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Distinct Configurations

24 Post author: Eliezer_Yudkowsky 12 April 2008 04:42AM

Previously in seriesJoint Configurations

Yesterday's experiment carried two key lessons:

First, we saw that because amplitude flows can cancel out, and because our magic measure of squared modulus is not linear, the identity of configurations is nailed down—you can't reorganize configurations the way you can regroup possible worlds.  Which configurations are the same, and which are distinct, has experimental consequences; it is an observable fact.

Second, we saw that configurations are about multiple particles.  If there are two photons entering the apparatus, that doesn't mean there are two initial configurations.  Instead the initial configuration's identity is "Two photons coming in."  (Ideally, each configuration we talk about would include every particle in the experiment—including the particles making up the mirrors and detectors.  And in the real universe, every configuration is about all the particles... everywhere.)

What makes for distinct configurations is not distinct particles.  Each configuration is about every particle.  What makes configurations distinct, is particles occupying different positions—at least one particle in a different state.

To take one important demonstration...

Fig5_2 This is the same experiment as Figure 2,  with one important change:  Between A and C has been placed a sensitive thingy, S.  The key attribute of S is that if a photon goes past S, S ends up in a slightly different state.

Let's say that the two possible states of S are Yes and NoS starts out in state No, and ends up in state Yes if a photon goes past.

Then the initial configuration is:

"A photon heading toward A; and S in state No."  (-1 + 0i)

Next, the action of the half-silvered mirror at A.  In the previous version of this experiment, without the sensitive thingy, the two resultant configurations were "A to B" with amplitude -i and "A to C" with amplitude -1.  Now, though, a new element has been introduced into the system, and all configurations are about all particles, and so every configuration mentions the new element.  So the amplitude flows from the initial configuration are to:

"Photon from A to B; and S in state No."  (0 + -i)
"Photon from A to C; and S in state Yes."  (-1 + 0i)

Next, the action of the full mirrors at B and C:

"Photon from B to D; and S in state No."  (1 + 0i)
"Photon from C to D; and S in state Yes."  (0 + -i)

And then the action of the half-mirror at D, on the amplitude flowing from both of the above configurations:

  1. "Photon from D to E; and S in state No."  (0 + i)
  2. "Photon from D to F; and S in state No."  (1 + 0i)
  3. "Photon from D to E; and S in state Yes."  (0 + -i)
  4. "Photon from D to F; and S in state Yes."  (1 + 0i)

When we did this experiment without the sensitive thingy, the amplitude flows (1) and (3) of (0 + i) and (0 + -i) to the "D to E" configuration canceled each other out.  We were left with no amplitude for a photon going to Detector 1 (way up at the experimental level, we never observe a photon striking Detector 1).

But in this case, the two amplitude flows (1) and (3) are now to distinct configurations; at least one entity, S, is in a different state between (1) and (3).  The amplitudes don't cancel out.

When we wave our magical squared-modulus-ratio detector over the four final configurations, we find that the squared moduli of all are equal:  25% probability each.  Way up at the level of the real world, we find that the photon has an equal chance of striking Detector 1 and Detector 2.

All the above is true, even if we, the researchers, don't care about the state of S.  Unlike possible worlds, configurations cannot be regrouped on a whim.  The laws of physics say the two configurations are distinct; it's not a question of how we can most conveniently parse up the world.

All the above is true, even if we don't bother to look at the state of S.  The configurations (1) and (3) are distinct in physics, even if we don't know the distinction.

All the above is true, even if we don't know S exists.  The configurations (1) and (3) are distinct whether or not we have distinct mental representations for the two possibilities.

All the above is true, even if we're in space, and S transmits a new photon off toward the interstellar void in two distinct directions, depending on whether the photon of interest passed it or not.  So that we couldn't ever find out whether S had been in Yes or No.  The state of S would be embodied in the photon transmitted off to nowhere.  The lost photon can be an implied invisible, and the state of S pragmatically undetectable; but the configurations are still distinct.

(The main reason it wouldn't work, is if S were nudged, but S had an original spread in configuration space that was larger than the nudge.  Then you couldn't rely on the nudge to separate the amplitude distribution over configuration space into distinct lumps.  In reality, all this takes place within a differentiable amplitude distribution over a continuous configuration space.)

Configurations are not belief states.  Their distinctness is an objective fact with experimental consequences.  The configurations are distinct even if no one knows the state of S; distinct even if no intelligent entity can ever find out.  The configurations are distinct so long as at least one particle in the universe anywhere is in a different position.  This is experimentally demonstrable.

Why am I emphasizing this?  Because back in the dark ages when no one understood quantum physics...

Fig2_2

Okay, so imagine that you've got no clue what's really going on, and you try the experiment in Figure 2, and no photons show up at Detector 1.  Cool.

