- #1
Peter 727
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- 0
- TL;DR Summary
- When tackling most gravitational problems, one must include the distance between the objects doing the gravitating. Why is this measure not in the cosmological model?
The standard answer: “In GR, only average density matters.”
That is what Friedmann’s equations (1) say—mathematically—but he does not derive that conclusion. He starts with it.
Friedmann does not start with a messy, real-world model of the universe, one that has fractured into galaxy clusters, each gravitationally bound together, and collapsing locally against the backdrop of distant expansion. He does not show that the devil-in-the-details becomes an angel using General Relativity. He leaves out the details. He starts with a model of uniform density, wherein only average density matters. He does not show it.
Figure 3, below, shows why distance matters in a 4-body system. In A, the distance between 4 bodies of mass M is doubled, and the energy required to do so calculated. In B, the distance between 2 bodies of mass 2M is doubled, starting and ending with the same density as in A. It takes less energy to expand the clumpier gravitational system than the smoother one. The calculation is done for only 4 bodies, but the result is generic, and applies to all n-body systems: Clumping in a many-body system reduces the energy associated with expansion between clumps. As clouds of gas collapse to form stars and galaxies, the cosmic expansion, beyond these centers-of-collapse, involves less energy. Yet there is no accounting of this effect in the standard model. Why not?
In our experience, gravity is constant. Newton offered that it varies, in proportion to mass and inverse-distance-squared (2). Einstein added a third factor, velocity (3)...and some “new math.” Yet in Friedmann’s equations, the foundation of modern cosmology, gravity’s three measures—mass, distance and velocity—revert to just two: density and expansion rate. Mass and distance-between are rolled into a single parameter, density. Wait…wasn’t General Relativity supposed to make things more complicated, not less?
Example: Q. Comet-tails always point away from the sun, so the dust-motes are on expanding orbits. Does this expansion slow or accelerate?
A. Comet dust is driven into interstellar space by the solar wind. Its velocity depends on a number of factors, but the only variables are the strength of the solar wind, and distance from the sun. Both the pushing—the solar wind—and the pulling—gravity—decrease with inverse-distance-squared. Hence, distance cancels out, and dust expands away from the sun at a constant rate, neither slowing nor accelerating, in a constant solar-wind.
I cannot find any such justification for the “cancellation of distance” in the standard model. In fact, a more nuanced model would account for the fact that the solar wind is composed partially of ions, which do slow down with distance from the sun. Distance has only a small, “second-order” effect on comet dust. Friedmann starts with distance already gone. There is no clumping in his model, ergo, no need to specify distance-between-clumps. He then calculates the change, or acceleration, based on these two parameters alone—plus the mysterious lambda (λ), or dark energy—for three cases: open; closed and flat universes.
How did this model—sans distance—work out? Great...until put to the test. The acceleration is small, magnitude 10-36/s2. This means a galaxy 1024 m away, over a period of 1012 s, will accelerate by 1 m/s. Such infinitesimal change can only be measured against vast time-scales, and when astronomers were finally able to do so, they found it to be positive (4, 5), not negative, as predicted.
But instead of taking additional factors into account—that is, clumping, wherein distance between clumps must be specified—cosmologists added a mystery: λ, or “dark energy.” Lambda had been assumed to be zero. It is small, magnitude 10-52/m2, but not quite zero. It was hurriedly put back in the equations. And it bears an uneasy resemblance to one of the missing pieces: inverse-distance-squared. Hmm…
Summary: The simplest possible model—a uniformly expanding gas with no stars or galaxies—got the sign wrong on acceleration. Friedmann does not justify this simplification, but scientists always start with the simplest model. If one includes clumping, the problem becomes fiendishly complex, as suggested by the calculation in Figure 3. At the very least, one must include rate-of-clumping, as well as distance between clumps.
My question is: Why wasn’t a distance-measure added to the model...as soon as the model without it failed?References:
1) Friedmann, A., Z. Phys., 1922
2) Newton, I, Principia, 1687
3) Einstein, A, Zur allgemeinen Relativitätstheorie, 4.11.1915
4) Perlmutter, S., Aldering, G., Goldhaber, G., et al. 1999, ApJ, 517, 565
5) Riess, A., Filippenko, A. ,Challis, P., et al.1998, AJ, 116, 1009
Footnote: In 2015, Ahmed Ali and Saurya Das made an indirect case for including distance (Physics Letters B, 2015). They showed that the assumption of quantum gravity forces the insertion of an inverse-distance-squared term into the equations, a term that looks exactly like dark energy. Ali and Das account for the acceleration, in a convoluted way, but without adding an unknown energy source.
