- #1
liometopum
- 127
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What are the uncertainty relations for the following:
1. position and energy?
2. position and time?
1. position and energy?
2. position and time?
liometopum said:But what about position and energy? I have values and am looking to check them.
The uncertainty principle for two observables A and B is ΔAΔB ≥ |<C>| with C = [A,B]. You cannot expect |<C>| to yield a general value like hbar/2 for arbitrary A and B because it is the expectation value of the operator C and thus depends on the state of the system.liometopum said:But what about position and energy? I have values and am looking to check them.
liometopum said:Let me just share what I calculated, using my own method:
Time-position uncertainty
ΔT×Δx= (Gℏ)/(c⁴) = 8.7114×10⁻⁷⁹ m s
Energy-position uncertainty:
ΔE×Δx=(cℏ)/2= 1.58076×10⁻²⁶ J m
Uncertainty relations refer to the mathematical relationships between two or more physical quantities that cannot be simultaneously measured with perfect accuracy. They are important in science because they help us understand the limitations of our ability to measure and predict the behavior of physical systems.
One example of an unusual uncertainty relation is the Heisenberg uncertainty principle, which states that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. This principle is unusual because it applies to pairs of complementary observables, such as position and momentum, rather than just individual quantities.
Uncertainty relations play a fundamental role in quantum mechanics, as they are a consequence of the probabilistic nature of quantum systems. They help us understand the inherent uncertainty in the behavior of particles at the subatomic level, and have led to the development of important theories, such as the Copenhagen interpretation of quantum mechanics.
Yes, uncertainty relations have many practical applications, particularly in the fields of quantum computing and cryptography. They also play a crucial role in the development of technologies such as MRI machines and atomic clocks. In addition, uncertainty relations have been used to better understand complex systems in fields such as biology and economics.
Scientists continue to study and improve our understanding of uncertainty relations through theoretical and experimental research. They use mathematical models and advanced technologies to test the limits of uncertainty relations and explore their implications in different fields of science. Ongoing research in this area is crucial to furthering our understanding of the fundamental principles of the universe.