Many-worlds: When does the universe split?

[kaplan]

For example, let's say that the "physics" of our 1TB drive is that each 1 Planck time period, all bytes are shift towards the end and the first byte is set to a random value.

There are no random events according to the MWI. The Schrodinger equation is a differential equation, so the wavefunction of the universe evolves deterministically.

Here's another way to say it. If everything available in W0 isn't enough to tell you which Wn we were going to end up in, then the choice that was made to get us to Wn involved other non-W0 information. And it's that other non-W0 information that changed our Wn - making it different from all the other Wn's.

There is no "Wn we end up in". We end up in all the worlds.

You seem to have some basic misunderstandings of the MWI.

 

[audioloop]

There are no random events according to the MWI. The Schrodinger equation is a differential equation, so the wavefunction of the universe evolves deterministically.
.

Right !



.

 

[.Scott]

There are no random events according to the MWI. The Schrodinger equation is a differential equation, so the wavefunction of the universe evolves deterministically.

There is no "Wn we end up in". We end up in all the worlds.

You seem to have some basic misunderstandings of the MWI.

As I understand it, a different version of us ends up in each world. For example, a dead cat in one and a live one in another.

It's nice that the Schrodinger equation is deterministic, but does it give a single unique result of a wave function collapse. If it gives a selection of possible results, then it is deterministic but incomplete. In order to complete it, you would need additional information.

 

[The_Duck]

It's nice that the Schrodinger equation is deterministic, but does it give a single unique result of a wave function collapse. If it gives a selection of possible results, then it is deterministic but incomplete. In order to complete it, you would need additional information.

Why? In MWI there is no wave function collapse.

 

[kaplan]

As I understand it, a different version of us ends up in each world. For example, a dead cat in one and a live one in another.

Yes.

It's nice that the Schrodinger equation is deterministic, but does it give a single unique result of a wave function collapse.

There's no collapse (in the sense of a projection) in MW. Instead, there's a split. And yes, the split is deterministic.

If it gives a selection of possible results, then it is deterministic but incomplete. In order to complete it, you would need additional information.

When you make a measurement and cause a split, one version of you obtains one result and the other version obtains the other. That's all there is, and no additional information is needed. (It's true that the Born rule is needed for splits that aren't equally weighted, but I've always suspected there's a way to derive it from some statistical considerations.)

 

[bhobba]

It's nice that the Schrodinger equation is deterministic, but does it give a single unique result of a wave function collapse. If it gives a selection of possible results, then it is deterministic but incomplete. In order to complete it, you would need additional information.

You just don't seem to get it.

In the MWI there is no collapse.

There is an issue about assigning a confidence level or probability to what world you experience - and how such comes about in a deterministic theory - but that is a subtle issue that has been thrashed out before - you can do a search and find the thread if interested.

Thanks
Bill

 

[bhobba]

but I've always suspected there's a way to derive it from some statistical considerations.)

There is eg Gleasons Theorem and arguments from decision theory by Wallace and others.

However they are somewhat controversial and a bit of a Google search will bring up both sides of the argument.

Thanks
Bill

 

[Jazzdude]

No. You missed the point of that post.

Fair enough. Then feel free to take my comments in the context of your post #24, where you argue like I thought you would also do in your later post.

Any one drive can hold 1TB which is 2^43 bits. That allows for each drive to be in any of 2^(2^43) states. So when a drive "splits" it moves to multiple states. And splits again into many more states. Ultimately, there will be more than 2^(2^43) 1TB drives in a single generation. At that point, some of those drives will have to have identical content to each other - a form of de-facto merging.

No. First of all, the complexity of a physical hard drive clearly exceeds the classical information stored on it. Secondly, you have an infinite(!) dimensional environment that can get entangled with your subsystem in any possible way. You will never run out of new different states, ever. This is pretty much Hilbert's Hotel.

The point of that exercise was to demonstrate that you really are using information capacity as you allow the 1TB drives to morph.

What is "morph" supposed to mean in this context? And like I said earlier, the unitarity of the evolution preserves global information.

