If so, what is its form and significance and is there a connection between temporal and spatial Uncertainty? For example, is the temporal uncertainty asymmetric, so that the forward component is associated with greater disorder?
If you would be into physics for as long as I have, the answer is a definite yes, it does apply to the energy-time domain.
Roughly speaking the uncertainty in the value of the energy, multiplied by the time the process is taking, must be larger or equal to a constant associated with Plancks constant. This constant has units of energy multiplied by time, namely action.
There are two separate uncertainty relations, one for energy-time and another for position-momentum along the same direction.
There is yet another for angular momentum-angle.
All this applies only to the microscopic domain, or quantum domain.
But Im curious about just why you would doubt it.
Sorry, I have not heard about time uncertainty asymmetry, why mention disorder or forward component? Do not know where you may have read about such things.
George and Stephen
By the way the uncertainty in quantum theory is quite different in origin
to one you may have by simply having a stochastic process. The uncertainty is
simply intrinsic in the nature of a quantum particle, such as an electron,with both wave and particle properties...believe it or not.
On my opinion, uncertainty principles, based only on terminology. Space and time frequencies is determined only in infinite space and time. If they consider the limited ones they have spectra of the frequencies and therefore the uncertainties.
I love to think abot physics in General, but as i am rather stupid in this domaine so better not in Detail.
So i prefer to look at it from far and thus i dare to ask: Is this Kind of formula our Heisenberg found out may be a Kind of innate principle in very many things and laws???
There are at least two forms of the uncertainty principle:
1) comes from Fourier transform. A function f(t) and its Fourier transform g(omega) cannot both be narrowly peaked. Mathematically, this can be expressed by saying that, if you take the squared modulus of f(t) and normalise it, then you can view |f(t)|^2 as a probability distribution and calculate its variance sigma_t. Under these circumstances, the squared modulus of g(omega) is also normalised, and so we may calculate the variance sigma_omega. The product of these variances have a lower bound, which is of order one. Its exact value depends on your convention for Fourier transforming.
2) In QM: if you repeatedly measure any observable A in a given state, you will generally get a variety of values, with a given variance depending both on the state and the observable A. By choosing either carefully, the variance can always be made arbitrarily small.
If now you measure in the same state, some times A and sometimes B, where A and B do not commute, then you will get a variance sigma_A and another sigma_B. Their product cannot be arbitrarily small, but have a lower bound, depending on the state and the commutator of A and B.
In QM, it is often (correctly) argued that time is not an observable, but rather a parameter. Indeed, we determine the state as a function of time, and thus we do not have an ``observable'' for time. So the time-energy uncertainty relation in QM is complicated and has been the subject of much debate. The idea is, essentially, to introduce an observable which corresponds classically to time, and with this one may indeed obtain something like a time-energy uncertainty.
But, personally, I would be very careful: this is a truly difficult issue. On the other hand, whenever you can frame your problem in terms of Fourier transform, the first version is true and unambiguous.
George - unless the downvoter has afforded all of us the courtesy of an explanation you are entitled to assume that he simply implies disagreement and objects to your expression of of your views. Ignore it! If I'm right this comment will also attract a downvote, which I will ignore.....
Perhaps, is that more simple? And Heisenberg Uncertainty Principle should be considered from "experimental" point of view. In quantum micro world there is quantum fluctuations, and so, results of all our measurements are the averaged values. Thus, than less time of experimental measurement means more probability to find shadow of these quantum fluctuations ...
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