# Wave-Function Story

Last time I started with wave-functions of quantum systems and the Schrödinger equation that describes them. The wave-like nature of quantum systems allows them to be merged (superposed) into combined quantum system so long as the coherence (the phase information) remains intact.

The big mystery of quantum wave-functions involves their apparent “collapse” when an interaction with (a “measurement” by) another system seemingly destroys their coherence and, thus, any superposed states. When this happens, the quantum behavior of the system is lost.

This time I’d like to explore what I think might be going on here.

To quickly review, the problem is that the Schrödinger equation describes the linear evolution of a quantum system. The abrupt change from this smooth evolution to a localized measurement represents a discontinuity we haven’t truly explained.

There are multiple connected issues.

For one, the photon always manifests as a point, being absorbed by just one atom, but the interference pattern requires it act like a wave during flight. This is the wave-particle duality in a nutshell.

For another, and this is spooky, nothing seems to predict where the photon actually lands — it appears genuinely random. This may be a property of nature, but it’s very hard for some to swallow.

The biggest mystery involves what physically happens when the photon ends its flight. That sudden change doesn’t have a consensus story among us yet.

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The wave-like flight of the photon through both slits invokes another mystery involving gravity.

A photon has energy, thus mass, and thus gravity. Tiny, but present. We can also use massive particles in the two-slit experiment; they’d have even more gravity. (Scientists have successfully interfered extremely large molecules.)

The point is, when the wave goes through both slits, as it must, what happens to its mass, its gravity? Do “particles” even manifest gravity as wave-functions?

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Here’s a story that tries to make physical sense of things by taking various physically sensible pieces from quantum mechanics. The story tries, as much as possible, to stick with mainstream physics ideas.

One of those ideas is quantum decoherence, which I wrote about last time.

Another is Quantum Field Theory (QFT), which sees quantum particles as long-lived vibrations or wave-packets in a quantum field. For example, all Up quarks are disturbances in the Up field.

Quantum fields permeate all of space because particles can be anywhere (and because physics is fundamentally isotropic). Where there are no particles, the field value is zero.

These fields are part of the mathematical description, the gauge theory, that QFT is built on, but we don’t know what they are physically. Since particles seem real, these fields must , in some fashion, also be real.

My speculation is that these fields have non-local properties (which, in fact, account for the non-local behaviors of the quantum world). I’ll come back to that.

(BTW: It is Heisenberg Uncertainty of values in these fields that allow virtual particle pairs to appear and quickly disappear. A point in the field suddenly has a value, has energy, which manifests as a particle wave-packet that necessarily vanishes.)

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Let’s consider in detail the photon’s flight from start to finish.

Few have any problem with the start: An excited electron in an atom drops to a lower energy level releasing a photon in the process. This is a common occurrence.

(A complicated one from a Schrödinger equation point of view, though. The electron has a wave-function, which entangles with the atom’s wave-function, which entangles with the surrounding atoms and so on up to a very complicated wave-function for the laser.)

Once the laser emits the photon, we’re able to view the photon as a mostly isolated quantum system with coherent phase. As such, it can interfere with itself. The Schrödinger equation describes the photon as a wave phenomenon, and there is a strong correlation with the behavior of mechanical waves.

Other than questions about the physicality of the Schrödinger equation and the wave-function, there isn’t much controversy so far. The controversy involves the photon being absorbedthe infamous measurement.

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Now my story gets a bit imaginative. I think the Schrödinger equation describes something real having to do with the quantum field.

According to QFT, a particle is the smallest quantum that manifests in the field — that is, that can be measured, or that can change the state of some other system (two ways of saying the same thing).

But what if lesser amount of energy could travel along the field? Think about the “wave” that spreads out from the laser towards the detector. It has volume, internal space. Suppose the energy of the particle spreads out exactly like a wave — exactly as the Schrödinger equation describes.

But since that energy is distributed over a volume, it’s not enough to manifest anywhere as a particle. It’s just a wave of tiny energy spreading out at light speed. (Very much as we’d imagine a big beam of light streaming out.)

