Saturday, July 10, 2010

Novel Concepts of Time (I)

It seems incredible that in an era nearly 100 years after special and general relativity, Newton's absolute concepts of time continue to hold so many minds in thrall. In fact, "time" as an invention of humans, is also a very elastic concept that can vary with the context. What I'd like to show in this blog (and the next) is some of this variation.

Variable time vector:

The concept of a variable time vector is not new. A. Achong first proposed a possible elastic temporal vector that could have uses in physics. He invoked an ansatz in which particles possess an internal (intrinsic) time vector arising from the internal structure of their individual constituents, including quarks. The individual time vectors for each particle are allowed to assume either (+) or (-) signs, depending on whether the constituent is associated with normal matter or anti-matter- and the direction of global time is determined by the dominant sign. [1]

A somewhat different take can be developed by using quantum set theory in relation to time, as originally developed by Finkelstein.[Quantum Sets and Clifford Algebras, in International Journal of Theoretical Physics, Vol. 21, Nos. 6/7, p. 489.] In line with this, we adopt time vectors such that there exist intrinsic variable magnitudes. I use the term tau (t) for these, based on the same unit from quantum set theory. According to this definition, 'one tau' is (Finkelstein, op. cit.):

10^-43 s < τ < 10^-23 s

This is an extremely small time unit to be sure, but up to twenty orders of magnitude larger than the Planck time (10^-44 s). The tau(τ ), or variable tau, can be thought of as a ‘building block’ or element of proper time. In another guise, as the smallest conceivable increment of temporal difference. An aggregate or set of elemental taus yields the normal, standardized units such as ‘second’, ‘minute’, ‘hour’ and so on. The cautionary note here being that all these can vary in duration (from an extrinsic objective observer’s view) depending on what its tau component is at the time of measurement.

Thus, from just the perspective of QM one can show time is not an absolute or intrinsic quantity nor are temporal "moments" only of one measure or type.

Why the Pre-Existing Quantum Bubble Had no Time:

Incredibly, even the most minute tau component did not exist within the pre-existing quantum bubble that gave rise to the cosmos. It was impossible because that quantum foam or bubble lacked any thermodynamic arrow of time or any recognizable process by which temporal elements could be parsed or "ticked off".

The spontaneous fluctuation within the bubble not only incepted an inital mass-energy
dE ~ h/ dt -> E/c^2 to give rise to the Big Bang, but also information! The information inception occurred acausally precisely because the Hilbert space states are different for a vacuum fluctuation than for ordinary QM.

To fix ideas, while the expectation value [E(Q,A)] of an observable represented by a bounded operator A, on separable Hilbert space H is given by:

[E(Q,A)] = tr (Q, A)

where Q is a statistical operator, this presumes the ensemble representation is deterministic or 'causal' if for all g in G: fA(g) in S(A) where S(A) is the spectrum of A with respect to the algebra L(H).

but the condition does not apply in the case of quantum fluctuations on L_p (the Planck length) . For this reason other avenues for formulation have been pursued - for example, using Riemann's Zeta function Z(E) in terms of divergent, infinite Dirichlet series that can be transformed into finite sums such as:

Z'(1/2 + iE) ~ 2 exp {- i pi N(E)} SIGMA m=1 to oo (E/2 pi)1/2 m-1/2 cos(E lnm - pi N(e))

in conjunction with Gutzwiller's trace equation, and a more germane representation for the trace: Tr G(E) ~ Tr G_o(E) ~ d/ dE {ln Z (E) }

This quantity, for example, will take into account the Poisson statistical nature attached to the fluctuations, whereby:

delta N = [N]^1/2 and d V ~ G[V]^1/2

where delta N is the fluctuation of Q-bits arising, and d V the corresponding fluctuation in volume.

It is important to note here that the preceding does not mean that the universe spontaneously creates mass-energy within its normal space-time. So, it does obey the first law of thermodynamics such that dU = - dW + dQ, where U, W and Q denote the internal energy, the work done on the system, and the heat absorbed by it.

Assuming a closed cosmology, dE= 0. The main point here is that the universe absorbs work by virtue of the negative pressure (p = -rho) acting on it, as opposed to a positive pressure that does work. Thus, for consistency one needs:

dW = - p = rho (energy density) and dQ = rho_vac c^2.

Again, the negative energy assures us that the zero point energy of the quantum vacuum will "tunnel through" to create an unstoppable expansion on fluctuation. The best evidence yet for an acausal cosmos and acausal origin.

Is Time Merely a Subjective Epiphenomenon of Consciousness?

In something called Minkowski space-time, Minkowski envisioned a kind of hyperspace in which events do not just 'happen'. Rather, they already are embedded in the space-time metric (geometry) and one comes across them, like towns along a highway (cf. Whittrow, G.J. 1972, The Nature of Time, Pelican Books, Great Britain, p. 103.)

For example, imagine the Minkowski temporal scale:

Past(-τ) <-----*(E1)--------(E2)*-------*(E3)---> Future (+τ)

where E1, E2 and E3 are three events, say: E1 = Explosion of the Hindenburg dirigible, E2 = John F. Kennedy's assassination, and E3 = some future asteroid impact in the 21st century. In the Minkowski hyperspace these have always been on the timeline, which is traversed in the same way one would traverse a space. Thus, one encounters the various events on the timeline as s/he might encounter towns or villages along a highway.

Movement can occur in time or in space, and have a complementary (space or time) equivalent. For example, stay where you are and let one minute elapse on your watch. You have performed a 'movement in time' without a corresponding movement in space. We say you have traversed imaginary space. This imaginary space can easily be computed:

Im(x) = i(300,000 km/s x 60 s) = 18,000,000(i) km

That is, you have traversed 18 million imaginary kilometers or 11.25 million miles in imaginary space. (Im(x) is the symbolic representation for an imaginary space (x) transition, recall our exposure to complex numbers).

Now, think of a movement in real space, but none in time. Is this possible? Well, I can get out my telescope and observe the Moon instantly - bearing my consciousness upon it - without taking the time to travel there. For all intents and purposes I am there. In this case, an imaginary time interval is the result, and again can be computed:

Im(τ) = (i) 384,000 km/ 300,000 km/s = 1.28i sec

That is, 1.28 imaginary seconds to get there. I note here that this imaginary time interval is equivalent to a real space interval: 384,000 km (space distance to Moon) = 1.28 i seconds. Thus, imaginary time and real space are interchangeable.

This has prompted at least one observer of the situation (to do with Minkowski spacetime) to observe (Whittrow, op. cit., p. 104.):

“In other words, the passage of time is merely to be regarded as a feature of consciousness that has no objective counterpart.”

If Whitrow's take is correct, and many physicists have now come to accept it, it means that time or temporal "moments" are not innate or intrinsic to the cosmos any more than wallpaper is to a wall. Instead, out of mental convenience, human project time onto situations to be able to compare them in consciousness.

Temporal 'wallpaper' if you will!

[1]Internal Time and Global Time, Proceedings of the 2nd Caribbean Physics Conference, University of the West Indies, Cave Hill, Barbados, Leo L. Mosely (Ed.)

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