You also discover that when you put a block between B and D, or a block between A and C, photons show up at Detector 1 and Detector 2 in equal proportions.  But only one at a time—Detector 1 or Detector 2 goes off, not both simultaneously.

So, yes, it does seem to you like you're dealing with a particle—the photon is only in one place at one time, every time you see it (we'll talk about the real reasons for this later).

And yet there's some kind of... mysterious phenomenon... that prevents the photon from showing up in Detector 1.  And this mysterious phenomenon depends on the photon being able to go both ways.  Even though the photon only shows up in one detector or the other, which shows, you would think, that the photon is only in one place at a time.

Fig3_2 Which makes the whole pattern of the experiments seem pretty bizarre!   After all, the photon either goes from A to C, or from A to B; one or the other.  (Or so you would think, if you were instinctively trying to break reality down into individually real particles.)  But when you block off one course or the other, you start getting different experimental results!

It's like the photon wants to be allowed to go both ways, even though (you would think) it only goes one way or the other.  And it can tell if you try to block it off, without actually going there—if it'd gone there, it would have run into the block, and not hit any detector at all. 

It's as if mere possibilities could have causal effects, in defiance of what the word "real" is usually thought to mean... 

But it's a bit early to jump to conclusions like that, when you don't have a complete picture of what goes on inside the experiment.

Fig5_4 So it occurs to you to put a sensor between A and C, so you can tell which way the photon really goes on each occasion.

And the mysterious phenomenon goes away.

I mean, now how crazy is that?  What kind of paranoia does that inspire in some poor scientist?

Okay, so in the 21st century we realize in order to "know" a photon's history, the particles making up your brain have to be correlated with the photon's history.  If having a tiny little sensitive thingy S that correlates to the photon's history, is enough to distinguish the final configurations and prevent the amplitude flows from canceling; then an entire sensor with a digital display, never mind a human brain, will put septillions of particles in different positions and prevent the amplitude flows from canceling.

But if you hadn't worked that out yet...

Then you would ponder the sensor having banished the Mysterious Phenomenon, and think:

The photon doesn't just want to be physically free to go either way.  It's not a little wave going along an unblocked pathway, because then just having a physically unblocked pathway would be enough.

No... I'm not allowed to know which way the photon went.

The mysterious phenomenon... doesn't want me looking at it too closely... while it's doing its mysterious thing.

It's not physical possibilities that have an effect on reality... only epistemic possibilities.  If I know which way the photon went, it's no longer plausible that it went the other way... which cuts off the mysterious phenomenon as effectively as putting a block between B and D.

I have to not observe which way the photon went, in order for it to always end up at Detector 2.  It has to be reasonable that the photon could have gone to either B or C.  What I can know is the determining factor, regardless of which physical paths I leave open or closed.

STOP THE PRESSES!  MIND IS FUNDAMENTAL AFTER ALL!  CONSCIOUS AWARENESS DETERMINES OUR EXPERIMENTAL RESULTS!

You can still read this kind of stuff.  In physics textbooks.  Even now, when a majority of theoretical physicists know better.  Stop the presses.  Please, stop the presses.

Hindsight is 20/20; and so it's easy to say that, in hindsight, there were certain clues that this interpretation was not correct.

Like, if you put the sensor between A and C but don't read it, the mysterious phenomenon still goes away, and the photon still sometimes ends up at Detector 1.  (Oh, but you could have read it, and possibilities are real now...)

But it doesn't even have to be a sensor, a scientific instrument that you built.  A single particle that gets nudged far enough will dispel the interference.  A photon radiating off to where you'll never see it again can do the trick.  Not much human involvement there.  Not a whole lot of conscious awareness.

Maybe before you pull the dualist fire alarm on human brains being physically special, you should provide experimental proof that a rock can't play the same role in dispelling the Mysterious Phenomenon as a human researcher?

But that's hindsight, and it's easy to call the shots in hindsight.  Do you really think you could've done better than John von Neumann, if you'd been alive at the time?  The point of this kind of retrospective analysis is to ask what kind of fully general clues you could have followed, and whether there are any similar clues you're ignoring now on current mysteries.

Though it is a little embarrassing that, even after the theory of amplitudes and configurations had been worked out—with the theory now giving the definite prediction that any nudged particle would do the trick—early scientists still didn't get it.

But you see... it had been established as Common Wisdom that configurations were possibilities, it was epistemic possibility that mattered, amplitudes were a very strange sort of partial information, and conscious observation made quantumness go away.  And that it was best to avoid thinking too hard about the whole business, so long as your experimental predictions came out right.

