The Quanta article doesn't appear to address the Bullet Cluster, nor the dark-matter-rich dwarf galaxies.
Looking forward to having a gander at the paper itself.
Edit for context: the challenging thing for MOND is that ΛCDM explains a number of precision observables and phenomena at once. MOND and TeVeS theories can fit individual facts in isolation, but not the ensemble simultaneously. ΛCDM fits those facts with only a single extra concept. It sounds like this iteration claims to address the seminal observation one and one of the most-tightly constrained observables simultaneously. There are several others. Will have to read the paper before saying more.
I'm not positive that's true. I think the most challenging thing for MOND is that basically no one will touch it unless they already have tenure because it's a death sentence.
I saw Pavel Kroupa (big name in Milgromian gravity) present in Heidelberg (big concentration of Astro), at the time Volker Springel (author of widely used LCDM simulation code "GADGET") was there and Illustris simulation sets (LCDM major project) had just been rolled out. And Pavel basically got heckled (in a very erudite and respectable way, but constant interruptions from the LCDM majority audience).
But Pavel had one slide, I can't find it now, but it was like 72 different problems that LCDM had not solved (ok, 72 is an exaggeration; you can troll his website for mentions of a lot of them https://astro.uni-bonn.de/~pavel/kroupa_SciLogs.html).
And like, Pavel's a big boy, he has some of the most cited papers in all of astronomy, he's got tenure, and he's set, so he can take it and not care. But grad students / postdocs I imagine would constantly have their work politely ignored and get shunted into underfunded groups.
I'm just trying to say that LCDM has things it can't explain, and MOND has things it can't explain, but the amount of resources in each theory is seriously lopsided so LCDM can frequently "tweak" itself to solve problems that MOND just doesn't have time or resources to to the same (for example disk formation in LCDM models used to be impossible until they had the supercomputing resources for the resolution required, and they found that the feedback coefficient could a) not promote disk growth, b) promote disk growth, and c) destroy disk growth, depending on how much they cranked it up. That's NOT a triumph of LCDM making an amazing replication of the observation, that's some grad student in a lab with enough CPU to tweak a meta-parameter until it looks good.
Also the CMB is extremely tightly constrained... and multiple huge tightly-constraining studies, WMAP, PLANCK, Gaia, are more than 3-sigma outside of each other's results, so... perhaps too tightly constrained.
My experience from MOND talks is that a proponent of MOND gets up, explains their theory, and then starts explaining how their theory explains the rotation curve of galaxies.
They're then confronted with a bunch of really basic questions from the audience: how does your theory explain the spatial spectrum of anisotropies in the Cosmic Microwave Background? Is your theory consistent with Big Bang Nucleosynthesis? Can your theory explain Weak Lensing measurements? How does your theory deal with the Bullet Cluster? The answer is then generally, "I'm not sure, but I'm working on it." That causes all the astrophysicists in the room to lose interest. Standard cosmology explains all of these basic observations with a minimal set of assumptions. If your theory can't or doesn't explain the most basic set of observations, and there's another theory that does, why should I care about your theory?
This reminds me of the old joke: When an academic says "That's a good question!", you should hear "I don't know the answer". Likewise, "I'm working on it." means "No.".
Imagine what proponents to heliocentrism such as Galileo had to face explaining their theory and how it explain a simplified elliptic orbit for the planets rather than the strange curly orbits known by geocentrists.
They'd be confronted with basic question from the audience: Why would things fall down if it was not the center? (That was before Newton) Wouldn't we see paralax in the stars (stars are much further away than what was believed at the time). Wouldn't we feel it if earth turns so fast? "Maybe that explains the tides" said Galileo (but it doesn't)
The previous model was also explaining the observations quite well at the time. Why should we care for another theory? (God works in mysterious ways.)
I'm not saying that MOND is correct. ("they also laughed at Bozo the Clown".) Just that the fact that there are some unexplained missing piece does not mean one should reject it so quickly.
