In other words, "If you believe my unproven theory of physics, and also had access to an unavailable amount of computing power, there might be a way to go faster than light."
Most scientists take a full stop at "my unproven theory of physics". He has yet to come up with testable predictions. Let alone trying to test them. Only then there might be a point in listening to the rest.
Or call it a mathematical model. It’s possible to work within a model and establish truths that follow within it as verifiably true assuming the conditions of the model. That’s actually a pretty interesting way to work in mathematics - ie whether you’re adding the point at infinity in complex analysis or not makes the topology similar to a sphere or plane, respectively.
Stephen Wolfram is creating computational models. It’s a natural evolution of reasoning about the universe with the potential to ask if the structure of the universe is computational itself.
Theory exists independently from any necessity to verify it, per se. I don't think he's ever said anything like "this is a theory that can be used to predict the dynamics of material reality".
Hypotheses, conjectures, speculations (however baroque) exist independently. The question is: what is needed for them to become 'theories' in math or science. A basic test is comparison to agreed-on facts. Prediction is considered to be a strong test because it uncovers -new- facts. Else: what's the point?
> Most scientists take a full stop at "my unproven theory of physics"
Not convinced that's true. Considering how many physicists still keep talking about String Theory, even though it hasn't produced a single testable prediction after 30+ years.
> hasn't produced a single testable prediction after 30+ years
Not completely true. It is able model some aspects of quark gluon plasma. [1] Not a high energy theorist myself, but this is the retort some of my friends would give. It also is well motivated by an entire human history's worth of experimental data which any new theory needs to reproduce. Wolfram fails even to show that this is the case for his work. Note: I'm also not a "true believer" of string theory, but comparing it to Wolfram isn't fair.
> Not convinced that's true.
Besides making a point about string theory, do you really have a reason to believe that? I know many high energy physics folks myself and work with some of them. I have never met someone that does this professionally that has given Wolfram's theories a second thought.
> He has yet to come up with testable predictions. Let alone trying to test them. Only then there might be a point in listening to the rest.
He is not presenting this as a scientific theory. This is a keynote speech for NASA folks. Just like science fiction is not science, it may still inspire scientists and be worth listening to IMHO.
> To give a preview of why doing this might devolve into an “engineering problem”, let’s consider a loose (but, in the end, not quite so loose) analogy. Imagine you’ve got molecules of gas in a room, all bouncing around and colliding with each other. Now imagine there’s a special molecule—or even a tiny speck of dust or a virus particle—somewhere in the room. Normally the special molecule will be buffeted by the molecules in the air, and will move in some kind of random walk, gradually diffusing across the room. But imagine that the special molecule somehow knows enough about the motion of the air molecules that it can compute exactly where to go to avoid being buffeted. Then that special molecule can travel much faster than diffusion—and effectively make a beeline from one side of the room to the other.
Of course this requires more knowledge and more computation than we currently imagine something like a molecule can muster (though it’s not clear this is true when we start thinking about explicitly constructing molecule-scale computers). But the point is that the limit on the speed of the molecule is less a question of what’s physically possible, and more a question of what’s “engineerable”.
This is posed as a computational resource problem, but it strikes me as an information problem.
How do you know where the aggressor molecules are and what their paths (i.e. future states) are?
Perhaps it’s possible to know the very local conditions and dodge an imminent collision, but does that generalize to arbitrarily long paths? Can I make it to the other end of the room, dodging only the molecules right in front of me? Or can I set out on a path from the beginning that has no solution in the end because it results in an unsolvable state?
And if the only way to know is to know the full state of the molecules that may affect my journey, beginning to end, doesn’t their state have to be known at the outset of the journey? If the information about their state itself has a speed limit, and if their state is not fully observable or fully deterministic, what sort of computation can defeat that?
More, it betrays a very simplistic view of physics.
How does the special molecule move? By magic? By willpower? By an internal combustion engine?
It needs some way of changing its course. Molecules don't have such a mechanism, except for bouncing off of other molecules.
And, how does the molecule know where the other molecules are? It's psychic? Lidar? Radar? How? What's it's energy source for emitting whatever it has to emit to be able to gather the information that it needs?
The analogy is, if we take a superficial knowledge of physics, and don't actually think about the details, we can construct a wonderful-sounding-but-not-actually-possible scenario. That's perhaps an accurate analogy for what Wolfram is really proposing.
It is actually computationally quite simple -- just follow Maxwell's Demon, it was already on it's way across the room to do the whole door closing thing, so it should be able to figure the path for you.
This special molecule of Stephen's is essentially a Maxwell's demon (it could use that information to open or close the door by choosing appropriate collisions, or simply act as the gate itself). There's a lot of literature about that.
Actually Stephen's special molecule is more powerful because it's omniscient. Ordinary Maxwell's demons just see fast or slow molecules coming at the gate and act accordingly. This one knows the momentum and position of every other particle it needs to know something about, which can be peculiar if you don't think about uncertainty.
> This is posed as a computational resource problem, but it strikes me as an information problem.
I thought the point of the gas illustration was to show how the assumption there's an information problem (i.e. heat, second law) is actually not correct.
That it only looks like an information problem and it's really a computation problem.
The theory being that if you can compute were the molecules are going to be, from the initial state or from interactions you have already learned from, then the motions don't appear random any more. There are no surprises; you have "decrypted" the apparently random movements.
It's just to illustrate the idea, and an immediate objection would be "but we can't know everything to that much detail".
That is addressed by a more subtle version of the argument, which says: Although you don't know all the motions precisely, your ability to compute motions from the information you obtained so far gives you progressively increasing knowledge about motions locally or which you recognise as related, and causes "regions of effective coherence" to expand. It's effective coherence not actual coherence, because the molecule motions don't change, only the precision with which you can anticipate some of them as well as relationships between them. What would have appeared random, now with the benefit of some prior information and computation resolves gradually into local clusters of more predictable related motions, even if you don't know every motion accurately. With the result that the effective fluid properties change, so your ability to "swim" through the gas changes.
In the 2d closed box model, with perfect balls and perfect interactions (i.e. a mathematically perfect simulation) it's plausible that this may work perfectly. That is, if you have your own "special" ball and it undergoes a number of collisions and you get perfect measurement of those collisions, eventually you end up with enough information to model the contents of the rest of the box. If in that model you can dynamically adjust something about the collisions of your "special" ball, for example changing the ball's shape, mass or radius, it's plausible that can be used to travel anywhere in the box much faster than diffusion, but only if you have the information up to that point and excellent computation - which might be irreducibly hard computation for a reasonably sized box.
> an immediate objection would be "but we can't know everything to that much detail".
No, the immediate objection would be "but it's physically impossible to know everything to that much detail, because you don't have enough bits of storage[0], and also because of Heisenberg's uncertainty principle". (Both objections are suffient on their own to make this not work except possibly for a homogenous spherical molecule-shaped unphysically-light and -compact hypercomputer in a frictionless vacuum.)
0: That is, it's physically impossible to pack enough bits to describe a cloud of gas onto a storage medium massing significantly less than the entire cloud of gas.
Inside the computer. That's what makes it a computational reducibility question and not a measurement information-availability objection.
(Also: For a twist, assume you have a quantum computer and they are quantum balls.)
> Heisenberg's uncertainty principle
This raises questions, certainly, but the answers aren't obvious when talking about repeated interactions with the many particles. In the box model, the balls are inevitably entangled with each other at the position-momentum level due to their collisions, even if that entanglement is undetectable in an analogous way to how their motions appear "random" classically.
Heisenberg does not apply to each ball independently when they are entangled. In this box model, as your little computer/mind/demon accumulates information-in-principle from many interactions, in addition to classical information it couples to that entangled state, and the independence of Heisenberg limits dissolves because they aren't really independent.
