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We review by dimensional analysis what is necessary for a variation in gravity as to the change in gravitons due to an explosion of a matter sample created by a laser. This is the template as to a graviton induced variation experiment. This is complimentary to work done with Dr. Baker as far as modeling a spinning barbell experiment impacted by Laser pulses which was accepted as a presentation in STAIF II, in April 2015. This document is in terms of an implosion of a pellet of matter leading to a subsequent explosion instead of a spinning barbell.

We first supply a dimensional analysis of what the necessary ingredients are to obtaining the flux of gravitons from a laser hitting a target, with a given power. The idea is an adaptation of a problem in a book written by [

Lightman et al. [^{−3} seconds.

Lightman et al., [

It should be understood that the relevant parameter is, that the energy be sufficiently strong so that there would be a way that the gravitons would be detectable. The issue is of flux, and that is over a surface area. The flux would be definable in the following manner. The number N defined above, to first approximation would be in a circular sphere, with a surface area of

If the radius were say of 2 meters, then the relevant division of presumed gravitons in a detector screen of one meter, squared, would be of the order of

Equation (2) is, if we assume a 1-meter, squared graviton detector screen, the simplest view, FLUX. i.e. this is graviton flux, per square meter, and from that we go to the issue of what the energy

According to [

It is in our interest to make the power, P, as large as possible, presuming ^{−5} seconds in duration. i.e. almost a delta function spike of power, being supplied, hitting a sample, with a laser.

Doing this, requires, then that re revisit Equation (1) and Equation (2).

If Equation (1) and Equation (2) are legitimate, with an effective presuming ^{−5} seconds, with the P, being very large, then what we are looking at is, if time

It really depends upon the effective power, P, delivered, presumably to initiate an explosion, at a site, plus the duration of the laser beam with a target, given by

Presumably, if the cross sectional area, of the detector is smaller, then Equation (4) would have a smaller value. This though, is the clearest derivation of all the relevant physics, via dimensional analysis, needed to initiate an inquiry as to this problem. We assume that Equation (1) and Equation (2) are effectively local variation of gravity, assuming gravitons are commensurate with GW and gravity itself. We will then, after looking at Equation (4) get to the matter of variation in gravity next.

From the book written by [

Integrate this, between two band widths of frequency for the graviton, or for a very narrow graviton frequency width

Note that ^{9} Hz, that if there is a boost in temperature, call it T increased that there will be a corresponding boost in the magnitude of Equation (6) above. To do this, we reference what Dr. Baker has suggested to the author, as far as variation in gravity [

Our job is to determine the quantity,

Note that our first approximation is to set up how to come up with a base line calculation for what we call

First, we look at

We should note what happens if the power, P, as given above in Equation (4) is given by the expression given by Dr. Baker [

Then we are looking at, if we have 2.95 times 10 to the 13^{th} Hertz for graviton frequency,

This is TINY. It is necessary, then to get more experimentally useful results via applying a power expression for Equation (11) which is substantially larger, i.e.

Then,

Assume then that the process is going on for about

Divide by

If one has a value of power, say

then one will have, instead,

We are assuming, for the purpose of our analysis, that we are working with Equation (14) in a 10 to the minus 3 interaction, with the result that one is looking at a temperature increase, due to power, as given above, in Equation (11) of the order of, if using forms similar to Equation (8) so one obtains

if we use an applied power given by Equation (11), so then that in 10 to the -3^{rd} seconds we get Equation (18) below.

Then, we have that if there are 2 times 10 to the 5^{th} gravitons entering a 1-meter squared surface area,

Then the assumption is, if we have a brief increase of gravity, due to 10 to the 7^{th} gravitons being produced, radially, is that there would be the following value of gravity increase, i.e. 10 to the 1^{st} power increase in local gravity due to increase of local gravitons given by, if we assume a frequency for the gravitons averaged to about 10 to the 13^{th} Hertz

Then to first approximation one could write:

Equation (20) put in with Equation (7) will, if there is a 10 to the −3^{rd} second interval where there are approximately 10 to the 5^{th} gravitons entering a 1-meter squared detector, 2 meters from a pellet, resulting due to a temperature increase of the order of Equation (17) above. This value of a length, given by Equation (20) with 2.95 times 10 to the 13^{th} frequencies associated with the graviton cold, is detectable. The 100,000 or so gravitons, if detected, lead to new ways to model gravitons, as opposed to our present very crude models. The author, with Dr. Baker looks forward to the implementation of such an experiment, in the coming year. The variation in local gravity expected would be approximately 10 times the average surface gravity value of 9.8 meters per second, squared.

As can be related, this analysis is meant to be complimentary to work which the author did with Dr. Baker, in modeling a laser driven torque of a barbell, i.e. the author finds that the barbell will, as a spinning rod [

The disadvantage of the method brought up in this document is that there may be in a period of micro seconds up to 100,000 or so gravitons generated, i.e. this would put a premium upon ultrafast electronics and signal processing, i.e. could a detector be able to process graviton flux that fast?

It is an open question.

The rotating dumb bell, while it could go on up to seconds of operation may have problems of stochastic noise, and this has been brought up by Dr. Li with Dr. Beckwith, as of November 2015. Needless to say, the author has had extensive discussions with laser theorists whom informed him that the TIMING of laser pulses up to 10^{−5} seconds separation between tapping the ends of a rotating rad, can be technically performed, and that with extensive R and D that there is no question as of the ability of laser technicians to perform the tapping of the ends of the dumb bell visualized in [

IMO, the disadvantage of the implosion/explosion of the target hit by the laser would be in evaluation of a flux of 100,000 or so gravitons in an extraordinarily short period of time.

The disadvantage of the rotating dumb bell may be in stochastic noise, i.e. making a noisy signal, i.e. both methods are feasible and would put a premium though upon R and D for extremely precise engineering.

Beckwith, A. (2017) Variation in Gravity Due to Laser Inducing an Explosion―Comparison with the Spinning Barbell Driven by Lasers. Journal of High Energy Physics, Gravitation and Cosmology, 3, 558-563. https://doi.org/10.4236/jhepgc.2017.34042