Many-worlds: When does the universe split?

[.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.

 

[.Scott]

You still don't address the issue that this classical information is erased by the next measurement.

The information I am talking about is not specific to the particle. I am not saying that the particle itself holds more information. I am saying that once a measurement is made of any truly "random" event (which would include the selection of an MWI world), there is more total information in the world.

And from everything that I can understand, this is exactly the sort of "physical information" that is suppose to be indestructible. I do need to continue looking at exactly what is meant by quantum information destruction. It's basically two different quantum states evolving into the same state - presumably not possible. But I am still looking and studying.

 

[.Scott]

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.

You go from 4 possibilities to 1. From Spin A+, A-, B+, B- to only one of them. With all of the other possibilities eliminated. What is important is not that you are loosing Spin A information when you measure along the B axis, but that the result of the Spin B measurement itself will be random. Of course, if Spin B has already been measure on an entangled particle, then it won't be random.
The real question is whether it is ever truly random.

 

[kith]

Bill is right: it is overdue that you give a definition of "information".

 

[kith]

You go from 4 possibilities to 1. From Spin A+, A-, B+, B- to only one of them.

What are A and B?

 

[Jazzdude]

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.

Nobody with a clue would call different interfering paths "particles" and specifically not "virtual particles". They're also not "constructing photons" or anything like that. They're just different interfering histories, if you want to enforce such a view. But it suggests that there is some classical reality underneath, so I consider it best to avoid that picture outside of perturbation calculations entirely. What happens is simply a unitary evolution of the quantum state, nothing else.

Cheers,

Jazz

 

[craigi]

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.

Are you aware of the Second Law of Thermodynamics?

Decoherence involves thermodynamically irreversible processes. This involves a loss of order and an increase in entropy as interference spreads to the surrounding environment and as such would require an increased amount of information to represent.

This entropy growth is nothing new. The understanding of it predates quantum mechanics by 100's of years.

The entropy growth involved in QM is a direct result of the formulation and is not interpretation dependent. It is the observer dependent reality that contains all relevant information. If you wish to consider the entropy in the MWI multiverse then I'd argue that it is zero and contains no information.

Regarding the enumeration of other possible universes as a measure of information content. The MWI doesn't differ in that respect. Those other possibilties are still there, the difference is that the MWI says they are inaccessible rather than just hypothetical.

When you refer to the "conservation of information". I think you're referring to the quantum no-deleting theorum. This is specific to quantum information stored in qubits, for instance. The classical world doesn't conserve information, otherwise it would break the second law of thermodynamics. A qubit can yield no more than one classical bit of information.

When entropy increases, a particle doesn't store extra information. The classic example is if you had n particles of type A in box C and n particles of type B in box D, then put them all in box E. The entropy has increased. The computing analog of this is n 0's followed by n 1's contains much less information than if they're all randomly ordered. The information stored can be measured by the theoretical minimum for the compressed size of those bits. The maths of information entropy is almost identical to that of thermodynamic entropy. They are effectively the same thing.

 

[bhobba]

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.

Sorry. But it is the SAME topic.

When a wavefunction is partitioned by decoherence because we are dealing with complex numbers it has exactly the same cardinality as the real line. Each world contains an infinite amount of information just like when you spit a real interval into two - each subinterval contains exactly the same information as the original interval. Its one of the screwy things about infinity.

Your book analogy is incorrect. Because we are dealing with a complex vector space your book effectively contains infinite pages. Divide such a book any way you like say in half and each half contains an infinite number of pages. It is this attribute that allows the partitioning of the universal wavefunction to continue indefinitely without altering the information in each subworld which is infinite. infinity/n = infinity.

Thanks
Bill

 

[bhobba]

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.

That is WAY wrong. A real or complex valued function encodes an infinite amount of information. That is why the partitioning of it can continue indefinitely and each sub partition contains an infinite amount of information.

QM is a MATEMATICAL MODEL and as such is exactly that - it contains mathematical objects created by mathematicians with whacky counter intuitive properties.

Thanks
Bill

 

[bhobba]

The information I am talking about is not specific to the particle. I am not saying that the particle itself holds more information. I am saying that once a measurement is made of any truly "random" event (which would include the selection of an MWI world), there is more total information in the world.

