### one espresso, many worlds

I walk up to a fully automated coffee dispenser and push the button to get an espresso.
What I do not know is that the button is connected to a device which consists of a radioactive source and a detector. The button activates the detector for 5 seconds and if it registers a particle from the radioactive material it will make an espresso and otherwise not (*). The probability to get my espresso, according to text book quantum theory, is exactly 50%.

But this raises the following question. There are many ways I can get the espresso, but there is only one way that it can fail. See, I push the button at 1pm, which here means I push it exactly at 1:00:00. Now the detector could register a particle at 1:00:01 or at 1:00:02 or ... at any time between 1:00:00 and 1:00:05. There is an infinite number of possibilities when and how the detector could register a particle.

But there is only one way it can not register a particle, with the detector shutting down at 1:00:05.

Since we all believe in the many worlds interpretation, this implies that there are many worlds where an espresso has been prepared and only one world where I fail to get it. So how can the probability be 50%?

Unless we assume that somehow the many different worlds are not equally real (x).

So perhaps the many worlds are not really real after all ?

(*) Actually, many automated dispensers in the real world follow a similar design.

(x) added later: There are proposals on how to save the appearances. Let me know if you find them convincing.

Anonymous said...

I guess I am missing your point. Do you mean that if the detector is shut off then the world does not split? And what if you change the detector time until the probability to get an espresso is one billionth? Do you still think that the non espresso world is less "real"?
And what about Anna Karenina? Does that mean that there are much less happy families?

RZ

wolfgang said...

My point is that in this example (I assume that) the probability to get an espresso is 50% , but there are many more worlds with espresso than without.
Therefore counting outcomes does not give the correct probability, therefore the worlds of m.w.i. cannot be (equally) real in the usual sense.

By the way, this is of course known already for a long time and several proposals have been made how to rescue the appearances. e.g.

arxiv.org/abs/quant-ph/9906127

Anonymous said...

So realizations can have different weights? How is this different from what goes on in plain old probability? (Maybe it is in the article, I haven't looked at it yet).
RZ

wolfgang said...

The Schroedinger equation is deterministic and so the question would be where the weights (probabilities) come from.

The Born rule is an unexplained add-on within the Copenhagen interpretation and m.w.i. proponents are/were hoping it can be derived.

Anonymous said...

There is an obvious solution to this puzzle. The worlds split at any point in time and therefore there are as many worlds with you having an espresso as there are worlds where you don't get one.

wolfgang said...

If you assume that for every t, 1:00:00 < t < 1:00:05, the worlds split in two (one with and one without espresso) then you can perhaps 'save the appearances' for the case that the probability is indeed 50%.
But what if the total probability to get an espresso is only 43% ?

Also, the radioactive material could consist of many different atoms and so the detector could register a particle in many different ways. But there is only one way it can not register a particle. So there are many different (classical) worlds how a particle was registered but only one where none has been detected (for every t).

David said...

I think I get your point.

Kind of like, if you set the probability of getting a espresso to be 0.999 and not getting it at 0.001, and you carried out this experiment 1000 times you'd still get 999 espressos.
But in MWI it would be a 50/50 probability since the universe always splits in half, no matter the probability.

Which is MWI's biggest problem

wolfgang said...

You can tweak it both ways.
You can have a probability for e of 99% and 1% for n and yet the worlds split only in two.

Or you can set it so that the probability is 50:50 and yet there are 999 worlds with e and only one with n.

As I wrote above, this is known already for quite a while.
I think it suggests that the worlds of mwi cannot be equally 'real' (in the sense of classical probability) no matter what the details are of a particular 'fix'.

David said...

How would you get 999 worlds with n and 1 with e from 50:50 probability?

wolfgang said...

I thought my blog post makes clear how you can get 999 different ways to get an espresso e but only one way not to get it.

The detector is active for 5 sec.
The probability that it detects a particle during these 5 sec is 50% (which results in e).
But there are 999 (and many more) ways when exactly it detects the particle; so there are 999 different worlds with e.
But there is only one way how the detector does not detect a particle within the 5 sec.
Therefore 999 worlds with e but only 1 world with n.
But the probability for e was 50%.

David said...

yes in your thought experiment that would be the case, but I was talking about mine with the light bulps.
Sorry I see I used your "e" and "n" for "espresso" and "none".

wolfgang said...

think of a detector D which consists of 999 sub-detectors D1, D2, ... D999 (if the Di are pixels in a digital camera we talk about 9Mio sub detectors!)
The detector D registers a photon with probability 50% (e.g. in a Mach Zehnder experiment).

But there are 999 macroscopically different ways how it can detect something, while there is only one way how it can not register the photon.

David said...

But (if I understand this correctly) this means that MWI can't make sense of probabilities at all?
Why isn't this adressed more thoroughly by more physicists (opponents and proponents of MWI) ?

Also which are the other good realist candidates without collapse?
deBroglie Bohm?
What interpretation do you adhere to?

wolfgang said...

