For the purposes of this discussion let's consider an idealized quantum experiment that has only two outcomes. You can think of this as measuring the spin of an electron or the polarization of a photon. Again, the details don't matter. All that matters is that there are two possible outcomes (let's call them A and B). Let's further suppose just for the sake of simplicity that both outcomes are equally likely.

So we do a bunch of experiments and collect a bunch of data. This data is in the form of a sequence of A's and B's, each corresponding to the outcome of one instance of the experiment. We analyze this sequence and it looks random. We apply a bunch of statistical tests and they call come back and say, yep, this is a random sequence. We wrack our brains to try to come up with a way to predict the outcome of the next experiment with odds better than chance and we fail. Does that prove that this sequence is in fact random?

No, of course not. We can trivially reproduce the exact same sequence in a purely deterministic way simply by playing back the record of the previous outcomes! So how can we know that the sequence wasn't generated this way the first time around? How do we know that there isn't a deterministic process out there in the universe somewhere that has pre-ordained the outcome of every quantum measurement we ever make?

It would seem that the fact that

*any*sequence of experimental outcomes

*could*be generated by playing back a record of them shows that we can

*never*be sure that it wasn't actually done that way. But this is wrong, and in fact it is easy to see exactly how and why it is wrong. You might want to stop here and see if you can figure it out on your own.

Here's a clue: if the sequence of experimental outcomes was the result of simply replaying a record, or indeed of any kind of deterministic computational process (of which replaying a record is just one trivial example), we should be able to find

*evidence*of that somewhere. In order to make a record we have to

*store information*somewhere. In order to make a computational process we have to

*make a computer*. If that information was stored in any kind of straightforward way, and in particular (no pun intended) if that information is stored in any kind of physical artifact made of atoms then we should be able to find it. Or at least we should be able to find some evidence that it exists.

But we can't. And if you think about it, it is

*absolutely impossible*for such an artifact to exist. Why? Because it would have to store the outcome not just for the experiments that we actually do, but for any experiment that we could possibly do, and it would have to store those outcomes for every particle in the universe on which we might choose to perform an experiment

*including the particles that make up the artifact that is supposedly storing all this information*!

Now, this is not yet an ironclad proof because there is one remaining possibility. We don't actually have to store a

*separate record*of the results of our experiments in order to be able to reproduce the same sequence of results. It is enough simply to hang on to the particles themselves. Once we have made a measurement on a particle, if we make the same measurement again we will get the same result. So it's possible that the information that determines the results of experiments performed on particles is stored

*in the particles themselves*.

The usual way to dispense with this possibility is to invoke Bell's theorem and to point out that it rules out local hidden variables. But there's a more elementary (and, I think, more compelling) argument.

It is true that if we do the

*same*experiment on a single particle twice in a row we will get the same result. But nothing constrains us from doing different experiments on a single particle. We could, for example, measure the position of a particle, and then its momentum, and then its position again, and then its momentum again. If we do this, every result will be (apparently) random, completely disconnected from anything that has gone before. And (and this is key) we can do this

*forever*. We can perform an

*infinite*(well, OK, unbounded) number of measurements on one particle. For the results to be deterministic, the state of the particle would have to store an

*infinite*(and this time I really do mean infinite) amount of information.

Well, how do we know that this is not in fact the case? Bohmian mechanics, for example, is a theory of exactly this sort. In Bohmian mechanics, particles have positions, and (it turns out) all of the potentially infinite information that can be read out (eventually) via quantum measurements is encoded in the initial position of the particle. This is possible because the position of the particle is metaphysically exact, represented by an actual real number with an infinite number of digits in its expansion and hence can contain an infinite amount of information.

How do we know that this is not what is actually happening?

Well, we don't. Bohmian mechanics reproduces the predictions of quantum mechanics exactly so there is no way to settle the question experimentally. There are nonetheless three good reasons to reject Bohm as an adequate explanation of physical reality.

