What is Physics

Relativity part...7

2020-07-26T10:36:00.000+05:30

After understanding the concepts of relativity and knowing that time and space are not absolute as Newton told us instead they follow Einstein's theory of special relativity.

Now I am going to go in depth ocean of time and space and let us figure out why these two simple known words are so difficult to understand and believe me it's really difficult and it requires deep imagination.

So, today's chapter is about simultaneity. is everything in this universe happening simultaneously. If no then why or if yes then with respect to whom.

7.1 The Relativity of Simultaneity

In order to understand the concept of simultaneity let us imagine we are calmly sitting in our spaceship which is in deep space and suddenly 2 other spaceships approach from opposite direction and pass each other as shown. They have equal velocities. Just as they pass we set off bolts of energy at points x1 and x2 simultaneously from our point of view. But are they simultaneous to the passengers in those spaceships?

Considering passenger who is in middle of spaceship he is not going to conclude that explosives were simultaneous because of the fact that during the time that light from x1 and x2 moves toward them at speed c, they move somewhat to the right because it is going to take some time for light to reach the eyes of passengers and also light is moving towards one and away from another.
So the passengers in spaceship A is going to conclude we were half way between x1 and x2 and we saw light from x2 first.

Now we can see just that change of Frame of reference changes the reality

7.2 Clock synchronization in single frame of reference

The way to synchronize two or more clocks are as follows.

We put 2 clocks and observers A and B beside each clock and measure the distance between them. Now we keep one flashbulb in the halfway of two clocks. Both the clocks are earlier synchronized and they have agreed to set their clocks at t=0 when the flash arrives. The flashbulb is then turned on and it is going to take equal time to reach both of the clocks and thus clocks are synchronized. This method can be use to synchronize any number of clocks

7.3 In the very process of synchronizing Two Clocks, a moving observer disagrees

Imagine we are sitting in train and train is moving with uniform velocity v towards left relative to two clocks A and B are being synchronized in frame of ground with the help of method discussed above. To us clocks move in right and the distance between them is contracted to
(D(✓1-v²/c²)) where D is the distance between two clocks. Now it is clear that from our frame of reference clock A intercepts the flash before clock B because A is moving towards the light source and B away from it.
This means clock A is ahed of clock B. And this proves that they are unsynchronized to us.

Now let's calculate the lag in time between two clocks from our point of view. To begin with, suppose our clocks read t=0 just as bulb fires. Between stages one and three of figure both clock A and left hand flash have moved as shown let the time they meet be t3 on our clock so light has moved a distance ct3 and clock A has moved a distance ct3, which together amount to half the distance between two clocks which is

(D/2)(✓1-v²/c²) and that is ,

ct3 +vt3=(D/2)(✓1-v²/c²)

t3=(D✓1-v²/c²)/2(c+v)

At stage four when light reaches clock B, suppose our clock reads t=t4 the right hand flash has traveled ct4 and clock B has traveled ct4. Clock B started a distance (D/2)(✓1-v²/c²) to right of flashbulb so

ct4=vt4 +(D/2)(✓1-v²/c²)

And therefore
t4= (D✓1-v²/c²)/2(c-v)

The time difference between the stages three and four is

∆t= t4-t3

∆t= Dv(1-v²/c²)/(c²-v²)

As measured by our clocks. Clock A is moving to us, so it runs slowby the factor (✓1-v²/c²) during time interval ∆t, so to us it will read time

t(A)=∆t(1-v²/c²)

= Dv(1-v²/c²)/(c²-v²)

t(A)= vD/c²

This means from our point of view clock A is set to zero first and by time clock B is set to zero, clock A has already advanced to time t(A).

In simple words moving clocks Will be out of synchronism by an amount vD/c² from our point of view.

Relativity...Part 6

2020-04-18T16:12:00.002+05:30

Albert Einstein

After understanding that time is not what we think and it is completely different and has lost his absolute character just because of constant nature of speed of light. Now we have to learn that to maintain constant nature of speed of light not only time but space also changes. So today we are going to see the difference between Newtonian space and Einsteinian space. According to Newton as he clear wrote in his famous book "The Principia" that "Absolute space, in its own nature, without regard to anything external, remains similar and immovable".

In Einstein's relativity space also lose its absolute character to keep the speed of light constant for both the observers who are in motion and who are not.

Transverse lengths

Two sprinters running opposite to each other having metersticks

Imagine 2 sprinters A and B are having a meterstick having a thin knife blade attached to the top end. They run towards each other at a high relative speed, holding the sticks perpendicular to direction of motion. If the stick are equally long, then the knives should hit each other. But if one stick is longer than other, it will be sliced off by the knife on the shorter stick.

