@ John Macken

If I have understood the GW experiment correctly, then it is not the 40 kg mirrors which move, but rather the space between the mirrors which stretches in one direction and shortens in the perpendicular direction as a result of the oscillatory nature of GWs.

A wave supplies the momentum. Therefore, after the wave will pass, the rigid body will be in motion away from the source. Logical?

@ John Macken

If I have understood the GW experiment correctly, then it is not the 40 kg mirrors which move, but rather the space between the mirrors which stretches in one direction and shortens in the perpendicular direction as a result of the oscillatory nature of GWs.

@ Dmitri

The order of amplitude (strain) of the GW was 10^-21 m or so; I do not expect it to impart any significant momentum; thats why it took very sensitive instruments and so long to detect it.

No: gravitational waves are quadrupole. That's why the arms of the interferometer are aimed 90 degrees relative.

It is possible to analyze the example I proposed of a neutron star with radius of 11 km and mass of 4 x 1030 kg encountering the recently detected gravitational wave with strain amplitude of A = 10-21 and frequency of 250 Hz.  If this wave was physically displacing the entire neutron star, how much force would be required to produce the implied oscillating displacement?  The maximum displacement in time 1/ω is:    ΔL = Ac/ω = 10-21 x c x 6 x 10-4 s ≈ 2 x 10-16 m.  The acceleration is not constant, but it is on the order of 10-22 m/s2.  Therefore, using F = ma, the force required to accelerate 4 x 1030 kg is about 5 x 108 N.  Clearly this ½ billion newton force cannot be generated by the gravitational wave which had an intensity of about 20 mw/m2. 

Therefore, there is no displacement of the center of mass.  However, does the gravitational wave displace any part of a physical object such as a rod or the neutron star?  Each part of a rod can momentarily be considered to be an isolated mass that feels no acceleration from the gravitational wave.  However a physical rod has forces connecting all the molecules of the rod.  When a gravitational wave changes the properties of spacetime, then the locally measured distance between molecules changes and the length of the rod expands and contracts to correspond to the distance scale introduced by the gravitational wave. The forces expanding or contracting the rod are balanced and generated within the rod.  Therefore the ends of the rod and the surface of the neutron star are accelerated.  The next question is: What is physically happening to spacetime when a gravitational wave passes?  This question can be answered on several levels.

The gravity wave passes so quickly that most receivers and objects will just vibrate one cycle around some neutral point line or plane. There is argument about which modes of vibration occur in quadruple state and spin of 2. Best way to understand is to describe the gravitational potential in space and how the wave briefly modifies it. Energy is moving away from the source, but every mass is already gravitating toward the source. Furthermore the wave carries  gravitational energy, as shown in merging black holes. The passing wave leaves the source field weaker, which represents a decease in the acceleration of the object toward the source. In merging black holes the wave energy can be enormously larger than the source field before or after the wave passes, for example in high speed mergers where mass is lost and converted to energy.

Understanding may be gained by evaluating the wave passing by an object that is already moving near light speed away from the source. Example is super nova collapse to neutron star shortly after stellar shells are blown away at near light speed. The gravity wave passes by the relativistic mass gradually enough to generate some opinions about how the wave interacts with the mass. The net result is the ejected mass is decelerated less after the wave passes than it was before. The departing wave decreases the gravity field of the remnant. So the wave must have the properties of a gravity field. Then in addition to vibration modes that may be transverse and longitudinal, the mass shell is attracted to the wave before, during, and after it passes the mass shell. Then the net action on the mass is one cycle of a vibration around a neutral surface of rotation that is continually getting larger, leaving the shell surface geometry with a somewhat faster rate of expansion than it would have without the wave.

The center of mass is a non-relativistic concept. By this reason the question asked is not

correct.

First understand what the relation between mass and gravitation is! Already the smallest objects in universe, the massive elementary particles, such as the electrons, the positrons and the quarks interact with the local gravitation field. So what is that gravitation field. It is a deformed continuum that interacts with the elementary particles. In fact the elementary particles are point-like and disrupt the continuity of the environment, which is formed by a continuum that embeds them. It is not a steady disruption. The point-like disruption is hopping around and the landing points are forming a coherent swarm. This swarm has some extension and can be characterized by a smooth location density distribution. That location density distribution corresponds with the squared modulus of the wave function of the particle. The gravitation field is a smoothed version of the more acquit embedding continuum and reacts on the hopping dance of the point-like particle with a smooth reaction. At some distance the swarm again looks like a single point-like object. Now look what happens when the embedding continuum vibrates. The swarm will vibrate with that continuum but the smoothing will mostly flatten the effect on the gravitation field.

http://vixra.org/abs/1603.0021

If the above story is right, then mass relates to the number of hops that are contained in the location swarm and the location swarm is regenerated by a stochastic process. This process can be seen as a combination of germ creator, such as a Poisson process, that works in combination with a binomial process, which is implemented by a spatial spread function. The spread function implements a location dependent attenuation of the primary Poisson process. A Poisson process in combination with an attenuating binomial process can be considered as a new Poisson process that has a lower efficiency. If the continuity disturbance corresponds with a spherical Green's function that follows 1/r, then a Gaussian spread function will cause a smoothed potential in the form of an ERF(r)/r function. This function does not show a trace of a singularity as the Green's function does, but at some distance is behaves as 1/r.  

