It’s a beauty of physics that not only the most successful laws of physics viz quantum mechanics and theory of relativity are super-set of the canonical laws of physics which is classical mechanics and over-binding on the latter but they are also a good extension of the latter. They are a modified version of the latter, hence they must all fall back onto the classical laws in their requisite limits.

In some situations this fact is amply reflected in the equations or ideas itself. I have hit upon two of these, while thinking of the same, another one is perhaps well known. The one that is known well enough is the so-called principle of relativity which is a set of transformations relations, between quantities in one frame-of-reference 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, the principle of relativity of ordinary classical mechanics, it lacks the characteristics of certain kind, which are only envisaged by Einstein.

I am going to show why the 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.

Property 1.

The first one is time dilation. Time dilation is strictly speaking not an 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 of energy 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 one’s 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 or theoretical parameter with better understanding, a better conceptual framework and precision methods.

But here in our clocks we actually measure “energy” itself. We feed the clock with energy and force something to rotate at a constant rate. And that tells us how much energy we are spending. Then we calibrate that as a unit or a few kind of units of measurement.

There is absolutely no time here except that’s what we want to measure, a calibrated way of spending energy. And given that its uniformly customized it gives us a sense of how to follow our 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. — And contraction.

It’s a little tricky to call this Newtonian because there are no equations, but essentially this is in line with Newtonian equations. One can see that if energy is conserved and energy being something like $\frac{1}{2}mv^2$, 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 constant 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 we 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. Here the units being longer we are having slower times, in-order-for speed (v) to be constant and energy conservation.

Therefore energy conservation is the reason why there is time dilation and there is nothing Einsteinian about it. What is Einsteinian is the exact form of time dilation because now there are more constraints, than just energy conservation — eg speed-of-light limit.

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. The rest frame and velocity of transformation, gives β and $\gamma$: the correction factors.

One sees that $\gamma$ is such a factor it again makes space and time units dilate or contract together. — I haven’t reviewed this but intuitively it seems so. Therefore the exact amount of time dilation is a $\gamma$ dependent quantity, but it comes from the fact that 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. That is, these speed changes are not insignificant, but compared to speed-of-light essentially zero.

The examples are when something moves really fast, there is a slight disappearance of energy — also known as 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 goes like $mV \sim \frac{1}{2}mv^2$ hence gravitational potential V goes like $v^2$.

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 “net” 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 — this is true not just for gravitational field, but for all sorts of energy.

This prompts us to check the principle of equivalence.  Which I mentioned in the last article.

Energy — due to acceleration $\sim v^2$.

— Gravitational potential are like acceleration, perhaps there is a –ve sign, $\sim v^2$ is a gravitational potential, as I proved from dimensional considerations.

$s\frac{dv}{dt} = v^2$.

— If s is distance, the above is ma*s = energy=m*potential.

Upon integration: $s \times \int v^{-2}dv = \int dt$ 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: $E = h \nu = \frac{h}{T}$ or time-unit is inversely proportional to energy. More energy less time-unit, time runs faster. Less energy similarly implies time runs slower.