In other threads vacuum space was discussed for possibilities of scale relativity, squeezed quantum states, and hierarchy of Plancks. In each or these a quantum state of local space is associated with large scale continuum space of GR.
Roger Penrose has on several ocations published gravity curvature as a possible cause of state vector reduction. Article Gravity and state vector reduction
Also in his book Emperor's New Mind the unitary evolution U in a quantum system continues to a critical point where state vector reduction R occurs, followed by a new evolution U to some higher state, and another state vector reduction R. The critical point was said to be an excess of gravitational curvature, building up a system of superimposed quantum states, entanglements until the excess energy causes state reduction, collapse of the wave function, selection of one state and rejection of the competing state.
When applied to vacuum space as Penrose did in the 1996 paper the state vector reduction was argued as a decoherence caused by increasing complexity and some additional triggering device that Penrose proposed as an accumulated gravitational curvature in excess of the system stability limit.
In many threads the researchers have been discussing the limitations of GR in respect to high speed transport in deep space. With little difficulty those discussions could be recast in the terminology of Penrose and state vector reduction.
The implication of the Penrose publications and the conclusions of high speed in deep space is that the many degrees of freedom in vacuum space entangle with the few degrees of freedom in a quantum system. That is to say the vacuum interacts physically with the objects that pass through it.
The present question relates to kinetic field energy at high speed in deep space where the progression of scales and change from one scale to another appears to be the same as U and R but in other terminology.
Does State Vector Reduction Occur In Vacuum Space Time?
In terms of high speed in deep space the Hierarchy of Plancks represents the present U to be evolution of our 4D space time with constant h representing the spin angular momentum of vacuum space quanta, and with GR describing gravity. In this representation the first state reduction R results in spin angular momentum of 2h and a new state evolution U represented by 5D like Kaluza Klein and others but in which the additional dimension is a second dimension of time.
The next state reduction R results in spin angular momentum of 3h, state evolution U represented by 6D in which there are three dimensions of time similar to the time like coordinates near light speed.
Kinetic field energy rather then gravity curvature is represented as the triggering device that causes state vector reduction in local vacuum. In this system the isotropic CMB becomes essential as a zero velocity reference frame everywhere.
It's straightforward to show that the main question doesn't make sense, because ``vacuum space'' doesn't make sense. There's a persistent misunderstanding in conflating phase space and space--and ignoring spacetime.
Whether space is empty, or not, isn't relevant.
In quantum mechanics, evolution of a state is described by the action of the unitary evolution operator, acting on the initial state of the system, e.g; U(t)|ψ>.
Now it's possible to express |ψ>=sum_{eigenstates of U(t=1)} c_n|φ>_n
where |φ>_n are the eigenstates of the evolution operator, at some reference time, that, if time translations are globally defined, therefore spacetime is flat, can be taken to be equal to 1. This is where spacetime enters the picture.
A measurement means that some other operator, M, acts on this state and produces the state MU(t)|ψ>.
This state can be similarly expressed as a linear combination of the same states-but the two linear combinations won't be identical, unless the initial state is an eigenstate and M commutes with U(t).
All this take place in phase space, not spacetime.
That's all that's needed. If the initial state; in particular, is the ground state of the Hamiltonian, then subsequent application of U simply gives the ground state, multiplied by a phase. If M commutes with U(t), then the measurement gives the ground state-just the phase is affected. If M doesn't commute with U(t), this means that its action on U(t)|ψ> will produce, not only the vacuum state, but excited states, also. Hence the probability to find the system in the ground state, upon realising this measurement, will no longer be equal to 1, but less, due to interference.
What Hawking realized was that, in curved spacetime, the ground state of a quantum system can't be uniquely defined, since time translations can't be globally defined. Therefore, the evolution operator of a quantum system, in curved spacetime, isn't globally defined, so new interference effects will occur, due to this fact. These can be computed, assuming the spacetime geometry, though curved, isn't affected by the quantum matter, that's evolving in it. It isn't known how spacetime geometry can be affected by quantum matter.
Thank you Stam Nicolis for reply.
I edited the title to be Vacuum Space Time rather than Vacuum Space where time is assumed. You make a number of points that should be considered.
In quantum systems phase space may differ from space time depending on the system. When vacuum space time is represented as the quantum system under consideration then the phase space must be mapped into space time or be contained with in it as some higher dimensionality. I simplify my system considerably by requiring acceleration to be in the direction of velocity, effectively decreasing the number of dimensions.
I will argue that the ground state of quantum space time can be uniquely defined by isotropic CMB in flat space, a view shared by some famous names, but not generally accepted in the research community.
In your explanation the other operator M is represented in my system as a fast moving vehicle which locally meets the measurement requirement. In most cases and in all of those described by GR, the moving vehicle referenced to isotropic CMB will not generate a high probability of excited states in vacuum space time.
Unusual cases of very high speed and kinetic energy are most interesting to me. This is where local quantum effects cannot be ignored in GR. I have argued that the probability of excited states becomes significant, and excited states become superimposed upon each other and upon the ground state.
As kinetic field energy continues to increase some limit is reached at which a state vector reduction may occur. Physically it is represented as a change of spin angular momentum of the space time quanta from h to 2h. This is the hierarchy of Plancks that occurs in other theories and research of the past 40 years.
If a state vector reduction occurs as R, the unitary evolution U continues locally as kinetic energy continues to increase, but this is not described by GR because h has become a local variable and local space time is in a squeezed quantum state. In this representation the velocity relative to CMB is approaching a substantial fraction of light speed, and the kinetic field energy is sufficient to change the quantum state of local space time as the vehicle passes through it.
In the present question I am asking if quantized vacuum space time can undergo a state vector reduction.
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