Archive for April, 2010

There is No Path

25 April 2010

Jigsaw Puzzle

Ploughing along through the quantum fields, I present my summary of some issues Bernard d’Espagnat raises in chapter four of his book On Physics and Philosophy (see publisher’s listing).

Holism vs Multitudinism
Previously D’Espagnat had been making the case that violation of Bell’s inequalities shows that localized particles cannot be making up the universe.

Double-slit Gas vs No Gas
Now he asks us to imagine a double-slit experiment where you can fill the room with gas and then measure the interference pattern.

Interference vs Non-interference
As a mind experiment, at least, one would stop seeing interference patterns when the space between light source and detector screen is filled with gas.

Full Particle vs Fraction of a Particle
In the original experiment with no gas the detector shows full particles not fractions of particles. This suggests each particle went through one and only one of two slits.

But then there’d be no reason for the interference pattern. D’Espagnat notes two solutions.

End Points vs In Between
The Broglie–Bohm model suggests a point-like particle is guided by a non-localized field or wave that interacts with both slits to indicate the interference pattern.

A different approach is to consider a concept’s “domain of validity”: it might be valid to think of a particle at the start and finish but not in between.

Just Waves vs Particles as Waves
The quantum wave function encodes information about the particle starting at the source. In between source and detector are the particles these waves or wave functions?

D’Espagnat says we should avoid overobjectifying. Keep in mind the concept’s domain of validity.

Path vs No Path
Whatever the formalism says, most physicists somehow imagine there is a real particle travelling from start to finish. And indeed if you apply the gas then the particle seems to have a definite path between source and detector.

Classical Particles vs Classical Gas
But if the transmitted particles are now acting classically then so should the gas particles. However, related experiments show a kind of interference pattern called “phenomena B,” so the gas is not acting classically.

Probability of Measurement vs Being
The wave function gives the probability a particle will be observed at various spots on the detector.

If you talk of the likelihood of its “being” somewhere then the particle would have to be pointlike, and hence there’d be no interference patterns.

Strongly Objective vs Weakly Objective
D’Espagnat proposes calling direct statements about attributes, “strongly objective,” and procedural statements about what you’ll find, “weakly objective.”

The Born rule takes the quantum wave function and yields probabilities of observation. It doesn’t describe “position” in a strongly objective way.

A “weakly objective” statement implies that there’s an observer (so it sounds subjective), but that the observations will be the same for any observer whatsoever (doesn’t sound quite so subjective now).

Observations vs Descriptions
The traces of “microblobs” in a cloud chamber are easily interpreted as well-defined trajectories.

However, quantum theory relies on “weak objectivity” and assigns probabilities that a microblob will be observed at some position.

Instead of “trajectories” we have “traces”: alignments of bubbles or microblobs. A theory that predicts observations can therefore compete with a descriptive theory.

Wide vs Narrow Domain of Validity
Quantum mechanics textbooks rarely discuss “domain of validity,” leaving the reader with the impression that a measurement “reduces the wave” and turns it into a pointlike particle.

This causes “ontological incongruities.” Neither “Heisenberg representation” nor a modified logic could restore strong objectivity to “orthodox” quantum mechanics.

Bohr vs Strong Objectivity
Some supporters of strong objectivity thought Bohr’s “intersubjectivity” of quantum description would rescue them. (But see below…)

Bohr’s Intersubjectivity vs Sociologists’ Intersubjectivity
D’Espagnat notes that the “intersubjectivity” used by philosophers and sociologists are at a higher level than the “raw, unanalyzed” sensations of quantum observation.

Only the second can be universal—and it’s not even assuming ontological reality.

Copernicus’s “Big” Revolution vs Quantum Mechanics’ “Small”
Some people say Copernicus’s revolution was much greater than quantum mechanics. But using quantum physics to explain classical physics undermines the standpoint of a strong objectivist.

Innovative Probabilities vs Innovative Objectivity
D’Espagnat also claims that the quantum physics’ main innovation compared to classical is that its statements are weakly objective.

