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I How the standard spacetime model relates to reality

  1. Dec 21, 2015 #1
    As I understand it, the standard spacetime model is a 4-dimensional geometric object, and that my personal history is just a particular curve in the model. Reality as I experience it though is that I move through time, and thus I have the concept of the present in which "now" corresponds to the furthest point in time that I have so far travelled. But what does the time travelling "I" correlate to in the spacetime model? In other words what in the standard spacetime model is experiencing moving through time?
     
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  3. Dec 21, 2015 #2
    So in this picture, the inside area of the future cone is all possible paths you can take from your present point in time without violating causality. Without getting into philosophy of conciousness and maybe refining your question to ignore for now the human PERCEPTION of time, lets just pretend you are a point particle. So the plane in this diagram called "the hyper-surface of the present" is all of 3D space at one instance of time. The surface of the future cone is how all photons emitted from your point and travelling at the speed of light will diverge into the future.
    481px-World_line.svg.png
    So the point particle that is "you" is moving along a path which is dictated by the curvature of space-time, which in turn, is a result of the Stress-energy tensor, which is a sort of measure of energy and momentum change and density in space-time. The entity experiencing time is just arbitrary, and you refer to it as a 'test particle'. You can make the test particle a collection of test particles if you want, and call it "i". Also you need to choose your type of spacetime too. You haven't made it clear, Minkowski spacetime is flat in special relativity, whereas you could be referring to the Riemannian manifold of space time in general relativity.
     
  4. Dec 21, 2015 #3
    When you say the point particle, that is me, is moving what do you mean? Does it not in the model exist at all the times along the path, so that it never leaves one coordinate of spacetime to arrive at another, but instead exists all along the curve? Though you show the "hypersurface of the present" in your diagram, I am not sure in the standard spacetime model how the "present" is distinguished from other times. Perhaps you could explain? I thought different observers could argue about what "present" of mine was simultaneous to theirs and all be correct in the standard interpretation. I am not clear of the difference between Minkowski spacetime or the Riemannian manifold of spacetime, so feel free to choose either when answering, but if it is just a gravity issue, then perhaps choose Minkowski to keep it simpler, unless you feel that the complication is relevant.
     
  5. Dec 21, 2015 #4

    Nugatory

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    The curve is just a trace of the path the particle (or you) are following through spacetime.

    When I'm walking across the ground I leave footprints. We can join them together to define a curved path across along the ground, but that doesn't mean that I exist at all points on that path or that I haven't moved along that path. I always exist at one point, the one at the end of that curved path, and every step that I take extends the tip by one step. Your path (properly called a "worldline") through spacetime works the same way - you exist at the tip of the path, and it moves forward by one second every second.

    You are right. Different observers moving at different speeds will have different hypersurfaces of simultaneity. Thus, the spacetime diagram doesn't distinguish "present" from other times. Instead, it distinguishes three types of events:
    1) Those in the future light cone. All observers agree that these happened after the event at the apex of the light cone.
    2) Those in the past light cone. All observers agree that these happened before the event at the apex of the light cone.
    3) Those outside of both light cones. This is the only region that can contain any observer's hypersurface of simultaneity, and different observers moving at different speeds will draw different hypersurfaces of simultaneity through this region.
     
  6. Dec 21, 2015 #5

    Dale

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    Usually, if we have a worldline, ##a##, then there exists an affine parameter, ##\tau## called the proper time which represents the time experienced by ##a##. Then, ##a(\tau)## picks out an event along that worldline, and the past light cone defines their "experience".

    The "now" that is represented by simultaneity is not something that is experienced. It is calculated after the fact. What is experienced is in the past light cone, everything beyond that is prediction and conjecture.
     
  7. Dec 21, 2015 #6
    But the experienced reality is that the present is distinguishable from other times. I experience the present as being the point I am currently at in my journey through time. Like with a journey across sand, there could be footsteps/memories of where I once was, but there will only be one point, so to speak, where I am. The spacetime model however seems to have me existing as a continuum across the spacetime coordinates, and as you mention, it doesn't reflect the reality of there being anything travelling through time experiencing the present, as it doesn't distinguish a present, nor does it allow for there to be a correct answer as to what you are experiencing while I am experiencing what I am experiencing, for any given moment of my experience, the model suggests that it is correct to suggest that you were experiencing multiple things (as different observers would be equally correct with their different suggestions of what you were experiencing).
     
