**I cannot believe this … (original Title) 7:30 pm**

**A thorough understanding of the concept of Principle of Equivalence, a beginning.**

*8th June 2012*, by Manmohan Dash

I wrote two *recent articles* on Relativity Theory and talked about how some of its *most popular and basic ideas* are actually not Relativistic in the sense of Einstein’s New Work, but, in the sense of the **ideas** that were **existent** *much before* **Einstein** and *these ideas*, simply, might not have had, the *name-sake* of the currently understood **ideas**, known in terms of **Relativity Theory of Einstein**.

I also proceeded to **define** an equation which *states* that “The **Principle of Least Action** *leads* to The **Equation of Motion** and the **Principle of Equivalence**“.

The fact, that, the principle of equivalence* follows* from the equation of motion of the **Newtonian Physics**, I *proved*, in one of the **two** articles, I *wrote*. But this later Principle of Least Action leading to equivalence principle *I haven’t proved yet* although I tried to do this and it seems closely possible.

**[**I** think ***within a few days of this article, this latter fact also, I have proved] *

The **proof** of Least Action (or stationary action ** ) leading to equations of motion is found in almost all textbooks of **classical mechanics** **[**I *guess*, its certainly in **Goldstein, ***the most famous Classical Mechanics text followed around the world***]** **so** it must be, *pertinent and imminent*, **suo-motu** that least action leads **to** principle of equivalence.

**Now**, Principle of Equivalence is *unnecessarily* and *complicatedly ***stated** to be ” the gravitational mass and the kinematic masses are the same”. I talked about its **3** *forms*, (strong, weak and medium-strong) in **one **recent article. **Why is it complicated?** (*and this is what I cannot believe*)

Its like *saying the nose (***仏 − 亻***) *in a **roundabout** *way* (a *popular phrase* from where I come from). As an **analogy** consider this: Men and Women are **equivalents** *because* their hands are *equivalent*, there is no generic anatomical differences there, this leads to, are men and women equivalent *everywhere*? Oh, we know a few places, where they are **not**.

But then we can **define** the functions of these organs or anatomical regions and we see that men and women are functionally equivalent but men and bears are **not**. The latter two **cannot** *perform* the same actions and you can easily see “*oh yeah sure, its obvious*”

**[** feminine and masculine bears are equivalent, except *carrying* a baby, and so are men and women, **not** equivalent for the carrying of babies, as a function, so far so good, *you see the idea and the usefulness of the equivalence*, through this **analogy**** ]**

But, what if, we define equivalence between men and women to be “*the male sexual organs and the female sexual organs perform the same job of reproduction and carnal pleasure*“. That would be a **specific** *condition* which actually fits in with, the idea of equivalence. Thats what it **is**, the **mass** of gravitational and kinematic *origin* **is** a specific condition that fits in the idea of principle of equivalence.

The **simpler** and the *more* **correct** and intuitively **proximal** *idea,* would be “*the kinetic energy and the potential energy are equivalent*“, in other words, the effect of these two forms of energy, **is,** the **same**, and, they would **transpire**, in the same way, into, **say**, other forms of **energy**, and so on, despite of their different source of origin. Its this **property** that forms the **basis** of principle of equivalence and its this property, that leads to, much more **profound** ideas of Physics, than, the fact that the *two kinds of masses are equivalent.*

That latter, **is**, just a **specific** *condition*, which, must be also **valid**, in any case, as you can imagine right away, the **mass** is a factor in the energy **so** mass being a **fundamentally** *measurable* quantity, it must be same, in both cases, gravitational and kinematic. **But,** perhaps, it was **unnecessary** to *envisage*, that, *they would be different*. (*gravitational* and *kinematic, mass, would be different, was unnecessary*)

*Because*, somebody could **also** argue that; gravitational and kinematic speed, g&k acceleration, g&k force, g&k potential or potential energy, could be different, they are **same** and thats principle of equivalence. But then the argument stopped at the mass, and did not lead to other physical variables, of fundamental nature.

So people who want to test the veracity of the principle of equivalence in its various, degree of strength of definition, as mentioned above, weak, strong, .. , want to test it on mass, which is easier to do, given how everything is formulated, drop two balls , or realize that planetary objects are constantly falling and so forth. But, the difference if there would be, could be ascribed to any fundamental physical variable, happily there isn’t, or they would totally blow up in some way or other and take away all the elegance of the edifice of the Theory of Relativity.

In-fact, one, **remarkable **aspect of Theory of Relativity, as I understand, intuitively and comprehensively, to the best of my knowledge, is the fact, that, special theory of Relativity is to kinetic energy what general theory of relativity is to potential energy. But then, through principle of equivalence, general theory of relativity **is** not just potential energy, but also kinetic energy, because, *these two are equivalents*. So you have; *special theory coming just from kinetic energy concepts* and then the rest **is** potential energy concepts. So, general theory (GT), **is** an **extension **of special theory, as GT, contains, both kinetic energy processes and potential energy processes.

Also **see** it this **way**, the kinetic energy gives you the **speed** as a **central** *parameter*. Then, various transformation properties are **determined** based on, Lorentz Transformation. eg the *mass changes with speed*. The principle of equivalence comes up, from the fact, that, one can **define** a potential also for kinetic energy, as one can, (define potential) for the potential energy. The **potential** or **force** is **not** *definable* for a uniform velocity, but, for a **velocity**, *that changes with time*, so that, **acceleration** and **force** are *defined*. Once there is a **force** there **must** be a **potential**.

**[** **force** is time-rate-of-change of **momentum**, classically, but, space-rate-of-change of **potential-energy** and potential energy divided by mass, **is**, the potential, for our discussion is centered about **mass**, and say, **not**, *charge*. **]**

So, there is no reason, **why,** the two different forms of potential and therefore two different forms of potential energy, the gravitational and the kinematic, should be different at all.

A kinetic energy can be associated with a **force** or **potential** and therefore, **not**, any different from a, **potential-energy**, that is, they are **equivalent,** and, in situations, when there is **no** *force* or *acceleration*, the amount, can still be equated, **to** a potential energy, *hence in all cases***, kinetic energy **is** equivalent **to** potential energy, **therefore**, acceleration is equivalent to gravity, **as**, acceleration **is** kinetic energy **and** gravity **is** potential energy**.

This also makes it clear, that, **special relativistic effects **are** equivalent **to** general relativistic effects**, this, must be the case, as,** kinetic energy **and** potential energy **are** equivalent, **so also**, all other variables, **such as** potential **and** acceleration**.

So, we should not have stopped at “**mass**” and one can go home, with the lesson, that, **principle of equivalence ***can be defined in terms of any variable we just discussed*. If that does not have the appeal of “

**mass**” because

*mass*can be touted to have come from different sources, but not

**potential**, perhaps you did not realize,

**Relativity**, in its actual flavor.

In that case, you can still talk about, the whole discussion: that**, perhaps, ***all the relativity ideas can spring from simple classical physics ideas*. One should be ready, to take pen and paper, enough thinking and

**calculate**

*stuff*.

In any case, once I *prove* least action leads to principle of equivalence (– **which I did, ***I shall only link*) one can have a similar approach, to any ideas of Relativity, and **find** *insightful conclusions,* to make for **Physics**.

That would be, satisfying, to a good passion of understanding; *what really Physics* **is**.

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