Before I compose a detailed reply to each of the points you raised; can you please tell me which part of my post is giving you trouble? Do you not understand the distinction between almost surely and surely? Or do you understand it but think it doesn't apply in the present discussion? Or think that Tegmark doesn't think it applies? I just want to figure out what level of misunderstanding we're having on this point. There's no question that I'm accurately relaying the math of infinitary probabllity theory. So there must be some disconnect between that and the physics. — fishfry

I look forward to your refutation of our best Cosological theory, right here, on this forum, by a true expert.

Maybe not. Maybe science will never explain the various constants, the 'six numbers' that purportedly underlie everything. Maybe the attempt to explain at that level is forever beyond science, and produces only pseudo-science, 'multiverses' being an example. — Wayfarer

You mean maybe the six numbers are magical? And of course the usual slur. How predictable!

OK then, my answer is simply "No, I do not intend to contact Mr Tegmark, as I have no reason to believe he needs correcting".

I see your suggestion about contacting him as irrelevant, as was the reference to the Nobel committee. — andrewk

When you have calmed down from your hissy fit, consider this:

An ergodic random field whose harmonic oscillator coefficients span {1,2,3,4,5,6} with a Gaussian distribution centred on 3.5. The field is in a state of superposition and decoheres for infinite time. What is the probability that the decoherence branch with initial condition "4" will be encountered in the multiverse?

I am not aware that Tegmark made the mistake of aggressively claiming that probability one means 'certain' in an infinite sample space, as you did. — andrewk

Being unaware is not an argument.

Your mistake is in mathematics, not in physics, so if you want to invoke a committee, it would be for something like the Fields medal, not the Nobel prize. — andrewk

Perhaps you would like to get in touch with Max Tegmark and give him the bad news?

Ask yourself why it’s a problem that needs solving. — Wayfarer

Science is about formulating problems and seeking solutions for them in terms of explanations, i.e. accounts of what exists in reality, how it behaves, and why.

So sure, if I look at the constants of nature, a perfectly natural question arises as to why they take particular values. Wouldn't it be nice to find a theory that predicts them? And if I look a little deeper and discover the sensitivity of Reality to slight changes in some of them, the slightly deeper question arises about why the had to take these values for there to be anyone to be questioning them.

In the face of Fine-Tuning it is impossible to maintain the Principle of Mediocrity without the Multiverse.

Because, if that is the motivation, then what is behind it? Is the suggestion of a 'fine-tuned Universe' one which most scientists would rather avoid? — Wayfarer

The Level 2 Multiverse solves the Fine-Tuning Problem.

fishfry is correct — andrewk

Will you inform the Nobel Prize Committee?

Your bullet items are probabilistic. And you are applying probability theory to an infinite event space. — fishfry

Are they probabilistic? Perhaps you could show what you mean by that, and which points comply with your meaning?

It is a fact that when you extend finite probability theory to infinitary realms, you lose certainty. — fishfry

Infinite realms? Loss of certainty?

You are applying without justification your intuitions and beliefs about finite probabilities to infinite ones. — fishfry

Intuitions, infinite probabilities?

You have to take this into account when making metaphysical claims based on probabilistic arguments, — fishfry

Metaphysical claims?

Organisms are cases where meaning takes physical form — Wayfarer

Quite!

Meaning isn't physical - the interpretive act is internal to thought. It's first person, although not necessarily 'subjective' in the sense we usually intend that word, 'pertaining only to oneself'. There are shared domains of meaning which are, therefore, 'inter-subjective'. But they comprise conventions and agreements between humans, in other words, they're dependent on the imputations which we agree with. — Wayfarer

If that is the case, how can the codes TAA, TAG, and TGA mean STOP in DNA encoding and UAA, UAG, UGA mean STOP in RNA encoding?

By the means appropriate to the subject. Science uses scientific and mathematical notation; poets deploy verse; painters use colour and texture; and so on. But always, there's an interpretive act going on; the mind is making something out of what it sees. — Wayfarer

But "making something out of what it sees" is a physical act requiring energy and an increase in entropy. Computers can do this, otherwise they could not do facial recognition, or win at chess, or drive a car.

That's like what I'm claiming - representation is one thing, and meaning another; it's a form of dualism. And the interpretation done by computers is only meaningful because they are in turn interpreted by humans; data has no intrinsic meaning to computers. — Wayfarer

I think there may be a need to draw a finer distinction. What do you think:

Representation - the physical encoding of an idea.
Meaning - the physical encoding of how to interpret the representation.
Quale - the subjective sensation of the act of giving meaning.