  8. Dec 21, 2015 #7

    robphy

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    One thing worth pointing out that a lot of the ideas discussed thus far
    can be seen in the ordinary position-vs-time graph of PHY 101 (a Galilean spacetime diagram).

    When distinguishes the spacetime diagram of special-relativity from Galilean-relativity is the
    geometric notion of perpendicularity (orthogonality) as defined by the metric...
    (which can be described as tangent to the unit-"circle").

    Given a worldline and an event on that worldline ["NOW, on that observer's worldline"],
    the hyperplane that is "perpendicular [in that geometry]" to the tangent-vector is used to define "simultaneity according to that observer".

    In the PHY-101 diagram, it turns out that, for a given event "NOW", the planes of simultaneity are co-planar (independent of the worldline through that NOW event)... hence "absolute simultaneity".

    In Special relativity, these corresponding planes are not co-planar... hence, no absolute simultaneity.
    (For an inertial observer in special-relativity, these planes correspond with hyperplanes from radar measurements.)
    The Euclidean analogue of this diagram already shows this non-coplanarity.
     
    Last edited: Dec 21, 2015
  9. Dec 21, 2015 #8
    The experienced reality is I am travelling through time in a certain direction, and where I am on that journey I can refer to as the present. It is that only one point would ever be the present, and that point is changing as the I that experiences it travels through time. With the standard spacetime model though it seems like a static geometry. I exist just as much in my past as I do in the present, it is just that I am spread across the coordinates. There is doesn't seem to be anything moving through time. The I that does isn't represented in it.
     
  10. Dec 21, 2015 #9

    Dale

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    Yes. That is ##a(\tau)## as I described above.
    That is just a philosophical interpretation. It doesn't matter mathematically or physically if you consider proper time as a parameter along a 1D path in a 4D spacetime or a parameter that selects a 0D point in a parameterized family of 3D spaces.
     
  11. Dec 21, 2015 #10

    Ibix

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    You now remember you one second ago. One second ago, you didn't remember you now. Memories accumulating in one direction is enough to explain the experience of time flowing (things have changed compared to how I remember them a second ago, and even more compared to two seconds ago) without reference to a specific interpretation of space-time.

    Pick the interpretation that makes most sense to you. It doesn't make any difference to the physics.
     
  12. Dec 21, 2015 #11

    Nugatory

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    The experienced reality is that the present where you are is distinguishable from other times. I have no problem saying that 10:59 on my wristwatch came before 11:00, that at 10:59 the 11:00 tick hadn't happened yet, and that at 11:00 the 10:59 tick has already happened. But if If it's happening somewhere else right now, it's not part of my experienced reality until sometime later. For example, all sorts of interesting and exciting things may be happening on alpha centauri right now, but that's 4.3 light years away so it will be sometime in the spring of 2020 before I can know about them or be influenced them.... and then I'll subtract 4.3 years from the current date and conclude that these interesting and exciting things actually happened during a few days before Christmas 2015. That's a very different thing then experiencing these events as part of the present in December 2015.
     
  13. Dec 21, 2015 #12
    Proper time is a real number. The real numbers form a complete totally ordered field. The math doesn't define a t which "moves" forward similar to footsteps walking along a path. This apparent movement is a result of the second law of thermodynamics. You need to provide a mathematical description of this movement. You need to provide math which shows 6:00 doesn't exist at 6:01. You have only made vague claims that they are mathematically equivalent.
     
  14. Dec 21, 2015 #13
    But the issue is how the model relates to reality.

    The standard interpretation as I understand it, has it that it is true that during a period of time of you experiencing, that I was experiencing a particular point in time... in the sense that one observer could correctly (according to the standard interpretation) claim that at a beginning point of the period of time that you experienced journeying through, I was experiencing a certain point X, and all through your journey through that period of time, other observers could correctly claim that simultaneous to whatever you were experiencing I was experiencing that certain point X. But reality we experience suggests that we are journeying through time, and that the answer will not be that I was experiencing one particular point in time for the whole duration of the period being considered that you were experiencing.

