Time. On. Essay. An. by Julian Moore

Dear Julian, I really enjoyed your contribution. I have a comment: in order to create a wormhole you have to remove two balls from a spacetime (or more precisely the region spanned by them on spacetime) and identify their surfaces. This identification also involves a change in the spacetime geometry around those boundaries in order to make them smooth. Thus figure 2 is somewhat deceiving,

the dotted lines would have to stay just outside the wormholes as their interior does not belong anymore to the spacetime.

Ettore, you are (partially) correct: please note that the diagram was faithfully reproduced from the Misner, Thorne, Yurtsever 1988 paper so I can only interpret, however...

One might choose to consider the small black circles as literal holes in the spacetime diagram; the dotted (null) lines can intersect the edge of any circle, but as you say, not reach "within" them: the light ray would pass through the wormhole and re-emerge from the circumference of the mouth at the other side of the diagram...

Fig 2 is Fig 1 (in which the throat is shown) with the fold removed and "viewed from on top".

I hope that helps and thank you for the appreciation.

PS To be precise, Fig 2 is Fig 1 as described but with a second spatial dimension suppressed to make room in the plane for the time direction.

A very enjoyable and thought provoking read, I do however have a question, ?it is time what

Dear Julian,

I enjoyed reading your essay, which is very well written, you have a good style. I also liked that you documented in all required aspects. I want to make only a small observation, about the possibility of having charged wormholes. When an electron enters through a wormhole in the mouth A and exists from the mouth B, the following happens. The mouth A is perceived as being charged with a negative charge, the mouth B with a positive charge, equal in absolute value with that of the electron. An observer near the mouth B will conclude that the mouth B emitted the electron, remaining positively charged. This accounts for the charge conservation, since what happened is that A gets charged with -1, and B with +1. This works with A and B joining two "different" manifolds, as well as in A and B are in the same manifold. Mathematically, in the first case the electron can go back only through the wormhole, and in the second, it can do this by avoiding wormholes. In the nice quote you give from MTW at page 5, the point is that we can have "charge without charge", as Wheeler's Geometrodynamics program showed. Wheeler and Misner rediscovered Rainich's idea that we can, in Einstein-Maxwell spacetimes, obtain the electromagnetic field from the spacetime curvature. They proposed a topological charge, based on cohomology. A classical charge is a singularity of the electromagnetic field. The field lines unite the singularity with the infinity. In a nontrivial topological spacetime, for example one containing a wormhole, the field lines may be closed, without having a source. We have Maxwell's equations dF=0 and d*F=J. If J=0, we can still obtain nontrivial electromagnetic fields, if the second cohomology group is not zero (i.e. if we use wormholes). The MTW quote simply states that if we apply the Gauss' theorem to nontrivial topologies and assume them trivial, we can interpret the result as showing that there is a charge, but the boundary is incomplete. To complete the boundary, we have to consider enclosing both mouths. In this case, Gauss' theorem will apply correctly, showing that there is no charge in the wormhole.

In the case of mass, the things are weirder. Perhaps the mass entering A and leaving B increases the mass of A and decreases the mass of B. This seems to allow negative mass for the mouth B.

Congratulations for your well-written essay.

I wish you all the best,

Cristi Stoica

Flowing with a Frozen River

Dear Cristi

Thank you for you kind words, and thank you for taking the time to explain some more about wormhole mass & charge; one reason for writing the essay was the hope that it might resolve at least one confusion.

I wish I could appreciate the niceties of cohomologies, but I don't, however, on reading your explanation w.r.t. charge - and here again ignorance speaks volumes - there is some residual confusion here.

Yes, I believe I understood that the original point of the NTW quote was to illustrate both the idea of "charge without charge" and the danger inherent in neglecting topology, and your point is well made that a boundary enclosing both mouths should apply in a wormhole geometry.

However, with regard to the electron and mouths A & B (the first part of your comment), this would seem simply to be a restatement of the fundamental point I was seeking to scrutinise, that in the absence of horizons I can see no justification for treating a pair of joined universes as separate - their topologies haven't even changed, one or other or both just seem to have become bigger. Without horizons where is/are the boundaries that effectively isolate two universes?

It seems to me that in stating that an observer near a wormhole mouth would perceive opposite residual charge to that which has just passed through the mouth relies upon precisely the misapplication of Gauss that I thought you were acknowledging.

I have no problem at all entertaining charge on a horizon (and hence no problem with the independent conservation of charge in two universes "separate but joined"), but the discussion was specifically predicated on traversable wormholes of the MTY type, i.e. without horizons.

With regard to the intra-universe universe wormhole, of course I agree that a boundary enclosing both wormhole mouths could properly be used as a discriminant of charge.

