A Different Kind of Theory of Everything
newyorker.com
newyorker.com
"Some researchers are attempting to wean physics off of space-time in order to pave the way toward this deeper theory. Currently, to predict how particles morph and scatter when they collide in space-time, physicists use a complicated diagrammatic scheme invented by Richard Feynman. The so-called Feynman diagrams indicate the probabilities, or “scattering amplitudes,” of different particle-collision outcomes. In 2013, Nima Arkani-Hamed and Jaroslav Trnka discovered a reformulation of scattering amplitudes that makes reference to neither space nor time. They found that the amplitudes of certain particle collisions are encoded in the volume of a jewel-like geometric object, which they dubbed the amplituhedron. Ever since, they and dozens of other researchers have been exploring this new geometric formulation of particle-scattering amplitudes, hoping that it will lead away from our everyday, space-time-bound conception to some grander explanatory structure."
The wikipedia page for amplituhedron provides some kind of simulated visualization but doesn't clarify in layman's terms how reality fits into this particular structure. It seems like an interesting concept, I wish I understood it better.
I suspect the folks reformulating QM in Clifford Algebras may have (or find) a way to explain why a geometric interpretation works the way it does.
The Rashomon effect occurs when an event is given contradictory interpretations by the individuals involved. The effect is named after Akira Kurosawa's 1950 film Rashomon, in which a murder is described in four contradictory ways by four witnesses.[1] The term addresses the motives, mechanism and occurrences of the reporting on the circumstance and addresses contested interpretations of events, the existence of disagreements regarding the evidence of events and subjectivity versus objectivity in human perception, memory and reporting.
https://en.wikipedia.org/wiki/Rashomon_effect
And here's a short video summary of the film:
It was a depiction of Hell.
Does it? I don't see why. If there are numerous equivalent ways of describing a phenomenon, that seems to suggest that most structures have inherent isomorphisms. I don't think anyone would find this is particularly surprising.
Conjecture: because this conversation is necessarily taking place in a universe where a certain level of intellectual and technological development was able to happen, which means one in which there is an evolutionary path to attaining such, which means one in which you can build a series of models of the universe, each progressively more accurate, but the early ones still give usefully accurate predictions.
Charle's Law states that Pressure * Volume = Temperature.
That's true and you can do a million experiments with a million balloons and liquids/gases to validate it - until you find a non-newtonian substance, try to apply it to a solid, introduce moving fluids, etc.
Charle's Law isn't a fundamental law of physics, but a consequence of the material properties and statistical outcomes of a large number of interacting molecules. Before atoms and molecules are characterized, it _does_ look like a fundamental law to an experimenter.
It doesn't seem to me that looking for "lower layers" of theoretical physics (holographics, quantum foam, strings, whathaveyou) is an infinite regress and doomed to never be a completed project. I do think that the project may reach some point where the theories fail to be scientific (read: falsifiable) because it could be possible that reaching deep enough through layers of physical abstraction can not be achieved / no physical instrument can provably be built to look deeper (as an analogy, no instrument can be built to probe the full amplitude space of a quantum state).
Visions of Future Physics https://www.quantamagazine.org/nima-arkani-hamed-and-the-fut...
A Jewel at the Heart of Quantum Physics https://www.quantamagazine.org/physicists-discover-geometry-...
Nima Arkani-Hameds Lecture: The Doom of Space Time: Why It Must Dissolve Into More Fundamental Structures https://www.youtube.com/watch?v=qTx98PUW6lE&t=860s
We've discovered a bunch of phenomena that happen to be able to be described by the mathematical tools we have because those are the only way we can understand them.
There's no reason to believe that any of them are fundamental to nature. There may be an uncountably infinite number of phenomena out there which are fundamentally unable to be formulated in any way which we can understand or predict them.
Our minds aren't constructed to understand reality, they're constructed to help our bodies survive in a savannah a few hundreds of thousands of years ago.
To say they're not constructed to understand reality may or may not be true, but is beside the point.
That said, I often share similar thoughts about progress towards the nature of reality.
Yes we're pretty dumb. I'm continually amazed at how stupid I am, and even other 'clever' people. The way I see it, we're only just barely sentient.
As you say, we've only just managed to get beyond the savannah. Behavioural modernity and the advanced cultures and technologies we have developed arose in insignificantly recent evolutionary time. Therefore we can't have much more than roughly the minimum necessary intellectual capacity to develop a technological civilization on a planet like ours. If we had less, we wouldn't have achieved what we have. If we had much more, well, we'd have developed it sooner and clearly we didn't.
It's possible there were some environmental factors that held back our technological development despite our intellectual capacity, but it's hard to see what those could have been. Our planet seems pretty abundant in resources and environments for us to colonise. It's also possible that once a species develops the required intellectual capacity for technology, it takes long enough to develop the basics to build on that we evolved significantly grater than the minimum intelligence by the time we actually developed a technological society.
I don't say this to incite a religious war or discussion (I've purposely omitted the use of the word "God" here), so if we could keep things philosophical that would be appropriate for such a site. I'm curious if this school of thought has another name beyond agnosticism.
I agree with your main point, however I don't find this a compelling argument. Regardless of what our brains are constructed for, with pen and paper and a set of rules we can roughly approximate a turing machine. Everything we as humanity know about computation suggests that at minimum this is equivalent to any computation possible using all known physical properties & interactions with some amount of overhead (even quantum can be simulated classically).
