**Stephen Paul King** (*stephenk1@home.com*)

*Mon, 04 Oct 1999 23:50:33 GMT*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 884] Clocking is observation = mapping representations to objects?"**Previous message:**Hitoshi Kitada: "[time 882] Re: [time 881] Matti's Theory"**In reply to:**Ben Goertzel: "[time 881] Matti's Theory"

Dear Mike,

Perhaps Hitoshi Kitada's Local Systems theory might answer

some of the time questions: http://www.kitada.com/

Kindest regards,

Stephen

http://members.home.net/stephenk1/Outlaw/Outlaw.html

On 2 Oct 1999 17:43:04 -0700, you wrote:

*>The recent discussion on Fock space has prompted me to put forward a few
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*>speculative ideas I have been working on, but now in the context of Fock
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*>space. These ideas are very speculative and maybe completely crazy and
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*>are not ready for publication. So far I haven't seen any reason to think
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*>they are off beam, but then I am not very well-educated in the realm of
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*>field theory, where I expect the biggest challenge to come from. (I was
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*>active as a researcher during the early 70s in the field of S-matrix
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*>phenomenology and very attracted to the bootstrap hypothesis of particle
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*>democracy.) Since the ideas are very challenging to what I believe to be
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*>the conventional viewpoint, I look forward to sparking a lively debate
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*>which I hope will inform my own enquiries, if no one else's.
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*>
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*>Typically, one looks at the Hilbert space H_i for a specific single
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*>particle i, defined by a fixed mass, charge, etc. When taking the
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*>product Hilbert space H_1*H_2 one usually does it for two such specific
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*>particles which may or may not be identical. And so on for 3, 4, ... , n
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*>specific particles.
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*>
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*>My idea is to take the Hilbert space defined by the complete range of
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*>quantum numbers that can be attributed to any isolated physical system.
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*>This could mean not just the space of known single particles but it
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*>could also mean all possible composite systems of any number of
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*>particles and any hypothetical single particles that might exist. We are
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*>then no longer limited to any mass shell or even to a set of mass
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*>shells. The energy-momentum vector can range anywhere in 4-space allowed
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*>for a composite physical state. Isospin, strangeness and any other
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*>quantum numbers we might know about or even hypothesize about would also
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*>be allowed to range over all values allowed for a composite physical
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*>state instead of being limited to those of a particular particle. Note
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*>that we concern ourselves at this stage only with the total quantum
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*>numbers of the system and do not enquire about the internal structure.
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*>For this reason we shall call the system "closed".
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*>
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*>The state vector |S> for a given physical system S can therefore be
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*>anywhere in this space, and the probability of finding the system in a
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*>specific state |p> which is a basis vector of H (and might be a
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*>particular particle for instance) is |<p|S>|^2.
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*>
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*>Now suppose we have two or more such isolated systems. The Fock space
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*>can be built by symmetrizing the space H*H and so on. Note that we have
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*>dropped the subscripts 1 and 2 which formerly distinguished two specific
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*>particles because, now that H ranges over all possible physical states
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*>for each system and each system has the same range of possible physical
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*>states we cannot distinguish between state "1" and state "2".
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*>Furthermore, as described in my spin-statistics paper
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*>(http://xxx.lanl.gov/abs/quant-ph/9908078) it is possible to do this
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*>symmetrization for all possible spins whether fermionic or bosonic. (In
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*>what follows, when we write H*H, we intend that this space has been
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*>symmetrized.)
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*>
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*>Now note that this new two-system system can also itself be described as
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*>a single isolated system if we don't enquire as to the separate systems.
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*>In other words we can either view the complete system as a single closed
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*>isolated system or as two isolated closed systems. In either case, it is
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*>apparent that the state vector describing the system can be placed in
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*>either H or in symmetrized H*H SIMULTANEOUSLY. Hence we can compute the
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*>probability that S is in a single state p from <p|S> or in a double
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*>state p_a,p_b from <p_a,p_b|S>. In general H, H*H, H*H*H,..etc all
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*>describe different ways of looking at the same physical space. This is,
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*>of course, nothing but a mathematical statement of the bootstrap
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*>principle of particle democracy. Every observable single particle is
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*>described by a vector in H which is also a vector in H*H (and therefore
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*>possibly describable as a two-particle system) and in H*H*H (a
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*>three-particle system) and so on.
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*>
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*>Now suppose we make two measurements. In the first case we detect a
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*>single set of quantum numbers p and in the second we detect a pair of
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*>sets of quantum numbers p_a and p_b. What has happened? Well we have
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*>observed a transition from p to p_a+p_b!! What is the probability of
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*>this transition? Well it is clearly |<p_a,p_b|p>|^2. In other words, the
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*>S-matrix element describing the transition from p to p_a+p_b is given by
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*>the scalar product of the two state vectors describing the initial and
