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Quantum mechanics and spacetime

  1. Sep 3, 2006 #1
    In the middle of all the talks about many worlds and what not, I find it curious that people don't seem to accept "static spacetime" ontology with QM the way they do with classical mechanics. After all, in relativity the light beam literally travels along its own simultaneity plane (if we are allowed to use such concepts in discussion), effectively causing it to arrive "at the same time" it begun its journey. Or rather, we should see the "motion of the light beam" as a static connection in spacetime which does not evolve over time in any sense, but rather simply exists just the way we find it to be in our experience. It is only in our point of view that the light is not found to be simultaneously at the origin and at the destination!

    The simple fact is that if simultaneity is relative, your future has already happened from the point of view of many observers in motion in your inertial frame. And nothing moves in spacetime; things are in motion only in our experience, time is an illusion and the future and past exist "all the time". Since this is what Einstein believed in, I find it curious that he was troubled by the "spooky action at a distance" associated with QM. Shouldn't it have been abundantly obvious to him, that when you talk about the "action at a distance" with entangled photons, there is absolutely no sense of thinking in terms of measurement causing a reaction elsewhere in spacetime "simultaneously".

    The reaction could be simultaneous only in one arbitrary inertial frame, and actually in his model the whole experiment existed as a static shape in spacetime. If one believes this, it shouldn't be too mysterious to find out that it seems like at the "departure" the photon already knew how it was going to be measured, and as such its "future" measurement appears to affect the entangled photon already at departure. It is not mysterious to find out that the universe seems to know about the future if you believe future exists all the time anyway.

    ---
    We see the energy of a so-called photon in one place at one instant, and little bit later we find it elsewhere. We have a certain idea about the motion of the photon that we think must have happened over a certain "period of time". One way to describe the mystery is to ask, how can all the "possible" routes of the photon interfere with each others when in measurements we always find the photon at one place after all? This is difficult to explain only in so far that you consider time to really flow forward.

    Relativity says that from the point of view of the photon itself no time passed at all "during" its travel. The state of the destination did not evolve in time "during" this travel, or another way to put it, the distance traveled was exactly 0, or yet another way to put it, the state of the destination was at the event "photon arrival" already when the photon "began its journey", or more accurate way to put it, the light [/b]did not travel at all; the "motion of the photon" is at most a static connection between origin and destination.

    Simply put, our idea about the trajectory of a photon is how a tiny particle would have traveled the distance in a newtonian world. In spacetime this trajectory is a static shape that exists all the time between the static shapes that are "the motion of measurement equipment". Also, the photon is an idea about a tiny particle, when we should probably avoid saying too much, and just talk about energy or information making its way from one piece of matter to another, one way or another.

    It should be plain to see how this shape of "information transfer" between pieces of matter could be determined by simple laws to exist in spacetime (not to "form" over time, but to "exist" in a static sense) exactly the way it is found to be by studying the reactions of matter. The "shape of the travel" is a wavelike shape where interference occurs, and there is no sense in claiming that measurements "at one point of time" cause something to change or move elsewhere in spacetime.

    In dual-slit experiment, the shape of the static connections simply *are* such that the energy indeed does use both routes from our point of view. If we put a piece of matter to block the other route we find the connections to exist accordingly. It is wrong to think "the photon would need to know about the slit on its way to the shade", because the light is at the source at the same moment it is at the slit.

    In delayed choice experiment - blocking the other slit while the photon "is already in its way" - from the point of view of the photon, the block was there already when the journey "began". To say we blocked the route after the photon departed is an assertion made from some arbitrary inertial frame, usually the lab frame. We can consider similar experiments with gravitational lensing, where the measured photons have been on their way for hundreds of years in our frame, and the simple fact is the same; the measurement device was in place when the photon started its journey, if a journey it may be called. There is no mystery at all in any delayed choice experiment, apart from the mystery of spacetime itself.

    So it seems to me that the "spooky action at a distance" could be seen as a case of two static connections that interfere with each others at one point in spacetime. When we measure a property of a photon, and this measurement appears to affect the state of another photon elsewhere "instantly" (in lab frame), in spacetime ontology the motion of photon A is a static connection between "departure" and "measurement", and motion of photon B is a static connection that exist in a different simultaneity plane, but their shapes are nevertheless connected at one point in spacetime; the point when in our experience the source "emitted the photons". Thus it is entirely possible, if not even likely, that the photons really do interfere at departure in such manner that the "future" measurement of photon A has a measurable effect on photon B. If you are clinging to newtonian terminology of time, it is as if the information about the measurement that occurred to photon A flowed backwards in time back into the source, where it interfered with the photon B as it was starting its journey. But in spacetime ontology all we see are static shapes.