Thus, while it's possible there is an unknown kind of interaction that we cannot understand or simulate classically, the fact that our brain is more or less designed around survival and reproduction is irrelevant; change or optimize our DNA and the new super-human will still be at best roughly equivalent to a turing machine in terms of computation.
So calling humans equivalent to standard Turing machine is ultimately wrong if you even start to assume quantum processes are important in our thinking. (which is actually unproven as of yet)
Then you need to start with a more intricate parallel quantum Turing machine, high end mathematics required already. It is already non-deterministic.
And no, quantum effects cannot be simulated efficiently classically. That is the difference between P and #P complexity classes. Add parallelism, you get #BQP. You would be able to tell something about the nature of reality by building physical instances of those problems and timing them. Timing attack on the structure of reality, structure of time itself, anyone? (Of course the required energies would be ridiculous.)
To falsify any Turing model, you need to answer the question: what cannot be done by any given machine? Or by any machine? It is possible that there's a Goedel trap in this question.
A parallel would be to find and answer to what cannot be computed efficiently by best human geniuses ever. Hard introspective question might I add. Answer probably requires building or finding something more than human.
And, I’m pretty sure that #BQP is too.
(Just with a large slowdown.)
Now, yes, there are models of computation which cannot be simulated by a Turing machine, but I don’t know of any substantial evidence that a physical process uncomputable.
Any computation which has a finite number of possible inputs is computable, using a lookup table, and therefore using a Turing machine.
So, for any physical process to be uncomputable, it must be such that there are infinitely many possible states of it, for it to proceed from.
And, the Bekenstein bound, if correct, would seem to suggest that no structure like that can exist within a bounded region of space.
Equivalent meaning computability, not complexity. The two machines can simulate each other (even w/ exponential slowdown) then it's equivalent.
> cannot be simulated efficiently classically
Efficiency isn't really the point. The OP is suggesting there's a literal wall which makes something impossible to understand. This would require a computational behavior that cannot be programmed as a turing machine.
> To falsify any Turing model, you need to answer the question: what cannot be done by any given machine?
Correct. The answer is that a turing machine can't decide a turing-complete decision problem, so hypercomputation is achieved by equipping a turing machine with an oracle for a turing-complete problem. This actually leads to a hierarchy that is each strictly more powerful than the previous ones by using oracles for problems that are "more undecidable" so to speak (see https://en.wikipedia.org/wiki/Arithmetical_hierarchy )
Either way, we have no evidence that suggests theres a natural process that lives higher up on the arithmetical hierarchy. An example of a physical process that would fulfill this criteria: suppose there were a type of particle that only sometimes collide with each other, and it turns out that they only collide not just by running into each other but also when the sum of their velocities encode halting turing machines, otherwise the particles pass right through each other. A classical turing machine cannot decide the halting problem, so it's impossible to simulate a system with these particles because you never know if they will collide or not.
Euclid will turn in his grave.
“To draw a line from any point to any non point”
The motivation for doing this is as follows. When the principle of least action was discovered, it was philosophically very puzzling: why should this equivalent, non-causal formulation of newton exist? The reason of course turned out to be quantum mechanics! (it's a kind of stationary phase approximation to the path integral formulation of quantum theory, roughly speaking). Now in the early 21st century, there is a whole bunch of hints that space and possibly time are not truly fundamental quantities (in analogy to how newtonian causality was not fundamental). So how do you proceed?
Method 1: make random guesses.
Method 2: attempt to extend existing physics in non-random ways (e.g. string theory)
Method 3: take a lesson from history
Method 1 never works, method 2 is apparently too hard this time, so they are attempting method 3: if you need to get rid of space-time, don't MODIFY existing physics, but REFORMULATE it so that it doesn't depend explicitly on that concept, in analogy to how lagrangian mechanics reformulates newtownian mechanics to not depend explicitly on causality ( & quantum theory is then a simple deformation away). And if you can reformulate state of the art quantum field theories so they don't depend on space-time explicitly, perhaps a deeper theory will just be a simpler deformation away as well.
A TL;DR; of TL;DR; : they are talking about reformulating laws of physics, so that formulas would not be dependent on space and time.
Each theory is pretty much based on a previous theory, with some aspect of the previous theory removed to make the theory a better assumption of reality. - A really cool example of this a scientist named Laplace presenting his work to Napoleon about the origins of the solar system. Previously, it was believed that God was involved somehow but his theory didn't include God. When Napoleon asked why God wasn't included, he said "I had no need for that hypothesis".
Einstein's equations are a pretty good way to explaining things but they break down in certain situations, just like Newton's equations did and Einstein's equations are really just Newton's equations extrapolated a bit more.
Scientists are now discovering ways of explaining the universe that doesn't require Einstein's aspect of space-time to describe motion but equally work quite as well as his theory of general and special relativity.
And although we still haven't found the dark matter directly, we notice its effect in the stars motion, galaxies' gravitational lenses, large-scale structure of the Universe and even notice the coinciding data in the cosmic background radiation. Sounds like too much for a "hotfix".
The closest physical theory would be the Mathematical Universe Hypothesis.
https://www.quantamagazine.org/why-black-hole-interiors-grow...
Also, if our universe is a simulation, then we have no idea how faithful that simulation is to the world it runs inside of. Could be a lot different. Maybe our simulated physics is fanciful. Maybe the hardware it runs on is nothing like anything we're familiar with. And maybe the software is completely alien.
To me it seems like the simulation argument is self-defeating, because you can't draw any conclusions about the real world from it in order to tell that it's actually a simulation.