
The Simple Truth about Physics - aluket
https://blogs.scientificamerican.com/observations/the-simple-truth-about-physics/
======
stabbles
Of course there is no guarantee truths about the universe are simple.
Newtonian mechanics is extremely simple, yet it is only true as a limiting
case of relativistic mechanics, which is not as simple. Maybe relativistic
mechanics is only true as a limiting case of an even more complex theory, et
cetera.

What we should value is not simplicity, but power of explanation.

~~~
tbabb
Each additional unchecked assumption that is added to a theory is another
opportunity to be wrong. These probabilities of failure, however small, are
compounded with multiplication, so the probability of failure rises
exponentially with the number of unchecked assumptions. (10 assumptions each
with 95% chance of correctness have only a collective 59% chance of being
right— .95^10 = .59).

To maximize the chance of choosing a model which corresponds to reality, we
must involve as few unchecked assumptions as possible when deciding between
theories that agree with the data; and this matters more than any particular
assumption having a relatively high chance of being right, because of this
exponential sensitivity.

So if we want theories that are correct, yes, we _should_ value simplicity.

~~~
vladf
I don't understand how we can reason with "probabilities of failure" about
such fundamental things such as laws of physics.

Under the frequentist interpretation of probability, 95% of having a "correct
assumption" means that as you observe iid experiments of this assumption, the
long-run average of them will have 95/100 of such experiments exhibit the
assumption as true. But "experiment" here isn't a physics experiment, it's a
_universe_ in which this assumption could be true. We're in some _fixed_
universe. This assumption holds in ours with probability 0 or 1 (we don't know
which).

So, I think the 95% you're referring to here is a Bayesian belief level. This
is coherent in that it doesn't require some ambient set of multiple universes
to meaningfully describe what is meant by "probability", but the prior
required for this interpretation is a bit of weird beast. That is, we have
some prior over the space of all possible assumptions for models of physics
and update our beliefs based on evidence (we can collect evidence from our
single universe multiple times and update our beliefs in a coherent way). In
the limit of evidence, this prior matters less, but constants matter here! How
much evidence do we need before we can be confident the "belief levels" we're
throwing around aren't that subjective anymore? We don't really have a good
sense for what the structure over this space of "assumptions of physical
models" is, so we can't really answer this question.

Within specific settings for statistical learning theory, we find that simple
models generalize well. But that's an implication: _if_ you have a class of
simple models and it fits the data well, _then_ you'll generalize well. When
it comes to answering the question, "Which theories generalize well?", such
analysis is incomplete.

~~~
tbabb
> I don't understand how we can reason with "probabilities of failure" about
> such fundamental things such as laws of physics.

A sketch: Suppose we have two theories, one ("A") with assumptions (a, b); the
other ("B") with assumptions (a, p, q, r, s, t); and our evidence 'e'.

Pr(A) ~= Pr(a|e) * Pr(b|e)

Pr(B) ~= Pr(a|e) * Pr(p|e) * Pr(q|e) * Pr(r|e) * Pr(s|e) * Pr(t|e)

That is, the probability of each theory being right is the probability that
each of its assumptions are simultaneously true. It might be difficult to come
up with a specific number for each of those component terms, but we'd do well
to estimate the total probability of each theory simply by counting the terms,
since in the limit that will matter more than the probability of each term
(assuming we think none of them are obviously low).

Also note that when counting, we can trivially factor out the common
assumptions "a" (a.k.a. the things we don't wish to doubt or vary between
theories, e.g. QM in "ordinary" regimes, GR, the Newtonian approximation to
GR, etc.)

Yes, there is a "ground truth" theory which is absolutely true or false, but
we don't have access to it. And I don't see how it's more problematic to use
probability here than on any other classical event on which we have imperfect
information, like a specific dice roll, or a baseball game, or the outcome of
an election— One specific thing will happen, and no other outcome was
possible, but we can still use probability to model our incomplete knowledge.
How is physics different?

Example stress tests of this idea:

e = the motion of the planets; A := "G = m1*m2/r^2"; B := [long list of
epicycle parameters] --> pick "A".

e = the varied appearance/adaptations of animals/species; A := [reproduction,
inheritance, variation, selection]; B := foreach animal x {"God zotted $x into
existence like that because just_so_story($x)" \--> pick "A".

e = my empty garage; A := "there's nothing in it"; B := "there's a dragon in
it; the dragon is invisible; the dragon dodges your touch; the dragon has no
heat signature; the dragon floats and leaves no footprints; ..." \--> pick
"A".

e = the behavior of the universe; A := [the standard model]; B := [the
standard model; also it's a simulation; there are intelligent beings who set
up the simulation; there is an external universe in which the simulation is
occurring; the number of simulations happening in this universe is large; ...]
--> pick "A".

