Comment by meroes | Hacker News Reader

Comment by meroes | Hacker News Reader

Parent Full thread

Black holes form before any infinities. They form when enough mass-energy occupies a small region of space. And neither quantity is infinity. Due to how energy is related to wavelength, and that we need smaller wavelengths to probe smaller, and because everything has wavelength, we get that smaller scales require more energy (this is a simplification but correct). At a certain small enough size, again not infinity, we get a black hole due to energy density of that region of space. And any more energy just makes a bigger black hole. So we can’t actually get endlesssly smaller scales. The singularity is also a mathematical one and not something most physicists claim exists physically. I mean as a related example, there’s no way to physically infinitely divide space so infinities of calculus don’t imply infinities of spatial division.

QM I’m less sure where you think infinities pop up physically? One interesting thing is you’d need an infinitely size measuring apparatus to have absolutely certain measurement results due to random fluctuations, but as per above we can’t have infinitely size devices except for infinitely sized black holes, which won’t really help us. A lot of this is said more rigorously by Nima Arkani Hamed in his recorded public lectures.

Thanks for that, that's super interesting.

With quantum mechanics it's just infinity in the opposite direction, going infinitely small. My very pedestrian understanding is that the field of quantum mechanics came about because people were having trouble explaining the behavior of atomic particles, particularly electrons, using newtonian mechanics, and quantum mechanics were able to explain everything in a more comprehensive framework. At first I always found the idea that electrons are 'nowhere' until they are observed very mysterious, but it made a lot more sense when I understood that probability densities are involved in qm equations. There's usually a similar source of confusion when we move from "probabilities" of discrete distrubutions, which is quite easy to understand, to probability densities, which can be done by taking limit of number of possible states to infinity, and where you can get "probabilities" larger than one.

Just to add to this -- In QM/QFT there is an inverse relationship between energy & distance, meaning small distances (or sizes) correspond to high energy interactions (see e.g. [1]). One consequence is that at small enough scale (the Planck scale), the energy scale gets so large that quantum gravity effects are expected to be non-negligible. Formulating a theory of quantum gravity that fits into the Standard Model of particle physics & agrees with general relativity is an open problem in physics, therefore the Planck scale is at least the smallest distance that can conceivably be modeled given our current knowledge.

[1] https://physics.stackexchange.com/questions/731971/equivalen...

"going infinitely small"

My personal guess at a first-cut resolution:

An electron moves as a wave that satisfies Schrödinger's equation. Maybe that wave goes through a Young's double slit then hits a wall of detectors. We get a detection. But, the electron was never a point particle that hit the detector. Instead the wave of the electron hit one of the waves in the detector -- no points were involved.

As a layperson, would what is beyond the edge of the (observable) universe, past the 'edge' of the expanding universe, be considered infinite? Or is that nothing / does not exist / null and void?

edit: Reading up on things (just wikipedia, bear with me), we don't know how big the universe beyond what is observable is. We can't know because we can't observe it, and what we can observe goes back ~13B years.

> The singularity is also a mathematical one and not something most physicists claim exists physically.

I didn't know that, that's cool. I understand why people would say that about coordinate singularities, since it's clearly an artifact of the language and not the underlying thing, but is that also true of other kinds of singularities? I'm curious about the different schools of thought.

Reply on news.ycombinator.com