Suppose B's stick is shorter than 1metre according to A. Then B's knife will slice off the top of A's stick. This fact does not depend on who is observing it. It is definitely A's stick that has been cut off. Now this cannot happen , according to Einstein's first postulate, because it would mean that there is a priori reason for preferring one reference frame over other. In such an originally symmetric experiment, with the laws of physics the same for both A and B, everything that happens to A should also happen to B. The one possibility remaining, that the knives hit one another is a symmetrical result showing that to either observer the metersticks have the same length. It means transverse lengths are unaffected by motion.

Longitudinal lengths

According to Einstein the body which are in motion their lengths get contracted. And it is given by the same factor Gamma that we have learnt in previous parts.

Length contraction

To understand this let us take a very simple example that will again blow our mind. Imagine there is stick of length "D" which is at rest in our frame of reference. A clock moving along side the right of stick with velocity "v". According to our frame of reference the time it take to reach right hand of length is

T=D/v
and we also know that it is going to take less time for moving clocks.

Now look at the same experiment with clock's frame of reference then the clock is at rest and it is the stick which is moving so what should be the time elapsed according to clock's frame it should be again D/v yes, but in reality from clock's frame of reference it is

T'=(D/v)(√1-(v/c)²

It again breaks our understanding of reality. Now why this happened is because-in order to maintain constant nature of speed of light according to Albert Einstein space also have got changed that is length of moving stick is not as same as length of stick which is at rest. It means length of stick is going to be less than original length and this length is given by "d" which is

d=D(√1-(v/c)²

Contraction in length of stick

And this also explains why time elapsed is different and this is called contraction of longitudinal lengths. In next part we will discuss more about weird things that takes place in space and remember is all because of constant nature of speed of light.

Relativity...Part 5

2020-04-14T15:32:00.000+05:30

After understanding that time is an dimension and space and time is merged into single space-time and time slows down for the things that are in motion by the factor of Gamma.

Now we will see how it happens and in what ways we can imagine and understand time dilation clearly. Here i will give some of the situations that will clearly make our mind to think what we actually mean by time. So the situation goes like this imagine a spaceship in which your friend is in and his heart is beating at the rate of 60 beats per minute. There are mechanical and digital watches which are ticking exactly at the same speed. Now there is also one flash bulb inside the spaceship and one plane mirror kept parallely to the flash bulb. Let us consider the distance between flash bulb and the mirror is "D" then if one is interested in finding the time that it takes for a beam of light to go from bulb to mirror and from mirror to flashlight due to reflection then it is simply calculated by equation that
T=2D/c
Where c is the speed of light approximately equal to 300000km/sec.
Now we say that spaceship along with with all the clocks is passing by us with velocity "v". And here on earth we also have a similar set of clocks all ticking at the same rate as one another. This follows from Einstein's first postulate that no inertial frame is fundamentally Better than any other. However if we observe the SpaceShip and find the difference in ticking rates of clock then only it will be cleared to all of us why velocity is important factor for the change in rate of time with respect to different observers. Now to find the time it takes for a beam of light emitted from flashlight to travel distance of "2D". In order to find the time we assume that light clock is oriented perpendicular to the direction of motion of spaceship moving with velocity "v". If we imagine this situation from our point of view we know that spaceship is in motion so the beam of light which goes from bulb to mirror and vice-versa is not going to be straight instead it is going to make some angle because as the ship is in motion the trajectory of light is going to appear different from our point of view. Its like someone is throwing ball from moving train vertically. Its going to be vertical from the ground frame but for the person who is in moving train its not going to be straight instead it is going to follow a parabolic trajectory. It means light has to travel greater distance in our frame just because its not straight. Speed of light is same in both frames of reference but the greater distance means it is going to take more time for clock to tick once from our point of view than it took for observers in spaceship. now we have to use simple mathematics to come to the conclusion. We know spaceship is moving with velocity v and speed of light is c and light is not going in straight direction from our point of view, using Pythagoras theorem the vertical component of light must be (√c²-v²) so the time it takes for light to go from our point of view is

T`= 2D/(√c²-v²) = 2D/c(√1-v²/c²)
= Time between ticks of our own light clock/√c²-v².

And this is how time changes for different observers. Time dilation means that it would take less time foe the people who are in moving space ship. Let us discuss one more example on this. Suppose a person wants to visit Alpha Centauri one of the nearest stars and their ship moves at the speed (4/5)c relative to Earth. The star is nearly at a distance of 4 light years that is it takes 4 years for light to cover the distance so the time it is going to take is from Earth's point of view is
T=4c.yrs/(4/5)c=5yrs
To arrive. Spaceship runs slow by the factor √1-(4/5)²=3/5, however so the trip takes only (3/5)*5yrs=3yrs according to spaceship clocks. All shipboard clocks runs slow do the person who is in spaceship is just only 3 years older when they arrive.