First, the way that Bohm handles spin is really weird, bordering on the perverse. Again for those who don't know, spin is a property of certain particles (mainly electrons) that can be measured and always produces one of two results (usually called "up" and "down" even though these don't actually have any physical significance). In Bohmian mechanics, the only metaphysically real property that a particle has is position (and hence also velocity, which is just the time derivative of the position as in classical mechanics). Spin is

*not*part of the metaphysically real state of a particle. When you think you're measuring spin, you're actually measuring the particle's

*position*(because that's all there is) but the wave function (the "pilot wave", the thing that's pushing the particle around) conspires to move the particle through spin-measurement apparatus in just such a way that it

*looks*as if the particle has spin, even though it really doesn't. Bohmian mechanics is

*quite literally*a cosmic conspiracy theory.

Second, Bohmian mechanics is

*causally non-local*. When you do an EPR-type experiment Bohm says that the underlying metaphysical reality is

*different*depending on the

*order*in which you perform the two measurements. But according to relativity, the order of space-like separated events is not well defined. So in order to extract an unambiguous description of physical reality from Bohm you have to arbitrarily assign an order to space-like separated events (the technical term for this is choosing a

*foliation*). There is no way to tell which foliation is

*correct*(if there were then you could experimentally falsify relativity) so the choice is arbitrary. But (and this is the crucial point) the fact that it is arbitrary

*completely undermines the whole point of adopting Bohmian mechanics to begin with*, which was to provide a complete description of physical reality that was compatible with classical intuition. Instead of one description of reality you have an arbitrary number of them, one for each possible foliation, and there's no way to tell which one is actually correct.

Third, although Bohm hangs his hat entirely on the physical reality of particle positions, it is

*fundamentally impossible*to know what the position of a particle actually is. Remember, when you measure the spin of a particle, on Bohmian mechanics you are not really measuring spin, you are really measuring position (because that's all there is). Well, it turns out that when you measure position you aren't really measuring position either. The only kind of measurement you can make is one that tells you whether or not the particle was inside or outside a particular (no pun intended) finite region of space. The actual position of a particle cannot be measured. So the one thing that Bohm advances as a description of physical reality turns out to be the operational equivalent of an invisible pink unicorn (IPU) — a thing that is posited to exist but which,

*by its very nature*, can never be measured.

There is an even simpler argument to demonstrate the non-measurability of Bohmian positions: a measurement can only ever produce a finite amount of information, but the information encoded in the particle's actual metaphysical position is necessarily infinite (because it has to encode the results of all possible

*future*measurements). So the results of position measurements

*must*contain errors.

And this is the crux of the matter: it just turns out as a matter of physical fact that a single particle can produce what appears to be an unbounded amount of information. There are only two possibilities: either that information is generated on the fly

*ex nihilo*, (that is, it's "really random") or it is stored somewhere. But no one has been able to identify any possible repository in the physical world where that information could be stored. In fact, QM

*fundamentally depends*on this not being possible! Interference effects only manifest themselves if there is

*no possible way to distinguish*two different states of a system. But to contain information, a system

*must*have distinguishable states -- that's what information

*means*! To be compatible with the data, a hypothetical repository of that information

*must necessarily*be an IPU. Any theory where the existence of such a repository was experimentally demonstrable would not be compatible with QM.

## 23 comments:

> Here's a clue: if the sequence of experimental outcomes was the result of simply replaying a record, or indeed of any kind of deterministic computational process (of which replaying a record is just one trivial example), we should be able to find

evidenceof that somewhere.So WP: Superdeterminism is just completely wrong? There's a quote from John Bell himself, there.

> So it's possible that the information that determines the results of experiments performed on particles is stored

in the particles themselves.>

> The usual way to dispense with this possibility is to invoke Bell's theorem and to point out that it rules out local hidden variables.

Yes you would need "nonlocal state" of some sort. Some day, I'd like someone to talk about what happens if you bombard an object with entangled particles which are spacelike separated upon impact. It seems to me that should do

somethinginteresting.> We can perform an

infinite(well, OK, unbounded) number of measurements on one particle. For the results to be deterministic, the state of the particle would have to store aninfinite(and this time I really do mean infinite) amount of information.Erm, you'd be constantly imparting impulses to the particle in the measurement process. Why would the particle have to store what you were going to do to it? (Things might change if you want to talk about weak measurement or interaction-free measurement, which I'd be happy to explore with you.)