    I realise that with the standard interpretation other observers could also correctly claim that I was experiencing other points during your journey. I realise that it might be questioned what I mean by simultaneously, but I do not think I risk being mislead in thinking that, assuming we are both experiencing, that while you are experiencing something, I am experiencing something, and that I do not experience more than one point of time simultaneously.
     
  15. Dec 21, 2015 #14
    This idea of progressing through time takes me back a bit.

    This idea was pushed to its limits in the books "The Serial Universe" (1934) and "An Experiment With Time" (1927) by J.W.Dunne. He showed that if you are moving through time, then you have a rate of moving, which required a secondary time dimension - so many seconds of time1 per second of time2. And this in turn led to an infinite regress, so that an infinity of time dimensions was required.

    Another approach was that of Fred Hoyle in his novel "October The First Is Too Late". (1966) He likened the present moment to a light moving along a film strip, lighting up each frame in turn, and then suggested that it did not matter in which order the frames were lit up, the result would be the same, and that provided the background for his time travel story. But he did not go the next step and say that all the frames could be lit up at the same time (note J.W.Dunne's secondary time dimension creeping in!). And that is the situation we experience - each moment on your timeline is its own "Now" and nothing moves into the future.

    Movement through time, and the experience of change and movement is all an illusion based on what we experience now and the memory of the immediate past. But it sure is a convincing illusion!

    Mike
     
  16. Dec 21, 2015 #15

    PAllen

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    and my friends have Hoyle to thank for all the cryptic comments I make every October 1 from reading his book at an impressionable age not long after it first came out.
     
  17. Dec 21, 2015 #16

    Dale

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    @name123 this comment by @Ibix is concise and important.
     
  18. Dec 21, 2015 #17

    Dale

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    I don't recognize any of this as being part of any standard interpretation.

    If by "reality" you mean "the outcome of experiments" then the model relates to reality with an excellent degree of precision. This is what I mean when I say "reality".

    If by "reality" you mean "the philosophical discipline of ontology", then the model is compatible with multiple ontologies, none of which are considered of great importance scientifically.
     
  19. Dec 21, 2015 #18
    None of this seems standard to me. What you say confuses me. It's not clear that you are talking about spacetime, only time. And you seem to be mixing up clock-readings with time intervals. Clock-readings last for no duration of time. You are saying that something that's a clock-reading to one person is a time interval to another. That cannot happen. Different observers may disagree on the clock-reading ##t## of some event, they may disagree on the time interval ##\Delta t## between two events, but at least they can make comparisons. There is no way to compare a clock-reading ##t## to a time interval ##\Delta t## and say that what one person experiences as clock-reading another experiences as a time interval. It just doesn't make sense to do that.

    If two events occur at the same place and at the same time, they are simultaneous. That is something all observers will agree on. The issue of simultaneity for spatially separated events, now that's something different observers may disagree on.
     
  20. Dec 22, 2015 #19
    I do not see that there need be an infinite regress, only that it is silly to think you could describe the rate in seconds. If you played a video image at half speed, and only referenced the scenes in the slowed down video in order to describe the laws of physics that were being shown in it, they would be the same laws as if you were watching the video at normal speed. Things would be dropping at the same rate in terms of the physics. But there is the experienced sense in which things were dropping slower in the slowed down video than they were in the video at full speed.

    As for the idea that it was an illusion that you were experiencing change, what were you thinking the reality was, that your experience was in fact static?
     
  21. Dec 22, 2015 #20
    Yes the experienced reality is that the present where I am is distinguishable from other times, and it is also that I am moving through time, or in other words I experience my experience changing. The issue I am getting at was that in the spacetime model the human I experience being does not move, it just exists along a path. Relating the change in experience to the clock times used in physics I do not experience being at one clock time point more than once on the journey. Yet as I have stated else where:
     
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