# How many branches are possible after measurement/splitting?

• lukephysics

#### lukephysics

TL;DR Summary
How many branches are possible after measurement?
Say you have a simplified 1d Gaussian wave function describing location of a particle.

Many worlds says that every outcome is a separate branch. Copenhagen says you will get one of those branches.
So how many distinct positions, imaginary or real, can you generate from a fixed segment of a Gaussian curve? Are there N plank lengths under that curve? Can those plank lengths be divided in half, or 10 or more?

Interesting thought, I can see no difference between Copenhagen and many worlds from the perspective of an observer. They are functionally the same. I guess this is sensible otherwise measurement would be wrong for one or the other.

So how many distinct positions, imaginary or real, can you generate from a fixed segment of a Gaussian curve?
A priori, there is no upper limit.
Are there N plank lengths under that curve? Can those plank lengths be divided in half, or 10 or more?
The many world interpretation, by itself, does not say anything about quantum gravity, so it doesn't have an answer to this question.

Interesting thought, I can see no difference between Copenhagen and many worlds from the perspective of an observer. They are functionally the same
That is true of all interpretations - it’s what makes them different interpretations instead of different competing theories.

• gentzen and Lord Jestocost
A priori, there is no upper limit.
branching implies a splitting of paths, so you have to apply splits somewhere. is it just bad terminology? can you provide some information how this is supposed to work?

what does it mean for a particle to collapse to one position with probabiliy 100% ? you cant measure something with infinite precision, so i assume the wave function doesnt collapse to a point/singularity, it remains a fuzzy area on some small scale. does position mean centre of mass of a particle? or centre of geometric volume?

what does it mean for a particle to collapse to one position with probabiliy 100% ? you cant measure something with infinite precision, so i assume the wave function doesnt collapse to a point/singularity, it remains a fuzzy area on some small scale. does position mean centre of mass of a particle? or centre of geometric volume?
Just because we can't measure a position with infinite precision does not mean that the collapse is into a "fuzzy area".

you cant measure something with infinite precision, so i assume the wave function doesnt collapse to a point/singularity
Yes.

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Just because we can't measure a position with infinite precision does not mean that the collapse is into a "fuzzy area".
I think "fuzzy area" can be interpreted as a collapse into something like a Gaussian.

• phinds
Some reflections...
TL;DR Summary: How many branches are possible after measurement?

Say you have a simplified 1d Gaussian wave function describing location of a particle.
If you already in the premises, assume that you have a gaussian, you implicitly assume that you are working in a continuum model, and infinite capacity to encoded information, thus there seems to be uncountably many branches? - unless there is something else in the theory that forbids this.

what does it mean for a particle to collapse to one position with probabiliy 100% ? you cant measure something with infinite precision, so i assume the wave function doesnt collapse to a point/singularity, it remains a fuzzy area on some small scale. does position mean centre of mass of a particle? or centre of geometric volume?
Even if you could "measure" the position with infinite precision, the observer might not be able to hold and encode this information with infinite precision and objective 100% confidence. Ie. the "receiver-end" gets saturated, and are forced to selectively discard information.

So the other flip of the coin is to ask, what is the resolution of observation and representation of the observer/measurement device? This would constraint the distinguishable branchings from the perspective of this observer.

In the classical copenhagen view, the whole macroscopic environment is what represents the "observer" with a potential classical network of measurement apparatouses. And unless we gets into cosmology this is effectively assumed infinite. So Then such infinite precision and encoding would seem possible because the whole macroscopic environment is never saturated. But then we ignore the timescale required for post-processing of this massive amount of data, and what happens if this exceeds the "measurement timescale" by orders of magniture? Here the current theory can't handle this or even pose these questions properly?

In a generalied view, of not necessarily classicale measurement devices, one can imagine that the number of branches is simply scaling with the complexity(mass) of the measurement device, which in itself may "explain" it's brownian like motion of collapses, as seen by another more complex observer.

I think a conceptual metaphor for such a "brownian observer" is that it is itself "100% confident" about it's observations, but "wrong", which is why it keeps getting "corrected". It's like you can, to your best of capability be "confident" in something, and still be wrong when putting it to test. It's also along the saying that "the more you learn about something, the more you realize how little you really know".

/Fredrik

Many years ago Sidney Coleman taught me something very important: in many worlds, there aren't many worlds. There's only one world. This sweeps away a lot of the brush. So in a very real sense, the number of branches is "one".