It's funny to see this on the front page of HN. I knew Chinmay (one of the authors of the paper) back when he was an undergrad at Caltech. Super cool dude - I knew he'd go on to do great stuff! Very happy for the team that obtained this result.
Chinmay was a TA for CS38—the required algorithms class for the computer science major at Caltech. I saved that class for the final quarter of my senior year. After finishing my last exam, I drove up to the Eastern Sierra to hike Caltech Peak to celebrate my (presumed) graduation; I was gone for a few days. When I returned and checked my email, I saw that my CS38 exam had been graded but that I didn't yet have a grade for the class.
On problem 2, Chinmay underlined my use of the royal "we" and told me to report myself to the the Caltech honor code committee if I'd taken the take-home exam with anyone else. I got a good chuckle out of that one. I tanked that question—1 out of 6 points!—so I wondered whether he thought I was part of the dumbing cheating group in history.
Haha — Chinmay here. Oh goodness I remember this! What actually happened is that there were two sols. submitted that we’re similar enough that we were concerned about cheating — both used the royal “we”. And the weird part was that very few people used royal “we” on that problem. The two were not direct copies so we thought we should just ask the submitters to self report to BoC rather than deal with an official report.
“ The three authors of the new paper, who had been collaborating on related projects over the past two years, came together to prove that one of the new codes had all the properties needed to make a quantum system of the sort that Freedman and Hastings had hypothesized. In so doing, they proved the NLTS conjecture.
Their result demonstrates that entanglement is not necessarily as fragile and sensitive to temperature as physicists thought. And it supports the quantum PCP conjecture, suggesting that even away from the ground energy, a quantum system’s energy can remain virtually impossible to calculate.
“It tells us that the thing that seemed unlikely to be true is true,” said Isaac Kim of the University of California, Davis. “Albeit in some very weird system.””
My view on life is that it's deterministic. The mental analogy I've come up with is this:
"If you were to roll a set of marbles down a hill, the outcome and trajectory would be identical no matter how many times you repeated the experiment given the same marble shapes and initial force."
Where the marbles here are an analogy for our genetics, and the hill + initial force our environment.
Reading the thought experiment it sounds like a similar analogy:
> "Run a bath, then dump a bunch of floating bar magnets into the water. Each magnet will flip its orientation back and forth, trying to align with its neighbors. It will push and pull on the other magnets and get pushed and pulled in return. Now try to answer this: What will be the system’s final arrangement?"
> "This problem and others like it, it turns out, are impossibly complicated."
Can someone explain why this is "impossibly complicated?"
The classical version is deterministic, but "deterministic" does not necessarily mean "calculable". There are plenty of deterministic problems that are not calculable (at least not in any reasonable time frame, where "reasonable" means "not of a much greater order of magnitude than the age of the universe") because they are so sensitive to precise conditions that miniscule differences quickly become unmanageably huge. And since we can never measure a system's state to exact precision, nor can we calculate things to exact precision, our model of a system is always imprecise, and for many systems, "imprecise" means "not calculable" even though the underlying laws are deterministic.
The quantum version is not even deterministic when measurements are involved.
Yes, there are (the many worlds interpretation and the Bohmian "pilot wave" interpretation are the two that come immediately to mind). I don't see what that has to do with "block universe", however, since that is an interpretation of relativity, not quantum mechanics.
We must be talking about different things. Block universe is the theory that the universe is fixed in advance (deterministic) as a 4 dimensional “block” (more dimensions to include many worlds, I suppose?) and we’re just exploring one probabilistic trace through it.
> more dimensions to include many worlds, I suppose?
There is no spacetime model of many worlds at all, as far as I know. Many worlds as an interpretation of QM is based on non-relativistic QM.
The "space" in which quantum states "live" is not spacetime but Hilbert space. "Many worlds" is really a misnomer in the sense that there is only one quantum state in Hilbert space. But quantum states in Hilbert space can have relationships to ordinary space that are not at all like those in classical physics: for example, a single quantum state can describe a system containing multiple entangled particles that are spatially separated; in such a state no particle by itself has any definite state at all (which is impossible in classical physics). That is true regardless of which QM interpretation you adopt.
Block universe, as a theory, is based on classical (non-quantum) relativity, and its model of 4-dimensional spacetime. It is not based on QM. Non-relativistic QM does not even use spacetime. Relativistic QM, aka quantum field theory, does use it, but is not a deterministic model and does not treat spacetime as fixed in the sense of all events within it being determined in advance.
> we’re just exploring one probabilistic trace through it
There is no such thing as a "probabilistic trace" through a deterministic 4-dimensional spacetime in which all events are fixed in advance.
So how does the universe itself “calculates” things in real time. How do so many operation “render” on the quantum/classical scale. Forces adapt in real time?
Even the idea that anything is being calculated is a supposition. There appear to be relationships between entities and some of them can be modelled using human math on human-accessible time scales.
But although some of the models have potentially infinite precision the universe itself clearly doesn't on any scale.
Or if it does, it's not accessible to us. So whatever is happening may use some other paradigm to manage relationships, and the entities and relationships we see are emergent and not at all fundamental.
It's not necessarily real time, you only experience time at the same rate, no matter how fast the universe is calculating in meta time. Or maybe time is a 4th spacial dimension, then the universe would be a finished, static thing, no more calculations needed (you would experience time in the sense that characters in a movie experience time, even though the film roll already contains all the frames)
the universe doesn't calculate anything. it just happens.
this is also why I think that artificial consciousness (big difference to intelligence) is a whole lot harder than many people think. a stack of papers where someone has manually written the neural net (or whatever technology) computation and results is unlikely to have a subjective experience. because there is an indirection between a simulation and the real world. the simulation is a computation. the real world happens.
Could we devise a process, which makes things "just happen", so that consciousness results? I think that is the question. I don't see, why it should be impossible to do so.
What you are saying aligns a lot with the “emergent consciousness” line of thinking. It means that consciousness appears out of the complexity of our wiring.
Physics is a model for us to estimate and in some way explain phenomena we see in the universe, it isn't the way that the universe itself produces phenomena
Small differences in the initial conditions can bring big differences in the final result. This is the main postulate of chaos theory started with one Edward Lorenz and giving birth to stuff like the butterfly effect.
Deterministic, yes. Calculable, no, because you can never know the precise initial conditions, either for statistical mechanics reasons (classical) or uncertainty limits (quantum).
This is similar to nondeterminacy, and is why we end up with all sorts of “interpretations” (Copenhagen, …). Indeterminacy makes the math really hard. I would like to say more, but I can’t do so and be correct. If you’re really interested, pick up all three volumes of “The Theoretical Minimum”, and come to your own opinion after learning the physics.
Your quest for knowledge should include examining the Double Pendulum. It is an extremely simplified device, easily explained and understood, whose motion is chaotic.
I always said that computer science was going to be the method to complete physics, whether it be finishing the Standard Model or proving finally Dark Matter is fiction, which is why we can't detect it. Maybe it's still not entirely clear, but just trust me.
Good lord no, just no. Computer Science is not going to be the method to "complete physics." "Complete physics" isn't even a sensible phrase. Source: me, (former) physicist.
If we can account for every phenomenon that occurs within the scales that we can observe then we can probably claim that physics is complete. Unfortunately it seems that even that might be impossible
No, we can’t claim that. It would still be at best an approximation. Perhaps more accurate and/or precise than what we’ve got now, but an approximation nonetheless. We’ve long ago given up on even getting close to what you propose anyway.
The computer hosts the models. Observing and experimenting with or in digital models reveal physics effectively unattainable with traditional models or real world observation and experimentation.
