What if TOE is non-analytic ?

[Dmitry67]

What if TOE is "non-analytic"?

I mean, what if there is a set of TOE equations, but there is no way to derive all notions we want to derive (space, time, gravity, number of generations) from it analytically. And the only way to do it would be a huge numerical simulation?

I had already happened in QCD. AFAIK there is no formula for say Mneutron/Mproton based on the quark masses and parameters of the Standard Model - it comes from experiment and/or simulation (but in fact quark masses are calculated based on that to fit the answer)

So even if we knew TOE equations if would be extremely diffuclt to derive Standard Model from TOE. But going back would be even more difficult - almost impossible!

 

[humanino]

formula for say Mneutron/Mproton based on the quark masses [...]
in fact quark masses are calculated based on that to fit the answer

The ratios of quark masses are usually fitted to the ratios of meson masses through chiral perturbations, not to the ratios of baryon masses.

QCD and general relativity are simple in the sense that we can deduce their structures from just a handful of general hypothesis, not in the sense that they are "easy". In fact, most proposals for TOE search exactly for such simplicity, and none of them are "easy".

 

[Fra]

I mean, what if there is a set of TOE equations, but there is no way to derive all notions we want to derive (space, time, gravity, number of generations) from it analytically. And the only way to do it would be a huge numerical simulation?

I for one sure don't expect analytic solutions to whatever the "TOE" or "TOE-lookalike" would be. I think the expectation of analytic solutions in closed form is extremely naive. Some properties will probably be analytically derivable, but not all. Which properties are inferrable from analytic manipulation would seem hard to say in advance. But I have no illusions.

I expect what we are looking for to more be a form of an evolving algorithm. Wich even renders an ordinary computer numerical simulation naive because the algorithm would evolve during the computation. The ultimate computer is probably simple a physical system.

So I think at some level most attempts are analytics or regular numerical analysis are approximations due to the constraints of human capabilities.

To me the deepest truth is still in the makeup and the self-modification of the algorithm, rather than the ultimate computation, because the algorithm would change during the computation unless you have a computer which can compute with infinite speed, and read and write from an infinite memory with infinite speed.

/Fredrik

 

[friend]

I for one sure don't expect analytic solutions to whatever the "TOE" or "TOE-lookalike" would be. I think the expectation of analytic solutions in closed form is extremely naive. Some properties will probably be analytically derivable, but not all. Which properties are inferrable from analytic manipulation would seem hard to say in advance. But I have no illusions.

Do you think that reality moves from one state to the next as a result of infinite calculations or because of simple relationships(rhetorical)? I think there must be some closed form that reflects some simple relationship, but we haven't found it yet. It may be that we need higher forms of math for a complete TOE.

To me the deepest truth is still in the makeup and the self-modification of the algorithm, rather than the ultimate computation, because the algorithm would change during the computation unless you have a computer which can compute with infinite speed, and read and write from an infinite memory with infinite speed.

Wouldn't evolving algorithms to compute physical relationships mean that the laws of physics are changing? All that means is that we have not yet found the laws that do not change which is what we are really looking for.

 

[Fra]

It may be that we need higher forms of math for a complete TOE.

Yes that's a possibility.

Wouldn't evolving algorithms to compute physical relationships mean that the laws of physics are changing?

Yes, this is exactly what I mean.

All that means is that we have not yet found the laws that do not change which is what we are really looking for.

I'd say not necessarily. A related comment on evolving is in post#45 in https://www.physicsforums.com/showthread.php?p=2328816.

Another possibility is that the search for law, or the improvement of relative knowledge, is the reason for the arrow of time. Then, the perfect law is closely related to the view of time, and timeless law, that rovelli and others have. If you think this, then your objection is valid.

But I don't. I'm more into the logic smolin suggests here.
"On the reality of time and the evolution of laws"
-- http://pirsa.org/08100049/ by Smolin

Either you like it or you don't. I like it, but Smolins argument could probably be stronger. Someone raises the point you do, that if law evolving then there must be a metalaw for evoluion of law, and we don't know this.

