Many worlds / parallel universes & improbable events

[t_siva03]

Hi,

I'm hoping that someone can explain one problem I have with the many worlds theory. If the many worlds theory is true, then we are currently living in a universe which is the product of an infinite number of splits in the past. Thus, looking at our history, we should have numerous extremely improbable events in our past. Although many other branch points/universes exist, our particular branch point is the result of infinite splits. Following all of these back we should see some instances of someone flipping a coin ten thousands times and always getting heads, etc. We do not have any such recorded events in our history, despite an infinite amount of splits leading us to our particular current branch.

Do you not think it is highly improbable, that out of an infinite amount of splits in our history, we live in the only branch in which no single recorded event exists which is highly improbable.

dragons_maw

 

[Fredrik]

There are a lot more histories with about 5000 heads than with 10000 heads, so chances are we'd find ourselves having lived through one of them.

 

[benk99nenm312]

Hi,

If the many worlds theory is true, then we are currently living in a universe which is the product of an infinite number of splits in the past. dragons_maw

I'm actually not so sure about this. I think that a particular event can split an infinite number of ways, but the number of splits in a given time period should be finite. One split every 10^-43 seconds over a period of 13 and a half billion years is a lot of splits though. You bring up a good point.

To add to this, if an event goes an infinite amount of different ways, and these all represent different universes, how is it that one is more 'probable' than the other? Where does probability come in?

 

[vanesch]

Do you not think it is highly improbable, that out of an infinite amount of splits in our history, we live in the only branch in which no single recorded event exists which is highly improbable.

If you look around you, what's the probability you think that things are the way they are ? To me the world is quite improbable :tongue2:

That said, you are right that there remains a problem in MWI, which is indeed "where do probabilities come from". A partial answer was given by de Witt. He showed that the whole of "worlds" (that is, all those components of the quantum state that can qualify as decohered "worlds") in which the Born probability rule is not on average true will tend to a total Hilbert norm 0 in the limit of "infinite splits". I formulate it here in a very unformal way.

Now, this is similar to the "frequency interpretation" of probabilities, in that probabilities only tell you something about outcomes effectively in "the limit of an infinite number of trials".
So in the limit of an infinite number of trials de Witt was able to demonstrate that those worlds having a systematic deviation from the Born probability rule tend to Hilbert norm 0.

 

[vanesch]

BTW, I merged your identical thread from the BTSM forum here. Please don't start different threads on the same topic in different subfora.

 

[t_siva03]

Thanks for the replies, especially the clarification of 'probabilities' in this setting.

I agree that the number of splits is not quite infinite, but considering the number of events that have occurred since the big bang, and an innumerous number of splits after each of these splits, it does create an unimaginable number of decohered worlds.

Even if we accept your explanation Fredrik that there are many more worlds in which probable events have occurred, making it always more likely to be living in one of these worlds, considering that our current world is the result of innumerous splits, there should be at least some extremely improbable events recorded in our current branch. It is much more unlikely that we live in the only branch that even after inummerable splits our recorded history does not contain any improbable events, than to have someone flip 10,000 heads in a row.

I think we can still define probabilities in the context of MW theory. Take for example flipping a coin three times.

H T
H T H T
HT HT HT HT

Here, we see only one branches in which we flipped 3 heads in a row and one in which we flipped 3 tails in a row. However, there are many more branches in which these less likely events have not occurred. So when one calculates probabilities, although every possible event will be realized, we are calculating the likelihood that we will occupy a certain branch point.

dragons_maw

 

[Fredrik]

Even if we accept your explanation Fredrik that there are many more worlds in which probable events have occurred, making it always more likely to be living in one of these worlds, considering that our current world is the result of innumerous splits, there should be at least some extremely improbable events recorded in our current branch.

I really don't see why you think so. Maybe you just don't understand just how improbable the things you have in mind are. Take your own example, flipping heads 10000 times in a row. The probability is less than 1 in 10³⁰⁰. As a comparison, the current age of the universe in seconds is only about 10¹⁸, and you're not talking about a time period of that length. You're talking about human history (which is what? A few thousand years?) and specifically about events that someone was able to observe and make a note of. We wouldn't even know about it if some water molecules in the ocean aligned in a weird pattern for a split second during a storm 20 million years ago, or if some extremely rare elementary particle interaction is happening in the Earth's core right now.

2¹⁰⁰⁰⁰=(2¹⁰)¹⁰⁰=1024¹⁰⁰>1000¹⁰⁰=(10³)¹⁰⁰=10³⁰⁰

 

[t_siva03]

Hi Fredrik. You are assuming that there is only 1 split that occurs per second in the history of the universe. Most physicists put the number of estimated particles in the universe at somewhere between 10^72 to 10^87. Consider just the last second that just elapsed. If I understand correctly, then quantum theory tells us that the exact position of all of these particles is not certain. So let's assume that they are in a flux between being 1 picometer to the left, versus, 1 picometer to the right. Now think of all of the permutations that are possible, particle #1 being 1 picometer to the left, and all the other particles in the universe being one picometer to the right, then particle #1 and #2 being to the left and everything else to the right, etc. Now this is considering only the possibility of being 1 picometer to the left or right. Now, consider the possibility of being 2 picometers to the right or left, etc.

Realize now that this accounts only for the position of the particle, and not many other measurable properties of each of these particles which are also in a state of flux and/or being realized in decohered worlds in MWI. Think of how many permutations are possible of all of the properties of all of the particles in the universe if you consider just the last second that elapsed. Then consider how many permutations are possible in 10^18 seconds.

Wouldn't you agree that this number is immensly bigger than 10^300. I agree that now that we are considering the entire universe, we would be unaware if some highly improbable event is occurring at the current moment in the andromeda galaxy. Also, I agree that while the possibility of this degree of decoherence exists, all of this decoherence may not be realized unless there is some advanced intergalactic species simultaneously measuring all of the particles in the universe.

dragons_maw