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
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