This spread out energy is sub-quantum at every particular location. It isn’t enough to change the state of any system it encounters. But it represents the sum of possible paths the particle could take. (It resembles Feynman’s summing of all possible paths. Another mainstream idea.)

If you want a visual image, imagine a 3D grid, finely meshed, of taut wires representing the quantum field. Imagine flicking a spot (the starting point) with a fingernail. Vibrations spread out from that point, ringing through the mesh.

This part is a bit similar to what’s called pilot wave theory.

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As this, pilot wave (for lack of a better word) spreads out and interacts with other systems, it ultimately selects one, and the spread-out energy “collapses” or “drains” into the selected interaction. This is what we perceive as wave-function collapse.

A key point is that the energy of this pilot wave isn’t sufficient to cause an interaction with any of the other systems until one is selected, and then the entire quanta of energy, previously spread throughout the field, is applied to the selected interaction.

This does require non-local behavior as the wave submits to the interaction.

At first, it seems asymmetrical in spreading at light speed (or sub-light speed for massive particles) but collapsing instantly (or nearly so).

Perhaps entrance and exit to the field are both instantaneous, regardless of whether the quantum is a point at insertion or a volume at exit. The “particle” is either there or not there, period. It starts at a point source, spreads out, and then “drains” into the interaction.

In other words: What looks like collapse to us really is a collapse of something. There is a physical reality to it.

To address the mysteries, there is no gravity question while the particle is a wave because its energy is distributed sub-quantum. It’s incapable of affecting the state of any other system. (It follows spacetime geodesics so paths are aware of the existing gravitational field.)

The fact that the quantum of energy has to find a system it can interact with is why we have point interactions. It’s always a “particle” interacting with another “particle” using the total of their energies per quantum physics.

The apparent randomness is either genuine, and reality really is random (a possibility I’m fine with), or something in the interaction of the spreading wave selects a destination system. If we ever figure out why one uranium atom decays rather than its neighbor, that’ll solve this one, too.

My guess, assuming it isn’t random, is that the combined wave-function of the photon and all the other systems, might select a target system as most probable, if not outright determined (thus removing the apparent randomness). There are no hidden variables; just the sum lots of interacting systems.

§ §

You may note I’ve made no mention of many worlds.

Everett, in his paper, provides: “Alternative 2: To limit the applicability of quantum mechanics by asserting that the quantum mechanical description fails when applied to observers, or to measuring apparatus, or more generally to systems approaching macroscopic size.”

This is exactly what I’m asserting. The photon is absorbed by the electron, its phase information is distributed — and effectively lost —among the many atoms in the detector.

In particular, that phase information is not amplified to include multiple states of the detector, let alone the scientist observing. It certainly has no power to create multiple worlds.

He goes on, in objection to this alternative, to say: “If we try to limit the applicability so as to exclude measuring apparatus, or in general systems of macroscopic size, we are faced with the difficulty of sharply defining the region of validity. For what n might a group of n particles be construed as forming a measuring device so that the quantum description fails?”

I’ve long suspected the boundary is fuzzy and hugely dependent on conditions. In more pristine conditions, n might be quite large. In messier conditions, n might be much smaller.

I think a qualitative understanding of n requires a deeper understanding of reality — at the least a reconciling of QFT and GR. For one thing, I wonder if n might depend on the gravity (mass) of the measuring system. It may be fundamentally stochastic or even random.

§ §

All quantum theories are weird; there is no exception here. There is also ontological speculation, so take it with a shaker of salt.

I will say it’s a speculation based on physical reality and mostly mainstream ideas. It has non-locality, but that seems required regardless.

The main guesswork involves the role of the quantum field and the potential for the “pilot wave” of sub-quantum energy to instantly “drain” into the interaction.

For me it’ll do until something better comes along.

Stay coherent, my friends!

The canonical fool on the hill watching the sunset and the rotation of the planet and thinking what he imagines are large thoughts. View all posts by Wyrd Smythe

#### 16 responses to “Wave-Function Story”

• Wyrd Smythe

One of the truly mind-bending things to think about under any quantum interpretation is the flight of a single photon from a distant star to Earth.

