ΔE.Δt ~ h
Δp.Δx ~ h
ΔL.Δθ ~ h
* Shouldn’t the constant above be ℏ/2 ? Let us first clear up some air of confusion.
The above relations are kind of vague even though look like canonically powerful ways to represent the formal concepts of the Heisenberg Uncertainty relationships. I have myself confused with these at times … with the added degree of confusion coming from h or h-cross?
But there is nothing to be ashamed of, if one makes such mistakes.
Does ℏ/2 come due to normalization of wave function or discrepancy in definition? eg do they come because variance (ΔE, Δx) and standard deviation (σx , σH ).
Even here I confused myself. ΔE, Δx; these are not necessarily, variance ! Due to usage of same symbol one may think they are. But in the above, these are simply; uncertainty, which can perhaps be, vaguely even, defined from differentials. A formal approach would be to derive them from the wave function formalism. But if these are cast into “standard deviation” such as [ σx , σH ] one gets the relations in terms of ℏ/2.
To understand the concepts of variance and standard deviation and normalization in detail, you can read this slideshow presentation uploaded recently on the subject.
These 3 are the famous Heisenberg’s Uncertainty Principles … just how famous, if we do not know it?
Before I explain whats uncertainty principle, I must clear one thing. These are not the only uncertainty relations in this regard as is popularly believed.
About 4 years ago, I had formulated some new forms of these relations. Those were sufficient to see why some the then discrepancies regarding speed of neutrino exceeding the speed of light, were squarely dealt by these new forms; to be a mere lack of basic understanding of Physics. A reason why my paper was not published in some archives.
The moment you bring out ridiculous lack of understanding in “pioneers” trying to overhaul age old theories they get more sympathy because “you know, can Einstein never be wrong?” No problem, first show us that he is wrong by showing you have good understanding about what you are trying to repeal.
Outstanding claims need outstanding evidences. But not only that, one first of all must be prepared to understand what one is trying to overhaul, actual misunderstanding or a firm understanding.
Talking about lack of understanding of basic Physics, at the same time I also calculated and found the so called Flyby Anomaly which is heralded as a fundamental anomaly due to fundamental misunderstanding of fundamental physics. I haven’t tried to publish the paper, … although the work is quite convincing to myself, so I will stop talking about that also.
So I hadn’t really stumbled upon anything new, but rather painfully, be it so, worked out from basics why the basics are still valid and amazingly so. Back then I wanted to know if such alternative forms of Uncertainty Relation exist.
[Linked article from 2012, which I might edit more, when it gets to me enough]
I didn’t get any answer from anyone though.
Also note that; uncertainty relations are described in much detail in most text books of Quantum Mechanics at the appropriate level. Today I came across something from one of these text books. I believe it was something I knew more than a decade ago, but totally forgotten, even when I wrote the above linked article from 2012, I wrote that small pointer article, only using my training, training often remains at subconscious, but not by invoking the equation which I am going to describe.
The equation that I had forgotten, but brings again to context: the alternative forms of Uncertainty Relations. Its called “Your name” uncertainty relation, and apparently a famous one. But its so famous only as to facilitate the forgetfulness of itself in regard to the only 3 forms we invoke anytime someone finds such necessary, such as when asked to state “whats uncertainty relation”.
So first of all I can call it Manmohan’s uncertainty relation .. although to my credit I actually found some myself, as is linked, especially here. We can e.g. call it Michael Jordan’s uncertainty relation, you can call it Parineeti Chopra uncertainty relation and so on, or by your own namesake.
How does it look like?
I haven’t gone through its details at the moment, and neither do I remember any, from the education 15 years ago, now that I remember I did know of it. But its in line with the fact, as described me already in the linked article, that energy e.g., contains in it distance and momentum. Momentum is an operator in “distance -wise” description.
Hence distance vs energy uncertainty relation is possible.
σxσH ≥ (ℏ)/(2m) | < p > |
Now that we see how this known but alternative form of uncertainty relation looks like, we see that instead of a simple h-cross we have an expectation value of momentum, the latter is an operator, as mentioned already, that is, its a “differential” step on the wave function, and can produce functional dependence on distance or speed etc.
This we have seen in the new linked forms of alternative uncertainty relations I have discovered. To see some further analogy realize that (ℏ/m) is nothing but the Compton wavelength which I have included in the linked forms.
Now I will explain the uncertainty relations as they are expressed here … but sometime later soon ! As soon as you are prepared to hear.