This gives a fairly good idea of what happens under the cover of the wave function. The covering function ERF(r)/r shows that something is underneath, but does not reveal any details. It provides a blurred picture of the point-like object and that picture is caused by the fierce dynamic hopping dance of the elementary particle. The swarm contains a very large number of hopping locations. Thus the statistical characteristics of the describing location density distribution are very stable and accurate. The inverse of Planck's constant indicates the order of magnitude of the number of hopping landing locations in the swarm. 

you need to specify with respect to what would the neutron star's CMS move. and if it does doesn't it move the entire spacetime with it? the same for the LIGO arms. the CMS does not move with respect to spacetime because there is no absolute spacetime to pin it down to. you can argue that even for the laser's photons there is no question of dislocation of the CMS of the mirrors but rather a red/blue shift in the wavelength.    

Vikash,   I agree with your answer as far as it goes.  However, the logical next question is: What is the underlying physics that allows space to stretch in one direction and shorten in the orthogonal direction? If spacetime is considered to be an empty void, then questions like this or questions of how matter achieves curved spacetime can never be answered.  Field theory says that spacetime is filled with zero point energy and the standard model says that multiple "fields" exist in space.  The next step is to characterize (quantify) the underlying physical structure of the quantum mechanical vacuum.  This will allow a complete understanding of how spacetime can increase distance in one direction and decrease distance in an orthogonal direction.  

I have written several papers and a book on this subject which are available on my RG home page.  The model of spacetime that I propose can generate curved spacetime from first principles.  This work also predicts that the distortion of spacetime produced by a gravitational wave turns spacetime into a birefringent medium which would produce a change in polarization on a laser beam.  It is much easier to detect a small polarization change than a small length change which competes with acoustic noise.     

A. M. Vinogradov is right: everyone should be talking center of momentum, not center of mass. But evidently no one understands the symmetry of a quadrupolar wave. The wave in one half-cycle squeezes in one direction and simultaneously stretches in the perpendicular direction. And in the next half cycle the reverse. So of course the center of momentum doesn't move.

James,  I have tried to think of examples where the center of mass differs from the center of momentum. I believe that all rigid objects, no matter their shape, have the same center of mass and center of momentum.  Can you give examples which require this distinction?  

Several previous answers agree with your description of a gravitational wave.  In the paragraph explaining my question I say. "A 'no' answer must explain how the distance between two interferometer mirrors changes without any displacement of the center of mass of the mirrors." Do you have any explanation for how this is accomplished?

John  --  Center of momentum would differ from center of mass if the body was significantly accelerated. So I suppose that excludes most bodies larger than atomic size. But if you consider composite bodies in a gravitational bound state (3 or more), you might find some difference between the two centers.

As to LIGO, it's not a single body. Each mirror and the emitter/ detector are anchored to the earth, presumably with damping mechanisms. The distance would change because the earth moves. If we had a LIGO in space you could think about a center of mass but I really don't see how that's relevant. Even in space the arms would participate in the oscillation induced by the quadrupole wave. I believe it's been calculated that maximum emission for 2 black holes would be in the polar directions, perpendicular to the plane of their orbits so it would seem the wave-length of the emissions would be related to the distance between the two. I don't know enough GR to figure how they calculated the black hole masses.

It seems I introduced a lot of paraphernalia. It amounts to this: no masses need be involved because general relativity makes gravitation into a space effect.

James,

Briefly yes. The Earth's motion is also not relevant.

James,

Our living space is a field and massive objects act as discrete items whose embedding disturbs the continuity of the field. It is also possible to use another view. Consider a coherent swarm of locations. The number of locations is huge. The location density distribution that describes this swarm can be seen as a part of the field that embeds the swarm. Thus, the continuum is a descriptor of what happens underneath its smooth cover. Now reduce the swarm to a single point-like element. In that case the disruption of the field is described by the Green's function of the field. The effect of the coherent swarm is that the effect of the Green's function is blurred to a much broader spread function. Unlike the green's function that spread function does no longer represent a singularity. Now two views are possible. One view focuses on the field and the other view looks to the swarm that corresponds to a deformation of the field that describes the swarm. In this way it is not important to analyze what is responsible for the cause. Neither the swarm, nor the field can exist without the other. The two items and the corresponding phenomena are intensively coupled. What is required is a methodology that describes the coupling between the two views. That methodology uses summation, differentiation and integration. The integration involves a convolution with the Green's function and the Green's function is a solution of a non-homogeneous second order partial differential equation. In multiple dimensions this methodology has still not completely matured. Studying this situation reveals unexpected results!

