# Pilot wave theory, fundamental forces

Demistifier,

There are 2 different problems as I understand:
1. Even in proton the number of quarks is not well defined. It is 3 if we use 'hard' measurements.
2. Some particles has non-integer particle content even for the 'hard' measurements
Check the list:
http://en.wikipedia.org/wiki/List_of_mesons
Kl, Ks, Eta prime with all that sqrt(2) and sqrt(6) in denominator

Demystifier
Gold Member
Demistifier,

There are 2 different problems as I understand:
1. Even in proton the number of quarks is not well defined. It is 3 if we use 'hard' measurements.
2. Some particles has non-integer particle content even for the 'hard' measurements
Check the list:
http://en.wikipedia.org/wiki/List_of_mesons
Kl, Ks, Eta prime with all that sqrt(2) and sqrt(6) in denominator
1. As far as I know, the number 3 is well defined.
2. According to the tables you gave, these particles are superpositions of 2-particle states, and a superposition of 2-particle states is a 2-particle state itself. And number 2, as far as I know, is a well-defined number as well.

I thought that you are talking about phenomena such as Bjorken scaling in which the number of particles appears to change as you change energy, but now I see that you talk about something much more trivial. As long as we talk about QM (rather than QFT), all these states have a well defined number of particles (3 for proton and 2 for mesons you mentioned), so the Bohmian interpretation also says that the number of particles is well defined (3 for proton and 2 for mesons). You must have misunderstood something about elementary QM, but I don't know what. To be sure, the numbers sqrt(2) and sqrt(6) are normalization factors, NOT the numbers of particles. Even MWI says that the number of particles is well defined for these states (3 for proton and 2 for mesons).

Before asking a question on BM, one should first know the corresponding basics of standard QM. In other words, one should know what one is talking about. You are often pretending that you understand some aspects of "ordinary" QM even when you don't. Perhaps such bluffing works for those who don't know you well, but it doesn't work for me.

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Demystifier
Gold Member
Maaneli, for a concise (and possibly more illuminating) summary of relativistic Bohmian mechanics, see also Sec. 2.1 of my last paper
http://xxx.lanl.gov/abs/1007.4946

Demystifier
Gold Member
Let me also present a brief comment on the Valentini's
http://xxx.lanl.gov/abs/0812.4941 [Phys. Lett. A 228 (1997) 215]
argument against Lorentz invariant BM.

Valentini correctly observes that the nonrelativistic BM has an Aristotelian (rather than Galilean) symmetry, which is related to the fact that the wave function (viewed as the fundamental "force") determines velocity (rather than acceleration). From this, he argues that attempts to generalize the theory to a Lorentz-invariant theory are misleading. However, that argument is wrong.

Let me explain why. He interprets Lorentz invariance as a generalization of Galilean invariance. On the other hand, in modern (Minkowski-like) view of relativity, Lorentz invariance is actually a generalization of ROTATIONAL invariance, not of Galilean invariance. And rotational invariance certainly IS a symmetry of nonrelativistic BM. Therefore, it is natural to search for a Lorentz-invariant generalization of BM.

Hrvoje,

Thanks for all your comments. I'm extremely busy at the moment and may not be able to reply for some time, possibly not until we meet at the Italy conference. Just letting you know.

Best,
Maaneli

Demystifier
Gold Member
Thanks, Maaneli.

Roughly, it reminds me to explanations of special relativity (in classical mechanics) in terms of a preferred Lorentz frame. As Lorentz has shown, it is possible as well (the Lorentz "eather"). Yet, it introduces more confusion than clarification. It is a very unnatural way to talk about special relativity and it is better to avoid it.
There is a counter-argumentation by Bell, "how to teach special relativity", where he argues
that it is, instead, the Minkowski interpretation which causes much more confusion.

It is published in "speakable and unspeakable".

Let me also present a brief comment on the Valentini's
http://xxx.lanl.gov/abs/0812.4941 [Phys. Lett. A 228 (1997) 215]
argument against Lorentz invariant BM.

Valentini correctly observes that the nonrelativistic BM has an Aristotelian (rather than Galilean) symmetry, which is related to the fact that the wave function (viewed as the fundamental "force") determines velocity (rather than acceleration). From this, he argues that attempts to generalize the theory to a Lorentz-invariant theory are misleading. However, that argument is wrong.

Let me explain why. He interprets Lorentz invariance as a generalization of Galilean invariance. On the other hand, in modern (Minkowski-like) view of relativity, Lorentz invariance is actually a generalization of ROTATIONAL invariance, not of Galilean invariance. And rotational invariance certainly IS a symmetry of nonrelativistic BM. Therefore, it is natural to search for a Lorentz-invariant generalization of BM.
I'm guessing that even if Valentini's argument isn't convincing, Albert's "narrative argument" still holds?
What it is for a theory to be metaphysically compatible with special relativity (which is to say: what it is for a theory to be compatible with special relativity in the highest degree) is for it to depict the world as unfolding in a four-dimensional Minkowskian space-time. And what it means to speak of the world as unfolding within a four-dimensional Minkowskian space-time is (i) that everything there is to say about the world can straightforwardly be read off of a catalogue of the local physical properties at every one of the continuous infinity of positions in a space-time like that, and (ii) that whatever lawlike relations there may be between the values of those local properties can be written down entirely in the language of a space-time [like] that—that whatever lawlike relations there may be between the values of those local properties are invariant under Lorentz-transformations...

What we do have (on the other hand) is a very straightforward trick by means of which a wide variety of theories are radically non-local and (moreover) are flatly incompatible with the proposition that the stage on which physical history unfolds is Minkowski-space can nonetheless be made fully and trivially Lorentz-invariant; a trick (that is), by way of which a wide variety of such theories can be made what you might call formally compatible with special relativity...

As things stand now we have let go not only of Minkowski-space as a realistic description of the stage on which the world is enacted, but (in so far as I can see) of any conception of that stage whatever. As things stand now (that is) we have let go of the idea of the world’s having anything along the lines of a narratable story at all! And all this just so as to guarantee that the fundamental laws remain exactly invariant under a certain hollowed-out set of mathematical transformations, a set which is now of no particularly deep conceptual interest, a set which is now utterly disconnected from any idea of an arena in which the world occurs.
I wonder if Albert would be satisfied even with a narrative, "realist" Lorentz invariant Bohmian formulation (assuming that is even possible)?

‘Special Relativity as an Open Question’

Physics and narrative
http://philosophyfaculty.ucsd.edu/faculty/wuthrich/PhilPhys/AlbertDavid2008Man_PhysicsNarrative.pdf [Broken]

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Demystifier
Gold Member
There is a counter-argumentation by Bell, "how to teach special relativity", where he argues
that it is, instead, the Minkowski interpretation which causes much more confusion.

It is published in "speakable and unspeakable".
I agree that Minkowski interpretation is confusing when you hear about it for the first time. But it is equally confusing (when you hear about it for the first time) that all 3 directions of space are on equal footing, and that there is no absolute up and down in space, and that people living in Australia can walk on Earth without falling down away from earth.

Demystifier
Gold Member
I'm guessing that even if Valentini's argument isn't convincing, Albert's "narrative argument" still holds?

I wonder if Albert would be satisfied even with a narrative, "realist" Lorentz invariant Bohmian formulation (assuming that is even possible)?

‘Special Relativity as an Open Question’