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.
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.
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".
> Because of this fact we cannot assume that OMs exist with an a priori
> well ordering. Time exists because everything cannot occur all at once.
It takes more than that though; time implies an ordering. I don't know
what an "observer moment" is, so I don't know whether one can overlap
another or not. What's an operational definition of an OM?
[SPK]
Time is not just an ordering. It is the ordering of events and the
transitions between events. I am trying to use the definition of OMs
that is used in this List. For example:
http://groups.google.com/group/everything-list/browse_thread/thread/c56e49173ab9070c
“An observer-moment is really all we have as our primary experience of
the world. The world around us may be fake; we may be in the Matrix or
a brain in a vat. Even our memories may be fake. But the fact that we
are having particular experiences at a particular moment cannot be faked.”
This definition speaks to the notion that you, we, have something
that is like having an experience of being in the world complete with
being in a place, colors, textures, sounds, etc.
Having an experience includes experiencing duration and sequence.
Russell posited that the OM could be defined as the “state of a
machine” in
http://www.mail-archive.com/everything-list@googlegroups.com/msg14307.html
Why would we suppose something static, like a "state", could constitute
an OM that includes the experience of time? That's why I think OMs are
vague and the term is not well defined.
Brent
> My argument is that the traditional notion of a measure does not
> apply because we cannot assume the simultaneous co-reliability of OMs,
> thus the DA is an artifact of misapplied statistics.
I don't understand that.
[SPK]
The Doomsday argument discusses the statistics of an ensemble of
possible humans.
http://en.wikipedia.org/wiki/Doomsday_argument
“The *Doomsday argument* (*DA*) is a probabilistic argument
<http://en.wikipedia.org/wiki/Probabilistic_argument> that claims to
predict <http://en.wikipedia.org/wiki/Predict> the number of future
members of the human species
<http://en.wikipedia.org/wiki/Human_species> given only an estimate of
the total number of humans born so far. Simply put, it says that
supposing the humans alive today are in a random place in the whole
human history timeline, chances are we are about halfway through it.”
My point is that “the whole human history timeline” assumes the
Newtonian (Laplacean Demon
<http://en.wikipedia.org/wiki/Laplace%27s_demon>) idea that all events
are observable by some hypothetical entity that is exterior to the
universe (aka God). Do I need to knock that rubbish pile over for you?
Onward!
Stephen
.
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