Still Unexplainable

We know what light does with remarkable precision.

We know how it reflects, refracts, interferes, polarizes, disperses and propagates.

We can calculate these effects closely enough to build lenses, fibres, interferometers, telescopes and communication systems around them.

None of this knowledge is trivial.

It is one of the great achievements of science.

And yet a question remains.

Why does reality contain these relations at all?

We can describe the relation.

We can predict its consequence.

We can use it.

We can move the explanation deeper.

But eventually we arrive at another relation that simply holds.

Still unexplainable.

What We Know

A lens focuses.

We can explain why.

Its geometry matters.

Its refractive index matters.

Wavelength matters.

Boundary conditions matter.

We can calculate the path of light through it with extraordinary accuracy.

Then we ask what refractive index is.

We move deeper.

The response of matter to an electromagnetic field.

Atomic structure.

Quantum mechanics.

Field interactions.

Each explanation is real.

Each one removes ignorance.

But each one also introduces a new level at which something is simply given.

A relation.

A constant.

A symmetry.

A rule.

A permitted transition.

A forbidden one.

And the question returns.

Why this relation?

Description and Origin

There is a temptation to think that once an equation becomes accurate enough, the thing has been explained completely.

But an equation is not the event.

It describes the event.

Light does not consult Maxwell’s equations before propagating.

Matter does not read quantum mechanics before responding.

The equations are ours.

The regularity is not.

This does not weaken science.

It strengthens the distinction between what science does extraordinarily well and what may still remain open.

Science discovers structure.

It measures.

It predicts.

It compresses repeated observation into relations precise enough to trust.

But description and origin are not the same question.

We often explain one phenomenon by referring to another.

A rainbow can be explained through refraction, dispersion and internal reflection.

Refraction can be explained through electromagnetic interaction with matter.

That interaction can be described through deeper physical theory.

And so on.

This is explanation by descent.

Each layer explains the one above.

But descent does not guarantee an end point where nothing remains to ask.

It may instead bring us to a layer where the question becomes sharper.

Not:

Why did the rainbow appear?

But:

Why does reality contain exactly these relations between light, matter, wavelength and geometry?

The Repertoire of Matter

The same pattern appears in matter.

We discover that iron binds oxygen in haem.

Lithium has useful electrochemical properties.

Certain rare-earth compounds produce powerful magnetic behaviour.

Silicon supports semiconductor devices.

Crystals exhibit birefringence.

Some materials fluoresce.

Others superconduct.

Some catalyse reactions with remarkable specificity.

We did not invent these properties.

We found them.

We learned how to arrange matter so that its existing relations became useful.

That is an extraordinary achievement.

But again the deeper question remains.

Why does matter contain this repertoire at all?

Not why a battery works.

We can answer that increasingly well.

Why is there a physical world in which this particular behaviour is available to be discovered?

When the Residual Speaks

Human perception complicates this further.

We often behave as though what we perceive is what exists.

But our senses sample only a narrow part of physical reality.

We see a thin band of electromagnetic radiation.

We do not directly see radio waves.

We do not see X-rays.

We do not see magnetic fields.

We do not see neutrinos.

We do not see gravitational waves.

We may not see dark matter, if dark matter exists.

Yet things outside direct perception can still leave effects.

They alter trajectories.

They change timing.

They bend light.

They transfer energy.

They constrain what visible things can do.

Sometimes we do not observe the thing itself.

We observe what becomes difficult to explain without it.

That is especially interesting.

A discrepancy is not merely an inconvenience.

It can be information.

A planet moves in a way that suggests another mass.

A galaxy rotates in a way that does not fit the luminous matter we can see.

A lensing pattern reveals gravitational influence not accounted for by what is visible.

We should be careful here.

Mathematics does not magically reveal hidden substances.

A discrepancy can mean that something unseen is present.

It can also mean that the model is incomplete.

But either way, the residual matters.

Reality has refused to fit the description we currently have.

This is where mathematics becomes more than calculation.

It becomes an instrument for noticing when the visible account is insufficient.