What we are saying is that is WRONG. The information encoded in the complex valued wavefunction (or more correctly state) of the universe is infinite. When that wavefunction is 'partitioned' by decoherence each world also contains infinite information. This can continue indefinitely without bound with no information being gained or lost.

Thanks
Bill

 

[bhobba]

They are effectively the same thing.

Which of course was one of Shannon's great discoveries. Its basically a measure of order. Chaos is coming - the universe is tending to disorder.

But I suspect Scott is not looking at it that way. For some reason he is thinking that with each observation information increases. He fails to understand in the MWI the information in a state is a useless concept because its not information that 'splits' - but the state.

Thanks
Bill

 

[craigi]

Which of course was one of Shannon's great discoveries. Its basically a measure of order. Chaos is coming - the universe is tending to disorder.

But I suspect Scott is not looking at it that way. For some reason he is thinking that with each observation information increases. He fails to understand in the MWI the information in a state is a useless concept because its not information that 'splits' - but the state.

Thanks
Bill

It does, doesn't it?

A measurement causes decoherence, which causes the interference to get dissipated into the environment, which causes an increase in entropy.

So in that respect he's right.

 

[bhobba]

It does, doesn't it?

Of course - in the context you are considering - but that is not the context he is thinking of.

In the MWI the wave-function gets partitioned by decoherence which can be viewed as a loss of information contained in the phase of a superposition - it gets jumbled up with the environment in a rough intuitive sort of way. But that doesn't change the information contained in the overall universal wave-function, which is not a useful concept in this context, doesn't change one whit.

Kith hit the nail on the head - he needs to give his definition of information and why it increases.

Even classically our knowledge of say the position of a particle is constantly increasing so in that sense information is increasing - but it is of zero relevance.

What is relevant to entropy is the configurations of particles that show no order is overwhelmingly greater that those that do - that's why entropy increases. Its not impossible for the particles of two gasses to suddenly separate - its that if you consider any configuration the number where they are randomly intermingled is overwhelmingly greater than if they are separate.

Although I have only given the analogy a superficial consideration I suspect it's exactly the same with decoherence - that information is lost to the environment is simply that is the much more likely scenario.

In MWI there would be worlds where gasses separated but they would be vastly outnumbered by what we usually experience.

Thanks
Bill

 

[craigi]

Of course - in the context you are considering - but that is not the context he is thinking of.

Kith hit the nail on the head - he needs to give his definition of information and why it increases.

I think in a roundabout way, he's actually right, if we use the defintion of information as entropy. He's of course, ignoring a formal defintion, but splitting does cause an increase in information (entropy), in the observer's reality.

Where I think he's wrong is in thinking that it's somehow special to the MWI. To me, the entropy increase at decoherence events is just a product of the second law.

 

[craigi]

Well well well...

I did a quick search on this and look what I found:

http://www.ipod.org.uk/reality/reality_decoherence.asp

Regarding change of entropy, in the Many Worlds interpretation, entropy increases after each universe-branching operation (the resultant universes being slightly more disordered). So Many Worlds **causes** an increase in entropy. But in the explanation of decoherence I presented in the main article, the increase in entropy due to the Second Law **causes** decoherence. So that is far more preferable to the Many Worlds cause/effect sequence. And decoherence is explained by an existing physical principle: the second law of thermodynamics.

...

The more I think about the Many Worlds interpretation, the less sense it makes.

Andrew Thomas, 27th October 2008

It seems that he has struggled with this concept too. I don't understand where his confusion lies though. Again, I just don't see why the MWI is considered different to the CI, in this respect. Reading the rest of this page, he does seem to be a strong opponent of the MWI and a proponent of physical collapse.

 

[bhobba]

I did a quick search on this and look what I found:

I think its pretty obvious entropy increases - if that what was being said - no problem.

But what he is claiming is that information increases and must eventually exceed the Beckenstein bound and that information is somehow increasing because of 'observations'.

First of all we need to see his definition of information in a quantum system and that it increases without bound.

Thanks
Bill