If it could be argued that the Quale was not physical, i.e. it was independent of matter, encoding, and interpretation, well, that would be very interesting, unless of course you posit some sort of spirit realm, which seems a very boring idea.

If the Quale (or the Meaning) is not physical, then how do we Represent them?

Because we are embodied beings, then a mental image has physical correlates. But in this case, the physical correlates are analogous to the role of 'representation' in the OP, in which 'meaning' and 'representation' are shown to be separable. — Wayfarer

Well I literally said that the "representation of it in your mind is physical". You seem to be claiming that representation can be physical, but meaning can't, as if representation is somehow easy and meaning isn't.

Even computer representations of geometric objects must be interpreted by computer programs and given meaning.

You won't find an image in a brain scan, or by examining someone else's brain. Well, not an image of a triangle — Wayfarer

And I was literally expecting to see an actual triangle in a brain-scan. How disappointing!

Although it would be pointless to argue that, because it’s plainly false. — Wayfarer

If the representation of the triangle in your brain is not physical, then why does it take energy to create, increase the entropy of your brain, causes visible changes in a brain-scan?

You can represent it physically, but it's an ideal object in the sense of being a geometric primitive. And surely the triangle I am just now imagining, is not physical, on account of it's a mental image. — Wayfarer

It may (or may not) be useful to draw a distinction between Material and Physical. The triangle is certainly not material, but it can be argued that the representation of it in your mind is physical.

Physics has made this distinction for quite a while: The First Law of thermodynamics is a material law, the Second Law is a physical law. One law governs the behaviour of matter, the other the behaviour of arrangements of matter.

Only speaking loosely. Ignorant of the physics. Asking if there's an explanation of why all states must occur. Is this all as in all? Or all as in statistically all, but possibly missing one or two with no harm done to the universe? — fishfry

All possible states must occur because of:

1. Infinity, which I have mentioned several times previously. Space must be infinite.

2. Mass fluctuations approach zero on large scales.

3. The mass densities at any set of points has a multivatiate Gaussian probability distribution.

Conditions 2 and 3 may be combined into the weaker condition that the correlation functions of all orders vanish in the limit of infinite spatial separation.

Together the above conditions are called ERGODICITY

The above prediction of Inflation can be traced back to the state of the conjectured scalar field, called the Inflaton, that permeates all of the infinite master space-time that our, and all the other universes and multiverses inflate from. The harmonic oscillator equations that determine the ground state of the Inflaton give a Gaussian wave function.

4. Infinity. But I've already mentioned that.

5. The Bekenstein Bound - the number of possible states scales with surface area, not volume.

That's very interesting. How does it know to do that? In the early moments of the universe it's cranking out all these possible configurations, and it's only got one more left. How does it know that? What if it forgets to do one particular configuration? Can it go back and do it later? Can the universe continue to exist or does this one single imbalance make the universe unstable in some way? — fishfry

Much of the attraction of the Multiverse is that it removes the requirement to explain particular initial conditions and physical constants because all are realised somewhere. If you wish to single out a single set of initial conditions for being forgotten or of being uniquely instantiated, then you are going to need a different physical theory than we already have. As I have mentioned a few times, it is a prediction of Inflation that all initial conditions are realised, and that their statistical distribution is ergodic.

Tegmark's view on how these initial conditions obtain is that the early universe, during Inflation (i.e. the inflaton field), is in a superposition of all its possible states. If this is the case (which it must be if physics is unitary) then the same fundamental physical process gives rise to the type 1 and 2 multiverses as type 3. This physical process is decoherence.

You know I just don't believe this duplicate earth story. Say there's a universe or a multiverse and it's got every possible state represented infinitely many times ... except there is one state that just happens to only occur once, by incredible amazing luck ... one little blue watery planet with bad politics, third from the sun ... and it's the only one like it in the entire multiverse. — fishfry

So, you prefer "incredible amazing luck" theory to our best theory of the universe? Do you even aspire to rationality?

But we're making progress if you agree that ergodicity by itself is not sufficient. — fishfry

Now you are straw-manning.

I did. I took the question for sarcasm and responded in kind when you persisted.

Given an initial 1m3 of space-time, what expansion rate is required to turn it into literally infinite volume in any finite time?

Not going to happen. — noAxioms

You are passing up a valuable learning opportunity! Go on, give it a try!