For example, let's say that the "physics" of our 1TB drive is that each 1 Planck time period, all bytes are shift towards the end and the first byte is set to a random value. In the WMI of this drive, if you look at the contents of the drive, the first byte will tell you which world this drive entered on the last Planck time cycle, and subsequent bytes tell you what happened on the cycles before that. After 1T cycles, information will be lost as the last byte on the drive is shifted into oblivion.

I have no idea what you're trying to say with that.

This is all fine for our 1T drive, but the prevailing thought in our universe is that information is never obliterated or created.
I am looking at the explanations that have been posted about how real-world MWI avoids this information inflation. I am not convinced that any of them avoid trivializing information conservation.

There is no objective information inflation at all. All the information that you think is generated is merely subjective to the restricted view of one world.

Also, in your past posts you have been demonstrating your confusion about some key concepts quite clearly. Just a few things: Decoherence is not random, it's a deterministic process. Virtual particles have nothing to do with interference minima.

Cheers,

Jazz

 

[kith]

I would love to start a thread on this. However I didn't get a lot of feedback in this forum and the general interest seemed to be rather low. So I'm still not sure this is appreciated.

As I mentioned in my previous post, I probably wouldn't read up on issues which take much time but I would at least ask some questions and share my point of view. The people who are interested in the factorization issue would probably at least comment, too. So give it a try ;-)

You could simply describe the idea like you did in the last post and link to paper(s). However, if they are arxiv-only, you may want to be cautious with claims and describe it in a more question-like manner.

 

[kith]

I am looking at the explanations that have been posted about how real-world MWI avoids this information inflation. I am not convinced that any of them avoid trivializing information conservation.

I think the problem of this thread is that you are talking about classical information while the other people talk about quantum information.

In a classical setup, you can predict the outcome of a coin toss if you know it's position, it's orientation and the respective velocities. So in principle a series of measurements which determines these values yields a state of maximal information which allows you to calculate whether you get a head or a tail.

In the QM setup, you can't know position and velocity at the same time. If you know the position of a coin, a measurement of the velocity has the effect that your coin will be put in a superposition of position eigenstates. So a state of maximal information can't include maximal information about position as well as velocity and doesn't allow you to calculate the outcome of a quantum coin toss.

In terms of classical information, information about position is destroyed by the velocity measurement of the quantum coin. You "forget" it's position by creating a superposition of position eigenstates. This is why quantum information is defined in a way which assigns equal information content to all pure quantum states. This is also reflected by the fact that being a superposition is not a property of the state (as I explained in post 42).

 

[.Scott]

Why? In MWI there is no wave function collapse.

There seems to be a persistent problem with terminology here. MWI explains the apparent wave function collapse. (and if that's not true, keep reading because my misunderstanding about what MWI really is won't matter to the final result). But it does so by allowing the wave function to collapse in more than one way - a different way for each world. Assuming there are more than one of these new worlds, that is sufficient to create additional information. It doesn't matter whether you consider the wave function to have collapsed or not. All that matters is that there is a one real observable world where a collapse was apparent and another one where a different collapse event was apparent.

We don't even need MWI for information inflation. If you stick to the notion of an event, a wave collapse or anything else, being created out of something more that its historic light cone, you have added information to the universe.

If you assert that there is anything other than a single deterministic path to the universe then:
1) For single world interpretation: You're saying that God rolls the dice to determine which of many possible wave function collapse results will become real. The information from those die rolls accumulates in our one universe.
2) For multiworld interpretation: God does not role the die. Instead, whenever multiple results are possible, multiple worlds split off, each with additional "which world" information.

There are only a limited number of ways of resolving this:
1) Accept that information is being continually pumped into our universe (or segment). If this is the case, it should be very possible (although beyond my knowledge) to calculate how fast this information inflation is occurring.
2) Eliminate all non-deterministic choices. I may not have the Physics terminology right on this, but it probably means recognizing that the wave models are not complete.
3) Find some information to destroy at the same time that new information is added. In principle, this is the same as "eliminate all non-deterministic choices", but it may be an easier approach to discovering what is missing in the wave models.

