Could we do QM without time evolution ?

[mhill]

could we do QM without time evolution ??

that is the idea, could we perform QM without referring to any coordinate called 'time' in the sense that the Hamiltonian and Schroedinguer equation would be

$$H \Psi (x) =0$$ and time and energy only appear as the pair

$$(p_0 , t)$$

the idea is , to perform a QM where there is no time evolution

 

[strangerep]

that is the idea, could we perform QM without referring to any coordinate called 'time' in the sense that the Hamiltonian and Schroedinguer equation would be

$$H \Psi (x) =0$$ and time and energy only appear as the pair

$$(p_0 , t)$$

the idea is , to perform a QM where there is no time evolution

If you mean perform some kind of generally-covariant quantization in a
generalized phase space, I think Henneaux & Teitelboim talk about some
of that in their textbook. One finds weird stuff such as zero Hamiltonians,
(iirc - my memory is a bit vague on the details).

Separately, there's also the old chestnut about how time in QM is a
parameter, not an operator, if we want to have a Hilbert space of
states containing a lowest-energy state.

 

[denian]

but only a time-energy relation.

The concept of time evolution is fundamental in quantum mechanics and cannot be completely eliminated from the theory. The Schrödinger equation, which is the cornerstone of quantum mechanics, explicitly describes the evolution of a quantum system over time. Without this concept, we would not be able to accurately predict the behavior of particles and systems in the quantum realm.

However, it is possible to approach quantum mechanics from a different perspective where time is not the central concept. This approach, known as timeless or relational quantum mechanics, focuses on the relationship between particles and their interactions rather than the concept of time. In this view, time is simply a measurement of the interactions between particles rather than a fundamental aspect of the theory.

While this approach has its merits and has been explored by some physicists, it is not widely accepted or used in the scientific community. Time evolution is a crucial aspect of quantum mechanics and has been proven through numerous experiments and observations. Removing it entirely from the theory would require a significant reworking of many fundamental principles and equations, making it a challenging and controversial concept to adopt.

In summary, while it is possible to consider alternative perspectives and interpretations of quantum mechanics that downplay the role of time, it is not feasible to completely eliminate time evolution from the theory. It is a crucial component that allows us to accurately understand and predict the behavior of quantum systems.