Damn it, but “Einstein”: your clock slows down when there is less energy, your clock stops when there is no battery. ..
I think this is most profound article, I have ever written, among my articles. It explains why time dilation occurs and removes some misunderstandings, that survived a century. Space is equivalent to time, but distance is not equivalent to time. Distance is equivalent to time-unit. Therefore space contracts, time contracts. space dilates, time dilates. They are equivalents. They would not be, if, they do not change, in the same way some other equivalent variables changes. There is some technicalities but this is understandable, by most people, who have any interest, as this is written in much simpler way.
Time Dilation is one of the simplest concepts of Physics.
Einstein is famous for this idea, of time-dilation, because, he gave a mathematical form to it. But here is the idea, in its qualitative understanding: time slows down because energy disappears.
That time slows down because energy disappears is one of the most general behavior of time dilation, I can think.
As an analogy, our ability to do something slows down, when we have less energy, when something “gradually” moves away from us there is time-dilation or slowing-of-time, as, there is less energy available to us … as in red-shift, when something “gradually” moves closer to us, there is time-contraction, rapidity or blue-shift.
Dilation means expansion or elongation. The duration-of-time has increased. What used to take 1 second now takes 1.3 seconds, as an example. Each unit-of-time has increased. Its like; our body is now more wide, so, each unit in our body has expanded. If, there are two lines (marks) on our body, and our body dilates, the separation between the two lines, has increased.
Similarly, the contraction is a shortening or decrease, in duration-of-time or separation-of-time-tics. It does not matter its time or distance we are talking about, as, time and distance are equivalent. But, we hear people saying: “time dilates and space or length contracts“. Thats like, saying, “women move to the left and men move to the right“. And then, we would realize, they can both, move, both, to the left and to the right.
Then we realize “men and women are equivalents” if not equal. We know, what it is, that does not let them, be equal, physically, but, apart from that, whats the difference between men and women? Really not much. Well, lets explore.
But then, why, people, experts, say; time dilates and space contracts? Because, thats what, is, written in the texts. They haven’t thought through the alternatives of “time contracts” and “space dilates“. If, that were not so, it would be absurd, to say; time and space are equivalents. Was Einstein mad to have said so? He had calculated his stuffs.
This is Special Relativity: a velocity (+, –) v means; disappearance (recession) or appearance (approach) of energy.
General Relativity: gravitational energy disappears in a gravity potential, potential is v(2) (for square of velocity), again energy disappears, that is, not available to us, hence we measure slower time.
Let me explain, a little more.
While musing about this, in a soft voice, to myself, like I am giving some lectures, I formed a better idea, and came with the reason; why this is so? (why the above is so)
What was really running in Einstein’s Mind for decades or years, when he came up, with his ideas of Relativity? Energy Conservation and the fact, that; everything runs because of energy. Even, time runs, if there is energy.
Time runs slower, if there is less energy, and time runs faster if there is more energy. Just like, a clock runs faster, if there is more energy in the spring. Our clock is then, adjusted; to run at the constant pace. But nature isn’t like that.
Nature does not fix its clocks; to run at the same pace. If nature runs out of energy, time runs slow and if, it gains energy; time runs faster. That is the only idea behind time-dilation. (and from now on also, time-contraction)
Also, the idea I gave you is, natural time is unbridled. The clocks in nature are not a constant-rate-clocks. (Although)I do not know one scientist in the world, including, the famous “greatest scientist” Hawking, who has so far, said so. Why I am saying this, because, they show these clocks, in the science books, and it creates an impression in the smart but layman’s mind, that, whenever time is mentioned, in Physics, it corresponds, to something; going on at a fix rate.
Thats why, I think, people never understood; time dilation is much simpler, and any one would have understood it.
OK, so, what was playing in Einstein’s mind? Energy Conservation and the fact that; energy is necessary for “running” of everything. Energy is more fundamental than time. Energy is physical and time is information (and a parameter). Although, this time, we have a physical apparatus which measures time. But the fact is they actually measure energy.
How do they measure, energy? They sometimes measure distance or speed or some such variable. In-fact everyone sees distance **, but no-one sees time. But then, more fundamentally, no-one sees distance either. Because, no-one sees energy. Each of them are correlated with the stuff we see around us, and then, we have studied much in detail, and found out ways; how-to measure one in terms of another.
