Pencils could be balanced on each other in this fashion, only if we didn't have the kind of gravity that we have now.

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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.

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What are Gauge Potential, Whats a “Theory” in Physics?

Potential was, as said above, is, energy per unit mass or charge. So, we see that, in defining the higher quantity energy or potential (higher therefore closer to action, hence more fundamental or unified) we have to INTEGRATE the lower variable, here, Force, Field or (Any ) 3-vector. This entails therefore arbitrariness into the Physical solution when we solve for these quantities. These physical problems, as they involve differentials or integration, leads to a differential equation. Under further suitable physical conditions called eg laws of nature or physics, become whats called a wave-equation or for particles, equation of motion. We can say equation of motion for particles or equation of motion for waves if they are separate.

Now that we understand what are potential, field, vector and gradient and integral in relation to each other, comes requirements called as symmetry or laws of nature or laws of physics or in simple, boundary conditions to these differential equations known as, wave equation or equation of motion of particles OR waves. ( — which are separate so far )

These equations constrained by the conditions or restrictions which are attributes of physical observation, must therefore unite these variables (potential, field) into one entity which would satisfy the wave or particle equations of motion, the differential equations of motion in PARTICULAR ways only, known as Laws of Nature or Physics. So they become, from their 3-vector or scalar attributes, 4-vectors (or still higher, Tensors).

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対称性 。。 壊れた−対称性 。。一回生 の 性質 「Unitarity」 。。単一化

Spontaneous Symmetry breaking, unitarity, unification, this article is written in Japanese.
簡単 の 単語 で 対象性 は 力 の 性質 です。 unitarity は 力 の 一回性 の 性質 と 同じ の 単語 で 力 の 変わらぬ性質 です。対象性 と unitarity を 一緒 に 認め できます。

この 例 を 取る。男 は 幹線道路 で ショッピングモール から 運転 と 家 で 達する。 ショッピングモール の 男 は 家 の 男 を 同じ の男 と 明白 にです。 なにか の 内部 の 力 は 男 から、 例 を ため に、熊 に 変わらない です。物体 の この 性質 は 対称性 さ 知られて いる です。 数学 の 法 で それ が unitarity の 力 で 記載する。

read more 対称性 。。 壊れた−対称性 。。一回生 の 性質 「Unitarity」 。。単一化