The faster the spaceship moves time will run more slowly because the person is as much possible going in space dimension so time has to contract itself. This all means that we don't understand what is time and we just know how to calculate it.

Relativity...Part 4

2020-04-03T16:56:00.001+05:30

Einstein about Space and time

Now we have come to know that Einstein imagined time as a dimension. It means size of the object is going to change as the rate of time changes for that particular object. But how is this possible we don't feel a change in our sizes even when we are in motion. So one thing what we have to clear now is that time is not we think instead to understand time we have to think like Einstein.

Einstein said that in order to keep the speed of light constant space and time change themselves now the question is at what rate they change themselves Einstein published this paper in 1905 what he later called "time dilation" in which he has given us the equation that shows at what rate time gets dilated for the object which is in motion with respect to the other frame of reference which is in rest. But just memorizing the equation will not help us to understand.

In order to understand the true behaviour of time one has to imagine the way Einstein imagined. I want my every reader to imagine the situation and it goes like this imagine you are standing on the railway platform saying bye-bye to your friend who is in train and as the train is in motion two lightning strikes takes place at the 100m distant apart at the same time now with respect to you who is on ground standing at the centre that is at the 50th metre will come to the conclusion that both the lightning strikes took place at the same time but with respect to your friend who is in moving train will not conclude that the both the lightning strikes took place at same time why? Because your friend is moving towards one and away from the other so your friend is going to conclude that in the direction that he was in motion that lightning strike will be detected by him and after some time the lightning strike opposite to his direction of motion now the question that comes what is the factor that changes rate of change of time and answer is it is the rate of change of displacement that is velocity. As i already mentioned it is just because of our position in space and time and as they are bounded into one so change in one affects the other.

Here is the link for the derivation of time dilation if anyone is interested please go through this

https://drive.google.com/file/d/1Cn7_OQ8Ezdfz4EzRB4RlgCMwlqOdcN8A/view?usp=drivesdk

The factor gamma

The Gamma factor

Is responsible for the changes that takes place. It means time is something which is affected by the velocity but speed of light is the ultimate limit and it also means that as faster we go in space time for us goes slowly. Now if the question comes to your mind what will be the time experienced by the person who goes with Speed of light itself then the answer is time for that person will be stopped as that person is moving with speed of light it means the person is just moving in space and dimension and motion in time dimension comes to 0. Going further we can come to conclusion that light don't experiences time itself because light moves with Speed of light. So light just moves in space dimension and motion in time dimension is absolutely zero. Now if we imagine ourselves going at the speed of light then with respect to us we will not feel flow of time as we will be completely in motion with highest speed in the universe.

Time Dilation

But if one imagines what will happen if we go more than speed of light then mathematically speaking time will go in backward direction but upto now no one has gone through even 1% of speed of light which is 2997.92458km/sec.

Variation of gamma factor with speed of light

In the next blog i will discuss more about time dilation, applications of time dilation and more about strange behaviour of single space-time that is still to discuss about.
And yes if you have any questions regarding these things or want to suggest something you can leave it in comment box.

Relativity... Part 3

2020-01-31T11:21:00.000+05:30

Now the question that we should ask to ourselves is why the speed of light remains the same. It should change yes,with respect to different observers or in other words with respect to different frames of reference but the experimental results show us that it remains the same.

Albert Einstein at the age of 16 imagined himself travelling alongside the light beam at the speed of light just because he was having the curiosity to understand light itself. He mastered both integral and differential calculus at the age of 15 and this shows his geniusness and curiosity too. Students don't really understand the real meaning of differentiation and he mastered it.

Special Relativity is because of light

In 1905, he published 4 papers which changed our understanding of physics forever. We will be discussing here about only one paper which he gave the title "On The Electrodynamics Of Moving Bodies". as we already came to know that Light is an electromagnetic wave with a velocity of 3*10^8m/s and this velocity remains the same with respect to everyone so what Einstein did is he changed the way we interpret the meaning of space and Time. Let's make it simple we know that

Speed=distance traveled/time taken
So if from experimental results speed remains the same we have to change distance traveled (space) and time. And this is what Einstein did. He does not thought space and time are 2 different physical quantities and they are different. Instead he combined them into 1 that is space-time. According to Einstein we are not living in 3 dimensions instead we are in 4 dimensions that is 3 dimensions of space and one single dimension of time. Now the thing is we cannot show 4 dimensions in 2 dimensional plane . But Einstein imagined it.

