Dimensional Reduction in the Sky

Thanks for the heads up, Jonathan.

"Imagine that spacetime and the universe could start out 2-d, and then evolve into a 4-d extension."

Fundamentally, I think that's the basis for all continuous function models and topologically based extradimensional theories for d > 4. While general relativity cannot avoid the singularity, string theory begins with the negative root, - 2, whose square is positive real, 4. This is one reason that I believe general relativity suffers no loss of generality when viewed as a model finite in space and unbounded in time; the singularity disappears, and the time parameter absent from discrete (Hilbert space) dynamics is restored.

Tom

Thanks greatly Giovanni!

I appreciate your commenting, and I hope you will check in on this thread from time to time, as your research develops. The work of your team is very interesting indeed. That fact that a D of 2 is robust, or appears to be independent of the seed features that drive the running of D, seems especially significant. Perhaps a more literal interpretation of the 'Universe as a Hologram' is in order.

I'll likely say more here, once I read about what Rainbow Gravity has to offer.

All the Best,

Jonathan

Thanks Tom,

Your comment is absolutely relevant and apropos. The continuous running of the parameter D allows topological features to be maintained or transformed as dimensionality evolves or emerges. Topology preserves information.

I'll have to ask you to explain the significance of -2 in String theory, as the meaning of that comment is lost. I do note however, that -2 is the furthest point from the origin in the Mandelbrot Set. I have no idea if that is relevant, though.

More Later,

Jonathan

I'll make a general comment here..

One of interesting the things about having a spectral dimension D that runs from 2 to 4, is that it implies spacetime can take on a fractal character in the middle ground (in the regime of changing dimension). As Sabine said in her blog, we need to be fairly specific about how we define dimension, in this context. In CDT; a random walk yields a measure of the local dimensionality, determined by how swiftly a walker returns. And it was found that this measure evolved when the simulation was run from very short to larger scales.

But the authors of the 'Dimensional reduction' paper state that having D as a running parameter can leave variations 'frozen' at the horizon, which makes it much easier to explain cosmological large scale structure fractality and the existence of extreme scale structure such as the Huge-LQG of Clowes and Campusano described in this paper in MNRAS and discussed in this FQXi Forum thread.

Since the notion being researched by Giovanni and his colleagues does not favor the Inflationary Universe scenario, this leaves the door open to other possibilities, where the homogeneity in the FLRW metric is not a requirement. In such a setting; a cluster like the Huge-LQG is not seen as a problem. I'll say more about this later.

All the Best,

Jonathan

Another comment here..

In case it escaped notice; I wanted to point out the comment about a scalar to tensor ratio, in the abstract of the paper under discussion. The authors state that this ratio "is fixed by the UV ratio between the speed of gravity and the speed of light."

The implication here, of course is that gravity propagates at a speed faster than light. This was first seriously discussed in a paper in Foundations of Physics by Tom VanFlandern, which appeared not long before his demise. But it appears that, if the Dimensional Reduction paper is on target; VanFlandern may have been right.

Anyhow; this could change the picture for primordial gravity waves, and so on. Yet one more reason to actually build next-generation GW detectors, such as the planned (and scrapped - I think) LISA probe. There is, of course, more to talk about with this subject.

All the Best,

Jonathan

Hello again folks;

I wanted to post a link, having located the Foundations of Physics paper by VanFlandern and Vigier - that I mentioned above. This paper suggests there may be a more rapid propagation for gravity, than for EM waves.

Experimental Repeal of the Speed Limit for Gravitational, Electrodynamic, and Quantum Field Interactions

I had the pleasure to meet Tom, who was a very colorful and flamboyant fellow, at CCC-2 - the 2nd Crisis in Cosmology Conference. He was one of the lead organizers for that event. Unfortunately; he passed away only months later.

All the Best,

Jonathan

Hi Jonathan,

I think that the - 2 in the Mandelbrot calculation is a mathematical artifact resulting from the properties of the 2 dimensional complex plane in which the object is constructed.

String theory takes 2 dimensions (the plane or "brane") as the fundamental space in which strings propagate. Witten discards the idea of spacetime and replaces it with a 2-dimensional field theory. That all of the physical world can be described in 2 dimensions eventually comes down to the holographic principle -- the information we can abstract from the surface of a black hole. Because black hole energy increases to the negative inverse (- 1) of temperature, and entropy simultaneously increases to the - 2 power, entropy increases with area (the surface of the black hole) which is r^2, radius squared.