We can create a model in which the spacetime has all times after time zero but does not contain time zero itself. The earlier the time (The smaller its time coordinate), the greater the universe density becomes, so that it increases without limit as t approaches zero. — andrewk

Not according to Inflation, the theory on which the Level 1 and Level 2 Multiverses are premised.

Suffice it to say that for the purposes of this thread, the declaration that space is infinite implies it was always infinite ever since it was space. The material/energy probably never fully interacted. — noAxioms

Precisely! No finite physical process can create something infinite out of something finite in finite time whether you choose to show your workings or not.

Edit: Just to point out that to travel between Level 2 multiverses, you would need to traverse the part of the infinite space-time that our universe emerged from. This would be extremely difficult as these regions of the Master Space-Time are still undergoing inflation. As if travelling between Level 1 multiverses were not difficult enough.

You persist with this. Is it a serious question? 6 days, after which enough expansion took place to qualify as infinite. On the 7th day, the expansion rested. I really don't know how else to answer that. — noAxioms

Maybe you should show your working? Given an initial 1m3 of space-time, what expansion rate is required to turn it into literally infinite volume in any finite time?

The comment here only makes sense if interpreted as sarcasm. It implies that there might have been finite hubble volumes, and after enough time, that goes to infinite. The greater the expansion, the less time it takes to do this. No, not my view. — noAxioms

So, what rate of expansion do you think might be required to turn a subatomic spec into a literally infinite universe in 13.8 billion years? Have you done the calculation?

The way I see it: If the geometry is such that the universe wraps (like the sphere of the balloon analogy), then there are finite Hubble-volumes. Assuming not, then if the expansion rate is increasing, there are infinite such volumes. If the rate is not increasing, light will eventually get from anywhere to anywhere else, and the universe is a single Hubble volume. At no point does "13.8 billions years" play into that. — noAxioms

Hubble Volumes are finite. If the "universe wraps" i.e. it is a finite 3-sphere, I think all bets are off for Level 1 (and Level 2) multiverse statistics.

The rate of expansion may be static, increasing, or decreasing. As long as there is a +ve Hubble constant, there will be Hubble Volumes.

Why do you think they don't? We are at the exact center of our Hubble volume. Isn't that amazing? From the perspective of a planet 10 BLY away to the left (all this is in comoving coordinates BTW), they are centered on a different volume that encompasses us way to the right. Their volume ends further to the right of us, but not a whole lot further. Some distant galaxy to our right can be seen from here but can never ever be seen by them. It is outside their Hubble Volume. Our volumes overlap else we couldn't see each other.
To say they're all nonoverlapping implies there are discreet chunks of disjoint space with one preferred point in each of them which is their center. My model doesn't look like that. — noAxioms

Sure, your Hubble volume and my Hubble volume might be slightly different in 14 billion years. In the mean time, there are an infinite number of Hubble volumes that were never in causal contact with ours.

Maybe my model is incorrect, but this seems wrong. Since the level-1 spheres overlap, they're all points in the beginning, and all the same point at that, else they'd not overlap. — noAxioms

How much expansion is required to produce a literally infinite universe from a point in a mere 13.8 billion years?

Why do you think Hubble Volumes were ever in contact or overlap?

Limits it given finite energy. If the initial infinite universe was actually a point, there is infinite energy/information there. But this actually kills my idea. Earth is a limited space with limited energy. The bound applies. Earth cannot be in a unique state that requires the history of the entire set of material that was once in its causal past. — noAxioms

The initial infinite universe cannot have been finite. No physical process can take something finite and make it infinite in finite time.

The initial energy density of the universe was also finite.

There are also Level 2 multiverse earths.

That's an arbitrary assumption, that the second is constant, and the year is variant. — Metaphysician Undercover

We know the Earth is Moving away from the Sun and that the year is getting longer. I's been measured.

We can measure and calculate the energy of transition between hyperfine ground states of the caesium atom.

For the energy of transition of caesium atoms to change - a change affecting all caesium atoms everywhere simultaneously I presume - what laws of physics do you propose to change?

Am still enjoying the concept. Perhaps a proof that no copy is possible then? The distant Earth might be outside our causal cone now, but it wasn't always. — noAxioms

Our visible universe may well have been the size of a point at the Big-Bang, but the entire Level 1 Multiverse was not. The Multiverse was as infinite then as it is now.

Inflation guarantees the immediate creation of causally disconnected regions.

Tegmark assumes Earth can be represented with finite state, and computes the distance needed to get the probability of a repro up to about 1. If if the state is no finite number, then no copy. — noAxioms

As I've mentioned several times, the Bekenstein bound severely limits the number of states available to any volume of space.

