On Saturday, October 26, 2019 at 9:15:56 PM UTC-5, Alan Grayson wrote:
>
>
>
> On Saturday, October 26, 2019 at 4:55:37 PM UTC-6, Lawrence Crowell wrote:
>>
>> 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
>>
>
> If one wants to quantize GR, one would have to quantize the underlying
> classical field of space-time. But what would pop out of the quantized
> field when a measurement occurs? I couldn't be a photon as in QED. What
> would be the quantized measurement? A graviton? AG
>
As I said, I think the gravitational field that might be quantized fully is
on event horizons. In the bulk with one dimension larger the quantized
gravitational field would be gravitons that are very red shifted. These
gravitons are then weak and asymptotically linear. The only possible
quantization would then, at least within what I think is a foreseeable
quantum gravitation theory, is a weak field graviton. In that setting it
would be linearized. A linear graviton that is a weak perturbation on the
background metric would be similar to a diphoton or HBT entangled photon
pair. To "climb" the ladder to some measure of nonlinearity would require
some perturbation series. A full quantum gravitation of the spacetime bulk
may really be impossible. In fact it may not really even exist. This is
then a substructure that would support an asymptotic quantum gravity in the
bulk similar to Weinberg's asymptotic safe q-gravity.
LC
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