Measuring the Decoherence

Realistically Speaking
Chapter eight of Bernard d’Espagnat’s On Physics and Philosophy is entitled, “Measurement and Decoherence, Universality Revisited.”

In some ways it was a very dense and difficult chapter to read (and summarize). However, in the end the main points seemed pretty reasonably clear:

  1. Quantum universalism and our perceptions of macroscopic reality at first appear to clash
  2. A macroscopic object easily shifts between numerous and narrow energy bands under the slightest influence from their environment
  3. Therefore it’s almost impossible to measure the exact quantum states of macroscopic objects
  4. Our lack of knowledge about large-scale systems in “decoherent” states leads to the apparent stability of the macroscopic world
  5. However, on the microscopic level a “realistic” interpretation of superpositions only works if a system includes unmeasurable components or we restrict what measurements we’ll make.

There’s a lot of material in this chapter so one could easily come up with some other highlights. In any event, here are my impressions of the chapter in greater detail…

Realist Statements vs Realist Philosophy
Instead of saying “I see a rock on the path” one could say “I know if I looked on the path to see if I would get the impression of seeing a rock there, I would actually get that impression.”

That would be cumbersome so we use “realistic” statements even if we don’t believe in hard-line realism. If we switch back to the microscopic realm realist-like statements might mislead.

Macroscopic Realism vs Quantum Universalism
If we assume quantum formalism is universal, then why don’t we see a rock in two places at the same time?

Macroscopic realism says macroscopic objects have mind-independent forms located in mind-independent places. So even before we look at it, a measuring device’s pointer will point to one and only one part of the dial.

A macroscopic state-vector therefore can’t be a quantum superposition A + B, and hence we can’t see a rock in two places at the same time.

Schrödinger Equation vs Macroscopic Realism
The problem is that the Schrödinger equation will often demand such a superposition. Realists respond by using something other than state-vectors to describe macroscopic objects.

D’Espagnat says that he showed (in 1976) that such attempts will fail, and a somewhat more general proof was found by Bassi and Ghirardi (in 2000).

Antirealism vs Macroscopic Realism
A different approach is to follow Plato and Kant. The senses are unreliable and deceive us. There’s no distinction between Locke’s reliable “primary” qualities and the less reliable “secondary” qualities.

The only thing certain are the quantum rules that predict our observations. All else is uncertain.

Probability vs Determinism
However, we don’t experience the world as a sequence of probabilistic predictions. We picture objects with definite forms, and we can predict the behaviour of these objects using classical laws that are deterministic.

Textbook Realism vs Quantum Predictive Rules
Part of the problem is that textbooks talk about the mathematics (including symbols for wave forms) as if they represent physical states that “exist” whether or not we’re taking a measurement.

D’Espagnat notes the same old difficulties of realist interpretations will  then reappear. He says symbols for the wave forms and other values should instead represent “epistemological realities.” They signify possible knowledge once the observer makes an observation.

In other words, the quantum rules predict observations, they don’t describe unobserved realities.

Absorbed vs Released Particles
In chapter four d’Espagnat assumed that a measured electron gets absorbed by the measuring instrument. In practice this rarely happens.

If the electron gets released, then the instrument and the electron form a “composite system.” Instrument and electron are “entangled” (in the quantum sense).

Composite States vs Measurements
If an electron is in a quantum superposition of two states, the instrument dial shows just one of those states (which you can confirm by using a second instrument to measure the first instrument).

If you test an “ensemble” of identical states all at once then some of your instruments will show one state while others will show the other state.

Note that the measurement points to the state of the electron after it’s measured, not before.

Measurements vs Quantum Collapse
Some physicists who won’t accept “weak objectivity” or mere “empirical reality” see the measurement process as “collapsing” a “real” wave function.

Quantum Collapse vs Quantum Universality

A quantum collapse is a “discontinuous” transition from the (differential hence continuous) Schrödinger equation.

If the quantum laws are universal, then what’s so special about a measuring instrument to produce this collapse?

Moveable Cuts vs Realism
Using the “von Neumann chain” idea, one can predict observations by placing a “cut” between observer and observed at various points. There’s nothing special about one particular instrument.

The cut may be placed between a measuring instrument and the particle, or between a second instrument (measuring the first instrument) and the first, or between a third instrument and the second, and so on.

Von Neumann showed that the results will be the same no matter where this cut is placed.

The problem is that the realist believes in a mind-independent reality, so presumably this cut should be in one and only one place. The collapse of a quantum system shouldn’t be at the whim of the observer (and his mind!).

