http://wolframcloud.com/obj/wolframphysics/Documents/some-re...
(2) The article above already discusses the derivation of the matter contribution to the Lagrangian density, the derivation of energy-momentum tensor, and Lorentz transformations for elementary particles.
(3) Both Hawking radiation and black hole entropy, and connections between our formalism and the AdS-CFT correspondence, are detailed here:
http://wolframcloud.com/obj/wolframphysics/Documents/some-qu...
(4) We do not yet know how to do this.
(5) The quantum mechanics paper above makes, for instance, quite specific predictions about the location of stretched horizons around non-semiclassical black holes.
(6) (7) This we are still working on.
Skimming through it, the links between the specific physics and the general statements about graphs seem to me to be rather weak. A typical section looks like setting up a bunch of very general definitions about graphs, and then suddenly jumping into a standard physics derivation in standard physics notation without even using the definitions you set up a page earlier. In other words, the graph stuff seems to not be doing much of the work!
But I do admit that I only skimmed. This could be an unfair assessment. I hope your papers get a good, thorough peer review.
"The class of problems that can be solved efficiently by quantum computers should be identical to the class of problems that can be solved efficiently by classical computers: More precisely, we predict in this appropriately coarse-grained case that P=BQP, where P and BQP denote the complexity classes of polynomial time and bounded error quantum polynomial time, respectively."
And:
"In other words, in order to maintain a causal invariant representation, the observer must perform a sufficient level of coarse-graining to ensure that any apparent advantage obtained through the use of a quantum computer over a classical one is effectively lost."
Am I missing something fundamental (most probably)? Are you predicting that quantum computers will not be able to, for example, factor RSA keys much faster than todays non-quantum machines?
Nobel laureate Gerard 't Hooft also has a cellular automaton theory and one of his conclusions is: "If engineers ever succeed in making such quantum computers, it seems to me that the CAT is falsified; no classical theory can explain quantum mechanics." By "such quantum computers" he means computers that can run Shor's algorithm. "...but factoring a number with millions of digits into its prime factors will not be possible – unless fundamentally improved classical algorithms turn out to exist."
> no classical theory can explain quantum mechanics."
Not sure I can agree with 't Hooft on this. A GR-based theory with closed timelike curves can easily have particles travelling through time to interfere with themselves, and thus reproduce the quantum phenomena like the double-slit experiment. There's been some work on this:
https://www.reddit.com/r/Physics/comments/1gjekn/the_logic_o...
[warning: uninformed tangent]
A more optimistic interpretation could be that quantum & non-quantum machines will be similar because we have huge leaps to make in non-quantum computer architecture.
This is strictly a theoretical thought-experiment for me, but it has always intrigued me that quantum computers sort-of model the problem itself in the hardware circuit & shove a bunch of qubits through it.
In digital computers, we mostly model Boolean logical structures & then, in software, translate our problem into that Boolean logic. This translation into discrete steps places a limit on the theoretical efficiency.
However, perhaps there is room in analog computing hardware to more closely model specific types of optimization problems & then shove a bunch of electrons through it (shouldn’t the electrons follow the path of least resistance?).
Ah, good point.
Though I was more thinking of Shor's algorithm and Grover's algorithm that tells us the theoretical expected performance that could be achieved with quantum computers. Normally these are described as showing the speedup provided by a possible quantum computer (in relation to non-quantum computers).
So, when reading the Wolfram Model paper I cited, I read the statement regarding quantum computers as dismissing the possibility of achieving qantum computers capable of realising Shor's and Grover's.
But one could of course read it in a flip-side way, that there are algorithms out there to be discovered that achieves the same lower bound complexities on non-quantum machines.
Considering that the Wolfram Model is all about graphs and cellular automata, the statement should probably be considered not based on a RAM complexity model, but something like PRAM that considers parallelism.
Congratulations, you've rediscovered quantum annealing!
Every physicist knows that if you want good criticism, you need to go to people with relevant expertise. That's what peer review is!
However, rarely are arxiv publications accompanied by such fan fare.
Specially for papers that claim new or bold things.
Why didn't you wait for approval of your HN comment?
1. a rebranding with improved documentation / learning resources for using those features (hey, documentation is hard! discoverability matters!), and
2. a set of really impressive rendering algorithms for visualizing these sorts of systems. (hey, visualizing mathematical objects is quite substantive! I'll happily pay good money for "low-effort pretty charts"!)
I addressed in the companion thread why I don't think this is particularly likely to result in "a new type of physics": https://news.ycombinator.com/item?id=22866284
Mathematica is good software. Pre-wolframengine I did shell out the $2K for Mathematica because it contains best-in-class implementations of some important algorithms. A high-quality reimplementation that matches Mathematica's performance would take me several years (in an area where I have a phd). Wolfram Research employs smart folks and lets them spend their time writing really high quality code, and the only way to access that code is by calling Mathematica's built-in functions.
