The Trouble with Quantum Questions: Dialogue II — On the Wavefunction

Characters:

Professor Quillibrace

Mr Blottisham

Miss Elowen Stray

---

Blottisham:

I’ve brought a diagram.

Quillibrace:

I feared as much.

Blottisham:

You’ll find it very helpful. A wavefunction, plotted nicely along an axis. Peaks here, troughs there. Quite elegant.

Quillibrace:

You’ve already drawn the wrong conclusion.

Blottisham:

I haven’t said a word!

Quillibrace:

You’ve drawn a picture.

Elowen Stray:

What’s the problem with picturing it?

Quillibrace:

Pictures insist on asking what it is a picture of.

Blottisham:

Of the system, obviously. Of where it is, or what it’s doing.

Quillibrace:

There we are again.

Blottisham:

The wavefunction describes the system’s state.

Quillibrace:

It encodes a rule.

Blottisham:

A rule for what?

Quillibrace:

For the distribution of possible instances.

Blottisham:

You’re evading the question.

Quillibrace:

I’m refusing the picture.

Elowen Stray:

So the wavefunction isn’t a wave?

Quillibrace:

It’s an unfortunate name.

Blottisham:

Then why does it interfere with itself?

Quillibrace:

Because probability spaces can have structure.

Blottisham:

That sounds suspiciously mathematical.

Quillibrace:

The wavefunction is mathematical.

Blottisham:

But mathematics represents something.

Quillibrace:

Sometimes. Sometimes it constrains.

Elowen Stray:

Constrains what can happen?

Quillibrace:

Constrains what counts as an outcome.

Blottisham:

Then the wavefunction exists in some abstract realm?

Quillibrace:

No.

Blottisham:

In physical space?

Quillibrace:

Also no.

Blottisham:

You’re being deliberately difficult.

Quillibrace:

I’m being ontologically tidy.

Elowen Stray:

So where is the wavefunction?

Quillibrace:

It isn’t.

Blottisham:

Outrageous.

Quillibrace:

It doesn’t need to be. It’s not the sort of thing that has a location.

Blottisham:

Then why do physicists talk about it “evolving”?

Quillibrace:

Because its constraints change with the system.

Blottisham:

Through time!

Quillibrace:

Through parameterisation.

Blottisham:

You’re just renaming time.

Quillibrace:

No. Time appears in instances, not in the theory of them.

Elowen Stray:

So the wavefunction doesn’t tell us what is happening now.

Quillibrace:

It tells us what could be made actual under different cuts.

Blottisham:

That sounds dangerously close to ignorance.

Quillibrace:

Ignorance has an owner. This does not.

Blottisham:

So it’s not a catalogue of unknown facts?

Quillibrace:

No facts are waiting.

Elowen Stray:

Then when people argue about whether the wavefunction is “real”…

Quillibrace:

—they are asking the wrong ontological question.

Blottisham:

Surely it must be either real or not.

Quillibrace:

Only if “real” means “thing-like”.

Blottisham:

Doesn’t it?

Quillibrace:

Not in a theory of instantiation.

Elowen Stray:

So the wavefunction is more like grammar than furniture?

Quillibrace:

A beautiful analogy.

Blottisham:

Grammar isn’t real.

Quillibrace:

Try violating it in public.

Blottisham:

That’s social convention.

Quillibrace:

And this is physical constraint.

Blottisham:

So the wavefunction tells reality how it may speak?

Quillibrace:

It tells us which utterances are available.

Elowen Stray:

And measurement chooses one utterance?

Quillibrace:

Actualises one.

Blottisham:

Then the wavefunction collapses?

Quillibrace:

No more than grammar collapses when you finish a sentence.

Blottisham:

But something changes.

Quillibrace:

Yes. The relevance of alternatives.

Blottisham:

You’re stripping all the drama out of it.

Quillibrace:

Drama is a sign of misplaced metaphysics.

Elowen Stray:

So the wavefunction doesn’t float around space.

Quillibrace:

It never did.

Blottisham:

Doesn’t split into worlds.

Quillibrace:

Only in bad novels.

Blottisham:

Doesn’t hide behind reality.

Quillibrace:

Reality has no backstage.

(A pause.)

Elowen Stray:

Then the real puzzle was why we expected the wavefunction to be a thing at all.

Quillibrace:

Because we are very fond of things.

Blottisham:

Even I must admit… this makes the arguments feel rather empty.

Quillibrace:

They were arguments about furniture in a grammar book.

Blottisham:

So the wavefunction isn’t a picture, or a wave, or a shadowy object.

Quillibrace:

It is a constraint on what may be actualised.

Blottisham:

Which exists—

Quillibrace:

—as a feature of the system-as-theory.

Elowen Stray:

And the trouble with the wavefunction…

Quillibrace:

…is that we keep asking what it is, instead of what it does.

Blottisham:

And what it does is—

Quillibrace:

—limit the ways reality can be made definite.

(Silence.)

Blottisham:

I shall have to redraw my diagram.

Quillibrace:

Or stop drawing altogether.