June 25, 2012
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 wil 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 could be called flat by definition, the energy is same at all regions.
Hence Gravity of an object of mass warps or curved the space and time that it occupies. [In Newtonian Physics just space]
One thing to note is in Newtonian Physics one has to say just space instead of space-time because they are not an unified variable yet. So the energy is a time-static [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.]
A surface is flat if you don’t roll over it, on its own. 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 -ve, because everything rolls towards earth. It does not escape away by the nature of space around earth.
Ok 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 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 your mama in asylum.
So where-ever there is some kind of energy there is a force thats associated with it. In ALL cases. [Then potential and 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, its called a kinetic energy and energy can be associated with existence which is called potential energy. There are ways through which they 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 has financial value, it can be sold and you can purchase like you can through direct money represents this. Thus all sorts of force which changes only your speed and therefore kinetic energy are associated with kinetic energy, its because of your motion only. But potential energy may or may not be associated with speed. Simply speaking energy is proportional to force and vice versa and all force are potential energy unless the energy is simply by the virtue of an objects kinematic-motion: 1/2mvv]
Now potential energy like 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. Its this current-object which is a kinematical 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 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 [because there are integrations involved, not just differentiation and speed: a rate/derivative] and vice versa. [so 4 ideas, eg how space-traversal in a given time translates itself into kinetic energy and potential energy]. They are to then satisfy many laws of nature. That gives the exact forms of many quantities and laws.
Now that potential energy is from occupying certain space and time [one of the possibilities] gravity is a force/potential energy that is solely because an object of mass occupies space and time.
eg when earth occupies the space-time around it, its effect/interaction/force is larger at a distance which is closer to the surface and smaller at a distance which is farther away, it decreases radially-linearly, not linearly as such. So there are equi-potential surfaces of gravity which are merely concentric spherical enclosures, one at each value of r=distance [tricky because it s a potential energy where the reference can be chosen arbitrarily in a given situation, that is potential energy being -ve its the absolute or modulus of the energy we are talking about, that is the force without the direction specified. Its interesting to note, thats because force is a vector and associated with direction and energy which is an integral of force because energy has to go on decreasing if it continues to produce a force, like a bank account, the more time you spend in a pub the more you have to spend, and that direction of the vector shows up as a +ve or -ve sign on the energy because its only one dimension which is considered, the radial direction here.]
So a satelite in orbit at say 856 kms above earth’s surface has less absolute(energy) [or |energy|] than an object of exact same mass as that of the satelite at surface of earth.
If you compare a region where there is no such objects of masses are placed 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. 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 is uniform and as a physical idea: flat.
Gravity theory was developed by Galileo, Newton and Kepler and Copernicus etal, 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 account in the sense of Galileo but he theorized/formalized/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?]
So as-if genius does not respect the boundaries of dullness, Einstein after his anus mirabilis [year of miracle: 5 fundamental physical problems were published in 1905, 2005 was celebrated as the “world year of physics”, 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/problem of gravity and solved major problems there of which was 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 massless 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. Then essentially these particles [and waves are always massless, why then sound waves not move at speed-of-light? because its speed-of-sound theory not light, the wave traverses at a speed which is a ratio of sound-wavelength vs sound time-period 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, 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 trajectorial 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 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 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]
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 [forces,speeds, accelerations, transformation of these quantities into other frames 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.
Ideally and intuitively.