Wormholes & Time Machines (again)

If you want to know the answer to a tough question, ask the experts... Doing exactly that over at Physics Stackexchange. You can follow progress there.

Scribble, scribble, scribble...

17th October, 230,000 words (admittedly we've slowed down... only 555 words per day since the last announcement).

Yesterday was a bit of a wipeout on account of Patch Tuesday's various Windows (in my case Vista HP) and other updates (Office etc.) being applied Wednesday night - leading to catastrophic failure of special goodies I've written to add functionality to Word to help me with navigating it...

To be specific, the ActiveX killbits patch not only prevents vulnerable ActiveX controls from being used by Internet Explorer it does so (via the "killbit") by stopping anything from running them... in my case MS Word - the Office XP Web Component I had on a userform simple wasn't there, which also meant the VBA code fell over "Cannot compile module" because the code referenced a now non-existent object.

However, lest you think it has been all work and no play (oh what fun to have to rebuild and restore one's work PC?) maybe I should share the news that traversable intra-universe wormhole mouths can not be charged! Took me a while to work it out (think: Gauss/divergence theorem + lack of horizon = lack of inside/outside distinction for a surface surrounding a wormhole mouth: think of the two types of circles that go around or though the hole in the middle of a torus/doughnut - they don't divide the surface)... but then I found confirmation in a footnote on p1200 of Misner, Thorne, Wheeler's Gravitation, which was nice. Still don't see how they can have mass either, I mean, come on...

Also worth mentioning, just in passing, something that occurred to me over a nice Lamb Madras at Indigo last night (a line of thought prompted by discussion of a recent New Scientist article on why the mind encourages superstition) which is that according to Your's Truly's theory of mind two contrasting styles of meditation (defocussing (e.g Zen ) vs. e.g. focussing (e.g. Tibetan though e.g. chanting)) lead to two different (but of course, the same) states of non-being, which we may summarise as:











If you know what I'm taking about, you know what I mean; if you know what I mean, why aren't you laughing?

We are in a jolly mood, aren't we?

Enlightening Stuff, eh?

Wormholes, Warp Drives and Time Machines - Part III

[You have read the Disclaimer, haven't you?]

The assiduous reader (that's you, O Sister Mine) who has been following the theme of Wormholes, Warp Drives and Time Machines has of course read Parts I and II - everyone else may wish to catch up...

So, dear Sister, take nieces Scarlet & Em on your knee and read on... I'm sure they'll enjoy this!

The story so far: many who probably know better than I am claiming to, say that one can construct a time machine by moving one mouth of a wormhole at very high velocity relative to the other (the closer the velocity is to the speed of light the better if we want a significant time machine). Time dilation - as per Einstein's Special Theory of Relativity - will then cause a time difference to occur between the two ends, but because the two ends are linked this makes a time machine (see Part II for how this is supposed to work).

My naive objection to this is that a separation in time is in fact a separation in spacetime - and the key words here are in and spacetime. The implied rhetorical question is: can one apply things like the Lorentz transformations to spacetime itself rather than to the separations of things and events in it. To which the unequivocal (but possibly wrong) answer has to be: No!

But' it's time for a diversion. Let's get practical - another little experiment will help illustrate the concepts. For this you will need a lump of some malleable substance, such as dough (e.g. pizza dough - in which case, make plenty in anticipation of pat IV) ; some superglue, and a finger.

• Take lump of dough and make a hole in it, slightly larger than your chosen finger
  
  Look at it for a moment - you've got a torus, a thing with a hole in in it. Now, flatten and stretch it slightly to make a fat pancake - but don't close the hole (it's still a torus - they don't have to be doughnut shaped: anything with one hole in it is topologically a torus) and then imagine that the dough is spacetime.
  
  You can go from one side of the pancake to the other one of two ways: you can either avoid the hole and go to the edge and round, or you can go through the hole. The hole is our experimental wormhole because, if you happen to be closer to the hole than to the edge, the distance you need to travel to get to the "same point" on the other side is less if you go through the hole. Note however (for future reference) that whether you go around or through, if you keep going you can get back to where you started - and are still facing the same way.
  
