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frankypoo
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I'm a newcomer to physics (know of any good beginner forums?) and was wondering why the uncertainty principle is true.
Originally posted by frankypoo
I'm a newcomer to physics (know of any good beginner forums?) and was wondering why the uncertainty principle is true.
Wow, I've never heard that before. Are you over-generalizing for the sake of clarity, or is this absolutely true? Can you give a simple proof?Originally posted by lethe
when the observables do not commute, they can be shown to be Fourier transforms of one another, ...
Originally posted by turin
Wow, I've never heard that before. Are you over-generalizing for the sake of clarity, or is this absolutely true? Can you give a simple proof?
Originally posted by turin
Can you give a simple proof?
yes, very good. what i said is only true for variables obeying canonical commutation relations.Originally posted by Ambitwistor
I think Lethe really meant two observables which obey canonical commutation relations, i.e. [itex][\hat{A},\hat{B}] = i\hbar[/itex], at least concerning the Fourier transform bit
Does this condition contain a condition of non-degeneracy? I guess it doesn't matter since you are taking the derivative of the delta function (something I thought you would've frowned upon, though)?Originally posted by lethe
... observables A, and B with continuous spectra ...
This was the main part of my confusion.Originally posted by lethe
yes, very good. what i said is only true for variables obeying canonical commutation relations.
Originally posted by turin
Does this condition contain a condition of non-degeneracy? I guess it doesn't matter since you are taking the derivative of the delta function (something I thought you would've frowned upon, though)?
The uncertainty principle, also known as Heisenberg's uncertainty principle, is a fundamental principle in quantum mechanics that states that the more precisely you know the position of a particle, the less precisely you can know its momentum, and vice versa.
The uncertainty principle was first proposed by German physicist Werner Heisenberg in 1927.
The uncertainty principle is significant because it sets a limit on the precision with which certain pairs of physical properties can be measured. It also challenges our traditional understanding of determinism in physics.
The uncertainty principle is applied in various fields, such as quantum computing, nuclear physics, and chemistry. It helps in understanding the behavior of subatomic particles and plays a crucial role in modern technology, such as MRI machines and transistors.
No, the uncertainty principle is a fundamental principle of nature and cannot be violated. However, there are ways to minimize the effects of uncertainty through advanced techniques and technology.