Think about the wave-function that has spread out over hundreds of light years. (To the photon, of course, no time passes, which is just weird-squared.) Consider what the sum of paths must be for such a photon.

As I said at the beginning: Reality is Too Weird For Words!

• Wyrd Smythe

For those with more background in quantum theory:

When the electron absorbs the photon both quantum states merge into a new quantum state — which describes the excited electron. The phase of the photon merges with the phase of the electron, so the electron wave-function has (almost certainly) a shifted phase from what either had initially.

The electron is part of an atom, which is part of an assembly of atoms, and, as described in the previous post, any phase information from the photon is quickly distributed into the larger quantum system. Meanwhile the electron is interacting with the overall system such that its phase (and any imprint from the photon) is quickly smeared.

If the photon hit the wall, nothing else happens. The disturbance is quickly lost in the much larger system of the wall.

If the photon hit the detector, and the detector is capable of recording individual photons, it’s state must obviously change. The electron absorbing the photon must be amplified to something sufficiently macro to affect a recording or display device.

To the extent the detector can be said to be in a superposed state, it would necessarily be between detecting and not detecting. This requires a coherent phase for the entire detector, and I’m not sure that’s possible. Any coherence among the atoms of the detector should be instantly dissipated.

• SelfAwarePatterns

An interesting interpretation Wyrd! Unfortunately, my knowledge of QM isn’t really sufficient for me to judge its merits, but I do appreciate that you recognize and acknowledge the cost, in your case, non-locality.

One question that does occur to me. Your example is done using a photon, where the photon’s existence unequivocally comes to an end. If we run through the scenario with an electron, or some other fermion, does it change things? Just curious.

• Wyrd Smythe

Thanks! Yeah, it’s always gotta be something with quantum. One has to pick one’s weirdness. (As I mentioned at the end of the previous post, experiments with Bell’s Inequality seem to make it clear we’re stuck with non-locality. Or, at least, most interpretations are forced to provisionally accept it. If I have to swallow a weirdness pill, that one seems kind of already on the plate.)

“If we run through the scenario with an electron, or some other fermion, does it change things? Just curious.”

I’d want to do a little research into exactly what happens when we throw electrons at something. (For that matter, what about uncharged heavy molecules? What happens to them??)

I can speculate based on some things we do know…

Firing electrons at something raises its charge. It can raise it to the point of having enough negative charge to repel further electrons (unless they’re moving very fast). The phosphor coating in CRTs is electrically grounded to drain that charge. CRTs wouldn’t work otherwise.

So the electron can’t vanish. (Off the top of my head, I’m not sure what events absorb electrons. Some weak interactions, maybe? Certainly meeting a positron would do it.) As you may know, while current moves at high speed, the actual electrons move very slowly (like walking pace slowly). They just of buzz around the material. I assume what happens is that the incoming electron merges with that cloud of electrons, raising the overall charge by one electron. In the right kind of system, that can be detected, and I’d want to look into the details of exactly how that electron is amplified to macro levels.

What I do think, in terms of wave-function, is that the incoming electron’s wave-function merges (superposes) with the particles of the detector and, in turn, its wave-function becomes a superposition of everything it interacts with. Its quantum state essentially becomes the quantum state of the detector.

What I don’t see happening is the detector’s state becoming a superposition of detecting and not detecting. I don’t see how the detector can be in any kind of coherent state due to all its atoms and being connected to the environment. The decoherence for a system that size in a hot messy environment is below the Planck time.

I’ve come to realize that hidden assumption in Everett’s work is the idea that the wave-function of a single particle can have a significant effect on the wave-function of a much larger system. Part of the argument rests on us not knowing how to define “much larger system” but (as I touched on in the post) I’m beginning to think answering that is where the key to all this lies.

(I’m really wondering if this sort of thing is where Baggott is headed with that ‘no big deal’ stuff. Reading his book was something of a shared mind experience for me.)

• SelfAwarePatterns

Thanks for speculating!

I haven’t read Everett directly, but on the particle not having much of an effect, I can see that being true for a non-measuring device, like a brick. But as you noted for the film, isn’t a measuring device constructed to amplify the effects of that one particle? It seems like that would give the particle far more causal power than it would have on a non-measuring device. Or am I missing your point?