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*>final states.
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*>
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*>In other words, the scattering operator is the identity operator! There
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*>is no interaction Hamiltonian -- merely spontaneous transition. What is
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*>more, the scalar product describing the transition amplitude should be
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*>familiar from a well-known problem in quantum mechanics -- the addition
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*>of discrete quantum numbers. For instance, if the only measurable
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*>quantum number in the universe was isospin, then our transition
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*>amplitudes would be just the Clebsch-Gordon coefficients relating two
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*>isospin states to a single composite isospin state and, as is well
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*>known, these are computed by reducing composite group representations to
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*>irreducible representations -- the direct analogue of our requirement
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*>that H, H*H and H*H*H... represent the same physical space!
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*>
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*>Before the howls of outrage get too loud, let me just anticipate some of
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*>the issues I expect to be raised...
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*>
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*>First objection: This model has (so far) no place for time. As we all
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*>know the decay p->p_a+p_b is described by a half-life or decay RATE.
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*>There appears to be nothing in the scalar product <p_a,p_b|p> which
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*>depends on time. Response: Actually this is reasonable. The probability
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*>of spontaneous decay is independent of how long the particle has been in
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*>existence. So how do we get a time scale into the picture? The answer is
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*>very simple, we compute ratios of different decay amplitudes. These give
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*>us ratios of decay rates, known as branching ratios. Any one branch can
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*>serve as our time scale to measure other branches. The absence of time
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*>in our model goes hand-in-hand with the absence of a Hamiltonian. We
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*>simply don't care about it, becaase it comes out in the wash anyway!
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*>
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*>Second objection: If particles are spontaneously transforming how do we
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*>ever get any continuity of observation? If we observe a particle p at
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*>one observation, don't we expect to observe it again a moment later?
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*>Response: Yes we do. The scalar product <p|p> is always 1. Every other
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*>scalar product <x|p> will be < 1. The continued existence of an observed
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*>state exactly as it is will always be the most likely result of a
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*>subsequent observation until a change occurs, and then the new state
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*>will be the most likely result of future observations. However, change
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*>is the most predictable feature of our universe. It is why we have any
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*>concept of time at all. Every observable rate of change can be reduced
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*>to a ratio of scalar products of the observed change relative to some
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*>standard scalar product describing what is essentially the behavior of a
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*>clock.
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*>
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*>Third objection: if the scattering operator is the identity operator,
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*>doesn't this diagonalize the S-matrix, preventing any transition at all?
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*>Response: For the traditional S-matrix, defined by a mathematical trick
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*>(taking the limit t->infinity of asymptotically free particle states)
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*>this would be the case, because the initial and final state vectors are
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*>treated as part of the same orthogonal set and therefore all mutually
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*>orthogonal. (For this reason, transition can only take place, in the old
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*>model, when the hand of God intervenes in the form of an interaction
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*>Hamiltonian.) In my model described above, this is not the case, in
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*>general. Of course, there are specific examples where diagonalization is
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*>true. For instance if we only observe composite quantum numbers of
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*>single systems, then yes, the S-matrix will be diagonalized. This
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*>amounts to nothing more than conservation of the observed quantum
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*>numbers. But as soon as we permit simultaneous observation of two or
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*>more subsystems, then we break the condition that all state vectors are
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*>mutually orthogonal and get non-vanishing scalar products for differing
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*>states.
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*>
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*>Fourth objection: If the scattering amplitude is simply a computable
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*>scalar product, then why can't you compute it for all known possible
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*>values of observable quantum numbers, find the singularities and
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*>therefore explain the entire particle spectrum? Answer: Although simple
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*>coupling coefficients for discrete quantum numbers such as
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*>Clebsch-Gordon coefficients are computable with relative ease (assuming
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*>one knows the complete set of observable quantum numbers and the
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*>appropriate groups), I don't have enough knowledge myself to compute
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*>coupling coefficients for continuous variables such as energy-momentum. I
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*>am guessing that the first place to look for this would be the Poincare
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*>group, or some variation of it, but I don't know how myself. Any help
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*>with solving this problem would be much appreciated!!!
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*>
*

*>Mike
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*>
*

**Next message:**Stephen P. King: "[time 884] Clocking is observation = mapping representations to objects?"**Previous message:**Hitoshi Kitada: "[time 882] Re: [time 881] Matti's Theory"**In reply to:**Ben Goertzel: "[time 881] Matti's Theory"

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