    This may not readily explain everything about QM, but shouldn't we nevertheless use the concept of spacetime absolutely when thinking about QM phenomena, at least in so far as we think spacetime is a valid concept at all?

    If I can kick off the criticism myself, it seems to me, that the difficulties with this view are mostly the same ontological difficulties that are associated to relativity theory, namely that our future already exists and nothing moves in spacetime, which makes it much harder to explain what in the physical world causes us to experience motion in our conscious experience, or what causes us to experience there is a "now" moment at all. What causes the illusion? If instead motion really was metaphysically real instead of spacetime, we would be much closer to explaining conscious experience. For this reason I would not be too surprised if someone came up with more elegant model where motion metaphysically exists, where there is only one "now" moment, and past and future does not exist apart from our own ideas about them.

    Well, I guess what I'm asking is, why are we talking about ideas where measurement causes a metaphysical motion/change somewhere in spacetime when at the same time we don't believe anything moves in spacetime?
     
  2. jcsd
  3. Sep 3, 2006 #2
    ** In the middle of all the talks about many worlds and what not, I find it curious that people don't seem to accept "static spacetime" ontology with QM the way they do with classical mechanics. After all, in relativity the light beam literally travels along its own simultaneity plane (if we are allowed to use such concepts in discussion), effectively causing it to arrive "at the same time" it begun its journey. Or rather, we should see the "motion of the light beam" as a static connection in spacetime which does not evolve over time in any sense, but rather simply exists just the way we find it to be in our experience. It is only in our point of view that the light is not found to be simultaneously at the origin and at the destination!

    The simple fact is that if simultaneity is relative, your future has already happened from the point of view of many observers in motion in your inertial frame. And nothing moves in spacetime; things are in motion only in our experience, time is an illusion and the future and past exist "all the time". Since this is what Einstein believed in, I find it curious that he was troubled by the "spooky action at a distance" associated with QM. Shouldn't it have been abundantly obvious to him, that when you talk about the "action at a distance" with entangled photons, there is absolutely no sense of thinking in terms of measurement causing a reaction elsewhere in spacetime "simultaneously".

    The reaction could be simultaneous only in one arbitrary inertial frame, and actually in his model the whole experiment existed as a static shape in spacetime. If one believes this, it shouldn't be too mysterious to find out that it seems like at the "departure" the photon already knew how it was going to be measured, and as such its "future" measurement appears to affect the entangled photon already at departure. It is not mysterious to find out that the universe seems to know about the future if you believe future exists all the time anyway. ***


    Just a small reaction on this; there are a few ``problems'' you will encounter:
    (a) We all have the feeling that there is a time which proceeds, time is *not* an illusion
    (b) more technical, it is possible to allow for as well the advanced as retarded Green function by fixing the boundary conditions in the infinite past as well as infinite future. In Maxwell's theory for example, one could take a A_ret + (1-a) A_adv, a constant, work in the Lorentz gauge and fix the boundary conditions. This will act as a constraint on the possible matter configurations by Maxwell's theory since no solutions to the homogeneous equations are included. Although in classical physics, such as radiation back reaction phenomena in Maxwell's theory, we prefer to work only with the retarded Green's function (the antisymmetric part 1/2 (A_ret - A_adv ) being associated to radiation -antisymmetric boundary conditions in the infinite future and past -, the symmetric part being the static Coulomb potential. The problem here is of course that the infinite future is going to influence the now, and most of the macroscopic phenomena we observe in nature are well described by the retarded Green function alone. Only quantum mechanics, if one believes in all its predictions, could be interpreted as suggesting this (this reminds me about the austrian psychologist Alfred Adler whose work I studied in my high school time :wink: ). So yeh, why not, but you will have to be careful motivating the quantum from this point of view... in the sense that you will have to explain in detail why the big stuff in our world has the ``retarded'' philosophy :smile:

    But it is an option I have entertained myself a few years ago and wich comes back from time to time in the context of ``boundary value'' formulations in cellular automata. Why Einstein did not ``get'' it? Well, it takes a big leap to stop interpreting the universe as a ``evolving'' (in the sense that the arrow of time also indicates the logical arrow of evolution) quantity.

