On 5/9/2011 3:22 PM, Stephen Paul King wrote:
Hi Brent,
*From:* meekerdb <mailto:meeke...@verizon.net>
*Sent:* Monday, May 09, 2011 12:17 PM
*To:* everything-list@googlegroups.com <mailto:everything-list@googlegroups.com>
*Subject:* Re: Against the Doomsday hypothesis
On 5/8/2011 10:22 PM, Stephen Paul King wrote:
Hi Bent,
*From:* meekerdb <mailto:meeke...@verizon.net>
*Sent:* Monday, May 09, 2011 12:31 AM
*To:* everything-list@googlegroups.com <mailto:everything-list@googlegroups.com>
*Subject:* Re: Against the Doomsday hypothesis
On 5/8/2011 9:19 PM, Stephen Paul King wrote:
> Hi Brent,
>     No, the Newtonian case would be such that the logical
> non-contradiction requirement would be trivial as the number of
> physical alternatives that could occur next per state is one, this
> generates a one to one to one to one to one ... type of sequencing.
> There is no “choice” in the Newtonian case.

And hence no measure problem.
[SPK]
    I agree. But the universe we experience is not Newtonian...

> On the other hand, in QM we have a clear example of irreducible and
> non-trivial alternatives that could occur next per state. IN QM,
> observables are defined in terms of complex valued amplitudes which do
> not have a well ordering as Real numbered valuations do.

No, observables are defined by Hermitean operators which have real
eigenvalues.  The Hamiltonian generates time evolution.
[SPK]
I am sorry but you are wrong. The Hamiltonian generation of time evolution is only known for the non-relativistic version of QM, simple cases of relativistic particle dynamics and quantum field theory as currently defined. These use the absolute time of Newton. It is well known that the Newtonian version of time is disallowed by General Relativity. Chris Isham discuses this here: http://arxiv.org/abs/grqc/9210011 “The problem of time in quantum gravity is deeply connected with the special role as- signed to temporal concepts in standard theories of physics. In particular, in Newtonian physics, time—the parameter with respect to which change is manifest—is external to the system itself. This is reflected in the special status of time in conventional quantum
theory:”

I'm well aware of the problem of time in quantum gravity. But I don't think you need to consider relativistic QFT and solve the problem of quantum gravity just to have examples of "non-trivial alternatives that could occur". I don't see the relevance to ordering OMs.

[SPKnew]
But it is the same problem! If our notion of OMs is not related to the content of observations involved in such things as “inertial reference frames” and the general covariance of physical laws, what is the point of OMs?
The Hermitean operators only requires that the observed “pointer bases” are Real numbers. In other words, the Hermiticity requirement only applies to the outcomes of measurements, it does not pre-order the measurements.

No, but they are not unordered because the wave-function is complex valued as you implied. The observables, which are presumably the content of OMs are real valued and would be ordered by, for example, reading a clock.
[SPK]
Did you actually read what I wrote? I was explicit. There was no implication that “they are not unordered because the wave-function is complex valued“, maybe I need to be even more clear and explicit. The Hermiticity requirement of observables DOES NOT GENERATE A WELL ORDER. Can you read that? The fact that each measurement is required to manifest as some Real number does not sequentially map the measurements into the Real line.
    I welcome you to show otherwise.

What you wrote was." On the other hand, in QM we have a clear example of irreducible and non-trivial alternatives that could occur next per state .IN QM, observables are defined in terms of complex valued amplitudes which do not have a well ordering as Real numbered valuations do."


Thus it does not lend itself to a well ordering that can be attributed to a dimension of time in the sense of a unique map to the Positive Reals. I am truly surprised that this is not well known!

It is well know that time is not an operator in QM. Physical time (as opposed to coordinate time) has to be introduced by some physical "clock".
[SPK]
But “duration” can be defined as an operator that is the conjugate to energy.

Look as Isham's discussion of eqn 2.1.5.  A duration operator is ruled out.

That is a different issue. The main problem here is that the restrictions that general covariance places on the topology of space-time is such that our notion of clocks breaks down when subject to the Heisenberg uncertainty principle. To know exactly where the hands of the clock (or physical equivalent) is subject to the restrictions of the HUP. This is well trodden ground...

You don't need to invoke covariance or spacetime topology to see that a real clock must have some probability of running backwards.

Brent

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