive index, perhaps …)

    > build the clocks to control for all of those parameters to the best of your ability

    Well — in order to learn about my (or anybody’s) ability to “control for certain

    parameters” (such as the distance ratio of to given pairs of mirrors) in past trials, and

    perhaps even to hold a concrete range of expectations about those abilities for trials yet to be conducted (or yet to be evaluated), one should have been able to practically _measure_ the

    parameter(s) under consideration, in the corresponding concrete past trials.

    And if it was possible to carry out the corresponding measurement operations (as it should have been), then these may be equally practised in any further trial as well.

    Eric Lund wrote (#15, May 2, 2013):
    > The separation of the mirrors depends on your reference frame.

    We’re talking primarily about proper quantities here; i.e. whatever characterizes the mirrors under consideration _themselves_ in relation to each other, not necessarily in relation to any additional participants.
    So, if some “reference frame” should be considered, then primarily that of the mirrors under consideration _themselves_.

    Which raises the question: how ought to be determined whether two given mirrors belong together to the same “reference frame“? …

    > A better scheme would be to define the length in terms of a certain number of wavelengths of a certain atomic transition.

    In which sense might “atomic transitions” of various samples (of “atoms“, I presume) and/or in various trials be _certain_??

    And what relates “their wavelength” to “length” or “distance” which characterizes certain pairs of mirrors, for instance?

  19. #19 Eric Lund
    May 3, 2013

    We’re talking primarily about proper quantities here; i.e. whatever characterizes the mirrors under consideration _themselves_ in relation to each other, not necessarily in relation to any additional participants.

    The problem with that argument is that there is nothing special about that frame. The laws of physics are the same for anybody moving at a constant velocity with respect to that frame. Special relativity is what you get when you combine that postulate with the postulate that the speed of light is the same for all observers regardless of frame. One of the consequences is that observers in different frames will not agree on the transit time of a photon between the two mirrors. They can agree that the photon was launched at time t0, but they will have different ideas as to t1 when the photon reaches the other mirror. At least in this case, since a photon is involved, they will agree that t1 > t0. There are other scenarios in which some observers will see t1 > t0 and others t1 < t0.

    What’s different about single-atom systems is that the relevant parameters are not affected by relative motion. No matter what frame I’m in, I can determine that this is the right kind of atom, and I can therefore (in principle) measure unit length and unit time in that atom’s rest frame. I will find that they are not the same as the unit length and unit time in my rest frame.

  20. #20 Sean T
    May 3, 2013

    Eric,

    I understand your objection to my scheme, but I think you are objecting to something that I did not claim. I never claimed my system could be used to define a second, or some other unit of time. My system is only meant to overcome the objection that someone made that you cannot define a “regular, repeating system” without first defining time. To put it in more formal language, the system I described is a regular repeating system if, in a reference frame where mirror A has zero velocity, mirror B also has zero velocity. This system would under that condition be a regular repeating system.

    Of course, there’s nothing special about this reference frame in which the mirrors are not moving. However, it still can serve as a standard for regularity. If you have a system and you wish to determine its regularity, simply bring your system to the standard and stop moving. If it’s regular, then for any n, where n is the number of times the light beam oscillates between the mirrors in the standard, you will measure some m, where m is the number of “ticks” on the clock you are trying to compare to the standard. Repeated measurements should yield the same m each time. To the degree which m varies, your clock is imprecise.

    Obviously, to use this system to define a second (or other time unit) you would need a definition of a distance standard. Then, you would define a time unit by specifying a distance between the mirrors and a number of oscillations of the light beam between them. Of course, in actual practice, it’s possible to define a time standard with greater precision than it is a distance standard, so we don’t define a time standard in this manner.

  21. #21 Sean T
    May 3, 2013

    Eric,

    You’ll have to pardon me. I’m not a physicist, so while I have a pretty good handle on the basic ideas of relativity, I cannot claim to have a good handle on the details.

    My argument above is based on the idea that, for an observer in any inertial reference frame, the distance between the two mirrors will remain constant. This distance will not be the same in different reference frames, but from any given reference frame, the distance between the mirrors is constant.

    If that’s the case, then my system does pass the test for a regularity standard. If d is the distance in any given inertial reference frame, then 2d/c is the time required for the light beam to make one trip back and forth between the mirrors. If d is a constant, then c is obviously a constant, so this time remains constant as well.

    Like I said, I do understand the basic ideas, but this may be a case where I am mistaken about the details. If I’m wrong, and the distance between the mirrors does not remain constant for an observer in an arbitrary reference frame, then I stand corrected and will admit that my regularity standard is not really a good standard.

  22. #22 Eric Lund
    May 3, 2013

    Sean @19: As long as neither frame is accelerating, the distance between the mirrors remains the same for each observer. That much you have right. But you still run into problems because the orientation of the mirror arrangement matters. Say that I am moving at constant velocity v in the X direction with respect to your frame, in which you have set up two of these things, one oriented in the X direction and the other in the Y direction. You say the distance between the mirrors is the same for both pairs. I disagree: I think the pair in the X direction is closer together than the pair in the Y direction, because the contraction due to our relative motion is in the X direction and the Y direction is unaffected. A third observer moving with respect to your frame at constant velocity v’ in the Y direction will think the pair in the Y direction is closer together than the pair in the X direction. And we are each right in our respective rest frames.