~~~
vladf
I think that you may have missed my point.

First off, why are assumptions independent? Why are you allowed to factor
p(a|e) * p(b|e) = p(a,b|e)? Assumptions aren't just independent binary
variables -- it's not necessarily true that you can have some product measure
over the set of assumptions (a, b, p, q, r, s, t) simultaneously.

More importantly, you dived write into some notation (Pr) without telling me
what it _means_, which is what my OP was about.

> And I don't see how it's more problematic to use probability here than on
> any other classical event on which we have imperfect information, like a
> specific dice roll, or a baseball game, or the outcome of an election— One
> specific thing will happen, and no other outcome was possible, but we can
> still use probability to model our incomplete knowledge. How is physics
> different?

Here's a crucial difference. We can roll a die 100 times, 1000 times, 10K
times, and the frequency of a six landing as we increase the number of trials
will tend to 1/6\. That's what we mean (if we're frequentists) when we say the
probability of a six landing is 1/6\. We can't "roll" universes with physics
models.

~~~
tbabb
> First off, why are assumptions independent?

Because I've defined them that way. I mean them to be independent choices you
could make when designing your model that could be varied to fit the data. If
two aspects of the model are not independent; i.e. they are covariant in some
way, then there is some common parameter that explains them both, and _that_
parameter is the one that should be seen as an input to the model.

> We can roll a die 100 times, 1000 times, 10K times [...] That's what we mean
> (if we're frequentists)

We're not frequentists.

You can't "re-roll" the 2016 election 10K times, either. There was only one,
and there was only one way it could come out; we just didn't know enough to
say what it would be before it happened. All the particles in all the voters
were obeying the laws of physics at every moment; never was there any freedom
for a different outcome. Nonetheless, even though there was/is only one
"ground truth" that could ever be, we assigned probabilities to each possible
outcome, given our incomplete knowledge.

This is a pretty standard application of probability. State estimators (e.g.
the Kalman filter) are doing the same thing— you have some noisy readings of
reality, and you use Bayesian logic on some assumed probability distributions
to pick the estimate from the space of possible "ground truths" that has the
highest probability of being the right one.

Concretely: I'm measuring roll rate, local acceleration, compass heading,
barometric pressure, and GPS, all with significant error, and I want to know
where my quadcopter is most likely to be at the current moment. There is only
_one_ true answer to that question, the quadcopter is in _one_ place, not
10,000 places (or 10,000 flights), there is a _single_ ground truth. But Bayes
will give me a probability, given my readings, that any given estimate is the
true ground truth (and some math will help me solve for the highest one).

In this case, instead of assigning probabilities to possible election outcomes
or system state "ground truths", the "configuration space" is models of
reality. But all we've changed is the domain of our probability distribution;
the math doesn't care what kind of thing our "ground truth" represents. And it
doesn't matter if reality contains only one "ground truth" or many; the fact
is that _we_ are choosing between many options (and we are ranking them by
likelihood).

~~~
vladf
Re independence: identifying whether or not these physical assumptions covary
is not that easy. That's my point: assumptions a, b, c, d could easily have
some mutual incompatibility that makes them non-independent. It's an active
area of research.

Re probability, I'm glad you committed to the Bayesian interpretation. Bayes
gives you a _degree of belief_, based on your priors.

It's quite fortuitous that you mention the 2016 election. As you say, there's
only one instance here. Which is why the prior matters a lot. We can
incorporate (partial) evidence from past elections, but it's going to be very
sensitive to the priors that we place, since the net amount of evidence we're
working with is very small.

