I Multiverse theory -- Why don't strange things happen here sometimes?

[gentzen]

Do you have a reference for this discussion?

See for example in Griffiths' book Consistent Quantum Theory

Ch. 10 Consistent Histories: Text ( PostScript or PDF )

at the top of page 124:

Must the orthogonality conditions in (10.20) be satisfied exactly, or should one allow small deviations from consistency? Inasmuch as the consistency conditions form part of the axiomatic structure of quantum theory, in the same sense as the Born rule discussed in the previous chapter, it is natural to require that they be satisfied exactly. On the other hand, as first pointed out by Dowker and Kent, it is plausible that when the off-diagonal terms $\langle K(Y^\alpha), K(Y^\beta)\rangle$ in (10.24) are small compared to the diagonal terms $\langle K(Y^\alpha), K(Y^\alpha)\rangle$, one can find a “nearby” family of histories in which the consistency conditions are satisfied exactly. A nearby family is one in which the original projectors used to define the events (properties at a particular time) making up the histories in the family are replaced by projectors onto nearby subspaces of the same dimension. For example, [...]. Of course, the histories in the nearby family are not the same as those in the original family. Nonetheless, since the subspaces which define the events are close to the original subspaces, their physical interpretation will be rather similar. In that case one would not commit a serious error by ignoring a small lack of consistency in the original family.

But let me add that I just mentioned this trouble with inexact zeros in CH to avoid that my comment gets misinterpreted as an attack on MWI or some of its proponents. I didn't want to attack CH or open an unrelated discussion about CH in this thread.

 

[kered rettop]

These alternative worlds with habitually flying pigs cannot be assumed to exist until the model has been tested in this respect.

In the third case, a tweak to QM could rule out the existence of habitually bizarre worlds.

Which is why I was careful to say "And a huge number of those worlds will be ones where pigs have been observed flying to a warmer clime for the winter." "Have been observed", not "are habitually observed". Now, I'm pretty sure that a one-off very unlikely event could be concocted which would leave a more-or-less permanent change to pig-genetics, but I wanted to avoid splitting that particular hair. Consider the flying pigs - and the galaxy that experiences them - to be Boltzmann brains. That is very much in the spirit of the OP's question and relegates QM to the role of providing a statistical ensemble of parallel worlds which, in MWI, co-exist. I agree that I have made the assumption that it does so without making exceptions for flying pigs. Peter Donis has pointed out that although it is widely assumed, it is not, in his experience, ever actually proven.

 

[PeroK]

It's largely irrelevant to the argument but "flying to a warmer clime for winter" carries more than a hint of habitual behaviour, IMO.

Moreover, it's far more likely that pigs on the wing would be caused by freak weather than QM improbabilities. The former is by no means impossible.

 

[DaveC426913]

"And a huge number of those worlds will be ones where pigs have been observed flying to a warmer clime for the winter."

In the world of flying pigs, flying pigs are not considered weird, so they think their world is the normal one.

In our world...

• of duck-billed, poison-spurred, egg-laying mammals : platypus' are not deemed weird...
• with a moon that is 400 times smaller than our sun - as well as 400 times closer than our sun : perfect total eclipses are not deemed weird...
• where the universe's curvature is as close to flat as we can measure - and in danger of neither the Big Crunch nor the Big Freeeze nor the Big Rip - timescales on the order of 100 trillion years...are not deemed weird...

... so we think our world is the normal one.

"What does a fish know about the water in which he swims all his life?"

 

[kered rettop]

It's largely irrelevant to the argument but "flying to a warmer clime for winter" carries more than a hint of habitual behaviour, IMO.

Yeah, sometimes when someone uses a phrase like "have been observed" readers may not immediately realize that it's there for a reason, not just to pad out the sentence.

Moreover, it's far more likely that pigs on the wing would be caused by freak weather than QM improbabilities. The former is by no means impossible.

Indeed so. However the discussion here is not about finding the best explanation of strange events, it's whether some strange events do actually occur because of "QM improbabilities". (Sounds like something from HHGG!)

