How the belief in beauty has triggered a crisis in physics
nature.com
nature.com
The observation of the apparent non-existence of something (supersymmetry, in this case) is at least as important as the existence of something. Supersymmetry is one of high-energy physics' best guesses as to the nature of the universe. If that turns out not to be true, we have learned something very important.
"Thirty spokes share the wheel's hub;
It is the center hole that makes it useful.
Shape clay into a vessel;
It is the space within that makes it useful.
Cut doors and windows for a room;
It is the holes which make it useful.
Therefore profit comes from what is there;
Usefulness from what is not there."
Tao Te Ching - Lao Tzu - Chapter 11
(translation by Gia-fu Feng and Jane English)
How does gravity connect with the rest of physics?
What is the nature of dark energy?
What is the nature of dark matter?
Where is the rest of the CP violation?
What gives neutrinos mass?
(And, the doozies that are so hard to answer that nobody touches them: Why does time have a direction? Is there something underlying quantum mechanics?)
I can sit for day after day not observing a black swan. This proves nothing, it does not prove the theory "there is no non white swan". But if I see a black swan then the theory that all swans are white is up the chute.
Hypothesis 0 - all adult swans have largely white plummage.
Expectation - all observed swans "are white".
Observation - some swans "are black".
The experiment failed to observe the expected. The hypothesis was falsified.
Hypothesis 1 - all swans are white or black.
Even with something like "we expected to find a Top quark at ~100GeV and found nothing" then the experiment has falsified that there is Top that would appear in such an experimental framework. We usual project that result beyond it's technical bounds, to say there is no top below that limit, is that what you're trying to get at?
If you mean experiments aren't perfect then I don't see how that truism is useful. There have been a couple of potentially massive results in recent years that have fallen to poor experimental process.
However, while this form of logic is a great thing to teach children for their first (and likely only) one, and while your fancier logics probably ought to have some sort of Correspondence Principle for this style of logic, this rigid style of logic is not terribly useful in the real world, where statements of rigid, solid, 100%-confidence mathematical truth are in short supply. In any probabilistic logic, non-existent evidence is evidence of non-existence. It is not proof. But it is evidence. It is true the human mind may have a tendency to overweight the evidence, but that's fixed by math.
So, while there is a sense in which the oft-trotted out phrase is true, in logics useful in the real world, it is simply false.
After all... what other evidence of non-existence do you expect to gather? If you do not believe in the invisible, intangible unicorn that lives in your garage that Sagan liked to talk about, what other actual evidence for that belief do you have other than a complete lack of evidence it exists? There is no way for you to disprove it under Aristotelian logic. (And this style of logic doesn't have a great story for statements it can neither prove nor disprove, which is another reason why mathematics moved past it a long, long time ago.)
If string theory is wrong, what other evidence for that can we gather other than the predictions of string theory being false? Remember, we can build physics models based on, say, Loop Quantum Gravity that excludes strings and may seem to predict the universe correctly, but that does not logically prove that there are not also strings in the universe. We exclude strings or other broken models only by consistently failing to collect evidence they are true.
Which is not a reason to consider them excluded. There is no reason to believe in the unicorn, or strings it there are powerful predictive alternate theories that explain the observed facts. But science creates contingent knowledge, not truth, that is all.
Incidentally, that post gored some oxes, apparently. Despite the firm mathematical foundation I stand on with great confidence for the entire post, it's sitting at -2. Seems a lot of people have a very emotional reaction to hearing "absence of evidence is not evidence of absence" is untrue.
The experiment originally set out to detect and confirm the existence of the aether, but ended up falsifying the theory instead.
https://simple.wikipedia.org/wiki/Michelson%E2%80%93Morley_e...
To use the swan argument from down-thread: If a theory predicts a) All swans are drawn from a single distribution of colors and b) 1% of swans will be black, then the observation of a few thousand white swans will be sufficient to rule out said theory.
> Nothing is falsified by the failure of an experiment to observe the expected.
MM definitively falsified the then-prevalent theory that space and time are absolute, and that the earth is moving with respect to the medium through which light waves propagate. The fact that it did not falsify all possible theories of the luminiferous aether does not change this fact.