 

Part of The Quantum Physics Sequence

Next post: "Where Philosophy Meets Science"

Previous post: "Joint Configurations"

Comments (21)

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Comment author: Will_Pearson 12 April 2008 06:48:26AM 3 points [-]

Eliezer or anyone else: I am puzzled why the mirror itself doesn't act as a sensitive thingy. A mirror that deflects a photon gains some momentum (hence solar sails or whatever), so I'd expect the configurations to be

"Photon from A to B; and mirror at A with momentum X+e." (0 + -i) "Photon from A to C; and mirror at A with momentum X." (-1 + 0i)

Comment author: Eliezer_Yudkowsky 12 April 2008 07:19:07AM 2 points [-]

Pearson, my guess is that the natural spread of the mirror's particles over configuration space, and the natural spread of the photon's momentum, is greater than the momentum the mirror's particles gain from the photon bouncing. As a result, the blobs of amplitude in configuration space mostly overlap. Remember, in the real world, all of this happens in a continuous configuration space with a differentiable amplitude distribution.

Comment author: simon2 12 April 2008 09:15:30AM 1 point [-]

MIND IS FUNDAMENTAL AFTER ALL! CONSCIOUS AWARENESS DETERMINES OUR EXPERIMENTAL RESULTS!

You can still read this kind of stuff. In physics textbooks.

I hope this is just a strawman of the Copenhagen interpretation. If not, what textbooks are you reading?

Comment author: billswift 12 April 2008 11:41:39AM 0 points [-]

Good post. For anyone wanting to read further, I recommend

Lindley, David. Where Does the Weirdness Go? Stenger, Victor J. The Unconscious Quantum: Metaphysics in Modern Physics & Cosmology

Both are interesting and readable. The problem with textbooks is that they are too much work for things are aren't particularly imprtant to you at the time.

Comment author: Allan_Crossman 12 April 2008 12:56:15PM 0 points [-]

I should have asked this back when Figure 3 came up originally:

In Figure 3, is the total number of hits registered in the detectors equal to the total number of hits registered in Figure 2? Or is it half that number, because (intuitively and probably wrongly?) half the photons are hitting the wall?

Or to state it another way, if you launch a single photon in Figure 3, are we guaranteed to see a hit registered on a detector? Or does that happen just half the time?

Comment author: Allan_Crossman 12 April 2008 01:05:34PM 2 points [-]

Oops, sorry to post twice in a row.

"Like, if you put the sensor between A and C but don't read it, the mysterious phenomenon still goes away, and the photon still always ends up at Detector 1."

Is this sentence correct? I thought the "mysterious phenomenon" was that photons never went to Detector 1, when you would expect them to reach it half the time. So if the mysterious phenomenon goes away, you should see half the photons at Detector 1 and half at Detector 2, not all at 1.

Or have I misread this?

Comment author: Ian_Maxwell 12 April 2008 04:44:17PM 1 point [-]

This is the first clear explanation of the phenomenon of quantum entanglement that I have ever read (though I gather it's still a simplification since we're assuming the mirrors aren't actually made out of particles like everything else). I have never really understood this phenomenon of "observation", but suddenly it's obvious why it should make a difference. Thank you.

Comment author: Eliezer_Yudkowsky 12 April 2008 06:43:10PM 2 points [-]

Allan: Is this sentence correct?

No. Ouch. Fixed.

Allan: In Figure 3, is the total number of hits registered in the detectors equal to the total number of hits registered in Figure 2? Or is it half that number, because (intuitively and probably wrongly?) half the photons are hitting the wall?

Half the number. Because amplitude flows to a configuration where the photon hits the wall, and way up at the level of observation, that means we sometimes see no photon in any detector.

Comment author: Nick_Tarleton 12 April 2008 07:07:48PM 3 points [-]

Remember, in the real world, all of this happens in a continuous configuration space with a differentiable amplitude distribution.

So, in reality, since gravitational interactions and whatnot cause the photon to always have a tiny effect, even with no sensor, it will very rarely show up at Detector 1. And as the level of interaction with the rest of reality increases, P(D1) approaches 50%. Right?

Comment author: Eliezer_Yudkowsky 12 April 2008 07:18:21PM 2 points [-]

Correct as I understand it, Nick.

Comment author: Richard_Hollerith2 12 April 2008 10:25:06PM 0 points [-]

I agree that humans are much too prone to regard conscious awareness and subject experience as an inalienable part of the fabric of reality (and that quantum physicists have not been immune to this bias). Let us pray that humans will avoid this mistake when the stakes get higher.

Comment author: Silas 13 April 2008 01:25:13AM 0 points [-]

Very few comments on this one, but my confusion hasn't been extinguished.

