The simulation argument comes from the fact that there a quite a lot of physics effects that are both surprising, and look an awful lot like dirty hacks that a programmer might put it.
Quantum physics looks a lot like lazy evaluation (State doesn't exist until "observed").
The speed of light seems like a hack to prevent an n squared problem of everything in the universe effecting everything at the same time.
In a classical word, you must simulate only one path. In a quantum word, you must simulate both. You don´t need some magical conscious observer to force the collapse of the wave function. A CCD detector of a camera or a simple wall is enough to force that the "wave" collapse into a "particle" and the detector or wall gets a small spot where the "particle" hits it.
A similar experiment is possible with spin, and you can use that to get a qbit. In a classical word, a qbit is simply a bit and you only have to chose between the 0 or 1 state and simulate it. In a quantum word, you must simulate both.
But it's worst with many qbits. Let's say you have a 10 qbits computer. In a classical word you pick a value for each of them and simulate each one, so the total computation is ~10. In a quantum word, you can combine any of the states of the 10 qbits and you must simulate the 1024 states.
So the idea that a quantum computers is better than the classical computer is opposed to the idea that quantum physics is some hack to reduce computational resources.
I think that the main problem is the quantum mechanics is weird, use a lot of linear algebra, but the calculations are somewhat straightforward and well defined. But the popularization explanations try to avoid the algebra and make some simplifications, so the explanation only keeps the weird part.
I've been watching a few video series by mathematicians on quantum computers and they're pretty interesting. I wish they could hook up with some animators to make it a little easier to understand.
There's a lot of complex maths and polar notation. There are a couple of good simulators out there that lets you play with qubits and their probabilistic coefficients.
I'll be honest that I was never all that great at the higher maths and a lot of this taxes my brain or goes way above my head. But all these quantum computers are deterministic. The simulators can fully simulate them.
It's just that simulating several qubits requires gigs and gigs of ram. A real quantum computer can't do anything you can't do with a traditional computer, it can just do it in a more computational faster time and fewer resources.
You can run small quantum programs yourself on the IBM cloud quantum platform. They allow people to queue up programs to run, similar to old punch card systems:
> In a classical word, a qbit is simply a bit and you only have to chose between the 0 or 1 state and simulate it. In a quantum word, you must simulate both.
Not just "both", you have to consider all quantum states.
It is more like adding an imaginary component to a real probability making it a complex probability. It is possible to calculate with the complex probabilities and only collapse to the field of R in the end.
> In a classical word, you must simulate only one path. In a quantum word, you must simulate both. You don´t need some magical conscious observer to force the collapse of the wave function. A CCD detector of a camera or a simple wall is enough to force that the "wave" collapse into a "particle" and the detector or wall gets a small spot where the "particle" hits it.
While the alternative seems a little too far out to be true, I have to ask, how do you know?
> So the idea that a quantum computers is better than the classical computer is opposed to the idea that quantum physics is some hack to reduce computational resources.
Keep in mind, not all operations in a computer take the same amount of time. If those qubits are entangled, you are going to get the state of all of them from a single "operation". Finally, we assume deterministic and stochastic computation take the same time, but that's only true for us because we perform stochastic computations deterministically - I'm pretty sure we could squeeze a lot more performance out of our silicon if we relaxed our accuracy constraints.
Additionally, if the universe is a computing system, the probabilistic nature of quantum mechanics may be a way to work around paradoxes, i.e. Godel's incompleteness theorem.
Absolutely not. The uncertainty in Heisenberg's uncertainty principle stems from the fact that you can not have a signal simultaneously well localized in both time and frequency. If you want a signal that is very well localized in time, then you need a short signal, a single spike. But the frequency of a single spike is not well defined, if you want a signal with a well defined frequency, you need something like a sine wave. And to make the frequency of a sine wave well defined, you need a long piece of it which of course means that the signal is no longer well localized in time. That is the heart of Heisenberg's uncertainty principle, you can not have signals that are simultaneously well localized in time and frequency.
