On Sunday, October 27, 2019 at 8:26:07 AM UTC-5, Lawrence Crowell wrote:
>
> 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
>
*Emergent 4-dimensional linearized gravity from spin foam models*
https://arxiv.org/pdf/1812.02110.pdf
In this paper, we show for the first time that smooth solutions of
4-dimensional Einstein equation emerge from Spin Foam Models (SFMs) under
an appropriate semiclassical continuum limit (SCL).
@philipthrift
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