(Also: Once you invoke Heisenberg, you've also invoked quantum particles in a box self-interfering. In a box that reduces the amount of information you need to represent a single particle's state to an integer, bounded if the energy is bounded. I'm not sure if that also applies to multiple particles interacting chaotically.)
> except possibly for a homogenous spherical molecule in a frictionless vacuum.
Well, the model actually is about homogeneous spherical molecules, and vacuum at the molecular level is frictionless, so that's ok :-)
> the particles are inevitably entangled with each other
That increases the information content, from O(N) for N particles to (worst case) O(2^N). Using a quantum computer at best reduces that back down to O(N) qubits.
> the model actually is about homogeneous spherical molecules
I don't think electron orbitals are spherical enough for that, much less nuclei or polyatomic molecules, but edited anyway.
> That increases the information content, from O(N) for N particles to (worst case) O(2^N).
Classical (model) molecules have infinite bits of information: Their motion parameters are "analogue", which you can think of as real numbers, or infinite precision numbers.
For a digital computer, that takes infinite bits unless you know of a constraint upon them.
You can't call that O(N). And you can't say they have mass proportional to that kind of information either, because that would be infinite mass.
The quantum molecules are in a bounded box. Individual eigenstates are constrained by quantum mechanics in a box into bound states, which are countably enumerable as integers. If you have an upper bound on the energy of the entire box contents, there's a maximum integer required, therefore finite bits to encode an eigenstate.
The coefficients associated to each eigenstate in the general wavefunction are complex (and therefore infinite bits), while subject to various constraints, but they are unobservable. Observations select among eigenstates, each of which is represented in finite bits.
So is it infinite (like the classical model) or finite?
But observation is meaningless in the "special ball is a quantum computer" model. How much information does the "special ball" need from its environment, if it's allowed to entangle with that environment, to outsmart the quantized chaos around itself? Qubits linked to physical measurements and actions are full of paradoxes arising from the mathematics, which makes thought experiments useful. Where does the computation even take place, given that entanglement makes qubits non-local? In the special ball, or in all the balls it's entangled with, affecting them all subtly? I don't think this information question is simple enough to hand-wave as O(N) or O(2^N).
Being omniscient this special molecule can tell which identical molecule is which in the gas, that's some interesting physics.
Of course it can also predict the final states of collisions between other molecules. Even when that information just doesn't exist in the perfect a priori knowledge about the system, which is something that if this special molecule could obtain somehow and then store for later use should violate half a dozen theorems or so.
Really this could make some sense if we were talking about an ideal gas of classical particles that obey deterministic mechanics, but then not even the special molecule would be able to determine the initial conditions with sufficient precision to make useful predictions, beyond a short path and a few collisions in the system.
> it can also predict the final states of collisions between other molecules. Even when that information just doesn't exist in the perfect a priori knowledge
Obviously the special molecule is a thought experiment to illustrate an idea under certain simplifying assumptions and extreme parameters, to understand the consequences. Nobody expects to make one.
And you are doing a proper job of arguing why it cannot work, as you are supposed to with a thought experiment.
But... it's not correct to reason that "it can't predict" when the "information just doesn't exist [...] a priori".
If the special molecule senses, computes and reacts entirely in the quantum realm itself, then its processing will be entangled with those other molecules.
Despite the absence of a priori final states, the special molecule is, in principle, able to select an entangled reaction to those final states anyway.
It's a bit like saying "I don't know if particle X will move to A or B later (and particle X hasn't decided either), but I can prepare myself into a state where if X moves to A then I will already be at A', and if X moves to B then I will already be at B'".
And if being at A' when X moves to A, or B' when X moves to B, means that X can't actually move to A or B, that entangled reaction will affect X so the question of A or B doesn't even arise in the first place.
"Most scientists take a full stop at "my unproven theory of physics". He has yet to come up with testable predictions. Let alone trying to test them. Only then there might be a point in listening to the rest."
This is dumb.
Einstein's theories were not proven overnight and many were skepticals at the time.
Let's see. Einstein published his general relativity paper in 1915. One of the things it explained was the precesion of Mercury, but that was already known - it wasn't a prediction or a test. When was the observation of the sun bending starlight during a solar eclipse? 1919 - and Einstein proposed the test. He found ways to test the predictions rather quickly.
Einstein's theories were based on existing experimental results. In fact for Special Relativity he merely stated what must be true for the Michaelson-Morley experiment to fail to show any speed difference with respect to the ether.
Lorentz and other physicists had already derived a set of equations(called Lorentz transformations) that must be true given the experimental failure. But they considered it unthinkable that the speed of light could be constant in all inertial reference frames, so they thought those equations were wrong or that there was something they were missing.
The only thing Einstein did in that situation was come in and say "hey what if that unthinkable thing were actually true?"
Contrast this with Wolfram's article, where he's postulating the existence of an entire kind of physics without any experimental or phenomenological basis. The comparison is without any basis.
A very Stephen Wolfram article. As usual, if you assume all his unproven priors (ie, reality is actually a hypergraph with well defined update rules, the hypergraph has premade nonlocal 'long threads' in it) and go along with his redefinition of the speed of light as the speed of causality then the article makes perfect sense.
Where the trouble starts is that there seems to be no evidence whatsoever to support the axioms, and also no way to actually measure the predicted effects. It is not so different from saying "There might be a godlike being out there that can just teleport us anywhere we want, but we have no way of contacting it or even of being sure it exists". A cool theory, but until any proofs or falsifications come along it is indistinguishable from science fiction.
But is still worth noting. Science tends to be pretty rigid, and often dismissive of outlandish theories because participants in the field are too close to 'socially accepted facts'. Which as we know from human existence - humans have small minds due to social conformity.....
Mind expanding ideas are - because they help the mind to make connections in the future in which they involved. The field of science contains numerous personality types, some of which are creative, some of which are analytical. It is often worth the analytical (who must see data) to entertain those with creativity or intuition to make the jump - since often data does not lead to leap insights.
Incremental science happens because of data; leap science happens because of creativity and intuition to explore the areas data hasn't 'gapped to'. And it is the difference when 'the data does not yet lead there, so we can't think there' that I refer to for social conformity.
> almost all theories of this ilk tend to be dismissed because they break the laws of physics.
Actually no.
Theories of this ilk which demonstrate their consistency with laws of physics to the level of observations already made and significantly beyond, tend to end up studied more, by more people.
Especially ones that take an unusual angle, and end up deriving existing laws of physics almost as a surprising side effect. It suggests a useful insight.
Even better if they take an unusual angle, predict some differences from assumed existing laws but only in unusual circumstances nobody has tried to observe so far, and are consistent with those laws in areas already observed.
Or ones which explain existing laws better than current explanations. Notably the inconsistencies between general relativity and quantum mechanics mean that anything which can explain both at the same time and give correct answers to both is quite interesting.
The ones that get dismissed quickly are those which aren't consistent with laws of physics that are already assumed, especially at the level of existing observations.
I'd like to know if you can give some evidence in the past (say) 20 years that science has discarded or delayed acceptance of a good theory because of 'social conformity'.
I'm talking at the individual level - humans are socially pressured to conform to their field of study current beliefs (in any field). It takes long periods of time for ideas that go against the grain to bubble up to become 'mass conscious' within a field. Especially in areas requiring higher mathematics where practitioners can feel inferior.
Which I'm saying I don't believe. Show me recent examples where it happened, I asked.
