Gravitational Anomaly.

Gravitational Anomaly: (asked by a student for very simple explanation)

Basically it means the new laws of physics known as Quantum Mechanics invalidates the sanctity of nature’s principles or laws (that is QM brings exceptions to the validity of the physical laws of nature itself)

Let us discuss this in simpler ideas from the basics only.

Remember the most basic physics, that of principle of conservation of energy and the principle of conservation of (linear) momentum.

In the more rigorous formalism of physics these two principles emanate (that is derivable) from two ideas of symmetry. In-fact every conservation principle of physics are manifestations of a corresponding principle of symmetry and vice-a-versa (also every symmetry must correspond to a conservation law). This general idea of connection between conservation laws and symmetry is collectively known as Noether’s theorem and is a central underpinning in all of today’s conceptual physics.

New forms of Uncertainty Relationships in Quantum Mechanics.

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 ).