Thanks, Mark. I recall from WMAP's site that the accelerated expansion of the universe may be explained by Einstein's cosmological constant, or possibly by quintessence. From article in your link, the reason for prefering the cosmological constant is because the force of dark energy appears to be static, is this correct?
Also, what is the consensus on the Unruh effect? Is this why you said (here) that QFT predicts a large, unobserved vacuum mass?
the reason for preferring the cosmological constant is because the force of dark energy appears to be static
If I am reading it correctly the reported observations imply that Einstein's cosmological constant provides the best fit to the data. Preferable, depends on your point of view. In one sense it is good because a lot of work has already been done modeling the effects of ECC. In another sense it is bad because it leaves us with the same list of unanswered questions we already had.
I had not thought about the Unruh effect when I was writing my reply to Guido thread. In fact I had forgotten that the effect had a name. As I understand the phenomenon it is an unavoidable consequence of applying QFT to a curved space-time. In the applications of the Unruh effect I have seen the feedback from the changes in QFT field(s) which should influence the space-time curvature are to the best of my knowledge either missing or ad-hoc.
If I am reading it correctly the reported observations imply that Einstein's cosmological constant provides the best fit to the data. Preferable, depends on your point of view. In one sense it is good because a lot of work has already been done modeling the effects of ECC. In another sense it is bad because it leaves us with the same list of unanswered questions we already had.
Yes, on Wikipedia's Lambda-CDM page it's said we're stuck with a 'useful parameterization of ignorance'...
Why isn't the bridge between QFT and GR, then, in Special Relativity?
Why isn't the bridge between QFT and GR, then, in Special Relativity?
Special Relativity is GR with a flat space-time and almost always built into Quantum Field Theories. Without SR, QFT would not work as well as they do.
If there was a catalog of all (or even a broad subset) of the solutions to the equations of GR scientist might be able make some progress toward a theory of quantum gravity. But we are still struggling with the simplest case of binary black holes. Lacking such a catalog it is necessary to attempt to apply the simpler tools that work in flat spaces.
Taking Classical Electro-Dynamics as an example one of the problems you encounter is the infinite self energy of a charged particle i.e. the potential energy of a pair of charges being proportional charge1*charge2/separation becomes charge^2/0 when considering a charged particles interaction with its own electro-magnetic field. This problem carries over into Quantum Electro-Dynamics but the singularity is charge^2*Log[0]. Now Log[x] is the integral of 1/x or x^(-1), however the integral x^(-.99) is x^(.01)/.01 which is not singular at 0. Thus Log[0] is called a soft singularity and quantum theorist use this in a process called renormalization to remove the singularities. In fact there is a genre of mathematics called Renormalization Theory which studies renormalization transformations and forms a large part of the underpinnings of QFT.
In a workable quantum field theory there are a finite number of renormalization transformations that remove all of the infinities. This happy state of affairs does not exist when you attempt to quantize GR. As yet the infinite number of renormalization transformations required makes a workable quantum theory of gravity at least as intractable as GR.
Thanks, Mark. I can definitely appreciate problems with equations when there's a zero in the demoninator. However, setting aside the math for a moment, as I wonder about the nature of the 'grip' that spacetime has on mass (and mass on spacetime), I'd like to ask about the following possibility:
There is clearly an interaction between normal matter and the vacuum of spacetime in which it's observed. To some extent, matter displaces spacetime (as with gravitational lensing). Further, spacetime is quantized into a sea of virtual particles, and each quanta of spacetime has some fundamental energy/mass. This sea is displaced (compressed?) by galaxies into dark matter halos. I guess that it would be displaced mostly by normal matter, and less by radiation pressure from photons. But while there is an interaction between matter and spacetime (which would be the source of gravity), there is also a different interaction between spacetime and itself, which would be the source of the dark energy.
Are there obvious reasons why the above is not possible, that I've failed to consider?
Is there a model for this scenario?
Thanks for your help, Mark.
I do not understand what you are proposing so I can't really comment.
I was afraid of that. The part I left out are the details. I definitely still need to work on it, then, a lot. Answers to these questions will be helpful:
If I describe spacetime with math terms, and say that it is 'locally irregular', but yet it is 'globally regular' (loosely analogous to the distribution of prime numbers on the number line), does this make sense with regard to QFT on macroscopic scales?