As we found out in 2016, that means these beliefs aren't worth much in such
low data scenarios, since the prior has a large impact!
[https://projects.fivethirtyeight.com/2016-election-
forecast/](https://projects.fivethirtyeight.com/2016-election-forecast/)

This brings me to my original point:

> In the limit of evidence, this prior matters less, but constants matter
> here! How much evidence do we need before we can be confident the "belief
> levels" we're throwing around aren't that subjective anymore? We don't
> really have a good sense for what the structure over this space of
> "assumptions of physical models" is, so we can't really answer this
> question.

~~~
tbabb
> identifying whether or not these physical assumptions covary is not that
> easy

But still tractable, I'd say. My core claim is that counting independently-
variable assumptions will be a highly performant way to select between
theories which agree with the data. Or put another way, it's the best Fermi
approximation calculation for measuring "how good is your theory". How you do
that for any given theory, while important to do correctly, is an
implementation detail which I think is secondary to the discussion of whether
doing it at all is a good idea. :) (seems like we might agree that it is?)

> We can incorporate (partial) evidence from past elections, but it's going to
> be very sensitive to the priors

To the extent that election forecasts are unreliable, I think that's because
they are forced to involve a lot of assumptions (e.g. similarity to past
elections) that turn out not to correspond well to reality. Models which make
fewer such assumptions will do likely do better! (and IMO fivethirtyeight's
forecasts did the best job of this out of any; most of the rest put Hillary at
around 97%).

Unfortunately with elections, there is a comparatively high lower bound on the
number of assumptions we must make, thanks to the complexity of their dynamics
and sparsity of data/knowledge we have about each. I think this is much less
the case with physics, where we are varying comparatively small physical
assumptions to explain mountains of data. But in either case, I contend that
the most performant models will make fewer (unmeasured) independent
assumptions.

> How much evidence do we need before we can be confident the "belief levels"
> we're throwing around aren't that subjective anymore?

The point I'm trying to make is bigger-picture than the above level of detail:
Counting independent assumptions, in the limit, matters more than the specific
constants of each assumption (assuming they're not low/zero), precisely
_because_ it's so hard to come up with "accurate" numbers for each.

That is to say, the probability is not _sensitive_ to those belief levels: We
could choose widely varying distributions for the probabilities of our
assumptions, including choosing probabilities very close to 1, and it will
hardly ever matter to the total probability as much as the absolute number of
independent assumptions we make.

------
imglorp
Heard an interesting idea about the overlap of information theory and physics
in one of Sean Carroll's recent podcast discussions. They blew past it but I
think it bears its own subject.

The idea goes like this. If you want to talk about simplicity, beauty, or
elegance of a physical law--maybe because you think that's more likely to be
correct than a complicated law--then we've already got tools like Kolmogorov
complexity to talk about such laws.

~~~
btrettel
This seems to be the particular podcast:

[https://www.preposterousuniverse.com/podcast/2019/12/09/76-n...](https://www.preposterousuniverse.com/podcast/2019/12/09/76-ned-
hall-on-possible-worlds-and-the-laws-of-nature/)

------
montalbano
This doesn't just apply to physics.

All scientists should strive for parsimony.

In other words Occam's Razor: "It is futile to do with more things that which
can be done with fewer", where _things_ in scientific theories can be
considered _assumptions_.

Parsimony, along with falsifiability, are the two most important features of
any reasonable scientific theory.

We need to teach more philosphy of science at all levels of science education.
I was quite surprised to read that a physics post-doc would openly seek to
complicate their models just for the sake of appearance.

~~~
TheOtherHobbes
Occam's razor only applies if your model actually solves the problem it claims
to solve.

Plenty of beautiful, elegant, parsimonious, wonderful, understated,
aesthetically pleasing models in physics turned out to be complete bunk when
confronted with real data.

~~~
montalbano
Agreed, that's why i mention falsifiability along with parsimony.

------
improbable22
Half the article is about the social observation that making your work
unnecessarily complicated is, too often, a way to impress people. Especially
those, like funding agencies, who try to judge without understanding it. Many
will be impressed to see you flexing large calculational muscles, even if they
can't quite see why.

