Long ago, I read an explanation of inertia as being the cumulative gravitational effect of all the matter in the universe acting on a body. Assuming this to be correct, does the inifornity of inertia in all directions suggest that the distribution of matter in all directions must be equal, and therefore, that we actually are at the centre of it all?
Silly question about inertia/momentum
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That's Mach's principle and it's really only a hypothesis. Anywhere you are in the universe, you appear to be at the centre with most galaxies receding from you (apart from relatively local ones), the speed of recession increasing with distance. Only matter within the cosmic horizon has any gravitational influence. Space time for the most distant galaxies is expanding such that their effective recessional velocity is greater than the speed of light and they have no gravitational influence. As far as we can tell from the curvature of space time being effectively zero, the universe is vastly bigger than what we can observe.
As for homogeneity, there appear to be large voids but that doesn't mean they don't contain dark matter and dark energy.
I'm not aware that the constancy of inertial mass has been tested in different directions. The equivalence of gravitational mass and inertial mass has been tested, of course.
Now I think on it, I wonder whether the accelerating expansion of the universe has had much, if any, effect on inertial mass over time. If the effect of dark energy persists, the universe will gradually be ripped apart.
As more stuff disappears over the horizon, perhaps inertial mass will decrease to a point where biological life as we know it is impossible due to expanding atomic radii. Stellar fusion processes might also be affected and stars become unstable.
Thinking off the top of my head so expect corrections.
ETA: The theory of quantised inertia proposes that there is a minimum possible acceleration because of the Unruh effect and the Rindler horizon (I'll let you google those). This has been proposed as an alternative to dark matter. It might also explain why the EM drive works (if it really does). It seems there is scope there to falsify such a proposal.
As for homogeneity, there appear to be large voids but that doesn't mean they don't contain dark matter and dark energy.
I'm not aware that the constancy of inertial mass has been tested in different directions. The equivalence of gravitational mass and inertial mass has been tested, of course.
Now I think on it, I wonder whether the accelerating expansion of the universe has had much, if any, effect on inertial mass over time. If the effect of dark energy persists, the universe will gradually be ripped apart.
As more stuff disappears over the horizon, perhaps inertial mass will decrease to a point where biological life as we know it is impossible due to expanding atomic radii. Stellar fusion processes might also be affected and stars become unstable.
Thinking off the top of my head so expect corrections.
ETA: The theory of quantised inertia proposes that there is a minimum possible acceleration because of the Unruh effect and the Rindler horizon (I'll let you google those). This has been proposed as an alternative to dark matter. It might also explain why the EM drive works (if it really does). It seems there is scope there to falsify such a proposal.
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If Mach's principle is correct and inertial mass is due to the gravitational inductive effect (see *** below) of the rest of the mass of the universe within the cosmological comoving horizon, a simple non-General Relativistic treatment (also not taking into account Unruh radiation and the Rindler horizon) would suggest that the following relationship applies:
H^2 = 2*pi*G*rho
H is Hubble's constant, G is the gravitational constant, and rho is the average mass-energy density of the universe (including ordinary matter, radiation, neutrinos, dark matter, and dark energy).
If the mass-energy density of the universe is equal to the critical density (which appears to be the case to within 0.5% from cosmic microwave background data) then the following relationship applies:
H^2 = 8/3*pi*G*rho
The two equations, derived in different ways, agree quite well, which seems to suggest there might be something to Mach's principle.
*** The additional inductive force Fi between accelerating masses (the gravitational analogue of EM inductive force between accelerating charges) is assumed to take the form:
Fi = G*m*M*a/r*c^2
M and m are the gravitational masses, a is the acceleration, r is the distance between the masses, and c is the speed of light. As the force goes as 1/r rather than 1/r^2, distant masses have a greater relative effect than for ordinary gravitational attractive force. Of course, a proper treatment would use General Relativity, although there are several variants on how exactly this should be done.
H^2 = 2*pi*G*rho
H is Hubble's constant, G is the gravitational constant, and rho is the average mass-energy density of the universe (including ordinary matter, radiation, neutrinos, dark matter, and dark energy).
If the mass-energy density of the universe is equal to the critical density (which appears to be the case to within 0.5% from cosmic microwave background data) then the following relationship applies:
H^2 = 8/3*pi*G*rho
The two equations, derived in different ways, agree quite well, which seems to suggest there might be something to Mach's principle.
*** The additional inductive force Fi between accelerating masses (the gravitational analogue of EM inductive force between accelerating charges) is assumed to take the form:
Fi = G*m*M*a/r*c^2
M and m are the gravitational masses, a is the acceleration, r is the distance between the masses, and c is the speed of light. As the force goes as 1/r rather than 1/r^2, distant masses have a greater relative effect than for ordinary gravitational attractive force. Of course, a proper treatment would use General Relativity, although there are several variants on how exactly this should be done.
I hope it all pans out
A way can be had to harvest the inertia of another object?
https://www.centauri-dreams.org/2006/02/16/the-felber-antigravity-thesis-and-cosmology/
https://physics.stackexchange.com/q...ert-felber-model-of-repulsive-gravity-correct
That may have to wait until Gliese 710 gives our system a close shave a million years from now--or some hypervelocity star to get in front of.
Early on, some thought that IBEX found an accretion disk nearby. That didn't pan out--so no HALO drive from that.
https://arxiv.org/pdf/1903.03423.pdf
A way can be had to harvest the inertia of another object?
https://www.centauri-dreams.org/2006/02/16/the-felber-antigravity-thesis-and-cosmology/
https://physics.stackexchange.com/q...ert-felber-model-of-repulsive-gravity-correct
That may have to wait until Gliese 710 gives our system a close shave a million years from now--or some hypervelocity star to get in front of.
Early on, some thought that IBEX found an accretion disk nearby. That didn't pan out--so no HALO drive from that.
https://arxiv.org/pdf/1903.03423.pdf
Of course, we already take advantage of gravitational assists to the velocity of spacecraft, stealing a minute amount of momentum from this or that planet, although never in the velocity regime proposed in those links.
As Gliese 710 isn't moving*** relative to the Sun at anything like c/sqrt(3), my expectation is that it isn't going to allow a suitable test of the hypothesis even if there's anyone around in a million and quarter years time.
*** Its radial velocity is roughly -15 km/s or about c/20,000, which is much less than c/1.732.
As Gliese 710 isn't moving*** relative to the Sun at anything like c/sqrt(3), my expectation is that it isn't going to allow a suitable test of the hypothesis even if there's anyone around in a million and quarter years time.
*** Its radial velocity is roughly -15 km/s or about c/20,000, which is much less than c/1.732.
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