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The Present Moment in Spacetime?

  1. Apr 24, 2009 #1

    ConradDJ

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    It’s often asserted that there’s a contradiction between Special Relativity and our experience of living in the present moment. Einstein made a few statements like that, and it seems many physicists assume that if the theory is correct, this very basic feature of our awareness of the world must somehow be illusory.

    I don’t believe there’s any such contradiction. And I think it’s worthwhile trying to clear up this misunderstanding, because it leads to confusion about the structure of spacetime.

    What Relativity tells us is that there is no universal, absolute definition of simultaneity between distant events. There’s no unique way to identify the moment I’m experiencing now with a specific moment in the experience of an observer on Mars. There’s no unique spacelike hypersurface extending throughout the universe, defining a single “present time” that’s simultaneous everywhere.

    But does that have anything to do with the now I experience? Obviously no one has ever experienced a set of spacelike-separated events. What Relativity tells me about the present time I actually experience is that it consists of local events, and events that are equidistant from me in time and space, i.e. “on my past light-cone.”

    Simultaneity is not a significant issue, if we’re trying to understand the nature of the physical present moment. The issue of whether two events are simultaneous is the same whether those events are happening now or at any other time.

    My present moment as I write this, and yours as you read it, are clearly not simultaneous. But that hardly means neither is real, or that there is no such thing as the present moment, for me or for you, or for anything else in the world. It just means our present moments are interconnected in spacetime in a very different way than we’re used to imagining.

    It makes no more sense to say that my now is “subjective” – only existing “in my head” – than it does to say that my location here in space is subjective. If there’s any illusion involved here, it’s in the classical notion that the whole universe exists “all at once,” and “moves through time” as a single vast object. Relativity tells us, this is not how space and time work. But we still tend to picture the world that way, despite its evident inaccuracy.

    It’s easy for us to imagine the universe in 4 dimensions of space and time. Whenever we map the trajectory of a moving object onto a diagram with space and time axes, this is the picture we have in mind, with time as a 4th dimension of space. And this picture can be very helpful, even for explaining spacetime relationships in Relativity – e.g. in the light-cone diagram.

    But it can also be very misleading, since the geometry and even the topology of 4-dimensional space is very different from that of Minkowski spacetime, where space and time coordinates have opposite signs. For example, in Minkowski spacetime, all events “on the light-cone” are contiguous.

    I think this is an important issue, because the spacetime of Relativity is so often described as a “block universe” in which all the events of past history and everything that will ever happen in the future all co-exist at once. This picture actually made sense in classical physics, but it badly misrepresents how events are physically connected in Minkowski spacetime.

    So long as we’re satisfied with this picture of the world in 4-space, we’re not rising to the challenge of conceptualizing the world we actually inhabit, where the present moments of different observers are causally interconnected in quite complicated ways. By dismissing the now as an illusion irrelevant to physics, we’re conveniently ignoring what may well be a fundamental aspect of the physical world.
     
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  3. Apr 24, 2009 #2

    Mentz114

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    I've never heard of any physical theory outside Kaluza-Klein that has 4 spatial dimensions ( KK has time as well in a Lorentzian way ). My point is that no-one can be 'satisfied' with a 4-spatial dimension description of the world because it doesn't conform to our experience, and stable orbits are impossible in 4 spatial dimensions.

    Where did you get the idea from ?
     
  4. Apr 24, 2009 #3

    NWH

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    So what would you concider the extra seven dimensions of string theory to be? 3-Space, 1-Time, 7-String. Are they not concidered spacial dimensions? Or are they still mere mathamatical artifacts?
     
  5. Apr 24, 2009 #4

    Mentz114

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    They are compactified so they aren't what the OP was referring to. In fact the extra dimension in the KK theories ( pre-cursor to the strings ) is also compactified.

    There aren't more than 3 observable degrees of spatial freedom, is my point.
     
  6. Apr 24, 2009 #5

    NWH

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    Yeah, I had a feeling it would be something like that. Was just curious whether the extra dimensions predicted in string theory were concidered spacial, as if they were, a ten dimension description must drive people crazy if people are never satisfied with four spacial dimensions. Anyway, this is probably for another forum, but thanks for clearing that up.
     
  7. Apr 25, 2009 #6

    ConradDJ

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    No, I realize Special Relativity as a theory describes a 3-space integrated with time. My point was that very often time is visualized as if it were a 4th spatial dimension, i.e. as if the spacetime "distance" between events were the square root of x2+y2+z2+ct2 instead of x2+y2+z2-ct2. An example is this familiar diagram of the present moment in spacetime, which presents it as a spacelike hyperplane.

    world_line.JPG

    This sort of diagram is very useful for explaining the difference between spacelike and timelike intervals. But the "present moment" pictured here is nothing like the present moment anyone (or anything) actually experiences (is affected by). That consists only of interaction taking place along the past light-cone and in the immediate vicinity inside the past light-cone.

