| 18-Mar-2012 |
We agree with Einstein’s Relativity that the space and time are not absolute, and the space and time are distorted by the strong gravitational field. It means that when the gravitational field changes, then space and time also change. But we can’t agree with the second postulate of Einstein’s Special Relativity, that the velocity of light is constant. In fact, the velocity of light depends on the gravitational field and it changes as space and time change.
A proof for this is shown as follows:
As you know, the gravitational field of a black Hole is very strong and it distorts space and time around it. If our measurements of space and time are km , (a kilometre) and s , (a second ), then a Black hole’s measurements of space and time will be km’= km.γ and s.γ . (Of which γ is the dilation coefficient. To understand it , please read “Light velocity changes as space and time change”, at website: https://wbabin.net/feast/cuong27.pdf )
In a case of a Black Hole, the dilation coefficient: γ can reach ∞ . For example, a Black Hole’s time passage being s ( a second) is equivalent to our Earth’s time passage of a year.
Now, we consider the velocity of light in the space of a Black Hole. It is easy to understand for us when we assume the experiments as follows:
Assume that in the empty space of the universe, there are two points, which are A and B. A distance from A to B is length: AB=450,000,000 km. At a point: A is our Earth and at a point: B is a Planet with its mass equal to the mass of the Earth. It means that the gravitational fields of the Planet and the Earth are a same. So, the space and time’s measurements of the Planet and the Earth are also the same. At the Earth, we place a lamp to shine a ray of light to the planet and a clock in order to measure the time, t for the ray of light to move from A to B, after, that reflecting from B to return A. At the planet, we put a mirror so that the reflecting a ray of light returns to Earth. Please seeing the illustation at a figure: 1
A Figure: 1
We turn on a lamp and calculate the time t when the ray of light moves from A (the Earth) to B ( a mirror at the Planet), after that it reflects to return A . Taking into consideration the principle of constancy of velocity of light, ( c=300,000km/s as second postulate of Einstein’s Special relativity ), we who are the observers on the Earth calculate a time t , which is :
Time = 2 (Light path: AB /velocity: c )
t = 2(90,000,000km / (300,000 km/s)) = 600 s
In this case, time t when a ray of light moves from A to B and reflecting from B to return A with the velocity c=300,000km/s is t = 600 s . This is normal. But if we assume that at a point: B, the Planet is replaced by a Black Hole and the distance from A to B is still AB=90,000,000km, then the time for a reflected ray of light will be different, -not t = 600s. This is because space and time around a Black Hole are distorted by the gravitational field, so theybecome a space measurement: km’=km.γ and a time measurement: s’=s.γ .
The first postulate of Einstein’s Special Relativity: “ The laws by which the states of a physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion.” We find that a Black Hole is equivalent to the system or the frame of reference when it moves with rapid velocity making achange in its space and time. And at a Black Hole, we must calculate every physical factor with a Black Hole’s measurement. If the observers on the earth calculate velocity with their measurement of space: km, and of time: s , then the observers on a Black Hole will also calculate velocity with their measurement of space: km’= km.γ and of time: s’=s.γ . That is why, if the velocity of light at the Earth is c=300,000km/s, then the velocity of light at a Black Hole will be c’=300,000km.γ/s.γ .
With c’=300,000km.γ/s.γ in space of a Black Hole and is c=300,000km/s in space of the Earth, we always make mistake of calculating as follows:
c’= 300,000 km.γ/s.γ = c =300,000km/s
I think that we can’t calculate c’ = c . Because with a length: AB=90,000,000 km and c’ = c , we are right to calculate the time passage: t when a ray of light moves from A (the Earth) to B (a Black Hole) and reflecting from B to A :
t = 2.(AI/c + IB/c’)
t = 2.﴾45.000.000km/(300.000km/s)+45.000.000km/(300.000km/s)﴿ = 600 s
A time passage of: t=600s in first case, (when a ray of light moves in the space of the Planet) and a result of time passing: t=600s in this case, (when a ray of light moves in space of a Black Hole) are a same. It means that there isn’t any change of time at a Black Hole. Because of this, Einstein’s Relativity is incorrect and we can’t say that time passage at a Black Hole is slower than a time passage at our Earth.
