Could Einstein have thought; Equivalence from simple notions of Geometry ? Yes.
In some articles here on this website I have at times tried to peep through the mind of the most well known Physicist of our times, Albert Einstein. Its fun, since, if we can see the lines of thoughts we can only relate the threads to the knots and untie the puzzles, it only adds to our understanding from where, we can understand further, most of it will add to our knowledge but some might even lead in a bizarre path of innovative discoveries.
Here is one more such idea that just flashed to me. When I was running random thoughts in my head.
Could Einstein have thought Equivalence Principles from simple notions of Geometry ?
Lets try to put the things in perspective.
Newton knew and told us so, things would move in straight lines, unless and until something buzzed it aside.
That thing that buzzes us aside; when we are mindful of our business, is called as Force.
Now depending on how aside something pushes us, and in what manner; all forces can be Constructed or Construed. So, given something buzzes me sideways or longitudinally or more and more sideways gradually, the forces would be known as transverse, translational or longitudinal and rotational or angular. [Note that; translation is often used in the sense of 1-D or longitudinal motion at an uniform rate of translation or speed and longitudinal means along certain reference, eg a Force's direction.]
Then towards the end of his life, Newton had to deal with the Concepts of Pseudo Forces of the rotational kind; for which he performed his bucket experiment. But he successfully could not explain the rotational effects that were later linked to an effect called as Mach’s Principle also explained by me, in this website; by the same name “Mach’s Principle”. These forces were to be very successfully and as a revolution of ideas, discovered and explained, by Albert Einstein whose mind; I am dissecting here without impunity, prejudice or clinical license.
So, central to the above exposition; is a concept called as inertia. Inertia is that quality, attribute, characteristic or property of physical objects by which they show their tendency to remain in their state of motion without paying heed to the outside world, until and unless a force comes along and buzzes them, sideways, longitudinally or more and more longitudinally or more and more sideways etc.
So we learned two things here, by; what humanity has been observing for a long time.
(1) You are either in a state of uniformity, that is past and future for you are monotonous. You have an inner tendency known as inertia to be in that state, how much you will be able to withstand a force which is trying to overcome that inertia is a matter of how much inertia you have which is a function of the conditions you are bestowed with and also the force that is given to buzz you.
(2) If you are no longer moving in a straight line or even if you are moving (in) one but without that uniformity, there is an agent that’s causing such changes to your state of motion and; the agent is called a Force. This Force is easily given as an acceleration. (F = force = accelerating factor, which is proportional to another physical attribute called as mass = m, that gives the amount of inertia you have and called an inertial or gravitational mass depending on the context, all in all given as Newton’s Law: F= m.a)
This much was given to Einstein. He knew that the great problem of rotational inertia which is connected to Mach’s Principle ** has not been solved by Newton, the great. How could he proceed with his Physics?
** Mach’s Principle: Distant stars have to be brought into reference in order to fix the exact amount of rotational discrepancy of objects, on surface of earth, hence stars are a good way to be serving as inertial frames of references ( — against the menace of the non-inertial ones like earth surface where we spend almost all our time — ) , once you understood the two points above, 1 and 2, inertial frames are frames where Newton’s Law of F=m.a is valid and non-inertial frames are references where they are not valid, due to such rotational discrepancies, but lo-and-behold and hang on, life is easier as, such validity of Newton’s can be brought back; by employing an additional technique called as Pseudo Force.
So you recognize not all references are INERTIAL or NEWTONIAN in nature, due to presence of accelerations that are rotational in nature, in other words; Forces that are buzzing you sideways or buzzing you sideways constantly, creating circular motion. When such forces or references are in the problem; one introduces pseudo forces which are in some cases -ve signed real forces. ( — that is; Real Force = F, Pseudo Force = -F, such substitutions bring back peace to those who want to apply Newtonian Method, F does not satisfy Newton’s Law ANYMORE but -F does — )
One word of caution which the literature hasn’t paid any attention to is the concepts of inertial forces and non-inertial forces. In considering only one terminology, non-inertial forces, that is the forces of non-inertial or rotational, non-Newtonian or pseudo origin are simply called as; inertial forces instead of non-inertial forces. Its a grave mistake I pointed out a year or more ago to some Students of Physics in an online discussion I was having. Its an obvious blunder of Physics Literature. }
So, from above explanations, it should have been clear to any Average Student of Physics that things that are now not moving in straight line are so doing because of influence of forces. Forces being proportional to accelerations, a curvature ( — sideways motion entails a curvature for the objects in motion, the more the curvature, the more the force or acceleration} is directly connected with an acceleration.
Now a curvature is simply an angle. An angle is a ratio albeit of two distance segments. So far so good, the acceleration is a change of speed due to a given change of time, per that change (of time) just as the speed is a change of distance. So acceleration is angle or a change in angle per that angle. This is possible only if speed is an angle. But speed can’t be angle: its distance to time. That’s where Einstein argued: it can be, it must be, it is so only if distance and time are equivalents. And practically we are seeing that accelerations are angles and there is no other ghost work involved here. Hence, if he were to think like this; he could have seen how it is that space and time are equivalents.
Now it may also be related that light bends in a denser media compared to a rarer media because an additional rotational force is working. In other words, the definition of straight line has to change in the medium, that is of different density, because path of light is changing. Light is the guy who suffers the least when something tries to buzz it, because its inertial property of mass is zero. The curvature of light or the bending or deflection known as Refraction is thus a measure of the sideways force or energy.
Thus speed of light in different media is a measure of this bending or curvature and is known as Snail’s law ( — Pun intended, its actually; Snell’s Law — ) . Automatically when distance and time have to readjust, to produce an angle or bending, known as refraction ( — possible because distance and time can produce an angle if they are equivalents — ) the speed must also change.
All these are inter related. Light refracts and its speed changes, in relative change in density of media because there are rotational or non-inertial effects.
( — or additional energy is available, or a force is acting to bring a curvature in light’s path, perhaps the electromagnetic effects of the molecules? Its not only distance or time that are equivalents, read one article of mine “All You Need To Know About Relativity” to understand; how energy and time and distance and in short all Physical Variables are equivalents of each other — )
I am feeling great now, because this idea just occurred to me. And its 3.30 am, and I am not sleeping as yet, as I want to read again, when I hit the Publish Button, not for cross-checking, who cares for mistakes, just because I am elated at such an idea.
This article thus makes me sleep at 4 am. Read one article which I wrote ‘fter I woke u at 3 am. Again; Physics does not let me sleep, in one piece.