 

[kered rettop]

If an amplitude of 10^-1000 leads to totally different conclusions than an amplitude which is exactly zero, then the corresponding interpretation has robustness issues.

10^-1000? Is that Gentzen's Constant? Never heard of it.

Matter of fact, it happens to be equal to a very well known amplitude, namely that of a Schroedinger Cat world - as defined on PF recently (#30) - with about one second time resolution. Hardly small in the grand scheme of things where amplitudes routinely drop below a googolth.

The point being, of course, that MWI worlds often have unimaginably small amplitudes, and if there were a threshold, MWI would be easily testable - as the universe (or our rational response to it) would change dramatically when the threshold was reached.

It's hard to see why small numbers should entail robustness issues. Unless you refer it to some other state, an amplitude in QM is meaningless. In fact, the self-locating uncertainty you refer to is a justification for normalising the amplitude - once we are considering just a single world from the point of view of an embedded observer.

(If somebody objects that this amplitude of $10^{-1000}$ still implies the existence of some outcome, one could counter this by analyzing the role played by that existence in some popular MWI approaches, and how MWI actually makes things better instead of worse by not insisting on the impossibility of those outcomes.)

Please do. (Analyse it, I mean.) This is what I was/am going to PM you about.

I'm not sure what you mean by "makes things better". You seem to be saying that the impossibilities disappear if you refrain from postulating that the possibilities disappear. That looks suspiciously like a tautology!

 

[PeroK]

We have a thread on QM where it's the statement that pigs can't fly that draws the skeptical response!

To be honest, I don't think the key characteristic of QM is that people can walk through walls or pigs can fly - or sing the US national anthem in the style of a barbershop quartet. QM is there to predict and understand natural phenomena that can be tested by experiment. Once you go beyond that, it becomes increasingly difficult to assess the meaningfulness of what is being discussed.

The fundamental difference between mathematics, physics and philosophy is that mathematics and physics can be demonstrated to be correct in some sense - either through a formal proof, numerical analysis or experimental corroboration. Once you talk about things that a) have no realistic likelihood or ever being observed; and, b) may not even be predicted by the theory in any case; then, you can say anything you like and claim that QM supports you. That seems to me a vacuous philosophy.

 

[Orodruin]

Why is our universe so "normal" if there is always a chance of strange things happening?

Because even if there is a chance, that chance may be vanishingly small.

 

[kered rettop]

We have a thread on QM where it's the statement that pigs can't fly that draws the skeptical response!

Don't tempt me!

To be honest, I don't think the key characteristic of QM is that people can walk through walls or pigs can fly - or sing the US national anthem in the style of a barbershop quartet. QM is there to predict and understand natural phenomena that can be tested by experiment. Once you go beyond that, it becomes increasingly difficult to assess the meaningfulness of what is being discussed.

I actually agree with that. But only up to "increasingly difficult". We can't experimentally prove that lab-scale two-slit interference occurs in a distant galaxy, but that doesn't make the prediction meaningless. It's trivial to add a caveat saying "we can extrapolate our local findings" or "invoking Occam's Razor to rule out ad-hoc additions" etc. Yes, that is slightly more difficult than discussing local experiments, but it's hardly catastrophic. Flying pig worlds requires a few caveats too including the curious fact that a mentor here is unaware of any peer-reviewed paper justifying the assumption of a non-zero amplitude which everybody else seems to take for granted. But once it's all pinned down, why should it be any less meaningful, just because we don't have a quantum telescope to look at the pigs as they fly past?

The fundamental difference between mathematics, physics and philosophy is that mathematics and physics can be demonstrated to be correct in some sense - either through a formal proof, numerical analysis or experimental corroboration. Once you talk about things that a) have no realistic likelihood or ever being observed; and, b) may not even be predicted by the theory in any case; then, you can say anything you like and claim that QM supports you. That seems to me a vacuous philosophy.

Not at all. The "no realistic likelihood of being observed" is specious for the reasons I just gave. However the "may not even be predicted" is a genuine concern. But it's a simple question of fact: either the theory does predict it or it doesn't. In either case the proposition is meaningful: in the first it is true, in the second it is false. The fact that we don't know which doesn't make it meaningless.

