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When it comes to the simulation vs. experiment debate, some proponents of simulations argue they have equal epistemic value because computer simulations are physical processes happening inside a computer.

Taking this argument further with quantum mechanics, could it be said that simulating quantum mechanics using a quantum computer, which operates using quantum mechanics, could be considered an experiment? In that case, wouldn't it have equal epistemic value to doing an experiment at some physics laboratory?

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  • What is the exact difference between an experiment and a simulation? I would think that a simulation is a subclass of an experiment. Some experiments are simulations and some aren't. If I drop a rock and it falls to earth, did I conduct an experiment of gravity or a simulation of gravity?
    – user4894
    Commented Mar 27, 2016 at 21:54
  • ps -- some proponents of simulations argue they have equal epistemic value because computer simulations are physical processes happening inside a computer. -- I find this mysterious. It seems to apply far more to analog computers than to a digital simulation. Why should a digital implementation of a physical theory be a perfect analog of nature?
    – user4894
    Commented Mar 27, 2016 at 22:41
  • @user4894 >What is the exact difference between an experiment and a simulation? Well I'm trying to argue that they're basically the same thing so I probably wouldn't be the best to ask this, although admittedly I probably should have a good idea of the position I'm arguing against. >It seems to apply far more to analog computers than to a digital simulation. But "digital" simulation are really just electronic, which is physical. Computers aren't magical black boxes, every process has physical components.
    – Nullius in Verba
    Commented Mar 27, 2016 at 23:08
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    Would this question be equivalent to asking if it's an experiment or a simulation to run electric simulations in an electric computer? Or is there anything unique to quantum mechanics here?
    – Alpha
    Commented Apr 2, 2016 at 16:53
  • @Alpha This question would probably be equivalent to asking whether a regular computer would count as an electric simulation or an electric experiment. A quantum computer simulates quantum mechanics like an electric computer would simulate electricity.You could consider this a "special case" of the experiment vs. simulation argument.
    – Nullius in Verba
    Commented Apr 2, 2016 at 18:16

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The concept of simulation and experiment are not mutually exclusive: When a biologist performs a biochemistry or molecular biology experiment in a lab setting, they are also simulating a process that occurs in Nature. A materials engineer performing stress tests on a new alloy in the lab is simulating the conditions that this alloy will endure when it is used to build a bridge or an airplane. This applies to just about any physical science where researchers try to replicate real world conditions in a lab setting. So in general, something can and often does count as both an experiment and a simulation. You must distinguish between simulation in general, which does overlap with experimentation, and computer simulation, which are a mathematical tool for performing calculations based on theoretical models.

To answer your specific question about quantum computers: Richard Feynman when he originally proposed quantum computers in 1981, clearly indicated that they would be universal quantum simulators, see Section 4 of his paper on the talk (Feynman, R.P "Simulating Physics with Computers" - International Journal of Theoretical Physics, VoL 21, Nos. 6/7, 1982).

Back to the broader question of computer simulations: The epistemic value of computer simulations doesn't come from the fact that they are physical processes. Computer simulations are a tool for solving mathematical problems. We have already assumed that a given real world phenomena is accurately represented by a given theoretical/mathematical model, now we are just using the computer to perform the calculations based on the model - presumably because they are too complex to perform by hand.

The SEP has a pretty good article on the Epistemology of Computer Simulations.

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I can't see how there is any debate about simulation vs experiment, especially if the simulation is run on a computer.

Do you consider calculating the weight of a piece of paper in writing a simulation or an experiment? Or what if you do something more complex, like solving a set of differential equations to calculate the energy needed to make a crease in the paper, also by using a pen and paper? (Similar to @Alpha's comment about electronic computer simulations but even more fundamental and close the person asking the question)

We do experiments to gain knowledge of the underlying workings of a system. With this knowledge we can build mathematical models that represent the system to a certain desired degree of accuracy and detail.

These models are programmed into a computer to run simulations and extrapolate a possible outcome based on the boundary conditions entered by a user. In order to verify the computer's results it is ambiguous to say that you ran two simulations and the results are the same, thus it is correct. You need to verify the results by doing tests (experiments) in the real-life situation.

You can do as many quantum mechanical simulations on a quantum computer as you like, the simulations will never give you more fundamental knowledge about a system than that which you put into it.

Scientists used simulation to postulate the existence of the Higg's Boson, but only until they did an experiment in the Large Hadron Collider, did they physically find it and so could confirm that their mathematical models were indeed correct, but until that moment everything was just speculation, no matter what the simulations tell.

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When it comes to the simulation vs. experiment debate, some proponents of simulations argue they have equal epistemic value because computer simulations are physical processes happening inside a computer.

You are a physical system, so when you think about something, that's a physical process happening in your brain. So should thinking about something count as an experiment? Something has gone quite badly wrong here.

Taking this argument further with quantum mechanics, could it be said that simulating quantum mechanics using a quantum computer, which operates using quantum mechanics, could be considered an experiment? In that case, wouldn't it have equal epistemic value to doing an experiment at some physics laboratory?

The point of an experiment is to test a theory. If you do an experiment and your theory predicts result X and you don't get that result, then your theory is in trouble. Either you did the experiment wrong, or you misinterpreted the result or the theory is wrong.

In order to do a simulation, you have to guess the equation of motion for the relevant system. You then have to come up with a program for computing the evolution under that equation of motion with the relevant set of initial conditions. Once you have done that, a suitable universal computer can simulate the system you are interested in to any desired degree of accuracy. And not only can you program it to produce the correct end result, it can also simulate all the stages intermediate between the initial conditions and the final result to any desired degree of accuracy.

So the simulation enables you to work out the consequences of a guess about the equation of motion of a system in cases where you could not work it out yourself. The simulation produces predictions that can be tested with the actual system. So running the simulation is not the same as doing the experiment since the point of the experiment is to test whether you are right about the conjectured equation of motion, and a simulation can't do that.

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The real line in the sand probably varies from individual to individual, so I would not expect just one answer. However, as someone who does a great deal with simulations, I would draw the line like this:

In a simulation, you have all of the information required to know the final outcome. It may not be in a convenient form. You may need to run it through a few trillion transistors to get it into a readable form, but no new information is generated in the simulation process itself. You're merely distilling value out of existing information. The only times the results of simulation "surprise" you, giving the appearance of new information is when the inputs to the simulation contained information you had not fully processed.

By contrast, I see an experiment as something which has the potential to reveal new information that you did not have. The information that defines the result has not been captured already. There is typically a physical component here, in that not all of the outcome of the experiment has been put into a form which is information.

From this focus on "information," I would say it depends on the quantum program you run. If the quantum program you run is explicitly written such that the quantum effects are unimportant for the final output, I would call it a simulation. However, if the quantum program is written such that the quantum effects in the implementation affect the output in a meaningful way, it may be an experiment.

The line I choose to draw is highly related to the difference between syntax and semantics. If the result can be arrived at purely through the syntax of the information and processes which manipulate that information, I tend to think of it as a simulation. If the result can only be derived from the semantics of the inputs and the process, such as the particular behaviors of this particular device under test, I call it more of an experiment.

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Both simulations and experiments instantiate ideas. A simulation can instantiate any idea in any substrate, while an experiment must instantiate a particular kind of idea — a proposed explanation or conjecture — in a particular form — one that it is believed will change our belief in that proposed explanation or conjecture.

Running a program about some aspect of quantum mechanics anywhere (quantum computer or not) that meets these requirements constitutes an experiment.

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