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 ( σ_{x }*,

*σ*

_{H}).

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 [ *σ _{x }, σ_{H }*]

*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.

σ_{x}σ_{H}≥ (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.

Categories: Heisenberg Relations, particles and their properties, quantum mechanics, Relativistic Quantum Mechanics, uncertainty relations

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