    Cheers,

    Careful

    PS: I see no need for consciousness in such model.
     
    Last edited: Sep 3, 2006
  4. Sep 3, 2006 #3
    Yes, I can't think of any meaningful counter-argument to this. Which is why I mentioned this point myself as well in the post as a criticism against myself :) For this very reason I certainly wish to be quite careful with any model that incorporates an idea of a static spacetime, and unfortunately relativity is just such model.

    Very well put indeed. And even when you start to become accustomed to think about these situations in terms of spacetime, you still don't have any language or proper terminology to talk about it in such terms. Language becomes incomprehensible without using words such as "at such and such moment" or "during its travel".

    Consciousness and the philosophy of the mind is a huge issue I've spent years thinking about.. Well, haven't we all :P

    Nevertheless, consciousness is not a good word because it entails some "thing" that is conscious or consciousness, but the existence of a conscious experience (as an emergent phenomenon) is what is almost explainable if only motion really exists and not only appears to exist in our semantical models of reality. If the state of the brains really is such and such and it really is in motion, it can be explained why some physical patterns would have such and such meaning to themselves against other patterns, and we would actually experience "now" because there is a "now". (I wish not to go too much into details in this thread or at this forum :)
     
  5. Sep 3, 2006 #4
    ***
    Consciousness and the philosophy of the mind is a huge issue I've spent years thinking about.. Well, haven't we all :P ***

    Well, as I said, I was busy with such things in my youth (I am not that old yet :wink:) but I saw no place for it in physics (unless you mean by consciousness ... ``the physics of observation'' instead of something ``metaphysical''.). But if one day, someone comes up with a theory of it (whatever ``it'' may be), without denying some form of objective reality which you don't seem to do below (which is good) then I will be all ears.

    **
    Nevertheless, consciousness is not a good word because it entails some "thing" that is conscious or consciousness, but the existence of a conscious experience (as an emergent phenomenon) is what is almost explainable if only motion really exists and not only appears to exist in our semantical models of reality. If the state of the brains really is such and such and it really is in motion, it can be explained why some physical patterns would have such and such meaning to themselves against other patterns, and we would actually experience "now" because there is a "now". **

    ** (I wish not to go too much into details in this thread or at this forum :) **

    I understand your concern :smile:
     
    Last edited: Sep 3, 2006
  6. Sep 3, 2006 #5
    Hi Careful,

    To bring the response to your question back to physics, I will quote you a paper with an elegant restatement of your question by Misner, Thorne, and Wheeler:

    " The term “3-geometry” makes sense as well in quantum geometrodynamics as in classical theory. So does superspace. But space-time does not. Give a 3-geometry, and give its time rate of change. That is enough, under typical circumstances to fix the whole time-evolution of the geometry; enough in other words, to determine the entire four-dimensional space-time geometry, provided one is considering the problem in the context of classical physics. In the real world of quantum physics, however, one cannot give both a dynamic variable and its time-rate of change. The principle of complementarity forbids. Given the precise 3-geometry at one instant, one cannot also know at that instant the time-rate of change of the 3-geometry. . . .The uncertainty principle thus deprives one of any way whatsoever to predict, or even to give meaning to, “the deterministic classical history of space evolving in time.” No prediction of spacetime, therefore no meaning for spacetime, is the verdict of the quantum principle.
    Misner, Thorne, Wheeler 1973 "

    Now if you are familiar with the first-order formulation of Bohmian mechanics (BM), you will see that since knowledge of the particle position and velocity are not restricted by the HUP in BM, then one can resolve this conceptual problem of quantum gravity simply by insisting on ontological clarity and consistency - that particles in QM always have positions.

    http://arxiv.org/abs/quant-ph/9902018

    ~Maaneli
     
    Last edited: Sep 3, 2006
  7. Sep 4, 2006 #6
    ***
    To bring the response to your question back to physics, I will quote you a paper with an elegant restatement of your question by Misner, Thorne, and Wheeler:

