Friday, November 19, 2010

Mickelson-Morley experiment revisited again

For almost year ago I told about a variant of Mickelson Morley experiment performed by Martin Grusenick. He found that the interference pattern changed during vertical rotation. The experiment generated enthusiasm in people taking seriously the notion of aether although the explanation in terms of aether was excluded by very simple considerations. I proposed a possible explanation of the effect (assuming it is real) in terms of new gravitational physics possibly provided by TGD. The model involved one parameter whose size determined whether the effect is there or not.

I am grateful for Frank Pearce for informing me almost year later (20.11. 2010) that he has carried out the Grusenick experiment again. There is small movement of the interference pattern during vertical rotation but nothing comparable to that detected by Grusenick so that the effect is very probably an artifact due to instabilities associated with the central mirror. An excellent video Vertical Michelson Morley Interferometer Experiment 11 12 2010 about Pearce's version of the experiment can be found here.

24 Comments:

At 3:34 PM, Blogger nige said...

Thank you for the links to these videos of the 1887 Michelson-Morley experiment. It is good news that the experiment can be done with such simple equipment.

FitzGerald's original explanation (published in Science in 1889, about four years before Lorentz) of the failure of the experiment to detect the absolute velocity of light that James Clerk Maxwell postulated when proposing the experiment, was simply that the instrument contracted in the direction of motion, shortening the instrument so the two-way path of light in the direction of motion was shortened, compensating for the effect of absolute motion and preventing the shift in interference fringes from being observable.

Thus, FitzGerald preserved the ether and the absolute velocity of light, with the contraction formula. Einstein's special relativity doesn't debunk FitzGerald's explanation, because Einstein still has the same contraction formula, the FitzGerald-Lorentz contraction.

The Earth is going around the sun at 30 km/s and the Milky Way is going towards Andromeda at 600 km/s. If the speed of light was always constant, then the contraction of the instrument would produce interference fringe shifts as it was rotated, by shortening one two-way light beam path. Thus, if the instrument contracts in the direction of the Earth's motion, then this would produce interference fringe shifts unless the velocity of light changes with direction, preventing such shifts.

 
At 8:07 PM, Blogger Matti Pitkanen said...

I do not remember the details of the history of aether hypothesis but my impression is that the aether explanation became more and more complex as further experimental anomalies against it appeared and simplicity and elegance plus predictive power selected special relativity as a unique manner to proceed.


The interpretation of Grusenick's finding in terms of aether in Newtonian sense (no postulate about contraction) was excluded from beginning. The simple argument based on the fact that the claimed effect was not observed in tangential direction is given in the previous posting.


If the effect would have been real, an additional contribution to standard 1/r^2 force would provide a possible explanation and TGD allows to imagine this kind of contribution.

My naive estimate was that the contraction of instrument due to its own weight was not enough to explain the effect reported by Grusenick.


Allais effect is by the way a mysterious effect which appears when Sun, Earth, and Moon are at same line and suggests that something is not understood in gravitation. My proposal is in terms of large hbar gravitons and interference of gravitons.

 
At 5:55 AM, Blogger nige said...

This comment has been removed by the author.

 
At 6:03 AM, Blogger nige said...

I accept your conclusion that the vertical Grusenick effect was due to gravitational forces acting as the instrument was rotated in the vertical plane. What I'm getting at is the fact that special relativity demands absolute velocity of light, to compensate for the contraction of the Michelson-Morley instrument in the direction of its motion:

Professor A. S. Eddington (who confirmed Einstein’s general theory of relativity in 1919), MA, MSc, FRS, Space Time and Gravitation: An Outline of the General Relativity Theory, Cambridge University Press, Cambridge, 1921, pp. 20, 152:

"The Michelson-Morley experiment has thus failed to detect our motion through the aether, because the effect looked for – the delay of one of the light waves – is exactly compensated by an automatic contraction of the matter forming the apparatus ... The great stumbing-block for a philosophy which denies absolute space is the experimental detection of absolute rotation."

