The content of the article is very interesting and worth reading, but the framing feels circular. Some laws of nature are fundamental and other laws are inevitable consequences of those laws. If the inevitable laws were not inevitable, then they would be fundamental. As our knowledge and explanatory power grows, some laws that first appeared fundamental have been explained in terms of deeper laws, but we must still ask why the deeper laws exist.
“This is rather as if you imagine a puddle waking up one morning and thinking, 'This is an interesting world I find myself in — an interesting hole I find myself in — fits me rather neatly, doesn't it? In fact it fits me staggeringly well, must have been made to have me in it!'"
Anthropic Principle: "a philosophical consideration that observations of the universe must be compatible with the conscious and sapient life that observes it, and that there is hence a survivorship bias."
I concluded this early in my life, which makes me a minority amongst beliefers. I believe in God and that creatìon shows occasional traces of his genious, but I don't think they are unambigous enough to warrant the christian god as a necessary conclusion.
I feel similar. Although, I don't believe in God so much as a belief in some form of intelligent design. Or I guess, the belief that existence has some kind of reason, and hopefully, my conscious mind does too.
I feel that the christian God fits this bill especially well, when you look at him a bit more abstractly: He is able to give purpose (does care and is something absolute rather than mending to what one particular human beliefs), is interested in staying in contact with his creation (as opposed to deistic Gods), values existence so high that 1) it should be contiued eternally and 2) not in a replaced, but a renewed form. Many christians, many opinions, but I feel confident in this faith. I can recommend C.S.Lewis, who is great about putting God, heaven, hell in terms that make sense and don't reek of religious fanaticism.
I would be Buddhist if I would not be christian, but I am glad I can be christian. If what I believe is true, then boy are we lucky!
As mentioned elsewhere in this thread it sounds as if what you're asking is related to the anthropic principle. Maybe it would be more appropriate to argue that "the set of physical laws that arise from the known fundamental constants are inevitable".
But this itself is not strictly logical because changing the fundamental constants doesn't imply a change of the fundamental laws. The fundamental laws may very well work fine with different constants but we may just not be there to observe them in action because the outcomes may not result in a universe conducive to life (hence: anthropic principle).
As a bad analogy, physics affects an egg falling to the surface of a planet in low gravity in the same way as an egg falling in high gravity. The outcomes may be different, but the laws are the same. And of course, in the latter case it's less likely for something to survive the fall and live to even ask these questions in the first place.
There are some interesting possibilities that arise at this point. e.g. What if this Universe is only "somewhat" tuned for intelligent life? What if, on some more "appropriate" level of "tuning", more stable, fundamental particles are observable for longer periods of time yielding even more insight into the fundamental laws of the universe?
Lots of interesting stuff to talk about around a camp fire...
I agree with this. I've always found theories of everything to be unsatisfying in this way, because they never explain how the laws of physics got the way they are.
Assuming the existence of some abstraction called spin to derive the fundamental forces is a great exercise in internal consistency, but hardly meets any definition of "bootstrapping" as I understand the term.
The only theory I've ever encountered that passes this smell test to me is the mathematical universe hypothesis[0] because it's intuitive to me that math just "is" in some sense and does not require any upstream mechanisms or assumptions. As far as I'm concerned, if you have to assume the existence of anything whatsoever, it's not bootstrapping.
I was expecting Noether’s theorem to make an appearance in this article, because it is utterly fundamental to this kind of work. Her insight was that mathematical symmetries (like the spin symmetries that the article discusses) lead to laws of conservation, and vice versa. So laws like conservation of momentum correspond to translation symmetry, i.e. the assumption that the laws of the universe apply everywhere equally.
As to how the laws got where they are Lee Smolin and Roberto Ungar say that it's possible they were not always the way they are and that they evolved spontaneously over time. And that the spontaneity just is the way things are i.e. there's no explanation for it. At least that's my recollection from reading their book.
The other explanation seems to be the multiverse. i.e. we just got a random set of self consistent laws. Again there seems to be no explanation as to why or how the multiverse came to be, is there?
> not always the way they are and that they evolved spontaneously over time
But how did they get any way at all? How and why do they evolve?
> multiverse. i.e. we just got a random set of self consistent laws.
This raises even more questions. Why are there any multiverses with any laws at all? From where did the stuff in the multiverses come from? What initiated this chain of multiverse creation, or why is it inevitable?
A bootstrapping theory would explain why anything is inevitable, or why there is something rather than nothing. Otherwise it is just a low-level physics theory.
