Friday, March 07, 2008

T-Shirt


For the pleasure of Michael and others, here again is the Universe on a T-shirt. From this perspective it is not very complicated. Everything can be described with 1-2 equations that a child could understand. Amazingly, our big Universe is really very simple.

The circle represents our entire Universe, with dimensions x, y, and z compressed into the screen. Like an ant on the surface of a globe, any direction that you travel in Space keeps you in that surface. There is no centre in Space, for every bit resembles every other bit. There is a centre in Time, commonly called a "Big Bang." We are separated from that origin by t, age of the Universe.

Relativity tells us that Space and Time are one phenomenon related by speed of light c. Scale R of the Universe is age t multiplied by c:

R = ct.

This predicts an expanding Universe, for as t increases R expands.

The Universe can't expand at the same rate continuously, for gravity slows it down. By doing some maths we can turn Einstein's thought into an equation:

GM=tc^3

Where G is Newton's Gravitational constant, M is Mass of the Universe. When t was tiny c was enormous and the Universe expanded like a Bang. Now that t is billions of years, c decreases at a rate too small to detect until recently.

Physicists are fond of using Planck units, made from combinations of h, c and G. In Planck units these equations are combined into an even simpler form:

M = R = t

Where M is Mass, R and t are expressed in Planck units.

These simple equations tell everything you wanted to know about the Universe but were afraid to ask: the size, mass, rate of expansion, and the speed of light. Mathematics predicts that the proportion of baryonic matter is 4.507034%, the amount of "dark" mass is 23.87%, and many other things. Until recently Humans have not understood something so simple, but that too is changing.

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8 Comments:

Blogger Matti Pitkanen said...

Off topic comment which I already added to Kea's blog: my only excuse is that I am a little bit happy.

TGD based model for Flyby anomaly predicts the energy increment in flyby process. The prediction was qualitatively correct but about quantitative details I did not know.

The reason was I simply could not force mysel fto purchase the article online: the price is really dirty, 25 dollars. Hence I decided to take the risk of ridiculizing myself in case that the prediction is only qualitatively correct.

I got this morning the PRL article as email. The prediction was correct! I can safely predict that this is for TGD based view about dark matter what perihelion shift of Mercury was for general relativity.

For the model see my blog.

11:28 PM  
Anonymous Tony Smith said...

Matti, thanks for your analysis of the flyby anomaly.
You said in your web site material (blog and tgdgrt.pdf file):
"... Authors suggest that the Earth's rotation is somehow involved with the effect.
The first thing to notice is that the gravimagnetic field of Earth, call it BE, predicted by General Relativity is quite too weak to explain the effect as a gravimagnetic force on spacecraft ...
The gravimagnetic force ... could explain this deformation as a kind of frame drag effect ...
M. Tajmar and C. J. Matos ... have made an amazing claim of having detected strong gravimagnetism with gravimagnetic field having a magnitude which is about 20 orders of magnitude higher than predicted by General Relativity ...".

If Tajmar-type gravimagnetism is a valid explanation of the flyby effect,
then any physics model with such gravimagnetism would be an explanation,
including conformal gravity models (like mine) would also have such an effect,
and
also variable-speed-of-light models (like Louise's) since the variable-speed-of-light can be formulated as varying light-cone-angles which in turn can be formulated in terms of conformal transformations.

Such points of similarity among TGD, Louise's model, and my model are quite interesting.

Tony Smith

PS - For reference, I think that the work of Tajmar et al is at gr-qc/0603033 and gr-qc/0603032 and cond-mat/0602591
and
I am happy to note that de Matos and Tajman in cond-mat/0602591 actually cited in their references (along with some very interesting papers by G.A. Sardinashvily and one by Bluhm and Kostelecky) my pre-Cornell-blacklist papers at hep-th/9402003 and hep-th/9403007 .

It is interesting to see that blacklisted work,
such as Matti's TGD with gravitomagnetism and Louise's variable-speed-of-light and my conformal graviphotons
seems to be capable to explaining experimental data better than the establishment consensus models that the sheeple of the physics community are compelled to follow rigidly under penalty of excommunication.

2:57 AM  
Blogger Matti Pitkanen said...

Dear Tony,

thank you for comments.

