This is version-II; Version-I is locked to prevent interference.
A general reader or a general member interested in Physics would believe that it is General Theory of Relativity that says gravity warps space-time. Thats a misunderstanding of all of Physics, not just Relativity. I can prove this in two lines but I will perhaps coerce myself into writing a blog. In any-case there is nothing Einsteinian that space-time is warped [– or in one-dimensional terms curved] its a Newtonian aspect. Whats Einsteinian is “exactly” how-much is curved.
Here is the two lines first.
Gravity is Potential Energy which is a function of space and time and the energy goes down proportional to 1/r hence the farther in space-time you are the lesser is your energy. In a space-time which would be called flat, by definition, the energy is same at all regions.
Hence Gravity of an object of mass warps or curves the space and time that it occupies and the space and time that continues to be available to the object to infinite distance. [– In Newtonian Physics just space is warped or curved in presence of mass, the advanced understanding is that in Einsteinian framework the warping is a function of space and time and due to mass-energy-momentum not only due to mass, and this warping is also subjected to various laws that act as constraints to result in relations among these variables known as Laws of Gravity or General Theory of Relativity]
Here is a diagram that explains this.
One thing to note is; in Newtonian Physics one has to say, just space, instead of space-time because space and time are not an unified variable yet. So the energy is a constant of time. [– Energy is a stationary distribution in conceptual time, A potential energy is just a function of space or as is said configuration. In general a potential energy can depend on velocity, their derivatives and so on. Viscosity is a velocity dependent force or potential, corresponding to every force there si a potential and vice-a-versa.]
A surface is flat if you don’t roll over it, on its own. However if you roll over just by the nature of the surface it is said that, that surface is not flat or uniform, its curved with respect to something thats flat. This is the reason why gravitational energy is negative in value, and as a result “everything” rolls towards earth. Objects do not escape away by their own nature if they are sufficiently trapped in the gravitational field of earth, by the nature of space (– and time) around earth. When a secondary object (– such as a falling meteor or satellite) is trapped in the gravitational field of a primary object (– such as earth) the gravitational energy of the duo is negative as to escape from this configuration, each of these primary and 2ndary objects have to do work, therefore spend energy aside from the energy of the gravity-interaction, which is negative and of no use anymore. Its like a negative bank balance is not useful for you to be used towards any other purchase you would like to ensue, the more negative it is for a transaction the more trapped you are.
Okay, so lets start by being very basic about it all. In any given physical situation there is whats called Energy, Force, speed, distance [— an interval in space], time [— an interval in passage of time].
Energy is the amount by which you are capable of doing something and Force is the driver or process of that capability. In other words energy is like your financial budget and force is like your credit card. If you do not have money, swipe your card to humor your kids or humor your mama if she is in asylum, as these are of no use anymore, just like negative gravitational energy or zero gravitational energy, negative or zero bank balance have rendered your cards unusable.
So where-ever there is some kind of energy there is a force thats associated with it. In ALL cases. Then potential, potential-field or simply field such as electric field are very convenient variables from energy and force. The energy if it depends solely on speed, is called a kinetic energy and energy can be associated with existence which is called potential energy. (– while existence is not a term often used, whats used is configuration or interaction, one can see it this way, because something exists it interacts) There are ways through which energy can transform into each other in any physical process.
How-to see potential energy is an energy associated with existence? Think of your property. The fact that you have assets, which have financial value, they can be sold and you can purchase from this value, like you can purchase through direct money, represents potential or existential value. Thus all sorts of force which changes only your speed and therefore kinetic energy are associated with kinetic energy, such energy is because of your motion only. But potential energy may or may not be associated with speed, its a more general case of force or energy. Simply speaking energy is proportional to force and vice versa. All forces are potential energy unless the energy is simply by the virtue of an objects kinematics or motion: this amount is always given as (1/2)m*v*v, where m is the mass of the object and v is the speed of the object.
Now potential energy such as gravity are simply because some objects or source-of-a-force exists, whether thats a mass-object, charge-object or current-object and so on. For gravity its a potential energy that arises from mass or more generally from mass-energy-momentum. Other examples of potential energy are eg due to current. Its this current-object for example which is a kinematic-motion of the charges but the force is a potential energy which keeps on changing, depending on how the kinetic energy of the charges in the current change. So all in all there is charge which can have potential energy or kinetic energy, but once the charge has a kinetic energy that creates another fundamental parameter called current and the current can have two forms of energy again: kinetic energy or potential energy, depending on how the source-of-current itself is moving.