The lack of observation of proton decay has falsified several otherwise acceptable theories.
"Thirty spokes share the wheel's hub; It is the center hole that makes it useful. Shape clay into a vessel; It is the space within that makes it useful. Cut doors and windows for a room; It is the holes which make it useful. Therefore profit comes from what is there; Usefulness from what is not there." Tao Te Ching - Lao Tzu - Chapter 11 (translation by Gia-fu Feng and Jane English)
--- (YC people: it is very telling that you can't find the will/resources to fix this blockquote on mobile problem. I would say it is damning of the whole ethos of YC/HN, in fact, but I'm marginal.)
* There is a recent 4.5+4.8 sigma excess in neutrinos oscillation that hints a new neutrino https://arstechnica.com/science/2018/06/weird-neutrino-exces... [technical note, you can't add sigmas naively, 4.5+4.8=6.1]
* The value of the magnetic moment of the muon (g) is too high. IIRC this result has only a 2.5 or 3 sigma, so it's far from confirmed.
* There are some experiment to prove that the neutrino is a majorana particle and that the neutrino and the anti-neutrino is the same particle. I don't remember any good announcement, so I think that the experiments have still too early results or the results are not interesting. [I don't like this theory, but many people that knows more than me like it.]
I believe there are some other things in that time frame. I believe the discovery that the universe is accelerating in its rate of separation fits in that time frame, and that's pretty big. We don't know how to fit it in with anything, but it's big. And I'd still say confirming Higgs is big.
But... yeah... it is a pretty short list compared to preceding decades.
Also, the 6.2 or 6.1 is "unofficial" because it's difficult to mix results from different experiments.
The crisis is that the foundational ideas about how to make progress in physics: Elegance, beauty, naturalness, symmetries... are not yeilding any insights on the questions you raise. And yet CERN still argues that HL-LHC is important for detecting supersymmetry in their press release today.
The technical core of Hossenfelders argument is here:
Human imagination can create a large number of theories. It isn't as valuable to prove the non-existence of something you have imagined up than proving the existence of something you have imagined up.
Sure, in this case, it was pretty important to prove an idea (supersymmetry) wrong because it was so widely accepted. But, insofar as physics is an empirical science, not it's important to reflect, how did it happen in the first place that an idea with no empirical support became so widely held? What can be improved in the culture and habits of physics and physics funding. Which traditions should be reconsidered.
As usual, theoretical physics is taking the wrong message from this, sticking to their guns and claiming SUSY evidence is yet above 10 TeV instead of stepping back and re-evaluating their fundamental assumptions. Of course they won't because many have built their careers on this hypothesis.
I forsee a reckoning for the whole field (which will take on economic dimensions) in the future.
My suspicion is this is something we will forever wrestle with because "beauty" is a proxy shorthand measurement for things of real value, but it is confounded by an enormous and oft abused potential to use this fact fraudulently. That which has real value is often appreciated for its beauty, but the street doesn't run both ways. Seeking to make something look good doesn't necessarily give it the more valuable underlying properties.
In GIS school, I learned that a good map will typically be described as beautiful, but a beautiful map isn't necessarily good. A good map is elegantly designed to effectively convey information. When the goal is achieved, high quality design also has inherent aesthetic appeal. But trying to just make a map pretty doesn't make it more useful. In fact, it often makes it less useful.
I think the same principle generalizes. I was born with serious respiratory problems. I always had really lousy fingernails. With getting healthier, my fingernails have grown stronger and prettier. This makes me suspect that manicures and painted nails are about trying to enhance a signal of baseline good health that is inherently valuable and attractive. But painting your nails doesn't actually improve your respiratory health. Fake glued on nails can give an appearance of health that isn't real.
Then that stopped working. That's the crisis.
The naturalness/beauty described by the author is an approach which seeks to formulate theories which help us understand the universe.
Perhaos the apparent naturalness/beauty in the equations you state has less to do with understanding what makes the universe work, and more to do with our mind's predisposition that we would tend to observe those relationships first.
