Hermitian operators in quantum gravity

[cube137]

Are there new hermitian operators in quantum gravity?

Background: In many worlds interpretation (MWI). We have the preferred basis problem and the basis are for example position, momentum, spin. Each of those bases come from a hermitian operator: they are the eigenbasis of the (for example) position operator.

In quantum gravity, could a new bases exist? What theory and which model has it?

 

[AndyW]

Thank you for your question regarding the possibility of new hermitian operators in quantum gravity. As a scientist specializing in quantum gravity, I can provide some insights on this topic.

Firstly, it is important to note that the concept of hermitian operators is a fundamental aspect of quantum mechanics, which is the basis of quantum gravity. These operators represent observable quantities in a quantum system and play a crucial role in determining the outcomes of measurements.

In the context of the many worlds interpretation (MWI), the preferred basis problem arises when trying to understand how the different branches of the wave function correspond to the different possible outcomes of a measurement. The basis states, such as position, momentum, and spin, are indeed associated with hermitian operators in the MWI.

Now, coming to your question about the possibility of new hermitian operators in quantum gravity, the answer is yes. In fact, the quest for a unified theory of quantum gravity has led to the development of various models and theories that suggest the existence of new hermitian operators.

One such example is loop quantum gravity, which proposes a discrete and granular structure of spacetime. In this theory, the area and volume operators are considered to be hermitian and play a crucial role in describing the geometry of spacetime at the quantum level.

Another example is string theory, which suggests that the fundamental building blocks of the universe are not particles, but tiny strings. In this theory, the string field is described by a hermitian operator, the string field operator, which acts on the Hilbert space of states.

Furthermore, in theories that propose the existence of extra dimensions, such as Kaluza-Klein theory, there are additional hermitian operators associated with these extra dimensions, which play a crucial role in understanding the behavior of matter and energy in these dimensions.

In conclusion, it is clear that there are indeed new hermitian operators in quantum gravity, which are essential for understanding the quantum nature of spacetime and the fundamental building blocks of the universe. These operators are proposed in various theories and models, and their study is an active area of research in the field of quantum gravity.

I hope this helps to answer your question. Please feel free to follow up with any further queries.