Some comments. (Yes, I am a physicist, no I am not a gravity theorist or cosmologist or string theory person who would have active expertise in the
area).
1) Apparently in the description of the theory by Droescher and Hauser, the existence of the "fifth force" (what this really is) is not the same as
the existence of the "parallel space" which is far far more speculative, in my opinon.
2) The structure of the theory is very much unlike that of the string theories, and given that it was originated in the 50's and 60's it very likely
does not include the experimentally observed particle interactions since then, e.g. QCD.
From what I can read, D&H describe a *classical* field theory, "general relativity on steroids and crystal meth", and then assign the all the new
geometric cross terms between the normal metric tensor as "forces". It's very unclear that they actually reproduce the real thing as we know.
But where is the quantization??? That was always the hard part, getting GR to play nice---and this is just making GR all that more complicated.
Perhaps the Heim theory is a classical approximation to the true underlying quantized Theory of Everything (strings or whatever). If it's real,
then it would be extremely useful---the weak gravity (Newtonian limit) of the theory would be more on the level of Maxwell's equations than QM;
something fabulous. If if if it's real.
3) According to D&H it predicts a direct effectively new electromagnetic interaction: photons have the usual scalar potential, vector potential
(classic Maxwell-Einstein electromagnetism) plus a new tensor potential.
In Dröscher and Hauser (2004) an experiment was suggested to measure the gravitophoton force. Above a stationary
superconducting magnetic coil there is a rotating torus like a flywheel of some 100 kg. Due to the Heim-Lorentz
formula, Eq. (15), there should be a gravitophoton force generated in the rotating torus. From the Lorentz
force, F=q Eq vT×B , in our experiment vT denotes the velocity of the rotating torus), there follows the existence
of a scalar electric potential ϕ and a vector potential A with components Ai=0Qvi /R where Qvi denotes
the total current in the magnetic coil and i=1,2,3. However, as can be seen from Eq. (7), the metric tensor for the
photon comprises an electric potential, a vector potential, and a tensor potential, representing a new force applying
the geometrization principle of Einstein to Heim space H8. The complete electromagnetic interaction is therefore
given by a 4-dimensional tensor potential (ϕ, Ai, Aik) with i,k =1,2,3. The tensor potential plays a crucial role in
providing the acceleration concept by converting photons into gravitophoton pairs as will be outlined in the following
section.
Holy cripes Batman. Classical electromagnetism is so extremely well tested it would appear to be beyond reasonable that there was something missed
there all along, unless one can make an argument why the new force would be extremely small in all normal circumstances---which would make it
exceptionally difficult to use for any useful engineering purposes.
What are the problems? Well, if there is a new potential field then all sorts statistical mechanics relating to electromagnetism, e.g. photon gases,
woudl be wrong since energy would surely be leaking into the new degrees of freedom. We would have noticed---it would be as if photons had additional
degrees of polarization (this time in a higher order space than the conventional one). It would seem that you couldn't add up (E^2+B^2)/2pi and say
"there's the electromagnetic energy". Capacitors might have more capacitance. Would classical E&M have a nonlinear interaction? Then photons
would scatter off themselves and radio waves would self interfere. All sorts of things would be wrong, and yet our experiments work extremely well.
The real killer: QED. QED has been verified stupendously precisely now, and it adds up just simple interactions of point spin 1/2 electrons and
photons. If photons had all sorts of new effective polarizations the computations wouldn't be right as there would be many more Feynman diagrams to
include. There would have to be a good reason why these other interactions are usually so small---and that makes it insanely difficult to engineer.
On the upside: maybe these degrees of freedom relate to the the "dark energy field" seen cosmologically which is presently utterly inexplicable, as
is the tiny Pioneer 10/11 orbital anomaly.
The D&H paper skips enormous steps between assertions which are just as well explained as "and then another miracle occurs so that..."
4) Just because you somehow are in "parallel space" doens't mean that the stuff in interstellar medium goes away---presumably particles of matter
have instantiations in all the spaces and so you will be running into them at titanic speeds causing massive radiation damage to any crew.
It may be possible to make Luke Skywalker's floating landspeeder, but not interstellar warp travel.