  
• Now, apply superglue to your chosen finger in a narrow ring around the first joint
  
• Insert finger into the pre-pared hole and squeeze the dough onto the ring of superglue

You should now be superglued to the dough. And since the dough represents spacetime and the hole in the dough the wormhole, we can simulate moving the wormhole by moving our finger. Try it - gently.

As you move your finger, dough piles up against the forward edge of your finger and gets stretched everywhere else. If a real wormhole is going to move, it will do something similar - or we will have find a way to stop dough piling up in front and stretching thin behind.

The reason for saying that spacetime "piles up" or "stretches out" and that a moving wormhole has to deal with such things is that one cannot create and destroy spacetime - there's no such thing as "Cut and Paste" spacetime", no "delete" let alone "insert" (unless perhaps you are a theoretical cosmological topologist. Don't be shy in coming forward). However, one can stretch and squeeze space(time), thereby changing the separations between things, which, strangely is all that gravity is about really.

So a small digression is in order, and without reproducing and trying to explain the Einstein field equations... Oh what they hell, there are are, courtesy of Wikipedia (see Einstein Field Equations) - because it is one of the most beautiful equations in physics.


What this this says is this. The left hand side of the equation, the "G" thing, is The Einstein Tensor - it is a (nonlinear) function of the metric, which is that thing that tells us how bendy and twisty spacetime is at every point. The right hand side of the equation, the "T" thing, is the Stress-Energy Tensor, which describes the density and flux of energy due to everything at a point except gravity. So the bendiness and twistiness of space(time) is determined by the matter and energy in it, or as I believe John Wheeler so beautifully put it "Space tells matter how to move, matter tells space how to curve".

Without matter etc. spacetime would be flat, but put in some ordinary mass and it bends in just the right way to produce what we previously thought of as the mysterious force of gravity. The usual analogy for this is a bowling ball on a trampoline: the big heavy ball causes a dent towards which any peas, marbles, or other small round objects therefore move (don't overthink the analogy, it will just make your head hurt). A nice little animation from YouTube shows the Sun denting spacetime, earth circling around and the way that light also gets bent by the gravitational dent - until the sun "disappears", at which point, there being no "T" thing, all the curvature disappears...



The key point here is that without the "T" thing to keep spacetime bent and/or twisted it will flatten out, thus, returning finally to our wormhole, we need some T in the wormhole to squeeze stuff up on the leading edge and some effectively "anti-T" to stretch it out behind.

Now, I have previously drawn an analogy between this stretching and squeezing with that of the Alcubierre "warp drive", which also squeezes up the space in front (so you have less to travel across) and stretches it out behind (so that space overall doesn't get an overall pinch in it.

At that time and rather unfortunately for the eternal optimist, it occurred to me that the Alcubierre drive couldn't work, because I had assumed that the whole point of this Faster Than Light warp drive was that you could point somewhere, intone "Engage!", and then be off, and that therefore the warp bubble was somehow propagated from its initial position just like a wave. This clearly wouldn't work, I thought, because when the metric does change the effects propagate at the speed of light (speed of gravity = speed of light) and what would be the point of an "FTL" drive when you had to wait four years to sail across the four light years that had then been reduced to a mere, say, centifurlong.

And indeed it seems I was not the first to raise an eyebrow in Alcubierre's direction - but since they know better, it seems the experts never for a moment thought the metric change would be propagated... so they said it wouldn't work because you'd have to traverse the entire route in advance in order to deposit suitable amounts of T and anti-T along the way. It turns out that the Wikipedia article on the Alcubierre drive makes this point (see "Difficulties), quoting Krasnikov and Dr David Coule's work to the effect that "there's no warp drive without warp drive" (and thanks to DHC for providing a copy of his original paper).

Or, to spoil a rather nice line, if we do ever get any sort of warp drive we will only be able "To boldly go where at least one other has been before."