I don’t think what you’re asking for is possible, and the answer lies more in the realm of philosophy than in physics.
You can always keep asking the question ‘why?’ At some point, either you have just accept something as fundamental, or the answer justifies itself, or you have an infinite regress of whys.
I agree with this generally, but I don't think questions like "why are the laws of physics the way they are" are obviously questions for philosophers only and I'm not simply asking "why?"
Only very low-level ontological questions meet this criteria, like "why is there something rather than nothing," but even then, I am open to the possibility that there are reasonable explanations for these things that we just can't articulate yet.
Mathematics is just a set of internally consistent rules.
There is no reason the universe needs to follow an internally consistent ruleset (although so far our measurements seem to find it to be, quite precisely).
Not quite what you're arguing, but related: you might be interested in the strong anthropic principle. PBS Spacetime did a fairly accessible video about the reasoning behind it recently:
I agree that the article plays a little loose with terminology; however, I wouldn't go as far to say that it's a circular argument.
To snitch an example from mathematics, consider formal logic and set theory. These are oft considered the epitome of rigor, enough so that they form "the foundation of modern mathematics." However, when first begining to study these fields, one encounters a sort of philosophical conundrum, "How do you even state the rules if you start from literally nothing?" You can write them on a piece of paper, but without some system of processing, all those rules end up as just ink on paper. The standard terminology for just such a system is "metalogic."
Anyway, at first blush it seems like any such metalogic is inaccesible to mathematical inquiry, but we can use a trick to "lift" the metalogic and logic one layer up. For example, we can (using some metalogic) start with standard Zermelo-Frenkel set theory (ZF), and then ask ourselves, "Is this ZF powerful enough to iplement a version of ZF within itself?" In other words, if ZF is too weak to implement ZF, then clearly out metalogic must be something stronger and more complicated.
Fortunately, it turns out that ZF can implement itself just fine, and in fact, there are much simpler (read weaker) logics also capable of implementing ZF. Said another way, the bare mininum needed to write a program capable of verifying ZF proofs is quite bare and minimal, indeed. Counter-intuitively, perhaps, this line of inquiry has ended up discovering pretty nifty proofs of previously intractible problems. It also has practical implications for proof verifiers and the like (see Metamath[0]).
So, by analogy, I read this article as saying something similar about the metaphysics of our physics. I.e. it turns out that there are some really simple rules capable of generating the complex physics that is the Standard Model. How much can we whittle down the metaphysics? What does that say about our universe?
I think the bigger mystery is why there are less fundamental laws than inevitable ones. That the universe principles arise from simple rules.
How comes there are not millions of different quark types? Why not 5180 fundamental forces? Going smaller nature becomes simpler.
It is hard to express but I have always felt this universe has a complexification ability, where at every level it seems possible for simple rules to lead to complex outcomes.
The fact that the “line of reasoning is circular” is kind of the point: they are invariant fixed points in the space of possible sets of laws, such that they remain unaffected by iteration upon themselves. Kind of like Y Combinator or Turing’s Theta Combinator.
It rules out having a universe with particles that have the known spins and completely different forces. It could have ended up different, they could have found that the possible forces are not constrained by particle spin configurations.
I think we still have too poor understanding of the what to be pondering the why. If past history is any guide, such attempts tend to mislead - e.g. Einstein's "God doesn't play dice".
with which you can prove a theorem by assuming it in the first place, using infinitary (or circular) proofs and an algorithm to transform these proofs into usual proofs.
> When bootstrapping, physicists determine how elementary particles with different amounts of “spin,” or intrinsic angular momentum, can consistently behave. In doing this, they rediscover the four fundamental forces that shape the universe.
They have derived gravity through quantum mechanics? What rock have I been living under?
Not a physicist by any means, but from the article it talks about gravity in the context of the graviton (as one plausible solution to the problem mentioned). Which is still hypothetical, so it's not like they've proven gravity from first principle or anything.
no like, "addition is closed over the integers" is something you can show to be True (for all members of an infinite set, no less -- so it's not empirical.)
And yet, funnily enough, your phone needs a more thorough understanding of gravity than you do. The GPS system must correct for relativistic effects that cause the atomic clocks to shift relative to ground.
There is a nice derivation of Newton’s law from quantum field theory in Zee‘s book „Quantum Field theory in a nutshell“. You can also arrive at Einstein’s field equations by deriving the beta function of bosonic string theory and (2-2 scattering to be precise) and requiring that it is constant.
