ZRPerry

Superfluous vs. Non-Observable

Hi ZRPerry. Here is the stuff I promised about "superfluous versus non observable".

I'm thinking that in a physical theory we normally have some variables which are, by assumption, observable, things that are supposed to describe the configurations of the ordinary objects of our experience (such as the particle configuration in Classical Mechanics or in dBB). Let us call those "directly observable". We also have variables in the theory which are "indirectly observable": variables that, according to the dynamics of the theory, can be forced (through the manipulation of experimental equipment) to become correlated with the "directly observable" variables.

For instance, in Maxwell's theory, the charges would be "directly observable". The magnectic field would be "indirectly observable": according to the theory, the motion of a test charge is influenced (through the Lorentz Force) by the magnectic field; the experimenter, by watching the motion of the test charge (and performing some computations), can measure the magnectic field.

Consider now a theory having variables x=x(t) and y=y(t). The x's are supposed to be directly observable (by assumption). The y's are supposed to be physically real (like the magnectic field), but not directly observable. Assume that the dynamics of the x's does not mention the y's, but that the dynamics of the y's is given as y(t)=f(x(t)), where f is some function. The y's seem to be superfluous here in the strongest possible sense. However, if you believe in the theory, you could say that you can measure the y's: simply (directly) observe x(t) and compute y(t)=f(x(t)).

I realize that this is a very artificial example (but, have in mind that, in order to give examples of stuff that are superfluous in a very strong sense, one is kinda forced to consider artificial examples). You could also object that, while the magnectic field (which is indirectly observable) influences the test charge (which is directly observable), in my example, the y's (which are supposed to be indirectly observable) do not influence the x's (which are supposed to be directly observable). And that for that reason you wouldn't count "computing f(x(t))" as observing y(t).

Have in mind, however, that I could modify my example in order to make it less artificial. Assume that the dynamics of x's and y's is given in terms of a system of first order ODE:

$dx/dt=u(x,y)$, $dy/dt=v(x,y)$.

If the theory is described like that, it certainly looks like the x's and the y's are mutually influencing each other. However, it could turn out to be the case that one can get rid of the y's and write simply a second order differential equation for the x's:

$d^{2}x/dt^{2}=w(x,dx/dt)$

and to write the y's as a function of x and dx/dt (for a concrete example: Hamilton's equations constitute a first order system of ODE for the q's and the p's, but they are equivalent to the Euler-Lagrange equation, which is a second order ODE for the q's).Dvtausk (talk) 03:19, 3 December 2009 (UTC)

Hey Dvtausk. Don't worry about artificial examples, I generally prefer them. I think you're right about there being a sense of "observable" such that, according to a given theory, even a "superfluous" entity which had no influence on observation could be observable. However, I'm not sure I like the idea of what is and is not observable being something made true of a theory by "assumption". I was thinking of a sense of "observable" that was less theory-dependent than that.

Here's a rough (and slightly convoluted) sketch of what I was thinking: We observe the world to be a certain way (full of tables, chairs, mountains, telephone poles, etc.). Physical theories posit the existence of entities that behave in such a way as to account for us making such observations. Of course, we can (presumably) reduce away the "observation" talk in the last two sentences. We would then understand our "observing" something as just our brains and sense organs (physical objects, or whatever the theory says they are) moving and shaking in a certain way, and our physical theory would posit entities which behaved (more moving and shaking, presumably) in such a way as to imply that our brains and sense organs shook and moved in a certain way. Let us call a physical theory that gets it right (where 'it' is the particular way of moving and shaking and to get it 'right' is to have it correspond to our particular experience of the world) an "observationally adequate" theory.

I was thinking of "x, in theory P, is superfluous" (understood in the empirical sense that was being used in the discussion on the dBBt page) as saying roughly the same thing as "Theory P* which is identical to theory P except for the removal of x's as real entities is observationally adequate" (Where theory P is an observationally adequate physical theory). The argument from superfluity to unobservability would run as follows: To be observable is to be an entity whose moving and shaking (at least in part) produces the particular moving and shaking of my brain and sense organs which corresponds to my experience. If x is superfluous, then its moving and shaking cannot, even in part, be what is producing my experience, since P* is observationally adequate as well. Hence, if x is superfluous then x is unobservable.

This was the charitable reading I had tried to give someone who interprets superfluity as implying unobservability. I don't endorse any part of this argument, but it is what I think is at work when someone misunderstands Bohmian mechanics as being something like the chimerical Bohmian-Particles-plus-Everettian-Wavefunction-view, and reasons from the patent superfluity of the particles to their unobservability.

I think you're right that, given the truth of some physical theory, we can "observe" something superfluous. I was thinking of the objector in question as relying on the question "what is it that we observe?" being answerable before the question of which physical theory is true was settled (though after it had been partly settled).

In general, I'm having trouble coming up with a natural sounding sense of "superfluous" under which Everett's actual criticism of dBBt is one based on real superfluousness. If we assume that x is superfluous if we can make do with everything else exactly as it is but without x, then dBBt particles aren't superfluous even if Everett's objection goes through. Why? The Everettian wavefunction is quite different from the particle-mover dBBt wavefunction. This means that, while the number of fundamental entities is smaller, it isn't that the Everettian is making do with a proper subset of the Bohmian's fundamental posits. Rather, the Everettian makes do with different fundamental posits, and it just so happens to be that the number of posits the Everettian makes use of is smaller than the number of posits the Bohmian makes use of.