Comparing oneself to Galileo is generally viewed as a sign of crackpotery, especially if it's used as a response to legitimate criticism.
> Just that the fact that there are some unexplained missing piece does not mean one should reject it so quickly.
It's not just one missing piece. It's a whole series of basic properties of the observed universe. Most MOND theories are tailored to match one particular observation, but fail to match everything else. Until there's a MOND theory that matches a basic set of observations (like CMB anisotropies and the large-scale structure of the Universe, the ratios of abundances of the light elements, weak lensing measurements, etc.), MOND is simply uninteresting to most astrophysicists.
> Imagine what proponents to heliocentrism such as Galileo had to face explaining their theory and how it explain a simplified elliptic orbit for the planets rather than the strange curly orbits known by geocentrists.
They did. In fact, the audience was quite more brutal. And it did not only delay the progress of physics, but also destroy the local research, leading to the entire community being rebuilt on England.
But, well, as you said, we always have to remember they also laughed about Bozo the Clown.
It's also worth pointing out that LCDM is a cosmological framework. MOND (typically) has no cosmology.
And then even if MOND is correct - you likely still need something like DM to explain clusters (particularly the bullet cluster). It has also been included in the paper posted by OP as scalar field at early times, which then washes out at late times.
It is true though, MOND is hard to touch as an early career researcher!
I'm not entirely sure which one of the two, Dark Matter or MOND, is conceptually the bigger disaster. Dark matter pretty much sounds like the invisible ether that was suspected to carry EM waves. A physical theory that depends on the scale at which you look at space seems similarly awkward to me.
You could have said the same stuff about the neutrino after Pauli introduced it in 1930 to explain the missing pieces in the beta decay. The alternative could have been giving up on the conservation of energy-momentum, but then if you have a continuous energy spectrum in an apparent two-body decay, it makes sense to think there's a third body there that makes it all work as expected despite you being unable to detect it at the time.
It took 26 years to confirm, and that's thanks to having man-made high flux sources. Detection of solar neutrinos had to wait until the 60s. Funnily there was a puzzle with those, as around two thirds of the ones you could expect seemed to not being there (again). This mismatch took another 40 years or so to confirm, so now we know that there are neutrinos indeed and that they show flavour oscillation, that's why if your experiment is looking for a particular leptonic flavour, well you're missing the other two.
So this is not the first time such there must be something there I can't see, yet I can say something about so it all fits together does the job. Hopefully it won't be the last time.
Very nice breakdown of the history of the neutrino! I fully agree. Whether a theory is a conceptual desaster or not is completely unrelated to its success. And I totally get that the hope of physicists is that such theories continue to be successful, since it means new physics which can be discovered. But, still if there is a theory that manages to explain observations, without postulating an otherwise unmeasurable quantity, Ockham’s razor tells you that it would be reasonable to prefer those.
The main difference is that the aether was only ever a theoretical construct, whereas we have lots of indirect observational evidence that "dark matter" is a phenomenon that really exists. We don't know what it consists of, but it certainly seems like there is more of it in some places than others, and it has mass and momentum (see e.g. the Bullet Cluster that was already mentioned in this thread), so "matter" seems as good a name for it as any.
Ok, I would be curious about evidence that dark matter has momentum, because my favorite theory at the moment is that spacetime itself has certain topology on large scales, which isn’t tied to any masses. If one could show that dark matter has momentum, I would reconsider, but I don’t think that is what Bullet Cluster shows.
Edit: even if it turns out that dark matter is the best theory, it would still be a conceptual disaster. But so is QM. Nature seems not to care what we find conceptually appealing.
Is this why there are a bazillion of theories of the foundations of QM? I get that the mathematics is incredibly elegant, but concepts behind the mathematics are not really “understandable” to quote Feynman.
