“Logic is the foundation of the certainty of all the knowledge we acquire” – Leonhard Euler.

Using logic and memory, we found answers to many of the old questions regarding the various phenomenon. From counting the sheep to accounting for changes in movements of the star, we have also been able to leave the planet which was considered a dream. From quantum to macroscopic celestial bodies, there are various laws that define a single concept. Also, various formulae describe only a single phenomenon in various other cases. Among all of these mind-boggling ideas, we are here going on a journey from basics concepts like time and gravity towards the unification of laws of physics which is what we call, "The Hunt for Theory Of Everything".

Time is one of the common and yet the greatest mystery in physics, and we consider it valuable because once it passes, it never comes back.

Then there’s gravity, considered as a force by Newtonians and a curve in the so-called fabric of space-time Einsteinites. And what’s surprising is that we use formulas that were derived by both, because they help us in our calculations and have never failed us. Newton’s formulae on gravity help us do calculations related to orbital velocity and other critical values for an artificial satellite while the formulae devised by Einstein help us do some time dilation stuff – like making the GPS more accurate.

So there’s time and then there’s gravity. Let’s mix these confusing things up and see what Russian salad we get.

We know that doing the gravity of the situation increases stress and nervousness and then it makes us feel that time has slowed down, but actually, that's just an illusion from our mind because the rate of signals – that our brain is receiving – has increased. But there's a related fact that the "gravity" not the "gravity of the situation" can relatively slow downtime for an observer in that respected frame of reference. The so-called beasts of the gravity - which are called Blackholes – rip the fabric of space-time and thus cause a singularity. Now, considering the gravity as a force, it is too strong near a black hole that it doesn't even let the light escape! And yes, light is the cosmic king of speed. And by escape we mean that the path of light doesn't remain unaffected here.
Pic credit- Pyle/CALTECH/MIT/LIGO LAB

Now, for the time-dilation part, consider that the speed of light is constant in a vacuum, and also here we consider space to be a vacuum. We cannot go to space just for the sake of this example, but let's consider a simple extensible fabric and a marker to trace the path of light. Now make two points A, B on corners of the extensible fabric. Connect the two points and measure the length. Let this length be L and then by any means cause depression in somewhere in the path by putting a metallic ball near or on the line traced. Then as the fabric is extensible so we see the line is stretched nearby that mass. And thus the new length for this line will be more than the original one.

The time for the calculations now, let be the original length and be the new length. The speed of light c=299792458m/s , and then let t0,t1 be the time taken for the first and second cases respectively.

Using the old-school formula:

For the l0 we have,

Now for

where k is a positive number, so we have,

Equating the , we get,

Here, as , so, , as time dilates or increases for the second case. The same goes for the heavenly bodies that we just examined using the homemade stuff available. The real fancy formula for time dilation goes like:

Where is the original time, is the dilated time, and is the speed of the body traveling and speed of light in a vacuum respectively.

Here, we compare the formula by Einstein to that of ours ( jokes aside, but yes, we just invented a formula).

Here we got another formula, but unfortunately, it was already done by Einstein.

This formula lays down the basis for the phenomenon called length contraction.

So from this, we also deduce that the length of a body traveling at velocities near the speed of light, contracts and this is given by our formula derived above.

Written by Ijaz Ahmad, Pakistan