^{*}

We are reviewing Freeman Dyson’s paper which alleged that detection of gravitons via LIGO, or by outer space experiments (due to probabilistic calculations which we review in the document), an impossibility. The disagreement we have with Dr. Dyson is that his probability calculations are taking place in almost infinite spatial domains, which renders the detection protocols, using his probability scheme, impossible. After we summarize the Dyson outer space arguments, and how Dyson got them, we will refer the reader to the very strain calculation done in the referenced PRD article, so cited, as to how a nuclear weapon could generate GW, and then afterwards, refer the reader to a 2
^{nd} paper, of how Tokamaks could detect GW/ Gravitons, as detectable by the 3DSR effect. Nowhere are we suggesting DETONITION of a nuclear device to generate GW! The reader is referred to another Li
*et al.* PRD article, 2008, as to 3DSR, as to how detection of GW/Gravitons could occur due to something other than the Gertenshehtein effect, in this paper,
*i.e.* they can look it up, and then in a 2
^{nd} follow up paper learn how a Tokamak could be utilized to have a finite sized geometry, for using the 3DSR effect for GW generation. The first paper highlights how if one assumes that only by use of infinite spatial geometry, and by using only the Gertenshehtein effect, that indeed one can convince oneself as to not bothering with the very real prospects of earthbound generation of Gravitons and GW, and that in doing so, GW research will be strictly limited, even with the outstanding results of LIGO, which in no way should be criticized. The entire analysis makes the case that foundational research as to the nature of GRAVITY means moving beyond the mental limitations place on GW/Graviton research by Dyson’s 2009 paper.

Our paper is dedicated to two hypothesis. i.e. that if one initially evaluates gravitons as interacting in magnetic fields in an infinite spatial domain, that the supposition given by Dyson, in [

Secondly, we also state that Dyson, in making this construction has by default refused to consider Earth bound generation of Gravitons, and that in doing so, by selection bias, has negated measurement protocol which would not use the Gertenshtein effect, and that all Dyson has done has to shut the door by insisting upon only using Outer space generation of Gravitons, while not considering surface bound generation of Gravitons and Gravity waves. We state this in passing as a bridge to the 2^{nd} paper following this one, which will be to be to elaborate upon what is touched on in [

Later, in a 2^{nd} paper after this document we are examining graviton production in a finite sized device cavity, as stated in [

Why are we doing this? In a word, Dyson has in [

This selection bias as to GW generation and possible graviton detection due to experimental conditions not involving extraterrestrial generation of GW/Gravitons is shown to be counter intuitive, since as proved in [

From [

The possibility of producing gravitational radiation with nuclear explosives rests on the fact that the detonation of an asymmetric distribution of explosive would produce a rapidly varying quadrupole moment. As a hypothetical example, suppose one could arrange to detonate a mixture of deuterium and tritium in a cylindrical shape.

Preliminary investigations with say a .5 megaton blast give a crude strain value of h ~ 10^{−28} or so. This value of the strain is right in this PRD document.

What the author did, via back of the envelope calculations was to determine that a 15 megaton blast would have instead strain value of h ~ 10^{−25} to h ~ 10^{−26}.

I.e. in the case of Castle Bravo, 1954, which was a 15 megaton device if one had interferometer based gravitational wave detectors on standby it is not at all inconceivable that gravitational waves could have been detected decades before the 2016 announcement of GW.

The 3DSR measurement machine for GW according to Dr. Li allegedly has a h ~ 10^{−25} to h ~ 10^{−26} strain sensitivity. This was given to the author in numerous discussions with Dr. Li, in person, the last time being in December 2015, when the author was shown schematics of the 3DSR as planned by Dr. Li for deployment [

A referee objected to referencing [

Having said that, it is time to begin the review of the Dyson analysis, and to show its limitations.

Dyson in [

I.e. we emphasize that this only is relevant toward the analysis of extra-terrestrial generation of GW which is ignoring the evidence in [

Finally, we mention an error in Dyson’s argument against LIGO, in which he incorrectly rendered the value of gravitational constant G, times 1 solar mass, divided by the speed of light, squared as equal to about 10^{−}^{33} centimeters. The correct value is 1.5 kilometers.

The upshot, in all of this is that Dyson has mentally ruled out even considering earth bound experiments which could generate GW, and this in spite of [^{nd} follow up paper, to this one, which is the sequel to this document.

We will briefly report upon Dyson’s well written summary results, passing by necessity to the part on the likelihood of the Gertsenshtein effect occurring in a laboratory environment [

In general relativity the metric g_{ab}(x, t) is a set of numbers associated with each point which gives the distance to neighboring points. i.e. general relativity is a classical theory. By necessity, perturbations from flat Euclidian space, are usually configured as ripples in “flat space”, which are the imprint of gravitational waves in space-time. Our paper is to first of all give the probability of a pairing of photons to gravitons linkage, the Gertentshtein effect, as to how the signatures of a perturbation to the metric g_{ab}(x, t) is linkable to photons and vice versa. The Gertentshtein effect is linked to how there is a linkage, signal wise, between gravitons and photons. To do so let us look at the Dyson criteria as a minimum threshold for the Gertentshtein effect happening [

The propagation distance is given by D, the magnetic field by B, and the frequency of gravitational radiation is given by

Realistically the magnetic field is tiny and reference [

In the case of astronomical effects, he is effectively precluding ANY detection of gravitons, since the magnetic fields would be tiny. Furthermore the entire effect, above depends upon a photon to graviton conversion effect. Needless to say that in practical details Equation (3) would be less than 10^{−10} in value if Dyson’s initial assumptions about D and B held. However, there is a contradiction which shows up as follows.