But in an intuitive way, without much complexity, energy is fundamental, and we draw analogies. If you got energy, you can run, if you don’t have energy, you don’t. And being what we are, we understand then, what energy is, but we do not go any beyond, not everyone understands, this simple concept. We see space in a crude way, but not in the sense of distance. But then, the sense and vision, makes it possible for us; to know and calculate distance, in a humanly way.
Only when we develop devices far advance, do we measure distance, and gradually develop a sense of, what distance is and from there, we, also develop sense of what time is, eg, by developing, various kind of watches and clocks. We develop a sense of what speed is and connect it to measurable ways, because, we know distance and time. Energy comes in later when we realize that there must be something, which is like an account, from where, we can decide “how much” we can do stuff.
This “how much” is different from the “how much” of distance and “how much” of time, but we know intuitively, all these, “how much”, are correlated (mathematically) or connected (intuitively). In-fact, the only physical variable in the world is “how much”, rest is detail. I love you. How much? Poet: as much as an Ocean. Physicist: let me get a slide caliper.
** More truly no one sees distance either, they see matter and objects, and based on their past experience, visual ability and intuition etc, they form a sense for distance. But then, no one sees energy either. There is not a single physical variable, that we can see, its because, they are variables. (that is, mathematical quantities that have various distributed values.) No one sees a mathematical quantity.
So now that we know the two facts, that Einstein must have ran, in his mind;
1. Everything runs on the information of “how much”, it can run because “how much” is there, and this time Energy being well-defined in Physics, “Energy decides everything even time”
2. Energy is Conserved.
The 2. is; in any process “how much” we start with “as much” we end with, because, there is nothing that makes a human being capable of worldly logic, infer, that there is something, that invalidates the “constancy” of “how much”, or invalidates everything by a streak of indeterminacy.
I had 5 $s and at the same statement it can not be written or claimed, I had 9$s. Its determined and definitive, that, I had “how much” and given that there is nothing happening to such, it must remain “as much”. This is called a conservation principle of “muchness” or “quantity”, and in our discussion Energy.
So, intuitively, Einstein knew, Energy is conserved, and; amount of Energy determines the flow of time. ( — and determines everything else, because Energy is only equivalent to, every other physical variable.)
Then, how does it follow, from conservation principle of Energy, that, time dilates? For another matter, you can use the Relativistic Equations ( — or the mathematical principles of Relativity) that, E = m.c-square follows, from, conservation of energy and momentum. Similarly, time dilation would also follow.
But whats so simple about time-dilation? Time being decided by energy, more energy will allow faster time and less energy a slower time. This is time dilation, if you lose energy, (energy unavailable as in case of recession of objects from each other called Red Shift) and time contraction, if you gain energy. (energy available by gain as in case of approach of objects towards each other called Blue Shift)
This is Special Theory of Relativity. It involves only a v to the first order (v=velocity) or higher orders, as well. Because velocity essentially means energy, something receding with speed, velocity v is an unavailable corresponding energy and therefore slower time. A slower time is possible when time ticks appear at a longer duration. (duration of time or unit of time has increased, therefore, what used to take 1 second now takes 1.3 seconds or the unit is 1.3/1.0 which is > 1 hence unit has dilated or time has dilated)
In the same logic, time contraction occurs, if, something approaches you (Blue shift). But space and time being equivalents this means, space dilates and contracts and time dilates and contracts. Things to note: space has 3 dimensions, hence, the resulting space effects are a bit more complicated. I have a paper on binomial analysis of Doppler’s Effect and time dilation, contraction, which gives, all details; transverse and longitudinal Doppler Effect.
Now energy is conserved, that is, constant, hence, it must correspond, to a constant speed. (slightly tricky statement, isn’t it?) Because, Energy can only, be a function of speed (kinetic energy) or configuration (that is relative position etc, potential energy) But special Relativity is a matter of kinetic energy and general Relativity is a matter of potential energy.
In general behavior, Relativity is “more energy => faster time”, “less energy => slower time”, same energy => same speed, hence, both, faster and slower time, depending on, shorter or longer distance.
