Questions on exact details of the many worlds interpretation

[JohnColorado]

I have hard time thinking the many worlds interpretation is correct. I also find its description imprecise. Here are some questions I would like someone to answer about the interpretation.

1. When a wave form photon hits a screen and become a particle form photon, this event splits the world (universe) into multiple worlds. How many worlds? From what I read it says all possible worlds. Along the wave this would mean infinite or near infinite worlds. This seem ridiculous to me. Does anyone say how many worlds come into existence or how that number would be calculated?
2. When the worlds are created, does it mean all of the universe is split into two universes? So a galaxy 10 billion light years away is also split into different worlds? If not, then there is a boundary around the split that is localized. Right?
3. Is the interpretation saying that the entire universe is split into near infinite versions at every wave/particle event which happen a 10 to some huge number power of times per second? Does this not sound ridiculous?

What am I missing? Tthe explanations of the interpretation I have read do not go into the details.

Thanks,
John

 

[phyzguy]

For what it's worth, I share your opinion of the ridiculousness of the interpretation. However, since the alternate universes are inaccessible to us, there is no experiment one can do that can show the interpretation is wrong.

 

[Brage]

I think there is quite a common misconception about the "splitting of universes". From Everett own work we referes to an object not being described by the wave funciton as a superposition of states, but rather that the object IS the superposition of all its states. That is to say each state is like a different aspect of the photon. Now the concept of wave function collapse becomes a subjective and not a objective experience. Let our screen also be a superposition of all its possible states (whatever these might be).
The premisse is that each state of the poton "correlates" with each state of the screen. For example consider the photon in a superposition of states $|x>$, with respective measure $a(x)$ spanning some interval $x \in [x_0, x_1]$, where x is here translation along the screen from the centre. Then the states of the photon correlates with the screen such that the state of the whole system (which in Everett's theory is the actual object itself) is now each state of the photon "multiplied" by each state of the screen. Consider then the case where there is only one state of the screen, then it will appear as if the photon impacts one place on the screen, an impact at point d is just the state $|d>$ "corrolated" with the 1 state of the screen. However, all the other states $|x>$ for $x\neq d$ also corrolate with the screen and are seen as the photon impacting only at the point $x \neq d$ for each respective x. The probability that you will observe the photon in state $|x>$ is then $|a(x)|^2$.
The term "splitting" was introduced to say that although the whole object is still all the states of the photon "multiplied" by all the states of the screen (i.e. the photon hitting every point in the screen). We subjectively only experience one colission, because that happens to be the combined state of the now corrolated photon and screen where we find ourselves. Yet that is not to say that there are not other corrolated states of the photon and screen that exist. In other words, every time you observe aquantum even there is a different you observing every single possible outcome. While this might sound farfetched it is one of the few interpretations that are self-consistent and don't have wavefuncitons "collapsing". Also as any object can corrolate with any other object this means that even if a photon interacts with an electron, the electron is an observer for the photon and the photon is an observer for the election. This then removes the paradox of what is an observer and where the quantum realm begins and ends.

Another example which might be easier to consider is the interaction of two electron both described by $|\psi_i>=\frac{1}{\sqrt{2}}|up_i>+\frac{1}{\sqrt{2}}|down_i>$ where up and down denote spin up and spin down states and $i \in {1,2}$. When these two states become corrolated the resulting system is $|\psi_1> \otimes |\psi_2>=\left[\frac{1}{\sqrt{2}}|up_1>+\frac{1}{\sqrt{2}}|down_1>\right] \otimes \left[\frac{1}{\sqrt{2}}|up_2>+\frac{1}{\sqrt{2}}|down_2>\right]$. This then results in 4 differnt possible events (all equally as likely) and all physically real according to MWT. If we "are" electron 2, then we may either find ourselves in spin up, observing electron 1 with spin up or spin down; or find ourselves in spin down, observing electron 1 with spin up or spin down. Yet there is no mention of splitting anywhere, this only comes in in an attempt to visualise the interaction.

