iVenky said:Maxwell's demon ... How can it do that
The logic of the Maxwell's Demon argument starts "If there were such a thing, then..." and considers the consequences of that assumption. That logic is valid whether or not such a thing can actually be created.iVenky said:Maxwell's demon measures the position and velocity of the particle. How can it do that when it violates the uncertainty principle?
So you are saying even within the limits of uncertainty, the demon could produce a detectable effect hypothetically?Nugatory said:The logic of the Maxwell's Demon argument starts "If there were such a thing, then..." and considers the consequences of that assumption. That logic is valid whether or not such a thing can actually be created.
(It woud also be a good exercise to calculate the actual limits the uncertainty principle places on the effectiveness of a hypothetical Maxwell's Demon. The demon doesn't have to sort every single atom that comes by, just enough to produce a detectable effect).
I'm saying that you should try calculating an upper bound for yourselfiVenky said:So you are saying even within the limits of uncertainty, the demon could produce a detectable effect hypothetically?
The Maxwell's demon (being real or not) is supposed to measure all initial data that, according to a given theory, completely determine the future evolution of the system. If the given theory is classical mechanics, then those initial data are positions and velocities of all particles. But if the given theory is quantum mechanics, then the initial data is the initial state in the Hilbert space, the future evolution of which is determined by the Schrodinger equation. The latter corresponds to a quantum Maxwell's demon, which is compatible with the uncertainty principle.iVenky said:Maxwell's demon measures the position and velocity of the particle. How can it do that when it violates the uncertainty principle? Does that mean uncertainty principle is unavoidable otherwise we will violate II law of thermodynamics as in the case of Maxwell's demon?
Maxwell's Demon and the Uncertainty Principle are two important concepts in physics that relate to the fundamental laws of thermodynamics and quantum mechanics, respectively. Maxwell's Demon refers to a hypothetical creature that has the ability to sort particles according to their energy levels, seemingly violating the second law of thermodynamics. The Uncertainty Principle states that it is impossible to know both the exact position and momentum of a particle simultaneously.
Maxwell's Demon was first proposed by James Clerk Maxwell in 1867, while the Uncertainty Principle was formulated by Werner Heisenberg in 1927.
The second law of thermodynamics states that the total entropy (disorder) of a closed system will always increase over time. Maxwell's Demon appears to violate this law by being able to sort particles according to their energy levels, which would result in a decrease in entropy. However, this apparent violation is resolved when considering the energy cost of the Demon's actions, which ultimately leads to an increase in overall entropy.
The Uncertainty Principle has significant implications for our understanding of the physical world, particularly at the quantum level. It means that there is a fundamental limit to our ability to know certain properties of particles, and that there will always be a degree of uncertainty in our measurements. This challenges the classical notion of determinism, where the exact state of a system can be predicted with complete accuracy.
Maxwell's Demon and the Uncertainty Principle have both been extensively studied and have numerous applications in physics and other fields. For example, the Uncertainty Principle is used in medical imaging techniques such as MRI, and in the development of quantum technologies. Maxwell's Demon has also been explored in the context of information processing and the development of more efficient engines. However, it should be noted that these applications are based on our understanding and interpretation of these concepts, rather than the existence of an actual Demon or inherent uncertainty in the physical world.