Carlos Barceló and Gil Jannes, ‘A Real Lorentz-FitzGerald Contraction’, published in the peer-reviewed journal Foundations of Physics, Volume 38, Number 2, February 2008, pp. 191-199, http://arxiv.org/PS_cache/arxiv/pdf/0705/0705.4652v2.pdf:

"... we show that a real Lorentz-FitzGerald contraction takes place, so that internal observers are unable to find out anything about their ‘absolute’ state of motion. ... The reason that special relativity was considered a better explanation than the Lorentz-FitzGerald hypothesis can best be illustrated by Einstein’s own words ... his formulation of special relativity was an advance within the given context, precisely because it avoided making any claim about the fundamental structure of matter, and limited itself to an effective macroscopic description."

G. Builder showed in a peer-reviewed journal in 1958 that absolute motion is implicit also in the "relativistic" time-dilation due to motion in special relativity:

"“we conclude that the relative retardation of clocks ... does indeed compel us to recognise the causal significance of absolute velocities.”

- G. Builder, “Ether and Relativity”, Australian Journal of Physics, v11, 1958.
(In 1971, J. C. Hafele flew atomic clocks around the world, citing Builder’s paper and confirming Builder’s conclusion therefore that the relative aging of clocks in different states of motion implies the existence of the means to detect the presence of absolute motion: Science, vol. 177, pp. 166-8.)

 
At 6:11 AM, Blogger nige said...

(1) Contraction in the direction of motion by the factor FitzGerald-Lorentz factor will cause interference fringe movement as the Michelson-Morley instrument is rotated around, due to the contraction of the instrument in the direction of motion (shortening one light path relative to the other) caused by the motion of the Earth.

(2) To get rid of the interference fringe shifts due to the Lorentz-FitzGerald contraction of the instrument in the direction of motion (shortening the path taken by one of the split light beams), you need to have a variable velocity of light!

If Einstein wanted to get rid of an absolute velocity of light, he would need to get rid of the FitzGerald-Lorentz contraction. He doesn't. He has the contraction! He doesn't realize that it is incompatible with his postulate of the constancy of the velocity of light, because he doesn't understand the Michelson-Morley experiment. He just focusses on Maxwell's equations. The FitzGerald-Lorentz contraction is a compensating factor for the absolute speed of light: if you want a non-absolute speed of light, you then have to get rid of that compensating factor, or else it (the contraction of the instrument) will shorten one light path and thus cause interference fringe shifts!

I'm just concerned that special relativity was actually misunderstood its alleged author, Einstein. Sir Edmund Whittaker's History of the Theories of Aether and Electricity, v2, 1951, attributed special relativity to Lorentz and Poincare, outraging Einstein's friend Abraham Pais, who then lent Einstein his original copy of Poincare's 1904 relativity paper, which Einstein had apparently never seen it before (this is in Pais' 1982 biography of Einstein, Subtle is the Lord). Einstein then instructed Born to give a public acknowledgement of Poincare's role, and Born said that Poincare had discovered relativity before Einstein. This made Pais furious, because Poincare's original relativity had three postulates, unlike the two in Einstein's. Pais ignores the points of Builder and Eddington. These people are completely pseudoscientific, putting religious style hero worship ahead of critical analysis. Bearing in mind that Einstein didn’t bother to read up the Michelson-Morley experiment or the papers of FitzGerald, Lorentz and Poincare, before rushing out his own paper, it is no wonder that he was confused.

 
At 8:45 PM, Blogger Matti Pitkanen said...

To avoid misunderstanding I want to repeat what I said. What I concluded was that if the vertical effect *would* have been there it *would* have been caused by gravitation in TGD Universe. The Grusenick effect is however very small and probably non-existing.

I would not take too seriously the arguments from the early days of special relativity (nor similar arguments represented today). It took time to learn the new 4-D geometric thinking and only quantum theory led to the realization that the notion of symmetry is what makes it possible to think clearly.

For instance (concerning Eddinton's argument), in special relativity absolute rotation cannot be compared with absolute linear motion since acceleration is involved and systems rotating with respect to each other are not related by symmetries of space-time metric.

I do not understand Builder's conclusion. Motion is always with respect to something, one must specify the coordinate system with respect to which system moves. One has always relativity. Either Galilean relativity with absolute time coordinate or Poincare relativity. These two views differ only by what one assumes about the symmetries of space-time.


The special relativistic approach relies on symmetries of Maxwell action, and reduces it to group theory and geometry. In quantum field theory this approach leads to spectacular predictions such as the existence of electron spin and antimattter. Geometric approach also leads to a theory of gravitation, which has been an experimental success story. The supersymmetric variant of general relativity is one of the two candidates for a divergence free quantum field theories! To me this looks almost magic demonstration about the power of general principles.