> There is no way to tell which foliation is

correct(if there were then you could experimentally falsify relativity) so the choice is arbitrary. But (and this is the crucial point) the fact that it is arbitrarycompletely undermines the whole point of adopting Bohmian mechanics to begin with, which was to provide a complete description of physical reality that was compatible with classical intuition.Have you seen Can Bohmian mechanics be made relativistic? (81 'citations')? Perhaps jump to the paragraph starting with "The aim of this paper".

> Third, although Bohm hangs his hat entirely on the physical reality of particle positions, it is

fundamentally impossibleto know what the position of a particle actually is.But we also cannot observe quarks directly: WP: Color confinement. So it's ok for some things to exist in theory but not be [directly] observable. Apparently, there is some important distinction between quarks and position in de Broglie–Bohm mechanics?

@Luke:

> So WP: Superdeterminism is just completely wrong?

Do humans have free will? Because if they do, then yes, superdeterminism is completely wrong.

> Some day, I'd like someone to talk about what happens if you bombard an object with entangled particles which are spacelike separated upon impact.

Such experiments have been done. A lot. We know exactly what happens in that case.

> Erm, you'd be constantly imparting impulses to the particle in the measurement process.

No. Consider a photon going through a cascade of polarizing beam splitters. Each level in the cascade is oriented at 45 degrees to the previous one. The photon doesn't actually get "measured" until the very end. You can do the same thing with an electron and a cascade of Stern-Gehrlach setups. Or just aim a photon at an arbitrarily large screen: if the result is deterministic, then the information about which atom in the screen is the one that ends up absorbing the photon has to be stored somewhere. If the screen has N atoms, then you need to store log2(N) bits of information somewhere.

There is no getting around the fact that quantum measurements produce an unbounded quantity of information. That information is either created ab-initio (i.e. quantum randomness is really random) or it is stored somewhere that is inherently inaccessible (i.e. it is an IPU) , or quantum mechanics is wrong. Those are the only possibilities.

> Have you seen Can Bohmian mechanics be made relativistic? (81 'citations')?

Yes. And the answer is: yes it can, but you have to choose a foliation. There is a whole paragraph about this in the OP.

> we also cannot observe quarks directly

We can't observe *anything* directly. *All* of the data we have about the world is indirect. When you look at (say) the moon you aren't actually seeing the moon, you are seeing photons emitted by the sun and reflected off the moon. And you aren't actually seeing those photons either because the human retina isn't sensitive enough to detect individual photons. What you are seeing is the result of a shit-ton of photons hitting your retina, triggering electrical impulses in your optic nerve which are then processed by your visual cortex to produce the subjective sensation of seeing something that you call "the moon".

"The moon" -- and "photons" and "optics nerves" -- are all just stories that we tell (i.e. they are theories) that explain our subjective experiences better than any other competing theory. "Quarks" are exactly the same: they explain the data related to nuclear phenomena better than any competing theory. It is an interesting fact that the theory predicts that quarks never exist in isolation, but this in no way diminishes their explanatory power. Despite the fact that they don't exist in isolation we still know how they exist in combinations, and how what kind of physical effects those combinations produce. So despite the fact that quarks can't exist in isolation, we can nonetheless infer their state from experimental data. It's not fundamentally different in any way from how we infer the existence of the moon.

Bohmian positions are fundamentally different. They are a hypothetical state of a system that the theory itself asserts

can never be inferred from any measurement. They therefore haveexactlythe same ontological status as an invisible pink unicorn. It doesn't matter whether you call it a "position" or an "IPU". What matters is that it isnecessarily hiddenfrom any possible observation."We can perform an infinite (well, OK, unbounded) number of measurements on one particle. For the results to be deterministic, the state of the particle would have to store an infinite (and this time I really do mean infinite) amount of information"

Really not sure why the information stored has to be an infinite number of pre-determined results rather than simply a deterministic process. ie my computer does not store every possible configuration of bits it will need to hold in its memory for every possible outcome of all my applications' machinations, it just stores a deterministic set of instructions.

@Coby:

> Really not sure why the information stored has to be an infinite number of pre-determined results rather than simply a deterministic process.

Excellent question! It's because for a deterministic process to produce an unbounded number of random bits it needs an unbounded amount of storage, i.e. it has to be a fully fledged Turing machine. If it's merely a finite state machine then it will necessarily loop at some point, If that happened, QM would be proven to be wrong.

