I'm starting from where I ended the previous episode. If not, you can fall.
1.
The dimension thing is not just about who is in which position, it is possible to find the distance of two points. For example, in graph paper, if Abul is at point (1,3), Babul is at point (4, -1), if their distance is ds, we find using Pythagoras theorem,
Hypotenuse ^ 2 = ground ^ 2 + perpendicular 2
ds ^ 2 = dx ^ 2 + dy ^ 2 = (4 -1) ^ 2 + (-1 -3) 2
ds ^ 2 = 25
Then the distance will be √25 = 5.
This time let's talk about our three-dimensional world. In the three-dimensional world, the distance between two points will be found in the three-dimensional form of Pythagoras' formula, which is,
ds ^ 2 = dx ^ 2 + dy ^ 2 + dy ^ 2
If the coordinates of Bakkar Bhai on the ground are (1, 3, 0),
And if the coordinates of Bakrina Apur floating in the flying saucer above the head are (2, 5, 7),
Then we get,
ds ^ 2 = dx ^ 2 + dy ^ 2 + dy ^ 2 = (2 - 1) ^ 2 + (5 - 3) ^ 2 + (7 - 0) 2
= 54
Then the distance will be 454 = 7.43
If our world were four-dimensional, then Pythagoras' formula for finding the distance between two points would be
ds ^ 2 = dx ^ 2 + dy ^ 2 + dy ^ 2 + dk ^ 2. Here the K axis is the number four axis, which is perpendicular to the previous three axes.
Notice, no matter what point I take, this distance is fixed. Measured with any good variety scale, Bakkar's brother, Bakrina Apur's distance will be the same. Bakkar's brother Bakrina Apu will get this distance only if she calculates how long it takes for the light to go by sending light to her. If I use a laser to measure the light of Bakkar Bhai, when I cross Apu, I will get the same distance (Apu will get very angry if I use a laser, it should never be).
Right or wrong?
Everyone knew for a long time.
The fact that Bakkar Bhai is closer to his sister at a social distance of seven and a half meters at this moment, before everyone thought it was a constant truth.
Rangpur is about 300 km away from Dhaka, everyone thought it was right for everyone.
Everyone knew that the distance of the sun from the earth is fifteen crore kilometers, it is the same for everyone. If you go to the sun to die, you must cross 150 million kilometers.
For a long time this idea was in everyone's mind, it may still be there, but Einstein proved that this idea is not correct.
Distance is not absolute, time is not absolute.
You can bring the sun in the palm of your hand if you want. The dwarf can touch the moon.
Because we actually have four dimensions. This is the number four level of time.
Let's understand how time is the number four level.
(The next part is copied from the book Tea Coffee and Quantum Mechanics)
2.
The whole thing starts with relativity.
I mean.
The sun rises in the east and sets in the west.
That is, the earth rotates from west to east.
This means that any light from the east will actually add to it the speed of rotation of the earth.
The speed of light will not be three lakh kilometers per second. It will increase even a little.
Again, any light from the west would actually subtract the speed of rotation of the earth from the speed of light.
The speed of light will be reduced from three lakhs.
Right or wrong?
Everyone say okay.
Good.
Scientists measured.
The result is surprising.
The speed of the light that came from the east did not increase by a single drop for the speed of the earth.
The speed of the light coming from the west did not decrease at all for the speed of the earth.
Imagine a train coming towards you at a speed of 200,000 kilometers per second when the lights are on.
You are standing in front of the train to die.
Before he died, his hobby was measuring the speed of light.
What will you see in Maple?
Three two five right?
Three million plus two million equals five million, right?
No. The speed of light will always be three lakh kilometers. Neither increase nor decrease.
Explaining this phenomenon is one of the most important works of Einstein's life.
The name of this explanation is relativity.
I mean.
Velocity means distance / time.
If I can't speed up, distance and time will change.
Suppose the speed limit is 300 kg per second.
It is not possible to have more speed.
I will go to Rangpur from Dhaka.