However, mindful of the revelation in Kip Thorne's book that horizons can not only carry charge, but that there is a whole "membrane paradigm" in which currents can flow etc. etc. I think I was wise to avoid the thorny (oops, not intended) questions of how external charges act on a horizon (i.e. whether a charge would attract a charged black hole to move); intuitively (intuition is all I have), it would seem to me that if there is charge and currents flow on the horizon, the overall metric will reflect these features - but whether the horizon would merely be distorted (which I suspect) rather than "moved" (which I doubt) did not seem to be a question amenable to mere logic.

With regard to mass, my mental picture was very simple - and perhaps overly simplistic - and relied upon mass as the source of curvature.

Consider a suitably long/large wormhole into which a suitably large number of masses are fed, one after another. If mouth A acquires mass as masses enter, it would be possible to arrange for a black hole/horizon to form - yet we could also arrange for the masses to be so strung out through the wormhole throat (thus avoiding possible complications at mouth B temporarily) that the mass is not all within the equivalent Schwarzschild radius (and in thought-experiment terms as far away from mouth A as one might like). One would then have to ask what the effective source of the mouth black-hole is.

I hope I have interpreted your points fairly and responded likewise, but I am not sure - and therein lies (at least part of) the problem! If I have missed the essential point of your argument I do apologise...

Certainly from my recollection of your essay (one of a number that intrigued me but which were "just a whisker" above my level of theoretical competence) I have no doubt you have a much greater understanding of the essential mathematics than I do, and no doubt everyone else is right - I just can't for the life of me understand why.

Thank you again for taking the trouble to attempt to enlighten me... and good luck to you too!

Julian Moore

Julian,

What a remarkably worded essay, inspite of the limitations of any language to describe one's thoughts/ideas! i am fascinated by your both the realism and the dream aspects of the writings. May be, our limitations are coming from the concept of space and time that have given us reliable theories of relativity, both special and General. One thing gives hope and that lies in the possible distortions in space and time. These generate mass and energy. After all, the universe in its evolution must have undergone through such distortions in many different ways. The start of the universe was too violent,the present is some kind of a steady state (this time is when all our modern physics has evolved). We don't know about future evolution and if there is , how it will all end. Nature's logic of Creation and destruction is still a secret for us!therefore, i will like to question our Physica developed thus far, in order to go further and understand the mysteries of the universe that are still with us. For example, i like the way you have suggested to model the behaviour of 'Black Holes' in another possible manner, say without invoking quantum gravity. In my view, if if we can work out alternatives to existing successful theories and have workable approaches that explains more observed facts than the existing theories, that will provide the break-throughs. I for one feel that some successful concepts may well be our hinderances- just a hunch and not at all any claim! If we suppose we start with curved space/time picture and bring changes in it both ways, more distortions as also movemet towards linearity of space/time, we may get a different picture to model our mathematical tools to understand the 'Mysteries of Reality of the Universe'. For it to happen, emphasis will be more on the control of the human mind in order that it may have the quietness to remove all existing bias and work in freedom based on logic and intuition. With some inspirations, it may well do wonders!

Dear Narendra,

Many thanks for your appreciative comments. It is important to look at the world many ways - but one must always strive to understand the limitations of the language, analogy, metaphor etc.: look for beauty then look again to see whether you have seen the beauty within the world or within an idealisation. Occam's Razor, so often quoted as implying that the simplest explanation is the correct explanation, merely says that the simplest explanation is to be preferred as an point of practicality, for which there are two reasons.

Firstly, if one otherwise chooses an explanation "at random" the effort involved in determining its utility is likely to be greater; secondly if one begins with the simplest explanation and finds, after some investigation, that it does not truly explain things, then one may proceed to the "next simplest" explanation - an explanation chosen at random that fails offers no guidance on where to look next.

Thus we must have our beautiful ideas but see clearly where and how they connect to reality, so that we may revise them accordingly.

I am well aware that in eschewing (for want of capability) a mathematical treatment of wormholes etc. I may have misled myself by taking certain features at face value; on the other hand, science, the eternal quest to magnify the mysteries of the universe, cannot proceed without that peculiarly human quality of creativity, so I create in words in the hope that they might be fruitful.

In our search for a theory that unifies quantum mechanics and general relativity, someone, somewhere, somewhen is going to have to believe at least one impossible thing - before or after breakfast - in order to make a beginning. I am much encouraged by the work of Lee Smolin and others on Loop Quantum Gravity, I have considerably sympathy with String/M theory, I am intrigued by some of the other approaches (dynamical causal triangulation etc.)... I eagerly await news of a synthetic epiphany!

Thank you again,

Julian Moore

That "He is generally unqualified to speak to such matters as Time, having only a basic BSc (hons) in Physics from the University of Bristol," belies and belittles those in the long chain from those first eyes that looked up to the stars in wonder and asked "who am I?"

Who qualifies whom to be human?

Thank you.