> They have derived gravity through quantum mechanics?
Sort of! The problem is that the solutions of the existing quantum field theories are not renormalizable so infinities arise in the solutions. The whole point of quantum gravity is to find realizable solutions.
Basically, Feynman starts with microscopic approach. We want to describe interaction where each piece of mass/energy is attracted to each other. So lets introduce a boson (whole number spin - 0, 1, 2, ...) to carry interaction. Then he talks about spin properties, rejects spin-1 boson (aka photon), somehow rejects spin-0 boson (I don't remember arguments) and start building microscopic theory of interacting via spin-2 massless bosons. Because they carry energy there is a self-interaction. He builds interaction rules, Feynman diagrams, and then goes to classical limit, where he derives macroscopic classic GR from microscopic quantum interactions. That's what I remember from reading this book. Apparently he did it on the fly, lots of errors in derivations which were noted and corrected in footnotes. Nevertheless, very entertaining approach...
This is a good article, but I think it's a little confusing -- it doesn't specify the scope of the bootstrap programme.
It's true that general considerations can give you very strong constraints on how particles of various spins can interact. For example, it's been known for decades that at low energies, massless spin 1 particles inevitably give you Yang-Mills and massless spin 2 particles inevitably give you general relativity. There is also a separate idea called the conformal bootstrap which seeks to use general principles to pin down everything about a theory, but my impression is that it only works well for simple conformal field theories in lower dimensions.
In particular, these ideas don't tell you anything about the detailed structure of the Standard Model: why it has the gauge groups it does, why there are 6 quarks, the values of the quark masses, how the spontaneous symmetry breaking works, the gauge couplings, and so on. That's the way with almost all theoretical tools: the flashier and more general in scope they are, the less details they actually pin down. So while formal theorists may be excited about this, experimentalists can't really use it for anything.
Wondering if anyone could recommend a layman's introduction to "spin". I've read the Wikipedia article, I broadly understand it, but just curious as to how it was discovered, why it is considered an "intrinsic" form of angular momentum, and why it is so fundamental a concept in our universe.
I like Physics from Symmetry by Jakob Schwichtenberg as an explanation of how spin arises from a modern understanding of physics. The book was written while the author was a Masters student, and so it is much closer to the way an undergrad physics student would explain it to another student. The author is willing to skip details in favor of more general understanding.
The way the book will describe it is from the perspective of group theory. If you assume that the laws of nature in a relativistic flat spacetime do not change under rotations, translations (in both space and time), and boosts (transformation between frames of reference of constant velocity), then these transformations define a Lie group called the Poincaré group. Representation theory then says that the representations of the Poincare group are characterized by two numbers. These two numbers are identified as a nonnegative mass and a spin. One interpretation is that these representations are indeed what "particles" are in Quantum Field Theory.
Objects with spin can be point-like but carry angular momentum. The electron is one such particle.
It is "intrinsic" because it has no known moving parts. If it had moving parts, and that motion had net angular momentum, we would refer to it in many contexts as "orbital angular momentum".
Spin should seem counterintuitive. There are no macroscopic objects that I am aware whose spin you can feel with your hands. Our research group has an object with 10^23 polarized spins (and negligible net magnetic moment) -- observing the angular momentum effects directly requires a sensitive modern torsion balance. https://arxiv.org/abs/0808.2673
It's totally counterintuitive. Classical angular momentum requires a choice of origin. All angular momentum is then relative to that origin. Any point particle lying at the origin should not be able to have any angular momentum.
Imagining the classic "figure skater experiment", the figure skater speeds up as she draws her arms inward, due to conservation of angular momentum. If she could shrink down to a point, her angular speed would tend to infinity. This is what I imagine happening to a black hole.
You need not worry about infinity in the black-hole case. Known physics ends at the black hole's event horizon, for an external observer. Black holes of a given mass can only have so much angular momentum.
As a rule of thumb, that angular momentum corresponds to that at which the equator of the black hole is moving at the speed of light.
This has important consequences for the mergers of two high-spin black holes that have aligned spins. The merger is actually delayed for a little while, just before merger, as the binary dumps angular momentum through gravitational radiation.
Excitations can carry dynamical properties. For example, jerk a rope once, and you will see a wave travel down the rope, which carries energy and momentum. If you give the rope a quick twist, the wave carries angular momentum.
I have the same problem with this analogy. The rope itself is just excitations of a quantum field. It feels like there is very little underpinning everything.
