How can the stress tensor be non-zero where there is no matter?

[DoctorSatori]

Summary: Curvature comes from the stress tensor so how can there be curvature when there is no mass?

You're on Earth. You throw a ball and watch its trajectory. It's curved. That's because the Earth is curving space-time at every point along the trajectory. But the Earth itself is not present along the trajectory - there is no matter along the trajectory (let's ignore the air and any radiation that might be present) - so how is it curving the space there? There's not supposed to be action at a distance. Does it have something to do with gravitational waves? If so (and perhaps even if not because I'm still curious), what part of the field equations point to the existence of gravitational waves?

My journal-published experiments (Saffman-Taylor Instabilities In The Radial Domain http://link.springer.com/article/10.1007%2FBF00191691#page-1) suggest that sine-wave troughs are inertial fields analogous to gravity wells. As the universe expands, it may be that something (some near-zero-mass particles) flow around these wells (unable to push them outward) taking the path of least resistance to expansion.

 

[Ibix]

My journal-published experiments (Saffman-Taylor Instabilities In The Radial Domain http://link.springer.com/article/10.1007%2FBF00191691#page-1) suggest that sine-wave troughs are inertial fields analogous to gravity wells. As the universe expands, it may be that something (some near-zero-mass particles) flow around these wells (unable to push them outward) taking the path of least resistance to expansion.

I can only see the first two pages of this paper since it's paywalled, but no such claim is made in the abstract and neither the references nor the papers citing this seem to suggest any work in that direction either.

 

[alantheastronomer]

This is a Newtonian analysis, not a GR analysis.

Yes that's true. SamRoss was confused as to how curvature could exist at a point where there is no mass there, so I used the simplest example I could think of to show that a field extends beyond the immediate location of the field's source.

 

[Dale]

And, perhaps, you miss my philosophical point: that our mathematical model of the universe is not our universe.

That is a completely non controversial point. I believe that only Max Tegemark might disagree, but as far as I know very few professional scientists take his idea seriously.

Nonetheless, this does not change the fact that your argument above was demonstrably wrong.

In any case, this forum is not for discussing philosophy, it is for discussing science as practiced by the professional scientific community.

 

[DoctorSatori]

I can only see the first two pages of this paper since it's paywalled, but no such claim is made in the abstract and neither the references nor the papers citing this seem to suggest any work in that direction either.

That is a completely non controversial point. I believe that only Max Tegemark might disagree, but as far as I know very few professional scientists take his idea seriously.

Nonetheless, this does not change the fact that your argument above was demonstrably wrong.

In any case, this forum is not for discussing philosophy, it is for discussing science as practiced by the professional scientific community.

The unsteady solution to the gravitational/density equation is found here (in a reference to my article): Chandrasekhar S (1961) Hydrodynamic and hydromagnetic stability. London: Oxford University Press (if anyone is interested in running the experiment. The paper I cited is mine and S.G. Advani's (work done at University of Delaware). It gives both the solutions to the analogous Instability on an expanding radial boundary from a source and the experimental setup through which the experimental space of the radial expansion was observed. The mathematical basis of the complex solution is The General Energy Equation across the expanding boundary.

[BOOK] Hydrodynamic and hydromagnetic stability
S Chandrasekhar - 2013 - books.google.com
Dr. Chandrasekhar's book received high praise when it first appeared in 1961 as part of
Oxford University Press' International Series of Monographs on Physics. Since then it has
been reprinted numerous times in its expensive hardcover format. This first lower-priced,
sturdy paperback edition will be welcomed by graduate physics students and scientists
familiar with Dr. Chandrasekhar's work, particularly in light of the resurgence of interest in
the Rayleigh-Bénard problem.

Gravitational Instability in an Expanding Universe. The expanding medium means that for any small density perturbation, there will be competition between its self-gravity which is attempting to increase the density, and the general expansion of the universe which decreases the density.
Gravitational Instability in an Expanding Universe

https://ned.ipac.caltech.edu/level5/Bothun2/Bothun5_1_4.html

 

[DoctorSatori]

That is a completely non controversial point. I believe that only Max Tegemark might disagree, but as far as I know very few professional scientists take his idea seriously.

Nonetheless, this does not change the fact that your argument above was demonstrably wrong.

In any case, this forum is not for discussing philosophy, it is for discussing science as practiced by the professional scientific community.

I am a member of the professional scientific community in that my research is published in juried journals. In case we forget before it was known as SCIENCE, it was called NATURAL PHILOSOPHY, which is the nature of the philosophy I refer to.

 

[Dale]

my research is published in juried journals

And in any of your peer-reviewed reviewed publications or in any peer reviewed publications by other authors did you ever see the generic claim that zero “is only mathematically used as a limit”? If not then spare me the lecture on philosophy and the professional posturing.

When you make a mistake the best thing to do is to simply say “oops”, and learn from it.

 

[PeterDonis]

Thread closed for moderation.