Theories:

Before we begin:

This is a theory entirely based on hypothetical conditions, the following concept here may or may not be proved yet- take the concepts here as a pinch of salt. These theories are provided with research and some of them contain mathematics, however, there are some legit explanations presented here, so it might be worth checking it out.

Saturday, June 2022

Pressure relation with Speed and Gravity…..

Revision 

Last time we talked about how gravity is related to pressure and how the warping of spacetime is considered a behavior rather than a force; blackholes bending the spacetime and causing light to deviate.

Considering the previous theories, we can connect concepts like time dilation with pressure and gravity. 

But for that, we first need to understand what is time, and what is space?

Space and Time

We already discussed that space and time - Spacetime is the 4th dimension, connecting both space and time as a whole-  are related to each other. 

How is Time Relative?

Einstein's Special Theory of Relativity explains how time changes concerning speed - the faster you move in space, the slower you move in time. According to Einstein, time is relative and could change its flow by the following factors:

1. Speed:

Speed is indirect to time, the faster you move in space, the slower you move in time.  This is called “Time Dilation”, where the course of time changes according to perspective. 

We can calculate the exact time dilation by the Lorentz factor, which is correlated with the speed of a body(v) and the speed of light ( c ). 

The equation is the formula to calculate time dilation. 

You may have heard that “Nothing can travel at the speed of light”, but why?

What happens if one could travel beyond it? Well, the laws of physics cannot explain this scenario so this is why it is simply terminated. 

Look at the equation and replace the body's velocity (v) with the speed of light (c ).

If ‘v’  is replaced by ‘c’ then the answer would be infinite. Hence, the time dilation will be infinite which is not possible ( our mathematics is not applicable). This is why we couldn't travel at the speed of light because the maths doesn’t seem to work.

But, if you travel near to the speed of light (v<c), the time dilation increases, and hence you will experience this phenomenon.

 In short, the faster you move in space, i.e ‘ v increases’, the slower you move in time because the value of time dilation (to) increases for you and experience slower time.

Time is indirectly proportional to speed.

...Eqn(1)

2. Gravity

The gravitational force is the second factor that affects the course of time. In the first factor speed, a special theory of relativity takes place whereas in this factor it is general relativity. 

Einstein first developed his idea of time with speed and later after years of research he found that acceleration is related to gravity. With acceleration regarding speed, this is when he proposed his 'general theory of relativity.

The general theory of relativity is a part of special theory because in special theory time decreases with the increase of speed and here in general theory its gravity changes the course of time.

Gravity bends space-time and decreases time. Hence, you can say that the higher the mass of a body, the higher the gravity and since gravity is increased, space-time bends even more which causes the time to decrease.

Since gravity changes the course of time to speed ( Special theory ) then we can connect general relativity with special theory i.e 

Gravity is related to speed since both factors change the course of time.

Here can do the same by replacing 's' with 'g'.  

We can also change the equation to find out how much time is dilated by gravity just as we did for speed.

..Eqn(2)

Gravity is indirectly proportional to time.

From Eqn(1) and Eqn(2), we can see how speed and gravity are related to each other. 

………………………..……………………………

Now, let's revise what we learned from the previous blog about pressure and gravity.

We found that when space is bent by a mass pressure is exerted and from that pressure, time is dilated. The higher the pressure of a body, the more space-time it bends and changes the time.

From here, you can see the connection between pressure and gravity. Pressure is another form of gravity if a body has a considerable amount of pressure then it certainly has a max gravity too.

This is why black holes have higher gravity- they have a very small area and since the area is inverse to pressure, its pressure is extremely high, with high pressure means high gravity.

 Moreover, gravity changes the course of time (2nd Eqn), so at last, it's time that is dilated.

Let's make a chained figure to understand more clearly. 

Here, Area is inverse to pressure, if area decreases the pressure of the body increases. Similarly, the pressure is directly related to gravity and if pressure increases gravity increases too.

And with gravity, time is dilated. 

In the context of black holes:

Area is very small = pressure increases immensely = gravity increases = finally, time dilates.

Note that the area of a black hole is so small it's a singularity, so its pressure is very intense( some even say that it tears the whole space-time and becomes a pathway to an alternate universe i.e wormholes )  which is why time is incredibly slow and gravity is nearly infinite. 

This is one of the reasons our laws of physics don’t work in the center of black holes, of course, there are other reasons like fluctuations and inflations which we'll explore another time.

Now that we connect gravity with pressure and time, it is the speed turn. We can directly include speed here, right? 

Yes, but also no.

Speed is direct to gravity, so we can include it in the chained figure too but there is no logical explanation of how speed changes with time. 

There are some theories behind how speed connects with gravity but for that, we need to understand length contraction.

                                     Length Contraction

When Einstein developed his special theory of relativity, lots of theories were also developed from it which were proven either theoretically or experimentally. One of the famous effects/theories is length contraction.

 When an object travels nearly at the speed of light, it is not only the time that gets dilated but also the length too. This sounds crazy, but it is true. Length contracts when the speed of a body is increasing the same formula for time dilation works for length contraction too.

Here, we can replace time with length.