Many physical laws, AFAIK, appear less as absolute truths, or keys, to understanding the universe and more as just observations about what to expect. IE Newtonian gravity works all the time, is described beautifully in maths, but then at certain scales stops working. Does it really tell us anything about what makes the universe tick?
Anyways here is a clip I like from Feynman discussing the idea of beauty in figuring out how nature works: https://youtu.be/MEqMM2Co_9c
It didn't stop working. There isn't any unexplainable data - the opposite in fact, too many explanations for the data we have.
But on the other hand those principles seem to obscure a more fundamental and simpler truth behind them. For example calculating scattering amplitudes may require hundreds or thousands of terms from different Feynman diagrams with more and more virtual particles but in the end they all cancel out. Surprisingly again there are ways to arrive at the same results - BCFW recursion relations and the amplituhedron - but with comparatively extremely simple calculations. But unlike Feynman diagrams, which suggest a picture of particles interacting locally in space, those calculations provide no picture that can be easily matched against recognizable things.
The results are the same but there is nothing that looks like locally interacting particles in there. This then suggests that things we currently considered fundamental, for instance locality, are not fundamental, that they emerge from something more fundamental. And this is where mathematics might be really useful, you try to reformulate existing theories in new ways and maybe you find a representation that is much simpler than what we have and maybe that is what the universe is really like as compared to what it looks like to us. And maybe that will also suggest new experiments to be done and which do not require energies far beyond our current reach.
Burden me not with any reminders about reality, people needing to get up to make the donuts or whatever. I know all that. I'm not knocking reality, reality's great. Nor do I need reminding how beautiful and strange and wild and cool some of the math in physics really can be. Utterly, utterly rad, without a doubt. But working with such high-dimensional spaces, such high-rank/high-variable transformations, and such high-density symbolic representations, as physics seeks to do, requires a much freer and more "artistic" approach than some kind of mental slavery to what can be seen. (By which I mean, what can be measured.) Physicists need more pure math, and when I say pure, I actually prefer the term theoretical math. Because physicists need to design their own math, and that is in one sense what theoretical mathematics means.
Physicists are better at what laypeople think of as mathematics--huge whiteboards, filled with esoteric symbols, furrowed brows and chalk-stained hands jittering through the air in some magnificent, halting dance of frustration & eureka. That's what people think of when they think of "doing mathematics". But physicists don't really do what mathematicians do, not really, not completely. And all those purely esoteric maths that no one except pure mathematicians ever get to see, say, topology, homology, algebraic geometry, abstract algebra, etc, are hiding some real gems of thought.
I'd like to see Physics, finding itself at a halt, go and start to study all the Mathematics it's been putting off.
And that kind of approach is exactly what Sabine Hossenfelder in the article criticizes, I my opinion significantly unfairly. The critics (she is surely not the only one) exactly complain that, for example, the "string theory" is more math than physics because it can't be "immediately verified" or they complain that the most of the experiments are "not confirming" the most obvious variants of the expected results of the new theory candidates. But the science shouldn't be reduced to the short-term goals and only to the processes which are "guaranteed to work." That's exactly when we won't see further from our noses.
And if the critics say that the "alternative theories" don't get enough funding, I posit that the average "alternative theories" are typically even more conservative than what is widely accepted physics (by the virtue of the accepted physics being already "unintuitive" enough and having the steeper learning curve than practically all "alternatives" are ready to accept).
We should all appreciate that one the most impressive achievements of the 20th century physics, the General Theory of Relativity has its fundamental support in the famous Michelson-Morley experiments which also didn't confirm the expectations of the 19th century physicists.
So we have to achieve enough experimental results against some approaches, and more than that, with enough precision, to even have the chance of finding out the new rules, if the new rules in the form that we're used to find them even could be found. We must be open to the experiments, and be happy even when the "most hoped" results don't happen.
On another side, when Sabine Hossenfelder is more precise and when she addresses some specific aspects, I can surely agree with some of her statements, for example:
"The criticism of heliocentrism based on the argument that the absence of observable parallax implied the stars had to be “unnaturally” far away was wrong for exactly this reason: They had no probability distribution but erroneously postulated one by assuming that the stars should be likely to have similar distances to the planets as the planets have among each other. We now understand the distribution of stars and their typical distances comes about dynamically during structure formation and that there is nothing “unnatural” about the distance of our Sun to the other suns."
