Time in a Steady-State Quantum System

[LarryS]

Suppose we are given an arbitrary multi-particle quantum system whose state function / probability density does not change with time. Given, Einstein’s definition of time, that “time is what a clock measures”, is it possible to build a “clock” within such a system? More generally, does time have any meaning in such a system? Thanks in advance.

 

[dmtr]

Suppose we are given an arbitrary multi-particle quantum system whose state function / probability density does not change with time. Given, Einstein’s definition of time, that “time is what a clock measures”, is it possible to build a “clock” within such a system? More generally, does time have any meaning in such a system? Thanks in advance.

IMO: I think it is possible to build "clock" within such a system, it also seems to me that this clock would stand still for an observer completely decoupled from the system.

I can think of several examples of such decouplings that vary (or stop) the unitary time evolution:
1) Quantum Zeno effect. See. [http://qserver.usc.edu/group/wp-content/uploads/2007/02/pra690323142004.pdf]
2) An observer in the accelerated reference frame (consider the system left behind the event horizon)

Here is a lengthy [and unresolved] discussion on the same subject. https://www.physicsforums.com/showthread.php?t=351259

 

[Entropia]

I can say that time does have a meaning in a steady-state quantum system, but it may not be the same as what we understand in classical physics. In a classical system, time is a continuous and linear progression, but in quantum mechanics, time is treated as an operator that acts on the state function. This means that time in a quantum system is not a fixed quantity, but rather it is a variable that is dependent on the state of the system.

In a steady-state quantum system, the state function does not change with time, which means that the system is in a stable and constant state. This does not mean that time has stopped or has no meaning, but rather it implies that the system is in a state of equilibrium where all the particles are in a balanced and unchanging distribution. In this case, it is possible to build a "clock" within the system, but it would not function in the same way as a classical clock. It would measure the flow of time in a quantum sense, which is not necessarily the same as what we experience in our daily lives.

Furthermore, the concept of time in quantum mechanics is not fully understood and is still a topic of debate among scientists. Some theories suggest that time may be an emergent property of the quantum system, while others propose that it may be a fundamental aspect of the universe. Therefore, it is difficult to say definitively whether time has any meaning in a steady-state quantum system, as our understanding of time in the quantum realm is still evolving.

In conclusion, while time may have a different meaning in a steady-state quantum system, it does not mean that it is non-existent or irrelevant. As scientists, we continue to explore and study the concept of time in the quantum world, and with further research and advancements, we may gain a better understanding of its true nature.