61–70 of 96 posts
> And the hour hand on a clock must spin around twice before it tells the same time again. Err, not on any clock I've ever seen! But points for effort.
This example definitely assumes familiarity with a 12-hour clock, which indeed spins around twice before getting back to the same time.
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.
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 a…
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 a…
> ... but we must still ask why the deeper laws exist. 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.
Earlier quoted context omitted.
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 r…
> Objects with spin can be point-like but carry angular momentum. This is where I get stuck. The particles are all excitations of a quantum field. So what does spin mean in that context?
> And the hour hand on a clock must spin around twice before it tells the same time again. Err, not on any clock I've ever seen! But points for effort.
Earlier quoted context omitted.
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.
Interesting, is there any reading material on the second point?
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 a…
Reminds me of the Douglas Adams quote: “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!'"