    Does anyone know another way of visualizing Minkowski spacetime that respects the difference in sign between the space and time coordinates?

    Here's a link to an interesting paper in which "simultaneity" is redefined to correspond to the spacetime structure of the "now" we actually experience. The author tentatively restates Special Relativity in these terms, and claims some advantages for his approach, e.g. in resolving the "Twin Paradox".

    http://web.ceu.hu/phil/benyami/Apparent%20Simultaneity.pdf" [Broken]

    I'm not sure whether redefining "simultaneity" is helpful or not, but I appreciate the attempt made here to understand what Special Relativity is telling us about the physical world we actually experience.
     
    Last edited by a moderator: May 4, 2017
  8. Apr 25, 2009 #7

    Mentz114

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    I read the first paragraph of that paper and found this

    There is no twins paradox in SR. If the author of that paper thinks there is then he doesn't undertand SR. Elapsed times for any journey can be found by integrating the proper time along the worldline. Where's the paradox ?

    On the question of simultaneity - it's common sense that simultaneity of spatially separated events is observer dependent and has no intrinsic significance - so why bother redefining it ?

    It may seem dogmatic to dismiss the work on the weakness of the first paragraph, but life is too short to waste on what seems to have no point and might be wrong.
     
  9. Apr 25, 2009 #8
    Hello ConradDJ

    I had a quick look at the paper you linked to. It seems pretty pointless. The author redefines simultaneity. There have been other definitions before but I cannot vouch for their usefulness. Below are a couple of paragraphs I picked out,which, although out of context, do give the an idea of the general flavour of the thing.

    -----.According to backward-light-cone simultaneity, what we now see through vacuum is what is happening now. The world is as it appears to be, in this respect. Science does not force us to reject our everyday view of the world.
    Since according to backward-light-cone simultaneity what appears to be happening now, that is, what we now see, is indeed happening now relative to us, this
    simultaneity can also be called Apparent Simultaneity. This is the phrase I shall use
    below. (The phrase ‘backward-light-cone’ should be rejected also because once these
    coordinates are accepted, that surface is no longer a cone but a plane.) A reservation should be noted at this place. According to Apparent Simultaneity what we see is occurring now relative to us only if we see through vacuum. In case any medium in which light’s speed is slower than in vacuum is between observer and light source, the event seen is inside the lightcone of the event of seeing it, and therefore earlier, relative to the observer, than the seeing event. The effect of this is perhaps negligible in actual cases: taking the refractive index of air a 1.0002926, and giving the atmosphere a generous 100 km height above the Earth’s surface (the speed of light in vacuum defined as 299,792,458 meters per second), light reaches the Earth less than 10-7 of a second later than it would through a vacuum. But such possibilities are of course of theoretical significance.

    The comment by Mentz 14 is of course enough to raise doubts as to the author's concept of relativity.

    Matheinste
     
  10. Apr 25, 2009 #9

    atyy

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    The first quote seems completely consonant with special and general relativity. So I don't understand your complaint in the second quote.
     
  11. Apr 26, 2009 #10
    The difference in sign is just a mathematical manipulation to make the set of variables consistent. The original statement of invariance is an equality requiring the resultant spatial component equal to ct. There are still only 3 independent variables!
     
  12. Apr 27, 2009 #11

    Dale

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    I agree with the OP for the most part. The universe cares about causality, cause preceeds effect in all frames. For all other events the order is not really important. Loosely speaking, although nature does not seem to suport a universal "now" it does seem to support a "here and now".
     
  13. Apr 27, 2009 #12
    The correlation between quantum entangled particles happens simultaneously regardless of how much one particle has been lorentz time shifted or where it is.
    So, in a sense, two entangled particles' quantum states are always linked. (IMO they do not recognize there spatial separation and behave as if always joined)

    Note: There is no strong causal link between the state correlations, so SR (Lorentz Invariance) does not need to apply to state correlation of entangled particle (there is no cause effect contradiction).

    I don't exactly understand what this does to the concept of time as in this thread and may be irrelevant, but I too am intrigued by the role of time. To me it is more fundamental than space.
     
  14. Apr 27, 2009 #13

    ConradDJ

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    Sorry, this was my slip-up. The author knows there is no "paradox" in a logical sense, but there is a "puzzle" in Einstein's formulation that makes it hard to see why things should work that way -- see pages 17-18. If SR is reformulated so as to be closer to the way we actually experience the world -- i.e. from the point of view of each observer's present moment, where "simultaneous" events are those on our past light-cone -- the difference in elapsed time between the two twins' experience is supposed arise more naturally, without the need to appeal to General Relativity or non-inertial motion.