Another way to look at it: random sequences are incompressible, so to produce a sequence of N random bits requires at least N bits of state. If the output length is unbounded, then the amount of storage needed is therefore also necessarily unbounded.

Note that we cannot rule out the Cosmic Turing Machine by experiment. It can only be eliminated by the Popperian criterion of being a bad explanation (because it's an IPU).

@Ron:

> Do humans have free will?

I have argued that they do, but IIRC you accepted zero of those arguments.

> > Some day, I'd like someone to talk about what happens if you bombard an object with entangled particles which are spacelike separated upon impact.

> Such experiments have been done. A lot. We know exactly what happens in that case.

Don't those experiments bombard

separateobjects (detectors), each getting one of the entangled particles?> > > We can perform an

infinite(well, OK, unbounded) number of measurements on one particle. For the results to be deterministic, the state of the particle would have to store aninfinite(and this time I really do mean infinite) amount of information.> > Erm, you'd be constantly imparting impulses to the particle in the measurement process.

> Consider a photon going through a cascade of polarizing beam splitters. Each level in the cascade is oriented at 45 degrees to the previous one. The photon doesn't actually get "measured" until the very end.

But the quoted text (from the OP) has there being more than one measurement—indeed, many measurements. Now there is one measurement. What gives?

> Or just aim a photon at an arbitrarily large screen: if the result is deterministic, then the information about which atom in the screen is the one that ends up absorbing the photon has to be stored somewhere. If the screen has N atoms, then you need to store log2(N) bits of information somewhere.

I'm interested enough in this question to ask a physics PhD. I'm pretty sure that in a sophomore physics class I took, aimed toward physics majors, it was shown that you just need double the amount of accessible information in order to yield completely deterministic time-evolution of state. I can try to find those notes.

> Yes. And the answer is: yes it can, but you have to choose a foliation. There is a whole paragraph about this in the OP.

From the paper I cited:

>> The aim of this paper is to question this perspective by suggesting a rather general strategy for making Bohmian theories compatible with fundamental relativity. In Bohmian theories, the dynamics of the particles (or fields) is defined in terms of structures extracted from the wave function. The strategy proposed here involves extracting from the wave function also a foliation of space–time into space-like hypersurfaces, which is used to define a Bohmian dynamics in a manner similar to the way equal-time hyperplanes are used to define the usual Bohmian dynamics.

We show how this extraction can itself be Lorentz invariant in an appropriate sense and argue that virtually any relativistic quantum theory, Bohmian or otherwise, will thus already contain a special space–time foliation, buried in the structure of the wave function.This makes it difficult to imagine how one could question the ‘seriously relativistic’ character of the Bohmian theories to be described, without simultaneously denying that any theory in which something similar to a universal wave function plays a fundamental role can be a candidate for serious compatibility with relativity. (Can Bohmian mechanics be made relativistic?)I wanted you to come across the bold bit.

> We can't observe *anything* directly.

So when WP: Color confinement contains "… therefore cannot be directly observed in normal conditions …", it's just 100% nonsense?

@Luke:

> > Do humans have free will?

> I have argued that they do, but IIRC you accepted zero of those arguments.

Yes, but if I'm trying to persuade *you* of something, particularly something that by its very nature cannot be ruled out by experiment, don't you think it's more effective to base those arguments on things that *you* believe?

> Don't those experiments bombard separate objects (detectors), each getting one of the entangled particles?

Um, yes. You wrote:

> Some day, I'd like someone to talk about what happens if you bombard an object with entangled particles which are spacelike separated upon impact.

How are you going to have space-like separation without having separate detectors?

> more than one measurement—indeed, many measurements. Now there is one measurement

Yes, one measurement with N possible outcomes for an arbitrarily large value of N. (I changed this to answer your objection that a measurement disturbs the system and so this disturbance could potentially be the source of the information produced by the measurement. In my original presentation this was a valid objection. In the revised version -- which is just an extreme riff on Wheeler's classic delayed choice experiment -- it is not. See, this is how peer review works: one party raises a valid objection, and the other either revises their argument or concedes.)

> I'm interested enough in this question to ask a physics PhD.