The distance is about three hundred kilos.
I can't lift the speed above three hundred kilos. So I can not go to Rangpur in less than 1 second?
Of course I can.
My speed, the closer I get to three hundred kilos, the shorter the road from Dhaka to Rangpur will be for me. Time will also be reduced.
Maybe one day I will see Rangpur next to my house.
Just three kilos away.
I will go to that three kilo place in 011 seconds.
What will be my speed then?
3 / .011 = 272.72 kilo seconds.
What is happening then?
I will try to increase the speed, the speed will not increase, the road will be shorter. Time will also decrease.
I am moving at the same speed as the road, but the road is moving in the opposite direction at the same speed as me.
Just as I would see the road getting smaller, someone standing on the side of the road would see me getting smaller.
I'll be small to the man standing on the side of the road.
The road will not be short for him.
The same will remain the same.
To him the road is fixed, therefore.
That means he will have three hundred kilos of roads, not three kilos.
I measured my speed relative to the road at 272.72 kg / sec.
The man standing on the side of the road will measure the same speed.
But he will measure the length of the road 300 kilos, not three kilos.
Again, velocity = distance / time.
Time = distance / velocity
= 300 / 272.72
= 1.1 seconds.
So, my .011 seconds time he will watch for 1.1 seconds.
Multiplying by 100 will help you understand.
My .011 × 100 = 1.1 seconds will see her time for 1.1 × 100 = 110 seconds.
If I kill a mosquito in these 1.1 seconds, he will see that I am killing the mosquito very slowly for 110 seconds.
Why?
Because, I'm moving too fast in relation to him.
I am moving very fast in relation to him, which means he is also moving in the opposite direction very fast in relation to me.
That means,
When a man standing on the side of the road kills a mosquito for a second, I will watch it for 90 seconds.
Just as the man standing on the side of the road will see me as small (flat), so will I see both the road and the man as small and flat.
Clear ??
The speed limit is not three hundred kilos, but three hundred thousand kilos per second.
The formula for adding velocity is not v '= u + v,
v '= (u + v) / (1 + uv / c ^ 2)
The way you accelerate, the way you try to increase the speed, put it in this formula, your speed will never pick up at the speed of light.
But can go very close.
One more thing to keep in mind, just time and distance will not change. The mass will also change. Mass is a measure of inertia. If you give energy, both mass and speed will change. In the end, as the velocity gets closer to infinity, the mass will continue to be closer to infinity. This will be discussed in detail in the next chapter.
3.
Voyager is moving at a speed of about 16 kilometers per second.
It takes four years for light to come from the nearest star after the sun.
That distance of Voyager will take about eighty thousand years.
Now hold on,
Suppose you are accelerating Voyager.
Not more, just 1 g.
9.8 meters per second.
Thus if only one year of acceleration can be given then you will reach the speed of 6% of the speed of light.
This one year will cut the earth to 1.19 years.
If you accelerate like this for 5 years, you will reach 99.999% of the speed of light.
In these 5 years, 63 years will pass in the world.
You will be about 63 light years away from the earth.
The people of the world will measure your height by 1 inch and your mass will measure by 6 tons.
If you accelerate for twelve years, your speed will be 0.99999999996c.
One hundred and thirteen thousand years will pass on the earth in these twelve years.
You will only cross the Milky Way in twelve years.
The people of the world will weigh you 9000 tons, and your height will be equal to that of bacteria.
But what is the harm? You don't have to go back to that nonsense world.
Thus acceleration is not possible.
One year will be spent consuming all the energy in the world to respond to acceleration.
It would have been a matter of really accelerating!
4.
From the law of velocity addition we see that the one whose velocity is less than the velocity of light will never reach the velocity of light.
Except for the light.
He was born with that speed.
Its speed will not increase, nor will it decrease.
What would your life be like if you were a photon?
Great, isn't it?
Wrong.
Time is fixed with respect to photons.
When we go from the earth to the sun, we see that it takes 6 minutes of light.
