It isn't, they are seperate things, which was my point. But nevermind.Originally Posted by JMessenger
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It isn't, they are seperate things, which was my point. But nevermind.
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SoI am definingwhere
is the negative stress-energy tensor of the residual energy density at a point where sensible matter is located.
, alright that's a definition.
So the equation you propose is
But that still leaves a definition for, ie what exactly does "negative stress-energy tensor of residual energy mean".
Is it?
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Technically,So
So the equation you propose is
But that still leaves a definition for
Is it, but yes.
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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.
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Didn't energy in GR come from the idea of the energy density causing gravity, and the energy of QM come from discrete steps from a reference assumed to be a 0 energy state?Ok, now we are connecting. Yes, I am trying to examine the assumptions made in the formation of the theories and looking for the most likely weak spots. To me that seems to lie along how we define energy density and its relation to a fluid model. I agree that your above questions are valid. While my proposal may seem ridiculous and well disputed many years ago, even among the works of Lorentz I cannot find any papers where he did not also directly connect theof a fluid with the
of the inertial mass we sense and the corresponding convention of energy equivalency. I am not looking to fool myself, just looking for a solid chain of how we came by the definitions of energy within GR and quantum theory.
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?
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It would be best if we simply went back to the original differential equation which describes gravity best and see exactly how that changes our assumptions of our cosmological model. You could state that this energy is of opposite sign as what we are made of (positive energy), but I think it is physically (and mathematically) closer to the truth that we are the absence of this pressure 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 thatI 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.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.
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?
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I can accept the rest of your responses as reasonable from your initial ideas. I am stuck with this one objection.
How is it that the magnitude of our absence of this pressure energy is much greater in magnitude than the magnitude of this pressure energy?
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What would lead you to believe that it is? Take for instance the 00 components in #243 rewritten:and
so
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Perhaps it is the gradient plots that has brought this question up. The scalar field potential on the left should be isotropic and flat, but the magnitudes grow with the radius. The magnitudes of the scalar field on the right increase but the gradient vector decreases with radius. The equivalency with gravitational force shows that it is the right gradient that is important for everyday gravity, but the left isotropic pressure on gravitational bound matter (derivatives in the fluid) that is important for accelerating expansion. The right scalar field potential is important because it gives a directional force (gradient vector) between each "mass", whereas the left is just an isotropic pressure force between all matter that increases with distance.
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Although...from the point of view of a force vector between two masses (such as the Newtonian field equation), that first plot should show a radially symmetric growing field potential from a zero middle potential. Repulsive vector grows linearly with distance. Duh and woops. Thanks utesfan100.
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.
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Then how is this different from the standard EFE without cosmological constant?Technically,
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Or perhaps more to the point, what does it matter if i writeor
? (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.
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I don't see anything more in your proposal than you saying that any numbercan 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.
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You are debating me on the meaning of the accelerating expansion and you make a post that is not only non-mainstream but mathematically incorrect? Do you understand the following paragraph in relation to what you are stating about adding a constant to the EFE has no effect?I don't see anything more in your proposal than you saying that any number
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 theis 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
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
very small.
Some physicists have thought that A mechanism must exist that makes
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
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If you are going to attempt to use the argument thatI don't see anything more in your proposal than you saying that any number
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.
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Except that you didn't add a constant to the EFE.
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What i'm saying is that adding a cosmological constant (representing a certain non-zero vacuum energy) to the EFE fits observational evidence for accelerating expansion. You have neither (no vacuum energy and no accelerating expansion). In fact your vacuum state is simply minkowski space because, as should be obvious by now, it is equivalent to the EFE without cosmological constant.If you are going to attempt to use the argument that
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No, not equal at all. Each tensor term gets its very own spot in the Newtonian also. See those "r"s in the equation? The EFE without the cosmological constant has two also. The second one is a ZERO. I have no ability to present a mathematical argument if we don't even agree on basic algebra.
.
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You are attempting to refute this theory based on an unproven hypothesis. Show me a citation where this has been accepted by the majority of scientists.
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For anybody else reading this thread, please understand the Sum Rule of Differentiation http://en.wikipedia.org/wiki/Sum_rul...ifferentiation
The Newtonian field equation is obtained through the Poison equation of the 00 terms.
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Here's the EFE:No, not equal at all. Each tensor term gets its very own spot in the Newtonian also. See those "r"s in the equation? The EFE without the cosmological constant has two also. The second one is a ZERO. I have no ability to present a mathematical argument if we don't even agree on basic algebra.
Here's what you have (with)
These are most obviously perfectly equivalent. If you think you'd get different results from using yours then you have made a mistake somewhere.
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But of course, just don't start integrating for distance.Here's the EFE:
Here's what you have (with
These are most obviously perfectly equivalent.
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That statement is not an unproven hypothesis. Note that i didn't say that dark energy is a cosmological constant, i said that it fits the observational evidence.
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Yes but your residuals are (must be) chosen in such a way as to exactly counteract any of its effect everywhere. Otherwise it wouldn't be equivalent, now would it.
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Are you claiming that?
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You statedShow me the mainstream citation where a certain non-zero vacuum energy is a cosmological constant accepted as the cause for the accelerating expansion.cosmological constant (representing a certain non-zero vacuum energy)
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You're twisting my words, i said that the cosmological constant represents a certain non-zero vacuum energy and that it fits the observational evidence. I never said it was "accepted as the cause for accelerating expansion".
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.
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I am claiming what we thought was one functionAre you claiming thatis actually the sum of two separate functions. I am claiming that it is a fundamental error in modeling to utilize a tensor for a fluid equation without understanding that if you have no volume of fluid in which the stress-energy can propagate due to a change in density or pressure, then by definition you do not have a fluid.
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Thank you for acknowledging that your theory is wrong because it predicts that gravity blows and we have evidence that it sucks!
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.
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So verify it. I would very much bet that any mainstream journal you find which publishes that verification also publishes the caveats of why it also doesn't fit. You are implying that the answers you are giving are in some way shape or form well accepted, when instead they are called "the worst prediction in physics" and a "cosmologists worst nightmare". The only thing that is agreed upon in any peer reviewed publications is that there seems to be a constant repulsion from something which seems to fit a constant in the EFE.
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