That is what Friedmann’s equations (1) say—mathematically—but he does not derive that conclusion. He starts with it.
Friedmann does not start with a messy, real-world model of the universe, one that has fractured into galaxy clusters, each gravitationally bound together, and collapsing locally against the backdrop of distant expansion. He does not show that the devil-in-the-details becomes an angel using General Relativity. He leaves out the details. He starts with a model of uniform density, wherein only average density matters. He does not show it.
Figure 3, below, shows why distance matters in a 4-body system. In A, the distance between 4 bodies of mass M is doubled, and the energy required to do so calculated. In B, the distance between 2 bodies of mass 2M is doubled, starting and ending with the same density as in A. It takes less energy to expand the clumpier gravitational system than the smoother one. The calculation is done for only 4 bodies, but the result is generic, and applies to all n-body systems: Clumping in a many-body system reduces the energy associated with expansion between clumps. As clouds of gas collapse to form stars and galaxies, the cosmic expansion, beyond these centers-of-collapse, involves less energy. Yet there is no accounting of this effect in the standard model. Why not?
In our experience, gravity is constant. Newton offered that it varies, in proportion to mass and inverse-distance-squared (2). Einstein added a third factor, velocity (3)...and some “new math.” Yet in Friedmann’s equations, the foundation of modern cosmology, gravity’s three measures—mass, distance and velocity—revert to just two: density and expansion rate. Mass and distance-between are rolled into a single parameter, density. Wait…wasn’t General Relativity supposed to make things more complicated, not less?
Example: Q. Comet-tails always point away from the sun, so the dust-motes are on expanding orbits. Does this expansion slow or accelerate?
A. Comet dust is driven into interstellar space by the solar wind. Its velocity depends on a number of factors, but the only variables are the strength of the solar wind, and distance from the sun. Both the pushing—the solar wind—and the pulling—gravity—decrease with inverse-distance-squared. Hence, distance cancels out, and dust expands away from the sun at a constant rate, neither slowing nor accelerating, in a constant solar-wind.
I cannot find any such justification for the “cancellation of distance” in the standard model. In fact, a more nuanced model would account for the fact that the solar wind is composed partially of ions, which do slow down with distance from the sun. Distance has only a small, “second-order” effect on comet dust. Friedmann starts with distance already gone. There is no clumping in his model, ergo, no need to specify distance-between-clumps. He then calculates the change, or acceleration, based on these two parameters alone—plus the mysterious lambda (λ), or dark energy—for three cases: open; closed and flat universes.
How did this model—sans distance—work out? Great...until put to the test. The acceleration is small, magnitude 10-36/s2. This means a galaxy 1024 m away, over a period of 1012 s, will accelerate by 1 m/s. Such infinitesimal change can only be measured against vast time-scales, and when astronomers were finally able to do so, they found it to be positive (4, 5), not negative, as predicted.
But instead of taking additional factors into account—that is, clumping, wherein distance between clumps must be specified—cosmologists added a mystery: λ, or “dark energy.” Lambda had been assumed to be zero. It is small, magnitude 10-52/m2, but not quite zero. It was hurriedly put back in the equations. And it bears an uneasy resemblance to one of the missing pieces: inverse-distance-squared. Hmm…
Summary: The simplest possible model—a uniformly expanding gas with no stars or galaxies—got the sign wrong on acceleration. Friedmann does not justify this simplification, but scientists always start with the simplest model. If one includes clumping, the problem becomes fiendishly complex, as suggested by the calculation in Figure 3. At the very least, one must include rate-of-clumping, as well as distance between clumps.
My question is: Why wasn’t a distance-measure added to the model...as soon as the model without it failed?References:
1) Friedmann, A., Z. Phys., 1922
2) Newton, I, Principia, 1687
3) Einstein, A, Zur allgemeinen Relativitätstheorie, 4.11.1915
4) Perlmutter, S., Aldering, G., Goldhaber, G., et al. 1999, ApJ, 517, 565
5) Riess, A., Filippenko, A. ,Challis, P., et al.1998, AJ, 116, 1009
Footnote: In 2015, Ahmed Ali and Saurya Das made an indirect case for including distance (Physics Letters B, 2015). They showed that the assumption of quantum gravity forces the insertion of an inverse-distance-squared term into the equations, a term that looks exactly like dark energy. Ali and Das account for the acceleration, in a convoluted way, but without adding an unknown energy source.