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Relativity and Time Measurement

  1. Oct 25, 2014 #1
    Hey guys, I've been learning about relativity recently and have a few thought experiments I'm pondering over. I'd appreciate input on the errors and validities of the consequences I've arrived at in my thoughts.

    The first thought experiment involves measurement of time. If we have an analog clock, we can look at its state twice and get the initial angle and the final angle. If the angle is , then the change in angle can be said to be Δθ.

    Now, since I've learned about relativity, it seems to me to be a presumption to say that a change in angle of clock hands correlates to a change in time ΔT. We would say Δθ=ΔT or that the slope of the variables theta and T is one in arbitrary but consistent units of T.

    That make sense to me. However, the problem comes in when you're comparing time between two clocks. If we had to clocks that we observed for a million years, and Δθ was the same for both clocks, we would say Δθ=Δθ for both clocks. Again, no problem.

    The problem comes from the presumption that the rate of change Δθ/ΔT for both clocks is equal, because all we have observed is simply comparable change in motion-for instance, if the unit of time were different for the clocks, but from your observation point one clock was traveling faster through time, you would observe Δθ=Δθ for the clocks, but you're canceling the change in time ΔT to presume this.

    Now, you could normally throw a clock between the two points and (switching from infinitesimals to differentials) you observe d^2θ on the freely falling clock relative to dθ of a stationary clock and know the time dilation between the two points. However, there seems to be a problem here: how do you start with two clocks that you are absolutely sure measure the same unit of time? Wouldn't that require an observation of two clocks in the exact same space?

    Another experiment I pondered is asymmetrical gravity on a sphere. Say, for instance, that you had a perfect sphere with variable gravity at constant height h. Let's say you can't jump or throw anything, so you can't observe free fall. All you have is a clock in your hand. Since you can't observe acceleration due to gravity, the only method you have to measure it's acceleration is with a scale. So now we take Newton's law of gravitational force. Height h is constant, so r^2 is the same for all measurements. Your mass isn't changing, so m is constant, and obviously the gravitational constant is constant. This means that force is changing only with respect to the variable gravitational field.

    We also know that force=mass dot acceleration, or mass dot length over seconds squared. So let's look at this equation: we know force is changing. We know that mass is constant. This means that acceleration is changing with respect to force. Force is length over seconds squared.

    Since time dilates with respect to gravitational force, does this imply that an increase in gravitational force changes gravity because length is changing, or because time is changing?

    It seems to me that length would be constant in all still frames of reference on the sphere. If gravitational force increases but time slows down-meaning the rate of change of what you observe speeds up-then wouldn't the units of T decrease in your reference frame?

    In other words, the point I am getting at is if all of your observations are at height h-do you actually notice the changing force with respect to gravity?

    Sorry if my math is confusing, but hopefully you can help me figure out these problems more accurately. Thank you.
  2. jcsd
  3. Oct 25, 2014 #2


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    Staff: Mentor

    Einstein once remarked that "time is what a clock measures" (and it's worth googling for that phrase). By this he meant that there is no way of defining or measuring time except by observing some changing system. It may be the graying of my hair, the passage of sand through an hourglass, the cycle of the sun across the sky, the decay of a piece of unrefrigerated meat, .... Or the changing angle of the hands of your clock.

    The unwarranted presumption is not that a change ##\Delta\theta## in the angle of the hands of the clock corresponds to a change ##\Delta{T}## in time. The unwarranted presumption is deeper than that; it is a mistake to think that there is a ##\Delta{T}## out there that is somehow more "real" than the ##\Delta\theta## that is happening right under our nose. Give up that notion and you don't have to worry about how you map the position of the hands to it.

    From this perspective, the famous time dilation formula should not be interpreted as saying that "time slows down as you move faster"; that would be trying to say that a smaller ##\Delta\theta## corresponds to the same amount of time as you move faster. Instead, it is a relationship between the ##\Delta\theta## on my clock and the ##\Delta\theta## on your clock when we are moving relative to one another.

    (you should also google for "relativity of simultaneity" and "Einstein train simultaneity" if you are not familiar with these topics)
  4. Oct 25, 2014 #3
    I see. This is partly troubling to me and it's a conclusion I've been attempting to work around to see if I can avoid a philosophical consequence.

    What you're saying is that there is no such thing as absolute time-right? In other words, there's no sense in describing time at all. It's simply a placeholder that we give for relative motion. This is a conclusion that I have run into in my thoughts, and it's one that's so disturbing to my ingrained sense of reality that it's hard to do thought experiments and come to proper conclusions in short time.

    The philosophical problem this leads to is one of free will-in classical interpretations, we have consistent times and orders of events. Without these, however, it seems possible to construct scenarios wherein causal determinations depend on your perspective. If this is so-a person's actions cannot be "free" as their actions are determined depending on how you view them.

    Note that I'm not implying a philosophical determinism. Humans may be indeterministic, as in unpredictable given a starting condition. However, if a person's actions can precede their "decision" to make that action depending on the reference frame, then that decision isn't causing the action.

    Sorry if philosophical discussions are frowned upon on this forum. If I should avoid them, please inform me. Thank you.
  5. Oct 25, 2014 #4


    Staff: Mentor

    this forum is for discussions of science, not philosophy, and certainly not for discussions of free will.
  6. Oct 25, 2014 #5


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    Staff: Mentor

    no, that doesn't follow, because....
    It is not possible to construct such a scenario (as long as we avoid faster than light travel - this may be the most fundamental reason why special relativity prohibits such travel). If A causes B, than all observers in all states of motion will agree that A happened before B (we would say that A and B are "time-like separated", and that's another term worth googling for). Conversely, if any observers could disagree about whether A or B happened first, then it would be impossible for a signal traveling at or below the speed of light to travel between them, there would be no possibility of any cause and effect relationship between them, and we would say that they were "space-like separated").

    Note that I have managed to keep free will out of the discussion; as DaleSpam says, that topic has no place here. If you think you've discovered any conflict between free will and relativity... You're misunderstanding relativity.
  7. Oct 26, 2014 #6


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    Staff: Mentor

    Yes, of course: you design and construct the clocks exactly the same and then you observer them together for a while to ensure they are properly calibrated to measure the same/correct time. That's how you ensure accuracy with any scientific instrument!
    That doesn't follow. Just because there is no absolute time, that doesn't imply there is no time. There is no requirement that time be absolute.
    No. Motion has units that include both distance and time, so motion is not itself time. We can use motion as a convenient way to measure time, but it isn't the only way to measure time.
    Fortunately, your understanding of what time is/how it works is wrong, so that's a non-starter. Time exists.
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