That's because people were totally focused on physics, and math was just a useful tool sometimes. Doing physics was the true goal and observation the final arbiter of truth.
Nowadays, that distinction is blurred but for the opposite reason; people think that anything conceived by sound math must be true, and observation has taken a back seat.
If it was not possible to simulate, I think we'd be less invested in the math and physics of it.
> “Physicists are much less concerned than mathematicians about rigorous proofs,” says Timothy Gowers, a mathematician at the Collège de France and a Fields Medal winner. Sometimes, he says, that “allows physicists to explore mathematical terrain more quickly than mathematicians.”
GP is right that the currently observed physical laws go far beyond our ability to observe them in reality because of the cost of observations. International effort over decades is required to create facilities capable of making helpful new observations: think of LHC, LIGO, James Webb, etc.
On the other hand, once the facilities are built and ground-breaking observations appear, we suddenly have a debt of theoretical and simulated exploration to understand all their implications. The low cost of computation greatly extends the value we can take from every truly new observation of reality.
In order to observe something new, we must be able differentiate it from something already understood. It seems like the physics and math communities are currently in a season of increasing our understanding of the existing models well enough to motivate trying to break them.
Are you saying that one day we will be able to devise experiments to observe these things?
The problem is that we might be on an exponential scale. So instead of decades it could be centuries assuming the humanity survives and keep develop new technologies and tools.
Back in the late 1800s physicists thought they were done, other than adding a few more decimals to the values of fundamental constants. There were a few "small areas" where things didn't make sense, but they "would figure them out". One of those small areas turned out to be relativity, and the other quantum mechanics. There are some known areas where we still don't know what is going on, but a lot of physics is adding more decimals to constants (finding fundamental particles were we expect them for example)
The real question - that we cannot answer - are the things we don't understand small things we will figure out, or major things that will again turn our understanding of the universe upside down. Your guess is as good as mine.
But there are also active researchers doing real research. Physics postdocs aren’t just sitting around in a circle making up stories about what the universe is like.
i ask out of layman curiosity
Maybe a more direct answer to your question would be the discovery of the tetraneutron.
Personally I think the ER=EPR conjecture and the complexity/action duality hypothesis are incredibly interesting. Technically ER=EPR was formulated in 2000s (maybe 90s?) and CA-duality is approaching if not just past 10 years old, but the thing about asking for breakthroughs is that they take a while to percolate. Ex Hawking radiation wasn't formulated until, like, 50-70 years after the "basis" (schwarzshild, Schrodinger) was formed.
There's also been a ton of productive research integrsting computer science and physics lately ( on hn last week: https://arxiv.org/abs/2403.16850 and 2022 novel prize; https://www.scientificamerican.com/article/the-universe-is-n...)
Also JWST just keeps on giving, and gravitational waves were only confirmed in 2017. If you extend a bit further higgs was in the 2010s
So, in summary, in the late 10 years - we've shown a break in our intuition of physics (nonloca-realness, that 2022 paper) - proposed some novel yet elegant theories (CA-duality, and I'd hope you'd begrudge me er=EPR) - confirmed some insane provings to the underlying reality (gravitational waves)
If those aren't noteworthy, I'd ask what you consider noteworthy any why you consider it noteworthy
There have been almost no truly significant, novel predictions that have a hope in hell of panning out in like, 40 years or more. The only mildly interesting, novel idea in physics has been quantum computing, and even that was first published in 1980.
> So, in summary, in the late 10 years - we've shown a break in our intuition of physics (nonloca-realness, that 2022 paper)
This paper showed no such thing, it has the same superdeterminism loophole as every other paper attempting to refute local realism.
Physics is stuck in a local QM-GR minimum, and some truly novel ideas are needed to kickstart things again. Oppenheim's postquantum gravity is the first truly novel idea I've seen in awhile.
I also agree that JWST is giving us great data, some of which has placed LCDM on the ropes, but astrophysicists are hard at work adding epicycles to keep it alive.