The points is that this is not neccesarily the case. It could be that for information limiting reasons, it's not POSSIBLE for a physical system to have certain information about the metalaw. This is why evolution would contains elements of unpreditcability beyond the type that is captured by statistics or probabilistic predictions-

/Fredrik

 

[Fra]

Note that this also makes sense of why cosmological arrow of time is obvious, while the microscopic isn't - the laws of physics encoded for microphysics is encoded in a massive context/environment, which yields an effectively timeless description of symmetry. But the inside-out view, that we do have in cosmology really inviolates many of the statistical frameworks that particle physics RELIES on. It is simply invalid - there IS NO massive context to encode the symmetry of cosmological scale physics because there is no outside environment! No offense to anyone but I think the multiverse or ensemble of UNIVERSES talk is just baloney IMHO. The reasoning used is really flawed. These ensembles of universes are totally imaginary and lacks physics basis IMO.

One has to see the difference between an ensemble of a small subsystem, or the entire world. The former makes sense, the latter don't

There are several angles to this point, Smolin has raised it in several different ways in various places. Papers, books talks.

/Fredrik

 

[Vanadium 50]

I mean, what if there is a set of TOE equations, but there is no way to derive all notions we want to derive (space, time, gravity, number of generations) from it analytically.

That's almost certainly going to be the case, as this would incorporate QCD and QCD is already in this boat.

 

[tom.stoer]

That's almost certainly going to be the case, as this would incorporate QCD and QCD is already in this boat.

I agree

 

[Coin]

I mean, what if there is a set of TOE equations, but there is no way to derive all notions we want to derive (space, time, gravity, number of generations) from it analytically. And the only way to do it would be a huge numerical simulation?

Well first off, that would mean that I (as a programmer, and so someone who is better at numerical simulations than analytic mathematics) would become extremely excited :)

However more realistically what I'd wonder is whether this would just mean that scientists would begin looking for analytic approximations to the TOE simulation procedure.

 

[DSM]

I mean, what if there is a set of TOE equations, but there is no way to derive all notions we want to derive (space, time, gravity, number of generations) from it analytically... And the only way to do it would be a huge numerical simulation? difficult - almost impossible!

There is no analytic solution to the non-relativistic Schrodinger equation for the helium atom. So what's the big deal? There are numerical solutions of any accuracy you want... name your decimal place and someone can do it

IMHO, the quest for analytic solutions is a big red herring in modern physics.

 

[Fra]

Well first off, that would mean that I (as a programmer, and so someone who is better at numerical simulations than analytic mathematics) would become extremely excited :)

I think there is a lot of interesting things about numerical anaysis and algorithms that relates to fundamental physics, in particular the information theoretic inference view that I personally have. The reason is that any physical inference and and physical interaction is constrained by resources, the complexity of the interacting parties, also inferences are physical processes that have inertia. Here is an analogy with physical computer resources and computing power. Algorithms can have different fittness if you consider their "computability" or their speed. Clearly a good algorithm is one which leads you to the answers with the least amount of occupied resources and comupting power. And this also makes it clear why there can no be a fundamentall universal perfect algorithm, the preference for an algorithm is not only dependent on data streams, but also on the computer hardware (by analogy here, the microstructure of the observer).

Part of my own personal amateur research I do simulations to test ideas. There are also other interesting things with computing that again has analogies to physical systems evolving. It's the issue of rounding errors and propagationg of these, and thus stability. This means that the "resolution" of an observable does impact the fitness of algoritms.

There is an analogy to this, and the idea I have about what happens to physical interactions and symmetries, as the observer is SCALED in complexity.

It's like asking, how does a the most fit algorithm need to SCALE, if you SCALE the resources of the PC? say cpu power, or memory? At some point, the computable/compatible algorithms that are of any use are highly constrained!

I think of unification in a similar faishon. The "algorithm" corresponds to the physical action and somehow physical law.

The quest for timeless objective fixed universal law, is about as sensible as the quest for the perfect algorithm that is perfect for any computer of any size. It simply doesn't acknowledge the relativity of fitness, and that ANYTHING, any inference is like a computation, so there is always an implicit computer.

At minimum the implict computer for use is the human brain, but we are clever enough to try to imagine how the inferences we do, would transform into another inference host.

/Fredrik