• Wyrd Smythe

Not at all, and it’s something I’m still chewing on (and will no doubt explore thru writing about). My sense at this point is there’s a difference between causal power and wave-function. I need to look into the details of single particle detection to understand exactly what’s happening there. My understanding currently is that such systems have a stored energy level that’s analogous to a set mousetrap. The detection of a small force releases that stored energy.

The film molecules (I’m guessing) are in a non-minimal energy configuration that a photon unlocks and releases. It might be analogous to a super-chilled solution where a tiny disturbance seeds a phase change that expands throughout the solution. (I love watching it. In the winter I leave capped but opened bottles of water in my garage, after shaking them to get as much air out of the solution as possible. Often, when it’s sub-zero for a day or two, I can go out and flick one and watch the phase change of freezing spread through the super-chilled water. Very cool. Literally. 😀 )

Such systems, whether through phase change or other energy release mechanism, consist of large numbers of molecules, all of which are connected to the environment (which includes things like all the radio waves passing by — tons and tons of photons streaming through the detector every second; their energy levels don’t permit direct interaction, which is why they pass through, but their wave-functions certainly interact).

The only way we ever get superposition is when the self-interacting single system, or the two interacting systems, both have coherent phase; that’s the only way it’s possible. When a system is large enough to decohere, that’s lost. I forget where I read this (Tegmark?) but, IIRC, the decoherence time for a lone hydrogen atom in deep intergalactic space, about as isolated as possible in the universe, is on the order of microseconds.

With larger or more environmentally linked systems, the time drops rapidly. AIUI, it quickly drops below Planck time.

• SelfAwarePatterns

Not sure what to make of the Planck time part. It does make sense that an atom in an intergalactic void is still being buffeted by the CMB, so it would still quickly decohere. Although it does make me wonder what might happen once the CMB disappears in the distant future.

But consider this. Under MWI, with the measuring device just sitting there, its wave function is branching zillions and zillions of times per second. (“Zillions” being a very technical term for ginormous number. (“Ginormous” also being a very technical term.))

So it’s not just the particle that is going to throw it into superposition. All the particle does is lightly perturb it. But the device is designed to magnify that perturbation into something a human can perceive. So the particle ends up having large scale effects on the state of the device.

So among the zillions and zillions of branches the device’s wave function is constantly splitting into, a portion of them will now contain the detection state. The portion should be in proportional to the probability of the device making the detection. (I think. I’m winging this.)

That’s the thing about the MWI. We have to remember that it’s not just the measurement throwing out all these branches, but everything else as well.

That said, I’m guessing this makes it even more ludicrous in your eyes. 🙂

• Wyrd Smythe

Once the CMB fades out, isolated atoms in intergalactic space would be very isolated, indeed!

The more I read, the more I question what we mean by the “wave-function of the detector” — it’s not something we’re able to calculate, and I’ve begun to wonder if we’re even thinking about it in a sensible manner. The detector would certainly have a wave-function, but I’m not sure quite what to make of it.

For one, there is the de Broglie wavelength, which gives the wavelength for a given mass. The formula is simply h/mv, but with h as the numerator, the mass and velocity must be equally tiny for the wavelength to amount to anything at all.

Another puzzle is that the wave-function of the detector is a summation of every particle that comprises it, so the detector’s ψ encodes a mind-boggling number of contributing states. Superposition involves the notion of observables, and I’m not quite sure how to apply that notion to a macro object like a detector. On its own, it’s always observed to be a detector sitting in the same spot you saw it last with the same energy level and basic atomic configuration.

The deep puzzle, of course, is how to view its detecting something, and that’s something I want to research a little before I go too far out on a limb.

“So the particle ends up having large scale effects on the state of the device.”

Yep, right with ya.

“The portion should be in proportional to the probability of the device making the detection.”

You mean the portion of entire detectors that have detected something, yes? You’re talking about the MWI view of it? (Assuming so, yes, that’s what it posits.)

