Quantum Cosmology - Imaginary Time

[putongren]

I have trouble understanding the concept of imaginary time. As I understand it (by reading other online sources), imaginary time was developed by Stephen Hawking and Hartle in their theory of quantum cosmology. Quantum cosmology is applying quantum mechanical principles to cosmology as a whole, so the concept of the wave function is applied to the universe as a whole. There are infinite number of parallel universes as a consequence of applying the wave function to the universe. Also, an application of imaginary time can be found in quantum tunneling. When a particle is in the process of quantum tunneling, it is said to be in imaginary time. There are other technical terms I encountered during my reading such as Wick's rotation and Sum Over History Path Integral which I wasn't able to understand. Is my understanding of this topic accurate at all? Is there more to the story than this?

 

[azntoon]

Imaginary time is indeed a concept developed by Stephen Hawking and Hartle in their theory of quantum cosmology. It is related to the idea of a quantum wave function applied to the universe as a whole, which suggests that there are an infinite number of parallel universes. In this framework, imaginary time (also known as Euclidean time) is used to calculate probabilities for different outcomes in the universe. This is often referred to as the Sum Over Histories Path Integral, and it involves a Wick's rotation, which is a mathematical transformation that converts physical time into imaginary time.It is important to note that imaginary time is not a real "time" that can be experienced or measured in our physical universe. Instead, it is a mathematical tool used to understand quantum mechanics and cosmology. In quantum tunneling, particles are said to be in imaginary time because they are transitioning between states without spending any "real" time in between them.In summary, imaginary time is a concept developed in quantum cosmology that involves using a mathematical tool called Wick's rotation to convert physical time into imaginary time in order to calculate probabilities for different outcomes in the universe. It is not a real "time" that can be experienced or measured, but rather a mathematical tool used to understand quantum mechanics and cosmology.

 

[Entropia]

Your understanding of quantum cosmology and imaginary time is largely accurate. Imaginary time is a concept introduced by Hawking and Hartle in their theory of quantum cosmology, which seeks to apply quantum mechanics to the entire universe. In this theory, the wave function of the universe is described as a sum over all possible histories, including an infinite number of parallel universes.

One way to understand imaginary time is through the concept of Wick's rotation, which is essentially a mathematical trick used to simplify equations in quantum field theory. By rotating time from a real number to an imaginary number, certain complex calculations become easier to solve. It is important to note that this is just a mathematical tool and does not necessarily represent a physical reality.

Another application of imaginary time is in quantum tunneling, where particles are able to pass through energy barriers that would be impossible in classical physics. In this process, the particle is said to exist in imaginary time, which allows it to temporarily violate the laws of classical physics.

While your understanding of the topic is generally accurate, there is certainly more to the story than this. Quantum cosmology and imaginary time are complex and ongoing areas of research, and there are many nuances and intricacies that go beyond a brief explanation. It is also worth noting that there is still much debate and discussion within the scientific community about the validity and implications of these concepts. As with any scientific topic, it is always important to continue learning and staying informed about new developments and advancements in the field.