The Universe is Deterministic

[martu]

Bell's theorem is a mathematical theorem that applies to a class of models, so it doesn't require evidence. The relevant evidence are experiments that show Bell's inequality is violated, which means that the certain class of theories to which his theorem applies (deterministic, local, and "real") are not good descriptions of the world

After a bit of reading up I again wonder at how simple mathematics is very powerful indeed.

One thing I could not quite grasp is do the hidden variables only apply to things we could (in principle) measure? Many of the references discussed that there could exist properties we will one day 'discover' (with better measuring devices perhaps) but what if these variables were forever hidden from us? For example what if they were properties of a 4 dimensional object we'd never be able to measure in our 3 dimensional space?

 

[sol invictus]

After a bit of reading up I again wonder at how simple mathematics is very powerful indeed.

Amazing, isn't it?

One thing I could not quite grasp is do the hidden variables only apply to things we could (in principle) measure? Many of the references discussed that there could exist properties we will one day 'discover' (with better measuring devices perhaps) but what if these variables were forever hidden from us? For example what if they were properties of a 4 dimensional object we'd never be able to measure in our 3 dimensional space?

Let's see... what's needed for Bell to prove his inequality is just that the property be determined (plus the other assumptions we've discussed). Of course if you can't ever measure that property (for practical reasons or otherwise) you'll never know whether the inequality for it is violated or not, so the existence of such determined-but-unmeasurable properties doesn't sound like it conflicts with anything. But if there are some things that are determined and some that aren't, you'd still call the theory non-deterministic.

You would have to be careful that these unmeasurable properties don't affect measurable ones in any way that conflicts with observation, though.

 

[martu]

Amazing, isn't it?

It is one of those "Why didn't someone think of it before" scenarios, so simple yet so rich.

Let's see... what's needed for Bell to prove his inequality is just that the property be determined (plus the other assumptions we've discussed). Of course if you can't ever measure that property (for practical reasons or otherwise) you'll never know whether the inequality for it is violated or not, so the existence of such determined-but-unmeasurable properties doesn't sound like it conflicts with anything. But if there are some things that are determined and some that aren't, you'd still call the theory non-deterministic.

You would have to be careful that these unmeasurable properties don't affect measurable ones in any way that conflicts with observation, though.

I get the first paragraph but not the second. Can you elaborate? If an unmeasurable property affects a measureable one how could we know? Or are you saying that, as in all physics, observation is key so don't 'make anything up' that is counter to experiment?

 

[sol invictus]

I get the first paragraph but not the second. Can you elaborate? If an unmeasurable property affects a measureable one how could we know? Or are you saying that, as in all physics, observation is key so don't 'make anything up' that is counter to experiment?

I meant only that if you were to produce a model with some apparently unmeasurable quantities, you'd have to be careful to be sure they were truly unmeasurable before being able to draw such conclusions. Sometimes, in fact just about all the time, any such change will in fact influence other aspects of the theory, thereby becoming measurable.

 

[martu]

I meant only that if you were to produce a model with some apparently unmeasurable quantities, you'd have to be careful to be sure they were truly unmeasurable before being able to draw such conclusions. Sometimes, in fact just about all the time, any such change will in fact influence other aspects of the theory, thereby becoming measurable.

Right thanks.

 

[Xulld]

We can know that the model is deterministic or not. We'll never know for certain whether the universe is.

Thank you, that is precisely what I took away from that paper. However I am not a philosopher, especially not one that confuses epistemic (knowledge), and ontic (what happens).

 

[dlorde]

Excuse me if I ramble a bit, but this thread has triggered some questions that have been lurking on the back of my mind for some time.

As an old-time fan of science-fiction, the Many-Worlds interpretation of QM has always appealed emotionally (and appears to have the advantage of saving us from indeterminism, if not uncertainty), but, due to a lack of understanding, I've always had a problem with the 'practicality' of it, i.e. how it works...

One issue is what is meant by the universe 'splitting', so an observer of a QM event (wf collapse) becomes multiple observers, each in a universe where an alternate outcome has occurred. This seems rather profligate - having the entire universe replicating with every wf collapse. Do the 'duplicate' universes already exist in some sense? If not, where does the energy to duplicate an entire universe come from, and how is the split proposed to occur?

Either way, the spooky philosophical implication seems to be that everything that can happen has happened and will happen (in some universe or other).

Does it make more sense to think of it as a single universe wave-function in a superposition of all the states it can have taken since it started, and all the 'local' wave-function collapses we observe being artifacts of our restricted viewpoint (where we are actually included in the greater superposition)? If so, how should we view our own place in this superposition - is what feels like a continuous/contiguous individual consciousness really an ever spreading superposition of selves?

I feel the need for some kind of sum-over-histories approach, where the many worlds are somehow averaged out to the apparent reality we find ourselves in - but I suspect I'm being optimistic.

ISTR reading about a theory that spacetime has a fractal structure, where the outcome of a QM measurement/event depends somehow on the fractal boundaries within which the measurement occurs, the probabilities being determined by the percentage of spacetime within a particular boundary - but wouldn't that make the structure spacetime itself a kind of hidden variable...? I may be way off with this one - it wasn't easy to follow, but it sounded interesting.