>> this means that MWI can't make sense of probabilities at all?

yes

>> Why isn't this adressed more thoroughly by more physicists (opponents and proponents of MWI) ?

it is a well known problem of MWI and people try to find ways around it.

>> What interpretation do you adhere to?
The interpretation problem is an unsolved problem as far as I can see, which really bothers me.
Unfortunately, for practical purposes any interpretation will be sufficient to sweep this under the rug.

David said...

How well does this attempt at getting around the problem work?

Also if they can't dervive born rule, can't they just postulate it as a axiom?

wolfgang said...

>> How well does this attempt at getting around the problem work?

It makes several non-trivial assumptions ad hoc and I am not convinced.

>> Also if they can't derive born rule, can't they just postulate it as a axiom?

The Born rule makes sense within the Copenhagen interpretation and in this context we know what it means.

I am not sure what 'probability' even means in the context of mwi if the number of worlds does not match the Born probability.

David said...

But you surely don't believe in the copenhagen interpretation where "collapse" is a reality?

Is the probability problem the "only" problem MWI face?

wolfgang said...

>> But you surely don't believe in >> the copenhagen interpretation

as I wrote above, I think the interpretation problem is an unsolved problem.

>>Is the probability problem the >>"only" problem MWI face?

There are other problems, e.g. the issue of the preferred basis.

David said...

Thanks a lot.

I'm not a physicist but I try my best to understand these things (which sometimes takes hours of reading up :P ).
How "crucial" is this argument against MWI?

I know the probability problem is always brought up, but I rarely see the preferred basis objection.
I've heard it a few times, but the MWI proponents usually dismiss it.
So I guess I thought it wasn't really a big issue at all.

wolfgang said...

>> How "crucial" is this argument against MWI?

I think it is important.
But one should not forget that mwi is much more ambitious than other attempts to solve the interpretation problem.
The idea that the quantum dynamics of the wave function is all there is (no collapse, no hidden variables etc.) is actually very ambitious.

Copenhagen simply assumes the existence of a (quasi)classical domain while mwi needs to derive it (the problem of the preferred basis). And while Copenhagen can simply state the Born rule as an axiom, it somehow has to be derived within mwi (the problem of the probabilities).

Therefore, mwi is more interesting than Copenhagen and others, but as I understand it important questions remain unanswered.

David said...

When you say more ambitious, what do you mean by that?

Some would argue that Intelligent Design is very amibtious because it's supposed to explain EVERYTHING, yet it's the most crackpot idea in history...

Do you mean MWI may have a chance of being correct?

If MWI has atleast these 3 problems: can't account for probability which we observe 24/7, can't account for special relativity and has this preferred basis problem...

Doesn't that disprove MWI to the point where it can't be true?
No matter how much you twist and bend it?

wolfgang said...

>> When you say more ambitious, what do you mean by that?

well, mwi tries to explain the same as other interpretations, but with less assumptions. i think this makes it more ambitious.

ps: i am not aware that there is a problem with relativity...

David said...

sure, but ambitious doesn't equal more likely or even sensible.

Do you feel MWI is sensible ?

A "world" is defined relative to an instantaneous value of the universal wavefunction. but that wavefunction then becomes a frame-dependent object, depending on a particular time-slicing of spacetime.
This violates the spirit of relativity, according to which all the things that are actually real are frame-independent.

wolfgang said...

>>Do you feel MWI is sensible ?
no, not yet.

>> depending on a particular time-slicing of spacetime.

the concept of space-time assumes implicitly classical objects and mwi leaves open where they come from.
(in other words mwi leaves open where classical observers and their reference frames come from).
In this sense there is a problem.

As H.D. Zeh and others pointed out, mwi requires one to take quantum gravity into consideration and of course this is an unsolved problem ...

DaviD said...

No not yet?
Do that imply that you feel MWI needs modification before it's sensible, or that you have more to learn?

I read that earlier and I agree it's a problem, but it doesn't adress MWI's problem with relativity?

wolfgang said...

>> Do that imply that you feel MWI needs modification before it's sensible, or that you have more to learn?

probably both

David said...

So you do not feel that the current problems with MWI is enough to dismiss the version of MWI that people adhere to today (unmodified) ?

wolfgang said...

as i wrote above, i have not seen a plausible, convincing solution to the interpretation problem yet.

David said...

Which I'm aware of ofcourse ^^
I'm rather asking if you feel that the problems specially against MWI is enough to DISMISS it?
I could give you my email instead so we don't have to fill up your whole comment section if you want to discuss it further?

wolfgang said...

>> the problems specially against MWI is enough to DISMISS it?

mwi solves the interpretation problem, but introduces 2 or 3 new unsolved problems.
People discuss for many years now if/how these problems can be resolved somehow. So let them work on it and see what happens...

Personally, I would look somewhere else to think about the interpretation problem.

>> so we don't have to fill up your whole comment section