Higgs/Bell/GW were experimental results, I was indeed trying to show that there's a huge lag between prediction and observation.
Imo the paradigm shift that we're slowly undergoing is thinking about physics from a information theoretic perspective instead of a kinematics one. I'd argue that's even more fundamental of a change than Newtonian physics to early GR & QM.
CA-duality is again mathematically interesting, but physically dubious because it's based on anti-de Sitter space, which does not describe our universe.
Information theoretical formulations of QM are mildly interesting, but I don't think they will be revolutionary, and I don't think they are tackling the core problem, which is QM's linearity where we classically observe a non-linear universe.
You can't rhetorically gloss over something as important as experimentally validating a 1964 prediction as though it doesn't matter or didn't happen.
If your contention is that a validation of something we already suspected to be true doesn't shatter/shift our paradigm, then how often would you expect that to happen? I would expect it a lot in small ways (so almost every person working in some niche area has probably had some "niche breakthrough" happen in their area that has really changed things) but not a lot in really fundamental overarching ways which for physics I think you could reasonably say has happened about 4 or 5 times in the last 400 years maybe idk: Newton, GR/SR/ quantum mechanics and then whichever ones you want to count out of Maxwell's equations and whatnot.
So to expect something like that every decade is not realistic.
I'm not, I'm pointing out that theoretical progress has stagnated. Experimentalists are doing great.
> So to expect something like that every decade is not realistic.
I'm not expecting it every decade, but we've had 4 decades of recycling the same ideas using the same failed approaches to try to patch gaps in existing theory using bogus arguments, which ends up funding poorly motivated experiments that then find nothing. I think Sabine Hossenfelder elaborated the problems here in excellent detail (see "Lost in Math").
I suspect "breakthrough" is supposed to mean "huge definitive paradigm shift." We haven't had many of those in all of history, and we certainly haven't had one in the last decade.
Everyone is still very, very confused about quantum fundamentals. Non-local realness is really a Bohmian idea, and that's certainly not new. Universe-as-information is new but there's a huge gap between that and the Standard Model.
And so on. None of these problems are settled in the way that GR and QM settled various issues.
You may say that's too high a bar and things are moving. But there's been more of a history of missteps (string theory, supersymmetry, so far at least) that were sold as potential breakthroughs than genuinely transformative insights.
That said: I'll submit the first detection of gravitational waves as two black holes merged together in 2020 as meeting the bar of "notable breakthrough in the last decade".
2015. (Your point is otherwise taken).
https://en.wikipedia.org/wiki/First_observation_of_gravitati...
https://en.m.wikipedia.org/wiki/List_of_unsolved_problems_in...
Direct observation of gravitational waves (2015)[2]
exoplanets going from theoretically quite likely to being actually observable things that we find all over the place [3]
...would seem to be examples of very notable results during my lifetime. This is barely scratching the surface and I'm not a physicist but those seem very important to me and likely to stand the test of time and be thought of as important in the future.
Non-breakthroughs:
These guys who are responsible for the goddam blue leds that on every second device these days always keep me from getting a decent dark nights sleep when travelling until I hunt them all down in the hotel room I'm in or whatever and cover them up.[4]
[1] https://www.nobelprize.org/prizes/physics/2013/summary/
[2] https://www.nobelprize.org/prizes/physics/2017/summary/
I was bitten by this last week. I am enrolled in an aops physics course, titled Mechanics. So the last time I took any Mechanics was 40 years ago as a high school student in India. Most of the curriculum then was about stuff banging into each other aka collisions, & asking what happens to the result. Like some golf ball rolls down an inclined plane at some angle theta & hits a identical stationary ball & the objects stick together & we're supposed to compute where they end up. I was curious what American students learn, so I enrolled in this aops course.
