*Hiding in the Mirror,*Lawrence Krauss

At http://www.math.columbia.edu/~woit/blog/, Dr Peter Woit comments: 'I’ve just finished reading Lawrence Krauss’s new book Hiding in the Mirror: The Mysterious Allure of Extra Dimensions, from Plato to String Theory and Beyond, and it’s very, very good.'

Plato fooled me! See http://eskesthai.blogspot.com/2005/08/fifth-dimension-is-spacetime-fabric.html . It appears Plato and Dr Gerard t'Hooft are as alike as Dr Jekyl and Mr Hyde.

I wanted a way for a spacetime fabric to give light speed gravity force and seized on Plato's idea: "The Fifth Dimension, is the Spacetime Fabric. Perhaps Quantum Gravity can be Handled by thoroughly reconsidering Quantum Mechanics itself? by Gerard t' Hooft. I

*was attracted to Nigel Cook's statement on Peter Woits blog..*."

Notice the vanity, because I'm mentioned personally, I automatically lower my guard a bit. Is the 5th dimension really the spacetime fabric? I use it at http://nigelcook0.tripod.com/ as just a vague explanation of the speed of gravity pressure. It doesn't appear in the calculations at all.

So we don't need the 5th dimension? http://www.math.columbia.edu/~woit/wordpress/?p=280#comment-5478 :

As for QM and QFT, we know the fabric of space is filled with virtual particles. Normally particles like gas molecules can't carry transverse waves, only a solid normally allows transverse waves. But suppose the virtual particles have a spin, like real ones? Then you get transverse waves. Dr John Baez has some ideas on this for quantum gravity here http://math.ucr.edu/home/baez/loops05/ which seem to account for the light speed of gravity while preserving a pressure mechanism.

My understanding is that this is reinventing the wheel, since Maxwell's 1873

*Treatise*section 822-3:

"The ... action of magnetism on polarised light [discovered by Faraday not Maxwell] leads ... to the conclusion that in a medium ... is something belonging to the mathematical class as an angular velocity ... This ... cannot be that of any portion of the medium of sensible dimensions rotating as a whole. We must therefore conceive the rotation to be that of very small portions of the medium, each rotating on its own axis... The displacements of the medium, during the propagation of light, will produce a disturbance of the vortices ... We shall therefore assume that the variation of vortices caused by the displacement of the medium is subject to the same conditions which Helmholtz, in his great memoir on Vortex-motion, has shewn to regulate the variation of the vortices of a perfect fluid."

*So I may have been hiding in the mirror for a bit myself, because of Plato!*

## 4 Comments:

Copy of a comment posted on Dr Lubos Motl's blog:

Dear Lumos,

Just in case you are "hard of understanding" let me simplify a bit. The curvature of spacetime by another dimension would keep Pi at the normal value 3.14159265...

However, Feynman points out that an easier way to grasp GR is that spacetime fabric pressure compresses masses (in addition to simply pushing masses together, gravity). The compression, which is ignored by Newton's math, is (1/3)MG/c^2 = 1.5 mm for earth's mass. The pressure from a perfect fluid spacetime fabric is only in the radial direction toward the centre of mass, and it permeates the interatomic spaces without sideways diffusion, so it is only a contraction in the radial direction, as Feynman points out in his Lectures, c42 p6, where he gives his equation 42.3 correctly for excess radius being equal to predicted radius minus measured radius, but then on the same page in the text says ‘… actual radius exceeded the predicted radius …’ Talking about ‘curvature’ when dealing with radii is not helpful and probably caused the confusion. The use of Minkowski light ray diagrams and string ‘theory’ to obfuscate the cause of gravity with talk over ‘curved space’ stems to the false model of space by the surface of a waterbed, in which heavy objects roll towards one another. This model when extended to volume type, real, space shows that space has a pressurised fabric which is shielded by mass, causing gravity.

We are used to the fact that if we squeeze something, the circumference remains the same, so it wrinkles up or distorts. However, this contraction of radius does not affect the circumference at all. This is physically the fourth dimension taking some curvature to keep Pi intact. Otherwise, Pi will increase. On the Earth's surface the increase in Pi due to the earth's mass is by the factor (earth's radius + 1.5 mm)/(earth's radius) = 1 + (2x10^-10). Hence, Pi is increased by 0.00000002 % (2x10^-8%).

Why does the variation of Pi get ignored by pure mathematicians?

Best wishes,

Nigel

Nigel,

You ask "

Why does the variation of Pi get ignored by pure mathematicians?"Mostly because "spacetime" is "physics", not "pure mathematics".

In fact, as you point out it's not Pi that's varying, but the radius. What you've got are different radii depending on whether you're measuring radially or tangentially. It's not really any more odd than the "apparent mass" of an electron being different being different depending on which direction you're measuring it in.

You have to add an extra term to deal with the situation.

Kevin,

Circumference / diameter = Pi.

This is the sophisticated formula. Circumference is transverse to radius and so is not affected by radial contraction in GR. The diameter is reduced by twice the GR radii contraction. Therefore, Pi rises.

The maximum possible value of Pi seems to appear at the event horizon to a black hole. Black hole radius = 2GM/c^2. Excess radius = (1/3)GM/c^2. Hence it appears that Pi for a black hole = (7/6)3.14159265... = 3.665...

My understanding is that Feynman's argument for the reality of time as a 4th dimension, hence curvature, is based on the fact that Pi can't really vary, and the apparent variation that this radius contraction shows is accounted for by curvature.

If you draw a circle on the side of a sphere like a globe, Pi can appear to get SMALLER because the curved diameter is a longer line than the diameter of the same circle as drawn on flat paper.

However, in GR this analogy is not right because Pi gets BIGGER, rather than smaller.

Here's another interesting detail. When light travels at right angles to a gravitational field, it is falls by twice the amount of slow matter, because light cannot speed up so all the gravitational potential gained must go into additional deflection, not speeding up.

This means that light orbiting a black hole at the event horizon will be subject to twice the deflection that Newtonian gravity predicts. Hence the gravitationally-confined EM model of matter is altered slightly.

Best wishes,

Nigel

Nigel,

You wrote: "If you draw a circle on the side of a sphere like a globe, Pi can appear to get SMALLER because the curved diameter is a longer line than the diameter of the same circle as drawn on flat paper."

You will also find that the angles of a triangle drawn on the surface of the sphere don't add up to 180 degrees, and that parallel lines drawn on the surface cross, which means that Euclid's Fifth Axiom doesn't apply, which just means that we're now doing non-Euclidian geometry. So what? It took a long time for it to sink in that "parallel lines meet at infinity" is a definition, not a statement of "absolute truth". One Jesuit mathematician might have got there sooner if he hadn't got his maths and his theology mixed up.

The problem you're having is not that Pi is varying, but that you're using the Euclidian (plane) geometry equations when you should be using a more complicated version.

This is of course why people

willsay that space is curved.Post a Comment

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