Hi Brent,

From: meekerdb 
Sent: Monday, May 09, 2011 12:17 PM
To: 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 
  Sent: Monday, May 09, 2011 12:31 AM
  To: 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.


  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. 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...



  > 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.   

[SPK] Certainly, and thus if we are considering the content of experience of an 
observer and its “shortest moment” then an Observer moment would involve those.


  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.




[SPK] I will let Russell answer that question. It was his proposal that I 
quoted...

Onward!

Stephen

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