Tuesday, December 5, 2023

Fields and finetuning

Here is an interesting fine-tuning issue, inspired by a talk I heard from Brian Cutter at the 2023 ACPA meeting.

It seems likely that physical reality will involve one or more fields: objects that assign values to points in space (“ordinary” space or configuration space), which values then govern the evolution of the universe.

The fine-tuning issue is this. A plausible rearrangement principle should allow any mathematical assignment of values of the field to the points in space as metaphysically possible. But intuitively “most” such assignments result in a configuration that cannot meaningfully evolve according to our laws of nature. So we want to have an explanation of the fine-tuning—why are we so lucky as to have an assignment that plays nice with the laws of nature.

For a toy example, consider an electric field, which is a vector field E that generates a force F = qE on a particle of charge q. Intuitively, “most” vector fields will be nonmeasurable. But for a nonmeasurable electric field, we have no hope for a meaningful solution to the differential equations of motion. (OK, I’m ignoring the evolution of the field itself.)

For another example, suppose we think of the quantum wavefunction as a function over configuration space rather than as a vector in Hilbert space (though I prefer the latter formulation). If that function is nonmeasurable—and intuitively “most” are nonmeasurable—then we have no way to use quantum mechanics to predict the further evolution of this wavefunction. And if that function, while measurable, is not square integrable (I don’t know if there is a sense of “most” that applies here), then we have no way to use the Born rule to generate measurement predictions.


StardustyPsyche said...

Why is god so lucky to be fine tuned to be all that it is imagined to be?
Speculating god only makes the supposed problem worse.
We know a cosmos of these proportions is ontologically possible.
We have no evidence that a god of the fine tuned proportions of god is possible at all.

"rearrangement principle should allow any mathematical assignment of values of the field to the points in space as metaphysically possible."
Why are you treating ontological necessities as free random variables?

When physicists look for unification theories they don't look for a giant multivariable random number generator. The goal is to derive a set of expressions that show how the observed forces "freeze out" by necessity.

If a natural phenomena follows, for example, an inverse square relation with distance we don't go looking at a random number for the exponent that is supposed to possibly be any real number. Nor do we assign the fact that the exponent in the denominator is 2, to a god who plucked the number 2 out of all possible real numbers and miraculously jammed the number 2 into the exponent position in the denominator.

We don't consider this to be a fine tuning problem to be solved by god, it is just a physical necessity understood as area increasing with the square of distance.

Alexander R Pruss said...

The values that the electromagnetic field has in various spacetime locations are clearly contingent.

StardustyPsyche said...

Not on a necessary deterministic cosmos. In that case everything is necessary.

StardustyPsyche said...

The fact that a wave function manifests a probability distribution is evidence of an underlying deterministic structure. A deterministic structure with a particular function will exhibit apparent weighted stochastic behavior when sampled chaotically.

By contrast, if there could be such a thing as an intrinsically stochastic process it could have only a flat probability distribution. If the probability distribution is not flat no truly stochastic process could account for a weighting function.

Further, even if somehow there could be a truly stochastic process behind the electromagnetic field values that in no way indicates that so-called fine tuned parameters, such as the permittivity of the vacuum, are contingent.

Such parameters have been measured to be fixed in the standard model for any particular set of local conditions, thus, not contingent over human life time scales.

Wesley C. said...

Couldn't one just view the value or values of the field (or really, any of the classical constant appealled to in fine-tuning) as just a natural property of the material substance in question? For example, water is a substance that boils at 100 C, and this attribute is rooted in the nature of water as H20. If we had a substance just like water except it only boiled at 200 C, then it would be a very similar but still distinct substance altogether - having a nature different from that of water, meaning it's a different material substance.

Similarly, couldn't one say the values of a field that supports life in the universe is a natural accident or property of the substance that the field is, and if the field had different values that didn't support life, this would just mean it's a different type of field that exists?

Because a lot of fine-tuning arguments treat the tuned values as if they were extrinsic to the substance that has it, as if the material entity in question could exist and be exactly the type of material being it is / be exactly what it is no matter what the values of the constants are.

Now it may also be possible for there to be such extrinsic values that can be different and aren't essential properties of a material substance, but I don't think we can rule out the above option that it IS an essential property of a specific material substance's nature either.

Of course, I think one could still make a more cosmological fine-tuning argument out of this by asking WHY it is the case that this specific type of substance exists which can support life instead of all the other substances that are also fully compatible with the nature of matter as it exists in our universe but DOESN'T support life. And this may still lead us to the existence of God as the creator who chose to create this type of substance as opposed to another for life-causing purposes.

What do you think?

StardustyPsyche said...

"What do you think?"

I think the speculation of god only makes the asserted fine tuning problem worse.

To paraphrase you, if you don't mind...
--WHY it is the case that this specific type of god exists which can support life instead of all the other types of beings that are also fully compatible with the nature of existence?---

The speculation of god makes the assertion of fine tuning worse because it just pushes the problem back a step, so we are called by reason to ask the same question about the speculated god that we ask about our observed cosmos.

But we know that a cosmos such as ours can, in point of ontological fact, exist, and exist in precisely the way that it does in fact exist, and that existence is slightly compatible with life at the very margins of the cosmos, that is, in a tiny percentage of the cosmos.

Most of the cosmos is extremely hostile to life. Based on how harsh most of existence is, it might be that we are the only place in all existence that has life at all, hardly a case of a cosmos fine tuned to be hospitable to life generally.

But with the speculation of god we don't even have that much! Of all the logically possible sorts of gods most would not or could not produce any life at all. Plus, even in that narrowly fine tuned sort of god we have no evidence such a god even exists, much less evidence of how such a god goes about tinkering with physical parameters to concoct a cosmos that has at leas a tiny sliver of it hospitable to life.

What do I think?
I think the fine tuning argument for the existence of god is specious at best.

Alexander R Pruss said...

We wouldn't have a fine-tuning argument if the life-relevant constants in the laws of physics were all neat "numbers" like 0, 1 or infinity.

The life-relevant constants in the nature of God are all neat "numbers":
- Number of Gods: 1
- Amount of good: infinity
- Amount of evil: 0
- Amount of knowledge: infinity
- Amount of power: infinity.