The Many-Worlds Interpretation is the simplest one, because it makes no assumptions beyond, "The basic rules of Quantum Mechanics are correct." It's also very counter-intuitive, but very elegant.
> Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's laws to account for observed properties of galaxies. It is an alternative to the hypothesis of dark matter in terms of explaining why galaxies do not appear to obey the currently understood laws of physics.
Help me understand why this is so controversial in the scientific community. I'm neither a physicist nor do I study any other relevant fields, so I'm asking as a "layman" as it were.
A cursory search shows that "dark matter" hasn't been observed at any point in time. It looks like it's a sort-of mathematical placeholder for the "something" that's missing that we can't see (or can't see _yet_.) Am I correct in my understanding that these alternative theories are trying to prove that there's a way to explain these discrepancies without inventing something unobserved?
Why is that so controversial? To me, again as an outside observer, it feels so counter-intuitive to _invent_ a new type of matter you can't observe than to just say that your calculation is close but not right and to start over. Is it not a crutch?
If I were to take this approach into another field that has an equal amount of controversy where there is a huge gap in my proof, and say that the cause is an "unseen force" that I just invented to explain how my theory works despite the fact that I can't prove in any way that the key part of my theory exists, would I not be laughed out of a room? How did dark matter become accepted while being invented instead of observed?
(I hope my tone isn't coming off as mocking. I'm genuinely trying to understand without a lot of knowledge on the subject, and I don't intend to discredit the current accepted theory nor support the alternative ones, only to understand why the scientific community came to accept the one that is accepted.)
> Am I correct in my understanding that these alternative theories are trying to prove that there's a way to explain these discrepancies without inventing something unobserved?
I would say MOND is just postulating a different "unobserved" thing--an alternate theory of gravity, or an additional "field" that looks like an alternative theory of gravity, instead of dark matter. I don't think MOND has any advantage in the Occam's Razor department.
Or, to put it another way, the word "unobserved" is not quite correct. We have actual observations that can't be accounted for, as best we can tell, with our current theories of physics, without adding some new element. Dark matter and MOND are just two different choices for what new element to add. Neither one can say it's not adding anything new.
> Why is that so controversial? To me, again as an outside observer, it feels so counter-intuitive to _invent_ a new type of matter you can't observe than to just say that your calculation is close but not right and to start over
MOND is not just doing a different calculation that is claimed to be more accurate within existing physics. It is adding new physics. See above.
"Starting over" would be something like finding errors in the calculations based on existing physics (GR and the observed distribution of visible matter) that, when corrected, removed the discrepancy between observations and theory. Nobody has done that, and the calculations based on existing physics have been checked every which way, so it seems highly unlikely that there is an error lurking there that hasn't been found.
> why the scientific community came to accept the one that is accepted
My understanding is that MOND, in general, does not close the gap between observation and theory as well as dark matter does. The paper referenced in this article appears to be claiming that its version of MOND "catches up" with dark matter in terms of closing that gap. I haven't had a chance to read the paper in detail so I can't say how credible I think that claim is at this point.
Dark matter (at least any of the non cold baryonic matter and standard model WIMP candidates) adds new physics too it’s just adds it in different field of physics that often is much less related to cosmology than gravity is.
> I don't think MOND has any advantage in the Occam's Razor department.
It has one: there's no need to worry about finding a dark matter particle when there's no room in the standard model for one. I'm surprised how astrophysicists take for granted that such a particle will show up in a collider eventually, if they even think that far ahead.
>It has one: there's no need to worry about finding a dark matter particle when there's no room in the standard model for one.
This is a weird argument. The standard model is incomplete, we know it's incomplete, we don't expect it to be complete, and MOND doesn't fit in the standard model either.
Even if you limit it to things we have observed, the standard model simply doesn't explain gravity. It doesn't explain why neutrinos have mass. It doesn't explain matter/antimatter asymmetry.