However, there are no logical explanations for this phenomenon, it is just a part of relativity. The reason we don’t experience time dilation and length contraction is that our nature doesn’t have enough speed. This phenomenon does occur in our daily life but at a very small value; we can replace ‘v’ with our normal speed, but the value of time dilation/length contraction is near 0. So, we must travel near the speed of light to experience these phenomena(Remember, at exactly ‘c’, the dilation is infinite.)

This weird phenomenon, however,  can only be observed by the observer-observing reference.

Let me clarify :

If 'A' is traveling at high speed and 'B' is observing:

When A sees his clock, he doesn't notice anything. For him the clock is stable, but when he observes the B clock, he will notice his time being slow down. The same goes for B when B observes his watch he doesn't see any difference,  but when he sees A's clock he will notice it running slower than his.

This is a paradoxical situation:

Even though A is traveling at high speed, he sees only B's clock slowing down and for B, it's A's clock slowing down. Which is correct?

-     B is correct.

This is exactly the twin brother's paradox,  but scientists have found the answer to this paradox. Even though it feels like A clock is not showing down to itself.

Think of it this way: 

Let's say that Alice is on a bus and Steve is exactly on the side of another bus. 

                There is nothing else except the two buses - not even the environment,  it's just plain white.

Let's say that Alice's bus starts to move(at constant velocity), she looks at Steve's bus and notices he is slowly moving far from her. Now here is the thing,  for Alice, it is not her bus moving, it is Steve's. Since there is nothing else to compare and the environment is white, she would only see Steve's bus and it would be really hard for her to determine which one is moving.

The same goes for Steve, he will see his bus moving away and cannot determine which bus is moving.

Who is correct, then?

Well, both Alice and Steve are correct in their ways. This is where relativity kicks in. From Alice's perspective, she is the observer and she sees Steve's bus in motion. But from Steve's perspective, it's Alice that is moving in motion.

How to find the solution?

To find the solution, there must be a comparable element. What do I mean by that?

Let's do this same scenario,  but this time Bob is watching them from the top. Since Bob is now a comparable element,  he can easily conclude which bus is moving. Being on top, he can observe which bus is moving. 

What's cool about Relativity is you can use this concept anywhere: whether you are on a local bus or train- the key thing here is constant motion then only one can feel it.

………………………………………………………

Length Contraction with gravity?

So we know that when an object travels at high speed, the length contracts. Similarly, we discussed how pressure is indirect to the Area, the denser the object, the higher the gravity.

We can apply this there, when the length of the body contracts, the area that covers also changes significantly, and since the area is indirect to pressure, the body's pressure also increases. 

Since we found out how pressure changes with gravity(chain figure) we can say that gravity also increases. 

To sum up, when a body travels at high speed (extremely high but less than c) its length contracts and area decreases. With the area decrease, its overall pressure increases, and hence gravity increases too and decreases time.

This is how speed changes the course of time.

We can also connect speed, time, gravity, and pressure to the same factor since they are dependent one way or another.

Schwarzschild Radius with gravity

This is a weird concept that connects the radius with gravity at a new level. To understand this, we need to first understand the Schwarzschild radius. We discussed this previously, Schwarzschild radius is the minimum radius that a body can obtain.

All of the mass containing the body has its Schwarzschild radius.

When a ball has compressed the radius of the body changes, hence its pressure also increases. But there is always a limit to this continuity, the ball has its certain point where it can no longer be compressed- the radius becomes extremely minimum. In this case, however, the pressure extremely increases. Since pressure is direct to gravity, the force of gravity also changes immensely. (if you find this confusing, you can read the previous blog where I explained this concept with figures and mathematics.)

So, the Schwarzschild radius is the radius of a body(compressed), in which the gravity is extremely high. This body changes to a black hole. 

Yes, it is true. Any bodies and objects can be changed to black holes if the radius is lower than the Schwarzschild radius. Similarly, black holes are nothing but singular particles. They have high gravity because they are highly dense objects which bend the space-time very deep.

Max - Gravity(n):

If we try to connect the concepts of both theories- Schwarzschild and gravity- we can somehow be between this concept of ‘max gravity’.

‘Max Gravity(n)’ is the maximum gravity that an object can have, just like the Schwarzschild concept. Every object has its minimum radius and if they are in its minimum state, it changes into a black hole. The gravity exerted during this final process is max gravity.

We can say that ‘n’ is a constant value of an object (max) and it can never be greater than its original gravity. 

When an object travels at the speed of light–length contracts--area decreases--pressure increases--gravity increases… The original gravity(g) of the body now increases and when the radius is exactly equal to its minimum, then gravity becomes maximum and changes to max-gravity(n). We can do this same with pressure and length but gravity is more intriguing to me.  

Remember these are just some theories from general relativity and other modern physics. Some concepts here are proven and used in space stuff. Try to take this blog lightly- our message is to create what we love regardless of making mistakes.

Gravity is even more complex than this. Science has not yet answered the mysterious force of gravity, black holes, and others which allow all the space enthusiasts like us to put forth our explanations.

My Books:

1.  https://notionpress.com/read/understanding-basic-quantum-physics-part-ii

2. https://notionpress.com/read/theories-for-modern-physics

3. https://notionpress.com/read/understanding-basic-quantum-physics

In the next blog, we will go deeper into the Quantum era and understand fluctuations, cosmic microwaves, and others.