 

[vanhees71]

We have a thread on QM where it's the statement that pigs can't fly that draws the skeptical response!

To be honest, I don't think the key characteristic of QM is that people can walk through walls or pigs can fly - or sing the US national anthem in the style of a barbershop quartet. QM is there to predict and understand natural phenomena that can be tested by experiment. Once you go beyond that, it becomes increasingly difficult to assess the meaningfulness of what is being discussed.

The fundamental difference between mathematics, physics and philosophy is that mathematics and physics can be demonstrated to be correct in some sense - either through a formal proof, numerical analysis or experimental corroboration. Once you talk about things that a) have no realistic likelihood or ever being observed; and, b) may not even be predicted by the theory in any case; then, you can say anything you like and claim that QM supports you. That seems to me a vacuous philosophy.

This reminds me that quantum theory is sometimes considered to belong to esoterics. Once, I went to a book shop and asked for some popular-science book about QM (I think it was the nice book by Zeilinger "Einsteins Schleier", of which I surprisingly can't find an English translation), because I couldn't find it under "natural sciences". They told me, I should look at the shelf with books on esoterics. To my surprise, indeed the book was there!

 

[PeroK]

The "no realistic likelihood of being observed" is specious for the reasons I just gave.

It's not specious, it's standard scientific thought. You can't extrapolate any theory to the ultimate degree without experimental evidence. In general, the more you extrapolate the more careful you have to be with your conclusions. Perhaps no one has ever dropped a pig and a chicken in a vacuum chamber to see whether they fall at the same rate. But, that's a minor extrapolation of the experiments that have been done to confirm that aspect of the law of gravity. Hence it's a perfectly valid conclusion without a specific experiment.

What is specious is to put flying pigs on the same footing as assumptions based on the observations of distant stars, whose spectroscopy corroborates the idea that the laws of physics there are the same as the laws of physics here.

Moreover, such an assumption is capable of being falsified. Which your flying pigs are not! We might discover anomalies in distant observations - in fact, apparently anomalous galactic rotation curves have resulted in theories suggesting a modification to the law of gravity (MOND). This is what mainstream science looks like.

The theory of spectroscopy is robust. Whereas, one theoretical tweak to the universal wavefunction and your whole universe of flying pigs disappears in a puff of mathematics.

Your theory of flying pigs relies on an untested and uncorroborated interpretation of QM. What if branching is finite? What if the wavefunction is an approximation of natural processes (in the same way that a continuous mass distribution is an approximation of a large number of atoms)? Then "everything possible" happens, but it is a finite set of outcomes that stays within certain bounds and doesn't admit flying pigs.

I note that your posts have almost exclusively focused on the extreme aspects of QM. Half-alive, half-dead cats; ghastly universes; flying pigs. These may be extreme apsects of what QM may predict - although there are plenty of physicists who don't believe this stuff at all. The fact that some physicists do believe in these aspects of the theory does not make it valid in anything like the sense that spectroscopy is valid. From that point of view, you cannot put these potential apsects of QM on the same footing as established experiments like the double-slit.

 

[kered rettop]

I note that your posts have almost exclusively focused on the extreme aspects of QM.

I would be interested to know what conclusions you draw from that. It sounds suspiciously like a thinly-veiled ad hominem. There several possible explanations: I could be a crank. I could just be interested in MWI. I could have studied QM to degree level and been revisiting some topics which were obscure.

 

[kered rettop]

What is specious is to put flying pigs on the same footing as assumptions based on the observations of distant stars, whose spectroscopy corroborates the idea that the laws of physics there are the same as the laws of physics here.

Which is precisely why I used a different example where such corroboration does not exist.

The theory of spectroscopy is robust. Whereas, one theoretical tweak to the universal wavefunction and your whole universe of flying pigs disappears in a puff of mathematics.

Good. I hope it does. I am not arguing that flying pig worlds actually exist, I am only saying that under "standard" MWI they do.