So what really matters is whether the QM models are fully deterministic and create a single unique result - at least in principle. In other words, does your QM model really result in both a live cat and a dead cat? If it does, then the rest of the language is immaterial and the conditions exist for information inflation.If you don't like information inflation, then treat your QM model as incomplete. If information inflation is OK, then model it and test it against experimental observation.

 

[.Scott]

I think the problem of this thread is that you are talking about classical information while the other people talk about quantum information.

In a classical setup, you can predict the outcome of a coin toss if you know it's position, it's orientation and the respective velocities. So in principle a series of measurements which determines these values yields a state of maximal information which allows you to calculate whether you get a head or a tail.

In the QM setup, you can't know position and velocity at the same time. If you know the position of a coin, a measurement of the velocity has the effect that your coin will be put in a superposition of position eigenstates. So a state of maximal information can't include maximal information about position as well as velocity and doesn't allow you to calculate the outcome of a quantum coin toss.

In terms of classical information, information about position is destroyed by the velocity measurement of the quantum coin. You "forget" it's position by creating a superposition of position eigenstates. This is why quantum information is defined in a way which assigns equal information content to all pure quantum states. This is also reflected by the fact that being a superposition is not a property of the state (as I explained in post 42).

That's really interesting. When I read about the Bekenstein limits, the discussion is about bits and the information contained in the quantum states of, for example, a sphere. It sounds as though its the same thing as the "which world" information.

I'm suspecting that many people are forgetting about which world information. If photons are passing through a pair of slits, there is no which world information to accumulate. If you open the box and find a dead cat, you have discovered which world information.

 

[bhobba]

There seems to be a persistent problem with terminology here. MWI explains the apparent wave function collapse. (and if that's not true, keep reading because my misunderstanding about what MWI really is won't matter to the final result). But it does so by allowing the wave function to collapse in more than one way - a different way for each world.

Again you are just not getting it.

After decoherence, which is a deterministic process, we have the improper mixed state Ʃ pi |ui><ui|. It is an INTERPRETATIVE assumption of MWI that each |ui><ui| is a world.

In Schrodinger's Cat we have two such states - one where the cat is alive, one where it is dead. No collapse has occurred.

This was all explained in the paper I linked to on decoherence that you claimed to have read. All I can surmise is you didn't really understand it.

Before you can grasp what the MWI is about you need to really understand this.

Thanks
Bill

 

[.Scott]

There is no objective information inflation at all. All the information that you think is generated is merely subjective to the restricted view of one world.

Okay, but when a Physics experiment is conducted, it is conducted in each of many worlds with the "merely subjective" results based on that worlds restricted view.

Decoherence is not random, it's a deterministic process.

Yes, I remember using that term when I meant wave collapse. I don;t usually converse in these terms.

Virtual particles have nothing to do with interference minima.

I know that "virtual particles" most often refer to those flighty things that pop up in a vacuum, but I believe they can also refer to the different paths a photon can follow before it is finally detected. In any case, "virtual" or not, these "construction" photons are commonly used in the Physics literature. If you wish, I will call them "construction" photons or anything else. But I believe "virtual" is a correct term for them.

 

[kith]

That's really interesting. When I read about the Bekenstein limits, the discussion is about bits and the information contained in the quantum states of, for example, a sphere.

I think what you have read about is the Bloch sphere which is a way of visualizing the possible states of a single qubit.

A qubit is a system which yields two different outcomes in measurements, so it is the quantum analogon to the bit. Yet its classical information content is already infinity, because you need an infinite number of measurements (yes or no questions) to determine its state. This is because the coefficients of a superposition a|0>+b|1> are continuous.

a and b span a two dimensional plane which is bent into a sphere by the normalization condition of a and b. That's how you get the Bloch sphere.

 

[.Scott]

In Schrodinger's Cat we have two such states - one where the cat is alive, one where it is dead. No collapse has occurred.