By all means. I'd be interested to hear what they have to say.

> I wanted you to come across the bold bit.

I did. I don't understand why you think it's relevant.

> So when WP: Color confinement contains "… therefore cannot be directly observed in normal conditions …", it's just 100% nonsense?

Um, no. Why would you think that?

@Ron:

> Yes, but if I'm trying to persuade *you* of something, particularly something that by its very nature cannot be ruled out by experiment, don't you think it's more effective to base those arguments on things that *you* believe?

That depends on whether the most consistent system I know of which accommodates the thing you are persuading me of is

yourway of thinking ormine. In this case, I'm running withyourway of thinking because you have rejected mine so often and so thoroughly whenever it disagrees with yours. (I'm not sure I've changed your mind on more than two things in all our interaction.)> How are you going to have space-like separation without having separate detectors?

By having an object extended in space where the paths taken by each pair of entangled photons is carefully controlled. Ostensibly, you could bombard a single atom with entangled photons from different angles.

> By all means. I'd be interested to hear what they have to say.

Will do.

> I did. I don't understand why you think it's relevant.

If the alternatives to de Broglie–Bohm mechanics

alsorequire "a special space–time foliation", then how is this a liability of de Broglie–Bohm, compared to the otherextantinterpretations?> [OP]: Third, although Bohm hangs his hat entirely on the physical reality of particle positions, it is

fundamentally impossibleto know what the position of a particle actually is.> Luke: we also cannot observe quarks directly

> Ron: We can't observe *anything* directly.

> Luke: So when WP: Color confinement contains "… therefore cannot be directly observed in normal conditions …", it's just 100% nonsense?

> Ron: Um, no. Why would you think that?

Because of what you wrote: "We can't observe *anything* directly." WP: Color confinement is clearly assuming that plenty of things

can"be directly observed in normal conditions". Otherwise, it'd make no sense to say that you can't do something with quarks that you can't doanywhere.@Luke:

> By having an object extended in space where the paths taken by each pair of entangled photons is carefully controlled. Ostensibly, you could bombard a single atom with entangled photons from different angles.

Ah. So what I *think* you're saying is that you want to take one atom and put it in a superposition of position states, and then do an EPR experiment with the two locations of the single atom being the targets of the two members of the entangled pair. Is that right?

I'm not aware of any such experiment ever having been done. I also see no reason to think that anything particularly interesting to happen if you did.

> If the alternatives to de Broglie–Bohm mechanics also require "a special space–time foliation"

They don't. Some do (and those that do can be rejected IMHO) but not all do.

There are really only four interpretations of QM that are at all tenable: Bohm, GRW collapse, Multiple Worlds, and QIT/relative-state/QBism/many-minds/whatever-you-want-to-call-it. And even those last two are really the same (except that the many-worlders would vehemently deny this). Which of these you choose is largely a matter of taste. Personally I have a distaste for Bohm, but if it makes you feel warm and fuzzy to think particles have actual positions, don't let me stand in the way of your happiness.

> WP: Color confinement is clearly assuming that plenty of things can "be directly observed in normal conditions"

Ah, I see what you're saying. Yes, this is misleading. A more accurate way of putting it is that individual quarks can't be observed *in isolation" from one another under normal conditions (you'd need a temperature of two trillion degrees or so).

P.S.:

> quarks can't be observed *in isolation" from one another under normal conditions

By way of very stark contrast, Bohmian positions can't be known (except approximately) under *any* circumstances.

>> Really not sure why the information stored has to be an infinite number of pre-determined

>> results rather than simply a deterministic process.

> Excellent question! It's because for a deterministic process to produce an

> unbounded number of random bits it needs an unbounded amount of storage,

I think your answer is assuming the thing you're trying to assess. i.e. is the behaviour really random? Can't a finite and deterministic process produce results that are hard (impossible maybe, I wouldn't know) to distinguish from randomness given a chaotic sequence of inputs?

> Can't a finite and deterministic process produce results that are hard (impossible maybe, I wouldn't know) to distinguish from randomness given a chaotic sequence of inputs?

Nope. All finite deterministic processes must eventually either halt or loop.