    " The term “3-geometry” makes sense as well in quantum geometrodynamics as in classical theory. So does superspace. But space-time does not. Give a 3-geometry, and give its time rate of change. That is enough, under typical circumstances to fix the whole time-evolution of the geometry; enough in other words, to determine the entire four-dimensional space-time geometry, provided one is considering the problem in the context of classical physics. In the real world of quantum physics, however, one cannot give both a dynamic variable and its time-rate of change. The principle of complementarity forbids. Given the precise 3-geometry at one instant, one cannot also know at that instant the time-rate of change of the 3-geometry. . . .The uncertainty principle thus deprives one of any way whatsoever to predict, or even to give meaning to, “the deterministic classical history of space evolving in time.” No prediction of spacetime, therefore no meaning for spacetime, is the verdict of the quantum principle.
    Misner, Thorne, Wheeler 1973 "
    ***

    Well, you know that I do not necessarily agree with this interpretation, I clearly stated that bringing in the future is *one* option. For example, it might very well be that some determinstic theory is underlying quantum mechanics as we know it now.

    **
    Now if you are familiar with the first-order formulation of Bohmian mechanics (BM), you will see that since knowledge of the particle position and velocity are not restricted by the HUP in BM, then one can resolve this conceptual problem of quantum gravity simply by insisting on ontological clarity and consistency - that particles in QM always have positions. **

    I think I have said that myself on many occasions :smile: The problem I have with BM is that the equations of motion for the particle trajectories are non local (and no causal mechanism is clearly presented behind it), if you want to have a theory which is compatible with GR, one needs to have at least a causal mechanism (ie. one which originates from hyperbolic differential equations on spacetime). Preferably, I would like to have the arrow of time also define the logical order of evolution (no advanced Green functions), so BM as it stands now does not fit in that picture ...

    Careful
     
    Last edited: Sep 4, 2006
  8. Sep 4, 2006 #7
    Well, back to the topic for me as well, and to one of the most obvious problems of such spacetime interpretation. Specifically, "why the big stuff in our world has the ''retarded'' philosophy"

    Obviously first thing that comes to mind is that we could easily expect any information that has relativistic speed to behave in advanced & retarded sense from our perspective. But I realize that doesn't explain why we also observe things with mass, like full atoms, to behave as if their possible paths interfere. Is this a dead-end or can it be solved? I don't know the details of experiments carried out with complete atoms. Are they pushed around by an electromagnetic field?

    Also, I don't quite understand what "quantum decoherence" would imply about this. Is there a simple way to explain it to a simpleton?

    Hmm, and regardless of the details, I think the main question about the relationship between spacetime and quantum mechanics is still valid; why do we have models where measurement causes a metaphysical change here and there in spacetime when nothing moves in spacetime? We simply cannot say "when", metaphysically, the measurement took place. We cannot say when the change occured to the spacetime. The measurement had already happened when spacetime was first formed (where using the idea of "was formed" makes no sense either... Oh well :)
     
  9. Sep 4, 2006 #8
    Oh hi,

    ** Well, back to the topic for me as well, and to one of the most obvious problems of such spacetime interpretation. Specifically, "why the big stuff in our world has the ''retarded'' philosophy" **

    You could imagine that the weight of the advanced Green function (how far you look into the future) is inverse proportional to the mass of the object in it's restframe (you can put in a regulator to take the limit m -> 0 properly). This will give you a model where there is for every pair of identical particles a critical length scale (dependent upon the mass) beyond which EPR correlations will start to decrease. A causal, relativistic ``variant'' of GRW if you want to. This answers also ...

    **
    Also, I don't quite understand what "quantum decoherence" would imply about this. Is there a simple way to explain it to a simpleton? **

    Anyway, this is just my first thought about it (The reference to EM was just to provide an example).

    Cheers,

    Careful
     
    Last edited: Sep 4, 2006
  10. Sep 5, 2006 #9
    Does this mean that what I described can actually be a valid deterministic interpretation if only spacetime exists?
     
  11. Sep 5, 2006 #10
    Well, provided you have a universal function of time (to have ``motion'') I see no obvious objection (which does not imply it is going to be easy) against this - I guess many scientists have toyed with a similar idea, Wheeler included.

