Does the MWI Imply Reality Splits When Observing Photon Paths?

[entropy1]

I am sorry to bore you people with a very, very simple question (there is no catch unless QM throws it ):

If we have a half silvered mirror and we fire a single photon at it at an angle of 45°, it either passes or reflects from the mirror. To be more precise, the photon becomes in a superposition of both, and is taking two paths simultaneously after encountering the mirror, aka 'superposition'.

So, when we have two observers, A at the end of the photon's path passing the mirror, and B at the end of the photon's path reflecting from the mirror, the/a photon is detected either by A or by B, but not both A and B.

Is it right to refer to the MWI and presuppose that reality is split in two, one version where A detects the photon, and one version where B detects the photon? I just wonder if it is that simple.

Where is this split created?

Is the superposition a way of QM to reconcile the particle having to be sliced into smaller pieces by the mirror?

 

[mfb]

Is it right to refer to the MWI and presuppose that reality is split in two, one version where A detects the photon, and one version where B detects the photon? I just wonder if it is that simple.

That is MWI, yes. It is the natural result if you assume the wave function is physical and follows unitary evolution everywhere.

Where is this split created?

The "split" is just our interpretation of the state - in practice you can say it happens from decoherence.

Is the superposition a way of QM to reconcile the particle having to be sliced into smaller pieces by the mirror?

I don't understand that question.

 

[entropy1]

Does the split only occur as a result of superposition? Or are there other possible causes?

 

[mfb]

The split is a superposition - of things that stopped influencing each other.

 

[entropy1]

The split is a superposition - of things that stopped influencing each other.

In my example, which things stopped influencing each other?

 

[mfb]

The part of the wave function we describe as "A saw the photon" and the part "B saw the photon".

 

[entropy1]

I have to think about that. Thanks!

 

[AlexCaledin]

Just found this remarkable D.Wallace's statement, in the book Many Worlds?: Everett, Quantum Theory, & Reality :

Decoherence causes the Universe to develop an emergent branching structure. The existence of this branching is a robust (albeit emergent) feature of reality; so is the modsquared amplitude for any macroscopically described history. But there is no non-arbitrary decomposition of macroscopically described histories into 'finest grained' histories, and no non-arbitrary way of counting those histories.

(page 68)
____________

- so, things like "particle having to be sliced" are our arbitrary ideas about the objective mathematics that is generating the potential variants for our experience.

 

[entropy1]

Is the superposition a way of QM to reconcile the particle having to be sliced into smaller pieces by the mirror?

I don't understand that question.

The mirror doesn't slice the photon in half, but sends it on its way to A or B. However, in case of this setup:

since only the right detector detects a photon due to interference of the two photon paths (M1, M2), the photon seemingly (in my mind) is sliced in two in order to interfere with itself. But this slicing is not possible since the irreducability of a particle, hence the way out using superposition?

 

[entropy1]

If the half-silvered mirror is 70% silvered, do we then get a superposition of the photon of α|A> + β|B> with α=√0.7 and β=√0.3?

 

[mfb]

The mirror doesn't slice the photon in half, but sends it on its way to A or B.

I don't think either of these is a good description. The mirror creates a superposition of |A> and |B>.

If the half-silvered mirror is 70% silvered, do we then get a superposition of the photon of α|A> + β|B> with α=√0.7 and β=√0.3?

Sure.

 

[entropy1]

I don't think either of these is a good description. The mirror creates a superposition of |A> and |B>.

So is it correct that this setup should be discussed in terms of states/wavefunctions instead of in terms of 'photons'?

 

[mfb]

It should be discussed with states of photons.

 

[entropy1]

It should be discussed with states of photons.

If the photon takes both paths, in order to be able to interfere with itself, then what is 'traveling' along both paths exactly? Two full photons or two half photons?

 

[mfb]

Two full photons or two half photons?

Neither.

A state with a given amplitude. To understand the system you have to consider the whole state - the superposition of both paths.

 

[entropy1]

The split is a superposition - of things that stopped influencing each other.

Is the stopping of influencing related to the orthogonality of |A> and |B>?

 

[Derek P]

The split is a superposition - of things that stopped influencing each other.

This may be a pedantic point but they never did influence each other. Different states in superposition evolve independently. The only things that influence each other are different subsystems. What I'm sure you mean is interference. But in interference the "separate" wavefunctions pass through each other without influencing each other. The interference is seen when the observer resolves the superposition in a new basis. The worlds split when this interference is no longer possible because phase coherence has been lost - which makes the split irreversible.

 

[mfb]

Different states in superposition evolve independently.

Technically correct, but in practice you certainly want to consider them together in many cases, as you need this to evaluate amplitudes.

 

[Derek P]

I am sorry to bore you people with a very, very simple question (there is no catch unless QM throws it ):

If we have a half silvered mirror and we fire a single photon at it at an angle of 45°, it either passes or reflects from the mirror. To be more precise, the photon becomes in a superposition of both, and is taking two paths simultaneously after encountering the mirror, aka 'superposition'.

So, when we have two observers, A at the end of the photon's path passing the mirror, and B at the end of the photon's path reflecting from the mirror, the/a photon is detected either by A or by B, but not both A and B.

Is it right to refer to the MWI and presuppose that reality is split in two, one version where A detects the photon, and one version where B detects the photon? I just wonder if it is that simple.

Where is this split created?

Is the superposition a way of QM to reconcile the particle having to be sliced into smaller pieces by the mirror?

Yes it is that simple. As long as you mean phenomenal reality or, as AlexCaledin's Wallace quote calls the worlds, "macroscopically described histories". The universe becomes a superposition of these phenomenal worlds.

The spit is created when the coherent state of the photon interacts with the macroscopic system. This system is then ridiculously complicated but you can ignore the fine detail and closely approximate it as a probability distribution over the macroscopic states of the detectors.

The idea is simple, the maths is not.

You can certainly view superposition as a way of avoiding the paradox of an indivisible particle being in two places at once. For simplicity you could first postulate that different observable states can coexist. |A> state coexisting with |B> would then be written as the superposition |A>+|B>.

Note: It does not necessarily follow that the superposition has to be interpreted as different observable states co-existing. MWI shows that different worlds emerge, it does not insist on the original coherent quantum state being regarded that way. In fact people do argue whether it should or should not be.

 

[Derek P]

- so, things like "particle having to be sliced" are our arbitrary ideas about the objective mathematics that is generating the potential variants for our experience.

I don't think so. Wallace is talking about decomposing a branch into many finest-grained histories. The branches map 1:1 to the "slices" i.e. the components of the superposition. So the decomposition in that basis is neither arbitrary nor any more fine-grained than the branching itself.