However, at least my intuition is not clearly leading me astray, so maybe the dénouement (when it arrives) will be worth the wait, though if I have not in fact drifted a long way off track the geodesics of Mr Stuff's idea space have clearly been severely bent bythe abnormal density and flux of... well, I suppose, Stuff, so I should probably let you digest this properly before going on...

Spacetime - Bendy, Twisty, Wavy Stuff

The Dogon of Mali, Sirius and Stuff

Here is a Dogon joke:

Q: How many people are there in a Dogon family?
A: Five - two parents, two children and a French anthropologist.

Anthropologists just love the Dogon - and why not, they are a fascinating people - Mali is on my list of Must-See places as soon as IT is finished and I reap the reward of some hard earned globe-trotting (No, you may not go first Dean - I mentioned Namibia once and the next thing I know he's swooping over the desert at head height in a light aircraft!).

Anyway, the Wikipedia article is rather long on the whole "Sirius Mystery" angle: how come the Dogon know so much about Sirius - and even the existence of Sirius B which you need a pretty large telescope to see, etc. etc. eh?

Unfortunately, no one is without a reasonable argument: they learned all about Sirius from aliens (who, after all, should be expected to know) or they learned about it from missionaries - the god-bothering brigade of olden days, being gentlemanly in their pursuits, being rather keen on the whole astronomy thing don't you know?

However, I digress... but before returning to the topic, where did I hear that the Dogon also talk of Sirius C - whose existence wasn't detected until a very few years ago? Hmmm? Are missionaries now providing real-time hookups to Hubble as they go? [Found it: le Renard Pâle, p475... "The star emme ya” emme ya tolo is more voluminous than po tolo and four times lighter. It also orbits around Sirius...]

Anyway, what the Wikipedia article doesn't mention are some other, y'know, like "wow!" things the Dogon believe in... if you put the right spin on them.

This came home to me as I was reading Essai sur las Cosmogonie des Dogon a book by a French anthropologist (see?) called Eric Geurrier, which also references the seminal work mentioned above, "Le Renard Pâle" by Marcel Griaule and Germaine Dieterlen, 1965 (guess their nationality and occupation!).

According to this, the Dogon speak of le "monde d’étoiles en spirale" - the spiral word of stars - which sounds remarkably like a galaxy to me... furthermore, they don't just speak of Le Monde, they speak of Les Mondes, a veritable plethora of galaxies.

But, they are not merely masters of the macrocosm, they are pretty good on the microcosm too... this is the (heavily edited and badly translated by me) story of creation:

In the beginning, before all things, was the god Amma, who rested on nothing. The rolled-up ("en boule") egg of Amma was closed [in upon itself], but divided into four pieces called “clavicles”

The four clavicles are equally prefigurations of the four elements the “four things” water, air, earth and fire; similarly the bisections which separated them, marked the four collateral directions the “four angles”, which is to say, space

But Amma was not very pleased with the result, so he started again...

‘Oeuf D’Amma” Second Genesis (again my translation from the French)

He opened his eyes. This act caused the emergence of the yala from the spiral which, turning in the egg prefigured - in the interior of the egg - the future expansion of the universe.

Thus Amma had pierced the envelope of his breast, and his “eye”, appearing as if from a hole, had become a light, which lit up the universe and revealed the existence of all things in creation.

The universe in the breast of Amma was timeless and without extent, space and time merged by mutual agreement.

When I read this, I was astonished to find myself contemplating the very creation of space and time, their intrinsic inter-connectedness, the Big Bang, etc. etc. described in mythic terms by the Dogon. [If only I could track down the article I read once in which somebody brilliantly re-wrote modern particle physics as a piece of wizardry on a par with Lord of The Rings]

But, enough about Sirius already- lets big-up the Dogon for their whole intuitive appreciation of Special Relativity, General Relativity, cosmology, the Big Bang, etc. etc. and come to think of it, the whole en-boule thing which is really about Grand Unification of the four forces, possibly even, via the "chevron dance", anticipating String Theory.

Can I make this an urban myth? Nope - that's up to you!

PS French anthropology is great! You should read "The Raw and the Cooked" (Le Cru et le Cuit) by Levi Strauss - he has a wonderful transformational theory that can explain everything.