The MWT by Everett arrises naturally if you only consider probability theory and then apply it to quantum mechanics, as was his method. The whole "splitting" term is misleading and was only introduced to describe states of a system that will forever be inaccessible to us. Visually it might help people understand what is happening, but it is just that, a visual aid and doesn't actually imply that the universe has "multiplied" and that there now are as many times the energy of the universe as there are possible ways to corrolate the states of two systems.

I hope this helps you understand the concept a bit better, Everett's work is facinating and self consistent, but is unfortunately often talked away or dismissed as noncense by people who have not actually taken the time to go through his paper and follow the mathematics which lead only to the conclusion that all possible outcomes are real, yet we can only observe one!

 

[bhobba]

Worlds don't split.

As a result of decoherence you end up with a mixed state Σpi |bi><bi| where each |bi><bi| is the possible outcome with probability pi. In MW instead of outcome |bi><bi| occurring (technically the mixed state is taken to be proper mixed state - in MW that assumption is not made) each |bi><bi| is interpreted as a separate world. No collapse occurs and everything continues to evolve deterministically.

To really understand MW you should study a modern text on it:
https://www.amazon.com/dp/0198707541/?tag=pfamazon01-20

Thanks
Bill

 

[JohnColorado]

Thanks for the responses! Bill, thanks for pointing me to a good source. I ordered the book you referenced. Brage, thank you for your explanation. It nudged my slow brain along in the right direction.

I think I am missing a significant concept around this. One question that keeps popping up for me is local verses universal affect. Excuse my terminology but it sounds that a superposition of states for one object is coupled with another superposition of states of another object and the resulting system of two objects is the combination of superposition of states for both. To me this is a very local, isolated event. My question is about the rest of the universe: How does the rest of the universe change or combine with new combination of superposition of states?

Thanks,
John

 

[bhobba]

To me this is a very local, isolated event. My question is about the rest of the universe: How does the rest of the universe change or combine with new combination of superposition of states?

Its simply if you observe one part of entangled objects and chug through the quantum math then you get a mixed state which is as I posted. Here is the math (see post 22):
https://www.physicsforums.com/threads/is-the-cat-alive-dead-both-or-unknown.819497/page-2

Thanks
Bill

 

[Brage]

Thanks for the responses! Bill, thanks for pointing me to a good source. I ordered the book you referenced. Brage, thank you for your explanation. It nudged my slow brain along in the right direction.

I think I am missing a significant concept around this. One question that keeps popping up for me is local verses universal affect. Excuse my terminology but it sounds that a superposition of states for one object is coupled with another superposition of states of another object and the resulting system of two objects is the combination of superposition of states for both. To me this is a very local, isolated event. My question is about the rest of the universe: How does the rest of the universe change or combine with new combination of superposition of states?

Thanks,
John

Well consider that every state of every particle in the universe is already corrolated with every other state of every other particle in the universe. Then a local interaction is not an isolated event, but an event that gains you knowledge about which state of the universe you belong to. So its not so much that because of an interaction you appear in a state, but rather an interaction let's you know what state you were/are in. The states are there whether observed or know, and what is referred to as a wavefunction "collapse" is just us gaining knowledge about our own state.

 

[mfb]

3. Is the interpretation saying that the entire universe is split into near infinite versions at every wave/particle event which happen a 10 to some huge number power of times per second? Does this not sound ridiculous?

Keep in mind that many worlds is not adding anything to quantum mechanics. Those "many worlds" (decoherent components) appear naturally if you apply the equations of quantum mechanics. Doesn't it sound ridiculous to assume that all but one of those worlds magically disappear?

 

[bhobba]

Keep in mind that many worlds is not adding anything to quantum mechanics. Those "many worlds" (decoherent components) appear naturally if you apply the equations of quantum mechanics. Doesn't it sound ridiculous to assume that all but one of those worlds magically disappear?

People that have issues with MW often forget that. As I often say of all the interpretations this is the most beautiful - in fact its beauty incarnate. Personally it's not my cup of tea - but that means diddly squat.

Thanks
Bill

 

[stevendaryl]

For what it's worth, I share your opinion of the ridiculousness of the interpretation. However, since the alternate universes are inaccessible to us, there is no experiment one can do that can show the interpretation is wrong.

For me, the problem is that there does not exist a non-ridiculous interpretation, except "shut up and calculate", maybe.