  23. #23 Frank Wappler
    http://123456789ABCDE.123456789ABCD..123456789ABC...
    May 4, 2013

    Eric Lund wrote (#18, May 3, 2013):
    > The problem with that argument is that there is nothing special about that frame. [...]

    Do you agree that, when considering Relativity, we’re supposed to consider various distinguishable, recognizable participants?,
    such as those which Einstein explicitly mentioned: “A”, “B”, “M”, “M'”; and one may readily think of still more, such as “A'”, “B'” (btw. isn’t this notation style of Einstein just awful?!); and surely point out even more, such as “J”, “K” and others?

    (Correspondingly, MTW, Box 13.1, write of “principal identifiable[s]“.)

    Further, when considering Special Relativity, do you agree that we are supposed to have (agreed on) a method for determining which pairs of such distinct participants were, are, and remained “at rest to each other”, and which are not?,
    such as for instance A and B and M having been at (pairwise) at rest to each other, while A and M’ were not;
    or for instance the prescription that J and K are supposed to be at rest to each other, while neither A and J, nor A and K, nor B and J, nor B and K were?

    If so, then you should be able to understand that the “(inertial) frame)”, of which A is a member (along which B, M, …; but not J, K, …), is very special indeed; because it is the _only_ “(inertial) frame)” of which A is a member, and thus as distinguishable and recognizible as A itself.

    And when we’re referring for instance to the “distance between A and M” it should be quite unabiguous and proper that this is to be distinguished from the “distance between J and K”, “distance between A’ and M'” as well as from “distance between A and B”;
    and that (real-number) ratios between any pair of such distances may be meaningfully measured.

    > One of the consequences is that observers in different frames will not agree on the transit time of a photon between the two mirrors.

    Would similarly observers in different frames not agree for instance on the “mean lifetimes” (or at least: their ratios) published by the pdg.lbl.gov ?

    > What’s different about single-atom systems is that the relevant parameters are not affected by relative motion.

    Different??
    Is the distance between A and B “affected by relative motion“? (of anyone, such as M’, or J, or …)
    (Provided, of course, the state of A and B is indeed an eigenstate of the distance operator, i.e. A and B were at rest to each other.)

    Is the ratio of distance between A and M to distance between A and B “affected by relative motion“?
    (Provided, again, all three were members of the same “(inertial) frame“.)

    > No matter what frame I’m in, I can determine that this is the right kind of atom, and I can therefore (in principle) measure [...]

    How would you suggest to determine “the right kind of atom“, at least in principle?
    Perhaps from distance ratios which present the “distributions of constituents” (such as “electrons”, “nucleons” …)?
    (If so, how would you suggest to determine such distance ratios, at least in principle? MTW/EPS’s “ideal rulers” come to mind …)

    Sean T wrote (#18, May 3, 2013):
    > [...] the system I described is a regular repeating system if, in a reference frame where mirror A has zero velocity, mirror B also has zero velocity.

    How should “velocity” be measured (at least as far as determining whether “zero velocity” applies, or not);
    especially concerning participants, such as A and B, which are separate from each other?

  24. #24 Eric Lund
    May 4, 2013

    How would you suggest to determine “the right kind of atom“, at least in principle?

    I can determine the atomic number, the total number of nucleons, and the total number of electrons. (There are standard techniques for measuring these things.) None of these parameters depends on what frame of reference I’m in, as they are pure numbers–if the atom in question happens to be krypton-86, all observers in all frames will agree that it is krypton-86. If I know these things, then I know what the spectrum of transitions should look like, and if I find that they are shifted from what they should be in my rest frame, I can determine the atom’s line-of-sight velocity with respect to me. This procedure, more or less, is how galactic redshifts are actually measured. Or I can invert the procedure: look at the spectrum, look for the best match in my catalog of spectral lines, and determine both the kind of atom involved and its velocity relative to me. Either way, I am not depending on a distance constructed by somebody else in a different frame.

    the “(inertial) frame)”, of which A is a member (along which B, M, …; but not J, K, …), is very special indeed; because it is the _only_ “(inertial) frame)” of which A is a member

    The inertial frame of which A is a member is special to A because that is A’s rest frame. It is not special to any observer in any other frame of reference. That’s the whole point of the relativity principle: there are no privileged inertial frames. We might label that frame for our convenience, but that doesn’t make it special.

  25. #25 Frank Wappler
    http://pocket.full.of.relativity
    May 5, 2013

    Eric Lund wrote (#23, May 4, 2013):
    > I can determine the atomic number, the total number of nucleons, and the total number of electrons.

    Fine, let’s suppose we can count and (roughly) distinguish those constituents.
    (That’s for instance neglecting the measurements of whether some given number of charged leptons are equally “electrons“, or not; and whether some given number of (charged, or neutral) baryons are equally “nucleons” and not “hyperons” and so on.)

    > (There are standard techniques for measuring these things.)

