Subject: The 'mysterious time' of Bill Unruh, 1988
Date: Thu, 04 Mar 2004 15:36:18 +0200
From: Dimi Chakalov <>
To: William G Unruh <>

Dear Professor Unruh,

In my email of Tue, 18 Feb 2003 11:42:52 +0200,

I mentioned your 'mysterious time' introduced in 1988,

May I ask you to comment on a recent research paper by Paul Davies [Ref. 1], which elaborates on Peres' quantum clock of 1980.

It seems to me that the issue has crucial cosmological implications: please see the nonlinear matching problem in [Ref. 2]. Neil Turok and Paul Seinhardt are "encouraged by the simplicity and uniqueness of the matching rule in linearised gravity" [Ibid.], but have not addressed the problem known since 1917,

I've mentioned briefly the conflict between the equivalence principle and QM at

It boils down to our understanding of the "point", literally speaking, at which we define the equivalence principle, and obliterate your 'mysterious time', which I call 'global mode of spacetime',

I think you 'hit the jackpot' by introducing your so-called mysterious time: an explicit (but unmeasureable) time [Ref. 3].

To avoid criticism along the lines of the old Tanzanian saying,

I suggested the notion of 'global mode of spacetime'. It is explicit but unmeasureable by an inanimate physical clock,

Your comments will be highly appreciated.

Thank you, once more, for your email of 1999 regarding negative energy densities,

Sincerely yours,

Dimi Chakalov


[Ref. 1] Paul Davies, Quantum mechanics and the equivalence principle, quant-ph/0403027 v1, Wed, 3 Mar 2004 04:26:27 GMT,

"To investigate this scenario, it is necessary to have a clear definition of the time of flight of the quantum particle. Two problems then present themselves. First, in the case of narrow wave packets one may follow, say, the peak or the median position of the packet as it moves. But this strategy will not work for spread-out energy
eigenstates. So how can one measure the time of flight of a particle between fixed points in space when its position uncertainty is very great, without collapsing the wave function to a position eigenstate in the process? Fortunately this problem was solved long ago by Peres (1980), who introduced a simple model quantum clock. The clock measures the time difference that a particle takes to travel between two points in space, without disclosing the absolute time of passage. This avoids collapsing the wave function to a position eigenstate.

"I have restricted attention to the so-called weak equivalence principle. One might also enquire into the status of the strong or Einstein equivalence principles in quantum mechanics. Einstein made the postulate that all of physics in a uniform gravitational field should be locally equivalent to the physics in a uniformly accelerated frame.

"Under the transformation (4.1), the eigenfunctions (4.4) do not transform into (4.3). The equation of motion may transform correctly, but the energy eigenstates do not. Rather, the Airy functions will be complicated linear combinations of plane wave solutions (4.4) and their complex conjugates. (The transformation of plane wave solutions into accelerated reference frames is a well-studied problem; see, for example, Birrell & Davies (1982), section 4.5.) This would not matter if the results of the analysis were linear in the wave function. That is indeed the case for the behaviour of wave packets which are made up of linear combinations of plane waves. But it is not the case for a measurement of the transit time, at least when such a measurement is made using the Peres clock prescription considered here. That is because the time interval depends on a measurement of the phase change, and the sum of the phases of a superposition of waves is generally not the same
as the phase of the sum. A Peres clock will generally respond to a superposition of states in a very complicated way."

[Ref. 2] Neil Turok, Paul J. Seinhardt, Beyond Inflation: A Cyclic Universe Scenario, hep-th/0403020 v1. Talk given at the Nobel Symposium 'String Theory and Cosmology', 2003,

"The key challenge facing the scenario is that of passing through the cosmic singularity at t=0.

"Are the cycles eternally continuing? A naive (and perhaps correct) argument is as follows. In any particular region of the cyclic universe, a highly improbable quantum jump could always occur to end the cycling. However, with overwhelming probability, the cycling would continue in most of the universe. The argument is similar to that usually invoked to justify eternal inflation.

"The new scenario is incomplete at present. We do not yet have a full prescription for nonlinear matching across t = 0. Nevertheless, we are encouraged by the simplicity and uniqueness of the matching rule in linearised gravity, and by the simplifications wrought by ultralocality. We are led to conjecture that there exists a consistent analytic continuation in nonlinear gravity generalising our linearised treatment.

"If the nonlinear matching problem is solved, and cyclic solutions such as we discuss are allowed, an entirely new approach to the basic problems of cosmology is opened. The state of the universe may be determined from the laws of physics in much the same way as is the equilibrium state in statistical mechanics. There would be neither a need for a special initial condition, nor one for strong anthropic

[Ref. 3] W.G. Unruh, Professor

Research Interests

*  applying quantum mechanics to gravity and the role of time in
    such a theory. Due to coordinate invariance, the theory is usually
    formulated with no explicit time, but must be interpreted with time
    defined (rather than measured) by clock readings. This leads to
    peculiar difficulties, suggesting that one reformulate the theory
    with explicit (but unmeasureable) time.


Subject: Re: Request for preprint
Date: Wed, 16 Jun 2004 02:30:12 +0300
From: Dimi Chakalov <>
To: Bill Unruh <>

P.S. The reason why I need your paper on the explicit (but unmeasureable) time (why not spacetime?) is explained at

Best - Dimi

On Tue, 15 Jun 2004 23:50:45 +0300, Dimi Chakalov wrote:


Subject: The explicit (but unmeasureable) time
Date: Wed, 01 Jun 2005 04:36:28 +0300
From: Dimi Chakalov <>
To: William G Unruh <>
CC: Karel Kuchar <>,

Dear Bill,

I mentioned some ideas about the so-called dark energy and LIGO at

Bottom line as the alleged virtual/global component of gravity,

which refers to your explicit (but unmeasureable) time and Karel's hidden unmoved mover (Karel Kuchar, "The Problem of Time In Quantum Geometrodynamics", in "The Arguments of Time", ed. by Jeremy Butterfield, Oxford University Press, Oxford, 1999, p. 193). Both are missing in the current GR, and are completely "dark". If you wish to read about the implications for the Advanced LIGO, click on the first link above.

I presume you hold different opinion on the LIGO mafia, so please don't feel obliged to reply.

Kindest regards,


Subject: Netiquette
Date: Mon, 26 Nov 2007 15:32:25 +0200
From: Dimi Chakalov <>
To: Bill Unruh <>

Hi Bill,

I mentioned again your 'explicit (but unmeasureable) time' at

In case you again choose to ignore my communications, let me wish you
a very merry Christmas, a happy New Year, and all the best for your
2008 summer vacation.