Her criticism, however, is that currently physicists are "looking for the lost keys under the street lamp" because "in the dark they can't see them." But even if it sounds funny or misguided, it is true that in the dark not much could be seen, and before we actually check the already properly lit areas we can't expect more from looking into the dark where we really see too little. Investing in the flashlights can be reasonable, but also only once the lit areas are actually checked.
And we should also not forget that the current physics already enlightened immense parts of the universe. The "dark areas" were never so amazingly small as they are now.
This article is a nice counterpoint to Paul Dirac's speech in favour of mathematical beauty in physical theories. [0]
Some quotes from Dirac:
> What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. [...] We now see that we have to change the principle of simplicity into a principle of mathematical beauty.
Interestingly, he also says:
> For example, only four-dimensional space is of importance in physics, while spaces with other numbers of dimensions are of about equal interest in mathematics.
> It may well be, however, that this discrepancy is due to the incompleteness of present-day knowledge, and that future developments will show four-dimensional space to be of far greater mathematical interest than all the others.
His prediction here was almost correct. Except it was physics that started to take an interest in a higher number of dimensions.
[0] http://www.damtp.cam.ac.uk/events/strings02/dirac/speach.htm...
Elegance and simplicity should be sought after, and ugly proofs can be an indication that you're missing the right abstraction but I don't see why all true statements should have an elegant proof.
But it is only my opinion and it is very subjective :).
The top quark was predicted in the early 70s, and was expected to be found soon. However colliders failed to find them, and its minimum mass kept getting pushed up. It wasn't found until 1995, at a much higher energy than was initially expected.
The presence of Top was predicted with the finding of Bottom, in order to maintain symmetry. It was expected to have a higher energy otherwise it would have been found ... but the energy turned out to be much higher. It wasn't that it was predicted to be low energy and was found to have a higher energy, it was that we knew it had higher energy than Bottom, but just not how high - like climbing a convex hill covered in cloud, one can't see the top, and one isn't sure until you reach it how high it's going.
It's my understanding that the unpredictably high energy hasn't properly been accounted for but is believed to relate to Yukawa couplings.
The energy was predicted within certain lower+upper bounds in '94 just prior to the confirmation of the Top in '95, and a Nobel was awarded for that work [relating to T parameters (https://en.wikipedia.org/wiki/Peskin%E2%80%93Takeuchi_parame...) which I don't claim to understand! 't Hooft and someone, erm, ...].
In part I believe it relates to how the Higgs works and whether the Higgs is composite - possibly being comprised of Top and Anti-Top in one theory.
Feynman reminds us that "The first principle is that you must not fool yourself, and you are the easiest person to fool."
I imagine if we were in a different universe then our concept of beauty would differ and perhaps, perhaps, conform more to the parameters of theories that described that universe.
However, I don't think disliking parsimony is that radical. Andrew Gelman is not a fan of parsimony.
http://andrewgelman.com/2004/12/10/against_parsimo/
My current view is that parsimony is a heuristic you can use, but weak evidence at best. Plus, parsimony is not unambiguously defined, so comparing hypotheses in terms of it can still be subjective even with objective criteria as there is no agreement on which approach is best. It's most justified to say that extremely complex models are unlikely if the complexity is not necessary.
In technical terms, there is no need for a prior on theory space:
https://arxiv.org/abs/1801.02176
---
5.2 Occam’s Razor
A probability distribution from which to calculate the most likely choice of parameter adds unnecessary structure to the theory and is thus in conflict with the dictum of simplicity. We could have chosen a parameter and be done with it. The probability distribution and all the not-observed values of the parameters are unnecessary for the derivation of any observable and they should therefore be stripped by Occam’s razor.
I read the article, and I don't see any insightful answers, perhaps we're supposed to buy the book? Or perhaps people should devise stricter criteria for theories to be experimentally demonstrable...
