In his new book, The Universe in a Nutshell, Professor Hawking provides a graphic image of the history of the universe as a nutshell in imaginary time. Imaginary time is a theoretical construct, a dimension of imaginary numbers at right angles to the plane of ordinary space and time. Imaginary time is a dimension just like those of space. It can have loops that go backwards or forwards on it, and it can be bent and curved, just like spatial dimensions. We can travel back and forth on imaginary time, at least in principle. The actual mechanics of doing so are unknown. By contrast, real time is rather unsatisfactory as a dimension, partly because we cannot move backwards and forwards on real time. Past time is merely a memory and a theoretical construct. We can't go there. Future time is an expectation and a theoretical construct. We can't go there either. When we speak of curved space-time, what we really mean is that space is curved and clocks slow down or speed up. The spatial and temporal dimensions are not measured in the same way.
Imaginary time is still a useful construct even if we reintroduce the idea of universal simultaneity to real time, which we can certainly do, despite relativity, if we can make instantaneous apports to anywhere. Imaginary time is still useful, even if we reject the reality of ordinary time altogether, and say it is merely a measure of the rate of change of things in 3D space. Mathematically, living in 3D space has many advantages, since it is only in 3D space that electron orbits or planetary orbits are stable. Henceforth, when I speak of space-time, it will be understood that I refer to this theoretical construct of time as a continuum of imaginary numbers plus the 3 dimensions of space. An imaginary number is an ordinary number times the square root of minus one. Thus, if we square it, it introduces a negative term. For instance, the 4-dimensional distance between 2 events is invariant for every observer, and it is
The nutshell that describes our universe is not perfectly smooth or round, but a bit rumpled, flattened and irregular. The surface of this nutshell is another theoretical construct which arises from the theory of supersymmetric strings. Supersymmetry requires that for every ordinary Boson, there is a supersymmetric new Fermion, and for every ordinary Fermion, there is a supersymmetric new Boson. Such supersymmetry would exist only at very high temperatures, much hotter than any place in the universe, much hotter than any temperature that can be produced in a man-made collider. This has evolved into M-theory, which has "branes," a fragment of the word "membranes." Furthermore, we can represent a brane graphically as a surface. So imagine the surface of our rumpled nutshell as being a 4-dimensional brane in a 5-dimensional universe. The inside of the nutshell is the fifth-dimension, in which there is no time, so transits across the interior of the nutshell take no time. And this, I am sure, is how apports work. Instead of bending space, they take a short-cut through the fifth spatial dimension inside the nutshell of imaginary time. All these ideas are testable.
Stephen Hawking is a cutting edge theorist. This means his ideas are very speculative and mostly untested. It also means that every other theorist has a different idea. Few of them accept his idea of imaginary time, although it is a very elegant solution to the problem of singularities, especially the one at the Big Bang. Hawking's universes are closed in imaginary time, although they have no boundaries. One of the consequences of this is that the Big Bang is part of the normal universe, obeys normal physical laws, and does not require any Deus Ex Machina to bring the universe into being. Once we get the correct physical laws, we will understand why there are no singularities, not even at the Big Bang or the Big Crunch, if that should happen.
According to Hawking, it is supersymmetry which saves us from having an infinite energy in the vacuum. "In a supersymmetric theory, the infinite positive and negative energies of these ground state fluctuations cancel out between particles of different spin." (Hawking, 2001, p. 97) I like the way this man thinks, because he obviously wants to create a physical theory without singularities or infinities. I also like his ideas, because his 5-dimensional universe in a nutshell provides a way for any number of apports to happen simultaneously, since apports can take a shortcut through the fifth dimension inside the nutshell, without having to bend space-time so that one part of it touches another part.
Copyright © Dr.H 2002
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