On Saturday, October 26, 2019 at 4:24:13 PM UTC-5, Alan Grayson wrote:
>
>
>
> On Saturday, October 26, 2019 at 3:17:15 PM UTC-6, Philip Thrift wrote:
>>
>>
>>
>> On Saturday, October 26, 2019 at 3:57:01 PM UTC-5, Brent wrote:
>>>
>>> What creates the problem at microscopic level is that the stress-energy
>>> tensor on the right hand side will be due to the wave function of a quantum
>>> particle and so would only have a probabilistic interpretation. We an do
>>> semi-classical computations by replacing the wave function by it's expected
>>> value at each point. But that avoids the point that the metric stuff on
>>> the left hand side needs to be represented by a probabilistic function to
>>> match the right hand side.
>>>
>>> Brent
>>>
>>>
>>>
>> That's an interesting way to express it.
>>
>> @philipthrift
>>
>
> In effect, what Brent is getting at, is that GR is a classical theory,
> which assumes a classical space-time field. But if you assume a classical
> field at the microscopic level, will GR give answers which are contradicted
> by measurements? AG
>
Brent has a part of the problem laid out. The semiclassical approach to
physics is that T_{ab} - ½Rg_{ab} = 8πG<T_{ab}>, and the curvature stuff on
the left is nonlinear. Quantum mechanics is not good with nonlinear
operators. If we try to make the Ricci curvature an operator, the
nonlinearity of the operator causes troubles. The only way to fix this is
to impose Wightman conditions that quantum oscillators for the field are
localized to a point and independent on spatial manifolds. General
relativity has problems with this because curvature is evaluated by a loop
in spacetime and is the field through that area. Gravity is then more
nonlocal. There is another problem that spacetime has with quantum physics.
Putative operators for gravitation are evaluated on a metric signature
(+,-,-,-), which results in negative probabilities.
Are there ways around this? I think so. For one thing quantization only
makes sense on event horizons, where the area curvature is evaluated on is
dual to a point. So we can with holography I think quantize gravitation on
horizons and then compute amplitudes in the bulk. The negative probability
problem can be worked around with coherent states, such as those with laser
physics. The gravitational quantum states are then a condensate or massive
entanglement of states. The maximally mixed states that are an apparent
problem then have probability p = 1/N, for N modes, and we can evaluate a
relative entropy S(ρ*|ρ) = N + S(ρ) for ρ* and ρ the density operators for
maximally mixed states and the coherent states on the horizon.
In this way the states on the horizon are near Planck energy oscillators,
and the mixed states the Hawking radiation. This relative entropy is then a
dualism between the UV fields on the horizon and the IR fields beyond, or
in the bulk. This is then
UV-fields of quantum gravity = IR-fields of gauge interactions and fermions
If you think about it this is a way of writing the Einstein field equation.
LC
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To view this discussion on the web visit
https://groups.google.com/d/msgid/everything-list/e67fe09b-73af-45b6-aced-647e3d9e0c6a%40googlegroups.com.