Less innovative is quantum physics’ use of intrinsic probabilities.

Weakly Objective Knowledge vs No-influence Signals
As previously noted, the “supplementary theorem” says faster-than-light influences between particles cannot convey matter, energy, or usable signals.

But how can you have influences without signals?

Since quantum mechanics is so successful, why not apply its weak objectivity to special relativity?

If you do so, then the emphasis on knowledge rather than realism means you don’t have to worry about signals.

No signals… no influences.

Philosophers vs Reality “As It Really Is”
Philosophers know there’s no proof that our representations of reality show “reality as it really is.” So they’re ahead of most physics textbooks.

Physics vs Realist Language
But philosophers still use a realist language “as if” we could describe reality-per-se. Physics tells us to give up this language, or at least let go of its universalism.

Ordinary vs Quantum Complementarity
In ordinary life two separate photographs of the same object provide more information than just one photograph.

Bohr’s complementarity principle says you can’t do that with quantum systems.

Human-independent vs Weak Objectivity
Bohr adds that experimental conditions are an “inherent element” of our descriptions.

The experimentalist chooses those conditions, so “physical reality” cannot be “human-independent” reality.

Therefore reality cannot be strongly objective. The hopes of the strong objectivists were dashed.

Praise vs Use
Bohr admitted his thoughts about micro-objects were weakly objective.

Physicists formally praised the principle, but rarely used it on the measurement problem or anything else.

D’Espagnat won’t be using the principle either.

Multiple States vs Single Pointer
Imagine a group of electrons that have three possible states: state a, state b, and state c.

Let state c be the sum of the other two states. Then shouldn’t a measuring instrument’s pointer be in state A and state B at the same time?

Theoretical vs Practical Measurements
Decoherence theory tells us that quantum objects easily interact with their immediate environment—often before they can interact with a measuring instrument.

An ensemble of electrons in states a and states b produce such complex values that it’s almost impossible to measure them.

Therefore you don’t have to worry in practice about a fuzzy pointer, though there are other (rare) experiments that show quantum superposition among macro-objects.

Similarly it would be almost impossible to measure correlations between photons and gas particles in the double-slit experiment.

Simple Subjectivity vs Intersubjectivity
In the double-slit experiment without gas it’s often said you’ll get no interference fringes if you try to measure which slit the particle passes through.

That sounds like simple subjectivity. But it actually depends on the instrument you try to use. If it’s set up incorrectly the fringes show up. If the instrument has a fault the fringes show up.

Since you’re depending on the instrument, you’re measuring a “public” property, hence it’s intersubjective, which is to say, weakly objective.

Strongly Objective vs Epistemological Truth
If you exclude practically impossible tests then you can make statements that are empirically true or false such as talking about macroscopic objects and classical fields.

They’re weakly objective statements that are “epistemologically” true or false.

Someone who doesn’t know quantum mechanics or doesn’t believe in its universality might think they’re strongly objective.

Observing vs Observed Instrument
Properties of a physical system are encoded into a “wave function” or “state vector.” The Schrödinger equation and Born rule can then calculate probabilities of certain observations.

The mathematical formalism says we can ignore details of the observer’s eye, optical neurons, and so on.

John von Neumann said various elements can be assigned to either the quantum side or the macrosystem side of a calculation.

Because of this “von Neumann chain” an instrument can either be an observer or the observed.

It’s usually easiest to put the instrument on the classical, perceiving subject side.

Born Rule vs Wave Collapse
It can be hard to distinguish using the Born rule to come up with probabilities of observations on the one hand and talk of a “reduction” or “collapse” of the wave function.

Descriptive vs Predictive Method
Although useful in practice, this “reduction” is not required by quantum theory. For a simple photon pair the descriptive approach may be replaced by the predictive method.

Realism vs Non-realism
D’Espagnat says these concerns about the conceptual foundations of quantum mechanics make the issue of realism even more pressing.