So if we're speaking of a fundamentally geometric theory that applies arithmetic functions, as string theory does, we need all those mathematical artifacts that originate in the complex plane C, as a closed algebra, imaginary roots and all. Otherwise, we would be (mathematically) stuck in the infinitely open plane and could not escape incompleteness. String theory, although based in quantum field theory, is -- like special and general relativity -- mathematically complete.

______

I hope you and the group will forgive me for being self-serving at this point -- I have invested a lot of time and thought into constructing an alternative basis for encoding information in n-finite dimensions of space while nevertheless preserving a time metric. For this discussion, we only refer to 1.3 -- 1.10 in the draft paper linked. The table explains correspondence of the plane to the integer - 2.

All best,

Tom

Hi Jonathan,

Van Flandern's abstract reads in part: "If angular momentum conservation is invoked in the geometric interpretation to explain experiments, the causality principle is violated. The field interpretation avoids this problem by allowing faster-than-light propagation of gravity in forward time."

My essay explains why the conservation of angular momentum does not violate causality in a geometric theory of continuous functions.

Another problem with Van Flandern's hypothesis, though, is that of simultaneity. Remember that thought experimenbt where the Sun suddenly disappears, and we don't know it until approximately 8 minutes later? If it were possible for any physical influence -- including gravity -- to propagate faster than the speed of light, it would also be possible to observe action at a distance simultaneously affect two or more spacetime separated cosmic events and we would be able to observe this correlation. As it is, gravity seems to work just as Newton and Einstein described it -- as a function of mass and time reversible dynamics indexed to the speed of light.

Best,

Tom

Not so fast (or maybe faster) Tom;

The work of Jenkins and Fischbach on varying rates of nuclear decay has resulted in an interesting development. Specifically; it was found there is a seasonal dependence where the rate of decay half-life varies measurably, with a cycle that appears to relate to Sun-Earth distance. But once a greater degree of precision was achieved, it was found that this variation is also observed during a Coronal Mass Ejection or CME.

My guess is that, because these events move a significant amount of mass in a very short time, this ripples or deforms the fabric of spacetime. So if there was a discrepancy between the scalar mode and tensor mode propagation, one would expect that arrival time for such a signal would be less than 8 minutes. This is apparently exactly what is observed. Now Professor Jenkins has a Patent pending for an Early Warning System for CME events - and he even appeared on the Weather Channel to talk about it.

A topological spacetime fabric is the simplest explanation, as light travels around, while gravity acts center to center, and the ripple is felt at the sub-atomic scale.

Regards,

Jonathan

Jonathan,

I discuss the Jenkins and Fischbach data in "The Chromodynamics War" and propose that, based on my model of particle physics, it is due to solar neutrinos. I do not know what the CME mechanisms are, but if they result in an increase of solar neutrinos, this would be consistent with my model. This seems to be much simpler than "a topological space-time fabric".

In fact, I just googled and found: "Aug 30, 2010 - Jenkins and Fischbach suggest that the changes in the decay rates are due to interactions with solar neutrinos, nearly weightless particles ..."

This was what I suggested to them in 2009 when I sent them a complimentary copy of "The Chromodynamics War" upon receipt of permission to publish their data.

I'm also interested in your remarks about possible difference in the speed of light and gravity. Are there any arXiv or viXra papers on this?

Also, if you or Tom would explain the angular momentum problem, I would be interested.

And, FYI, I have gotten another competent physicist interested in Kauffmann's work. (Each one teach one!)

I don't know how you stay so up to date on these topics. Do you sleep?

Best regards,

Edwin Eugene Klingman

I just wanted to point out..

To an extent; one can draw an analogy by equating 'from the inside' with 'probing on a small level of scale' and 'from the outside' with 'probing on a larger level of scale' because the observer or detection platform always has a particular size, and there will be larger spaces 'out there' than whatever space is contained 'in here' - the space from which observations are taking place. This connects up with what Tom Ray said in his essay from last year, that observation always takes place from a center and defines a sense of toward and away.

Have Fun,

Jonathan

Hello again,

It appears that the idea for 'Rainbow Gravity' was first set out in a paper by Magueijo and Smolin called Gravity's Rainbow that appeared in 'Classical and Quantum Gravity' in '04. The most important piece of that work to the current effort and the 'Dimensional Reduction..' paper is found in the following excerpt.