Hmm. Well I don't claim any sophisticated knowledge of the underlying topic, I''m mostly just challenging your reasoning here so we might be talking past each other.

Now, clearly a deterministic and finite process can produce an infinite sequence of random outputs where the output depends on some kind of input and where that input is itself random.

F(x) = x + 1 will do so fed a random and infinite sequence of x's.

So if a quantum particle is governed by some kind of deterministic process and that process is receiving some chaotic sequence of inputs why can't it's behaviour have the appearance of randomness?

eg. Our particle's behaviour is governed by this process: "If my position is measured in a manner with value = x, appear at position F(x)" and those property values are chaotic or random then the position at time of measurement appears random, but is actually deterministic.

What am I missing here?

> So if a quantum particle is governed by some kind of deterministic process and that process is receiving some chaotic sequence of inputs why can't it's behaviour have the appearance of randomness?

That's possible, but it begs the question. Where is the chaotic input coming from? It has to be coming from some physical process, and that physical process has to have some state. Where could that state possibly be stored?

> That's possible, but it begs the question. Where is the chaotic input coming from?

Indeed, it does. I'd say it's turtles, all the way down.

But more seriously, this is a problem with your argument IMO and really with the whole logical proof approach to a physical system model's underlying nature. The model either does a good enough job for what we can measure or it does not.

Personally, I am happy with quantum indeterminism because it seems that without it, or something else non-deterministic governing the universe, we can not escape the conclusion that the future is baked in to the present and unalterable.

I don't believe that it is, but I'm really not convinced that this can ever be conclusively proven. I take it as an article of faith.

I don't recall all of the reasoning that got me there, but I long ago concluded that there is no belief system possible that does not begin with some initial leap of faith somewhere, even the most rigorously rational and scientific belief system. (That's not to say all leaps of faith are equally defensible...!)

Sorry if I'm kind of verbally meandering out loud.

@Coby:

> turtles, all the way down

You do realize that phrase was originally the punch line of a joke, right?

The fact that you cannot give a serious answer to that question (and neither can anyone else) is all the evidence necessary to show that your theory is false.

> no belief system possible that does not begin with some initial leap of faith somewhere

That's actually not true. See:

http://blog.rongarret.info/2015/03/why-some-assumptions-are-better-than.html

> The fact that you cannot give a serious answer to that question (and

> neither can anyone else) is all the evidence necessary to show that your theory is false.

Um, it's your proposition we are discussing. You constructed an argument purporting to show that deterministic behavior of a quantum particle is impossible and I pointed to what I thought was a hole in your argument. (And you did concede this above - "That's possible").

So I guess "my theory" is that it is not impossible, given what we know today, that there is a deterministic process governing a particle's behavior. I do not have to find the mechanism to show I'm correct, I only have to show how it could be possible.

But like most long enough internet discussions we are likely past the useful point. Showing something is possible in the abstract is not the same as arguing it is there and I don't have an issue with non-deterministic behaviors. I do, however, remain open to the possibility that there is in fact something more than random going on.

I'll try to read your other article tomorrow.

Kind regards from Australia

> So I guess "my theory" is that it is not impossible, given what we know today, that there is a deterministic process governing a particle's behavior. I do not have to find the mechanism to show I'm correct, I only have to show how it could be possible.

Yes, but you haven't done that. "Turtles all the way down" is not a serious proposal for how it could be possible.

If you try to construct a non-joke proposal for how it could be possible you will find that one of the following will be the case:

1. Your proposal will be an IPU.

2. Your proposal will involve assuming that QM is somehow wrong but without specifying how.

3. You will win the Nobel prize in physics.

You really REALLY need to read chapter 7 of "The Fabric of Reality".

The Rods. It's The Rods@Ron:

And you aren't actually seeing those photons either because the human retina isn't sensitive enough to detect individual photons.Direct detection of a single photon by humans

Correspondence: Still no evidence for single photon detection by humans - maybe

DIY: Observing Single Photons

The Human Eye Could Help Test Quantum Mechanics

A brief history of quantum alternatives

Correction for nitpickers:

"And you aren't actually seeing those photons either because the human retina isn't sensitive enough to detect individual photons WHILE YOU ARE LOOKING AT THE MOON."