But just because the goal is perhaps a bit grandois and the presentation definitely breathless doesn't mean there's "nothing of substance".
[1] https://www.wolframcloud.com/obj/wolframphysics/Tools/guide-...
Building a more general tool can sometimes solve a specific problem than trying to tackle the specific problem directly.
I also think you're missing the forest for the trees here. There are many general relationships in physics that are spontaneously appearing in the structure of Wolfram's hypergraphs. That's interesting enough on its own to be worth further research.
In one sense, this shared structure shouldn't be surprising, because it's often harder to not make something Turing complete, so in a way I expect a lot of shared structure between physics and various general computational models. On the other hand, it's getting harder to squeeze more progress out of traditional approaches, so shrinking a computational model to exactly match physics on long timescales is a unique attack vector worth exploring.
I have an unfounded suspicion that there exists a simple algebra akin to a continuous geometric algebra that allows all of physics and only physics.
Something that's bothered me for years about contemporary physics is the use of constraints "on top of" a general purpose algebra over the infinite precision real or complex numbers.
Mathematicians would argue that it's all "equivalent", but to me it feels arbitrary and in a sense missing the point. The final theory whatever it is, shouldn't sound like "everything except almost everything leaving one thing". It should sound like "this one thing only, that can be no other thing".
A friend of mine once put it this way: Ask a mathematician to describe a Rubik's Cube and he'll start with the space of all possible transformations, whittle it down to some space of discrete modular transformations by throwing out all other continuous and infinite transformations, then by throwing out even more transformations eventually wind up with a set of rules that matches a Rubik's Cube. If you ask him to draw what it looks like he'll start spouting about how that's impossible and you just need to "learn the maths", pointing at a stack of textbooks.
Modern theoretical physics has the same problem.
> If you can find any other view of the world which agrees over the entire range where things have already been observed, but disagrees somewhere else, you have made a great discovery. It is very nearly impossible, but not quite, to find any theory which agrees with experiments over the entire range in which all theories have been checked, and yet gives different consequences in some other range, even a theory whose different consequences do not turn out to agree with nature. A new idea is extremely difficult to think of. It takes a fantastic imagination.
Right now I'm toying around with a particularly mathematically elegant model with (IMHO) incredibly beautiful "symmetry" in the sense that the equations are both trivially simple yet capable of producing a rich particle zoo, but still limited to a small finite set. My problem is that I'd need a few petabytes of memory to play around with it sufficiently to see if it passes the basic tests.
I'm hoping Moore's law will allow me to run some simulations before I die of old age...
It’s $5M/mo to rent 1 PB of RAM on EC2 and $21,000/mo per PB in S3.
Conceivably, your dreams will be possible in a decade — they are feasible, but likely too costly now.
Best of luck!
I will quote you with this amazing analogy. Thank you!
https://www.wolframphysics.org/technical-introduction/potent...
Languages are just packaging. In order to have content, you have to nail down specifics, and here the choice of language can be useful because the specifics might be more naturally expressed in some languages than others. But Wolfram hasn't begun this journey.
...
also,
> In our previous paper[1], we formally introduced the Wolfram Model[2] - a new discrete spacetime formalism in which space is represented by a hypergraph, and in which laws of physics are modeled by transformation rules on set systems - and investigated its various relativistic and gravitational properties in the continuum limit, as first discussed in Stephen Wolfram’s A New Kind of Science (NKS)[3]. Our central result was the proof that large classes of such models, with transformation rules obeying particular constraints, were mathematically consistent with discrete forms of both special and general relativity
https://www.wolframcloud.com/obj/wolframphysics/Documents/so...
1. make a set of dynamical rules that matches general relativity in the low energy limit, such as recovering Lorentz invariance and the Einstein field equation (this is supposed to be the easiest part -- without at least doing this, a theory of everything is worth less than the graph doodles in my middle school notebooks)
2. demonstrate that you can add something that looks like matter
3. reproduce effects that we know have to appear in quantum gravity in the semiclassical limit, such as Hawking radiation and black hole entropy
4. demonstrate that you can add matter that behaves like the Standard Model
5. make specific predictions that we didn't already know from purely semiclassical considerations
6. find a way to verify those predictions
7. have the predictions actually be correct upon verification
These 7 steps are hard, which is why nobody has managed to do them. But it looks like Wolfram hasn't even bothered to start on step 1. His new book is just hundreds and hundreds of pages of pretty graphs and big words. It's more akin to a reformulation of the foundations of mathematics than a theory of physics -- and it's not a particularly good one, at that.
It's the same complaint I have about category theorists trying to do applied physics. (And category theory is a much more powerful language than Wolfram's!) Yes, you might have an incredibly general language, with which you can talk about vast swaths of possible physical theories. But we already had way too many possibilities using ordinary mathematics! We need to narrow down on specifics, not muddy the waters by making things even more general. I mean, it's like trying to rescue a startup by translating the documentation into Esperanto.