We know gravity exists. We know neutrinos have mass. We know there is more matter than antimatter in the universe. These aren't remotely controversial, and the standard model either doesn't incorporate them or gets them wrong.
> I don't think MOND has any advantage in the Occam's Razor department.
MOND has a much more homogeneous behavior, that requires many less variables added to your theory. So I'll disagree, it has the Occam's Razor preference - for the same reason that ever instance of it has been quickly falsified.
Thanks! I think this helps clarify it quite a lot. The use of the word "observed" was a critical part of my misunderstanding, as to me it felt like it was saying that by not being observed it was "made up" instead, when really it's more accurate to say that it's part of the model and we know it exists but have a hard time describing it?
I have a background in physics (but not astrophysics) and to me MOND seems much more ad hoc than dark matter does. Dark matter posits that there is some kind of particle we have not observed directly that has a large effect on cosmological scales. We already believe that the standard model of particle physics is incomplete, so this is at least plausible. These particles are not in anyway "unobservable" in an absolute sense, they must at least interact via gravity in order to do what we need them to. They may even interact via the nuclear forces. They just don't interact via the electromagnetic force. We can make hypotheses about these particles, put constraints on their properties from observational data, use particle physics theory to come up with candidates, and do experiments to find them. They are not "unobservable", the are simply hard to observe and require advances in experimental technology. MOND on the other hand was discounted in the early days exactly because it was a fudge factor in Newton's second law. We saw some anomaly in galaxy rotation curves, MOND fixed it by adding a fudge factor to Newton, a theory which we already knew at the time to be incomplete! That is why most physicists preferred dark matter to MOND. Since then, other observational data has increased the evidence for the existence of dark matter (most famously the Bullet Cluster mentioned by others), making MOND that much more unpopular. There has been some work, like this RelMOND theory, that work to integrate the original MOND theory with general relativity. Critically, however, the way in which RelMOND is doing this is by positing the existence of an additional field that can act in the "clumpy" way required by observation. Basically, they have just reinvented dark matter. So I do not doubt this new theory fits the observation, but it does so by adding a new degree of freedom which plays the part of dark matter. This talk (https://www.youtube.com/watch?v=iu7LDGhSi1A) is somewhat technical, but it goes in to some detail as to why we can't explain current observation by messing around with gravity.
The Bullet Cluster (https://en.wikipedia.org/wiki/Bullet_Cluster) is a big reason why: it's a collision of two clusters of galaxies. We can see where the gas and stars are, but gravitational lensing indicates the bulk of the mass is elsewhere.
It is not that dark matter has not been observed. It has. It is called "matter" because its gravitational influence has been observed. Therefore at one level we know it exists because something is impacting gravity at large scales, we are just unsure about its other properties. We cannot see it directly but there are lots of things we don't see directly and that doesn't mean we aren't sure they exist. So it isn't a total invention to make the math work. It is a 'best fit' for a gap in our knowledge.
IIRC, dark matter is supposed to be a different kind of matter that interacts "less than normal" with ordinary matter.
Or is there a version in which it's ordinary matter, just "hidden" by something or in some exotic "other dimension", black hole or parallel universe thingy?
It is thought to reacted less with normal matter because we aren't seeing it react with normal matter. So one potential explanation is a particle that is so tiny/fast, with no electrical charge, that it is can fly through planets without hitting anything: a "ghost" particle like the neutrino. The term used is WIMP (Weakly Interacting Massive Particle). Are we know is that it has mass, because it influences gravity. That's one possible explanation for dark matter.
Ideas based on extra dimensions are becoming less popular. We have evidence that gravity experiences the same dimensions that light does. Gravity waves from things like neutron stars merging seem to arrive at earth at the same time as light. So it is doubtful that extra dimensions can explain dark matter.
> To me, again as an outside observer, it feels so counter-intuitive to _invent_ a new type of matter you can't observe than to just say that your calculation is close but not right and to start over. Is it not a crutch?