SO talking about charge you have two kinds of kinetic energy and two kinds of potential energy. The kinetic energy are due to charge or current and would be known as electric-kinetic-energy and magnetic-kinetic-energy. But the two kinds of potential energy would be known as electric-potential-energy and magnetic-potential energy. Then they are divided into two classes, these 4 forms of energy, into statics and dynamics. In statics both sources, the charge and the current are at rest, hence the kinetic energy is zero, what remains is only the potential energy. But in dynamics which is a generalization of them, the interaction between the sources as well as the resulting extra energies due to motion (kinetic energy) and resulting extra interaction (potential energy) due to the motion are all to be included. So Dynamics is the most general and it includes for charges and currents 2 kind of kinetic energy and 2 kinds of potential energy.
In all generality there is only DYNAMICS. (– should be called electrodynamics for only charge, magneto-dynamics for only current, but most of the time electrodynamics is used to mean both electric and magnetic charges and currents, its because if you love opera you would also love folk dance and someone sometimes does not care to mention where he is taking you)
So here is the general idea. Potential energy translates itself into traversing space and time. Potential energy translates itself into simply occupying space and time. [– as in a process or static existence but there is nothing called absolute rest]. That are two forms.
Kinetic energy translates itself into the rate at which space is traversed in a given time or the opposite how much time is traversed for a given space and vice versa. [– because there are integration involved, not just differentiation and speed: is a rate/derivative] . so again 4 ideas, eg how space-traversal in a given time translates itself into kinetic energy and potential energy. These are to then satisfy many laws of nature (laws of nature are relations among variables or parameters because there are certain restrictions that come for example from observations or common sense of physical attributes) . That gives the exact forms of many quantities and laws in Physics.
Now that potential energy is from occupying certain space and time [– one of the possibilities of potential energy] gravity is a force or potential energy that is solely possible because an object of mass occupies space and time. (– in generality because energy-mass-momentum occupies space-time subjected to restrictions or relations among these quantities and known as laws of nature or Physical laws or laws of physics)
eg when earth occupies the space-time around it, its effect, interaction or force is larger at a distance which is closer to the surface and smaller at a distance which is farther away, the force decreases radially-linearly, not linearly as such. So there are equipotential surfaces of gravity which are merely concentric spherical enclosures, one at each value of r=distance. This is tricky because its a potential energy where the reference can be chosen arbitrarily in a given situation. In other words, potential energy being negative, its the absolute or modulus of the energy we are talking about. In essence this is to say, the force without the direction specified.
Its interesting to note, thats so because force is a vector and associated with direction and energy being an integral of force, energy has to go on decreasing if energy continues to produce a force. This is again similar to a situation where like a bank account, the more time you spend in a pub the more you have to spend.
Also to be noted; direction of the (Force) vector shows up as a positive or negative sign on the energy, because its only one dimension here which we have considered, the radial direction.
So a satellite in orbit at say 856 kms above earth’s surface (– this is the perigee of the Flyby-II, satellite Galileo) has less absolute (energy) [– or |energy|] than an object of exact same mass as that of the satellite at surface of earth.
If you compare a region where there is no such objects of masses are found we would call it a flat space-time because no matter where you go in that space-time axis, your energy, therefore any other purported physical variable, changes at all. Its the same everywhere, hence flat or uniform.
That is space-time is gravitationally uniform in absence of a gravitational force. Whats the big deal? A force is known to be a fence-bender. Here space-time is the fence and gravity-force which is associated with that object of mass bends the fence of space-time. Since there is no force there is no bending. Since there is no bending we call it flat.
And mathematically force or acceleration is zero hence not only the integral is zero [– energy is the total force or integral-of-force] but the function whose derivative is force has to be uniform. If the potential or force depends on space-time only, its evidently the space-time as a mathematical variable: uniform and as a physical idea: flat.
Gravity theory was developed by Galileo, Newton and Kepler and Copernicus et-al, in different times and person-independently the various segments of the field of study. In all total it can be called Galilean or Newtonian gravity since they were the greatest pioneers of gravity. Galileo was an observational astronomer as well as a theoretician, experimentalist, mathematician, polymath, visionary and what not.
So was Newton who did not have observational astronomy to his resume in the sense of Galileo but he theorized, formalized and worked out much of cosmological motion. eg Newton worked out apoapsis of moon and so on, which were later exactified because they were not completely correct.
Last year I had started studying some of these in conjunction with the general theory of relativity, special theory in motion of planetary objects and so on. I had to stop after a while. You can not take too many studies without finishing them all in reasonable clarity. A physicist’s job is often incomplete despite their capabilities. Thats where it becomes humanly.
But there were problems in Gravity theory of Newton such as perihelion of mercury. [– the gradual deviation of the orbit of mercury around sun due to spin of mercury?]