For these reasons people wanting to replace this approach with aether of something analogous have to build all the physics since Maxwell from scratch and do it even better to get others convinced. Already the explanation of Mickelson-Morley requires a mechanism. There are many other experiments and each experiment requires its own mechanism. In special relativity single postulate- Poincare symmetry- makes this zoo of mechanisms un-necessary.

This tendency to think that some clever mechanism might always solve the problem is deeply rooted in our practical western thinking. This tendency has strengthened during computer era which emphasizes practical skills. How many exotic particles have been introduced just to explain dark matter! How many mechanisms of CP breaking and matter antimatter asymmetry have been proposed! And think of all these variants of Higgs mechanism and its supersymmetric counterpart! And the desperate attempts to reproduce standard model from M-theory or F-theory! Most of this activity turns out to be waste of time once the deeper principles have been found. But this is not the
time for principles.

 
At 4:38 AM, Blogger nige said...

Thanks Matti. You address only the second point in the Eddington quotation above. The first point is that the [1 - (v/c)^2]^{1/2} contraction factor is FitzGerald's compensation factor for an absolute velocity of light; the instrument shrinks in the direction of motion, reducing the relevant path that light has to go. Einstein retains this compensation factor. If light velocity is relative (always c and not c + v) and you retain the contraction factor, then the contraction factor itself will cause interference fringe shifts! Such shifts are not seen in the Michelson-Morley experiment, so if we retain the contraction factor, then we must conclude that the velocity of light is actually c + v.

"I do not understand Builder's conclusion. Motion is always with respect to something, one must specify the coordinate system with respect to which system moves."

Builder disproves this idea youn have that "motion is always with respect to something"! Builder says you do not to specify any coordinate system whatsoever. Simply two atomic clocks, move them around, then without needing any specified coordinate system or reference point you can tell which has been in motion. The one showing the earlier time has been moving! However this is explained (using special or general relativity) is irrelevant because the effect is easy to demonstrate by moving atomic clocks around. Just see which one slows down the most, and that is the one which has undergone the most motion. You don't need to specify any coordinate systems, just to compare readings. The comparison of the readings eliminates any need to specify coordinate systems.

"This tendency to think that some clever mechanism might always solve the problem is deeply rooted in our practical western thinking."

It's not a very clever mechanism. The vacuum contains fields like the gravity field. Something moves in that field and gets contracted due to the interaction with the field. There is nothing clever here.

"How many exotic particles have been introduced just to explain dark matter! How many mechanisms of CP breaking and matter antimatter asymmetry have been proposed! And think of all these variants of Higgs mechanism and its supersymmetric counterpart! And the desperate attempts to reproduce standard model from M-theory or F-theory! Most of this activity turns out to be waste of time once the deeper principles have been found."

This problem is caused by starting with a "beautiful" mathematical model, and then introducing complex mechanisms to try to force the mathematical model to not disagree with nature. It's the epicycles problem. Beautiful mathematical idea: perfect circular orbits. Problem: it doesn't work. (The same happens in stabilizing the Calabi-Yau 6-d manifold with Rube-Goldberg machines, leading to a landscape of 10^500 metastable vacuum state string theories.) Solution: complex epicycles. Feynman's call for simple mechanisms in the first place is ignored.

 
At 6:12 AM, Blogger Matti Pitkanen said...

I cannot see how the Mickelson Morley experiment should involve the contraction factor. I have the feeling that Galiean formula is applied in special relativity, this gives something wrong and one blames special relativity for this.

Also In the experiment of Builder the motion must be relative to some system, if not anything else, then observer. The whole notion of motion (change) is non-sensical unless one specifies the system in which it takes place (which changes). You can do the specification in an abstract manner to hide it but you must do it. The sound produce by the clap of single hand might be the counterpart for the notion of absolute velocity.


String model is beautiful mathematically in its original form and geometrizes very elegantly interactions resembling gauge interactions. Our world is however 4-D rather than 2-D and this led to spontaneous compactification and all the misery implied by it.

It is sad that people did not realize and -probably because of their vanity- refuse still to realize how elegantly the generalization of conformal invariance to that of light-like 3-surfaces implies 4-D space-time and M^4xCP_2 as imbedding space. Many many euros go down to the drain.