> Especially in areas requiring higher mathematics
I just don't recognise this at all. Why do you say this? The journals are full of new discoveries, my experience with mathematicians is they're a very open and accommodating bunch (ok, it's not my field, but still)
I'm not sure if it meets your 20 year criteria, but science believed that peptic ulcers were the result of over production of stomach acid when one researcher proved that a bacteria was the cause of the majority of them. He had to buck general scientific consensus
My understanding was that he provided the strong evidence (by experimenting on himself), and things changed. If he'd provided the evidence then been told to take a running jump by everyone else, I'd say you have a point.
Older: Wegener's theory of Continental Drift was dismissed for around four decades before it was reinvented by someone else and accepted by geologists.
Recently: transgenerational epigenetics was considered a violation of the Central Dogma of biology, but since then evidence has piled up and it's now considered a legitimate area of research.
The jury is out in high energy physics where SUSY and string theory elbowed some (possibly) more interesting competitors out of the way. It's too early to tell how that will work out - but it is clear that some approaches get a lot more funding and attention than others, and this seems to be for political rather than objectively scientific reasons.
If you would think for a moment about the time scale over which these things develop ("one funeral at a time") you'd recognize how absurd a question this is.
This comment displays yet again the conflation between "exploratory model" and "explanatory model".
This model does not purport (in its current iteration) to explain material reality. It purports to generate a theory of physics without going so far as to claim that that theory coincides with the dynamics of our universe specifically.
It is taking the idea of "physical model" and abstracting it to see how flexible of a theoretical substrate can be used to demonstrate certain behaviors within the defined set of axioms which we would expect out of any model of physics, i.e., causality, limits of information propagation rates, etc.
In short: it is not a theory of the physics, but just a physics.
Without modelling the real world, and in describing it's own rules, I think you might better describe it as a branch of mathematics, and not a physics, no?
Superstring theory is considered a branch of physics but it's in a similar position (not saying there's anything of value in the wolfram article, just saying sometimes purely theoretical frameworks can be called physics even though they have not reached a predictive or even postdictive state yet)
Are you sure? Because https://writings.stephenwolfram.com/2020/04/finally-we-may-h... definitely implies that he believes his "hypergraph with update rules" model is how the universe actually works and what remains is to find the particular structure and update rules that describe our own universe.
Don't get me wrong, I think it's a very interesting model that is quite flexible and could be used for a great many things. But if we're moving the goalposts from "can we go faster than the speed of light in our own universe" to "can we go faster than the speed of light in a universe I constructed from arbitrary rules" then the result becomes much less interesting.
It'd be weird if the guy forwarding a theory didn't believe in it. An I think there is room in between believing a framework can explain things and believing it is.
> definitely implies that he believes his "hypergraph with update rules" model is how the universe actually works and what remains is to find the particular structure and update rules that describe our own universe.
This goes back to his obsession with cellular automata. There's an outstanding amount of references to "I" in your link. Great works of science usually reference the works of others...
It makes sense that the first steps toward developing a sufficiently robust theory is making sure your model can recreate the various phenomena that you are interested in modelling, no?
The goal is to get to a theory that reflects the behavior of the universe, and figuring out how to emulate the various idiosyncracies inherent in how the universe evolves over time (finite speed of information propagation, etc.). Finding testable aspects of the model is only possible after actually applying the theory, seeing where it falls short, and identifying ways to validate ambiguous conclusions.
> redefinition of the speed of light as the speed of causality
Since when this is redefinition? As far as I understand, this was always the definition. In fact, calling it the speed of light was always a bit misleading, since, first off, actual speed of light depends on environment, and second, there is nothing really special about light. It's just under ideal circumstances it can propagate with the maximum possible speed, i.e. the speed of causality. Light isn't fundamental for the laws of physics, causality is.
Haven't read the article yet, so I don't judge the merits of his proposal, but unproven priors is exactly how science is built. A scientific hypothesis is taken without proof, then you derive its consequences and try to falsify them.
What Wolfram has to do is to replicate known physics at a minimum and ideally derive new testable predictions that we can attempt to falsify.
If he does that his unproven priors will become the new "taken for granted" priors.
That would be nice and he mentions that he can already replicate a few of the observed effects from relativity. But my point was exactly that he has (so far) not generated any testable predictions. I'd love it if he did.
What do we do with a theory that conforms to every measurement ever made, but whose predictions aren’t testable? After all, we’re already there. We’ll never measure the interior of a black hole, for example. I think our theory selection criteria needs work.
> We’ll never measure the interior of a black hole, for example
Don't say 'never'. You can say we are pretty confident that the interior of black holes can't be measured now or in the future, given our current understanding. But science is not made of absolutes.
> What do we do with a theory that conforms to every measurement ever made, but whose predictions aren’t testable
Then it's kinda worthless, at last for physics. If two explanations agree with all observations (so far) that means they are completely interchangeable. You might as well use Occam's Razor and pick the simplest one. Until such time we find experimental differences, then we can compare again.
The mainstream theory is that whatever reality is, its consequences on measurable length-scales are as-yet indistinguishable from an almost-everywhere-continuous medium. (I.e. away from black hole singularities.). Until we have the ability to measure not just deviations of reality from theory, but deviations from what any continuum theory might predict, the question of whether hypergraphs have the correct asymptotic continuum behavior is largely moot. Wolfram has been pushing an atomistic program of cellular automata as models of physical systems for many years. They are beautiful, but so far they are only useful insofar as they approximate continuum mechanics-- which is to say, they are of limited application.
The thing about continuous media is that they involve dynamics on all length scales: .1 meters, .1 nanometers, 1e-10 nm, etc. Because of wave-particle duality, length scales and energy scales run inversely: a low energy experiment just does not exhibit any measurable dependence on extremely short-range behavior of the universe. Only high-energy experiments have a wavelength short enough to be sensitive to this unknown sector. Low energy physics is “well understood” in the sense that any experiment with a modest number of component particles can be totally predicted from theory, to the limits of experimental accuracy. Granted that many real-world problems involve stupendous numbers of particles, and exhibit challenging-to-explain emergent behavior: but this is not evidence of unexplained fundamental phenomena, just of the limits of our mathematical insight into finding good abstractions for many-body problems, and evidence of the limits of our computational power to try and work around the lack of good abstractions.
It is known that the most generous interpretation of current theories is that they are self-consistent to arbitrary high energies (renormalizable is the term). That does not mean they are consistent with actual reality, just with themselves.
So... hypergraphs are a big lift, an unneeded multiplication of entities. Until an experiment reveals non-continuum behavior of space-time, what we have here is a solution to a non-issue.
I just wanted to say that this is a really fantastic explanation of the current state of the art, particularly the way you state the high-level motivation for ultra high energy colliders. Of course, without a few orders of magnitude gain in acceleration gradient, the necessary collider size is impractically large, so these sorts of questions may not be investigated for a while.
If I can take a shot at this, there are broadly two: the quantum mechanic explanation and the relativity explanation. But we seem to only be talking about relativity.
Relativity explains a couple of counter intuitive things that we actually see:
1. Apparently there is no particular velocity that can be called absolutely stopped or special in any way: every velocity is just as valid as every other.
2. Observers moving at different velocities disagree on 3D distances and time intervals between events.
3. But they all agree on the spacetime distance between events. Which is to say, there is a simple formula that resembles a distance formula in 4D where one of the dimensions is time.[0] We know that using this formula, all observers at all velocities get the same result.
gravity is not being discussed but relativity addresses it as well.
So relativity explains actual (but counter intuitive) observations. If we had the simpler Newtonian universe then we could fly around at unlimited relative speeds and time would flow unambiguously at constant rate and be completely unconnected to distance/space. But by direct observation, we see we don't live in such a universe.