4 dimensional space

To understand space-time in simple terms let's take a simple example suppose you are at rest with respect to ground now according to Einstein you are just moving in time dimension it means your rate of flow in the the fastest, but your motion in space is 0 and if you start moving your motion in space is going to affect time because speed of light is the limit. And according to Einstein nothing can travel Faster than light because if anything goes at the speed of light time will be stopped for that body.

Space time cone

We will be discussing about time in next blog separately. Because understanding time itself is not a easy thing. but upto now just try to imagine yourself moving at the speed of light.

Relativity...Part 2

2020-01-28T12:48:00.000+05:30

After understanding Newtonian mechanics now it is time to understand where the problem exists. One cannot doubt Sir Issac Newton because we all know him from our childhood his equations of motion are so accurate that one can easily apply them to go to Sun or even any other place in the universe. Einstein himself was a very big fan of Newton. After understanding Galileo's principle of relativity one can check that it is impossible to say which objects are at rest or which are in motion. Everything is relative. The problem comes is with Light. Maxwell showed through his equations which he published in 1873 that light is an electromagnetic wave and its velocity is about 300000km/sec in vacuum.

Special Relativity is because of light

Now what is so special about light is we don't really understand light too. First of all its speed is something which is very hard to imagine . Can you imagine urself going with the speed of light, if you then one can easily go around the Earth 7 times in one second.

Another interesting thing about nature of light is its speed is irrespective of frame of reference and its going to be the same with respect to everyone. To understand this let's take another example imagine you and your friend are standing 100metres apart both of you have laser and the device to measure the speed of light. Now if you throws the beam of light to your friend who is at rest his device is going to show him that the velocity is 300000km/sec only and it is going to take 0.0000000333seconds to reach your friend but now just tell your friend to move away from your original position and keep moving away from him and now if you throw beam of light towards him according to Galileo, Newton and even according to everyone the speed should decrease because as your friend is moving away from its original position it is going to take more time for light to touch him and velocity should be c-v where c is speed of light and v is friend's moving speed but in reality weird things happen and the device is going to show the speed as just c only. now how this is possible in one sense it breaks our understanding of physics but we have to accept this because this is true. Consider the second situation where your friend is moving towards you now the velocity should increase(c+v) but still it is c only.

And this is where world requires a true genius to solve this problem and this where Albert Einstein come into the picture. now the relativity is becoming special, isn't it?..

Relativity...Part 1

2020-01-27T13:31:00.000+05:30

What's Relativity..

In one sense it can just be defined as how one thing appears to be with respect to the other. People speak a lot about Einstein's special theory of relativity but they don't really understand it. It does not start with Einstein it starts with Galileo Galilei who first gave the principle of relativity which says that " it is impossible by mechanical means to say whether we are moving or staying at rest" now this is very common to us and there is no problem with it. Suppose 2 trains are moving with same velocity and in same direction the person in the either of the train is going to say that the other train is at rest because velocities are additive and subtractive in nature so in this contrast both are correct.

Newton's principles of relativity

We think that understanding space and Time is very easy for us because we never felt the change in the behaviour of these two and according to Newton space and Time are absolute now what does it mean is space is something where events takes place and time is defined as duration to complete the event . Time is absolute means everywhere in the universe time is going to be the same regardless of your position in space and at the rate at which you are moving. To understand this let's take a simple example imagine you are in train which is moving with uniform velocity and your friend is watching you from ground and you drop a ball to the ground now your friend who is on ground is going to see that ball is falling straight to the ground but with respect to you ball is not falling straight instead it is following parabolic trajectory as you are in motion. Now the interesting thing here is even though the trajectories are different with respect to different observers but the time taken is the same. You and your friend are going to conclude at the same time only that the ball has touched the ground.

But it is just a beginning of this topic there is more to come.

Father of modern Science

Physics...

2019-11-25T20:44:00.000+05:30

Physics is the branch of science that deals with the study of matter and energy. If anyone wants to understand how universe behaves it is absolutely for them. From the smallest particle to the largest galaxy every question must have a logical answer . The thing that make physics beautiful is the mathematics. The use of mathematics is necessary to understand this world around us in the most simplest way. But physics is not just about equations instead it is about how one looks out at the outside world and have curiosity to understand that phenomena . From centuries people have tried to understand different phenomena happening around them but only those people have got the success who asked the right questions for example it is myth that Newton discovered gravity when apple falled on him but the real thing was that he just saw an apple falling from the tree and at the same time he observed Moon in the orbit then he asked himself "if the apple falls does the moon also fall" and this is the way to be a good physicist. Physics requires one to look out deep into the nature and then make use of mathematics to understand that phenomena. Either it is Einstein or Newton what made them genius is their own curiosity to understand and nothing else. So at last i would like to say that physics is less about equations and more about understanding this beautiful nature around us.