In fact, the physical scientists always confirm that a time passing at a Black Hole is very slow and a formula of delated time t’=t.γ in Einstein’s Special Relativity is correct. Thus, we must accept an equation, which is:
c’ = 300,000 km.γ/s.γ ≠ c = 300,000 km/s
The observers on the Earth view and measure their velocity of light: c=300,000 km/s , is true. And the observers on a Black Hole also view and measure their velocity of light: c’=300,000 km.γ/s.γ , is also a true. But c’ ≠ c , so the velocity of light: c’ in space of Black Hole is only similar to c , but c’ is not equal to c . That is why, we are right to declare that the velocity of light is not constant.
With c’=300,000 km.γ/s.γ , the observers on the Earth can think that a ray of light winds in space of a Black Hole from I to B as a illustation in a figure: 2 .
A Figure: 2
We find that a ray of light can’t wind from I to B in the space of a Black Hole as such. Because the velocity of light is a vector, a ray of light can only move in straight lines. Further, the strong gravitational field of a Black Hole forces a ray of light to move straight to a Back Hole’s center.
Because of the first postulate of Einstein’s Relativity, at a Black Hole we must calculate every physical factor with a Black Hole’s measurement. And a length IB=45,000,000km.γ on a black Hole is equivalent to a length IB=45,000,000km on the Earth. So, the observers on the Earth are right when calculating a time passage: t when a ray of light moves from A to B and reflecting from B to return A in the straight dirrection as follows:
t =2.(AI/c + IB/c’)
t = 2.﴾45.000.000 km/(300.000 km/s) + 45.000.000 km.γ /(300.000 km.γ/s.γ)﴿= 2.( 150 s + 150 s.γ)
How fast does a light in space of a Black Hole move as viewed by the observers on Earth?
From the result of time: t’=t.γ = 150s.γ when a light moves from I to B in the space of a Black Hole as viewed by the observers on the Earth and in fact, the observers on the Earth only view a length: IB=45,000,000km, the velocity of light when it moves in space of a Black Hole can be calculated by :
c’ = IB/t’ = 45,000,000km /150s.γ = 300,000 km/s.γ
we find that if γ reachs ∞ , then the velocity of light when it moves from I to B in the space of a Black Hole will be very slow, and is nearly motionless. Please see illustation in figure: 3 .
A Figure: 3
Or, we can illustrate the velocity of light when it moves from A to B as a graph. Please seeing a figure: 4 :
A Figure: 4
A ray of light when it moves in the space of a Black Hole is very slow, then how fast does a material body move in the space of a Black Hole when viewed by observers on Earth ?
Assume that there is a material body, which moves in the space of the Earth with velocity: v= km/s. After that, a material body falls in space of a Black Hole. As a case of the velocity of light in space of a Black Hole, with the viewed by the observers in a Black Hole, that material body moves with velocity v’= km.γ/s.γ . But Regarding the viewing of the observers on the Earth, the velocity of a material body in space of a Black hole is v=km/s.γ . Because a length: km.γ in space of a Black Hole is contracted and it is only equivalent to a length: km as the viewing of the observes on the Earth. So, with the viewing of the observers on the Earth, the velocity of a material body in the space of a Black Hole is slower than velocity of a material body in space of the Earth.
We should understand that the gravitational field of a Black Hole is very strong. So, if any material body falls in the space of a Black Hole, it will be converted to become the energy of a super nucleus as a formula: E=m.c2 infers. And as a material body falls near they Black Hole’s center, it is converted. Thus, there isn’t any material body in the Black Hole’s center.
Conclusion
If we accept that time passage at a Black Hole is very slow, we will have to accept the velocity of light when it moves in space of a Black Hole is also very slow and almost motionless, even as it approaches the Black hole’s center. To accept this, we will may be able to understand further the nature of space and time as well asthe nature of the universe.
Einstein’s relativity is correct when it illustrates the change of space and time. But Einstein’s Relativity is a failure when it confirms that the velocity of light is constant in the universe. In fact, if space and time are constant, then the velocity of light will be constant.
Thanks to Einstein’s Relativity, which has shown the change of space and time, we know the translation of light in the space of a Black Hole.
Lê văn Cường
Hanoi, March 19, 2011