If causality could percolate at unlimited speeds then we would not observe any these things and the formulas for relativity would not work but the formulas of Newton would. For one, there would be infinite frames of reference for which you arrive before you depart and these frames of reference could use faster than light travel reverse casualty.
I know of one other non-mainstream explanation from Max Tegmark: the mathematical universe hypothesis says reality is actually mathematics.
I'm not sure your explanation is an alternative explanation of what reality is. You've laid out some characteristics and consequences, but haven't described what's at the bottom of it.
I've heard that matter is a consequence of quantum field excitations, but what is a field? From the little bit I've read it sounds like mathematics again.
The concept of a field can be described using mathematics but does that really mean mathematics is actually what the universe is made of?
Suppose for example we found that protons, neutrons, and electrons really were fundamental. Their behavior can be described with mathematics but wouldn't we say it's still the elementary particles that our compose our universe?
Tegmark's theory says exactly that - the particles are ultimately mathematics. Not that they can be modeled with mathematical methods, but that they are actually constructed from mathematical structures.
What does the mean, though? Mathematics as we understand it is an abstraction. If the universe is fundamentally abstract, what breathes fire into the models? Consciousness?
Modal realism. A mathematical structure is "real" to its conscious inhabitants (if any), and merely an abstraction from the perspective of those who are not, i.e. the inhabitants of other mathematical structures.
All fundamental theoretical physics starts by building a model idea and exploring what the possible consequences are in a mathematical way.
The goal is to model the real world, but it's far too difficult to go straight from a fundamental model up to the world observations to find out if the model works.
Doing that "work out the consequences" work can take decades, and a lot of people.
So models are built, explored, their consequences worked out, and if they match something interesting in other more well-established theories, then the models are looked at with more interest and developed further. If not, the models are tweaked or thrown away.
You could call it a branch of mathematics, but in a sense all theoretical physics starts out that way, so we just call it theoretical physics when the goal is to model observed reality while providing a useful underlying model.
Browse the papers on arXiv.org or any theoretical physics journal and there's a lot of exploratory model-building like this. It's very common.
Graph-space models are also not unique to Stephen Wolfram. Several physicists (paid ones) are exploring these models as an approach to reconciling relativity and quantum physics. In a sense, this is what deriving from observation looks like: We've observed relativity and quantum, and we still haven't figured out how to understand the logical consequences of both together, so exploring theoretical underlying models like this is necessary to understand current observations.
The article's theory is not "philosophical" or "metaphysical" theory where nothing can be tested in principle. He explicitly talks about measurable effects differing from other models, albeit with many difficulties and potential intractibility due to computational limits.
But the point is there are, in principle, observable differences, making it more than just a metaphysical model, and if it's intractable to access them we can't figure that out without studying the model further. Even if we can't, there not being able to may have consequences as well (like the way the Heisenberg uncertainty principle turns out to have logical consequences, not just preventing measurements).
Wolfram seems to have a narcissistic ego that demands stroking, maybe the result of being a child prodigy and the subsequent expectations of those around him, but he seems to yearn for praise and turns salty when he doesn’t get it.
I dunno. Wolfram has earned a bit of self-assurance in my view.
As for the theory itself, I'm in the "wait and see" camp. If it's true or at least on the right path, then it should be generating testable hypothesizes soon enough.
Put another way, say his theory was the same in every way, but instead of purporting to prove the fundamentals of our own existence it instead made the claim that there was a two dimensional world with its own constants and physics and that this other universe existed as much as ours does, but that we could never reach it due to what the foundations of the theory laid out. Then I'd be completely uninterested. At least until we were able to simulate this universe with perfect fidelity in a computer.
But since it's our very existence then it's only a matter of time until the theory generates a prediction that we can use as the hypothesis for real experimentation and then the theory can rise or die. But until then I'm going to try to keep an open mind.
This has been repeated ad nauseum in Wolfram threads for many years. Please let's not go there again. Regardless of what you think of Wolfram, it's low-quality discussion and nothing new will ever come of it.
Dang, I’d say it’s relevant because the actual article contains complaints from Wolfram as well as bashing the concept peer reviews.
There’s a similar issue with the ABC conjecture proof. You just can’t dump your magnus opus on the scientific academic community and then expect everyone to realize your genius and rubber stamp it.
Peer review is at the core of science. Whatever value Wolfram’s theory has, until it can move from backpatching and curve fitting into making testable predictions, then it will, like string theory, remain in the realm of pure mathematical model and as you may know there’s a nigh infinite number of parameterizable models you can fit, but if they don’t make any new predictions, there’s no reason to adopt them.
Every Wolfram article contains provocative Wolfram-statements. It's our job to ignore the provocations and talk about the interesting bits. There usually are some.
If information is related to energy (as it appears to be), then saying that FTL would require more processing power than can be embodied in the universe is equivalent to saying (as some current theories do) that it would require more energy than can be harnessed in the universe.
There was a discussion about dimensionality, but I couldn't decipher -- is there something intrinsic that pushes this model to look like three dimensions? It looked like any dimensionality is equally at home in this model, and generally a random infinite hypergraph would require infinite dimensions to represent as a manifold (or at least I'd think so after a quick think about it). So that we ended up in a universe with three seems quite arbitrary. If Wolfram can find a simple non-arbitrary explanation of why three dimensions, that would be a big step.
The concept of updating rules underlies this model. Each rule determine the evolution of the hypergraph which is space itself, much like a cellular automata. It seems that some rules have the property that as "times goes by" the hypergraph converges to a manifold with dimension d. One can estimate the dimension of such hypergraph using, for example, the growth of the volume of balls[0].
It also seems that this concept is very generic, and many properties of the model do not depend on the dimensionality neither on the manifold or the rule itself.
Because this concept is so generic, one hopes that there is a rule that the hypergraph converges to d=3 as in our world. This would also raise questions on why in the very early universe there was a "inflationary" phase.
He hasn't derived 3 dimensions from this framework yet... The whole program is very interesting, it might find general laws not only for Physics but for many phenomena, but I feel like Wolfram has jumped the gun on connecting Physics to it...
Particularly, I think that quantum non-locality might be evidence that fundamentally 3 dimensions is just an emergent property, but that has yet to be derived from this hypergraph framework...
I think it's pretty good. These questions have been keeping me awake at night for the last 30 years or so, and after one big false start that I sadly realized was just a complicated method that was identical to QM, I have come to something pretty similar to this as the next approach to check out. It's pretty cool to see that others are looking in this direction too.
I'm nowhere as smart as Wolfram, nor is my new approach anywhere near as developed, but the dimensionality is the thing that has been bugging me since the beginning for my own thing as well. Why three dimensions? Seems like if we can show a reason for that without too much hackery then we may be on the path to enlightenment.
Wolfram's mode of operations - independently wealthy, publishing things he's interested in on his own terms, in formats and spaces he chooses to - is far closer to how the science of yore operated. Ultimately his ideas will live or die on their merit, not because he did things unconventionally.
Given their lack of any ingress into mainstream scientific acceptance, it's fair to say then they have died, merit-wise - or are only kept alive outside of science while he is able to command the esteem of programmers and the like in fora like this.
Wolfram's theory was already very politely but firmly shown to be wrong 20 years ago, by people who took a look into it. Scott Aaronson for example. https://arxiv.org/abs/quant-ph/0206089
If i understand it correctly (which is doubtful), in section 2, the cellular automaton conjecture is dismissed because 110 as a computer suffers from exponential slowdown.
>"To prove that 110 is NP-complete, what is needed is to show that Rule 110 allows efficient simulation of Turing machines"
But if the universe is a 'computation', then the efficiency of it doesn't really matter right?