Physicist here. If you're doing applied physics or engineering, this certainly would be a crutch. But when we're talking about fundamental physics, talking about new kinds of matter that nobody has seen before is not a crutch -- it's literally the core thing we do. That's what makes it fundamental!
Saw a track in the bubble chamber curving the wrong way? Invent a new kind of matter: antimatter.
Saw short-lived particles in the bubble chamber that shouldn't have made it there? Invent a new kind of matter: mesons that decay into the observed particles.
Problems with getting solar reactions to work out right? Invent a new kind of matter: neutrinos.
Amount of neutrinos detected not quite right? Invent multiple neutrinos and neutrino oscillations.
Saw some weird long-lived particles? Invent a new kind of matter: "strange" mesons and baryons.
Want to explain the pattern of mesons and baryons? Invent a new particle: "quarks", along with the stipulation that they can never be observed, even in principle.
Standard Model seems a little off-balance at this point? Invent a new particle: "charm" quarks to balance out the strange ones, at an energy high enough that nobody has seen them yet.
But the mesons and hadron patterns still aren't consistent with the Pauli exclusion principle! Invent a new force: color charge, carried by "gluons", which are also postulated to be unobservable.
Some particular meson and baryon decays acting weird? Invent a new force: the weak force, carried by "weak bosons", which are too heavy to be observable at the time.
Can't get the weak bosons to have mass? Invent a new interaction, the Higgs interaction, carried by an invented new field, the Higgs field, which gets a vev from an invented new function, the Higgs potential, whose elementary excitations are an invented new particle, the Higgs boson.
Of course, not every weird thing is explained by a new type of matter; many anomalies fade away after careful checking. But the anomalous observations that motivate dark matter persisted for almost a century, they're been only building in strength as we get more data, and all attempts we've made to explain them in terms of "normal" physics have failed. So the case for explaining it in terms of something new is at least as strong, in fact far stronger, than the examples I gave above.
I guess what is different about dark matter is that it has to outmass regular matter by a large factor. It feels unparsimonious to invent four-five times the mass of the known universe just to patch a discrepancy between observations and a theory of gravitation. It feels like the theory would better be adjusted to match observation than to patch observations to match theory.
Today I learned that the mass of the neutrinos we know about (which were similarly invented, though since detected) about matches the mass of all the stars.
Actually, in the context of astrophysics, that exact objection has been employed many times. For example, the most famous argument against heliocentrism was that it would require the stars to be ridiculously far away and ridiculously big to patch away the lack of parallax, which felt unparsimonious. Similarly, people believed that galaxies weren't galaxies, because it seems unparsimonious to expand the universe far beyond the Milky Way just to patch up some weird features of fuzzy nebula. And even in our galaxy, the mass in dust and interstellar gas exceed that in stars.
Literally all progress in fundamental physics is "just" "invented". Each time it must triumph against the objections of the same, thousand-year-old philosophical arguments.
Inventing a new particle to explain a discrepancy has worked really well before[0]. Past results are never a guarantee, obviously! But there are lots of ways that a dark matter particle might exist but be really hard to detect; it would not at all be surprising that another particle or class of particles exist that are just really, really hard to see.
>A cursory search shows that "dark matter" hasn't been observed at any point in time. It looks like it's a sort-of mathematical placeholder for the "something" that's missing that we can't see (or can't see _yet_.)
Define "see" - that's the scope of the problem. We can see the effects of dark matter. We can measure the effects. What is or isn't seeing is hard to define on this sort of scale.
>Am I correct in my understanding that these alternative theories are trying to prove that there's a way to explain these discrepancies without inventing something unobserved?
More or less.
>Why is that so controversial? To me, again as an outside observer, it feels so counter-intuitive to _invent_ a new type of matter you can't observe than to just say that your calculation is close but not right and to start over. Is it not a crutch?