Longing for Realism vs the Practice of Operationalism
D’Espagnat says a lot of physicists suffer from a kind of logical “shaky balance.” They want to believe in realism but in their working methods they use “operational” methods (which therefore don’t require a belief in realism).

Schrödinger’s Cat vs Quantum Superposition
Getting back to the composite system of instrument and electron, if the electron was prepared by a superposition of two states, then the composite system is represented by aA + bB. The small letters represent the “states” of the electron, and the big letters represent the states of the instruments.

But the measuring instruments will point to A or B on the dial, not both at the same time. Schrödinger imagined a cat that’s dead or alive depending on the results of the experiment.

We don’t see an instrument pointing to two parts of the dial simultaneously, nor can we imagine the cat is both dead and alive simultaneously.

Quantum Superposition vs Probabilities
The measuring instruments will show one result each time. Quantum rules predict the probability that a particular result will be seen, not that several results will be seen at the same time.

Probabilities vs Ensembles
To test probabilities we can create a really large ensemble of identical conditions and see what results we get. Imagine we create a whole lot of composite systems with an entangled electron and measuring instrument.

On each of those instrument dials we’ll measure one result or another, not both, and not something in between.

Identical States vs a “Proper” Mixture
Staying with the electron that was prepared as a superposition of states, we calculate a percentage probability that we’ll measure that electron as “being” in one specific “state” and another probability it’ll “be” in another “state.”

What if instead of a large number of identical states and identical measuring instruments we prepare some electrons in one state and some others prepared in the other state? We’ll determine how many of each by the predictions for the superposed state.

If we then just measure, say, position, we’ll get (approximately) the same results as predicted for the superposition of states. But if we try measuring something other than position our results may violate these predictions.

So unless we ignore everything but position, measurements on our ensemble of electrons in superposed states will differ from our proper mixture of electrons in pure quantum states.

Coherent vs Decoherent Measurements
Imagine we measure an entangled system of an electron (with states in superposition) and an atom. Then an ensemble of identical superposed states cannot be approximated by a “proper mixture” of separate pure states.

But if the atom and electron interact with a molecule that is too complex to measure, our measurements of the electron–atom system will be the same whether we measure an ensemble of identical states or a proper mixture.

The system has become “decoherent.”

Electron–Instrument vs Electron–Instrument–Environment Systems
It’s already hard enough to measure the “state” of an electron using an instrument. If we try to measure the “state” of the electron and the instrument in relation to the environment then we have a big problem.

Macroscopic vs Microscopic Energy Levels
A macroscopic object’s energy levels are very close to each other, so a very small disturbance from its environment (or its internal constituents) will shift its energy level.

Measurement Imprecision vs Quantum Precision
There is thus so much environmental influence on an instrument that we cannot measure the “state” of the instrument and electron as a system in the same way we were able to measure just the “state” of the electron.

That’s why we can’t perform an experiment similar to our earlier one that found differences between measurements on the ensemble of superposed states and the proper mixture of separate pure states.

Therefore an instrument pointer, which is a macroscopic object, will act like it’s in a single state, not a superposition.

Ensembles vs Double-slit Experiments
In the “Young slit experiment” we imagine a particle source, a barrier with two slits, and a detector screen (see chapter four). Normally the screen would show fringe-like patterns because of the quantum system’s wavelike nature.

However, if you add a dense gas to the area between the barrier and the detector screen then you’ll just see two “blobs,” therefore showing no evidence of wave-like interference.

The molecules in front of the screen are analogous to the molecules that are near an electron–atom system. The molecules form part of a system but are not themselves measured. In both cases we lose the effects of superposition.

Independent vs Empirical Reality
Because the insertion of unmeasurable molecules prompts us to infer distinct beams with distinct states (corresponding to the “up” or “bottom” slit), this shows how decoherence creates the illusion of a macroscopic reality.

D’Espagnat acknowledges it’s a bit artificial to make this distinction since we know about the particle source. But it reminds us that decoherence is what provides the illusion of an independent reality, although it’s really just an “empirical” reality.

Entanglement vs Reduced States
If one system gets “entangled” with another (such as an electron with an atom) then each system loses its own distinct wave function. There’ll now be a wave function for the combined system.

But the quantum formalism allows some information about the original system to be recovered if we imagine a large ensemble of its replicas. The mathematics that represents this is called a “reduced state.”

Quantum Prediction vs Decoherence
Imagine an ensemble of grain sands or dust specks. They’re small but still macroscopic. The quantum formalism predicts these small objects would be enough to produce the macroscopic effects in the Young slit experiment.

