Null Spacetime Intervals and Quantum Superposition

[XilOnGlennSt]

TL;DR Summary

Delayed-choice experiments, and "spooky action at a distance" observations seem to be based on the spacetime frame of the observer, not that of the photon.

In Abner Shimony's paper "The Reality of the Quantum World", the choice between particle detector and wave interference detector is said to be made "after the photon had interacted with the beam splitter".

A: Isn't it true that, at light speed, time is not passing for the photon? And so, with reference to Shimony's clock, nothing can be said about "where" the photon "is" at any particular time. So, no statement can be made about what time would be "after" the photon had passed through the beam splitter.

B: Furthermore; since no time passes for the photon between emission and absorption, there is no basis for the assertion that for some period of time the photon existed in a superposed state.

C: For the same reason, entangled photons that are emitted in opposite directions can never be said to be "distant" from one another, until one or the other is absorbed. The spacetime intervals for each are null, so they are adjacent in spacetime. There is no need to suppose some signal traveling at faster than light.

Please help me understand any misconceptions. Thanks for your comments.

 

[Mister T]

Isn't it true that, at light speed, time is not passing for the photon?

No, that is not true. It is not possible to define the passage of time for a beam of light in a vacuum. But that does not stop us from being able to measure the amount of time that it takes for a flash of light to travel some known distance.

 

[Ibix]

A: Isn't it true that, at light speed, time is not passing for the photon?

No. Your whole argument depends on discussing the rest frame of a photon, but there is no meaningful way to define such a thing. This is a direct consequence of Einstein's second postulate that the speed of light is the same in all inertial frames. This means that, in a frame traveling along with a light pulse, you claim that the speed of light is both zero and $c$.

Nothing helpful follows from such a self-contradiction. That's why you cannot make sense of your "photon's perspective". The whole idea is fundamentally flawed.

 

[PeterDonis]

Isn't it true that, at light speed, time is not passing for the photon?

No. We have a FAQ on this:

https://www.physicsforums.com/threads/rest-frame-of-a-photon.511170/

 

[PeterDonis]

Moderator's note: Changed thread level to "I".

 

[Pencilvester]

photons that are emitted in opposite directions can never be said to be "distant" from one another, until one or the other is absorbed. The spacetime intervals for each are null, so they are adjacent in spacetime.

The spacetime interval between a point on light ray A and a point on light ray B (assuming they were emitted at the same point) will always be spacelike, not null. (EDIT: unless one of the points is the emission—then it’s null.) In that sense, they can definitely be said to be distant from each other.

Perhaps you are only saying that the spacetime interval between any two points on a single light ray is null. This is true, but one: that tells you nothing about how to compare one light ray to another; and two: how close two points on a light ray are to each other is a frame-dependent statement. In some frames they can appear arbitrarily close, and in others they can appear very distant.

 

[XilOnGlennSt]

No, that is not true. It is not possible to define the passage of time for a beam of light in a vacuum. But that does not stop us from being able to measure the amount of time that it takes for a flash of light to travel some known distance.

Thanks for your response, and please consider the following humble questions: It seems to me that measuring when a photon arrives at a position, and assuming you know when a photon "passes" that position are two different things; especially in experiments which seem to highlight the importance of observer participancy; especially when proposed explanations of observed phenomena strain credulity to this degree. Superposition, multiverses, determinism are extravagant hypotheses. Time has already been severely bent by spacetime. Time is undefined for lightlike particles. Why not suppose that time and position for photons are resolved only when they are absorbed? Is that more extravagant? Thanks for any comments.

 

[PeterDonis]

It seems to me that measuring when a photon arrives at a position, and assuming you know when a photon "passes" that position are two different things

This is correct, but not for the reason you appear to think. See below.

Time is undefined for lightlike particles.

Again, this is correct, but it doesn't mean what you appear to think it means. See below.

Why not suppose that time and position for photons are resolved only when they are absorbed?

Because that supposition, at least the way you appear to mean it, doesn't work.

What does work is to understand that, if you do not measure a particle, you cannot definitely say when it is at a particular position, for example by knowing the distance from the source to that position and the time when the particle was emitted by the source, because you cannot assume the particle travels with a definite speed when it is not being measured. The particle has amplitudes to travel along various different trajectories in spacetime, and this can be viewed as having amplitudes to travel at various different speeds; for example, a photon has amplitudes to travel at speeds other than the speed of light.