The answer is in the question. The gravitational field alters the weight, but not the mass. Thus the center of mass doesn't change.

It is interesting, but why does electromagnetic wave indroduce pressure and gravitational wave not?

Eugene,

In my opinion photons move in the same field in which gravitation waves move. They do not represent oscillations of the EM field.

Hans,  I have written 2 papers which support your statement that "photons move in the same field in which gravitation waves move."  I have proposed a new constant of nature which I call the "charge conversion constant".  It has units of meters/coulomb and it converts the unit of coulomb to a distortion of spacetime.  This conversion has passed every test that I have been able to devise.  In particular, when the impedance of free space Zo = 377 ohms is converted to a property of spacetime it becomes Zs = c3/G which is the impedance of spacetime experienced by gravitational waves.  This implies that photons propagate in the same "spacetime field" as gravitational waves. You can read about this in the attached paper starting on page 13. 

Eugene, The intensity of the detected gravitational wave was about 20 mw/m2.  If all of this was absorbed or reflected by bosonic matter, then it would exert the same pressure as light with this intensity.  However, gravitational waves experience the impedance of spacetime Zs= c3/G = 4x1035 kg/s.  This impedance is more than 25 orders of magnitude larger than the acoustic impedance of tungsten.  The gravitational waves pass right through matter with almost no absorption or reflection.  There is a slight reflection, but it is such a small effect that it is far below the theoretical detectable limit.   

Chapter Spacetime Based Foundation of Quantum Mechanics and General Relativity

John,

It is interesting that Zs = c3/G according to Blair et al. I didn't find anything about it on the Internet. Could you please provide the details how this calculus has been performed?

Thierry,    Sorry that it has taken me 5 days to answer your question.  I am on a trip.  It is true that Blair does not show the derivation of the impedance of spacetime: Zs = c3/G. It is mentioned both in has 1991 book and his 2012 book.  I independently derived the impedance of spacetime by comparing an equation for the intensity of an acoustic wave to the intensity of a gravitational wave.  The equations that I compared are in section 2.1 in the attached paper.  It is obvious that the gravitational wave equation has an amplitude term, a frequency term and c3/G must be the impedance term. This also has the correct units for impedance when amplitude is a dimensionless strain amplitude.  There is no doubt this is the correct impedance of spacetime because I have used it over 100 times in various analysis equations and it has always yielded correct results. 

Article Energetic Spacetime: the New Aether

Pretty darn close to the precise solution. I suggest considering the photons as a latency to the actual monopoles (gravitinos/tachyons)  that cause the inertial action to start on the quantum level in the object in the path of the advancing waves, far in advance of the photons being observed on a real-time scale for any observer. As far as electromagnetic effects, these are then secondary, and much slower wavefunctions to emerge. Since we don't observe the monopoles presently, lacking technical expertise,, the only real-time measurements we have mislead us a bit.

@ John: thank you for the details. Whatever the real meaning of the Plank scale could be, the space energy would then be in the order of 10^51 kg/m³ equivalent, while a proton has a density of the order of 10^-24 kg/m³.

If one considers the equivalent mass of the energy of a small ripple on the surface of water, compared with the water's density, that could give quite comparable results...

John and Thierry,

In the attached file is the “impedance of space time” (in a simple way) derived in the context of gravito-electromagnetism.  I start from the description of the gravitational field of an harmonically oscillating point mass (§6 - p. 66,.. in “Gravitation explained by the theory of informatons-2) .  

Article GRAVITO-ELECTROMAGNETISM EXPLAINED BY THE THEORY OF INFORMATONS-2

Yes, Thierry, I also think that all these particles are only ripples.

Regards,

Eugene.

Antoine: Great work! The gravitomagnetic approach indeed has proven its utmost high accuracy in solving the gravity issues.

I would just point out that the work of Tajmar and of Arbab in your references, as well as your section 5.2.3. are in contradiction with the sound methods that were used by Heaviside and by Jefimenko. Moreover, Tajmar's and Arbab's works are mutually contradictory w.r.t. Mercury's perihelion advance.

The correct interpretation of the Special Relativity Theory is explained in a full chapter by the late Jefimenko. He did not find the way to explain Mercury's perihelion advance by solely the solar system and by using GEM. However, when taking into account the motion of the solar system in the Milky Way, Mercury's perihelion advance can fully be explained by GEM without any artifices.

http://www.amazon.com/Electromagnetic-Retardation-Theory-Relativity-Classical/dp/0917406257/ref=asap_bc?ie=UTF8