    Careful
     
  12. Apr 24, 2007 #11
    AnssiH,

    When you say the motion is not real, doesn't that also direct one to conclude that energy is not a real quantity either? To start, this is always what I've thought of motion:

    1. Physical human movement is caused by contractions or dilations of muscular tissue.
    2. Muscular tissue moves after it responds to the nervous system.
    3. An action potential moves through a neuron, which stimulates electrical movement from neuron to neuron.
    4. This action impulse is really just the movement of sodium and potassium in a periodic manner along the axon of the neuron.
    5. Sodium and potassium 'move' in and out of the neuron because of the laws of diffusion.
    6. Diffusion is caused by the movement of atoms.
    7. Atoms move positions because of the amount of energy they have in their electrons. In fact, movement is actually caused by the actions of electric and magnetic fields.
    8. Electrons 'interact' with other electrons by the exchange of photons
    9. A photon moves at any speed but its intensity is based upon its frequency. Thus, the frequency defines the amount of energy a photon has.
    10. Photons are basically the true energy quantum. Their energy is what causes motion.

    So, I see how motion really isn't a formal change in position, but merely a change in varying energy and interactions via photons with other photons. But what I am confused about is what energy is in this problem. In thermodynamics, energy is defined as the potential to do work. Thus, does that mean that here the photon's energy is merely the potential to do change?

    Just an interesting philosophical question I have.
     
  13. Apr 24, 2007 #12

    JesseM

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    Simultaneity is relative, but whether one event lies in the future/past lightcone of another or outside it is absolute (at least in a spacetime with no timelike curves). If two events are simultaneous in one frame, they are outside each other's light cones in every frame.
    The issue isn't simultaneously vs. nonsimultaneously, it's that the events have a spacelike separation, i.e. neither lies in the other's past or future light cone. If we accept locality, this means events with a spacelike separation should be statistically independent, unless there's some event in their past light cone which determined their outcomes in advance in such a way as to guarantee a correlation (Bell's theorem shows that this sort of solution won't work, although I'm not sure why Einstein ruled out this kind of answer since his objections were made before Bell's theorem).
     
  14. Apr 25, 2007 #13
    I don't oppose defining motion the way you are defining it above, but the original post is talking about slightly different matter. It was simply about relativistic speed of information and quantum behaviour. In particular I was only concentrating on the behaviour of photons.

    I am not personally a big fan of static spacetime interpretation, but I wanted to note that if you choose to see relativity that way (which Einstein did, although initlally he wasn't too impressed about such an idea as "spacetime" at all), then you should see quantum behaviour that way too, and it actually takes away some tacitly held constraints of reality as they become meaningless, like the direction of causality ("advanced information" is trivially explained etc...)

    Of course.

    Because what Einstein was arguing was precisely that something like "collapse of a wave-function" could not be a real phenomenon since in the case of entangled properties it would require non-local information transfer when the collapse happens.

    Einstein was thinking of the way relativity would break down if there was non-local information, but actually if you assume reality is a static spacetime block, then first of all you cannot say which one of the entangled photons was measured first (whose collapse would cause the other one to follow accordingly), and second of all it is trivial to define the static spacetime in such a way that it only looks to us as if there is non-local information, but actually the photons take a specific "shape" already when they depart. This obviously wouldn't break anything with relativity. And yes, this is functionally very similar to transactional interpretation, but "transactional" is kind of a misnomer, or let's say it says more than is necessary, since it entails motion to spacetime itself.

    A related question (and far more important than anything above in my opinion) is whether locality is required for realism at all. It is required for such a specific interpretation of relativity where simultaneity is defined the way it usually is. Like Einstein also noted later on, it is the topology of spacetime (events) that we observe, not the simultaneity planes. There are many ways to define this scheme with identical observables (but with different sorts of simultaneity planes), and some entail absolute simultaneity, which could consequently be used to define non-local information in a coherent and logical manner. Unfortunately people are so used to think about relativity in terms of relative simultaneity (since that is the way it was originally defined, doh) that they tend to miss this option entirely.

    I don't wish to argue how one should define simultaneity in a detailed manner (The unobservable parts of "simultaneity planes", so to speak). I just want to note there are many options open to us.

