Many-worlds: When does the universe split?

[Jazzdude]

My whole point here was to make it obvious that when an MWI "split" happens, each world ends up with more information than it started with. If it splits into 32 worlds, at least for the moment while they are still unique, each of those 32 worlds has 5 bits more than it did before the split.

To go back to my original assertion, a "random" split should be fully dependent on the contents of its past light cone. If it is dependent on anything else, then the process is introducing information into the new worlds.

This is false, for a number of reasons. First of all, the unitary evolution of the universal state preserves all sensible information measures. Any additional world-specific entropy increase is due to the lack(!) of information about the rest of the state. This is counter intuitive, but mathematically consistent.

Secondly, you cannot apply the Beckenstein bound to the entirety of all multiverses, because each has to produce its own copy of quantum space time, which is what the bound applies to. So there is no measurable effect of the collection of multiverses on the space time structure of a single one of them.

Cheers,

Jazz

 

[.Scott]

Secondly, you cannot apply the Beckenstein bound to the entirety of all multiverses, because each has to produce its own copy of quantum space time, which is what the bound applies to. So there is no measurable effect of the collection of multiverses on the space time structure of a single one of them.

Cheers,

Jazz

I'm only applying the Bekenstein bound to each of the worlds, not to the collection. Each individual post-event world (Wn) will have additional information not contained in the original pre-random-event world (W0). I'm not addressing exactly how this information would show up in terms of entropy. I'm simply applying an overall "check" to whatever detailed calculations were used when someone concludes that there is no additional information.

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.

This is false, for a number of reasons. First of all, the unitary evolution of the universal state preserves all sensible information measures. Any additional world-specific entropy increase is due to the lack(!) of information about the rest of the state. This is counter intuitive, but mathematically consistent.

I had a more physics-oriented colleague translate that for me. Apparently you're claiming that the which-world information was already hidden in the pre-event world, W0. So when the "random" event occurs, it simply goes from hidden to apparent.

Unfortunately my argument against that is hard to state, but it's basically this: If there is hidden information affecting the transition from W0 to Wn, then let's try to find out more about that hidden information before we presume that n>1.

 

[The_Duck]

So how does this affect the minimum size of the universe? It increases the Berkenstein bound.

Unless there was a way of remerging universes, the result would be a universe that was continuously growing.

Worlds can merge. It happens all the time. Worlds "merge" whenever two lumps of probability amplitude converge in configuration space. For example, just after a particle passes through a double slit we could choose to describe its wave function as depicting two separate worlds, one in which the particle is just behind slit A and one in which the particle is just behind slit B. As the wave packets corresponding to these worlds propagate and expand, they overlap and the two worlds merge to some extent.

However, currently most of configuration space is empty and it is much more probable for lumps of probability amplitude to expand into empty regions of configuration space than it is for lumps to encounter other preexisting lumps of amplitude and merge.

In the far future, if there is a maximum entropy for the universe, eventually the wave function of the universe will have some nonzero amplitude for each possible configuration of the universe. The wave function of the universe will eventually "fill up" its configuration space. Then it will no longer make sense to talk of worlds splitting: there will already be a world for each configuration of the universe and all that can happen will be minor reshufflings of the amplitudes for each possibility. This is what the heat death of the universe looks like in MWI.

There are a couple of ways of using the Schrodinger's cat story. I always took it as a way of illustrating "measurement" as if the cat was subject to QM collapse - the notion that the cat's destiny was not determined until the box was opened. Since I never expected anyone would seriously think that the cat was really ever both dead and alive, I extended the cats predicament to what a particle would do when it crosses through both the left and right slit. Since the left and right particle "interact", so would the dead and alive cat.

The only "interaction" going on in either case is the interference of probability amplitudes. If you interrogate the final particle about its experiences, either you will find that either (a) there is no record of which slit it went through, and it is impossible to determine, or (b) it went through a definite slit and experienced no interaction with any version of itself that went through the other slit. In neither case will you find any "communication" between versions of the particle that went through different slits. Similarly, in no version of the experiment could Schrodinger's cat come out alive but with the experience of having communicated with the dead version of itself.

 

[kaplan]

An example of what I mentioned about light cones is here:

http://arxiv.org/abs/quant-ph/0201134

Although they didn't suitably separate photons 0 and 3 in this particular implementation, theory says that those photons become entangled even when they never share any einsteinian cone.

No, that's not accurate. Referring to Fig. 1 of that paper, theory makes predictions regarding what Victor will see when he makes a measurement on the photons he receives. But Victor's measurement is within the future lightcones of both Alice and Bob's measurements, so there is clearly no problem with causality even if Victor's measurements exhibit correlations.

It's true that in the (naive version of the) Copenhagen interpretation, Alice's measurement instantly entangles 0 and 3, even though they may be far out of her measurement's lightcone. Not so in MW, where Alice's measurement has no effect whatsoever on the states of 0 and 3. What it does do is produce a state that is very close to a density matrix diagonal in the basis corresponding to her measurements. That, together with Bob's measurement, produces a set of worlds in which Victor's measurements will exhibit correlations that he can detect given some information from Alice.