The explanation so far is that the amplitudes add back together as per complex addition. But then, "nudging" the photon at one point, eliminates the entire phenomenon involving combination and manipulation of (complex-valued) amplitudes? A nudging whose existence we can't even verify?

Why does the complex amplitude reality slip away upon thus nudge? Why can't I "explain away" any observation now by saying "ah, yeah man, there must have/not have been a nudge, problem solved".

Comment author: DaveInNYC 14 April 2008 10:58:49PM 0 points [-]

So I guess I get how this works in theory, but in practice, doesn't a particle going from A-B have SOME kind of effect that is different than if it went from B-C, even without the sensitive thingy? I don't know if it would be from bouncing off other particles on the way, or having some kind of minute gravitational effect on the rest of the universe, or what. And if that is the case, shouldn't the experiments always behave the as if there WERE that sensitive thingy there? Or is it really possible to set it up so there is literally NO difference in all the particle positions in the universe no matter which path is taken?

Comment author: taryneast 09 January 2011 06:17:10PM *  0 points [-]

One of the previous comments (I think in the previous post) pointed out that yes, indeed this does occur - but that these effects mainly cancel each other out.

In my mind this works somewhat like Brownian motion: lots of tiny pushes, but overall, it continues in roughly the same way. ie, mostly the photon carries on as though it hasn't changed configuration space in any significant way.

Comment author: Crunk_Monkey 13 June 2008 04:28:18PM -1 points [-]

So I guess I get how this works in theory, but in practice, doesn't a particle going from A-B have SOME kind of effect that is different than if it went from B-C, even without the sensitive thingy? I don't know if it would be from bouncing off other particles on the way, or having some kind of minute gravitational effect on the rest of the universe, or what. And if that is the case, shouldn't the experiments always behave the as if there WERE that sensitive thingy there? Or is it really possible to set it up so there is literally NO difference in all the particle positions in the universe no matter which path is taken?

Comment author: ksvanhorn 06 February 2011 06:55:03AM *  0 points [-]

Eliezer writes:

"It's as if mere possibilities could have causal effects, in defiance of what the word "real" is usually thought to mean..."

Actually, mere possibilities can make a difference... if you have effects that propagate backwards in time. Here's why.

To simplify, assume that you have a physical system that takes inputs (w,x) and produces outputs

(y,z) = F(w,x),

where w is an initial condition, x = z is an effect propagated back in time, and y is that portion of the system's output that is not propagated back in time. Then given a specific value of w as an initial condition, whatever happens is a solution to the fixed-point equation

(y,x) = F(w,x)

for x.

Given w, a "mere possibility" is a possible output of F that could occur for the right choice of x, but doesn't occur for the actual value of x. But these "mere possibilities" are properties of F. Changing the set of "mere possibilities" means changing the function F, and possibly getting a different fixed-point.

Why is this relevant to QM? Well, Cramer's Transactional Interpretation of QM uses both the retarded and advanced wave solutions to Schrodinger's equation. That is, it has "offer" waves going forward in time and "confirmation" waves going backwards in time. And I'm told that Aharonov's work in QM also postulates subtle influences propagating backwards in time.

Comment author: DanielLC 01 April 2012 07:13:28PM 0 points [-]

Actually, mere possibilities can make a difference... if you have effects that propagate backwards in time.

It still has to happen. It might happen in the future instead of the past, but it still has to happen.

Comment author: ksvanhorn 01 May 2012 03:45:08AM 1 point [-]

No, it doesn't have to happen. Consider the Elitzur-Vaidman bomb tester. The outcome depends on whether or not the bomb could have exploded, regardless of whether or not it actually does. You might object that in the Many Worlds Interpretation of quantum mechanics both happen, but the situation can equally well be described using Cramer's Transactional Interpretation of quantum mechanics, which involves waves that propagate backwards in time, and in which only one of the two possibilities (explode or don't explode) occurs. Whether MWI or TI or some other interpretation is the correct one, this demonstrates that backward-in-time signalling allows a "mere possibility", that does not actually occur, to have measurable effects.

Comment author: ciphergoth 01 May 2012 06:33:29AM 0 points [-]

In Eliezer's realist, MWI interpretation, there are definitely "worlds" in which the bomb explodes; they can have small amplitude but what we see in our world is because of events that straightforwardly happen in those other worlds. And of course there aren't really multiple worlds, there's one world, only part of which we can see and interact with once we've separated through decoherence.

Comment author: DanielLC 01 May 2012 05:55:53PM 0 points [-]

From what I can understand, Cramer's Transactional Interpretation is basically a way to justify waveform collapse. The tester sees what he does because the plunger sent the signals causing waveform collapse. As far as I can tell, he never says what triggers the wave-form collapse. If it's just too much stuff getting entangled, then that's what causes the result you see, not mere possibilities.