Magnetic moments, for the (essentially all) particles that have them are aligned parallel to the spin axis, as there isn't any other axis in the problem, but that doesn't mean that there is a direct link between magnetism and spin.
One example: Neutrinos have just as much spin as electrons, but they have not yet been observed to have magnetic moments.
It is true that most magnets get some, if not all, of their magnetism from polarized electrons. We often state that the magnetism comes from "spins", as it is an effective shorthand, but it is not strictly correct. Some magnets get substantial amounts of magnetization from orbital magnetic moments of electrons (SmCo_5, for example).
Furthermore, one can create a magnetic field simply by moving an electric charge. From that perspective, a magnetic field is consequence of combining special-relativity with electrostatics.
We know a lot, but there is so much more left to learn.
It was called spin because for a time the model of an electron was a solid sphere of charge that was spinning on its axis. It was known that the electron made a magnetic field, and since charge in motion makes a magnetic field that could be explained by a spinning electron. But if you actually do the math you'll be off by a factor of about two. Quantum mechanics had to be invented to explain this discrepancy and the name stuck.
I recommend reading about the Stern Gerlach experiment. I think that nails down what makes spin counterintuitive, and is a really clear example of how the predictions of quantum mechanics can't come from classical mechanics. The fundamental nature of it and the units can be reasoned out by looking at conservation of angular momentum.
Typically, angular momentum is just linear momentum plus an attachment. Imagine two weights spinning around each other in a circle, tied together with a rope. At a moment in time, each weight has some linear momentum, each in the opposite direction. The system has angular momentum because part of it has linear momentum in one direction and another part has linear momentum in another direction. In classical mechanics, it's all like that, with different pieces in different locations moving in different directions. But with a particle, there's only one piece. If it has angular momentum, it's gotta be a property of that piece, instead of the more emergent property of a system made of multiple pieces. Hence "intrinsic."
Max Tegmark was on the Sean Carroll podcast recently, talking about the different types of multiverse we could postulate may exist[0]. I found the quanta article fascinating, and I don't believe it's strictly speaking 'circular'. It can also be the case that multiple solutions exist mapping the relationships between a given set of fundamental laws. Prof. Tegmark discusses this in the '4th level' of multiverse which examines whether it's right to talk about a multiverse of all possible mathematically consistent universes.
If it is inevitable, why does the weak force only affect the left-handed fermions and not the right handed? Most of the article is just a discussion of the applications of the symmetry, not inevitability.
U(1) [aka electromagnetism] is probably inevitable, the rest is more controversial.
This brings to mind how Noether showed that conservation laws of physics must exist if universe has some specific symmetries.
Like translation symmetry, the simple fact that the laws of universe don't change as you move a bit to the side mathematically implies conservation of momentum.
Sounds to me like the higher order laws of physics are emergent properties of the lower level properties. Is this surprising? Every system in existence is the result of the emergent organisation of lower systems - why would the laws of physics be different?
It is one thing to say that something is plausible, and something quite a bit more to be able to show that not only is it plausible, but also that it is the way things actually are, and in a very specific way.
yes, but the reporting is as if the fact that emergence exists is itself surprising. I'm sure the actual science is a lot more sober and focused on the genuine revelations, around how such emergence plays out.
What that means is that gravity, at the quantum level, must be conveyed by a spin-2 particle, known as a ‘graviton’. It has not been detected, and probably never will be (due to technical limitations). We can broadly pin down its properties, but we do not yet have a full theory of how it interacts.
The existence of a solution to abstract equations that involve gravitons does not imply the existence of gravitons. Designing an experiment to measure and confirm the existence of the particle is a different endeavor.
What was discovered is the existence of gravitation waves, long wavelength limit to the weak quantum gravity (aka propagating and interacting gravitons)
I thought this was going to be about Twitter Bootstrap's UI library, and was thinking, "Oh good, I can read about simple consistent rules so that it's not so organic and unpredictable anymore!" It was not to be. Back to the UI trial-and-error slog...
I think with some equations there is a discontinuity at zero, like tan, but it still makes sense to talk about what happens asymptotically approaching zero and then it matters from which side you approach zero, hence positive and negative zero.
Yep, this is dogma. People seem to be hard-wired to believe in something, for some it's a god, for others it's a theory or hypothesis. As for the grand-unification surrounding the the four forces, aren't we currently questioning the existence of a fifth? That's a pretty short-lived god.