    -Anssi
     
  15. Apr 25, 2007 #14

    JesseM

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    Yes, but again, you can define "non-local" purely in terms of light cones, with no need to select a particular coordinate system or a particular definition of simultaneity.
    You don't have to worry about which was measured first, or about any "collapse". You can just think about the fact that the two measurement-events can be outside one another's light cones, with a spacelike separation between them. The "static spacetime block" still has a light cone structure, meaning that the outcome of an event should only be dependent on other events in its past light cone.
    Certainly correlations between spacelike-separated events can be explained in terms of both events being influenced or predetermined by some common cause which lies in both their past light cones.. In the case of entangled photons, if we notice they always have the same polarization when measured with filters set at the same angles, we could try to explain this in terms of the common cause of both being created at a single point in spacetime in identical polarization states--is this what you mean by "the photons take a specific 'shape' already when they depart"? The problem is, Bell's theorem shows that this strategy won't work! Are you familiar with Bell's theorem, and why any "local hidden variables" theory of this nature would imply that certain "Bell inequalites" should always be satisfied, when in fact they are actually violated in QM?
    Why is it similar to the transactional interpretation? I don't see any "retrocausality", i.e. the future affecting the past, in your suggestion.
     
  16. Apr 26, 2007 #15
    Just a quick reply since I've got only a minute....

    "the way relativity would break" was referring to non-local information moving backwards in time. Would be little bit problematic conclusion :)

    No

    Yes...

    ...if you go back to the original post, it should be pretty clear. I am talking about relativistic information transfer and how it could be used to explain delayed choice experiments. Imagine how the experiment looks like from the point of view of the photon. In a slightly incoherent way, you could say the photon is measured at the same moment as it departs (from its own "frame"). In a more coherent way, if you use the terminology of static spacetime, you could say its past is affected by its future. For example its polarization when it is "measured" affects how it "departs"; that measurement happens in its "future" only from our perspective. Well, it should be clear from the OP.

    -Anssi
     
    Last edited: Apr 26, 2007
  17. Apr 26, 2007 #16

    JesseM

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    OK, well certainly the "static spacetime" view makes it a little easier to understand how backwards causation might be possible, but would you disagree that it is also perfectly possible to imagine a static spacetime governed by laws that respect locality, and that there is every indication that the laws of our universe do respect locality, so Einstein's feeling that "action at a distance" is implausible was a reasonable one that has nothing to do with failing to think in terms of the static spacetime perspective? Any universe that allows a combination of information travelling backwards and forwards in time is going to violate locality--if you have two spacelike separated events A and B, there can be another event C that is in the future light cone of both A and B, and A can send a signal forward in time to C who then relays it back in time to B.

    Your argument also seems to be based specifically on the fact that the spacetime interval between points on a light beam's worldline is 0, but entanglement and interference in the double-slit experiment can both also be observed using massive particles like electrons for which this would not be true.
     
  18. Apr 27, 2007 #17
    Locality, or IOW "forward causation" (in this context). I would not disagree.

    Like I said, static spacetime interpretation just removes some tacitly (and intuitively) held constraints from reality (~that causation exists only in one direction in time). And I always wish to stress at this point that I am not personally a big fan of this interpretation, just wanted to note it makes quantum strangeness little bit easier to comprehend.

    And like you said, there is every indication that the laws of our universe respect "locality" (or "forward causation"), and in fact quantum behaviour is just about the only indication for backward causation, and even then only if someone wants to use such a concept in their explanation (there are clearly many other options available here)

    Well here's the thing; if you assume a static spacetime, you can also argue there could exist what we would call "backward causality" if we ever find any indications for such a thing... and in quantum behaviour we do.

    We would observe this as if there exists non-local information, but still there wouldn't be any "immediate changes" actually occurring to anything in that spacetime. There are no changes of any kind occurring to that spacetime during any experiment at all.

    So I would say "action at a distance" is a misnomer with entangled properties in the context of static spacetime, because it entails event A causing something to change somewhere else in spacetime. So what Einstein missed was simply that static spacetime makes backward causation logically viable option (as long as you manage to define it properly).

    You could put it that way but you have to be sure to see this without assuming any changes to spacetime. I.e. there never was such a state of reality where B had not yet received the message from C. And most of all remembar that B is receiving messages from C by measuring an entangled property with C, and whatever B measures is going to affect how C is measuring the property as well (the measurements of B & C "give" the photon its properties when it departs).

    It's easier to set the thought experiment as simply observer A & observer B who measure an entangled properties of photons, and the idea is that observer A tries to send a message to observer B by measuring the property in certain way that means something to observer B.

    There is no sense of who was "first to cause the wave-function collapse"; both observers will affect the property, and "action at a distance" is a misnomer.

    Exactly true. Like I said to "regent" "In particular I was only concentrating on the behaviour of photons". In this light, the way regent is attempting to define "motion" is actually fairly interesting IMHO :)

    -Anssi
     
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