B What's the confidence level of quantum to macro behavior?

[newjerseyrunner]

The 2016 Asimov Debate had a part where NGT was discussing whether or not if we could create the computer algorithm to compute all the fields, perturbations... of quantum physics and let it run, would the macro laws that we know fall out of the simulation? He mentioned the gas laws as an example.

I know the mathematics of such a calculation are beyond comprehendible, but we double our computing power every two years so in a few decades, such a simulation might be possible.

Would you expect the laws of the macro world to emerge from a simulation of the quantum mechanical laws as we understand them right now?

 

[mfb]

Certainly not without something else in the program. The simulation of a quantum system has a quantum system as output. There is nothing that could output "pV=NkT". You can define observables that represent the individual macroscopic parameters, and check if the system obeys those laws, but then you have to define the macroscopic observables. If you do that properly, the system will follow that law, of course (apart from fluctuations) - otherwise the law would not be valid.

 

[Strilanc]

Certainly not without something else in the program. The simulation of a quantum system has a quantum system as output. There is nothing that could output "pV=NkT". You can define observables that represent the individual macroscopic parameters, and check if the system obeys those laws, but then you have to define the macroscopic observables. If you do that properly, the system will follow that law, of course (apart from fluctuations) - otherwise the law would not be valid.

I don't understand this objection. The OP isn't asking if the simulation will infer mathematical equations, they're asking if a full-detail simulation of QFT would act like what we actually observe in reality. In particular they seem to be worried about there being a cutoff size where it stops working.

 

[mfb]

they're asking if a full-detail simulation of QFT would act like what we actually observe in reality.

To evaluate that, you have to define observables. And then you are back at the main point of my post that starts in the fourth sentence.

 

[newjerseyrunner]

I don't understand this objection. The OP isn't asking if the simulation will infer mathematical equations, they're asking if a full-detail simulation of QFT would act like what we actually observe in reality. In particular they seem to be worried about there being a cutoff size where it stops working.

Exactly, I wouldn't expect any sort of mathematical equation to be the outcome, I'm just wondering if the simulation of a trillion atoms of hydrogen plus some heat would behave like a trillion atoms of hydrogen plus that heat.

If you do that properly, the system will follow that law, of course (apart from fluctuations) - otherwise the law would not be valid.

Laws have discreet ranges that they are known to be valid for, simulations of this scale are far beyond the ability to currently calculate.

To evaluate that, you have to define observables. And then you are back at the main point of my post that starts in the fourth sentence.

The observable can be any known macro behavior.

Take a trillion metal atoms and bond them together in the shape of a spring of various lengths and thicknesses, then vary the amount of weight on the bottom of the spring (also using simulated atoms) and run the simulation, exactly calculating the length that the spring extends each time. Do you get Hooke's law?

If you simulate trillions of helium atoms at very low temperature and use a trillion more atoms to make a sold surface, will the the helium creep up the walls in the same way that real superfluid helium does?

If you create a boat of a trillion aluminum atoms on a sea of a trillion simulated water molecules, will it have the displacement that it's supposed to? Make the surface area smaller does it sink the way it's supposed to?How can quantum physicists be sure that their formulas actually describe the world at scales trillions of times what micro experiments probe. In my own world of programming, lots of times unit tests show that algorithms exactly do what I expect them to do when dealing with one or two objects, then when the numbers go way up, odd unexpected behavior emerges.

 

[mfb]

Exactly, I wouldn't expect any sort of mathematical equation to be the outcome, I'm just wondering if the simulation of a trillion atoms of hydrogen plus some heat would behave like a trillion atoms of hydrogen plus that heat.

Sure. We know the laws every particle follows. Why should a particle suddenly follow different laws? The amount of particles you consider is completely arbitrary, and doesn't have an effect on the particle.

The observable can be any known macro behavior.

It is not that easy to construct meaningful macroscopic observables for quantum systems. Do it properly and you get the macroscopic laws as result. Do it wrong and the results are just messed up.

 

[newjerseyrunner]

Sure. We know the laws every particle follows. Why should a particle suddenly follow different laws?

They won't, but small errors add up very quickly. If you're confident that you know exactly what two particles will do to a confidence level of 20 decimal places, how can you predict the behavior of trillions of interactions? Software engineers, often use a double precision floating point variable type for high precision calculations, but after only a handful of calculations, the confidence of the answer is greatly reduced.

Doesn't this type of problem already exist? Don't laws have to be "renormalized" at certain scales or you end up with lots of infinities?

 

[rubi]

We don't need to run computer simulations in order to predict the behaviour of macroscopic systems from the microscopic laws. This job is accomplished by statistical physics and it's a much more reasonable approach.

 

[mfb]

They won't, but small errors add up very quickly.

They also do not matter. That is the point of thermodynamics - in particular, the purely mathematical part of it.

Doesn't this type of problem already exist? Don't laws have to be "renormalized" at certain scales or you end up with lots of infinities?

If you want to do (perturbative) quantum field theory, which would be pointless for gas laws.