The other half appears to be an advert for the author's paper
[https://arxiv.org/abs/1910.13608](https://arxiv.org/abs/1910.13608) which
advocates a particular measure they call "explanatory depth". It's not
immediately obvious (to me) how this works, or how it relates to other
bayesian & information-based measures. But it seems worth a look.

------
deepnotderp
The formalism for this is Kolmogorov Complexity and Occam's Razor.

I also believe that we also value Sophistication, which is at least a partial
driver of the interest in string theory, with less free parameters.

------
tus88
Well we will soon be approaching a CENTURY without any significant advances in
physics or our understanding of the universe...no wonder they are desperate.

~~~
exmadscientist
Just off the top of my head, at the very least, electroweak unification (1970s
to 80s depending on where exactly you describe it as "understood") was a major
advance in our understanding.

Now if you had said "half century" instead of "century", I would be more
inclined to agree with you. Neutrino oscillations are a more recent
phenomenon, but they fit relatively cleanly into the Standard Model and have
little effect on the fundamentals. You say that "dark matter/energy" are
problematic, but I would argue that no serious physicist thinks they are
anything like "confirmed". (The DAMA/LIBRA collaboration aside, since no one
else believes them.) They are just the best available ideas to explain things;
the hope for a better explanation or experimental evidence for a particular
direction remains strong.

Back when I worked in this area, I was fond of pointing out that there hadn't
been much progress in fundamental theory since the '70s or so, then asking
when LSD was banned....

~~~
tus88
Well if we ever experience another big bang, electroweak will help us
understand why we are being vaporized.

~~~
exmadscientist
Your dismissive attitude implies that you think there are fundamental
discoveries waiting to happen that will affect our lives in the same way as
the great discoveries of classical and modern physics.

There are not.

At energy scales up through electroweak unification and the Higgs mechanism
(~10^2 GeV), the known forces of nature are basically completely understood at
the fundamental level. There are many _applications_ yet to be invented --
basically, solving the equations is _really hard_ for anything more
complicated than a hydrogen atom -- but the fundamental theory? It's done.

But what about quantum gravity? Dark energy? All those other weird things?

Well, the simple fact that we do not have experimental evidence to guide the
development of these theories is prima facie evidence that _they are not
important at everyday energy scales_. If we could access the requisite
domains, we would have that evidence! Yes, these theories are important
cosmologically or for true "fundamental" understanding, but so was electroweak
unification. They will never help us build better gadgets, full stop.

~~~
tus88
We can't even explain the double slit experiment. We are Neanderthals.

And you say there is nothing coming that could affect our day to day
life...they might have said that in 1901.

Who knows what might unfold...

~~~
exmadscientist
In 1901 there were major "catastrophies" all around, the ultraviolet
catastrophe being one of the best examples:
[https://en.wikipedia.org/wiki/Ultraviolet_catastrophe](https://en.wikipedia.org/wiki/Ultraviolet_catastrophe)

By 2019 we have exquisite verification that we do, in fact, understand things
at "everyday" energy scales:
[https://en.wikipedia.org/wiki/Precision_tests_of_QED](https://en.wikipedia.org/wiki/Precision_tests_of_QED)

I do not claim there is no new physics to be found.(In fact, the process of
renormalization used in modern field theories _explicitly parameterizes_ our
ignorance of very high energy scales.) I merely claim there is no new physics
to be found that can impact anything already constrained by a precision
measurement, and that such precision measurements cover the entire spectrum of
everyday phenomena.

(And just because you don't like some of the metaphysical interpretations of
the double-slit experiment doesn't mean we don't know how to calculate it...
very, very accurately. That, to me, suggests some level of understanding
surpassing a Neanderthal!)

~~~
tus88
I dare you to calculate the double slit experiment on the assumption light is
a particle.

~~~
Koshkin
But electrons, being particles, exhibit the same behavior.

~~~
aeternum
This is looking at the problem in the wrong way.

Quantized fields are the fundamental building blocks of our reality.
Everything else builds from that. The entire concept of a particle is a useful
but flawed model, similar to newtonian gravity.

~~~
Koshkin
> _useful_

Indeed - non-relativistic quantum mechanics does explain the double-slit
experiment and does not use the notion of a field.

