Damn it Einstein: your clock slows down when there is less energy, your clock stops when there is no battery ..
Time dilation is one of the simplest concepts of Physics. Einstein is famous because he gave a mathematical form to it. But here is the idea: time slows down because energy disappears.
And its one of the most general behavior of time dilation I can think.
As an analogy, your ability to do something slows down when you have less energy, when something moves away from you there is time dilation or slowing of time as there is less energy available to you … as in redshift, when something moves closer to you 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 your body is now more wide so each unit in your body has expanded. If there are two lines on your body and your body dilates the separation between the two lines has increased.
Similarly the contraction is a shortening or decrease in duration or separation. It does not matter its time or distance you are talking about as both are equivalent. But you will 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 you will realize they both move both to left and right. Then you will realize men and women are equivalents if not equal. You know what it is that does not let them be equal, physically, but apart from that whats the difference? 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. Similarly General Relativity: gravitational energy disappears in a gravity potential, potential is v^2 [square of velocity], again energy disappears, that is, not available to YOU, hence you 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]
Energy Conservation. 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. It 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 contraction] Also the idea I gave you natural time is unbridled. The clocks in nature are not a constant rate clocks. 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 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. Although this time we have 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 it 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/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 $s and at the same statement it can not be written/claimed I had 9$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 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 [mathematical principles of Relativity] that E=mcc 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 too. 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. Because Energy can only be a function of speed [kinetic energy] or configuration [that is relative position, 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 short 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 is 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, 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 dilation is clear its the same reason for general relativistic or potential energy type dilation/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 KE and PE appear in the same way 1/2 mv^2 is equivalent to mV where V is the gravity potential by definition. Hence a factor of arbitrariness notwithstanding mV 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 you consider potential energy only, as when, you 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 mean 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 a euphemism for time called clock. Thats an anthropic euphemism. Nature understands energy not, time not, speed not, momentum not, understands it: “how much”. That 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 millenia and never 10 years.
In gravity like potentials do you 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. 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 note its solution I have got 3 books but haven’t checked them yet. Off to dinner now.