"the geometry of spacetime may depend on the energy of a particle moving in it. Thus, spacetime geometry has an effective description; in the language of the renormalization group, geometry "runs." Hence there is no single spacetime dual to momentum space; the dual to momentum space is the energy dependent family of metrics."

That is; the spectral dimension D runs with the energy E we use, or equivalently with the smallness of scale we probe the dimensionality of space in, making spacetime appear 2-d as we approach a UV cutoff (toward the Planck scale) and 4-d toward the infrared, or as we approach the common level of scale. The 'family of metrics' noted in the quote above constitute the 'rainbow' of Rainbow Gravity.

More later,

Jonathan

The team of Jenkins and Fischbach attracted my attention for one reason. Nuclear disintegration are said to be random and impervious to anything. But every other spontaneous phenomenon are subjected to the local rate of passage of time!. Nuclear disintegration may be random but its rate should be subject to local time rate.

This is what I was looking for. I understand the relationship of gravity to the rate of passage of time like Unruh.(1) (Below), they are one and the same.

"A more accurate way of summarizing the lessons of General Relativity is

that gravity does not cause time to run differently in different places (e.g., faster far from the earth than near it). Gravity is the unequable flow of time from place to place. It is not that there are two separate phenomena, namely gravity and time and that the one, gravity,affects the other. Rather the theory states that the phenomena we usually ascribe to gravity are actually caused by time's flowing unequably from place to place."

From this, I was expecting time to run at different rates away from the Sun and nuclear disintegration rates to follow.

This was the basis of a gravitational wave detector I was thinking about... Passing gravitational waves (made of variations of time rate) would change in a specific way the variations in the rate of disintegration of radio-nuclide.... using particle emission time of flight to avoid temporary local time distorsions .... and coincidence detectors for direction ... The question is; how good are we at measuring short time interval? Better than "space" intervals?

Marcel,

Forgot the reference (1) to Unruh article. Here it is.

(1) arXiv:gr-qc/9312027v2 17 Dec 1993

Marcel,

Johnatan

My be h= 1.054x 10^-27g x sm^2/sec is 2-Dimensional quanta of the Universe wrapped in 3-Dimensional Space.Hint to Holographic universe...?

Yuri

Tom,

just stumbled upon this-

You wrote "If it were possible for any physical influence -- including gravity -- to propagate faster than the speed of light, it would also be possible to observe action at a distance simultaneously affect two or more spacetime separated cosmic events and we would be able to observe this correlation."

If the two events are separated by space-time then they are not seen as they were at the same time but a fabrication has been formed in which the two time separated events appear to be co-occurring in space-time. Even if the communication happens instantaneously, there will be a delay between that observed event. That's because of the space-time separation which means the two locations are not being seen at simultaneous times. The observed image is not a perfect replica of what is happening to the objects because of the distortion caused by the speed of light limitation. That's what I think anyway.

Hi Georgina,

You wrote, "Even if the communication happens instantaneously, there will be a delay between that observed event."

No. "Instantaneous" means that the two events are observed to be simultaneous. It doesn't happen, because all physical influences are communicated at less than the speed of light, making all events observer-dependent; i.e., there is some spacetime separation between any two events, such that observers in each inertial frame interpret the time of each event incident differently, and each interpretation is valid. There is no lapsed time for simultaneous events, just as there is no lapsed time between the endpoints of a beam of light.

Tom

Tom maybe I'm confused. How can *images* be -both- separated in (space-) time and observed to be -simultaneously- affecting each other i.e. happening at the same time?? I don't think they can but that doesn't mean there definitely isn't faster than light communication between the *objects*. It seems to me the separation of the images is more of a problem than the communication speed between the objects.

A question that comes to my mind is; Can the shape of the (medium of)space be changed faster than light can travel through it? If it can then there is the possibility that a phenomenon could be communicated faster than light speed.

Georgina,

You ask, "A question that comes to my mind is; Can the shape of the (medium of)space be changed faster than light can travel through it?"

What medium? Light propagates in a vacuum.

"If it can then there is the possibility that a phenomenon could be communicated faster than light speed."

That's how the worm creatures in Herbert's *Dune* series traveled faster than light -- they 'folded' space under the influence of some chemical. In the real world of relativity, however, space is not a physically real phenomenon independent of time; length contraction and time dilation guarantee that proper time seems to pass at the same rate for every observer everywhere in the universe, such that the laws of physics are uniform. One way to look at it, is that between photons at antipodal points of the universe, there is no duration.

Tom