The sign of the energy increment by the gravimagnetic field on the spacecraft changes when the sign of velocity is changed. What has been observed is that the sign is always same. Hence strong gravimagnetic field on space-craft is not a solution of the problem.


Also the observations about the size of the framedrag effect on satellite at equator exclude large deviations from GRT predictions at equator.

TGD predicts deviation which becomes large near poles since gravimagnetic field is not dipole field anymore but has only theta-component and its magnitude differs by 1/sin(theta) factor from theta-component of dipole field. Testing of TGD prediction would require a satellite moving outside equator.


The gravimagnetic field would in TGD based model affect the flux tube containing dark matter, and the effect on spacecraft would be ordinary gravitational force by the deformed dark matter tube. It is absolutely essential that dark matter tube is deformed to equatorial plane.

The anomalously high value of gravimagnetic field of Earth nearer to poles indeed favors in dynamical equilibrium the deformation of the tube containing dark matter along equatorial plane. In this sense flyby anomaly provides indirect support for TGD variant of gravimagnetic field.

The experiments of Tajmar and Matos are very interesting and I have discussed a model explaining the outcome of these experiments earlier.

4:31 AM  
Blogger L. Riofrio said...

Good news, Matti and Tony. I expect these ideas to get wider play in the future.

12:13 PM  
Anonymous Tony Smith said...

Matti said "... the observations about the size of the framedrag effect on satellite at equator exclude large deviations from GRT predictions at equator.
TGD predicts deviation which becomes large near poles ... Testing of TGD prediction would require a satellite moving outside equator. ...".

I think that framedragging satellite observations are NOT restricted to satellites with equatorial (inclination zero) orbits.

According to a 20 October 2004 space.com article by Robert Roy Britt:
"... Ciufolini's team analyzed millions of laser signals bounced off two satellites, called LAGEOS and LAGEOS 2. ... The researchers say their result is 99 percent of the predicted drag, with an error of up to 10 percent. ...".

According to a www.astronautix.com web page about LAGEOS:
"... LAGEOS 1 was developed by NASA and was placed into a high inclination orbit to permit viewing by ground stations located around the world. ... Inclination: 109.90 deg ...
Lageos 2 ... Inclination: 52.70 deg ...".

So LAGEOS observations do in fact "Test... TGD prediction" with "satellite[s] moving outside equator".

With respect to the conformal gravity 2-phase universe:
a high-energy phase with Segal-type conformal degrees of freedom (and varying c) that prevails in systems (including voids) that are not tightly bound gravitationally;
a gravitationally tightly bound conventional GRT phase (most of our solar system inside the orbit of Uranus),
the conformal freedom would apply to satellites in high-energy unbound orbits such as flyby orbits
but
the bound-to-earth orbits of LAGEOS etc satellites would not be in a phase to have the conformal degrees of freedom.

Note that the defining criteria for phase is not geographic location but energy,
although for a lot of purposes the orbit of Uranus can be seen (as in Pioneer data) to be a useful geographic criterion.

Tony Smith

PS - Sorry for using the word "geographic" to describe astronomical (beyond geo = earth) location, but my vocabulary is limited and I cannot think of an accurate English word.

6:16 AM  
Blogger nige said...

Your T-shirt quotes Einstein:

"When forced to summarise the General Theory of Relativity in one sentence, Time and Space and Gravity have no separate existence from Matter." - Albert Einstein

Then you give the equations R = ct and GM = tc^3. One way to get GM = tc^3 from general relativity is by applying mass-energy equivalence from special relativity to the equivalence principle between inertial and gravitational masses in general relativity:

inertial mass = gravitational mass

=>

inertial mass-energy = gravitational mass-energy

mc^2 = mMG/R (for a nice graphical illustration of this equivalence, see for example http://www.gravity.uk.com/galactic_rotation_curves.html).

Inserting R = ct into this equivalence of mc^2 = mMG/R gives you:

tc^3 = MG.

For the benefit of people who think that general relativity is not physics but merely a tensor mathematical representation of extra dimensions, there are various other compressions of general relativity of interest. E.g., Wheeler says that matter determines the curvature of spacetime, and the curvature explains the motion of matter/energy.