However, the amplitudes fall off as you get farther from the "classical" path in spacetime, the one you would calculate by assuming a definite speed for the particle, so you can't just wave your hands and say "well, the photon could be anywhere at any time until we measure it". It's much more constrained than that.

 

[Mister T]

Thanks for your response, and please consider the following humble questions: It seems to me that measuring when a photon arrives at a position, and assuming you know when a photon "passes" that position are two different things

Just speak of beams of light instead of photons. That makes your objection disappear. Once you understand what the special theory of relativity implies for the motion of a beam of light, then you can move on to quantum mechanics, and only then can you start looking at the behavior of photons.

Time passes when a light beam travels from one location to another, that is part of the foundation of special relativity. The spacetime interval between its emission and its reception is lightlike. Proper time doesn't exist for lightlike intervals, so you can't claim the proper time is zero. What you can claim is that the magnitude of the interval is zero, but that is not the same thing as proper time.

For an object moving at a speed less than the speed of light, the spacetime interval between its emission and its reception is not zero, and it's equal to the proper time that elapses for that object.

 

[XilOnGlennSt]

Thank you very much for your response. It has focused my study and thinking. I would appreciate any comments on the following conjectures. I hope I haven't left this thread fallow for too long.

If we can stick with classical spacetime:

ΔΓ=ΔT/ϒ

Relates proper time differences between two events, as measured in two different inertial reference frames. (My apologies if symbol usage isn't quite correct.) Of course, ϒ is the Lorentz factor. So, if v=c, the denominator is zero and the operation is undefined.

In math, and particularly differential calculus, dealing with such situations is common place. The derivative is dy/dx, as a limit as x->0. Works well for continuous functions, even though, strictly speaking, dy/dx is undefined for dx=0.

In the above equation, the limit as v->c is zero. The seeming implication is that the proper time measured ΔΓ approaches 0 (simultaneity) as a limit. So, I see that we can't look at the photon's perspective. But can't we say things like time is undefined for the photon, or time is not moving for the photon? As for accounting purposes, the photon is moving in space, and proper time intervals between emission/absorption could resolve according to distance and reference frame.

Given this, isn't it reasonable to question Shimony's Delayed Choice experiment because it assumes the location of the photon at certain proper times as measured in his lab? For example, the switch is activated after the photon had interacted with the beam splitter.

So, did I miss the boat on the math, the physics, or both? Thanks for your consideration. Sorry if I'm beating a dead horse.

 

[PeterDonis]

proper time differences between two events, as measured in two different inertial reference frames

There is no such thing; proper time is not frame-dependent. It is a property of a particular timelike worldline in spacetime: along any timelike worldline, the proper time between any two events on the worldline is an invariant.

Note that I specified a timelike worldline. Light travels on null worldlines, so the concept of "proper time" does not even apply to light.

The seeming implication is that the proper time measured ΔΓ approaches 0 (simultaneity) as a limit.

No. What you are seeing is that, as I said above, light travels on null worldlines. The arc length along a null worldline between any two events on the worldline is zero. But that is not the same thing as "simultaneity". Simultaneity only makes sense between events that are spacelike separated, not null separated. So the concept of simultaneity does not make sense along a null worldline, the path through spacetime of a light ray, any more than the concept of proper time does.

can't we say things like time is undefined for the photon, or time is not moving for the photon?

We can say that neither proper time nor simultaneity make sense along null worldlines, and light rays travel along null worldlines.

Trying to say anything else becomes vague and misleading, and is best avoided. Also, it is not necessary to say anything else in order to make predictions.

isn't it reasonable to question Shimony's Delayed Choice experiment because it assumes the location of the photon at certain proper times as measured in his lab?

It might be reasonable, but not for any of the reasons you are giving; whether or not it is reasonable in a particular experiment to make claims like "the choice of detector was made after the photon interacted with the beam splitter" has nothing whatever to do with the fact that light travels on null worldlines and therefore the concepts of proper time and simultaneity don't make sense along the worldlines that light travels on. You would have the same issue to assess with any quantum phenomenon, for example in a similar experiment using electrons.

The valid reason why it might be reasonable to question such statements has to do with quantum mechanics, and doesn't even require relativistic quantum mechanics (quantum field theory), since the relevant factors can be assessed in an approximation that doesn't bring in all the complexity of QFT. It is a matter of looking at the distance between the beam splitter and the detectors and comparing it with something like the coherence length of the photon. (I'm not sure if that's exactly the right technical term--heuristically, the idea is to look at the "spread" in spacetime of the photon's wave function, to see whether, over the distances used in the experiment, there is a significant probability amplitude for the photon to effectively travel at a speed other than the speed of light.)