I know there such a thing as the 'Swartzchild radius', a solution to a field equation, useful for understanding strong gravitational fields. Is there such a thing as a "Heisenberg radius" (by some other term), with regard to the principle of invariance (specifically the speed of light) imposed upon the uncertainty principle? In other words, is there a latency to the resolution of events within such a radius?
In an inertial frame, should I put QFT in gamma = 1 / sqrt(1- v^2 / c^2), or should QFT have gamma embedded in it? Or is it recursive (they're both in each other)? In other words, at what point on the 'local/global' scale should GR be imposed on QFT?
What is it that curves in a gravitational field of virtual particles?
If I describe spacetime with math terms, and say that it is 'locally irregular', but yet it is 'globally regular' (loosely analogous to the distribution of prime numbers on the number line), does this make sense with regard to QFT on macroscopic scales?
Sorry ChipperQ I still don't understand.
Quote:
Is there such a thing as a "Heisenberg radius"
Yes, mass times the speed of light divided by Plank's constant and 2 Pi. It is usually called the Plank radius.
Quote:
is there a latency to the resolution of events within such a radius?
The Plank radius is a kind of minimal uncertainty in a particles location for low energy interactions.
Quote:
In an inertial frame, ....
I think you are mixing special relativity with general relativity here. The gamma factor from special relativity can appear in quantum electro-dynamics. But the gamma factor is superseded by general covariance in general relativity.
Quote:
at what point on the 'local/global' scale should GR be imposed on QFT?
I would expect that a theory of quantum gravity should encompass the whole of space-time.
Quote:
What is it that curves in a gravitational field of virtual particles?
Okay, if I concentrate on a region of spacetime the size of a sphere of Planck radius, can I say that in a system that isn't gravitationally bound, the region will be perfectly spherical, and that in a system that is gravitationally bound, the region will be 'warped' or 'curved' or no longer perfectly spherical? Can I also say that the region, having size greater than zero, requires there to be a rule saying that resolution of events (summation of the 'stress energy tensor'?) cannot happen instantaneously?
oops, my bad, the formula I gave for "Heisenberg Radius" inverted. Should have been 2 times Pi time Plank's constant divded by mass divided by the speed of light.
Update on dark energy
)
Thanks, Mark. I recall from WMAP's site that the accelerated expansion of the universe may be explained by Einstein's cosmological constant, or possibly by quintessence. From article in your link, the reason for prefering the cosmological constant is because the force of dark energy appears to be static, is this correct?
Also, what is the consensus on the Unruh effect? Is this why you said (here) that QFT predicts a large, unobserved vacuum mass?
RE: the reason for
)
If I am reading it correctly the reported observations imply that Einstein's cosmological constant provides the best fit to the data. Preferable, depends on your point of view. In one sense it is good because a lot of work has already been done modeling the effects of ECC. In another sense it is bad because it leaves us with the same list of unanswered questions we already had.
I had not thought about the Unruh effect when I was writing my reply to Guido thread. In fact I had forgotten that the effect had a name. As I understand the phenomenon it is an unavoidable consequence of applying QFT to a curved space-time. In the applications of the Unruh effect I have seen the feedback from the changes in QFT field(s) which should influence the space-time curvature are to the best of my knowledge either missing or ad-hoc.
RE: If I am reading it
)
Yes, on Wikipedia's Lambda-CDM page it's said we're stuck with a 'useful parameterization of ignorance'...
Why isn't the bridge between QFT and GR, then, in Special Relativity?
RE: Why isn't the bridge
)
Special Relativity is GR with a flat space-time and almost always built into Quantum Field Theories. Without SR, QFT would not work as well as they do.
If there was a catalog of all (or even a broad subset) of the solutions to the equations of GR scientist might be able make some progress toward a theory of quantum gravity. But we are still struggling with the simplest case of binary black holes. Lacking such a catalog it is necessary to attempt to apply the simpler tools that work in flat spaces.