NINE NINE NINE NINE . . .Two articles from American Scientist on the same theme (author: Scott Aaronson)

The Quest for Randomness

Quantum Randomness

Tangentially related:

An essay on quasirandom numbers (author: Brian Hayes):

Quasirandom Ramblings

In the "Random Variations" section, he provides some interesting definitions.

"The concept of randomness in a set of numbers has at least three components.

* First, randomly chosen numbers are unpredictable: There is no fixed rule governing their selection. '

* Second, the numbers are independent, or uncorrelated: Knowing one number will not help you guess another.

* Finally, random numbers are unbiased, or uniformly distributed: No matter how you slice up the space of possible values, each region can expect to get its fair share."

"These concepts provide a useful key for distinguishing between truly random, pseudorandom, quasirandom and orderly sets. \

* True random numbers have all three characteristics: They are unpredictable, uncorrelated and unbiased.

* Pseudorandom numbers abandon unpredictability; they are generated by a definite arithmetic rule, and if you know the rule, you can reproduce the entire sequence. But pseudorandom numbers are still uncorrelated and unbiased (at least to a good approximation).

* Quasirandom numbers are both predictable and highly correlated. There’s a definite rule for generating them, and the patterns they form, although not as rigid as a crystal lattice, nonetheless have a lot of regularity. The one element of randomness that quasirandom numbers preserve is the uniform or equitable distribution. They are spread out as fairly and evenly as possible."

>> I do not have to find the mechanism to show I'm correct, I only

>> have to show how it could be possible.

>Yes, but you haven't done that.

Now you're just being stubborn. You've already conceded this at 6/12/2019 7:32 PM:

coby: So if a quantum particle is governed by some kind of deterministic process and that process is receiving some chaotic sequence of inputs why can't it's behavior have the appearance of randomness?

Ron: That's possible

You should just retreat from "determinism is not possible" to "given what we know, there is no reason to think quantum behavior is deterministic"

I grant you that "something no one has yet seen just might be there" is not a profound point to make but it is sufficient to refute your point that it is a logical impossibility.

>> If you try to construct a non-joke proposal for how it could be

>> possible you will find that one of the following will be the case:

>>

>> 1. Your proposal will be an IPU.

>>

>> 2. Your proposal will involve assuming that QM is somehow wrong

>> but without specifying how.

>>

>> 3. You will win the Nobel prize in physics.

Sigh. Models are not right or wrong, they are merely useful for a given purpose or not. History is littered with otherwise brilliant people who mistook their theories for Truth and could not conceive of any measurement they couldn't explain with it until one appeared, and sometimes not even then.

So I'll choose 2A: quantum mechanics is a fascinating and confounding model that successfully describes the universe as a strange and wonderful place, but there may yet be phenomena and measurements that will defy it's laws.

@Coby:

>>> I do not have to find the mechanism to show I'm correct, I only have to show HOW it could be possible. [emphasis added]

>>Yes, but you haven't done that.

> You've already conceded this

No, I didn't. I merely conceded THAT it was possible. I did not concede that you have shown HOW it could be possible. The word "how" is critical.

*Anything* is possible. It's possible that bigfoot is real. It's possible that the earth is flat. It's possible that the moon landings really were a conspiracy, and the advanced VR and mind control technology required to pull it off (so that not a single witness has ever come forward professing to have participated in the conspiracy) were provided by intelligent aliens. All of these things are possible.

But if you want to advance any of these hypotheses and have anyone not wearing a tinfoil hat take you seriously, you have to do more than stand up on a soap box and proclaim that because science does not yet understand everything, that it cannot rule out your crackpot theory. You have to provide an EXPLANATION of how your hypothesis fits into the currently known scheme of things. For example, if NASA used alien technology to produce the advanced special effects for the lunar landing fraud, why didn't they use this technology to, you know, GO TO THE MOON?

If you want someone to take seriously the hypothesis that quantum randomness is deterministic then you have to explain how this fits into the known mechanisms for producing deterministic processes. In particular, you have to explain WHERE THE STATE IS STORED. It's possible that you can do that, but so far you haven't done it. If you can do that in a way that is compatible with what is known about how the universe works, then you will, as I said, win the Nobel prize in physics. That is also not impossible. But I'll give you long odds against.

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