Last week's assignment asks me - under which scenario will conservation of momentum make an accurate prediction. The 3 scenarios are - truck collides with car, eagle comes to rest at perch after flying from far away, and two galaxies colliding into each other to form a third megagalaxy.
I naturally picked truck & car - so aops knocks off 2 points for the wrong answer! Apparently if a truck collides with a car there will be so much thermal energy produced by the friction of the road, any prediction you make about the final velocity of the car assuming conservation of momentum will be bogus.
So then I pick eagle coming to rest - aops knocks off 2 more points for the wrong answer! Apparently when eagle comes to land, it will open its giant wings to create air resistance, so momentum won't be conserved.
Ok so that leaves the 2 galaxies. I pick that & get my correct answer, a pathetic score of 3/7. I'm left wondering how do we even know this is correct. Galaxies are too far away to observe. How is one supposed to compute the mass of 2 separate galaxies, & then find their moving velocities accurately, & then find the final velocity of the combined galaxy, & thus confirm momentum was conserved ? Seems very far fetched. I would rather go with the car & truck.
If all we have is reasoning, with zero observation, then its equivalent to what JFK says in Oliver Stone's picture - "Theoretical physics can prove that an elephant can hang from a cliff with its tail tied to a daisy."
That said, the point of the law of conservation of momentum is we don't need to observe it to know that it happens. Momentum is conserved, that's a fact. So the question becomes, what is it that makes this law not produce a good prediction about a scenario? And the answer is that when the scenario involves other factors that can take kinetic energy away from the system. In the car & truck scenario, we have friction with the road as a pretty huge factor, that removes a lot of energy. Even without a collision, friction is why a car needs to constantly burn fuel in order to keep moving at the same speed. So it should be no surprise that a car & truck collision will lose a ton of energy to friction. In the eagle landing scenario, that's not even a simple collision between the eagle and the branch, the eagle uses its wings to slow down, and the branch is fixed to a tree and absorbs the remaining energy. An eagle landing on a branch is an eagle that comes to rest on the branch, it doesn't just not conserve momentum it gets rid of all of it. But in the colliding galaxies scenario, there's no surface to have friction with, there's no wings beating against air, there's no tree anchoring one of the objects in place, nothing to absorb any energy, no environment to dissipate energy in. Without anything to get rid of kinetic energy, conservation of momentum will predict the results.
I came to the same conclusion as the replier almost immediately as I was reading the question. It was obvious to me. But I do agree it’s a bad question as it relies on a lot of assumptions. Maybe the question is just testing if your ability to make reasonable estimates assumptions.
Accurate prediction of what?
If it's the velocity and location in the end state, the best answer is the eagle (once it comes to rest). The momentum of Earth is so huge that the eagle will end up precisely on the perch (if we disregard the inability of a living bird to be completely still)
For the cars, the exact end state depends on many other factors, as you say.
Finally, for the colliding galaxies, there may be some uncertainty about how dark matter and dark energy (or their absence) affect galaxy collisions. This may be beyond the understanding of whoever wrote the test, though.
You can’t prove anything by observation. You can gather evidence through repeat experiment and become reasonably confident as your theory continues to not be incompatible with the observed universe. Then the problem of induction says, “well, it isn’t incompatible with the part of the universe… that you’ve observed, yet!” And then you say, “ok, but I want to use my theory to invent an iPhone, and I think there are enough people in the part of the universe that I’ve already observed. I looked very hard to find evidence against my theory, and I don’t think anyone will find evidence against it before I’ve sold enough iPhones to retire.”
Math, of course, is that stuff which can’t be invalidated by observations. But it is very hard to do enough math to retire off it.
That a given model is the one and only model that accurately explains the known universe? Then I agree. Observation won’t get you there. Asymptotic at best.
But by “prove”, that it accurately or usefully makes predictions with respect to certain constraints (which may not be known)?
That’s a more modest use of “prove”, where observation is certainly a key factor.
With that in mind, "prove" is perfectly fine to use in the context of science.