And the quantum formalism also predicts that these objects will act macroscopically, supporting the role of decoherence in creating the illusion of a macroscopic reality.

Reduced State vs Localization
The matrix mathematics used to describe the reduced state suggests the reduced state can stand in for an infinite number of proper mixtures of pure quantum states, which threatens the idea of locality. Fortunately at least one of those proper mixtures is composed of quantum states that are localized.

Experimental Superposition vs Decoherence
In experiments by Brune et al. a “mesoscopic” object is put into a superposition of states. In the brief time before environmental interactions introduce decoherence, the object’s quantum properties can be observed.

The experiments therefore provide evidence both for decoherence and for the validity of quantum laws in objects larger than microscopic.

Quantum Universality vs Classical Laws
Brune’s experiments support quantum universality, but it would be good if we could also show how to derive the laws of classical physics from the rules of quantum prediction.

Classical Numbers vs Quantum Operators
In classical physics various properties of an object (such as a table’s length) are represented by numbers governed by classical mechanics. In quantum physics these properties are represented by (Heisenberg) operators and obey quantum equations.

Roland Omnès has proved that the observational predictions of both approaches coincide (in classical physics’ traditional domains).

Quantum Laws vs “Reifying by Thought”
Because classical physics and their predictive formulas are so reliable in the macroscopic realm we naturally infer that past objects and events have “caused” present ones, and present ones will “cause” future ones.

Counterfactuality vs Quantum Mechanics
Counterfactuality depends on locality, but Bell’s Theorem combined with the Aspect-type experiments show that nonlocality, and hence counterfactuality, is violated (relevant if we’re realists).

If we want to show classical and quantum predictions are the same in the macroscopic realm then we’re going to have to figure out how to “recover” the counterfactuality we imagine macroscopic reality possesses.

Is there action-at-a-distance with macroscopic darts? It turns out their orientation is a macroscopic variable that “washes away” microscopic variations.

In fact orientation is one of the “collective variables” that includes length, mass, and other classically measurable quantities. We’ve already noted that Omnès showed their values are consistent with quantum formalism.

Macroscopic Certainty vs Microscopic Uncertainty
Measuring a “complete set of compatible observables” will give you the state vector that “exists” after all the measurements were made, but that doesn’t help you figure out the state vector that “existed” before you made any measurements.

The idea of a measurement is usually that it measures something previously existing. By that standard you can’t figure out a state vector for sure no matter how many measurements you make.

By contrast, the mathematics behind a macroscopic ensemble’s “reduced state” will tell us which physical quantities may be measured without disturbing the system. We can therefore recover the “state” of a macroscopic member of that ensemble.

D’Espagnat says this ability helps shed light on our intuition that the properties of something must have been the same before we looked at it.

Realism vs Semirealism
D’Espagnat will discuss those who still cling to realism in the next chapter. However, he says there are “semirealist” approaches that manage to stay faithful to the quantum formalism.

A and B vs A or B
The “and–or problem” arises because when we measure a system of superposed states aA + bB we see it as either in state A or in state B, not in both states A and B at the same time. This shift from “and” to “or” is nowhere suggested in the equations. D’Espagnat suggests this is a conceptual not a mathematical issue.

One vs Many Realities
The mathematics of quantum formalism does not require there just be one and only one reality. Everett’s “relative state theory” interprets this formalism to suggest that the universe “branches off” when a superposed system is measured.

In a given branch only one of the superposed “states” is measured, but the overall multi-branch system is still represented by the same expression that combines superposition plus entanglement: aA + bB.

Common Sense vs Formalism
Some physicists are attracted to Everett’s branching universes because it agrees with the quantum formalism. They believe that following the formalism first rather than common sense could bring in a revolution similar to relativity’s own repudiation of common sense.

Zurek vs Reality
Zurek showed that the “reduced state” of a macroscopic ensemble is stable under certain measurements. He goes further and defines “reality” as whatever is out there that remains stable under such measurements.

Quantum Universality vs Classical Foundations
Decoherence theory tips the balance away from thinking classical physics is somehow more foundational than quantum physics. Decoherence theory shows how the rules of classical physics may be derived from quantum rules.

Physics vs Chemistry, Biology, and Other Disciplines
Decoherence theory can’t let us predict the structure of other disciplines though. The quantum formalism has to be simplified “by hand.” Quantum theory is still universal, but our human choices, our human ways of conceiving things, will crucially guide our perceptions.


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