So as-if genius does not respect the boundaries of dullness, Einstein after his anus mirabilis solved this fundamental problem of the motion of mercury and it was latter observationally vindicated.
year of miracle: Brilliant answers to 5 fundamental physical problems were published by Einstein in 1905, 2005 was celebrated as the “world year of physics” for that reason. I was “celebrating this” in Tampa Bay Florida, in 2005 March-April and purchased for myself from my graduate student salary about 500$ worth of books which included 3 volumes of Weinberg’s QFT, his history of particle physics, Feynman’s autobiographies and 1 or 2 other books which I could not recall. I also purchased a world year of physics 2005 tee-shirt which is as wearable today and another where physics equations were all flipped when you are drunk. Those were my real days of enjoying physics as a grad student.
So we all enjoy because one man had solved 5 difficult and fundamental problems that year, 100 years ago. Since Einstein did not know the boundaries of dullness he took up the question or as we say problem of gravity and solved major problems there of which was one, the “perihelion of mercury”.
What Einstein did was he generalized actual force of gravity based on his ideas of special relativity where special relativity was a change of Newtonian or Galilean relativity by introducing a few insightful simpler ideas such as increase in mass due to faster motion and a speed which can never be attained if you have mass because as you go on increasing your speed much of it goes into increasing your mass as well, not just speed.
Once you have reached nearer and nearer to speed-of-light you can not have the exact speed of light because light is mass-less and you have got mass. Well light constitutes of, not depending on your taste but the nature of things, wave-nature or particle nature, it is these particles that move at speed-of-light. The wave also move at that speed if you realize that speed of a wave is nothing but a ratio of wavelength to time period.
[– waves are always mass-less, why then sound waves not move at speed-of-light? because its speed-of-sound theory not light-theory, the wave traverses at a speed which is a ratio of sound-wavelength to sound-timeperiod and sound moves as the pressure and density in medium such as air or water and this pressure is observed to be moving at speed-of-sound, you can not manipulate observations]
These ideas summed with many other ideas many of which were known and many that were not, but were consequences of a few simple but great insight of Einstein led to what was called Lorentz transformation and special theory. When these were generalized onto kinetic energy, potential energy and so on Einstein explored and invented another great theory of nature called the general theory of relativity which was no mean extension of special theory.
The general theory is not only a theory of gravity but a theory of howto deal with potential and forces in a new frame work of Einsteinian-Relativity. Therefore it leads to time dilation by not only gravity but also any kind of energy such as heat energy. Much of this I have explained in numerous articles I have written over the last year and recently I posted a schematic which says special theory of relativity is to kinetic energy as general theory is to kinetic and potential energy. So potential energy is like extra-special relativity theory.
But isn’t that clear now since at the beginning of this article I said kinetic energy is simply speed but potential energy is speed as well as your existence and interaction. In literary terms a force is an interaction. Force is always potential energy unless it produces only and only kinematic-motion or trajectory-motion. So thats all that Einstein did although he is a genius because he was successful at the goal. A killer is a genius of murder. So if you interact by modifying space and time around you due to your mass (– or in general due to your mass, momentum and energy) thats gravity. Only then you produce some kinematic-motion and there is speed, then there is friction and so on.
It was easy for Einstein to know what the goal was because he was a Physicist but it is not so easy to solve all the problems that he did solve. It took him a life time. Never compare yourself to Einstein. [– Well time travel is your excuse, if you can travel back may be you can compare, or travel forward to a time when you have great theory as Einstein’s, nobody has ever reached there]
Just from a-priori intuitive insightful understanding Einstein generalized all the concepts of Physics known from before. Thats his contribution.
So being a great mathematician Einstein gave exactly what the form of gravitational derivatives are. [– forces, speeds, accelerations, transformation of these quantities into other frames-of-references and then you generalize them into tensors and so on].
In other words Einstein gave exactly how-much gravity or the force of existence and interaction of mass warps space-time but the fact is space-time was warped even by Newtonian gravitational forces because mathematically [– and intuitively] it is these derivatives that are zero, hence the derivatives of the functions of space and time are zero and these functions are therefore uniform or flat.
You would say Einstein unified space and time, but then wasn’t that the case in Galilean relativity? That was. Quantum Mechanics unifies wave and particle, but if you realize some phenomena this was rather known but not talked about in the way we do now, even during Newton’s time. If they hadn’t understood these facts they would not have developed all the suave theories and concepts that they did, so we can now stand on the shoulders of the giants.
Since flat space-time can be thought of in Newtonian mechanics as an absence of force or potential of gravity, its presence is ipso-facto a curvature of space and time, therefore space-time. Thats just another two lines to prove what I claimed, ideally and intuitively.