    This is interesting to me not because I'm trying to come up with an improved formulation of Relativity, but because I'm trying to think about the structure of the physical world we actually experience, "in real time". So to me it's interesting that SR can be formulated from the present-time standpoint we experience, and that this formulation might even be helpful in clarifying some of what Relativity tells us about the world.
     
  15. Apr 27, 2009 #14

    ConradDJ

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    But clearly there's a difference between Minkowski spacetime and a 4-space -- where there are 4 independent variables, and there's no built-in invariance between the temporal and spatial components.

    My point is that it's too easy to slide from the mathematical description of 3-1 spacetime to something much easier for us to imagine (4-space), overlooking the difference in structure as a mere "mathematical manipulation." If the only concern is doing the calculations correctly, it doesn't matter how we imagine the physical world. But if we want to go further and understand what physics is telling us about the kind of world we live in, and learn to imagine our world in a way that's more consistent with physics, we need to be more careful about the difference between space and time in Relativity. Many people seem to be working in this direction, but there is still a general impression out there that Relativity requires a "block universe" interpretation in which time is just another dimension of space.
     
  16. Apr 27, 2009 #15

    Mentz114

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    I suppose not having to resort to non-inertial frames is an understandable motive. But they are part part of reality and SR still works in so far as one can integrate the worldline if the acceleration function is given. This process is summing a lot of infinitesmal inertial worldlines.

    The essential structure is in the metric signature so it's bad news not to keep this firmly in mind.
     
  17. Apr 27, 2009 #16

    atyy

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    Try eg. p17 of http://books.google.com/books?id=YA8rxOn9H1sC&printsec=frontcover.

    Also http://blogs.discovermagazine.com/c...bering-the-past-is-like-imagining-the-future/ for the remarks about the second law. (Don't take the biology too seriously.)
     
    Last edited: Apr 27, 2009
  18. Apr 27, 2009 #17
    A system of entangled particles would have simultaneous correlation of states anywhere in the universe regardless of SR and GR. So, does this define a 'present time'?
     
  19. Apr 27, 2009 #18

    atyy

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    The OP is defining present time along a single worldline (ie. proper time), before defining simultaneity.

    In SR, entanglement does give an "absolute" (Lorentz covariant, not Lorentz invariant) definition of simultaneity, but it cannot be used to send classical information faster than light.

    There is no quantum theory of gravity yet.

    Peres and Terno, http://arxiv.org/abs/quant-ph/0212023
     
  20. Apr 27, 2009 #19
    Yes, (thanks for the refs) the entanglement correlation does not qualify as information transfer per se. But, IMO, its nevertheless a very fundamental simultaneity worthy of consideration. There is no explanation as to how it is achieved - which makes it even more interesting IMO. More interesting than SR and GR which IMO are (merely!) causal constraints.
     
  21. Apr 27, 2009 #20

    Dale

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    How so? I mean, operationally how would you use entanglement to define simultaneity?
     
  22. Apr 28, 2009 #21

    ConradDJ

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    I doubt that the supposedly instantaneous collapse of an entangled quantum system gives any way to determine that two distant events happen "at the same moment". When one observer measures the system, in the EPR scenario, he doesn't even know whether a distant observer has already measured it -- and which measurement occurs "first" doesn't matter to the outcome of either measurement -- all that matters is that they turn out to be correlated. So I suspect that it's not really meaningful to say the collapse happens "simultaneously".

    Right... as noted, whatever definition of simultaneity we use, events can be simultaneous with each other in the past, present or future. So simultaneity is a distinct issue.

    Traditionally, the viewpoint from which physics describes the world is in effect "outside" of space and time -- so the "present" is really not in the picture at all. When I say X happens at time "t", the description is the same whether it happened in the past or is happening now or is hypothetical. When we think from this viewpoint -- which is extremely natural to us and obviously very useful, in daily life as much as in science -- the issue of the now can only appear as if it were an issue of simultaneity.

    There are a number of consistent ways of defining simultaneity, including the synchronized-clock method Einstein used in his original paper on Relativity. But the I think the lesson of Relativity is that nothing physical depends on which definition you choose. This has been disputed by people who believe there is some absolute or "preferred" spacelike hypersurface connecting distant events "in the same moment". But my sense is that they're just hanging on to an outdated classical way of picturing the world.

    The paper I mentioned above treats an event as "simultaneous" with my present-time experience if it's available to me right now, on my past light-cone. This is a fairly weird idea of simultaneity because it's not reciprocal. When I look at a star, my present moment here includes an event (photon emission) that happened on the surface of that star maybe fifty years ago. Even though the star is far away, that event is "present" to me in this moment now – but I'm certainly not present to the star in this same moment!

    If I have instruments sensitive enough to pick up the cosmic microwave background, then even the early universe is still physically present to me, in this moment now – though as something 13.7 billion light-years away in space.

