SmithWillSuffice said:
I wonder why this topic got bumped into "Strings, Branes, & LQG"? I guess the geometrical background-free aspect of Heim theory bears a vague relation to LQG?
For my 2cw, I agree with Hdeasy's earlier posts: that the fundamental physics of Heim theory is far more important than the hyperdrive application. You have to be dreaming if you think that concept will be tested any time soon. NASA have enough problems getting conventional propulsion systems tested like NEP systems. If someone can indirectly validate Heim's ideas by demonstrating a working gravitophotonic propulsion system then all fine and good, but I doubt that will be the first test of the theory.
My money is on some brave physicists reworking Heim's mass formula and particle lifetimes using concepts that are more familiar to most physicists than those used by Heim and the Innsbruck group.
Another interesting piece of speculation was the report (unconfirmed) that I read in either the NewScientist piece or at the heim-group website or elsewhere, that claimed that discretization of spacetime is required, but it was unclear whether this is something that follows from the assumptions of Heim's structure theory or whether it is itself one of the assumptions, if the former then that'd be really interesting.
A further puzzle was that the NS article mentioned that Heim originally proposed 8 spacetime dimensions but then settled for 6D. Later on it is reported that Walter Droscher revived the gravitophoton propulsion idea using 8D. Then I see there's a report by a guy named Gary Stephenson (apparently a gravity-wave theorist writing for a consultancy called Seculine) that refers to a 12D theory, where there are 4 "non-metric" dimensions, whatever that means(?).
What someone really should do is write a better plain English description of Heim's structure theory. For instance, what exactly are the "particles" in his theory? If they are elements of geometry and not just abstract wave-functions or fields on a background spacetime then it should be possible to explain what the heck they are. Are they like 3D knots of flux tubes embedded in 6D or 8D spacetime, or are they more general topological structures? How does charge arise? If electric fields are simply attached to Heim's spacetime as extra fields as in the old geometrodynamics a la Misner-Wheeler then that would be extremely ugly don't you think? If not, then what's the difference between Heim's ideas and Kaluza-Klein models? Surely if Heim is saying that all physics is just higher dimensional geometry then a reformulation of his work using modern Kaluza-Klein pictures should be possible I would imagine. If not then there's got to be a point of departure that can be used to start attacking the problem of clarifying Heim's ideas.
Similarity to LQG: not only the geometrical background-free aspect, but also Heim's metron lattice is very like the spin lattice of LQG.
All the physicists working on Heim theory now are trying to re-formulate it in concepts more familiar to most physicists. E.g. instead of his 'selector calculus', which is form of
integer differencing as opposed to the usual calculus, the latter is being substituted for the former almost everywhere - only down around the Planck scale is the differencing method needed to avoid singularities. On the discretisation of space: Quoting Heim-theory.com:
"From Heim's computation of two extremum principles on the gravitational field quantum of a smallest mass, the product of two lengths resulted as a natural constant. This smallest surface is the square of the Planck length, which was also determined by Treder (1974) (Treder, H. J. 1974: Philosophische Probleme des physikalischen Raumes, Berlin: Akademie-Verlag) , and which is referred to by Heim as the Metron. Heim was the first to draw the conclusion from the discovery of this natural constant that this two dimensional element makes calculation with area differences necessary and thereby justifies 'Metron calculus' ". For details of the reasoning that Heim used, further reading would be needed - or maybe ask Dröscher himself!
As for the number of dimensions - the full exposition does require 12 dimensions it seems. Roughly speaking, the number should be a multiple of 4 as tensors with 2 or 3 indices over Einstein's 4-D space are involved. So 8 or 12 are prime candidates. In the 8-D version, the energy density tensor has only 36 non-zero elements and so Heim justifies restriction to a 6 x 6 space. 6 x 6 is enough for the mass formula derivation. Quoting Hauser & Droscher "The dimensional law derived by Heim requires a 12-dimensional space, but the additional four coordinates are needed only in the explanation of the steering of probability amplitudes (information)."
Particles are stable distortions in the metron lattice - the 'condensation' that results in a particle involves projection from 6 dimensional structures on 4-D. I confess that the details of this are hard to understand and I haven't got that far yet. Charge is associated with a partial-metric: the full metric is a 'poly-metric', with the normal g(i,j) of gravity and others for the other forces. That part is rather elegant and not at all 'ugly'. Heim acknowledged Kaluza-Klein theory as having the right idea. Only for Heim the extra dimensions are not compacted - there are 3 normal space dimensions, 3 time-like dimensions (including normal time) and the rest of an 'organisational' nature, having to do with quantum probabilities etc.
Von Ludwiger is working on transcribing tapes of Heim speaking on all this (in German admittedly) and wants to then have it translated into English and published as an
introduction. Apparently when he talks about it, it's much easier to understand where he's coming from.
Apropos: does anyone have an idea about publishers might be interested in that?