Not because mathematics stands outside nature with privileged access to truth.

But because a precise model gives us something against which observation can resist.

Without precision, disagreement is vague.

With precision, the residual has shape.

The mismatch becomes localizable.

Measurable.

Persistent.

Difficult to ignore.

We sometimes call that failure.

But it may be one of the most productive conditions in science.

The unexplained is not always where knowledge ends.

It is often where the next question becomes possible.

What Remains

There is another habit worth refusing.

When a theory predicts successfully, we sometimes begin to speak as though nature is executing the theory.

As though the equation is underneath the event, operating it.

As though physical reality contains an invisible calculation corresponding to our notation.

But perhaps that puts our description back into nature unnecessarily.

The field evolves.

The material responds.

The boundary constrains.

The event occurs.

We write mathematics that captures the regularity.

The mathematics may be astonishingly exact.

But it is still a description produced by an observer.

The event did not need our description in order to happen.

A boundary makes this especially clear.

Light reaches glass.

Something changes.

Part reflects.

Part transmits.

Direction changes.

Phase may change.

Under certain conditions, transmission ceases and total internal reflection remains.

We can express this with equations.

We can derive critical angles.

We can predict the result before the experiment.

But the boundary does not solve the equation.

The field does not pause while nature calculates.

The relation simply holds.

That is both satisfying and unsatisfying.

Satisfying because the regularity is precise.

Unsatisfying because precision does not answer why there is such a regularity at all.

Perhaps explanation is always relational.

We explain one thing by placing it inside a larger structure.

The apple falls because of gravity.

Gravity behaves according to a deeper theory.

The deeper theory depends on mathematical structure.

The mathematical structure contains constants, symmetries, admissible states.

At some point, explanation becomes:

Given this structure, this consequence follows.

That is enormously powerful.

But notice the phrase:

given this structure.

What explains the given?

Perhaps there is another level.

Perhaps there are deeper theories still.

History suggests caution before declaring anything fundamental.

Again and again, what appeared basic became derivative.

Atoms were once indivisible.

Then they were not.

Space and time seemed separate.

Then they were not.

Classical certainty seemed natural.

Then quantum mechanics arrived.

So it would be foolish to declare that today's deepest relations are final.

But it would be equally foolish to assume that one more layer automatically eliminates the problem.

A deeper law may explain the present law.

Then the deeper law becomes the next thing to ask about.

The question can recede without disappearing.

This does not mean knowledge is futile.

Quite the opposite.

Every successful explanation changes the character of the unknown.

Before explanation, ignorance is broad.

After explanation, what remains becomes narrower.

More exact.

Sometimes stranger.

We move from:

I do not know why this happens.

to:

I know exactly how this follows from these conditions, but I do not know why these conditions and relations exist as they do.

That is progress.

The residual is smaller.

But it may also be deeper.

Perhaps that is why certain questions survive centuries of scientific advance.

Not because science has failed to reach them.

Because science has reached them repeatedly, each time with greater precision.

We have become extraordinarily good at predicting what nature will do.

We route light.

We amplify signals.

We suppress noise.

We split wavelengths.

We build transistors.

We manipulate atoms.

We measure gravitational waves.

We infer structures we cannot directly see.

We make technology from regularities that existed before us.

And still, beneath every successful use, there remains the relation itself.

Why does light behave this way?

Why does matter permit these states?

Why do these constants have these values?

Why does mathematics describe physical regularity so effectively?

Why is there something with lawful structure rather than nothing at all?

Perhaps some of these questions will dissolve.

Perhaps some are badly formed.

Perhaps some will be answered by deeper theory.

Perhaps others will remain.

We do not know.

That uncertainty should not be filled with belief merely because silence is uncomfortable.

Science does not become smaller when we admit this.

It becomes cleaner.

The achievement is not diminished because the final question remains.

A map can be extraordinarily accurate without becoming the territory.

An equation can be extraordinarily predictive without becoming the event.

A theory can explain an enormous range of phenomena without explaining why there is a reality capable of supporting that theory.