Similar to creating a Blender rendering, it doesn't matter how long each frame takes to render compared to any other frame, as long as the observer sees a smooth sequence of images.
If you have a simulated virtual world completely isolated from the real world, does it matter if you simulate it at normal speed or 1/1,000th speed to the ones inside the simulation? I think not.
We already see this with existing simulations, though they are of much simpler objects than conscious beings. If I simulate water sloshing in a bucket, it doesn't matter how long the simulation runs, the results are the same.
Now, I may add in short cuts to make it closer to real time to support practical applications which leads to different results, but a slower machine running the same shortcuts will see the same differences.
If I understand correctly, condition 4 (see page 104) no longer holds. The new theory, in contrast to the old theory (see bottom of page 100), seems to be a multiway system.
I am somewhat surprised that it does not at least as far as I have read in the linked article, explicitly state that this model is 100% consistent with and I assume a consequence of assuming that we live in a simulation.
I.e. it would take a really light editing pass to change the description given of space-time from a proposal about the physics we live in,
to a prescription for a fairly obvious means of building a simulation that runs on some kind of discrete computation engine.
Wait a second. Correct me if I am wrong but does he write that he has a theory of spacetime from that both quantum mechanics and relativity can be derived? Would that not be a slam dunk Nobel prize?
Unless something has changed, he is in the camp of people like t' Hooft that claim QM is really an approximation to underlying classical/deterministic/superdeterminism.
And while that is possible, the trade-offs are usually far worse or harder to explain than the baggage QM brings. Or just based on an incorrect understanding of QM
That's not how this works. Anybody can come up with some random theory, but if it doesn't have testable predictions that can validate the theory, then it doesn't mean we solved quantum gravity. This is the case with Wolfram.
"OK, so what’s the bottom line? Is it in principle possible to go faster than light? And if so, how can we actually do it?"
"I’m pretty sure that, yes, in principle it’s possible. In fact, as soon as one views space as having an underlying structure, and not just being a mathematical manifold “all the way down”, it’s pretty much inevitable. But it still requires essentially “hacking” space, and “reverse engineering” its structure to find features like “space tunnels” that one can use."
Well, unless he shows what he means via rigourous mathematics or a foolproof demonstration, those are words without meanings.
I remember reading that E=mc^2 doesn't say that it's impossible to go faster than light, but rather says that accelerating something from less than the speed of light to the speed of light will take infinite energy.
The subtle difference is that if something just, uh, is going faster than light then everything works out. They're are two implications though, one is that it could never be decelerated below the speed of light and the other is that it'll probably have to be traveling backwards in time.
Making something that goes backwards in time and faster than light (without using infinite energy) is left as an exercise for the reader.
As far as I can tell, Wolfram has not invented a model of physics at all; he has invented a notation for talking about causal systems. It's not clear to me that his "hypergraph" imposes any constraints on what can be encoded. This at once makes it intriguing from a mathematical perspective, and completely useless as a physics theory, in the same way that epicycles can model a planet with an orbit shaped like Homer Simpson's head.
I am not surprised that Wolfram thinks FTL is possible - the real question is, is there anything he thinks is impossible?
Faster than light was never the problem. Einstein's Theories forbid as fast as light, but say nothing about faster than light travel. Of course, one probably must pass y to get to x.
Also, it seems pretty clear that Wolfram does not understand the concept of Warp drive, which is not used to propel the craft, but instead used to warp space to come to the craft, because there is nothing preventing space from traveling faster than light, and, indeed, the expansion of the Universe causes distant galaxies to recede from ours faster than the speed of light. So there you have it, we already have proof of faster than light travel, so we know it is possible.
But if FTL travel is not a one way trip, it will tend to introduce causality issues. Say you're somewhere far away and observe some event on Earth that arrived by the speed of light, like maybe a lotto drawing or who wins a game. You could zip back FTL, arrive before the lotto drawing or the result of the game, and bet on those numbers or the game winner. If you were far enough away, you could observe your own birth, and possibly zip back fast enough prevent that from occurring. The Universe may allow FTL travel, but I doubt it will allow such paradox.
> Einstein's Theories forbid as fast as light, but say nothing about faster than light travel.
Yes it does. This is a basic consequence of the underlying pseudo-Riemannian geometry. In terms of PDEs, the field value at any point is fully determined by the initial conditions on a Cauchy surface within its past light cone.
Quantum mechanically, field operators at spacelike-separated points commute.
> Also, it seems pretty clear that Wolfram does not understand the concept of Warp drive, which is not used to propel the craft, but instead used to warp space to come to the craft
You didn’t read the article. This is addressed at the end, under “What about warp bubbles and the Alcubierre metric?”.
The amount of hate in this thread is so typical HN, somebody should be concerned (oh but we must keep the forum civil). There isn't a single thread of consideration on the topic, only a dogpile of naysaying by anonymous commentariat of dubious credibility. Presented with a difficult read, the comments clearly show nobody here actually tried.
Can a forum of programmers and techies really not fathom a computational approach to physics? Graphs are only a social database to you?
You worship a framework of physics fraught with limitations, missing pieces, and paradoxes, which few of you understand beyond a simplification, and act like the Pope of Quantum Physics.
Disruption huurrrrrr. What a cesspool. You people are techno-sheep.
The knee jerk reactions to so quickly dismiss Stephen is sad.
Here you have someone doing novel explorations of our understanding and unquestionably adding to the total knowledge of our species regardless if he is closer to right or wrong.
I know that Wolfram has a reputation for being a bit of a hack; but in this case, I’m not a good enough physicist to see why. It all appears.. plausible? Although I don’t see new testable predictions, it does look like his theory reconciles quantum mechanics and general relativity and ties it all up with a nice bow. So, if I were a real physicist I think I’d be interested. Maybe part of the problem here is that Wolfram has a reputation for being a jerk, and a bit self important. I’ve spoken to people who saw him give a talk, and he evidently skipped all the other presentations, demanded a massive fee, and didn’t stick around for questions.
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[ 4.6 ms ] story [ 189 ms ] threadAre there any real scientists on this, or is it just a well funded crank site?
Most scientists take a full stop at "my unproven theory of physics". He has yet to come up with testable predictions. Let alone trying to test them. Only then there might be a point in listening to the rest.
See https://www.scientificamerican.com/article/physicists-critic... for more.
Stephen Wolfram is creating computational models. It’s a natural evolution of reasoning about the universe with the potential to ask if the structure of the universe is computational itself.
Not convinced that's true. Considering how many physicists still keep talking about String Theory, even though it hasn't produced a single testable prediction after 30+ years.
Not completely true. It is able model some aspects of quark gluon plasma. [1] Not a high energy theorist myself, but this is the retort some of my friends would give. It also is well motivated by an entire human history's worth of experimental data which any new theory needs to reproduce. Wolfram fails even to show that this is the case for his work. Note: I'm also not a "true believer" of string theory, but comparing it to Wolfram isn't fair.
> Not convinced that's true.
Besides making a point about string theory, do you really have a reason to believe that? I know many high energy physics folks myself and work with some of them. I have never met someone that does this professionally that has given Wolfram's theories a second thought.
[1] https://www.bnl.gov/rhic/news/091107/story2.asp
He is not presenting this as a scientific theory. This is a keynote speech for NASA folks. Just like science fiction is not science, it may still inspire scientists and be worth listening to IMHO.
This is posed as a computational resource problem, but it strikes me as an information problem.
How do you know where the aggressor molecules are and what their paths (i.e. future states) are?
Perhaps it’s possible to know the very local conditions and dodge an imminent collision, but does that generalize to arbitrarily long paths? Can I make it to the other end of the room, dodging only the molecules right in front of me? Or can I set out on a path from the beginning that has no solution in the end because it results in an unsolvable state?