It takes no time on its own.
Not at all.
All distance to his own is zero.
To me, the photon itself is not moving at all. Not moving his hands and feet at all. Just running.
The whole world is absolutely fixed to the photon.
Even better, if you were a photon, no information from the rest of the world would come to you.
Bigger than that, the whole universe would be zero length to you.
The distance is zero.
Time is zero.
Photons never age.
The photon that was born during the Big Bang still has that baby.
Time is zero so if you were a photon you would not experience anything.
Flattened, in a terrifying world of zero size, you are a completely blind child of eternity, a perfectly flattened idol to the outside world!
5.
This time I back to the level of words.
Earlier we knew that the distance from Dhaka to Rangpur is 300 kilometers. This distance is right for everyone.
Now I know, it's not true. The distance changes depending on who is going at what speed.
For light it will be even less than 0 meters.
That is, this distance constant is not exactly right. ds ^ 2 = dx ^ 2 + dz ^ 2 + dy ^ 2
It will give individual values to each individual.
But
If we come up with a new distance called dS ^ 2 = dx ^ 2 + dy c 2 + dz নতুন 2 - c ^ 2 dt ^ 2, that thing will be equal to all. If we go to the example of light,
In my opinion, the distance from the sun to the earth is 150 million kilometers. Light has to cover this distance.
That means,
dx ^ 2 + dy ^ 2 + dy ^ 2 = (150Million) 2
Again
Distance = Velocity * Time = c dt = 150Million
Then dS ^ 2 = dx ^ 2 + dy ^ 2 + dy ^ 2 - c ^ 2 dt ^ 2 = (150Million) ^ 2 - (150Million) 2 = 0
Again in his own reference frame of light he does not have to cross any distance. His time also increases by 0 seconds. So in the case of light,
dS ^ 2 = dx ^ 2 + dy ^ 2 + dy ^ 2 - c ^ 2 dt ^ 2 = (0) ^ 2 - (0) ^ 2 = 0
Bakkar Bhai is speeding near the light subject to me. I might see him go 2.5 lakh kilometers of road in 1 second. Light goes to 3 lakhs in a second, so we get by subtraction,
dS ^ 2 = dx ^ 2 + dy ^ 2 + dy ^ 2 - c ^ 2 dt ^ 2 = (0.3) ^ 2 - (0.25) ^ 2 = -2.75 * 10 ^ 10
Bakkar Bhai himself sees that he is giving a very short distance. His age is increasing very little. But the subtraction is also to him,
dS ^ 2 = dx ^ 2 + dy ^ 2 + dy ^ 2 - c ^ 2 dt ^ 2 The value of this thing will remain the same. -2.75 * 10 ^ 10.
Distance and time will change in such a way that this subtraction remains the same.
.
If we take the speed of light as a unit (use light second unit instead of meter), then the above formula will stand
dS ^ 2 = dx ^ 2 + dy ^ 2 + dz ^ 2 - dt ^ 2
We had the formula for distance in the four-dimensional world
ds ^ 2 = dx ^ 2 + dy ^ 2 + dz ^ 2 + dk ^ 2
If time is the number four dimension, then our formula is as follows:
dS ^ 2 = dx ^ 2 + dy ^ 2 + dz ^ 2 - dt ^ 2
Not only is dt replaced by dS, minus is preceded by the square of dt.
That is, if time is our number four dimension, it is not just perpendicular to the three axes X, Y, Z, it is actually the imagining axis. The square of the imaginary number is negative.
The name of this particular dS thing is the true distance of something through space time. Even if you sit quietly, if you think a little, you will understand that you are crossing a huge distance through space time every moment.
.
I have not given any true proof of the above formula. Maybe in the series, maybe I will go to the book and write. However, in the next episode, there will be a lot of talk about the distance through this special space time while explaining the Minkowski diagram.
Then we will see that there is nothing surprising in the speed of light. We are all running at the speed of light through space time.
Always!