Any comments, criticisms, comforts, and explanations welcome

 

[sol invictus]

One issue is what is meant by the universe 'splitting', so an observer of a QM event (wf collapse) becomes multiple observers, each in a universe where an alternate outcome has occurred. This seems rather profligate - having the entire universe replicating with every wf collapse.

True, it does seem that way. But in another more technical sense it's the simplest possibility consistent with experiment.

Do the 'duplicate' universes already exist in some sense? If not, where does the energy to duplicate an entire universe come from, and how is the split proposed to occur?

The energy doesn't change in the "splitting" process, because the total energy is not the sum of the energy of the two. In fact it's conservation of energy (or something very closely related) that tells us the universe must split that way.

Either way, the spooky philosophical implication seems to be that everything that can happen has happened and will happen (in some universe or other).

The way I see it, this interpretation actually defines what "can happen" means; that is, it puts probability on a physical footing.

I feel the need for some kind of sum-over-histories approach, where the many worlds are somehow averaged out to the apparent reality we find ourselves in - but I suspect I'm being optimistic.

Sum over histories is the correct approach. But the different histories only matter when they interfere with each other, like in a double slit experiment.
These MW "splits" don't interfere with each other at any detectable level because of decoherence.

ISTR reading about a theory that spacetime has a fractal structure, where the outcome of a QM measurement/event depends somehow on the fractal boundaries within which the measurement occurs, the probabilities being determined by the percentage of spacetime within a particular boundary... I may be way off with this one - it wasn't easy to follow, but it sounded interesting.

That's a whole different kettle of fish. There's no need to bring fancy spacetime structures into this, we can stick with plain old quantum field theory in flat smooth continuous space.

 

[dlorde]

The energy doesn't change in the "splitting" process, because the total energy is not the sum of the energy of the two. In fact it's conservation of energy (or something very closely related) that tells us the universe must split that way.

Hmm... doesn't the overall amount of information increase with every split? How does entropy factor into the evolution of the multiverse, if at all?

The way I see it, this interpretation actually defines what "can happen" means; that is, it puts probability on a physical footing.

Indeed, so the universes should have a seriously normal distribution (with our local group 'probably' somewhere high in the hump), but this still means that in some sense there is a universe 'out there' we can snigger about where the least probable event has always happened - doesn't it?

Sum over histories is the correct approach. But the different histories only matter when they interfere with each other, like in a double slit experiment.
These MW "splits" don't interfere with each other at any detectable level because of decoherence.

OK, I think I'm beginning to the hang of it, although, like so many things, the closer I try to look, the blurrier it becomes. Should have gone to SpecSavers

That's a whole different kettle of fish. There's no need to bring fancy spacetime structures into this, we can stick with plain old quantum field theory in flat smooth continuous space.

OK. 'Plain old' QFT it is

 

[sol invictus]

Hmm... doesn't the overall amount of information increase with every split?

No, that's precisely what doesn't happen. You see, if QM were really random, it would be losing information (generating entropy) every time a measurement is made. That's inconsistent with conservation of information (which is called "unitarity"). But in MW the evolution is unitary, so that every final state is uniquely related to an initial state.

You might be confused by the term "split", which sounds like a bifurcation where one line turns into two. But that's really not what happens in MW; there is no absolute separation between the two halves (although they interfere only extremely weakly).

How does entropy factor into the evolution of the multiverse, if at all?

The true microscopic entropy remains constant, as it does in any unitary evolution. But of course the thermodynamic entropy as measured in any one of the "worlds" will increase as usual.

Indeed, so the universes should have a seriously normal distribution (with our local group 'probably' somewhere high in the hump), but this still means that in some sense there is a universe 'out there' we can snigger about where the least probable event has always happened - doesn't it?

Yes. In MW probability is real in the sense that every possibility is realized in some branch of the wave function. More common events are realized more times and are therefore more typical.

 

[Perpetual Student]

s. i.:
Of the several interpretations of QM (link), MW seems to me to be the least likely. I find it curious that it is the one you prefer. I would be interested in hearing more about your reasons, if you would be willing to indulge me.

 

[LordoftheLeftHand]

Since all the interpretations gives the same predictions for any event, isn't it kind of silly to argue about which one is right and wrong? Personally I'd bet they are all wrong. But who knows.

 

[dlorde]

You might be confused by the term "split", which sounds like a bifurcation where one line turns into two. But that's really not what happens in MW; there is no absolute separation between the two halves (although they interfere only extremely weakly).

That was exactly the point that was causing my confusion. You've resolved the problem for me - I was torn between visualising it as a 'physical' split resulting in two 'copies', and seeing it as another set of 'ripples' in the overall wavefunction. The former leads to a host of problems & contradictions, but the latter, although it may not be entirely accurate, makes a lot more sense - particularly in terms of information, energy, entropy, interference, etc.

The difficulty now is in grasping why/how we see the particular aspects (universes) of this greater superposition that we do...