I apologize if the above is sort of all over the place. I've discovered that I can either write incomprehensibly and in a timely fashion, or write clearly and take forever. You have received a response in a timely fashion. ZRPerry (talk) 19:43, 3 December 2009 (UTC)

Don't worry, I think what you wrote is understandable. I should say that, like you, I don't really like the idea of the formulation of a theory including some explicit assumption about something (some local beable) being observable; I think the observability should be deduced from some other assumption (in fact, some explicit assumption about something being observable could even lead to inconsistencies). The trouble is: what kind of assumption would that be? I haven't found a way of formulating physical theories that satisfies me. Obviously, formulating a physical theory cannot be just presenting a few differential equations. If I give you just, say, Hamilton's equations, then absolutely nothing about Physics follows from that; I have to add some assumption, some sort of explanation, about what the q's and the p's in those equations mean (in that particular example, it would be enough to explain the q's). One possible proposal to formulate the assumptions that would allow one to conclude that the q's are observable, is in terms of psycho-physical parallelism: let's add to the assumptions of the theory that the state of mind of the observer is determined (or, at least, influenced) by the q's of the particles in his brain. Then, one could deduce that the q's of say, a table, are observable, by making some analysis (in terms of the dynamics of the theory), of how the q's of the table influence the q's of the brain of the observer (the psycho-physical paralellism would then be used to finish the argument, allowing the conclusion that the observer becomes aware of the table). But I should say that I'm not happy with this approach. To begin with, I don't like very much the idea of a physical theory having assumptions about brains and minds. Another possibility would be to have an assumption of the form "the ordinary objects of our experience should be found in the q's". This approach does not make me completely happy, as I think this approach strangely bypasses the need of analysing how the q's of a table influence the q's of the brain of the observer (maybe a way out of such strange bypass would be to declare that, in the absence of interaction between the q's of a table and the q's of a brain, the theory shouldn't count as "observationally adequate" or "empirically viable").

Anyway, there is an additional point I would like to make: it is hard to give a satisfactory formulation of the assumptions of a theory in such a way that one can prove that something is observable. Formulating those assumptions is difficult in, say, dBB, but it is also difficult in any other theory, such as Classical Mechanics (and, I think, that would be even more difficult in a theory like many-worlds). Sadly, oponents of dBB would like to make it look like this difficulty of formulation appears only in dBB, instead of recognizing that such formulation is difficult for all theories.Dvtausk (talk) 16:23, 4 December 2009 (UTC)

Permit me to interject and say that measurement and observation are easily handled in MWI. Measurements, or measurement-like interactions, are any interactions that correlate the observer's wf with the observed system's wf. A measurement, in the determinate case, simply induces:

$|O,i\rangle =>|O[i],i\rangle$

A measurement is complete when:

$\langle O[i]|O[j]\rangle =\delta _{ij}$

where O[i] represents the observer having detected the object system in the i-th state. Before the measurement has started the observer states are identical; after the measurement is complete the observer states are orthonormal. Thus a measurement defines the branching process: the branching is as well- or ill- defined as the measurement is. Thus branching is complete when the measurement is complete. Since the role of the observer and measurement per se plays no special role in MWI (measurements are handled as all other interactions are) there is no need for a precise definition of what an observer or a measurement is – just as in Newtonian physics no precise definition of either an observer or a measurement was required or expected. In all circumstances the universal wavefunction is still available to give a complete description of reality.

--Michael C. Price ^talk 18:57, 4 December 2009 (UTC)

Michael, you may (in this particular instance) interject and say whatever you like (within reason), but that doesn't mean you're saying something true. The ability to correlate the wavefunction of an experimenter and an electron does not an account of observation make. Since I'm under the impression that MWI can't handle observation/probabilities/etc at all, I'm going to disagree with you when you say that MWI can handle these things and, moreover, can do so "easily".

I am more than happy to be civil on the talk pages of articles in order to reach consensus and edit productively. However, the rule on my personal talk page is that if you are wrong about something, I shall inform you of this fact and (If I have time/interest/patience) I shall explain to you how wrong you are. You (seem to) believe that the MWI is correct (or, at least, that it doesn't have any fatal flaws). You are sorely mistaken. I do not have time to explain to you why this is so, but it is possible that I will feelhttp://en.wikipedia.org/skins-1.5/common/images/button_sig.png like doing so in a week or two. ZRPerry (talk) 20:46, 14 December 2009 (UTC)

Yes, I do believe that the MWI is correct. I look forward to hearing you views on why it isn't.--Michael C. Price ^talk 01:10, 15 December 2009 (UTC)

Oh, obviously I understand that the "conversion" of dBB into many-worlds does not involve just "removing the particles", so that the alleged superfluity of the particles could only hold here in a weak sense, not in the strong sense (like the strong sense in which the y's are superfluous in my theory of x's and y's).Dvtausk (talk) 16:23, 4 December 2009 (UTC)

Another point: it would be natural to assume that, "observer A observing y" should depend on y being responsible for some disturbance in A, i.e., y being a cause of an effect on A. My discussion of first order system of ODE versus second order ODE was supposed to make a point (I'm not sure if I made the point clear). The point is that assuming that y is a cause of an effect on A is necessary for "observation" of y by A to occur is a bit problematic: it is problematic, because cause/effect is problematic. As my discussion with first and second order ODE's show, a simple mathematically equivalent reformulation of a theory can give different appearances to matters of what causes what.Dvtausk (talk) 16:23, 4 December 2009 (UTC)