Both Albert Einstein and Louis de Broglie were dissatisfied with the type of quantum probabilities found in standard quantum mechanics. We have recently introduced a new formulation of quantum mechanics in which the quantum gravity probabilities are more closely aligned with what de Broglie was seeking and hoping for. We show that if energy is conserved, then the corresponding total aggregate collision-event count is also conserved. Furthermore, we suggest that there must exist a probability gap above zero, that is, a lowest non-zero individual probability. Individual quantum gravity probabilities are therefore not continuous from zero to one, but instead exhibit a finite probability gap. Quantities larger than one are not single probabilities; they are aggregate collision-event counts obtained by summing many bounded individual probabilities.
Both Albert Einstein and Louis de Broglie were dissatisfied with the type of quantum probabilities found in standard quantum mechanics. We have recently introduced a new formulation of quantum mechanics in which the quantum gravity probabilities are much more closely aligned with what de Broglie was seeking and hoping for. We show that if energy is conserved, then these new types of quantum gravity probabilities must also be conserved. Furthermore, we suggest that there must exist a probability gap above zero—that is, a lowest non-zero probability. In other words, quantum gravity probabilities are not continuous from zero to one, but instead exhibit a finite probability gap.
In the paradigmatic example of quantum measurements, whenever one measures a system which starts in a superposition of two states of a conserved quantity, it jumps to one of the two states, implying different final values for the quantity that should have been conserved. The standard law of conservation for quantum mechanics handles this jump by stating only that the total distribution of the conserved quantity over repeated measurements is unchanged, but states nothing about individual cases. Here however we show that one can go beyond this and have conservation in each individual instance. We made our arguments in the case of angular momentum of a particle on a circle, where many technicalities simplify, and bring arguments to show that this holds in full generality. Hence we argue that the conservation law in quantum mechanics should be rewritten, to go beyond its hitherto statistical formulation, to state that the total of a conserved quantity is unchanged in every individual measurement outcome. As a further crucial element, we show that conservation can be localised at the level of the system of interest and its relevant frame of reference, and is independent on any assumptions on the distribution of the conserved quantity over the entire universe.
Abstract We generalize the de Broglie-Bohm (dBB) formulation of quantum mechanics to the case of quantum gravity (QG) by using the effective action for a QG theory. This is done by replacing the dBB equations of motion with the effective action equations of motion, which is beneficial even in the non-gravitational case, since in this way one avoids the violations of the Heisenberg uncertainity relations and the absence of the classical trajectories for stationary bound states. Another advantage of the effective action formalism is that one can obtain the field configurations in the case of a quantum field theory (QFT). The proposed QG generalization is natural for Bohmiam mechanics because a dBB wavefunction is really a wavefunction of the Universe and in order to define the effective action for an arbitrary initial state one needs a QG path integral. The QG effective action can be constructed by using the piecewise flat quantum gravity (PFQG) theory and the PFQG effective action can be approximated by the QFT effective action for General Relativity coupled to matter, with a cutoff determined by the average edge length of the spacetime triangulation. One can then calculate the corresponding field configurations and from these field configurations one can obtain the trajectories for the corresponding elementary particles.
We develop a new formalism for constructing probabilities associated with the causal ordering of events in quantum theory, where an event is defined as the emergence of a measurement record on a detector. We start with constructing probabilities for the causal ordering events in classical physics, where events are defined in terms of worldline coincidences. Then, we show how these notions generalize to quantum systems, where there exists no fundamental notion of trajectory. The probabilities constructed here are experimentally accessible, at least in principle. Our analysis here clarifies that the existence of quantum orderings of events do not require quantum gravity effects: it is a consequence of the quantum dynamics of matter, and it appears in the presence of a fixed background spacetime.
The measurement problem of quantum mechanics was probably born in 1926: ‘Thus Schrödinger’s quantum mechanics gives a very definite answer to the question of the outcome of a collision; however, this does not involve any causal relationship. One obtains no answer to the question “what is the state after the collision,” but only to the question “how probable is a specific outcome of the collision” (in which the quantum-mechanical law of [conservation of] energy must of course be satisfied). This raises the entire problem of determinism. From the standpoint of our quantum mechanics, there is no quantity that could causally establish the outcome of a collision in each individual case; however, so far we are not aware of any experimental clue to the effect that there are internal properties of atoms that enforce some particular outcome. Should we hope to discover such properties that determine individual outcomes later (perhaps phases of the internal atomic motions)? Or should we believe that the agreement between theory and experiment concerning our inability to give conditions for a causal course of events is some pre-established harmony that is based on the non-existence of such conditions? I myself tend to relinquish determinism in the atomic world. But this is [also] a philosophical question, for which physical arguments alone are not decisive.’ (Born, 1926a, p. 866; translation by the author) These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
We argue that in quantum gravity there is no Born rule. The quantum-gravity regime, described by a non-normalisable Wheeler-DeWitt wave functional
Ψ, must be in quantum nonequilibrium with a probability distribution
P=∣Ψ∣2 (initially and always). A Born rule can emerge only in the semiclassical regime of quantum systems on a classical spacetime background, with normalisable Schrödinger wave functions
ψ. Conditioning on the underlying quantum-gravitational ensemble yields a nonequilibrium distribution
ρ=∣ψ∣2 at the beginning of the semiclassical regime, with quantum relaxation
ρ→∣ψ∣2 taking place only afterwards. Quantum gravity naturally creates an early nonequilibrium universe. We also show how small corrections to the Schrödinger equation yield an intermediate regime in which the Born rule is unstable: an initial distribution
ρ=∣ψ∣2 can evolve to a final distribution
ρ=∣ψ∣2. These results arise naturally in the de Broglie-Bohm pilot-wave formulation of quantum gravity. We show that quantum instability during inflation generates a large-scale deficit
∼1/k3 in the primordial power spectrum at wavenumber
k, though the effect is too small to observe. Similarly we find an unobservably large timescale for quantum instability in a radiation-dominated universe. Quantum instability may be important in black-hole evaporation, with a final burst of Hawking radiation that violates the Born rule. Deviations from the Born rule can also be generated for atomic systems in the gravitational field of the earth, though the effects are unlikely to be observable. The most promising scenario for the detection of Born-rule violations appears to be in radiation from exploding primordial black holes.