Simple Rules ‘Bootstrap’ the Laws of Physics
quantamagazine.org
quantamagazine.org
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...
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.
[0] https://en.wikipedia.org/wiki/Mathematical_universe_hypothes...
https://en.m.wikipedia.org/wiki/The_Singular_Universe_and_th...
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?
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.
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.
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.
Asking "why" is begging the question, though. Maybe there is simply no reason behind it. They change because they change.
https://www.discovermagazine.com/the-sciences/how-mathematic...
Why modus ponens? [0]
[0]:https://en.wikipedia.org/wiki/What_the_Tortoise_Said_to_Achi...
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).
Don't things have to stop somewhere, otherwise there's an infinite regress ("turtles all the way down")?
https://en.wikipedia.org/wiki/Infinitary_logic
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.
“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!'"
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!
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?
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.
They have derived gravity through quantum mechanics? What rock have I been living under?
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.
Deriving a description of gravity from first principles would be more appropriate
I can certainly prove things about, say, addition.
The Earth's gravity field is not deterministic.
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.
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
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.
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.
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.
This is where I get stuck. The particles are all excitations of a quantum field. So what does spin mean in that context?
I've not yet encountered an experimentally-testable explanation that goes deeper than that.
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.
[0]: https://www.preposterousuniverse.com/podcast/2019/12/02/75-m...
U(1) [aka electromagnetism] is probably inevitable, the rest is more controversial.
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.
Err, not on any clock I've ever seen! But points for effort.
So, has this been discovered recently? I was under the impression that the graviton was theoretical?
Huh?!?
spin-2 particle leading to GR was the prime essence of Feynman lectures on Gravitation, 1962
Is that a typo, or is it really possible to have spin -0?
;)
tan(π(x + 0.5)) = ∞~, x ∃ ℤ
(π on my screen doesn't look much like greek pi.)
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.