So we have:

Infinite universe+Inflation+all initial conditions+ergodicity+Bekenstein Bound = guaranteed copies of Hubble Volumes.

Yes, the second is defined that way, I am fully aware of this. However, the year is defined by the earth's orbit. For fdrake's claim that the caesium clock will continue to be as accurate as it is now for 100 million years to be true, the relationship between the earth's orbit, and the caesium frequency, must remain the same for 100 million years. The use of leap seconds demonstrates that this is highly unlikely. — Metaphysician Undercover

Right, so the second is defined by a physical constant, but the year is defined by a varying quantity. Certain mechanisms are employed to keep the invariant and varying quantity in good agreement. These include leap years and leap seconds.

The clock will not be as accurate as it is now in 100,000,000 years. No one is claiming that. The clock will certainly not exist then. However in 100,000,000 years, clocks may be 100% accurate.

Interesting, but the point is this. The reason why the frequency is precisely 9,192,631,770 times per second, rather than 5 billion, 10 billion, or some other arbitrary number, is that the second is already is defined in relation to the year. So if they chose one of those other numbers, 5 billion times per second, for example, there would not be the right number of seconds in a day, and in a year. So what this statement ("9,192,631,770 times per second") represents, is a relationship between the activity of those caesium atoms, and the motion of the earth in relation to the sun. If that relationship is not absolutely stable, then that number cannot be represented as a stable number. — Metaphysician Undercover

No it doesn't. The second is DEFINED with respect to a material property of Caesium. The new definition would have been chosen to be close to a previous definition which it superseded, for convenience, but needn't be the same. I presume you are familiar with leap seconds (and leap years)?

As a matter of interest, all Imperial units also changed slightly when they became defined in terms of S.I. units.

You need to watch this.

As it happens I've spent the afternoon chasing down ergodicity. I do know a little about it relative to the irrational rotations of a circle, which are ergodically dense in the circle. What I've learned today is that by the definition of ergodicity, any set that behaves badly must have measure zero. If that's correct, then my NO-duplicate earth possibility is still alive. Ergodicity is a statistical attribute that describes what happens almost surely. But not absolutely surely. — fishfry

Inflation generates all possible initial conditions. This means that all possible matter configurations exist in some Hubble Volume. The most likely initial conditions are those which are almost uniform with only slight variations in matter densities, which later become amplified by gravitational clustering. We inhabit a typical Hubble Volume.

The quantum mechanisms that generate the initial conditions do so effectively in the manner of an ergodic random field. What this means, is that given an ensemble of Hubble volumes, each with their own random initial conditions, then the probability distribution you get by sampling different Hubble Volumes is identical to the probability distribution you get if you sample parts of a single Hubble Volume.

It is precisely this property of ergodicity - a generic prediction of Inflation - that guarantees that everything that could have happened here, did in fact occur elsewhere, and that everything that did happen here has multiple copies.

This is my preliminary understanding. I no longer think ergodicity absolutely guarantees that there is a duplicate earth. If someone knows better and can walk me through the argument, I'd be grateful. — fishfry

You also need the Bekenstein Bound and infinity.

Anyway, who do you think are other examples? — WISDOMfromPO-MO

How about this guy:

So you are requiring the assumption that you are then claiming is true? Well by that logic you're certainly right. If you pre-load your desired conclusion into an assumption, your conclusion falls out at the end. — fishfry

Ergodicity is a PREDICTION of physics. If you don't like it, you'll need some new physics and some very good arguments and predictions.

I'm not the one claiming the universe is infinite. I'm simply pointing out that in an infinite collection of regions, with each region taking on one of a finite number of possible states, there's no reason that any particular state must be necessarily be shared by two regions. — fishfry

It's called ergodicity. I have mentioned that ergodicity is a requirement for Type 1 multiverse several times.

According to our best theory of cosmology, the universe is infinite and ergodic - both are predictions of inflation.

Now in the more realistic case there are zillions of possible state. Still finite, but very large. But then it's still the case that R1 might be in state 0, and every other region is in some other state. It's still the case that it is possible that some state never repeats. — fishfry

If the universe is infinite and ergodic, it is impossible that state 0 will not repeat.

NoAxioms and I just had a lengthy conversation disproving this very point. Could you please review those posts? What you say is simply not true. At best you have a probabilistic argument that falls short of certainty. — fishfry

If the universe is infinite, ergodic, expanding, and subject to the Bekenstein Bound, then it is certain that Hubble volumes exist which are identical to ours.