And if the only way to know is to know the full state of the molecules that may affect my journey, beginning to end, doesn’t their state have to be known at the outset of the journey? If the information about their state itself has a speed limit, and if their state is not fully observable or fully deterministic, what sort of computation can defeat that?
How does the special molecule move? By magic? By willpower? By an internal combustion engine?
It needs some way of changing its course. Molecules don't have such a mechanism, except for bouncing off of other molecules.
And, how does the molecule know where the other molecules are? It's psychic? Lidar? Radar? How? What's it's energy source for emitting whatever it has to emit to be able to gather the information that it needs?
The analogy is, if we take a superficial knowledge of physics, and don't actually think about the details, we can construct a wonderful-sounding-but-not-actually-possible scenario. That's perhaps an accurate analogy for what Wolfram is really proposing.
Actually Stephen's special molecule is more powerful because it's omniscient. Ordinary Maxwell's demons just see fast or slow molecules coming at the gate and act accordingly. This one knows the momentum and position of every other particle it needs to know something about, which can be peculiar if you don't think about uncertainty.
I thought the point of the gas illustration was to show how the assumption there's an information problem (i.e. heat, second law) is actually not correct.
That it only looks like an information problem and it's really a computation problem.
The theory being that if you can compute were the molecules are going to be, from the initial state or from interactions you have already learned from, then the motions don't appear random any more. There are no surprises; you have "decrypted" the apparently random movements.
It's just to illustrate the idea, and an immediate objection would be "but we can't know everything to that much detail".
That is addressed by a more subtle version of the argument, which says: Although you don't know all the motions precisely, your ability to compute motions from the information you obtained so far gives you progressively increasing knowledge about motions locally or which you recognise as related, and causes "regions of effective coherence" to expand. It's effective coherence not actual coherence, because the molecule motions don't change, only the precision with which you can anticipate some of them as well as relationships between them. What would have appeared random, now with the benefit of some prior information and computation resolves gradually into local clusters of more predictable related motions, even if you don't know every motion accurately. With the result that the effective fluid properties change, so your ability to "swim" through the gas changes.
In the 2d closed box model, with perfect balls and perfect interactions (i.e. a mathematically perfect simulation) it's plausible that this may work perfectly. That is, if you have your own "special" ball and it undergoes a number of collisions and you get perfect measurement of those collisions, eventually you end up with enough information to model the contents of the rest of the box. If in that model you can dynamically adjust something about the collisions of your "special" ball, for example changing the ball's shape, mass or radius, it's plausible that can be used to travel anywhere in the box much faster than diffusion, but only if you have the information up to that point and excellent computation - which might be irreducibly hard computation for a reasonably sized box.
No, the immediate objection would be "but it's physically impossible to know everything to that much detail, because you don't have enough bits of storage[0], and also because of Heisenberg's uncertainty principle". (Both objections are suffient on their own to make this not work except possibly for a homogenous spherical molecule-shaped unphysically-light and -compact hypercomputer in a frictionless vacuum.)
0: That is, it's physically impossible to pack enough bits to describe a cloud of gas onto a storage medium massing significantly less than the entire cloud of gas.
Inside the computer. That's what makes it a computational reducibility question and not a measurement information-availability objection.
(Also: For a twist, assume you have a quantum computer and they are quantum balls.)
> Heisenberg's uncertainty principle
This raises questions, certainly, but the answers aren't obvious when talking about repeated interactions with the many particles. In the box model, the balls are inevitably entangled with each other at the position-momentum level due to their collisions, even if that entanglement is undetectable in an analogous way to how their motions appear "random" classically.
Heisenberg does not apply to each ball independently when they are entangled. In this box model, as your little computer/mind/demon accumulates information-in-principle from many interactions, in addition to classical information it couples to that entangled state, and the independence of Heisenberg limits dissolves because they aren't really independent.
(Also: Once you invoke Heisenberg, you've also invoked quantum particles in a box self-interfering. In a box that reduces the amount of information you need to represent a single particle's state to an integer, bounded if the energy is bounded. I'm not sure if that also applies to multiple particles interacting chaotically.)
> except possibly for a homogenous spherical molecule in a frictionless vacuum.
Well, the model actually is about homogeneous spherical molecules, and vacuum at the molecular level is frictionless, so that's ok :-)
Edited to clairify, thanks.
> the particles are inevitably entangled with each other
That increases the information content, from O(N) for N particles to (worst case) O(2^N). Using a quantum computer at best reduces that back down to O(N) qubits.
> the model actually is about homogeneous spherical molecules
I don't think electron orbitals are spherical enough for that, much less nuclei or polyatomic molecules, but edited anyway.
Classical (model) molecules have infinite bits of information: Their motion parameters are "analogue", which you can think of as real numbers, or infinite precision numbers.
For a digital computer, that takes infinite bits unless you know of a constraint upon them.
You can't call that O(N). And you can't say they have mass proportional to that kind of information either, because that would be infinite mass.
The quantum molecules are in a bounded box. Individual eigenstates are constrained by quantum mechanics in a box into bound states, which are countably enumerable as integers. If you have an upper bound on the energy of the entire box contents, there's a maximum integer required, therefore finite bits to encode an eigenstate.
The coefficients associated to each eigenstate in the general wavefunction are complex (and therefore infinite bits), while subject to various constraints, but they are unobservable. Observations select among eigenstates, each of which is represented in finite bits.
So is it infinite (like the classical model) or finite?
But observation is meaningless in the "special ball is a quantum computer" model. How much information does the "special ball" need from its environment, if it's allowed to entangle with that environment, to outsmart the quantized chaos around itself? Qubits linked to physical measurements and actions are full of paradoxes arising from the mathematics, which makes thought experiments useful. Where does the computation even take place, given that entanglement makes qubits non-local? In the special ball, or in all the balls it's entangled with, affecting them all subtly? I don't think this information question is simple enough to hand-wave as O(N) or O(2^N).
Of course it can also predict the final states of collisions between other molecules. Even when that information just doesn't exist in the perfect a priori knowledge about the system, which is something that if this special molecule could obtain somehow and then store for later use should violate half a dozen theorems or so.
Really this could make some sense if we were talking about an ideal gas of classical particles that obey deterministic mechanics, but then not even the special molecule would be able to determine the initial conditions with sufficient precision to make useful predictions, beyond a short path and a few collisions in the system.
Obviously the special molecule is a thought experiment to illustrate an idea under certain simplifying assumptions and extreme parameters, to understand the consequences. Nobody expects to make one.
And you are doing a proper job of arguing why it cannot work, as you are supposed to with a thought experiment.
But... it's not correct to reason that "it can't predict" when the "information just doesn't exist [...] a priori".
If the special molecule senses, computes and reacts entirely in the quantum realm itself, then its processing will be entangled with those other molecules.
Despite the absence of a priori final states, the special molecule is, in principle, able to select an entangled reaction to those final states anyway.
It's a bit like saying "I don't know if particle X will move to A or B later (and particle X hasn't decided either), but I can prepare myself into a state where if X moves to A then I will already be at A', and if X moves to B then I will already be at B'".
And if being at A' when X moves to A, or B' when X moves to B, means that X can't actually move to A or B, that entangled reaction will affect X so the question of A or B doesn't even arise in the first place.
This is dumb.
Einstein's theories were not proven overnight and many were skepticals at the time.
Lorentz and other physicists had already derived a set of equations(called Lorentz transformations) that must be true given the experimental failure. But they considered it unthinkable that the speed of light could be constant in all inertial reference frames, so they thought those equations were wrong or that there was something they were missing.