 
At 1:51 PM, Blogger Ulla said...

A highly interesting link.
http://arxiv.org/PS_cache/arxiv/pdf/1011/1011.4125v1.pdf

 
At 1:07 AM, Blogger Ulla said...

http://zone-reflex.blogspot.com/2010/11/evolution-is-process.html

 
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The Last Chapter of the Symphony of Existence
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In this book, this phenomenon has been fully explained with its corresponding equations based on "The General Theory of Relativity", and I am willing to send you a free copy of my book if send me your postal address.

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My e-mail address: mohammad692@hotmail.com

 
At 11:18 AM, Blogger Ulla said...

http://arxiv.org/ftp/arxiv/papers/0909/0909.1856.pdf

 
At 2:13 PM, Blogger Jerry Decker - Amateur Astronomer said...

The principle of stress and strain says that every physical thing responds to a stress. Things like mass and light speed that are constants in special relativity must be allowed to become variables in general relativity. FitzGerald-Lorentz contraction is correctly applied to the differential length (dL’/dL) not the total length (L’/L) to allow special relativity to be taken over into general relativity.

Vertical light speed must be a variable to satisfy the principle of stress and strain. The proof is in any kind of black hole model you want to write. The visible horizon of faint microwaves 2.725 degrees Kelvin is blue shifted at the event horizon by gravity of the black hole. At the event horizon the blue shifted temperature is easily reaching the Planck limit of 3.5*10^32 Kelvin. It causes every description of any black hole to be discredited. In each case the remedy is to allow the speed of light to slow down in a gravity field and approach zero at the event horizon. It is just another way to describe curvature of space.

When light speed slows down in a gravity field, the Dirac Sea of energy can be proven by setting it equal to the gravity potential at the event horizon of a black hole, giving the same calculated value that Dirac got from quantum mechanics and Planck units. To get flat space it is necessary to partition the vacuum into equal potential energy for gravity and electromagnetic components. They counter act each other in stress energy of curvature, giving flat space with large total energy. Every process in space can be described as a departure from equal partition and the tendency to return to equilibrium later when a stress is removed. The Zero Point field is made of component states somewhat smaller than the Planck scale, but sufficient to describe average partition for clusters of oscillators. TGD is a more fundamental description on a smaller scale that should provide a support mechanism for the partition of space.

All of the physical laws must reside in the vacuum partitions possible, because the laws are nearly the same everywhere, and the vacuum is the only thing that goes everywhere. TGD can describe a complete physical system that averages to the partitions function in the vacuum.

Local properties of space and time must be measured by local variables. Gravity parameter MG is not local. Still it occurs in the metrics. I have proposed that local gravity acceleration g, is the correct measurement to describe the curvature of space. A simple prediction is made for nearly flat space.

d(c^2)/dr = - g

It is too small for measurement, only 10 parts in 9*10^16 near the earth and only about 150 parts near the sun. I don’t believe the experiments we can do will detect that precision.

 
At 2:17 PM, Blogger Jerry Decker - Amateur Astronomer said...

In strongly curved space the equation is modified for partition where Z is the electromagnetic fraction of the Dirac Sea. Light speed is modified by local gravity and vacuum partition.

d(c^2)/dr = -2 (1/Z )g

In flat space the partition function Z is equal to one half.
A complete model can be constructed of physical laws with variable light speed. The other physical parameters like gravity G are also variables where G* is the value in flat space.

d(G/G*) = - d(c^2/c*^2)

It makes a prediction that G increases near a black hole to twice the normal value in flat space.

Partition can be taken into general relativity where it predicts that light speed increases in the vicinity of a star ship as it accelerates at high speed. Then the proper velocity never exceeds local light speed. It predicts that star travel is less difficult and time consuming than in the conventional opinions.

c’ > v’

There are other predictions, for example time going backward when a star ship has proper velocity greater than standard light speed.

IF( v’ > c*, time goes backward, (else) time goes forward)

Special relativity does not object as long as the differential time is used (dt’/dt) instead of (t’/t) for the time intervals.

Vacuum Partition is ignored in science, because the qualified people all want to derive the more fundamental theory like TGD where the physical laws emerge as a consequence instead of being defined as features.

I expect the next big discoveries to be made at high speed in a starship, where hidden dimensions open up and small things become large enough to measure. The new science will be discovered, but maybe not published on Earth.