This was all explained in the paper I linked to on decoherence that you claimed to have read. All I can surmise is you didn't really understand it.

Before you can grasp what the MWI is about you need to really understand this.

Thanks
Bill

I fully understand what you are saying. What I am saying is that there can be more information in a component of a system then in a system as a whole - because a component of a system will include a "which component" designation.

So before the cat was put into the box (W0), we have a world where both a dead cat and a live cat are eventually possible. Later, our universe evolves deterministically with both the dead cat and the live cat worlds - and no information has been created. But then you open the box and discover that you are in the dead cat world (Wdead) - information that did not exist in W0.

 

[.Scott]

I think what you have read about is the Bloch sphere which is a way of visualizing the possible states of a single qubit.

Nope. I was referring to Bekenstein Bound.

 

[bhobba]

I fully understand what you are saying. What I am saying is that there can be more information in a component of a system then in a system as a whole - because a component of a system will include a "which component" designation.

That's not true.

Take a line. Conceptually consider a point in the middle that divides it in two. Do the same with each half and continue the process indefinitely. The information encoded in the line (which is a real infinity) is not changed at all by this conceptualization. This is the exact analog of decoherence - no information is added or taken away.

Arbitrarily labeling something does not alter any information encoded in it.

Thanks
Bill

 

[kith]

Nope. I was referring to Bekenstein Bound.

Yes. And you mentioned the quantum state of a sphere which is most certainly not what occurred in the text. The Bloch sphere visualizes the possible quantum states of a single quantum bit.

Don't you find it astonishing -and relevant to the thread- that the smallest unit of quantum information already corresponds to infinity when expressed in terms of classical information? You could roughly say that 1 qubit = ∞ bit

 

[bhobba]

Nope. I was referring to Bekenstein Bound.

What you don't seem to get is labeling something as a separate world changes nothing about its information carrying capacity.

Thanks
Bill

 

[kith]

So before the cat was put into the box (W0), we have a world where both a dead cat and a live cat are eventually possible. Later, our universe evolves deterministically with both the dead cat and the live cat worlds - and no information has been created. But then you open the box and discover that you are in the dead cat world (Wdead) - information that did not exist in W0.

Replace the cat by a coin and explain what I wrote in post 70 with this logic. The cat is a bad example because you can perform only one type of measurement. You need at least two.

 

[.Scott]

Replace the cat by a coin and explain what I wrote in post 70 with this logic. The cat is a bad example because you can perform only one type of measurement. You need at least two.

By "coin" you mean the QM "coin" you described in post 70. In that case your coin was acting according to Heisenberg uncertainty.
Okay, I think I know what your asking - but I'm not sure. Here's my shot at it:

Instead of a cat, Geiger counter, etc., our box now contains a quantum coin press. Soon after we close the box (W0), our coin press stamps out a coin with a "random" QM state where either orientation (heads/tales) or color (gold/silver) can be measured - but once one state is measured, all information about the other state is destroyed.

We then open the box, and choose a measurement. If we make this choice based on a Geiger counter result, we would be in either W(orientation) or W(color), so we've already added information. Once we make the measurement, we would discover we are part of W(heads), W(tails), W(gold), or W(silver).

I guessing this isn't exactly what you wanted. If it isn't, restate the problem and I'll take another shot at it.

 

[.Scott]

What you don't seem to get is labeling something as a separate world changes nothing about its information carrying capacity.

Thanks
Bill

The reason I mentioned the Bekenstein Bound was only to cite a work that is using the term "information" in the same way I am using it. I did this because there was a question about the uses of this term in these discussions.

Before addressing your comment directly, I need to contrast "information carrying capacity" with information content. When applied to our universe, I am not sure whether there is a real distinction. Are there really any unfilled "bits" in our universe. I suspect there are not. So if you add information to the universe, it would seem that you would have to either add real capacity to it or extinguish information somewhere else.

So what I am saying is that being on one particular page of a book constitutes more information that simply having a book. We are not just living in the universe, we are living on a particular page in the universe. That "which page" or "which world" information is real information that shows up in real physics. There is also "which time" and "which place" information. But that information isn't nearly as potentially inflationary as the "which world" information.