For instance, you can prove that Newton's laws are not 100% accurate.
This is a misunderstanding of what math is, I think. You can invent a perfectly valid mathematical theory that conflicts with observations. Math is just a sequence of "if this, then this" and if the conclusions follow from the premises, it's math. But if you demonstrate that in the universe we occupy, a premise isn't true, then the mathematical theory isn't any less valid, it's just not sound in our universe.
For example, there's a ton of completely valid mathematical work on the correspondence between anti-de Sitter spaces and Conformal Field Theory. However, much of this mathematics has no application in our universe, because our universe seems to be a de Sitter space (positive cosmological constant/expanding), not an anti-de Sitter space (negative cosmological constant/contracting). That doesn't make their math invalid, it just makes it not real.
You can also do a lot of math in Minkowski spaces, which are flat. But our universe isn't flat, it's curved. Doesn't mean it's not math, just that it's not real in our universe.
But, I say the math can’t be invalidated by observations; and you describe some cases where the math is valid but might or might not be applicable to certain physical cases. So actually, I’m not clear as to what you are saying I’m misunderstanding.
I meant, isn't a counter-example or proof by contradiction an invalidation by a type of observation?
Meaning that even if the inductive logic is 100% correct, the theory can be incorrect due to using mutually exclusive (in some non-obvious way) axioms.
I took your word "invalidate" to mean "be proven false" whereas I meant "valid" as in "logically coherent, even if not true."
Nice observation.
Epistemology is a harsh mistress.
I’m sure there are other examples but I’m not a mathematician.
I don't understand what this means, but it made me envision a McCarthy-esque witch hunt for "Platonist and Platonist sympathizers" lurking amongst the faculty
This debate played out in String Theory were some proponents claimed physics had progressed beyond the need for observation in favor of beautiful mathematical reasoning, that provided great explanatory power. But String Theory so far has failed to deliver a theory which describes our universe. Physics still needs to explain the actual world.
The saying that “the typical working mathematician is a platonist during the week and becomes a formalist on Sunday” is becoming increasingly familiar. During working days, they are convinced that they are dealing with an objective mathematical reality that is independent of them, and when on Sunday they meet a philosopher who begins to question this reality, they claim that mathematics is in fact the juggling of formal symbols (see Davis et al., 2012, p. 359). The Platonist attitude of the working (rather than philosophizing) mathematician is so common that Monk (1976, p. 3) was tempted to make a subjective estimate to the effect that sixty-five percent of mathematicians are platonists, thirty percent formalists, and five percent intuitionists. [1]
[1] - A Metaphysical Foundation for Mathematical Philosophy (Wójtowicz,Skowron 2022)
Some people were more narrowly focused, like Gauss who did mostly math (but an amazing breadth of math!)
There was a lot of hesitancy about math that couldn't be empirically illustrated by building out of atoms, like irrational numbers and then transcendental numbers and imaginary numbers and then infinite structures.
Geometry? Lobachevsky actually proposed a test on measuring sum of angles of a celestial triangle to decide which geometry actually applied to the real world.
I think there must have been a sense that it was true only as an axiom. Proving it from other axioms/theorems was then a goal to secure it's truth "further". But you'd only attempt that if you thought there was something questionable in the first place.
It's actually a 19th century idea. The discovery or acceptance of non-euclidean geometry in the 19th century untethered math from physics or physics from math.
> and it seems to be disappearing in the twenty-first.
It can't disappear because math is no longer tied to the physical world. Math is simply theorem generation regardless of whether the axioms and theorems apply to the physical world.
The math used in physics is only a tiny subset of possible math.
— V.I. Arnold: "On teaching mathematics" (1997)
Just like English isn't Physics even if you can have describe aspects of Physics using English.
For Math and English to be Physics, it needs to specifically define what physical meaning the variables and parameters involved have.
Typically, you recognize it as Physics when it comes with units.