Jerry Decker - not the one from Keely Net

 
At 3:25 AM, Anonymous kalle said...

genome's dark matter
http://www.technologyreview.com/biomedicine/26963/?nlid=3939

 
At 5:35 PM, Blogger Matti Pitkanen said...

Thank you. Fascinating results.

Matti

 
At 4:44 PM, Anonymous Anonymous said...

There is no reason to expect light speed to vary in special relativity. It is in general relative with curved space time that light speed might vary.

Albert Einstein wrote a series of papers for Annalen Der Physik in German beginning in 1911. The original papers are available from Augsburg University. Here is the index.

http://www.physik.uni-augsburg.de/annalen/history/Einstein-in-AdP.htm

The first article in the series leaves no doubt that Einstein was predicting light speed to change in a gravity field, but the difference near Earth is too small to measure. Here is the first article.

http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1911_35_898-908.pdf

Equation 3 is the conclusion.

c = co( 1 + Phi/c^2)

Originally Phi was MG/r, but later it became 2MG/r.

The following year Einstein introduced equivalence. Here is the link.

http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1912_38_355-369.pdf

Equation 6b gives light speed as a variable in an accelerating system. Once again the difference is too small to be detected on Earth.

The next paper is given here.

http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1912_38_443-458.pdf

It begins define the gravity field by the change in light speed as shown in equation 2. Later in the paper electromagnetic energy is added to the gradient at equation 4.
These three papers are not entirely in agreement, because the theory was changing.
By 1916 the theory had taken its present form. Here is the original paper in German.

http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1916_49_769-822.pdf

Equations 70 and 73 are the final version of light speed changing in a gravity field.

Jerry Decker has given slightly different but similar equations in his theory, based on a claimed error in the way equivalence is applied. Jerry demonstrated that a 4 dimensional observer can distinguish between gravity and mechanical acceleration. So GR must be restated with small changes in the second order differentials.

Matti’s theory could also be another way to express the same ideas.

These topics are seldom mentioned in English language, but Einstein reprinted it in his 1922 English language book, "The Meaning of Relativity" equation 107.

There is no doubt at all that Einstein intended the speed of light to change in a gravity field and in an accelerating system. It is found in his original papers and in his English Language book.

In every case the change is too small to detect on Earth, but becomes important near a black hole, or in a prolonged acceleration in space.

Sub Woofer, Friend of Jerry

 
At 4:53 PM, Anonymous Anonymous said...

It should say:

Originally Phi was ( - MG/r) , but later it became (-2MG/r).

Streamer 7. New Friend of Jerry

 
At 5:09 PM, Anonymous Anonymous said...

Sub Woofer didn’t mention the additional explanation from Einstein in his 1922 English language book. Einstein used the change in light speed to explain and predict the deflection of light passing near a star.

He is often misrepresented by others who claim light speed remains constant as is passes through curved space. In Einstein’s own words from a large university library, the curvature of space represents a change in light speed.

Seeker T

 
At 5:31 PM, Anonymous Anonymous said...

I heard that Jerry gets paid a lot not to publish anything new. He still writes, but for a private audience.

His published work is rapidly disappearing from public space. Science 2.0 deleted his article on magnetic engines for starships.

If Matti could express how TGD relates to light speed and star travel, then maybe he could get a private audience too, and a larger pay than he lost at university.
Jerry’s last publication said that light speed increases in prolonged acceleration. The traveler never reaches a speed limit. The magnetic engine always finds a field of pulsar beams to ride on. Jerry used Einstein, but with small changes. Then people around Jerry started talking about proliferation and powerful knowledge.

Jerry tells jokes about universities from decades of experience.

Writer A

 
At 8:50 PM, Anonymous matpitka@luukku.com said...

In special relavity maximal signal velocity (usually identified as speed of light) is constant.

In general relativity the constancy of speed of light hypothesis is replaced with hypothesis that at geometric optics limit massless particles move along light-like geodesics. This is the general coordinate invariant statement. In the conceptual framework of GRT the idea about modification of light velocity by gravity is wrong. Interesting that Einstein was wrong in the conceptual framework of GRT.