Secondly, the level-1 multiverse only requires a finite universe sufficiently large that light hasn't had time to get from one point to some other point in the age of the universe. — fishfry

How do you fit all possible Hubble Volumes instantiating all possible initial conditions into a finite universe? You obviously can't fit in an infinite number of copies of each, which is what you need for a multiverse.

What are "acausal interactions from beyond spacetime" supposed to mean? — Mr Bee

That would be non-locality a.k.a. spooky action at a distance.

Non-locality doesn't necessarily have to violate causality. — Mr Bee

Unitary Quantum Mechanics is a local theory. It is only when you ad-hoc modify it or burden it with metaphysical baggage like collapse, hidden variables, and unreality that are you forced to appeal to acausal interactions from beyond spacetime.

Copenhagen preserves locality by giving acausal spooky actions at a distance a different name. It calls them "correlations", as if that changes anything.

Well, you list others, so there are other known interpretations. Support of MWI is growing among physicists, but it has yet to reach a majority. For the record, my opinion rests with the MWI guys, but without a falsification test, it remains an interpretation, not a theory. — noAxioms

Interference experiments are a test of Many Worlds. Interaction free measurements test Many Worlds, as does the quantum computer.

Why are hidden variables disallowed? I think you're right actually in that it was proved somewhere that there can be no hidden variables, but its supporters obviously don't think the proof carries weight. — noAxioms

Bohmian mechanics is Many Worlds in a state of chronic denial. A valiant attempt at realism, but by making ad-hoc modifications to a theory, it goes against the scientific method. Non-relativistic QM is not the last word, it's just a handy regime in which to discuss ideas. Bohmian mechanics has not successfully been made relativistic. And let's not forget that both local and non-local hidden variables are ruled out experimentally. Still, there may be loopholes, so the task of looking for them continues.

My personal aversion to most of the other interpretation is non-locality. Bohmian doesn't necessarily have it, but the others do. The ability to alter the past seems a nastier pill to swallow than the (mostly religious) implications of what MWI does to one's biased ideas of personal identity. — noAxioms

With MW you get a standard scientific theory. It explains what is happening in terms of elements of reality that are real and interact locally. There is no measurement problem, and no spooky action at a distance. What is weirder, a reality that consists of many parallel worlds that we can detect by their interactions, and cooperate with in our technologies, or a reality that is not really there and that we are not allowed to question?

I

Perhaps I stand corrected. Are we talking about interpretations of QM? Or actually proven multiverses? — fishfry

Many Worlds is the only known interpretation of quantum mechanics.

Bohmian mechanics - adds hidden variables to QM, thus a different theory. Doesn't work.
GRW - ads stochastic collapse to QM, thus a different theory. Doesn't work.
Transactional - I really don't care.

Copenhagen is the tricky one, that has caused all the confusion. It suffers from a variety of problems, such as the measurement problem, and led many famous physicists to believe consciousness is responsible for wavefunction collapse. It is largely responsible for Deepak Chopra. It is a different theory from MW because it claims reality does not exist (MW claims it does) and it has the Born Rule as an axiom (MW does not).

Quote from the opening post:

(An odd but seldom noticed consequence of McTaggart's characterization of the A series and the B series is that, on that characterization, the A series is identical to the B series. For the items that make up the B series (namely, moments of time) are the same items that make up the A series, and the order of the items in the B series is the same as the order of the items in the A series; but there is nothing more to a series than some specific items in a particular order.) — https://plato.stanford.edu/entries/time/#McTArg — jorndoe

Um, the whole point of A-Theory vs B-Theory is that the series are the same. "Odd but seldom noticed"? I don't think so.

Multiverse theory, string theory, speculative theories that have zero experimental basis and that can't be experimentally verified even in theory. — fishfry

The quantum multiverse has been known about since 1950s. Schrödinger mentioned it in lectures, several other physicists discovered it independently, most famously Everett in his PhD thesis. The video shows that Hawking accepts it, Feynman discovered it independently, and that Penrose admits it is an inescapable consequence of quantum mechanics.

Many Worlds is at least 60 years old, and has not only passed every test, but has led to the discovery of decoherence and the quantum computer. Every quantum interference experiment is a test of Many Worlds, as are interaction free measurements and many other technological examples.

Oh, yes.

Give me an example of an A-series, true statements about the future, that becomes false. — Banno

Give me a statement that demonstrates you know what McTaggart was arguing towards.