Gödel's incompleteness theorems have in some sense much deeper reasons, they are based on the logical consistency of the entire construction. Maybe you can look at it in a similar way, a theory is an object like a signal above and the properties of being consistent and complete can not be realized at the same time. But I have a hard time imagining that this could really be similar to signals where you can trade localization in time for localization in frequency and vice versa, but how would you trade a bit of consistency for a bit of completeness?
EDIT: To be a bit more concrete, in classical mechanics you have to specify position and momentum (velocity) of a particle to specify its state, those are two independent properties that can have specific and independent values. That is not true in quantum mechanics, there position or momentum alone fully specify the state of the system. The wave function (in position space) tells you where the particle is with what probability, the frequencies of the wave function tell you what the momenta are with what probability.
And from here it is the same as above, if you force a particle into a very well localized position, i.e. make the wave function a narrow spike at some place, then the frequencies and therefore the momenta are no longer well defined. If, on the other hand, you make the wave function of the particle like a sine wave, then you get a well defined frequency and therefore momentum but the wave function becomes spread out across space and the position is therefore no longer well localized.
>In 1927 Heisenberg discovered that the ``more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa''. Four years later G\"odel showed that a finitely specified, consistent formal system which is large enough to include arithmetic is incomplete. As both results express some kind of impossibility it is natural to ask whether there is any relation between them, and, indeed, this question has been repeatedly asked for a long time. The main interest seems to have been in possible implications of incompleteness to physics. In this note we will take interest in the {\it converse} implication and will offer a positive answer to the question: Does uncertainty imply incompleteness? We will show that algorithmic randomness is equivalent to a ``formal uncertainty principle'' which implies Chaitin's information-theoretic incompleteness. We also show that the derived uncertainty relation, for many computers, is physical. In fact, the formal uncertainty principle applies to {\it all} systems governed by the wave equation, not just quantum waves. This fact supports the conjecture that uncertainty implies randomness not only in mathematics, but also in physics.
That sounds ridiculous. The double slit experiment is a small system. The detector apparatus is much larger. The world outside of that, even more so. If your view is how the universe works, the number of superpositions of states that must exist between the "magical human observer" and the experimental result must be huge. Every particle in contact with every other particle. It seems ridiculous that the entire universe must be in superposition to give humans this special property.
The "observer" here is simply an outside system.
(FWIW, we only covered the basics of quantum mechanics in my chemistry undergrad. Perhaps a physicist can explain better.)
> In a classical word, you must simulate only one path. In a quantum word, you must simulate both. You don´t need some magical conscious observer to force the collapse of the wave function. A CCD detector of a camera or a simple wall is enough to force that the "wave" collapse into a "particle" and the detector or wall gets a small spot where the "particle" hits it.
This is a common misconception (among programmers). There's zero experimental evidence for the effect you mention, and zero theoretical derivation. Circumstances under which wave function collapses is the greatest mystery of QM.
> Circumstances under which wave function collapses is the greatest mystery of QM.
I agree with that.
Anyway, if you have an optical system, you can assume that coherence is present while the light hits mirrors, lens and similar optical equipment. (If the difference in the optical paths are smaller than the coherence length of your laser or light source.) But as soon as the light hits a white screen or a brick wall, all the further calculations must use only the intensity of the light at each spot in the screen, forgetting about the phase angle. And all the spots are not coherent.
It's not clear what cause the wave function collapse, but if you are using photons in the visible spectrum probably a mirror will not collapse it, and a brick wall will collapse it. [Or your preferred rewrite with the multiple word interpretation, or the abstract Hilbert space calculations.) I'm guessing decoherence is the correct explanation, there is a nice comment in a reply.
For other particles, the abstract calculation is equivalent, but it's necessary to choose another system to do the experiments.
If you follow the equations of the wave packet of the particle arriving to the wall (or CCD) detector, you then need to solve the equation of the interaction of the particle + all the particles in the wall or the CCD. The challenge of the collapse is that simulating anything beyond a few dozen quantum particles is too demanding. Mathematical models that simulate millions of particles need to make assumptions (typically they are too hot, too cold, too strongly bound, so you can ignore most effects - think 1D Ising model, Bose-Einstein Condensates, Photon gases, etc). But the full description of a particle + all particles in a detector still escapes us.