Taking Classical Electro-Dynamics as an example one of the problems you encounter is the infinite self energy of a charged particle i.e. the potential energy of a pair of charges being proportional charge1*charge2/separation becomes charge^2/0 when considering a charged particles interaction with its own electro-magnetic field. This problem carries over into Quantum Electro-Dynamics but the singularity is charge^2*Log[0]. Now Log[x] is the integral of 1/x or x^(-1), however the integral x^(-.99) is x^(.01)/.01 which is not singular at 0. Thus Log[0] is called a soft singularity and quantum theorist use this in a process called renormalization to remove the singularities. In fact there is a genre of mathematics called Renormalization Theory which studies renormalization transformations and forms a large part of the underpinnings of QFT.
In a workable quantum field theory there are a finite number of renormalization transformations that remove all of the infinities. This happy state of affairs does not exist when you attempt to quantize GR. As yet the infinite number of renormalization transformations required makes a workable quantum theory of gravity at least as intractable as GR.
Thanks, Mark. I can
)
Thanks, Mark. I can definitely appreciate problems with equations when there's a zero in the demoninator. However, setting aside the math for a moment, as I wonder about the nature of the 'grip' that spacetime has on mass (and mass on spacetime), I'd like to ask about the following possibility:
There is clearly an interaction between normal matter and the vacuum of spacetime in which it's observed. To some extent, matter displaces spacetime (as with gravitational lensing). Further, spacetime is quantized into a sea of virtual particles, and each quanta of spacetime has some fundamental energy/mass. This sea is displaced (compressed?) by galaxies into dark matter halos. I guess that it would be displaced mostly by normal matter, and less by radiation pressure from photons. But while there is an interaction between matter and spacetime (which would be the source of gravity), there is also a different interaction between spacetime and itself, which would be the source of the dark energy.
Are there obvious reasons why the above is not possible, that I've failed to consider?
Is there a model for this scenario?
Thanks for your help, Mark.
ChiperQ I do not understand
)
ChiperQ
I do not understand what you are proposing so I can't really comment.
RE: I do not understand
)
I was afraid of that. The part I left out are the details. I definitely still need to work on it, then, a lot. Answers to these questions will be helpful:
If I describe spacetime with math terms, and say that it is 'locally irregular', but yet it is 'globally regular' (loosely analogous to the distribution of prime numbers on the number line), does this make sense with regard to QFT on macroscopic scales?
I know there such a thing as the 'Swartzchild radius', a solution to a field equation, useful for understanding strong gravitational fields. Is there such a thing as a "Heisenberg radius" (by some other term), with regard to the principle of invariance (specifically the speed of light) imposed upon the uncertainty principle? In other words, is there a latency to the resolution of events within such a radius?
In an inertial frame, should I put QFT in gamma = 1 / sqrt(1- v^2 / c^2), or should QFT have gamma embedded in it? Or is it recursive (they're both in each other)? In other words, at what point on the 'local/global' scale should GR be imposed on QFT?
What is it that curves in a gravitational field of virtual particles?
Thanks for the help! :)
RE: If I describe spacetime
)
Sorry ChipperQ I still don't understand.
Yes, mass times the speed of light divided by Plank's constant and 2 Pi. It is usually called the Plank radius.
The Plank radius is a kind of minimal uncertainty in a particles location for low energy interactions.
I think you are mixing special relativity with general relativity here. The gamma factor from special relativity can appear in quantum electro-dynamics. But the gamma factor is superseded by general covariance in general relativity.
I would expect that a theory of quantum gravity should encompass the whole of space-time.
Good question and I don’t know the answer.
Okay, if I concentrate on a
)
Okay, if I concentrate on a region of spacetime the size of a sphere of Planck radius, can I say that in a system that isn't gravitationally bound, the region will be perfectly spherical, and that in a system that is gravitationally bound, the region will be 'warped' or 'curved' or no longer perfectly spherical? Can I also say that the region, having size greater than zero, requires there to be a rule saying that resolution of events (summation of the 'stress energy tensor'?) cannot happen instantaneously?
oops, my bad, the formula I
)
oops, my bad, the formula I gave for "Heisenberg Radius" inverted. Should have been 2 times Pi time Plank's constant divded by mass divided by the speed of light.