The end result of the Dyson analysis is that only if one has ultrahigh frequencies will the last Equation (2) probability vanish. I.e. If one has such a high frequency, as given by Dyson, the of course, Equation (2) P would then be close to zero.

The question is, does Dyson’s Equation (2) make sense? Note that all it is assuming is ultrahigh frequencies; i.e. Dyson picked the values of B and also the picked value of

make the probability for the Gertsenshtein effect as almost non existent, even if Equation (1) were satisfied.

The question is, why did Dyson pick such an enormous initial frequency

Secondly, in finite spatial geometry, we would have to go to 3DSR, as Equation (2) would effectively force the probability to zero, since D would be tiny. So, this is why the 2^{nd} paper uses the 3DSR paradigm for evaluation of GW/graviton physics [

Does that last sentence make sense? Seriously.

We now review the particulars of Dyson’s analysis of the Earth as a GW detector [

In this formulation of gravitons hitting the surface of the Earth, using Dysons numbers, he claims that only 1 graviton out of 10 to the 32nd power of gravitons can be detected by the Earth’s surface, assuming a graviton has about a kilovolt of energy i.e. this is, in its heart a situation where Dyson [

From the LIGO foundation and the Advanced LIGO PROJECT BOOK [

From the Advanced LIGO PROJECT BOOK in reference [

Quote: From the Advanced LIGO PROJECT BOOK [

BH + BH mergers and ringdowns: When rapidly spinning BH’s collide, they should trigger large-amplitude, nonlinear oscillations of curved spacetime around their merging horizons. Little is known about the dynamics of spacetime under these extreme circumstances; we can learn about it by comparing LIGO’s observations of the emitted waves with supercomputer simulations. Advanced LIGO can detect the merger waves from BH binaries with total mass as great as 2000 solar mass to cosmological redshifts as large as z = 2.

We next will describe the signal strength of the Advanced LIGO device. Once again, note that has amply shown that the signal strength formulation in Equation (5) works superbly.

The signal strength of LIGO as given by LIGO in reference [

Here, r is the distance of this gravitational generation from the detector, and v/c is the ratio of say objects within the gravitational detector, and the speed of light. Usually, v/c is much less than 1. Equation (5) is particularly relevant to the problem of inspiraling black holes falling into each other, and so, now with this, we should review what Dyson had to say about gravitons, and GW, as well as LIGO.

Right before Dyson’s section 4 in [^{15} Hertz [^{−41} square centimeters per gram. For LIGO, the frequency range is about 10^{2} Hz for two black holes inspiraling into each other, not 10^{15} Hertz, so the option of having a single graviton displace an electron from an atom, is zero. Which leads us to consider the relation given by Dyson, as his reference [

If M is the mass of the sun, then the L.H.S. of Equation (6) is 1.482 times 10^{3} meters, i.e. roughly 1.5 kilometers, or approximately a mile. Assume that then we wish to compare Equation (5) with Equation (6) with a value of V/c ~ 10^{−3}, we obtain that two inspiraling black holes with a strain value of h ~ 10^{−22} are about 1000 light years from Earth, for two black holes , combined mass of about one solar mass.

Note again, that reference [

Ultimately the following would have to be investigated, if we wish to know if Gravitons

have mass, and how this would affect measurement of gravitons [

Equation (7) defines the range of values for graviton mass which need to be considered. i.e. the interesting point is that Pre-Planckian gravitons would be massless whereas the later day gravitons would have a small mass, and the point of transition between the two forms of graviton mass would likely influence the relic conditions which would show up in choosing between the alternatives given in [

This would be a great refinement if verified in the determination of the foundations of gravity, and also is integral to the 3DSR inquiry which would show up in the 2^{nd} paper, as to GW and Gravitons which involves Tokamaks.

We also leave open, the possibility of massive gravitons as given by [

Having said that, we urge the readers to review the 3DSR Tokamak document next.

This work is supported in part by National Nature Science Foundation of China grant No. 11375279.

The present document is presented to JHEPGC, on account of the refusal of Hindawi, in particular Advances in High energy physics to heed the recommendation of two invited Editors, for inclusion of this document in a special issue of Quantum gravity and applications. Contrary to the wishes of the two invited editors for the special edition, Advances in High energy physics authorized. Due to a violation of protocol, by Advances in high energy physics, this document and its companion piece was pulled from Advances in high energy physics and re submitted to the JHEPGC journal. This is due to Advances in high energy physics refusing to follow journalistic review protocol and micromanaging the acceptance of this document when in fact it was deemed worthy of acceptance by the invited editors.

Statement as to there being no conflict of interest: The author declares that there is no conflict of interest as to the publication of this document to the best of his knowledge.

Statement being that there is no conflict of interest due to the support of the National Nature foundation of China for the publishing of this document.

Beckwith, A.W. (2017) Part 1: Possible Graviton Detection, for Outer Space Treatment of the Gertenshehtein Effect. i.e. Dyson’s Construction/ Analysis Does Not Precludes Earth Bound Generation of Gravitons. Journal of High Energy Physics, Gravitation and Cosmology, 3, 1-8. http://dx.doi.org/10.4236/jhepgc.2017.31001