June 1, 2012
read also this one before or after http://mdashf.org/2012/05/28/time-dilation/
It’s a beauty of Physics that not only the most successful laws of Physics viz quantum mechanics and Relativity are superset of the canonical laws of Physics which is Classical mechanics and over-binding but they are also a good extension of the latter. They were a modified version of the latter hence they must all also fall back onto the classical laws in requisite limits.
In some situations these are amply reflected in the equations or ideas itself. I have hit upon two of these just while thinking of such but one before this is also known pretty well.
The one that is known well enough is the so-called principle of Relativity which is a set of transformations laws between quantities in one f.o.r. to another. But this is merely a different form of transformation laws, the principle of relativity being one known even in Newtonian Mechanics. In the latter they didn’t have the characteristics of certain kind which are only envisaged by Einstein.
I am going to show why two other such similarities of relativistic nature of our world known to be special relativistic properties are actually Newtonian properties. The only difference that crops up is perhaps in the newer ideas of Einstein, perhaps because I haven’t reviewed the constancy of speed of light.
The first one is time dilation. Time dilation is strictly speaking not a Einsteinian property. It’s a Newtonian property. And this I described in much detail in my last article “Time dilation”. Here one does not even need any equations explicitly to see the idea.
Why is time dilation a Newtonian property? Because as I explained in that article “time dilation is a result of energy disappearance or unavailability”. Period. And there is no special Einsteinian thinking here. If there is no energy there is no “running of time”. If there is less there is slower running of time and if there is more energy there is faster running of time. This will be grossly misunderstood in the classical world of everyday life if one does not employ his smart thinking. You will say time runs at the same rate, my clock runs at the same rate once the battery is there and if the battery is slightly exhausted it will still run at the same rate and only if a critical power is supplied the clock will run.
But that’s a fallacy we all face in an everyday thinking which is akin to no refined thinking. Because First of all as explained in that article “there is nothing really that you can call time”. Time starts as an intuition like every other physical variable and abstracted into a more conceptual/theoretical variable/parameter with better understanding, a better conceptual framework and precision methods. But here in your clocks you actually measure “energy” itself. You feed the clock with energy and force it to rotate at a constant rate. And that tells you how much energy you are spending. Then you calibrate that as a unit or a few kind of units of measurement. There is absolutely no time here except that’s what you want to measure a calibrated way of spending energy. And given that its uniformly cutout it gives you a sense of how to follow your day today routine.
But that’s not what time is all about. Time is merely an abstract intuitive way of saying, something started, something finished, something is running, something is running so that the same thing would have been running longer. What is longer is an abstract intuitive way of time. But its precisely not defined without Physics and the Physics is not precise if it does not respect nature. Its longer because we have developed a sense of day-to-day events which are unidirectional, the so-called arrow of time. That sense itself is intuitive and Physics is respectful of that.
But nature does not work with a sense of ours especially in the scale in which we do not directly see what’s going on. There the uniformity of time is only a special case. All sorts of units of time exist in a process. That is, time runs as long as there is a process going on or as long as there is energy. The rate at which this energy is expended is the rate of time and that’s not uniform. That energy is a measure of time but we have not calibrated it into uniform units. That means “given there is no energy time does not run”. That’s what happens in singularities. Time singularities are energy null points. When there is more energy time runs faster and when there is less energy time runs slower. This is time dilation.
It’s a little tricky to call this Newtonian because there are no equations but essentially this is in line with Newtonian equations. You can see that if energy is conserved and energy being something like (1/2)mvv, this implies v is constant. Hence distance and time ratios are constant. In other words distance and time can change but as per energy conservation. If there is slightly less energy available evidently both distance and time-units have shortened. This is space-unit and time-unit contraction. That does the trick of speed and energy conservation. Once space-unit =distance and time-unit are contracted it takes less time and it takes less space or distance to be covered and we say time is running faster and length contracted. [But in-fact as you just saw this is both time and space contraction] In the other situation when there is a slightly more energy available, both space and time units elongate and this is called dilation of space or dilation of time [not just time dilation]. Here the units being longer we are having slower times in-order-for speed [v] and energy conservation.
Therefore energy conservation is the reason why there is time dilation and there is nothing Einsteinian about it. Whats is Einsteinian is the exact form of time dilation because now there are more constraints than just energy conservation [eg speed-of-light]. In that situation mass changes, hence energy conservation does not necessarily mean speed constancy. The space and time units still contract and dilate. Einstein figured out quantitatively that mass changes involve a velocity term. That means how much mass changes depends upon how fast one object is wrt a frame which is at rest. [rest frame and velocity of transformation, this gives beta and gamma the correction factors]
One sees that gamma is such a factor it again makes space and time units dilate or contract together. [Haven’t reviewed but intuitively seems so] Therefore the exact amount of time dilation is a gamma dependent quantity but it comes from the fact the energy conservation is valid. Time dilation is not a special relativistic effect.
What is important is the examples. We use time dilation when there is very slight differences of energy. This entails very slight differences in speed. When speeds are not extremely high such smallness is essentially zero. [not insignificant, but compared to speed-of-light its zero] The examples are when something moves really fast, it’s a slight disappearance of energy [kinematic red-shift ] or a slight appearance of energy [because something is approaching the kinetic energy is slightly more compared to the gravitational energy as gravitational energy is less when something is closer and this is blue-shift, in case of red-shift the gravitational energy is slightly more compared to the kinetic energy but strictly speaking gravitational energy is another form of time dilation but again due to relative difference of position in a gravity field. If you want to see it without gravitational energy then you can see that when something is approaching there is less space between the object and you hence less time in-order-for energy conservation or energy would be less]
Again gravitational energy is a mV~(1/2)mvv hence gravitational potential V is vv [v-squared].
That is how it is defined, the potential of gravity. Kinetic energy is like an individual account in a Bank where as potential energy is like a joint account. Mr. A and Mr. B have kinetic energy accounts in Wachovia. They can have any balance [again speed-of-light constrains this]. But Mr. A and Mr. B have a joint account for potential energy. Potential energy is like a share. You can’t buy your own shares. You can buy in others. But how is it decided? Its decided through your potential. Your potential is defined to be a specific value which is unique for you at a given position. Potential energy is the contribution to the joint account. For a joint account one adds the potential energy contributions from both partners. Hence if you are farther away from a source of gravity you will have to contribute more energy than if you are near to have a joint account with the source of gravity. In the vicinity of a source of any gravity the potential and potential energy start as –ve and gradually become zero. You’re free only if you are sufficiently away. Therefore less energy is available to the clocks in gravitational field when closer than far away. Clocks will run slower in gravitational fields of closer positions than farther away.
Thus time dilation is just a result of how much energy is available to clocks and relatively less or more energy is available to clocks because of their relative motions and relative positions in fields of energy [not just gravitational field, all sorts of energy]
This prompts us to check the principle of equivalence. [Which I mentioned in the last article]
Energy[acceleration] = v-squared
[gravitational potential are like acceleration, perhaps there is a –ve sign, v-squared is a gravitational potential as I proved from dimensional considerations]
sdv/dt = vv
[s=distance, this is ma*s = energy=m*potential]
Upon integration: s*int[v^-2dv]=int[dt] or s=vt; which is nothing but the Newton’s equation of motion.
Thus if you differentiate Newton’s equation of motion you get the principle of equivalence.
If you want to see another way of time-dilation
E=h-neu=h/T or unit of time is inversely proportional to energy. More energy less time unit, time runs faster. Less energy similarly time runs slower.