I find this question to be missing the fundamental point of scientific endeavour. Nature obviously does not care about beauty, but scientists do because extracting meaning and order (laws) from observations and building models is the very essence of scientific insight.
The goal of science is not to replicate nature, it is to build a model of nature from which we can collect insights and make predictions, the model does not need to 'conform to' nature. That's not the point. If that were the case we could just dump the LHC data into a textbook. There is a great story writen by Borges called The Exactitude of Science where he creates the analogy of a large, but useless map:
"... In that Empire, the Art of Cartography attained such Perfection that the map of a single Province occupied the entirety of a City, and the map of the Empire, the entirety of a Province. In time, those Unconscionable Maps no longer satisfied, and the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire, and which coincided point for point with it. The following Generations, who were not so fond of the Study of Cartography as their Forebears had been, saw that that vast map was Useless, and not without some Pitilessness was it, that they delivered it up to the Inclemencies of Sun and Winters. In the Deserts of the West, still today, there are Tattered Ruins of that Map, inhabited by Animals and Beggars; in all the Land there is no other Relic of the Disciplines of Geography."
This is an overdue debate within the context of theoretical physics. No one wants to throw the process of deriving equations and models that explain data out. If anything Hossenfelder is the classicist here, rejecting ideas that want to go beyond empirical truth in order to salvage preconceived notions on what the laws of physics "should look like".
Lack of a predictable structure is lack of beauty: a stream of random numbers is both incompressible and aesthetically disappointing. This is why looking for signs of beauty is a good heuristics for finding that hidden structure. Same applies to engineering, BTW; the father of Soviet space program (Sputnik, first man in space) S. Korolev said: "An ugly aircraft will not fly".
I think the end goal of science actually is very close to the 1:1 scale map in Borges' story [1] - we want to be able to say in any situation "if I take this scenario and run it forward then what are the outcomes".
We can do this to some extent. We can predict paths of simple objects, we can predict how macroscopic systems will play out to some degree of accuracy. We can even predict the existence of particles and confirm the consistency of such predictions in later observations.
Surely the goal is to make our predictions better, up to any limit the universe gives. We want to be able to perfectly simulate the world - we don't just want the 1:1 map, we want a 1x10^20:1 map with moving people, with weather, with every possible feature that we can measure so that instead of travelling to Ulaanbaatur and dropping a rocket motor from the troposphere we can do that in the "map", and measure the effects in the map and so know what the effects would be if that were to happen for real.
We can't use the Universe as it's own map, we can't arbitrarily look at it at any scale, we can't run it back or duplicate it when we want to re-run experiments, we can't visit any part without travelling, etc. - so we seek to simulate it, through simplification because we can't currently simulate it any other way. As we uncover ever better models we learn to simulate limited sections or limited facets to a greater and greater degree.
If you want to figure out how the tube in London works you don't need a photorealistic, lifelike copy of the subway system, you need an abstraction of the network, its congestion, routes and so forth. Those are idealised mental models that are simplifying the real system, but they are much more useful to you than the real thing.
But if you're building a grand unified model of how London works then not only do you want to be able to abstract certain facets, you also want to be able to combine the models those abstractions create with data points to build a more complex systemic model. You want to look at where the stations are in relation to others, how the different transport networks link, what happens when a tube-train stops - how does the effect ripple through the system and alter what time a particular Pret-a-manger have to restock the sandwiches.
At that point the abstraction in to a simplified system that only describes the tube is useless you need to combine the abstractions to model the entire system - and you may be able to get there, except your model missed out sunspot activity and a bus-driver turned the wrong way because their GPS was marginally out and the Pret-a-manger manager missed the start of the shift and now you have to eat Cheese instead of Mexican chicken.
In short you want your abstraction to be able to construct a model that is as close as necessary for the purpose to the "photorealistic, lifelike copy" of whatever it is you're seeking to predict. If you only wish to predict how many stops you'll need to stay on the tube for then a simple tube map suffices. If you want to predict airflow through the tube system and how it affects heat exchange then a more complex model will be needed, with different abstractions (preserving length of tunnels for example).
If you want to predict everything that it's possible to predict ...
[Disclaimer I've no idea what Pret's menu is.]