The only thing Einstein did in that situation was come in and say "hey what if that unthinkable thing were actually true?"
Contrast this with Wolfram's article, where he's postulating the existence of an entire kind of physics without any experimental or phenomenological basis. The comparison is without any basis.
That does not mean he is wrong or that you can easily brush all this work away because it is too speculative for your taste.
String theory was also quite speculative.
Doesn't string theory take a lot of flak precisely for that reason?
But it also had a very strong following and sizeable public funds.
Where the trouble starts is that there seems to be no evidence whatsoever to support the axioms, and also no way to actually measure the predicted effects. It is not so different from saying "There might be a godlike being out there that can just teleport us anywhere we want, but we have no way of contacting it or even of being sure it exists". A cool theory, but until any proofs or falsifications come along it is indistinguishable from science fiction.
I say the future generations will be better off for Wolfram having gone down his rabbit holes.
And his wikipedia page has been thoroughly whitewashed, which suggests he is not content with the reputation he deserves.
Incremental science happens because of data; leap science happens because of creativity and intuition to explore the areas data hasn't 'gapped to'. And it is the difference when 'the data does not yet lead there, so we can't think there' that I refer to for social conformity.
Once in a blue moon one of these outsiders turns up something genuinely impressive.
There is no reason whatsoever to assume that is the case here.
Actually no.
Theories of this ilk which demonstrate their consistency with laws of physics to the level of observations already made and significantly beyond, tend to end up studied more, by more people.
Especially ones that take an unusual angle, and end up deriving existing laws of physics almost as a surprising side effect. It suggests a useful insight.
Even better if they take an unusual angle, predict some differences from assumed existing laws but only in unusual circumstances nobody has tried to observe so far, and are consistent with those laws in areas already observed.
Or ones which explain existing laws better than current explanations. Notably the inconsistencies between general relativity and quantum mechanics mean that anything which can explain both at the same time and give correct answers to both is quite interesting.
The ones that get dismissed quickly are those which aren't consistent with laws of physics that are already assumed, especially at the level of existing observations.
What new predictions (ie. not covered by existing theories) does this theory propose that are testable?
> Especially in areas requiring higher mathematics
I just don't recognise this at all. Why do you say this? The journals are full of new discoveries, my experience with mathematicians is they're a very open and accommodating bunch (ok, it's not my field, but still)
Recently: transgenerational epigenetics was considered a violation of the Central Dogma of biology, but since then evidence has piled up and it's now considered a legitimate area of research.
The jury is out in high energy physics where SUSY and string theory elbowed some (possibly) more interesting competitors out of the way. It's too early to tell how that will work out - but it is clear that some approaches get a lot more funding and attention than others, and this seems to be for political rather than objectively scientific reasons.
This model does not purport (in its current iteration) to explain material reality. It purports to generate a theory of physics without going so far as to claim that that theory coincides with the dynamics of our universe specifically.
It is taking the idea of "physical model" and abstracting it to see how flexible of a theoretical substrate can be used to demonstrate certain behaviors within the defined set of axioms which we would expect out of any model of physics, i.e., causality, limits of information propagation rates, etc.
In short: it is not a theory of the physics, but just a physics.
Without modelling the real world, and in describing it's own rules, I think you might better describe it as a branch of mathematics, and not a physics, no?
Don't get me wrong, I think it's a very interesting model that is quite flexible and could be used for a great many things. But if we're moving the goalposts from "can we go faster than the speed of light in our own universe" to "can we go faster than the speed of light in a universe I constructed from arbitrary rules" then the result becomes much less interesting.
This goes back to his obsession with cellular automata. There's an outstanding amount of references to "I" in your link. Great works of science usually reference the works of others...
The goal is to get to a theory that reflects the behavior of the universe, and figuring out how to emulate the various idiosyncracies inherent in how the universe evolves over time (finite speed of information propagation, etc.). Finding testable aspects of the model is only possible after actually applying the theory, seeing where it falls short, and identifying ways to validate ambiguous conclusions.
Since when this is redefinition? As far as I understand, this was always the definition. In fact, calling it the speed of light was always a bit misleading, since, first off, actual speed of light depends on environment, and second, there is nothing really special about light. It's just under ideal circumstances it can propagate with the maximum possible speed, i.e. the speed of causality. Light isn't fundamental for the laws of physics, causality is.
https://youtu.be/msVuCEs8Ydo has a great explanation from the always excellent PBS Space Time, for the curious.
What Wolfram has to do is to replicate known physics at a minimum and ideally derive new testable predictions that we can attempt to falsify.
If he does that his unproven priors will become the new "taken for granted" priors.
Until we can test it, we should avoid calling it a theory.
In the meantime develop it until we can test it. We continue observing until we find something that isn't quite right.
Don't say 'never'. You can say we are pretty confident that the interior of black holes can't be measured now or in the future, given our current understanding. But science is not made of absolutes.
> What do we do with a theory that conforms to every measurement ever made, but whose predictions aren’t testable
Then it's kinda worthless, at last for physics. If two explanations agree with all observations (so far) that means they are completely interchangeable. You might as well use Occam's Razor and pick the simplest one. Until such time we find experimental differences, then we can compare again.
If your theory allows an engineer to build a warp drive, your theory is sound.
If not, not.
What's the mainstream theory for what reality actually is?
The thing about continuous media is that they involve dynamics on all length scales: .1 meters, .1 nanometers, 1e-10 nm, etc. Because of wave-particle duality, length scales and energy scales run inversely: a low energy experiment just does not exhibit any measurable dependence on extremely short-range behavior of the universe. Only high-energy experiments have a wavelength short enough to be sensitive to this unknown sector. Low energy physics is “well understood” in the sense that any experiment with a modest number of component particles can be totally predicted from theory, to the limits of experimental accuracy. Granted that many real-world problems involve stupendous numbers of particles, and exhibit challenging-to-explain emergent behavior: but this is not evidence of unexplained fundamental phenomena, just of the limits of our mathematical insight into finding good abstractions for many-body problems, and evidence of the limits of our computational power to try and work around the lack of good abstractions.
It is known that the most generous interpretation of current theories is that they are self-consistent to arbitrary high energies (renormalizable is the term). That does not mean they are consistent with actual reality, just with themselves.
So... hypergraphs are a big lift, an unneeded multiplication of entities. Until an experiment reveals non-continuum behavior of space-time, what we have here is a solution to a non-issue.
Relativity explains a couple of counter intuitive things that we actually see:
1. Apparently there is no particular velocity that can be called absolutely stopped or special in any way: every velocity is just as valid as every other.
2. Observers moving at different velocities disagree on 3D distances and time intervals between events.
3. But they all agree on the spacetime distance between events. Which is to say, there is a simple formula that resembles a distance formula in 4D where one of the dimensions is time.[0] We know that using this formula, all observers at all velocities get the same result.
gravity is not being discussed but relativity addresses it as well.
So relativity explains actual (but counter intuitive) observations. If we had the simpler Newtonian universe then we could fly around at unlimited relative speeds and time would flow unambiguously at constant rate and be completely unconnected to distance/space. But by direct observation, we see we don't live in such a universe.
If causality could percolate at unlimited speeds then we would not observe any these things and the formulas for relativity would not work but the formulas of Newton would. For one, there would be infinite frames of reference for which you arrive before you depart and these frames of reference could use faster than light travel reverse casualty.
[0] https://en.wikipedia.org/wiki/Spacetime#Spacetime_interval
I'm not sure your explanation is an alternative explanation of what reality is. You've laid out some characteristics and consequences, but haven't described what's at the bottom of it.
