Comment by ackbar03 | Hacker News Reader

Comment by ackbar03 | Hacker News Reader

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>To understand the universe, scientists look to its outliers. “You always want to know about the extreme cases — the special cases that lie at the edge,”

Some of the books I've read recently touch upon things like quantum mechanics and black-holes and that kind of stuff.

As a decently technical person but with no formal training in physics, can I generally interpret the study of things like black-holes and quantum physics as the idea of understanding how the physical world behaves as we take limit towards zero or infinity? Is that a correct way to think about it?

For example, I've studied probability and statistics somewhat formally in undergrad. The idea that electrons taken on a distribution and are technically "nowhere" until they are observed (schrodingers cat) sounds just like the description of a continuous variable, or alternatively where you take limit on a discrete variable such that it approaches a continuous distribution. The probability of the variable being any value is technically 0 but its state can be observed. It's hard to "truly" comprehend in a realistic since but its what allows us to build statistical models of things

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.

I think you should be careful about taking analogies too literally in physics - wave functions in basic QM are kinda like probability distributions, for instance, but they are complex valued and change when you sample from them. So they actually behave very differently.

The best way to grok the models more deeply (in my opinion anyway) is to dive into the maths!

This is correct. Understanding is math.

>but they are complex valued and change when you sample from them

I see, that does sound pretty different

My personal haha-but-serious interpretation is that we live in a simulation, which has set limits (maximums and minimums) for essentially all quantities because of the numerical methods used.

The speed of light is the maximum speed of information propagation.

Black hole event horizons are the maximum entropy per unit surface area.

Planck's constant (h) is the numerical precision ("ulp") and is the minimum representable change in the simulation state.

Etc...

If you like to philosophise about this.. the game Eve had problems when too many players were in the same spot at the same time, and rendering everything in time.

Their solution? Time dilation..

Find your statement fascinating as well, but could also provide another haha-but-serious explanation that I personally like... which is that there are universes with an infinite permutation/computation/value of state variables, and our one could only be "simulated" within the one universe where these sort of limits exist.

  > Black hole event horizons are the maximum entropy per unit surface area.

This is an utterly fascinating way to look at it, especially in the context of your definitions of C and the Plank length.

I like to think of it as a limit imposed by the bandwidth limits between compute nodes.

A volume of computers connected in a grid with cables will have a bandwidth per unit area limit along all surfaces.

Similarly you can’t “know” about other matter in some direction away from you unless the information about it traverses the network links back towards you from there. Along a line that has a fixed upper limit. With more and more matter in some direction you get less and less information about it per unit of your time elapsing. It’s like watching a higher and higher resolution video with a fixed bandwidth — it has to play slower.

PS: hence the boundary of the visible universe is also an event horizon, it is the “depth” at which the total accumulated matter sums up to the same limit.

PS: The same line of thought works for the Anthropic principle as well! In the zoo of possible universes most have zero sentient life because the rules are not conducive to it. That’s the “core concept” but there is a nuanced version where many universes have just one species of sentient life. For example infinite travel speed would allow the first aggressive xenophobic and technically capable race to wipe out everyone else in short order. Hence, we’re more likely to be living in a universe with a speed limit where such “instant Borg assimilation” is physically impossible.

It only makes sense until you realize that flow of time is literally the first thing any simulation does simulate.

If you have the time maybe look towards a community college and take a modern mechanics class! I took one in undergrad and it gives you insight into special relativity and basic quantum. Though I don’t remember a lot of it, it was really exciting to be able to practice the math and be able to ask the professor my questions.

I feel like with these topics you need to dive into the details to gain a strong understanding but then you only realize how much there is to learn.

There are no metaphors when dealing with the fundimentals of the universe. Metaphor is a means of teaching (ie light is a wave) but once you understand then you realize that no metaphor can ever be accurate enough. Errors occur when people see similarities between metaphors which have no meaning in the real world.

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