Because despite many thousands of attempts to provide alternatives, none have passed muster. We couldn't "see" air for quite some time - did that mean it wasn't there? Would a theory positing its existence be a crutch?
No modified theory of gravity has come to close to explaining things like galactic mergers, dwarf galaxies with huge dark matter content, or the galaxies without dark matter content.
You have a situation where we can see gravities and measure their mass. We can figure out the non-dark matter content of galaxies. And galaxies react in a way that really only makes sense if there's additional matter we can't detect - what theory of gravity will explain why two galaxies with similar amount of observable stuff in them have massively different masses? Is the most logical explanation not that there is more stuff in them that we can't see, representing the additional mass? If I have two boxes and they look to be the same size, but when I go to pick them up, one is significantly heavier than the other, the logical explanation is there is more mass inside the other box, despite being unable to see it.
>If I were to take this approach into another field that has an equal amount of controversy where there is a huge gap in my proof, and say that the cause is an "unseen force" that I just invented to explain how my theory works despite the fact that I can't prove in any way that the key part of my theory exists, would I not be laughed out of a room? How did dark matter become accepted while being invented instead of observed?
It's really disingenuous to act like people did a bunch of math, it didn't work as expected, so they just made up some stuff to make it work. The fact of the matter is, you would be laughed out of the room if it was that simple. There has been a massive amount of work done to attempt to prove and disprove dark matter, and there's a reason that it's the most commonly accepted explanation for things. There's also a reason it's one of the theories that people have spent the most time attempting to come up with alternative explanations - and none of them to this day have been able to explain things.
Dark matter might not exist. But it's the best explanation we have at current. People should keep trying to come up with alternative explanations, and continue trying to prove its existence. That's how science works. But you can't expect an incomplete explanation that fails to account for a wide variety of other factors to dethrone one that does account for all of those factors.
The reason work on alternative theories of gravity is important:
We have one reality R, for which we have various possibly imperfect theories T(R) and a large set of possibly imperfect observations O(R).
For gravity, we know that general relativity doesn't perfectly match current observations -- GR(R) != O(R). Since R is the same in both sides, this is not supposed to happen.
There are three ways to resolve this:
- GR() is incomplete,
- O() is incomplete,
- both are incomplete.
Dark matter focuses on the second, MOND on the first. We shouldn't give up on any option until there's either a solution or a counterexample.
When we go looking for sources of dark matter, we have lots of options of things that aren't lit up. For example looking at the distribution of the sizes of the stars, we expect there to be a lot of giant gas balls that weren't quite big enough to start fusion. We don't see them, but we've got good reasons to believe that they are there and can even make a good guess as to how much of them there are.
However when we try to make estimates for each kind of dark matter that we think of, we come up a lot short of the amount of dark matter which is required to explain the gravitational dynamics of galaxies. This is when we are getting into the territory of imagining new kinds of particles that physics hasn't yet discovered.
Therefore the debate isn't about whether dark matter exists - it obviously does. It is about whether exotic forms of dark matter need to exist.
> when we try to make estimates for each kind of dark matter that we think of, we come up a lot short of the amount of dark matter which is required to explain the gravitational dynamics of galaxies
The dynamics of galaxies are not the only place where non-baryonic dark matter is needed. Our understanding of baryogenesis in the early universe places limits on how much total baryonic matter there can be in the universe. But the expansion history of the universe requires much more matter than that (about 5 times as much IIRC).
Not exactly if you need a little as in just enough to be explained by “missing” baryonic matter and other DM candidate that fit the standard model it’s not a weak argument on its own.
To me it all just sounds like quantum vs continuous.
Like at our scales we normally see only the continuous averages and we'd expect that to be even more so at galactic scales. But what if at the fringes of a galaxy gravity is so 'small' that it's really the quantum that ends up determining the macro results?
