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.
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?
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.
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.)
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 absorbed — the infamous measurement.
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.
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!