Therefore the transition between: superposition of paths -> particle lands at specific points has never been truly explored. The best description currently involves decoherence. Many theorems have been proven (and experiments done) in that area. The gist is that as you add particles to a system (2, 3, 4, 5, 10, ...) the superposition effects slowly cancel each other out. Another angle is the monogamy of entanglement (the more particles are entangled, the weaker the entanglement between any 2 particles). The idea of decoherence is that as things get larger, the weird effects of quantum physics become more "dilute". However, going from double slit to macroscopic reading still has many assumptions along the way.
Take the above explanation with a grain of salt (as I have tried to make it accessible).
The appearance that quantum effects might be attributed to 'hacks' probably has more to do with the hackish nature of the Copenhagen interpretation. For instance, there is no stated physical explanation for the collapse of a wavefunction--it is only an extremely convenient way of explaining many experiments. A crude analogy--you can describe the flipping of coins with simple probability, but this is a non-physical yet very convenient explanation.
Nothing changes at the time of "wave function collapse". When you measure one particle of an entangled pair, nothing actually happens to the other one. But you don't need to listen to me, check this out:
The wave function collapse and "spooky action at distance" for entangled particles are somewhat different concepts. The collapse idea arises as a part of Copenhagen interpretation, which states that particle always exists in a superposition state (aka wave function of probabilities). So when audience asks, "well why is it that my measurement device showing particle exists/doesn't exist in one place"? The interpretation then says, "That, my dear fried, is because the wave function collapsed to a single state just when you did the measurement". People have been trying to explain and figure out what/why/when this collapse occurs to make sense of Copenhagen interpretation.
That's true, but such proposed extensions or alternate interpretations are then filling in the gaps that would lead people down the path of the simulated universe in the first place.
Bohm's interpretation is just many worlds with a "world particle" tacked on. That particle doesn't affect anything and it's only purpose is to get rid of those pesky other worlds.
Not only is it superfluous structure it makes the theory non-local, which is hard to reconcile with relativity.
If you have no a priori reason to reject a multiverse Bohm's theory is quite uninteresting.
It's the most obvious counter-interpretation. I think it's become remarkably successful, but also suffers in its embrace of causality. While the Copenhagen interpretation can skirt the issue completely, Bohm's must wrangle with the implications of both relativity and non-locality and no one has been completely successful as such. Also, if it were the leading view, I don't think discussions of a simulated universe would be as popular.
> While the Copenhagen interpretation can skirt the issue completely, Bohm's must wrangle with the implications of both relativity and non-locality and no one has been completely successful as such.
Some might consider that a feature. John Bell of Bell's theorem thought QM's non-locality was the most important unresolved issue, so placing it front and center where it couldn't be ignored was a great idea. Interpretations like Copenhagen simply let you paper over the problems which will inevitably just arise elsewhere.
Finally, I think there's been some promising work in deriving covariant Bohmian mechanics. For instance, a preferred foliation of spacetime can be derived from the wave function itself [1], which means a preferred reference frame is actually a part of every interpretation of QM. This is the kind of result that probably would have never been found without research into Bohmian mechanics.
> Also, if it were the leading view, I don't think discussions of a simulated universe would be as popular.
I don't see why. Simulated reality is a purely logical argument [2].
You're right that simulation arguments generally don't rely on QM interpretations. I mention it as potentially detracting from simulation because a common argument includes the need for computational shortcuts. QM as it is popularized now simply fits the shortcut narrative better than it would under the Bohmian approach.
Yes. Many worlds is the single obvious solution. It seems some people don't understand many worlds though. Or maybe there is some other definition I am not aware. I want to describe my understanding here for people's benefit.
The idea is that when you make an observation nothing special happens at all. For one, there is no wave function collapse. This is more an idea about how the observer experiences making a measurement. The salient feature is that the observer is not external to the system. He is a part of the system. His belief that the result was heads or tails is coincident in the wave function with the coin being heads or tails. In other words, the user becomes entangled with the system.