This is a description of the tensor maths for any theory of gravitation, however, not specifically the unique Einstein-Hilbert field equation which subtracts from the Ricci tensor half the product of the metric tensor and trace of the Ricci tensor (i.e., the scalar sum of the diagonal components from top left to bottom right in the matrix representing the Ricci tensor, R_{mn}).

This is the brains of general relativity; otherwise the deflection of starlight by gravity will be the same as the deflection of a bullet according to Newton's law, not twice that amount. Writing Newton's gravity law in terms of curvature and mass-energy tensors gives something of the general equivalence (ignoring dimensionless factors like 4*Pi),

R_{mn} = T_{mn}.

This simple statement of gravity in terms of a curvature tensor is physically wrong because the divergence of the source term T_{mn} should always be zero, in order to conserve mass-energy (as explained here).

As explained on that just-linked page, this is analogous to the fact that the divergence of any application of a curl operator must be zero. Although you can prove it using algebra, you really don't need to. A curl operator produces a field line which forms a closed loop, often a circle but always a closed loop. A closed loop doesn't have divergence; the total sum of the vectors (small arrows) representing all the differential elements of the field line which is a closed loop is always zero. In order to have divergence, you would have to abandon closed loops and abandon, therefore, curls.

Similarly, the geodesics described by the stress energy tensor where mass-energy is conserved are in a sense closed loops. The Earth isn't always at a fixed distance from the sun; it is closest in January and it then has more kinetic energy than the average, and less gravitational potential energy than the average. Although objects can fall, this doesn't contravene conservation of mass-energy as all that happens is a conversion between kinetic energy and gravitational potential energy.

So in general relativity the stress-energy tensor is not equal to the Ricci curvature but had to have a correction factor subtracted from it to enable the resulting model to abide the conservation of mass-energy: [T_{mn}] - [(1/2)(g_{mn})T] where T is the trace of T_{mn} (i.e., T is simply the sum of energy and pressure components, T = T_00 + T_11 + T_22 + T_33).

As explained at the page here, this expression for the Ricci curvature, R_{mn} = [T_{mn}] - [(1/2)(g_{mn})T], is mathematically equivalent to the better known (but physically less intuitive) form of the Einstein-Hilbert field equation:

R_{mn} - [(1/2)(g_{mn})R] = [T_{mn}]

This doubles the amount of curvature (and thus light-deflection angles) you get when travelling at the velocity of light, as compared to that at non-relativistic velocities. Hence it was this particular correction that enabled Einstein to correctly predict that starlight when travelling near the sun gets deflected by twice the angle than that predicted for a bullet or other non-relativistic small mass moving along the same trajectory of approach to the sun.

Feynman, in his Lectures on Physics, explains extra-dimension curvature as the result of a contraction of spacetime which is produced by the existence of matter (including energy, pressure, etc.). If for simplicity (or as a first approximation) the matter (or energy field) can be treated as a uniform density sphere, then the radius is contracted by (1/3)MG/c^2, which is one-sixth of the horizon radius for a black hole of that mass.

The whole point of treating the time dimension as equivalent to an extra (fourth) spatial dimension in general relativity, is to mathematically model this contraction of spacetime radii around sources of gravitational fields.

Because it is the radial distance alone that is being contracted by the gravitational field, and not the circumference lines around a mass or energy field, you get geometric distortion if you try to continue using Euclidean geometry to model accurately the spatial extent of a mass (e.g., circumference is greater than 2*Pi*R because R is contracted by gravitation yet circumference is not contracted because it's at right angles to the gravitational field lines so is unaffected).

So by mathematically accounting for the extra curvature in terms of an extra dimension using time as a fourth spatial dimension, any actual physical mechanisms for real contraction of radial distance (suggesting the correct physical dynamics behind quantum gravity) are neatly ignored in general relativity, and everyone can live happily ever after (ignoring the physical dynamics, but content with a physically incomplete mathematical model of gravitation).

7:16 AM  
Blogger L. Riofrio said...

Again nige's long and thoughtful posts are appreciated. Funnythat such a simple and testable equation should encounter such resistance elsewhere. Did some physicists forget to take algebra?

7:51 PM  
Anonymous Anonymous said...

pie=r OUND {b+rnyz=sqr}

;)

What the hell are you egg head talking about!?! I am begging you, pleeeease post at least one (and for the nerds thats .5+.5) 1 post thats in dumb speak for me!

-steve

10:52 AM  

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