    Right. Do those techniques in any way require or depend on the determination of geometric relations, such as “distributions” (expressed in terms of distance ratios) directly of the constituents mentioned above, or (less directly) of elements of certain “setups”?

    (Recall that I’m mainly questioning your claim (#15, May 2, 2013) that “a better scheme would be to define the length in terms of a certain number of wavelengths of a certain atomic transition “; i.e. “better” than the “light clock scheme” of MTW/EPS.)

    Concretely:
    > [...] krypton-86

    How do you suppose to determine, at least in principle, whether some collection of 36 protons, 50 neutrons, and 36 electrons, in some particular trial, presented a “krypton-86“?, and not (for instance) two “argon-43″, or some of these 122 (suitable) constituents being members of one particlar “krypton-86” and the remaining constituents being members of another “krypton-86“, or whatever else might be distinguishable, if geometric relations between the constituents could be determined.

    > None of these parameters depends on what frame of reference I’m in [...]

    Right: since these determinations are not necessarily concerning yourself (or myself) but primarily the 122 (suitable) constituents under consideration;
    and since the method(s) of determining whether they presented a “krypton-86“, or not, ought to be equally applicable (reproducible) for _any_ set of 122 (suitable) constituents.

    And more generally: since the definitions/methods of determining geometric relations ought to be equally applicable (reproducible); not least the method of determining whether two given (distinguishable and separate) participants A and B were “at rest to each other”, in some particular trial, or not.

  26. #26 Michael Kelsey
    SLAC National Accelerator Laboratory
    May 6, 2013

    @Frank Wappler: Are you familiar with spectroscopy? If not, reading some of the basics of the technique might help you understand the points Eric Lund was making. Essentially all of your questions demonstrate nearly complete unfamiliarity with the subject, as well as unfamiliarity with entire field of atomic physics.

    Assuming that the behaviour of “122 (suitable) constituents” (i.e., completely separated protons, neutrons, and electrons in some sort of plasma) should be the same as the behaviour of a compat bound system is so far beyond naive as to be unanswerable. Do you really think that a large crate full of metal and plastic parts is equivalent in its behaviour to your car?

    Please, start with a basic understanding of physical principles before you try to engage in logical dissection of detailed theoretical constructs.

  27. #27 Kaleberg
    May 7, 2013

    Gee, no mention of time crystals. Their existence suggests that time has an intrinsic cyclic structure, just like a clock, at least if popular press reports are to be believed. This fits in nicely with your definition.

    Of course, a biologist would give a different answer: Time is that which is measured by our temporal neurons which let us impose an ordering on events, just as place neurons let us impose positions on objects. These cells evolved because it is biologically useful to be able to place events and objects in time and space so that organisms able to reason about such concepts have a higher chance of transmitting their genes to the next generation.

    I always liked Einstein’s quote, which is more profound than it sounds, “The only reason for time is so that everything doesn’t happen at once.”

  28. #28 Frank Wappler
    http://as.naive.as.the.most.naive.next.guy.imaginable--but.not.more.naive
    May 8, 2013

    Michael Kelsey wrote (#6, May 6, 2013):
    > Are you familiar with spectroscopy?

    By your response apparently enough to know that (determination, or presumption, of) certain geometric relations is relevant in spectroscopy.
    Those between the constituents of an “atom“, for instance.

    Or AFAIR, likewise, for instance those between constituents of a “grating” (and in turn even those between constituents of a “grating line”).

    Or AFAIR, closely related, geometric relations between (constituents of) regions of different “refractive index” values; such as, whether they are “separated by a smooth surface”, and if so, how such surfaces might be further characterized (being “plane”, or “piecewise plane”, or “cylindrically curved” etc.).

    (Determining whether two “light clock” mirrors are at rest to each other, or not, seems rather simple by comparison.)

    > Assuming that the behaviour of “122 (suitable) constituents” (i.e., completely separated protons, neutrons, and electrons in some sort of plasma) should be the same as the behaviour of a compa[c]t bound system [...]

    Assuming “behaviour“??
    Certainly not beyond the most basic (naive, prerequisite) anthropomorphic abilities, such as the ability of any participant, at least in principle, to judge order (or coincidence) of observations;
    as basis of determining geometric relations between several (such as to further quantify “compactness” or “completeness of separation”; not even to speak of further derived dynamic notions such as “boundedness”).

    Please do not invoke or presume parochial, derived notions when trying to engage in a discussion of foundational issues, such as “time”.

    p.s.
    Are you familiar with relativity? If not (yet), then please (start to) consider Einsteins approach (Ann. Phys. 17, 891, 1905; my translation from the original German):

    [...] firstly, to comprehend the word “time” as “the indication on my watch”

    and subsequently to obtain further relations between those “time“s, such as how to measure “simultaneity” (of indications of two separate participants) or how to measure “duration” (of some participant, between two indications of the watch of that participant)

    by practical stipulation

    .

  29. #29 Chad Orzel
    May 8, 2013

    This is beginning to tip into excessively personal pointless sniping. If you want to continue this discussion, everybody work on keeping a more civil tone. If you want to have an individual pissing contest, find another blog to host it, because I’m not interested.

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