I've heard that matter is a consequence of quantum field excitations, but what is a field? From the little bit I've read it sounds like mathematics again.
Suppose for example we found that protons, neutrons, and electrons really were fundamental. Their behavior can be described with mathematics but wouldn't we say it's still the elementary particles that our compose our universe?
It's definitely not a mainstream theory.
The goal is to model the real world, but it's far too difficult to go straight from a fundamental model up to the world observations to find out if the model works.
Doing that "work out the consequences" work can take decades, and a lot of people.
So models are built, explored, their consequences worked out, and if they match something interesting in other more well-established theories, then the models are looked at with more interest and developed further. If not, the models are tweaked or thrown away.
You could call it a branch of mathematics, but in a sense all theoretical physics starts out that way, so we just call it theoretical physics when the goal is to model observed reality while providing a useful underlying model.
Browse the papers on arXiv.org or any theoretical physics journal and there's a lot of exploratory model-building like this. It's very common.
Graph-space models are also not unique to Stephen Wolfram. Several physicists (paid ones) are exploring these models as an approach to reconciling relativity and quantum physics. In a sense, this is what deriving from observation looks like: We've observed relativity and quantum, and we still haven't figured out how to understand the logical consequences of both together, so exploring theoretical underlying models like this is necessary to understand current observations.
The article's theory is not "philosophical" or "metaphysical" theory where nothing can be tested in principle. He explicitly talks about measurable effects differing from other models, albeit with many difficulties and potential intractibility due to computational limits.
But the point is there are, in principle, observable differences, making it more than just a metaphysical model, and if it's intractable to access them we can't figure that out without studying the model further. Even if we can't, there not being able to may have consequences as well (like the way the Heisenberg uncertainty principle turns out to have logical consequences, not just preventing measurements).
As for the theory itself, I'm in the "wait and see" camp. If it's true or at least on the right path, then it should be generating testable hypothesizes soon enough.
Put another way, say his theory was the same in every way, but instead of purporting to prove the fundamentals of our own existence it instead made the claim that there was a two dimensional world with its own constants and physics and that this other universe existed as much as ours does, but that we could never reach it due to what the foundations of the theory laid out. Then I'd be completely uninterested. At least until we were able to simulate this universe with perfect fidelity in a computer.
But since it's our very existence then it's only a matter of time until the theory generates a prediction that we can use as the hypothesis for real experimentation and then the theory can rise or die. But until then I'm going to try to keep an open mind.
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There’s a similar issue with the ABC conjecture proof. You just can’t dump your magnus opus on the scientific academic community and then expect everyone to realize your genius and rubber stamp it.
Peer review is at the core of science. Whatever value Wolfram’s theory has, until it can move from backpatching and curve fitting into making testable predictions, then it will, like string theory, remain in the realm of pure mathematical model and as you may know there’s a nigh infinite number of parameterizable models you can fit, but if they don’t make any new predictions, there’s no reason to adopt them.
Every Wolfram article contains provocative Wolfram-statements. It's our job to ignore the provocations and talk about the interesting bits. There usually are some.
It also seems that this concept is very generic, and many properties of the model do not depend on the dimensionality neither on the manifold or the rule itself.
Because this concept is so generic, one hopes that there is a rule that the hypergraph converges to d=3 as in our world. This would also raise questions on why in the very early universe there was a "inflationary" phase.
[0] https://www.wolframphysics.org/technical-introduction/limiti...
I'm nowhere as smart as Wolfram, nor is my new approach anywhere near as developed, but the dimensionality is the thing that has been bugging me since the beginning for my own thing as well. Why three dimensions? Seems like if we can show a reason for that without too much hackery then we may be on the path to enlightenment.
https://news.ycombinator.com/newsguidelines.html
>"To prove that 110 is NP-complete, what is needed is to show that Rule 110 allows efficient simulation of Turing machines"
But if the universe is a 'computation', then the efficiency of it doesn't really matter right?
Similar to creating a Blender rendering, it doesn't matter how long each frame takes to render compared to any other frame, as long as the observer sees a smooth sequence of images.
We already see this with existing simulations, though they are of much simpler objects than conscious beings. If I simulate water sloshing in a bucket, it doesn't matter how long the simulation runs, the results are the same.
Now, I may add in short cuts to make it closer to real time to support practical applications which leads to different results, but a slower machine running the same shortcuts will see the same differences.
I am somewhat surprised that it does not at least as far as I have read in the linked article, explicitly state that this model is 100% consistent with and I assume a consequence of assuming that we live in a simulation.
I.e. it would take a really light editing pass to change the description given of space-time from a proposal about the physics we live in,
to a prescription for a fairly obvious means of building a simulation that runs on some kind of discrete computation engine.
And while that is possible, the trade-offs are usually far worse or harder to explain than the baggage QM brings. Or just based on an incorrect understanding of QM
Here is one breakdown: https://arxiv.org/pdf/quant-ph/0206089.pdf
Why can't you tell me even the most simple thing?
Wolfram Alpha could be great. And since it's exactly what school students want you can capture the market at a young age.
https://www.wolframalpha.com/input/?i=How+much++marijuana++c...
"I’m pretty sure that, yes, in principle it’s possible. In fact, as soon as one views space as having an underlying structure, and not just being a mathematical manifold “all the way down”, it’s pretty much inevitable. But it still requires essentially “hacking” space, and “reverse engineering” its structure to find features like “space tunnels” that one can use."
Well, unless he shows what he means via rigourous mathematics or a foolproof demonstration, those are words without meanings.
The subtle difference is that if something just, uh, is going faster than light then everything works out. They're are two implications though, one is that it could never be decelerated below the speed of light and the other is that it'll probably have to be traveling backwards in time.
Making something that goes backwards in time and faster than light (without using infinite energy) is left as an exercise for the reader.
I am not surprised that Wolfram thinks FTL is possible - the real question is, is there anything he thinks is impossible?
Also, it seems pretty clear that Wolfram does not understand the concept of Warp drive, which is not used to propel the craft, but instead used to warp space to come to the craft, because there is nothing preventing space from traveling faster than light, and, indeed, the expansion of the Universe causes distant galaxies to recede from ours faster than the speed of light. So there you have it, we already have proof of faster than light travel, so we know it is possible.
But if FTL travel is not a one way trip, it will tend to introduce causality issues. Say you're somewhere far away and observe some event on Earth that arrived by the speed of light, like maybe a lotto drawing or who wins a game. You could zip back FTL, arrive before the lotto drawing or the result of the game, and bet on those numbers or the game winner. If you were far enough away, you could observe your own birth, and possibly zip back fast enough prevent that from occurring. The Universe may allow FTL travel, but I doubt it will allow such paradox.
Yes it does. This is a basic consequence of the underlying pseudo-Riemannian geometry. In terms of PDEs, the field value at any point is fully determined by the initial conditions on a Cauchy surface within its past light cone.
Quantum mechanically, field operators at spacelike-separated points commute.
> Also, it seems pretty clear that Wolfram does not understand the concept of Warp drive, which is not used to propel the craft, but instead used to warp space to come to the craft
You didn’t read the article. This is addressed at the end, under “What about warp bubbles and the Alcubierre metric?”.
Can a forum of programmers and techies really not fathom a computational approach to physics? Graphs are only a social database to you?
You worship a framework of physics fraught with limitations, missing pieces, and paradoxes, which few of you understand beyond a simplification, and act like the Pope of Quantum Physics.
Disruption huurrrrrr. What a cesspool. You people are techno-sheep.
Here you have someone doing novel explorations of our understanding and unquestionably adding to the total knowledge of our species regardless if he is closer to right or wrong.
Why be so poisonous?
Sad.