I was thinking the next step could be to derive the Newtonian field equation for a spherical mass. Let me know if you want me to do it, or if you would like to. In order to properly critique my equation, it might best if you perform the steps to see what questions arise. Easiest (but algebraically justifiable) if we just jump to Poisson's equation of the 00 components of my equation.
Last edited by JMessenger; 2012-Jul-17 at 04:27 AM.
If the concept of energy in GR is offset, this should add a pressure to our physics due to a uniform distribution of mass from what we called a vacuum. If this is your argument, then I have two questions.
1) The accelerating expansion of the universe suggests that this energy offset should be negative. What is the physical nature of negative energy?
2) The energy density of this offset would be negligible on QM scales. Why is this energy level so close to 0?
I am a bit confused about why you define a new density equal to a reference density minus the classical density. I can understand changing a reference, but this appears to also change the sign of our energy. If this is motivated to make the energy density positive in the empty state, the above observations suggest that the magnitude of any realistic mass will be much larger than the vacuum density, resulting in a negative energy density.
3) Are you arguing that all observable energy is negative energy?
I have ideas concerning qm but I am not ready to defend them at the moment.2) The energy density of this offset would be negligible on QM scales. Why is this energy level so close to 0?
From post #214, caveman is about to get an awakening once he calculates the Newtonian field equation for a spherical mass. The difference between a differential equation like the EFE and the examples he gives are subtle at first but crucial. While I can substitute in my equation for the normal matter stress-energy tensor, they are only equivalent as long as no other dimensions are accounted for. The EFE only accounts for a point. Once spatial dimensions are integrated in, the symmetry between the two is broken since my equation has two terms (actually, the normal EFE has two terms also but how to make that term match empirical observations is the paradox). You have the option of stating that we are an increase in energy density, or from the reference point of an ideal fluid all energy is a decrease in pressure and density. Which is closer to the physical reality though will model cosmological evolution better.I am a bit confused about why you define a new density equal to a reference density minus the classical density. I can understand changing a reference, but this appears to also change the sign of our energy.
If by the empty state, you mean no sensible matter or radiation etc., then there still is no energy. That is why it is easiest to look at it from the view of a perfect fluid. Just because that isotropic and homogeneous perfect fluid exists, there is no concept of curvature or energy without derivatives of pressure and density within it. If you mean that the stress energy of the gravitational field is of the same sign as the mass energy, it does seem that would be true. I can't remember where I saw it but someone state that the overall energy of a system, when incorporating the gravitational fields, is less than their rest mass. That would be false from this theory so I am not sure what empirical evidence backed up what that person stated (I don't recall that they gave any).If this is motivated to make the energy density positive in the empty state, the above observations suggest that the magnitude of any realistic mass will be much larger than the vacuum density, resulting in a negative energy density.
From the perspective of the fluid, my tentative answer is yes. I say tentative since QM has other aspects such as anti-matter which I have not yet considered. Taking baby steps.3) Are you arguing that all observable energy is negative energy?
Edit: The combination of the two gradients should be something like this. Upside down sombrero hat with a rim that denotes zero gravitational force and linearly growing repulsion after that. 3D plotting these equations out should be my next step unless someone can come up with some mathematical or modeling flaw here. My mistake was knowing that there was zero curvature at those points and equating that with a flat field potential. This plot denotes the force vectors for a test mass, not the curvature of space-time. Interesting.
Last edited by JMessenger; 2012-Jul-17 at 07:42 PM.
Or perhaps more to the point, what does it matter if i write or ? (or whichever values would be in the respective components of the tensors)
Do you expect to get any different results that way? What exactly would be gained by using your notation? And don't say that you have a larger cosmological constant, because you have none whatsoever, you have a zero vacuum energy.
I don't see anything more in your proposal than you saying that any number can be written as for appropriate choice of and . Which should not surprise anybody. You're doing it with tensors rather than numbers but the point is the same.
General Relativity: An Introduction for PhysicistsFor a spherical mass M, the the gravitational field strength is easily found to be
Thus, in this case, we see that the cosmological constant term corresponds to a
gravitational repulsion whose strength increases linearly with r.
Do you realize that the is a local effect only, that with integration with radius the effect decreases? Do you realize that is an effect that is summed as it is integrated for distance? Do you realize with a differential equation you are looking at is the instantaneous effect of both at a point? How are the authors above wrong in their conclusion as to the effects of a tensor constant in the EFE?
This might help:
How can we calculate the energy density of the vacuum? This is one of the
major unsolved problems in physics. The simplest calculation involves summing
the quantum mechanical zero-point energies of all the fields known in Nature.
This gives an answer about 120 orders of magnitude higher than the upper limits
on set by cosmological observations. This is probably the worst theoretical
prediction in the history of physics! Nobody knows how to make sense of this
result. Some physical mechanism must exist that makes the cosmological constant
Some physicists have thought that A mechanism must exist that makes exactly
equal to zero. But in the last few years there has been increasing evidence that
the cosmological constant is small but non-zero. The strongest evidence comes
from observations of distant Type Ia supernovae that indicate that the expansion of
the universe is actually accelerating rather than decelerating. Normally, one would
have thought that the gravity of matter in the universe would cause the expansion
to slow down (perhaps even eventually halting the expansion and causing the
universe to collapse). But if the cosmological constant is non-zero, the negative
pressure of the vacuum can cause the universe to accelerate.
Whether these supernova observations are right or not is an area of active
research, and the theoretical problem of explaining the value of the cosmological
constant is one of the great challenges of theoretical physics. It is most likely
that we require a fully developed theory of quantum gravity (perhaps superstring
theory) before we can understand .
DETF 2006Although there is currently conclusive observational evidence for the existence of dark
energy, we know very little about its basic properties. It is not at present possible, even
with the latest results from ground and space observations, to determine whether a
cosmological constant, a dynamical fluid, or a modification of general relativity is the
correct explanation. We cannot yet even say whether dark energy evolves with time.
The Newtonian field equation is obtained through the Poison equation of the 00 terms. is preserved in the exact same way as .
ETA: those are two statements on my part, first that adding a cosmological constant to the EFE represents a certain non-zero vacuum energy. Which is easily verified. And second that this model fits the observational evidence, which is just as easily verified.
No one knows what causes the accelerating expansion of the universe.
We do know that it is trivial to show that a non-zerocosmologicall constant in GR will cause an accelerating expansion of the universe.
But it may be quintessence.