Say some near object should experience 5 quadrillion plus 0.1 gravity from continuous equations, whatever quantum happens with the 0.1 doesn't affect the results and maybe we can't even measure it. But way out in deep space where it would be 5.1 gravity that 0.1 matters a lot, for instance if it's 'rounded up' in some way (maybe it represents a graviton being just close enough or whatever).
Obviously this is just nonsense spitballing, but I wonder what you guys think about the idea of galactic outcomes reflecting the quantum rather than the continuous.
For the record, physics takes this on desperate faith.
It's an assumption in the face of a perceived to be hopeless alternative.
Special Relativity itself, Quantum Physics and this new modified MOND that is based on gravity not being universally constant are all pairing down the whole "there is one consensus reality" notion.
This isn't to say that there isn't consensus reality, only that the consensus bit keeps getting smaller and smaller as we learn more.
Observed galaxy rotation curves (the speed of rotation of stars around the galaxy's center as a function of distance from the center) cannot be accounted for using GR and the observed distribution of visible matter in the galaxies. You need to postulate some extra matter that is not visible ("dark matter") to account for the observed rotation curves using GR. That is the discrepancy that originally prompted physicists to postulate dark matter. Since then the same postulate has also been used to improve the match between theory and observation in other areas, notably our model of how the early universe evolved.
For a start: the speed at which stars rotate around the center of a galaxy. This should be due to gravity, yet the speed of stars further from the center isn't slower (as it should be). This holds true for the vast majority of galaxies.
A specific amount of extra (not yet observed) mass distributed in the right way throughout the galaxy could explain this.
It's worth pointing out that modified gravity has less acceptance than even string theory. It's worth working on, as a somewhat plausible alternative to the standard theory, but it's not very likely to end up being correct. It's worth ruling out fully, though (the same can't be said of e.g. flat Earthism).
This particular work seems like adding on epicycles, or overfitting as you'd call it in machine learning.
I disagree, it's not a common view. It's common for physicists to think string theory might be empty theorizing, but it doesn't look at all like epicycles. With epicycles, you start with an existing model and than add complexity. That's not strings. Strings starts with something entirely new, that's already complex.
You could study computer science and then go to a large corporation to help them maximise their ad revenue, or you could study and do something like this instead. Depends what motivates you.
I upvoted you because there is truth to this sentiment. But I want to add that physics is IMO one of the hardest fields intellectually of our time. Just to get your feet wet, you need to be well versed in an intimidating array of mathematical disciplines. DiffEQ, Discrete Math, Computer Science, Topology, Differential Geometry, High Level calculus,... the list goes on even at the undergrad level. To make a meaningful contribution is quite a feat.
I have massive respect for those who bravely tackle the frontiers of Physics; some physics majors have a broader understanding of Math than a mathematician! Though importantly, your average mathematician will have a much deeper understanding of more focused topics.
I don’t mean to suggest that any of Math, Physics, CompSci, etc is fundamentally harder than the others. Each field presents different challenges! But they are also intimately related IMO: the recent MIP*=RE proof has convinced me. In short, we’re all on the same side.
Just my 2 cents, but I would suggest from a programmer's perspective, a method of entry might be in game programing. You can explore a bunch of really interesting mathematical properties of the Universe in isolation and visualize (and even feel) them to some extent.
On my TODO list for example is to take a look at this project that maps a world to non-Euclidean space [1]. Writing these "simulations" and exploiting their nature to make interesting interactions is just unbelievably awesome.
P.S. Another interesting one (by the same person) is "MarbleMarcher" [2].
I get what you're saying, but people learn the math in 4-6 years or so, so while it's definitely a lot of work (not that many other things that people spend that much time learning), it's also fairly well bounded. You know that if you study hard for long enough you'll know most of what you need to know, and then the parts you don't know yet, you have enough awareness of to know when you need to learn more about them.
If the general hacker news sentiment is anything to go by, then it’s just hard because of the archaic mathematical notation. If we could just use better notation then a simple mathematical bootcamp would make mathematics accessible to all the brilliant self-taught programmers as well /sarcasm.