 

[XilOnGlennSt]

Thanks for your quick reply! I intend to study your response more thoroughly, but first, a possible clarification:

Isn't it valid to consider an idealized spacetime diagram (S) of this experiment like this:

And to imagine that Shimony's world line is the ct axis. Now we have a proper time for AG. Yes?

Then I'd like to measure AG in reference frames (S', S'', etc.) at successive velocities, moving to the right, to gain intuition about the limiting case. (I understand that in this experiment, the photon is zig-zagging, but each zig-zag would present a symmetric case +c, -c.) So, now plotting the spacetime invariant for each event, and plotting the tangent simultaneity lines for S'. I get this, for v=0.4c.

Moving to S'', at v=0.97c, the event simultaneity lines are getting closer and closer (on ct) suggesting the limiting case I tried to make previously. And further and further apart on ct'', suggesting slower and slower clock in S''.

I think I'm pretty far out on a limb here, looking for an intuition I like better than those on offer. I appreciate any further comments you think helpful. As you see, I've found the results of this experiment very puzzling.

Thanks

 

[PeterDonis]

Isn't it valid to consider an idealized spacetime diagram (S) of this experiment like this

No, because you're purposely constructing the diagram so it's consistent with your claim, by making the "choice" and "splitter" events spacelike separated, so you can change their time ordering by changing frames. But you don't know that that's true of the actual experiment. The "choice" event could be anywhere in the past light cone of the "switch" event in your diagram, and there are plenty of events in the past light cone of the "switch" event that are also in the future light cone of the "splitter" event, not spacelike separated from it.

 

[XilOnGlennSt]

No, because I wouldn't purposely mislead you. And besides, my point isn't about the order of events. It's about all of these events, from emission to absorption, approaching simultaneity as measured from a series of reference frames where v is approaching c.

Limit theory is based on epsilon-delta arguments. Give me an epsilon, in this case an elapsed proper time between events. And I can give you a delta, in this case a velocity at which a relative reference frame would measure elapsed proper time within epsilon. So, in the limit, as epsilon approaches zero, delta approaches c.

As I'm sure you know, limit theory was originated by Newton and Leibnitz (and possibly even as early as Archimedes) specifically for use in Physics. Why not allow it here?

Your comment that seems most relevant is:

We can say that neither proper time nor simultaneity make sense along null worldlines, and light rays travel along null worldlines.

Trying to say anything else becomes vague and misleading, and is best avoided. Also, it is not necessary to say anything else in order to make predictions.

It's great that current theory can make predictions. But it reminds me of the ancient astronomers, who used epicycles to predict the movement of the planets. That mathematics worked nicely, but didn't recognize the actual underlying reality.

 

[PeterDonis]

my point isn't about the order of events. It's about all of these events, from emission to absorption, approaching simultaneity as measured from a series of reference frames where v is approaching c.

You apparently did not grasp my point. If the "choice" and "splitter" events are not spacelike separated, it is impossible for them to be simultaneous in any frame.

Limit theory

Has nothing whatever to do with the question at issue. All you need to know is whether the "choice" and "splitter" events are spacelike separarated or not. You don't need to take any limits anywhere.

As you drew the diagram, it is perfectly possible for them not to be, since the only requirement for where the "choice" event has to be placed on the diagram is that it has to be in the past light cone of the "switch" event, and there are plenty of events in the past light cone of the "switch" event that are not spacelike separated from the "splitter" event. So your placement of the "choice" event on your diagram is not justified by our knowledge of the experiment, and cannot be used to prove anything.

That mathematics worked nicely, but didn't recognize the actual underlying reality.

You need to get a better understanding of what the theory actually says and doesn't say before making grandiose claims like this.

 

[PeterDonis]

As I'm sure you know, limit theory was originated by Newton and Leibnitz (and possibly even as early as Archimedes) specifically for use in Physics. Why not allow it here?

Because it's unnecessary and irrelevant. See my previous post.

 

[XilOnGlennSt]

I need to make a correction: The delayed-choice experiment I considered here wasn't Abner Shimony's. He discusses these experiments in a Scientific American article that I had saved from decades ago. Shimony credits these experiments to two independent groups: First, to Caroll O. Alley, Oleg G. Jakubowicz and William C. Wickes of the University of Maryland at College Park. Secondly, T. Hellmuth, H. Walther and Arthur G. Zajonc of the University of Munich.