 

[kered rettop]

I note that your posts have almost exclusively focused on the extreme aspects of QM. Half-alive, half-dead cats; ghastly universes; flying pigs. These may be extreme apsects of what QM may predict...

IMO, the most extreme prediction of QM is violation of the Bell Inequalities. What are flying pigs, compared with the incorrigible non-locality of the wave function?

 

[gentzen]

10^-1000? Is that Gentzen's Constant? Never heard of it.

No, my constant (or rather bound) was 1/3500000, i.e. not so vanishingly small.

The point being, of course, that MWI worlds often have unimaginably small amplitudes, and if there were a threshold, MWI would be easily testable - as the universe (or our rational response to it) would change dramatically when the threshold was reached.

I guess you try to apply the threshold too naively, namely by setting the amplitudes smaller than the threshold to 0. But that would still have robustness issues, as you point out. What one does in practice (of robust statistics) is rather the opposite, namely to treat all values smaller than the "bound" in the same way as the value of the bound itself. A typical example for this strategy is https://en.wikipedia.org/wiki/Huber_loss
In this way, everything stays continuous, and your "if there were a threshold, MWI would be easily testable" objction is avoided.

It's hard to see why small numbers should entail robustness issues. Unless you refer it to some other state, an amplitude in QM is meaningless. In fact, the self-locating uncertainty you refer to is a justification for normalising the amplitude - once we are considering just a single world from the point of view of an embedded observer.

I now gave two examples for CH of such robustness issues in another thread.

I'm not sure what you mean by "makes things better". You seem to be saying that the impossibilities disappear if you refrain from postulating that the possibilities disappear. That looks suspiciously like a tautology!

There was a follow-up post that gave an analogy to make it clearer what I mean by "make things better".

 

[kered rettop]

No, my constant (or rather bound) was 1/3500000, i.e. not so vanishingly small.

Sure. I understand they use 1% in British courts in order to provide some protection against the use of the Prosecutor's Fallacy and Meadow's Law.

But anyway, you seem to be talking about statistical techniques that "add robustness" to slightly flaky experimental data. Experimental data may contain outliers which have nothing to do with the thing you're trying to quantify: experimental errors, equipment malfunction, unhandled noise and so on. Not to mention plugs falling out. But in this case we're considering predicted frequencies in an idealised model so those things do not apply. Let's say it predicts some kind of Gaussian. You don't need to truncate it at five sigma just because they do that at CERN

 

[kered rettop]

The only thing which I find puzzling with the MWI is, why all of us experience obviously the same "branch of the universe".

Who is "all of us"? MWI explains precisely why all observers in the same branch experience the same world. It does not attempt to explain why observers in different branches experience the same world, because, by definition, they do not.

Also why don't I spontaneously experience a jump to another branch, i.e., I wake up one day and everything is at least slightly changed from yesterday?

How do you know you don't? You seem to assume that any such "jumping mind" would take its memories with it so it would notice the anomalies. Big assumption. You could be hopping around every couple of seconds and not be aware of it, if you have to adopt the memories of your brain in that branch.

The worlds of MWI cannot interact under quantum mechanics, so jumping would imply that you are a non-quantum entity. You can hardly criticise a quantum theory for not explaining how a non-quantum entity would work.

That said, Many Minds postulates that the brain in each branch has a mind which supervenes on the brain's configuration in that branch. Thus there are Many Minds. Seems sensible, seems obvious, and it avoids the problem you attribute to MWI.

 

[kered rettop]

@Lord Jestocost Why the sad reaction?

 

[physika]

All processes are fundamentally quantum.

I think there are irreducible emergent laws.

 

[PeterDonis]

I think there are irreducible emergent laws.

Personal speculation is off limits here. Please stick to the published literature on which the OP question is based.

 

[physika]

Personal speculation is off limits here. Please stick to the published literature on which the OP question is based.

Speculation ?
a lot of research in that area.
a lot of people.

 

[PeterDonis]

Speculation ?

As you stated it, yes.

a lot of research in that area.
a lot of people.

If this is the case, then (a) you should have stated it that way, and (b) you need to give references.