TAILIEUCHUNG - The Philosophy of Vacuum Part 22

The Philosophy of Vacuum Part 22. Physicists will find it extremely interesting, covering, as it does, technical subjects in an accessible way. For those with the necessary expertise, this book will provide an illuminating and authoritative exposition of a many-sided subject." -John D. Barrow, Times Literary Supplement. | Making Everything Out of Nothing 203 flat space-time is not empty. On this view then according to general relativity there cannot be a vacuum empty of all particles and fields because any space-time will at least contain a metric field. On the other hand will anyone who takes this view accept anything as a vacuum Is there any level of geometric structure which if it alone existed would count as being completely empty My view is that this issue is at least in part a matter of definition. Here I just want to mention that some people might not accept my equating geometry with the vacuum or as one sense of vacuum . The second question concerns the extent to which contemporary physics shows us how to carry out the details of the programme of constructing everything out of geometry. As we have seen in general relativity time and gravity are geometrized by extending the geometry of the universe to the four dimensions of space-time and identifying gravity with the metric curvature of space-time. Let us next consider electromagnetism and ask Can we give a geometrical account of the electromagnetic field within the framework of general relativity There are two answers to this which I want to briefly look at the already unified field theory of Rainich and the theory of Kaluza and Klein. 6 The Already Unified Field Theory This approach starts from the combined Einstein-Maxwell equations of standard general relativity Ruv - WFwv - UVFWZF 1 2 Fuvlw Pwu v Pvw u - 3 Here F is treated non-geometrically as a field that exists in addition to the geometry of space-time. Since F carries energy and momentum it is a source of the gravitational field and space-time is curved in its presence in accordance with the general relativistic field equation 1 while 2 and 3 are Maxwell s source-free equations. Now note that 1 with the anti-symmetry of F implies that the curvature-invariant R satisfies 204 R. Weingard R R 0 4 so that 1 becomes F FWV - FwzF . 5 Thinking of F as a non-geometrical .

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