A toy wave function would look like this (I am leaving off normalization since I can't write a square root of 2):
Coin flip result, no observer:
|heads> + |tails>
Coin flip with observer, "Tom":
|heads>|Tom: it was heads> + |tails>|Tom: it was tails>
There is no collapse here. However, to Tom it appears as if the world did collapse. For the "version" of him that thinks the coin flip came up heads, his entire world is consistent with the measurement coming up heads.
I assumed most people who really understand quantum mechanics believe this (but I may be wrong). And that among them, there is no effort to say "There is no collapse" because indeed the effective result of the measurement is a collapse. I also use the language "wave function collapse" to describe what happens. This not because it is an objective reality of the universe but because it is the way we observe the universe.
That was my understanding too. It's disappointing that it keeps getting explained along the lines of "every time there's a decision point at the quantum level, the universe splits in two", when it doesn't say anything of the sort (at least, not if I've understood it correctly).
This is the same confident, facile declaration by may technologists who blather on about how we are on the cusp (a decade or two away) of being able to "download" the state of a person's brain and so let them live forever, in a virtual simulation.
Such people are entirely ignorant of biology. The analogy to programming, the thing they do know something about, is and irresistible analogy because they don't know enough to see the massive flaws in the analogy.
To be more concrete, by using the computerese term of art "hack" you are begging the question.
His post gave concrete examples of how things look a little like hacks, while yours can literally be summarized as "technologists are ignorant of biology," which is a non-sequitur.
I think it's hubris to suggest that just because something is surprising to us that we explain it based on our experience with our own limited technology.
>The simulation argument comes from the fact that there a quite a lot of physics effects that are both surprising, and look an awful lot like dirty hacks that a programmer might put it.
Err, while this might be used to support the hypothesis, the popularized and most discussed version of the simulation argument doesn't even really mention this [0].
To me, it seems like evolution. Because when you get down "to the metal" of the universe, it's really just a bunch of dirty hacks that are thrown together and give off the illusion of uniformity and grace. The way things work at a macroscopic level seem so grand and ultimate, but on the microscopic level of all that it's utter chaos. Random acts of chemical bonding happened to create the life forms we interact with every day, including each other.
The universe is a giant hack job, and I think it evolved that way. I'm a big believer in the "multiple nested universes" theory that our universe began as an offshoot of another, parent universe, and that some of the larger/heavier black holes in our universe could be gateways to other child universes.
I'm curious, how can you be a "big believer" in something that is entirely made up with absolutely no evidence of any sort to back it up?
And how do you mean, dirty hacks. Our fundamental physics nowadays is quite elegant, I'd say, and still we have many questions still to be answered and much deeper to delve till we hit the "bare metal". We've only been in the universe-figuring-out business for real for about 200 years after all!
> I'm a big believer in the "multiple nested universes" theory that our universe began as an offshoot of another, parent universe, and that some of the larger/heavier black holes in our universe could be gateways to other child universes.
but then there's the question of what came before the universe(s) ours originated from and what came before that and so on, since, following our current understanding, everything has an origin
even if we were to argue our universe is a simulation, who/what's running the simulation and where did that originate from? how did it come about?
Don't they only seem like hacks through our understanding, though? Once it's starts looking like a hack isn't it just as likely we're missing something that isn't necessarily a simulation issue?
The simulation argument comes from the fact that our brains are a simulation of our environment. And since they are a simulation we seem to feel as if this world is not real. The world is out there, but our world is in here. Some other people below get down to some of this stuff. We want things to be like this. But they are out there not in here.
We do not observe states, we observe (measure) "observables"; both exist independently from any observers; while state evolves deterministically, an observable, when measured, takes a value, subject to a probability distribution on a set of values, which depends on both the state and the observable in question. (That's basically QM in a nutshell.)
I haven't heard the 'dirty hack' argument before. Perhaps we only see those things as 'dirty hacks' because of the incompleteness and inelegance of our own theories.
Quantum physics looks a lot like lazy evaluation (State doesn't exist until "observed").
The speed of light seems like a hack to prevent an n squared problem of everything in the universe effecting everything at the same time.