I'm not quite sure what you mean, could you perhaps expand? Under which circumstances are you referring to?Heirot said:Is there any a priori connection beetween the orders of magnitude of e.g. momentum, and its uncertainty? Why do we always assume that the momentum is the same order of magnitude as its uncertainy? I'm referring to all those "back of the envelope" calculations.
Thanks
The uncertainty in momentum can be related to the expectation value (average) of the momentum and momentum squared, which in turn can be related to the expectation value of the kinetic energy. It turns out that for a particle in a box, the expectation value of the kinetic energy of a particle is directly proportional to the expectation value of the square of the momentum and hence also directly proportional to the uncertainty in momentum.Heirot said:For example, let's put an electron in a box of length L. Since the electron is in the box, we know that delta x = L (or L/2, I'm not quite sure). Using uncertainty relations, we have delta p >= hbar / 2L. As L gets smaller, delta p gets bigger. So, the textbooks conclude, at one point delta p gets so big that there's enough energy to create a positon - electron pair! But energy increases with p, not delta p! For all we now, p could be zero all the time. Why do we assume that p increases as delta p increases?
Heisenberg's uncertainty principle is a fundamental concept in quantum mechanics that states that it is impossible to simultaneously determine the exact position and momentum of a subatomic particle.
The uncertainty principle states that the more precisely we know the position of a particle, the less we know about its momentum, and vice versa. This relationship is often expressed in terms of orders of magnitude, as the uncertainty in one variable is typically several orders of magnitude larger than the other.
Orders of magnitude play a crucial role in the uncertainty principle as they represent the difference in scale between the uncertainties in position and momentum. This highlights the inherent limitations in our ability to measure and predict the behavior of subatomic particles.
No, the uncertainty principle is a fundamental principle in quantum mechanics and cannot be violated by increasing our measurement precision. In fact, the more precisely we try to measure one variable, the less we know about the other variable, as dictated by the uncertainty principle.
Yes, the uncertainty principle has practical applications in various fields, including quantum computing, cryptography, and medical imaging. It also provides a fundamental understanding of the behavior of subatomic particles and has led to many groundbreaking discoveries in physics.