Hi Brent,

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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 -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.