In TGD framework sub-manifold gravitation makes possible the variation of the maximal signal velocity: the time for signal to travel from point A to B depends on space-time sheet along which it travels and there are several possibilities in principle. Each space-time sheet is curved and warped that time taken is longer than along light-like geodesic of the 8-D imbedding space (or actually that of M^4 in M^4xCP_2).

In this framework gravitation indeed effects speed of light measured in this manner. Einstein would be right in TGD framework!

There is also empirical support for this prediction: the time for light to travel to Moon and back is increasing, as if Moon were receding. The effect can be explained quantitatively correctly in terms of different light-velocities for the coordinate system assigned to distant stars and Earth respectively.

It would have been nice if neutrinos (which were claimed to move with superluminal speed) had made this visible but it turned out that the effect is too small or absent.

 
At 12:37 PM, Anonymous Anonymous said...

Thanks Matti for the explanation.

Would you say that Einstein’s mistake on equivalence led him to construct GRT in the wrong framework?

It is easy to prove an observer can discover a gravity field by its predictable gradient through several points at the same time in a pattern that mechanical acceleration can almost never duplicate.

There is equivalence, but not the one GRT embodies. GRT misses the higher order differentials.

Did I understand correctly that TGD can formulate GR in a framework that correctly treats equivalence?

Sub Woofer

 
At 7:21 PM, Anonymous matpitka@luukku.com said...

To Anonymous:

The question whether Einstein made mistake or misinterpretation relates to how the Poincare symmetry of special relativity implying basic conservation laws should be extended to GRT. To my view there was a misunderstanding here and still is.

Einstein might might have though that general coordinate invariance (GCI) extends Poincare invariance. This is not the case since GCI is a pure gauge invariance like symmetry. Indeed, Noether's theorem gives conserved energy momentum currents which vanish by Einstein's equations. This is just the problem which served as starting point for TGD. The general relativistic view about symmetries of special relativity is wrong to my opinion.

Second point is that Poincare symmetries does not even exist in GRT for general space-time topology. One might try to save Lorentz transformations as vierbein rotations of tangent space but they are not symmetries anymore. I think that the weakness of gravitational interaction led to the idea that we can be perhaps a little bit sloppy here and give up the demand of mathematical and conceptual rigor.


This all was about GCI. Its implications in TGD are much stronger than in GRT.

 
At 7:30 PM, Anonymous matpitka@luukku.com said...

To Anonymous:

GCI and Equivalence Principle (EP) are so great principles that they require separate post each;-). I already told about GCI.

EP is the second great principle of General Relativity stating essentially that gravitational mass and inertial mass are equivalent. The lift experiment is a good mass as also the dropping of objects of different masses from Pisa's tower with the same acceleration.

EP is in TGD framework reduced to so called coset representations at quantum level. Super-conformal symmetries give rise to algebra and its sub-algebra and the condition is that the differences of the superconformal generators of these two algebras annihilate the physical states. The two generators in difference could be called gravitational and inertial. As a special case one obtains also the equality of gravitational and inertial masses.

One should have EP also classically and Einstein's equations would give it. Hence at the long length scale limit one should obtains something Einstein's equations, possibly with cosmological constant. One natural possibility is that one obtains them in statistical sense for the matter topologically condensed around vacuum extremals and deforming them and in this manner giving rise to an energy momentum tensor which satisfies Einstein's equations.

The recent work with the preferred extremals of Kahler action however suggests that the counterparts of Einstein's equations could be satisfied exactly by all preferred extremals and in all scales! Not only statistically but in strict sense.

The point is that the covariant divergence of Maxwellian energy momentum tensor for Kahler action must vanish in order the field equations reduce to purely algebraic form and are satisfied. Non-vanishing components of energy momentum tensor and second fundamental form simply have no common index pairs! This algebraic miracle is guaranteed if Einstein's equations - possibly with cosmological term are satisfied! This result was a real surprise: I had never thought that from this point of view.

These algebraic field equations would be actually satisfied for both parts of the energy momentum tensor represented as sum of Einstein tensor and metric. Therefore the space-time surface would be also minimal surfaces just as string model inspired approach would predict (action as 4-volume).

These miracles require that preferred extremals a lot of symmetry. They indeed have. For Euclidian signature of metric Hermitian structure in 4-D sense and for Minkowskian signature its counterpart that I call Hamilton-Jacobi structure.These symmetries would extend the conformal invariance of string models from 2-D to 4-D context.

 

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