 

[bhobba]

So what I am saying is that being on one particular page of a book constitutes more information that simply having a book.

You do understand that a real interval of any length contains exactly the same information as a real interval of any other length? Split any length in two and each part contains exactly the same information as before it was split?

Have you studied Cantors theory of the infinite:
http://en.wikipedia.org/wiki/Infinity

That's the idea Kith was getting to with the Bloch sphere, its exactly the same concept as a real line.

Thanks
Bill

 

[kith]

I guessing this isn't exactly what you wanted. If it isn't, restate the problem and I'll take another shot at it.

I was talking about a sequence of measurements in post 70. In a sequence of position and velocity measurements, each measurements destroys the classical information obtained by the previous measurement. After a certain measurement, you don't have more information than you had previously. You simply have information about different properties of your system. Where do you see an increase in information here?

You don't see this feature with Schrödinger's cat because you cannot measure a property of the cat which has "dead and alive" as a possible outcome.

 

[.Scott]

You do understand that a real interval of any length contains exactly the same information as a real interval of any other length? Split any length in two and each part contains exactly the same information as before it was split?

The number of points on a line segment ant the amount of information in the universe are completely different topics. The cardinality of points on a line or line segment is Aleph 1.

 

[Maui]

You do understand that a real interval of any length contains exactly the same information as a real interval of any other length? Split any length in two and each part contains exactly the same information as before it was split?

Have you studied Cantors theory of the infinite:
http://en.wikipedia.org/wiki/Infinity

That's the idea Kith was getting to with the Bloch sphere, its exactly the same concept as a real line.

Thanks
Bill

For all practical purposes the length of the line determines how much information can be encoded upon it(there is always a practical limit). That is unless one considers the universe to be a mathematical object created by some mathematician but that'd be philosophy.

 

[.Scott]

I was talking about a sequence of measurements in post 70. In a sequence of position and velocity measurements, each measurements destroys the classical information obtained by the previous measurement. After a certain measurement, you don't have more information than you had previously. You simply have information about different properties of your system. Where do you see an increase in information here?

You don't see this feature with Schrödinger's cat because you cannot measure a property of the cat which has "dead and alive" as a possible outcome.

There are different answers for different basic theories. But let me give an example that follows the most vanilla, well-accepted scenario. This specific scenario will hold through to the end of this post:

You are about to measure the spin of a particle along a specific axis. QM predicts that the result of the experiment will be 50% chance of up, 50% chance of down - and there is nothing in the universe that will tell you which will happen - either practically or even in principle.

So that is the situation in my W0. At this point you have a 2-page document with no information about which page you will end up on.

Then you make the measurement, it is either up or down. You are still in the same universe with 2-pages, but now you know which page you are on. This was information that was non-existent in W0. So the information is simply which choice you end up living in. So you ask "where do you see the increase in information". My answer is that it that it can be very apparent at the macroscopic scale, it's the result of a measurement that could not be predicted before being made.

To the very limited extent that I understand the math, it's easy to see it there as well. If you have an equation that yields the set of all integers, that is less information than that same equation restricted to any particular choice. A quadratic equation that yields -4 and 6 as results is less information than the same equation restricted to either x>0 or x<0. As time moves on, our universe becomes more and more specific.

But shouldn't that show up as a world that is somehow growing? What does a particle with extra information look like? I don't know.

 

[Bill_K]

What does a particle with extra information look like? I don't know.

I think you should first try to understand what the word "information" means.

 

[kith]

Then you make the measurement, it is either up or down. You are still in the same universe with 2-pages, but now you know which page you are on. This was information that was non-existent in W0. So the information is simply which choice you end up living in. So you ask "where do you see the increase in information". My answer is that it that it can be very apparent at the macroscopic scale, it's the result of a measurement that could not be predicted before being made.

You still don't address the issue that by obtaining this classical information you are erasing the information you previously had - namely the spin in another direction.