It's actually undergraduate level of math (typically General relativity is taught in 4th year). It just seems overwhelming because it builds on top of four years of math courses. I'm not an expert, but this paper is interesting because of its leaps in physics rather than special math.
It takes 10 years of post-undergrad professional or academic work to become "conversant" in physics? Isn't that the undergrad GR and supporting math courses, themselves, generally? Or are you referring to a level of keeping up with the latest modern theory?
It’s not as inaccessible as you think. Once you understand/get used to some hard concept, then suddenly a lot of other ones make sense, and you’re ready to tackle the next conceptually hard thing. It might seem like advanced math is totally unreachable, but in fact it’s only maybe 10 steps away.
This isn't the culmination of a lifetime of math study. You just don't have a basis to understand it, but you could easily understand it with a few years of study in your free time. Chinese may be as inscrutable to you as math is but you understand that you just need to learn it for it to start making sense....
Note I'm talking about the math in the paper, not the paper itself.
The building blocks are multi-variable calc and linear algebra. The leap from elementary to advanced math occurs when one transitions from dealing with a single function to dealing with parametric arrays of implicit differentials, which are abbreviated in short-hand notation for brevity. Most people , even in tech/STEM, do not get a good foundation in those topics, so that precludes the possibility of deeper understanding.
We, as a society, produce enough of a surpluss that we are able to pay armies of researchers to do nothing but expand the frontier of human knowledge and pass that knowledge on to the next generation.
The answer is patience. Everything is easier once you've been working in the field for a few years, steeped in that world. Have you ever read legal texts? Or dug through a graphics rendering library? Or seen a grandmaster play chess? Or etc, etc, etc. Experts in a field can show you how complex things can be when you're working on hard problems and innovating, but that doesn't mean you're not capable of getting there if you're patient.
If you're down here with us stupids you can spend a lot of time on it, you'll get some insight into the basics, but you won't be good at it - certainly not good enough to do it for a living.
Yes, GR is taught at undergrad level. But that doesn't mean most undergrads really understand it, or can do much with it beyond solve a few toy exam problems. Because undergrad GR and QM are introductory courses for beginners.
It takes a PhD to start acquiring fluency, and that's years of constant grind doing nothing else but. It's also hugely helpful to have mentors and/or parents and/or other family members who can give personal help.
I have a degree in math. I've since moved onto 3D graphics rather than pure math, but I think I was fairly good at it. I can tell you it was damn hard work to get my degree. The only guy in my year whom it all seemed to come easy, I later found out was the son of one of the professors and had been essentially studying for the degree since he was 13.
Actually this is classical general relativity, the math is not particularly advanced. When I was doing Theoretical Physics I would have considered this paper "easy", at least relative to most papers on hep-th.I never believed in MOND and even this paper is not convincing, since the lagrangian is built ad-hoc rather than derived from a clean principle.
The problem with LCDM is that you are allowed to arbitrarily assign an anisotropic parameter in R^3 (dark matter density) to explain nearly any phenomenon.
Oh did you wake up with bed hair this morning? Could be dark matter. We'll never know.
This not the same; at the time when they were postulated due to mass defect in nuclear reactions, there was a reasonable mechanism of detecting them, if nothing else the principle of microscopic reversibility. With current dark matter there literally is no known way of detecting them that doesn't beg the question, and all of our attempts to identify them are literally "shots in the dark".
Looking forward to having a gander at the paper itself.
Edit for context: the challenging thing for MOND is that ΛCDM explains a number of precision observables and phenomena at once. MOND and TeVeS theories can fit individual facts in isolation, but not the ensemble simultaneously. ΛCDM fits those facts with only a single extra concept. It sounds like this iteration claims to address the seminal observation one and one of the most-tightly constrained observables simultaneously. There are several others. Will have to read the paper before saying more.