So given that speed v is constant, it means d/t ratio is same. That means d and t, change at the, same fraction. If time unit doubles, so does space units. Which is why; space and time are equivalents. We could have said, space dilation and time dilation. But understand the fact, that, unit of time and unit of space, are used in different mindset. We want everything to be slower, hence dilation of time, because dilation of time signifies “more time”, as the units have dilated or increased, which is also same as saying, time is slower, because, it takes longer time.
Time is material or you or me, (if) you take longer, time takes longer, there is nothing given special to time because we measure stuff via time. Its only that, we measure stuff via time, in a day-to-day affairs, but for Physics, everything is not measured via time, but that one supreme variable: “how much“.
When its a longer time, so also, its a, longer distance, so that, the ratio is same, and this ratio being speed, energy is same. Hence, Energy Conservation or Constancy of Energy means, time is dilated, or, slowed down, if, there is less energy available, which is when, thing go away from each other, or, things fall in a well of gravity.
The constancy of speed therefore is intermediate between constancy of energy and changes in units of time and distance in the same manner. Time dilates because energy disappears and time contracts because energy appears. If energy appeared distance is short, therefore, time unit must be short, which is, time is faster or clocks run faster or time contraction.
Its confusing, because, its actually, time unit contraction or time unit dilation. Space is equivalent to time but distance is equivalent to time-unit. If we were, this careful, for the last century, we did not need, so much new mathematics, because language would have sufficed to do much, how many equations did I use in this article ?, which is I guess, one very long article, because, I have been writing and writing. We’ll see how long it has turned out when I publish.
Now that time dilation from kinetic energy or special relativistic time dilation is clear its the same reason for general relativistic or potential energy type dilation or contraction.
Potential Energy is v(2) (v-squared). Why? Because, kinetic energy and potential energy appear, in the same way, in Equations of Physics. They have equal things to carry out, although, sometimes, they work in opposite, because, one is the source and the other is the benefactor. Since K.E. and P.E. appear in the same way, 1/2 m.v(2 ) is equivalent to m.V where, V, is; the gravity potential by definition. Hence, a factor of arbitrariness, notwithstanding, m.V is; the potential energy.
That means, from unit and dimension consideration, the potential (not potential energy but just potential of gravity) must be, v(2) and it also must be conserved, if we consider potential energy only, as and when, we have considered or will consider kinetic energy separately. Now kinetic energy is also v(2) but special relativity is formulated in terms of v which is still equivalent, to, v(2), because, one determined the other, only in one way, and, no more.
So, potential being V ~ v(2); V is constant if v is constant. So, only if speed is constant, potential and potential energy are constant. But, when speed v is constant, the ratio of d and t must be, as well. Which means, time-unit and distance are equivalents, and, they must, change in the same way, they dilate together and they contract together, with the variation of, energy or speed, kinetic or potential not withstanding.
Now this means, if you fall in a gravity, or, any kind of potential, that means, you are losing energy, and therefore, you are observing your time to be slowing down, because now, less energy is available to you, to your time, to your clock, to everything. You see, its “how much”, the one supreme variable, nothing else, for nature.
Nature does not have an euphemism for time, called, clock. Thats an anthropic euphemism. Nature understands energy not, time not, speed not, momentum not, understands it: “how much“. That how-much thing is arbitrary. That thing will never be completely, in line, with anthropic understandings, unless, humankind has a great stride to make, in unanimity, in a matter of centuries, and millennium and never 10 years.
In gravity like potentials do we ever gain energy so that the time runs faster? Not in gravity, because gravity is always sucking. But in other forms of potential energy its possible that time runs faster. (that form of potential would be relaxing the clock more and more by supplying energy, like UN can fund your project and un-trap you more)
Also you realize, that, relative locations of a clock in such field of gravity entails slower or faster clock-response.
The last thing I like to say is an equation which struck me. Since, by principle of equivalence, gravity-potential and acceleration, act equivalently, on everything, therefore, we have an equation.
dv/dt = v(2). (or is there a distance multiplied to LHS?) So, I think, this is a differential equation, and to find its solution I have got 3 books, but haven’t checked them yet. Off to dinner now.