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.## Advertising

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 timeevolution is only known for the non-relativistic version of QM,simple cases of relativistic particle dynamics and quantum ﬁeldtheory as currently defined. These use the absolute time of Newton.It is well known that the Newtonian version of time is disallowed byGeneral Relativity. Chris Isham discuses this here:http://arxiv.org/abs/grqc/9210011“The problem of time in quantum gravity is deeply connected with thespecial role as-signed to temporal concepts in standard theories of physics. Inparticular, in Newtonianphysics, time—the parameter with respect to which change ismanifest—is external tothe system itself. This is reﬂected in the special status of time inconventional quantumtheory:”I'm well aware of the problem of time in quantum gravity. But I don'tthink you need to consider relativistic QFT and solve the problem ofquantum gravity just to have examples of "non-trivial alternativesthat 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 tothe content of observations involved in such things as “inertialreference frames” and the general covariance of physical laws, what isthe point of OMs?The Hermitean operators only requires that the observed “pointerbases” are Real numbers. In other words, the Hermiticity requirementonly applies to the outcomes of measurements, it does not pre-orderthe measurements.No, but they are not unordered because the wave-function is complexvalued as you implied. The observables, which are presumably thecontent 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 noimplication that “they are not unordered because the wave-function iscomplex valued“, maybe I need to be even more clear and explicit. TheHermiticity requirement of observables DOES NOT GENERATE A WELL ORDER.Can you read that? The fact that each measurement is required tomanifest as some Real number does not sequentially map themeasurements 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 beattributed to a dimension of time in the sense of a unique map to thePositive 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 (asopposed to coordinate time) has to be introduced by some physical "clock".[SPK]But “duration” can be defined as an operator that is the conjugate toenergy.

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 therestrictions that general covariance places on the topology ofspace-time is such that our notion of clocks breaks down when subjectto the Heisenberg uncertainty principle. To know exactly where thehands of the clock (or physical equivalent) is subject to therestrictions 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.`

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