We’re at the point where I kind of want a physicist, because (per above) I’m not sure what to say about the detector being in superposition with itself. The de Broglie wavelength might be sub-Planck, and I’m not sure what effect that has on things. I’m not sure what effect all the particle and atom sub-systems have in swamping or damping out superposition.

Certainly the energy and atomic configuration has to change when, say, an electron lands after passing through two slits. It’s absolutely tempting to view the detection system as being in superposition between absorbing the electron and not… I’m not sure it’s the right picture. It’s kinda like an ocean liner hitting a life raft and being affected the same way as the raft. Maybe all that happens is the detector gets a little smear across its bow where the raft hit. Enough to say it happened.

But, yes, what you are suggesting is exactly what Everett proposed. I showed you a bit of this before, but maybe it’s even more relevant here. In the simplest form he presents:

$\psi^{S+O}=\phi^{S}_{i}\psi^{O}_{i}[...,a_{i}]$

Which translates to: (post observation) The wave-function of system S combined with observer O results in the product of the states of Φ and Ψ (the i subscript denotes superpositions; each i is an observable state). The brackets enclose the “memory” of O, the dots indicating the unchanged states leading to the observation, and the a representing the change in memory due to the observation. (This is all in Chapter IV Observation.)

But I keep thinking about ocean liners. 😉

• SelfAwarePatterns

I’m not really grasping the significance of the wavelengths. We do know that those decoherences have to happen, don’t we? (Or wave function collapse if classic Copenhagen?)

“You mean the portion of entire detectors that have detected something, yes? You’re talking about the MWI view of it?”

I was thinking of all the versions of the detector that could possibly detect something, which I suspect is what you meant, but just making sure. Definitely this is my take on MWI.

On matching Everett, that’s good to know. My reading of the popular accounts hasn’t been in vain. If I’m understanding the equation correctly, the two wavefunctions (the system and the observer) combine, which makes sense. I’m actually slightly stoked that I understand the equation at all!

• Wyrd Smythe

The de Broglie wavelength affects the wave behavior of a system in suggesting that above some threshold, there really is no wave behavior to speak of. I don’t know that it’s directly connected to decoherence, which is just the loss of phase of a quantum system (“loss” in the can’t measure it anymore sense).

As an example, that hydrogen atom in intergalactic space. The more CMB photons it absorbs, each with their own phase, the less we can say about the atom’s original phase. It gets combined with more and more photons. (Anywhere on Earth, it gets blasted with radio and IR photons.)

OTOH, the atom still has a wave-function we can measure, observables we can detect. We’ve just lost the earlier observables. There are measurements we could have made that we can no longer make. (Doesn’t really matter with the atom, but if it was a computing qbit we’d configured, that configuration is gone.)

FWIW, I visualize coherent (i.e. measurable) phase as a pure musical note. The more notes we add to it, the less it even sounds like a note, let alone can be identified as to what that note was (imagine someone played every note on the piano at once). If we add just one or two notes, though, we get new notes (harmonics) which is a lot like combining a limited number of quantum states.

The thing is, if we see decoherence as behind the “collapsing” of the wave-function, then all macro objects must be in permanently collapsed condition given the messy environment. (Quantum computers have to go to great lengths to maintain coherence long enough to make a computation.) There’s just no way for the detector to be in a coherent state such that interacting with a coherent system should affect it.

(As these posts suggest, maybe we need to rethink the whole “collapse” thing. At least in the case of the photon, it goes away so why should it be surprising its w-f goes away? The quantum information it had is absorbed and dissipated into the larger system, so no information is lost. If something analogous happens with more massive particles, we may have over thought the collapse mystery.)

• SelfAwarePatterns

Lots to think about, but I’m depleted for now. Thanks Wyrd!

• Wyrd Smythe

Now that’s a great exit line! Until next time.

• BB #73: Wavefunction Collapse | Logos con carne

[…] For what it’s worth, I’ve speculated on what I think might be going on with “collapse.” See Wave-Function Collapse and Wave-Function Story. […]

• Wavefunction Collapse | Logos con carne

[…] more musings on wavefunction collapse, see the paired Wave-Function Collapse and Wave-Function Story posts from May of 2020 and BB #73: Wavefunction Collapse from August of 2021. They may not add […]