I think he is drawing an unwarranted conclusion. The fact that a physical clock must have finite extent doesn't mean it can't work. Diffeomorphism invariance is a requirement we impose on our theories to reflect the fact that choice of coordinates is a matter of description, not physics. To suppose that somehow restricts what clocks can measure is to turn the principle on it's head.
Brent Meeker >-----Original Message----- >From: Stephen Paul King [mailto:[EMAIL PROTECTED] >Sent: Sunday, May 08, 2005 3:19 AM >To: Brent Meeker >Cc: Stephen P. King >Subject: Re: quantum field theories are problematic > > >Dear Brent, > > Did you understand the discussion of the implication of Diffeomorphism >invartiance? That is the key point to Hitoshi's point. This requirement that >the laws of physics are invariant under any possible coordinate >transformation requires that one's clocks and rules be definable only on >infinitesimal points. This destroys the possibility of defining a "physical >clock" and thus the "multi-fingered time" idea collapses. > >Stephen > > >----- Original Message ----- >From: "Brent Meeker" <[EMAIL PROTECTED]> >To: "Stephen Paul King" <[EMAIL PROTECTED]> >Sent: Saturday, May 07, 2005 2:22 PM >Subject: RE: quantum field theories are problematic > > >> >> >>>-----Original Message----- >>>From: Stephen Paul King [mailto:[EMAIL PROTECTED] >>>Sent: Sunday, May 08, 2005 12:41 AM >>>To: Brent Meeker >>>Subject: Re: quantum field theories are problematic >>> >>> >>>Dear Brent, >>> >>> Did you read Hitoshi's take on the problem on his website: >>>www.kitada.com? >>> >>>Thanks for the reference, I will find the book and read it. >>> >>>Stephen >> >> Yes I read it. Hitoshi seems confused to me. First, he supposes that the >> singularity theorems of Penrose and Hawking arise from imposing a global >> coordinate system. This is not so; the singularities are not artifacts of >> coordinate choice. >> >> Second, his discussion of time corresponds to what is called >> "many-fingered" >> time in GR - it's just the observation that physical time, as measured by >> a >> clock, is different for each different path the clock takes through >> spacetime. >> But that time is not necessarily the "t" that multiplies the Hamiltonian >> in >> exp(-itH). That "t" is just a coordinate and there is not uncertainity >> relation between it and the energy. Physical time is what is measured by >> a >> physical clock. >> >> Modeling an ideal clock in QM is non-trivial. Asher Peres has a good >> discussion of it in his text book "Quantum Theory, Concepts and Methods". >> The >> time that is measured by coupling such a physical clock to other QM events >> does >> have an uncertainity relation with energy. >> >> Brent Meeker >> > >