Thanks Sol, for your patient explanations

 

[sol invictus]

s. i.:
Of the several interpretations of QM (link), MW seems to me to be the least likely. I find it curious that it is the one you prefer. I would be interested in hearing more about your reasons, if you would be willing to indulge me.

I would but don't have much time now. I think if you search for posts of mine containing MW or many worlds you'll find a fair number, as I've discussed it here several times before.

Since all the interpretations gives the same predictions for any event, isn't it kind of silly to argue about which one is right and wrong?

They don't give the same predictions. Copenhagen isn't even well-defined enough to give predictions in some situations, because it doesn't specify precisely under what circumstances the wave function collapses (i.e. what a "measurement" is).

 

[Tumbleweed]

Yes, radioactive decay is entirely quantum mechanical.

Holy crap I got one right!

 

[Tumbleweed]

Why do you use the word choose? I know you've put it in quotes so I don't think it is a conscious choice but aren't we just saying that this object can be either 'up' or 'down' and we don't know which one it is until we measure it? This is no different to putting a spider in an empty dark room with one half of the floor red and the other blue (with magical walls it can't get up...) and letting it wander about. Until we turn on the light we don't know where the spider is but we know it is either on red or blue. By turning on the light we don't make the spider 'choose', the choice depends on the time we measure it which is the time we turn on the light.

I guess this goes to the heart of the Copenhagen interpretation and that famous cat


But are you putting an actual spider in that room or the possibility of a spider by putting a wave function of the spider in the room rather than an actual physical spider. So QM is saying that the process of observing - that in reality is bouncing photons off of a wave function, something that happens a lot in nature without us "observing" -- creates reality, or particles, out of a wave function, and where that spider ends up - on a red or blue tile is random. In addition a twin entangled spider is created when the wave function collapses that will always end up on the opposite color tile as the "created" spider does. Not only that but the possibilty exists that when the spider wave function is collapsed by bouncing a photon off of it, it may appear outside the room altogether along with its twin entangled spider. Is that kind of right?

 

[Perpetual Student]

I would but don't have much time now. I think if you search for posts of mine containing MW or many worlds you'll find a fair number, as I've discussed it here several times before.

OK, thinks. I'll try that.

 

[INRM]

Reality Check,

• can be interpreted in various ways and so does not "kind of defeats the whole Heisenberg uncertainty principle".
• did not "measure the energy state and velocity/location of the particles at the same time".

The statement "can be interpreted in various ways" may be so, but there is only one right answer regardless of how one chooses to interpret it.

Agree?

 

[Eggs Ackley]

No one seems to have mentioned that there are some respectable dissenters to the conventional interpretation of the Bell's theorem experiments that they confirm the universe is necessarily non-deterministic and/or non-local on a microscopic scale. The best known of these is probably Christian, who is an Oxford professor, and earned his doctorate under Abner Shimony, who is one of the prominent Bell's inequality theorists (Shiminoy being the S in the CHSH inequality described in the wikipedia article). Here is a quote from Christian's newest paper on the subject (http://arxiv.org/abs/0904.4259):

No-go theorems in physics are often founded on unjustified, if tacit assumptions, and Bell’s theorem is no exception.
It is no different, in this respect, from von Neumann’s theorem rejecting all hidden variables [1], or Coleman-Mandula
theorem neglecting supersymmetry [2]. Despite being in plain sight, the unjustified assumptions underlying the latter
two theorems seemed so innocuous to many that they escaped detection for decades. In the case of Coleman-Mandula
theorem—which concerned combining spacetime and internal symmetries—it took a truly imaginative development
of supersymmetry to finally bring about recognition of its limited veracity. In the curious case of von Neumann’s
theorem, however, even an explicit counterexample—namely, the pilot wave theory [3][4]—did not discourage a series
of similarly misguided “impossibility proofs” for decades [5]. Thus ensued over half a century of false belief that no
such completion of quantum mechanics is possible, even in principle. Unfortunately, as is evident from the widespread
belief in Bell’s theorem, such examples of institutionalized denial are not confined to the history of physics. Just as in
the premises of von Neumann and Coleman-Mandula theorems, the unjustified assumption underlying Bell’s theorem
is also in plain sight—in the very first equation of Bell’s paper [6]—and yet it has received little attention. As innocent
as this equation may seem, it amounts to assuming incorrect topology for the EPR elements of reality [7]. The aim
of the present paper is to bring out this topological error explicitly, and demonstrate that—once recognized and
corrected—it gives way to an intrinsically local and manifestly realistic underpinning of the EPR-type correlations,
thereby providing explicit counterexamples to Bell’s theorem and several of its variants [8][9][10][11][12].

 

[dasmiller]

I apologize if this has come up before, but-

Does the fact that the future isn't fully knowable imply that the past isn't fully knowable? So that (this seems really creepy to me) we don't, in fact, have a particular past?

In a related thought, I'd think that in MW, the number of universes wouldn't necessarily keep increasing because there'd be convergences just like there were bifurications.

I've warned before about my fuzziness on QM.