 

[kaplan]

In thinking about this it's perhaps useful to revisit the basic EPR setup. There, you can think of the entangled state of the two particle as corresponding to two worlds: one where Alice has the particle with spin up and Bob has the particle with spin down, and another with the opposite situation. Prior to making a measurement, Alice and Bob do not know which world they are in (actually, an identical copy of them exists in both worlds). After making a measurement the copies are no longer identical, because the state of the particle is now known to them, and each copy finds out which world it is in. In other words if Alice measures up, she knows she is the Alice in the world where Bob must measure down. Of course there is another branch with an Alice that measured down, and that Alice knows Bob must measure up.

So it's not that Alice's measurement affected the state of Bob's particle, it's simply that Alice learned which Alice she was, and hence what Bob must measure in her world (or already did measure, if his measurement is in her past).

The same logic works perfectly well in every QM experiment, although expressing it in words that way gets very cumbersome when the setup is as complicated as the one DrChinese linked to.

 

[.Scott]

Worlds can merge. It happens all the time. Worlds "merge" whenever two lumps of probability amplitude converge in configuration space. For example, just after a particle passes through a double slit we could choose to describe its wave function as depicting two separate worlds, one in which the particle is just behind slit A and one in which the particle is just behind slit B. As the wave packets corresponding to these worlds propagate and expand, they overlap and the two worlds merge to some extent.

From what I gather, most of the MWI advocates on this forum do not want to treat superpositioning and the MWI as basically the same thing. And I think they are right. In the case of superpositioning, you're modelling the photon in the period between the time a it is emitted and the time it is detected on the other side of the slits. But that is not to say that anything really happened during that period. The model may suggest intermediate states, but we know that there really isn't any which-way information. In contrast, the multi-world model says that you are creating multiple real worlds - each with its own permanent measurable photon location.

More to the point, if there is a maximum entropy for the universe, eventually the wave function of the universe will have some nonzero amplitude for each possible configuration of the universe. The wave function of the universe will eventually "fill up" its configuration space. Then it will no longer make sense to talk of worlds splitting: there will already be a world for each configuration of the universe and all that can happen will be minor reshufflings of the amplitudes for each possibility. This is what the heat death of the universe looks like in MWI.

I am not clear on the connection between entropy and information. Supposedly, entropy is increasing continuously while quantum information is neither created nor destroyed. Some of the conversation here seems to tie them together very closely.

 

[.Scott]

The only "interaction" going on in either case is the interference of probability amplitudes. If you interrogate the final particle about its experiences, either you will find that either (a) there is no record of which slit it went through, and it is impossible to determine, or (b) it went through a definite slit and experienced no interaction with any version of itself that went through the other slit. In neither case will you find any "communication" between versions of the particle that went through different slits. Similarly, in no version of the experiment could Schrodinger's cat come out alive but with the experience of having communicated with the dead version of itself.

Okay. Let's take the interferometer. If a particle shows up in the darkest area of the interference pattern, then could that be described as interacting with it's virtual partner that struck an obstacle before completing it path to interference?

 

[kaplan]

From what I gather, most of the MWI advocates on this forum do not want to treat superpositioning and the MWI as basically the same thing. And I think they are right. In the case of superpositioning, you're modelling the photon in the period between the time a it is emitted and the time it is detected on the other side of the slits. But that is not to say that anything really happened during that period. The model may suggest intermediate states, but we know that there really isn't any which-way information. In contrast, the multi-world model says that you are creating multiple real worlds - each with its own permanent measurable photon location.

The difference between the worlds of the MWI and a single particle in a superposition is only that in distinct worlds of the MWI, macroscopic objects are in superpositions of states with macroscopically distinct properties ("Schrodinger's cat states"), instead of just particles being in states with distinct particles. For example, a particle in a superposition of (approximate) position eigenstates separated by 10 meters versus a human being in a superposition of (approximate) position eigenstates separated by 10 meters.

The difference is simply one of degree - there is nothing fundamental that distinguishes between the two (especially when you remember that all states can be written as superpositions). The reason to draw the distinction is that due to decoherence, interference between states with macoscopic differences in at least some properties (like position) is extremely small, by contrast to interference between states in which only a few particles have properties that differ.

 

[Jazzdude]

I'm only applying the Bekenstein bound to each of the worlds, not to the collection.

In post #47 you add up the information on hard drives from all worlds that split off and argue that this information gets too much. So you ARE applying the bound on all the worlds, which you cannot do for reasons I listed earlier.

Also, you cannot even add information in general. Information is sub-additive.

Cheers,

Jazz

 

[.Scott]

In post #47 you add up the information on hard drives from all worlds that split off and argue that this information gets too much. So you ARE applying the bound on all the worlds, which you cannot do for reasons I listed earlier.

Also, you cannot even add information in general. Information is sub-additive.

Cheers,

Jazz

No. You missed the point of that 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.

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

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.

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.

 

[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.

 

[.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