Arcadian Functor

occasional meanderings in physics' brave new world

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Location: New Zealand

Marni D. Sheppeard

Friday, May 04, 2007

Blogging Bones

Around the blogosphere: Tommaso Dorigo just can't help rambling on about searches for fairy (ie. non existent) bosons, and we always enjoy his posts. Above is an artist's image of the newly discovered molten core of Mercury. Matti Pitkanen finds cold fusion is hot news, and for those who thought blogging was just a fad, my brother tells me his dog Barney now has a blog at a dog blogging site.


Blogger nige said...

Regarding Tommaso's experimental research, maybe I'm wrong but my feeling is that checking bosonic Higgs or superpartner predictions from very speculative theories (built entirely on unobservables) is similar to checking 'predictions' from ESP spoon-bending charlatans, or searching for the Lock Ness Monster, ghosts, etc. No matter how much money or scientific effort is put in, you can't get anywhere because the results are never 100% accurate and the crackpot theorist will cling on to the hope that some result will show up when accuracy improves some more. If Geller's brain doesn't bend the spoon, it's down to insufficient brain energy that day, or insufficient number of trials. You can't disprove a crackpot theory experimentally if the theory is 'not even wrong' and doesn't make precise predictions. Keep the theory endlessly adjustable like the landscape of variants of the Higgs theory and the landscape of supersymmetry theories, and it's a 'heads I win, tails you lose' situation. Whatever you do find, the theory will be able to accommodate with suitable fiddles and adjustments, while there is no risk of it failing because it hasn't made any precise (falsifiable) predictions anyway.

I've just finished reading Prof. Smolin's Trouble with Physics, which I've read in a random, non-linear way in bits and pieces over a long time. He has a very deep understanding of some vital concepts underlying spacetime which I find helpful to clarifying the issue of the role of time dimension(s).

Pages 42-43 are really useful. Prof. Smolin explains curvature of spacetime very simply there, especially figure 3 which plots the deceleration of a car as space (i.e. distance in direction of motion) versus time.

The curvature of the line (e.g. for space = time^2), is "curved spacetime".

I think this is a very good way to explain the curvature of spacetime! Quite often, you hear criticisms that nobody has ever seen the curvature of spacetime, but this makes it clear that the general relativity is addressing physical facts expressed mathematically.

It also makes it clear that "flat spacetime" is simply a non-curved line on a graphical plot of space versus time. Because special relativity applies to non-accelerating motion, it is restricted to flat spacetime. Profl Smolin writes (p42):

"Consider a straight line in space. Two particles can travel along it, but one travels at a uniform speed, while the other is constantly accelerating. As far as space is concerned, the two particles travel on the same path. But they travel on different paths in spacetime. The particle with a constant speed travels on a straight line, not only in space but also in spacetime. The accelerating particle travels on a curved path in spacetime (see Fig. 3).

"Hence, just as the geometry of space can distinguish a straight line from a curved path, the geometry of spacetime can distinguish a particle moving at a constant speed from one that is accelerating.

"But Einstein's equivalence principle tells us that the effects of gravity cannot be distinguished, over small distances, from the effects of acceleration. Hence, by telling which trajectories are accelerated and which are not, the geometry of spacetime describes the effects of gravity. The geometry of spacetime is therefore the gravitational field."

What I like most about it is that Prof. Smolin is explaining spacetime by matching up one spatial dimension with one time dimension.

Extend this to three spatial dimensions, and you would naively expect to require three time dimensions, instead of just one.

The simplification that there appears to be just one time dimension surely arises because the time dimensions are all expanding uniformly, so there is no mathematical difference between them.

In three spatial dimensions, if all the spatial dimensions are indistinguishable it is a case of spherical symmetry. In this case, x = y = z = r, where r is radial distance from the middle.

Hence, three dimensions can be treated as one, provided that they are similar: t_1 = t_2 = t_3 = t.

So the reason why three time dimensions can normally be treated as one time dimension is that time dimensions are symmetric to one another (unlike spatial dimensions). So the symmetry orthagonal group SO(3,3) is equivalent to SO(3,1), provided that the three time dimensions are identical.

May 05, 2007 2:20 AM  
Blogger Kea said...

...or searching for the Lock Ness Monster

LOL, Nigel. Reminds me of a time when I was in Scotland and the people (Aussies) I was travelling with insisted that we go to the flashy Loch Ness visitor centre, whereas I preferred to sit by the lake.

May 05, 2007 9:25 AM  
Blogger L. Riofrio said...

Coincidentally, we have the same taste in illustrations today. Great informative post by Kea, as always. Nigel has good points too; some of today's theorists sound like Uri Geller. (present company excepted)

May 06, 2007 4:22 AM  

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