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If spacetime has mass, physically occupies three dimensional space

and is displaced by matter are Einstein's gravitational wave and de Broglie's wave of wave-particle duality both waves in it?

Does spacetime having mass relate general relativity and quantum mechanics

If spacetime has mass is the "missing mass" the mass of the spacetime connected to and neighboring the matter which is displaced by the matter?

is the state of displacement of the spacetime the physical manifestation of curved spacetime?

If spacetime has mass is the state of displacement of the spacetime the physical manifestation of curved spacetime

Clarification, please: How can spacetime, having four dimensions, physically occupy three-dimensional space without also occupying time?

The best current understanding of the way matter displaces spacetime is Einstein's gravitational equations, and it is my understanding that the distortions predicted by these equations are already known, and do not include the "dark matter" that has not been accounted for. Dark matter remains unexplained, but Einstein's equations for the distortion of spacetime by matter do not account for it. To account for it, they would have to be revised, but such a revision would in all likelihood result in a form in which the additional displacement, which you would interpret as dark matter, would be symmetrically distributed about existing visible matter (at rest with the observer, or symmetrically distributed with respect to both its energy and momentum if moving with respect to the observer). A key question therefore is: Is the distribution of dark matter in the universe, as observed by astronomers, consistent with such a relationship with visible matter?

Whether or not spacetime has mass really has nothing to do with the statement that follows, which basically is self-verifying simply by reason of linguistic redundancy.

The Milky Way's halo is lopsided because it is moving through and displacing spacetime, analogous to a submarine moving through and displacing the water.

The faster an atomic clock moves through spacetime the greater the displacement of spacetime by the clock the greater the pressure exerted by the displaced spacetime toward and throughout the clock the slower the clock ticks.

Gravitational pressure is the pressure exerted by the displaced spacetime. The Earth displaces spacetime. The displaced spacetime pushes back and exerts pressure toward the Earth.

QuoteThe Milky Way's halo is lopsided because it is moving through and displacing spacetime, analogous to a submarine moving through and displacing the water.Then presumably, we are able to calculate the speed of the Milky Way (that of its center of mass) with respect to the spacetime through which it is traveling. Meaning, if that is so, then we know how to come to a state of rest with respect to spacetime. That presumably would be an absolute zero of velocity, at least as it applies to our local vicinity. If there is an absolute zero of velocity, then is or is not the speed of light seen to be the same for all inertial observers regardless of their speed? And if it is the same for all inertial observers, then how can that be reconciled with the idea that light is the propagation of a wave in the spacetime that has a definite fixed state of rest?

Quote The faster an atomic clock moves through spacetime the greater the displacement of spacetime by the clock the greater the pressure exerted by the displaced spacetime toward and throughout the clock the slower the clock ticks.Then if I am moving along with the clock, spacetime exerts more pressure on me than an observer fixed at "rest", so that my time will be slowed like that of the clock, and the clock will seem to be to be running normally. One problem, however: according to your analysis of the Milky Way halo, spacetime has a definite state of rest, at least as pertains to the vicinity of the experiments in question. Therefore, an observer back on the "ground" who is at rest with respect to spacetime, is experiencing less pressure from spacetime than is the observer moving with the flying clock, and therefore his time will be running faster, because it is not pressured. And, I who am flying with the flying clock should observe his clock as running faster than mine. One problem: Einstein's equations as well as experiment say that's not the way it is: To me who am flying, the ground clock will seem to be running slower, not faster, than mine, even as mine seems to the ground observer to be running slower than his. This contradiction cannot be resolved if spacetime has a definite state of rest.

"Relative to the atomic time scale of the U.S. Naval Observatory, the flying clocks lost 59+/-10 nanoseconds during the eastward trip and gained 273+/-7 nanosecond during the westward trip"

QuoteGravitational pressure is the pressure exerted by the displaced spacetime. The Earth displaces spacetime. The displaced spacetime pushes back and exerts pressure toward the Earth.This is a different phomenon than when spacetime allegedly exerts pressure on an object moving with uniform speed. The Principle of Equivalence declares that gravitational effects are indistinguishable to the affected observer from those produced by acceleration.

Does spacetime have mass?No.

If spacetime has mass, physically occupies three dimensional space and is displaced by matter are Einstein's gravitational wave and de Broglie's wave of wave-particle duality both waves in it?

Does spacetime having mass relate general relativity and quantum mechanics?

The spacetime displaced by the Earth pushing back and exerting pressure toward the Earth is constantly pushing against you and keeping you 'tied' to the Earth.

Note: Your question is very poorly worded. So bad that its hard for me to understand what you're asking. Can you please reword it for me? Thanks!

This implies that the Earth is orbiting through this spacetime, and pushing this spacetime aside keeps you and the atmosphere fastened to the Earth (what we call "gravity").But here in the antipodies, I have a problem. If this spacetime is pushing you towards the center of the Earth, then it must be sucking me off the Earth (and sucking away the atmosphere over my head, too).But when my class did the experiment in high school, we worked out that objects fell with an acceleration of about 10m/s^{2} (with a significant measurement error, as I recall). But pretty much what you would measure other places on the Earth.So I don't see how pushing spacetime aside can account for gravity... (unless you also believe in a flat Earth?)

"Imagine the Earth as if it were immersed in honey. As the planet rotates, the honey around it would swirl, and it's the same with space and time," said Francis Everitt, GP-B principal investigator at Stanford University.

In Special Relativity, changes in space-time, due to velocity, will generate changes in relativistic mass.

"It is shown that the force exerted on a particle by an ideal fluid produces two effects: i) resistance to acceleration and, ii) an increase of mass with velocity. ... The interaction between the particle and the entrained space flow gives rise to the observed properties of inertia and the relativistic increase of mass. ... Accordingly, in this framework the non resistance of a particle in uniform motion through an ideal fluid (D’Alembert’s paradox) corresponds to Newton’s first law. The law of inertia suggests that the physical vacuum can be modeled as an ideal fluid, agreeing with the space-time ideal fluid approach from general relativity."

The relativistic mass of an object is the mass of the object

Does the 'stuff'

Please define stuff