    This way of thinking about “the present” treats it as something entirely local. I only share this present moment with things near enough to me that we can interact "in real time." Distant observers have their own present moments, that are connected with mine only with a time-lag.

    I'm not insisting this is right and every other way of seeing it is wrong. It's just a different picture, but to me a very interesting one.

    Instead of a “block universe” in all events just co-exist in a static pattern, I’m imagining a web of events that’s woven through space and time. From any given point of view, there’s a unique “now” that includes the immediate locality, and reaches out into space and back in time.

    What happens here and now can be physically affected only by what just happened right here in my immediate vicinity, and what happened elsewhere in the universe on my past light-cone. And whatever happens here and now can only make a difference to a certain set of events in the future – those very close in space and time, and those on my future light-cone.

    So we can maybe come up with a picture in which the world is evolving in time, but along many largely independent threads. Quantum entanglement must be telling us something important about how these threads are related to each other. But it seems to be describing something about the information-structure of the web that's distinct from its spacetime structure.
     
  23. Apr 28, 2009 #22
    The photon we viewed from the distant star showed the star 50 years ago, but if an entangled partner had been kept on the distant star, then the quantum states would be correlated in the present moment. So, in this example the correlation would end on both the star and at our location on observation. The entangled partner on the star would be 50 years 'older' (in spacetime-speak) than ours, but nevertheless simultaneous disentanglement happens. Meaningless? Well, I am not talking about information travel here. Are correlated states meaningless? In a sense yes, in another sense, no.
     
  24. Apr 28, 2009 #23
    If you are saying 'interpret the world in terms of physics instead of mathematical models', then I agree. Then you need to define time, subjective, objective, or whatever.
     
  25. Apr 29, 2009 #24
    That's an interesting scenario, but how would one entice a photon to hang around any one place for 50 years? The only thing I can think of is the event horizon of a black hole, which is basically just another way of saying that you "stopped time" for that photon for 50 years.

    In that case, when you pluck it out and observe it, the events are effectively still simultaneous.
     
  26. May 1, 2009 #25

    ConradDJ

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    The correlation is certainly meaningful. When we observe the photon at our end, we know that 50 years ago its partner would have been found to have an opposite spin, had it been measured on the star. And it's even meaningful to say the two measurements are "simultaneous" -- but only if we redefine "simultaneous" events as those happening on our backward light-cone.

    QM says -- until I measure the spin of the entangled photon, it remains in a superposition. When I measure it, I "simultaneously" determine the spin of the photon here and now, and also the spin of its partner 50 years ago on the star.

    Is it a paradox that a measurement can affect something that "already happened"? I think the sense of paradox occurs only because we're imagining the entire world as "moving forward in time" at once, as in the classical picture. QM tells us that the "instantaneous collapse" of an entangled system corresponds to the "null interval" in Minkowski spacetime, between events on the star 50 years ago and events here and now.

    An observer closer to me in space would see my measurement of the entangled system as happening first. An observer closer to the star would see the other measurement as happening first. But in Relativistic spacetime, neither "really" happens first and "causes" the other. That's why I think quantum correlation describes something about the informational structure of the world that's distinct from its spacetime structure.


    In some ways this is similar to the other issue raised above, about the "twin paradox" that only seems to be paradoxical, because we're still thinking in terms of a classical notion of simultaneity.
    This current thread in this forum is an example --

    https://www.physicsforums.com/showthread.php?t=311007

    It raises the question regarding the twin paradox -- why is it that the twin who goes to the distant star and back can be travelling inertially for the entire time, except for a brief point in the trip where he turns around, and the age difference still occurs? Further, the age difference is proportional to the distance he travels inertially, to the star and back, not to anything that occurs during the period of acceleration. The paper I cited quotes Einstein as saying, the usual mathematical solutions leave a skeptical reader "more convicted than convinced."

    I don't think there's any question that the mathematics of SR is right and that it resolves the issue, technically. But because there's no way to understand this intuitively, it's at least reasonable to imagine that rewriting the equations using the "backward light-cone" definition of simultaneity gives a better idea of what's physically going on.

    If anyone's interested, here's the link again.

    http://web.ceu.hu/phil/benyami/Apparent%20Simultaneity.pdf" [Broken]

    My basic point in this thread is that when we describe the world mathematically, we get the right answers... but if we still tend to imagine the world in a classical way, we haven't really succeeded in understanding what the math is telling us.

    Ever since Relativity and QM came on the scene, progress has been made by focusing on getting the right equations, even though what they seemed to say about the world looked paradoxical. Nothing wrong with that! But these "paradoxes" may be pointing to another way of picturing space and time, that might be more illuminating. I suspect that has to do with seeing the world as happening "in real time", along the "present moment" worldlines of different observers.
     
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