23. Confrontation of black hole and length contraction

   A black hole is a very gravitational star. So black holes devour the surrounding matter, and even light cannot escape them. There is a singular point in the very center of a black hole. When an object is sucked into this singularity, its appearance is very strange.

   As the object is sucked into the black hole, it is sucked into the singular point as the length increases infinitely by tidal gravity in the vicinity of the horizon. This part is very characteristic. In the theory of length contraction, however, this is a little bit different.

In length contraction theory, when the speed of an object reaches a relativistic speed, the length approaches zero. It means that it gets very short. This part collides head-on with the explanation that the length of the black hole is increased by tidal gravity to infinity. So, now I will ask you a question.

When an object falls into a black hole,

Does the length of the object shrink to zero?

Or is it stretching to infinity?

The theory of length contraction tells us that the length of an object becomes infinitely small. But most theories are against it. If this position of length contraction is correct, then all of the theories and observations about black holes found by many world scholars including Hawking should be ignored and discarded in the trash. From now on, to get a closer look at this issue, let's start with the tidal gravity of a black hole.

Tidal gravity

   The arrow of the gravity of a certain star can be expressed as below. The tip of the arrow indicates the direction of gravity, and the size of the arrow indicates the magnitude of gravity. This arrow can represent several things. Because the radius is different at the center of the star, it can show a variety of information, such as the size of gravity, the degree of warping of space-time, and the size of Lorentz factor.

Figure 1. The gravitational field of a star

All arrows point to the center of the star. However, there is a dotted line in Figure 1 above. Let's take a closer look at this dotted-line square shape.

Figure 2. Effect of gravity on astronauts(observed from outside)

If the astronaut is floating in the air, the detailed arrows will look like Figure 2. However, this is when you see stars and astronauts from the outside. It can be seen as the magnitude of the gravity on the astronauts. But he (a cosmonaut) feels a bit different from this. The power that the astronaut feels is a little different. From his point of view, it would look like this: (I'll use the universal concept of gravity rather than space-time curvature.)

Figure 3. Effect of gravity on astronauts(observed from inside)

   The astronaut feels like pulling in various directions, focusing on himself. This is what we call tidal gravity. It seems like we are not that big, but the power that the astronaut feels is enormous. Tidal gravity exists everywhere in the space.

Figure 4. Tidal gravity by the Moon

We live on Earth every day feeling this power. The low tide and high tides that occur twice a day are caused by the tidal force of the moon's gravity. It is caused by a moon much smaller than the Earth, but its effect cannot be ignored.

Humanity has witnessed the power of this tidal gravity in person. In 1994, a comet named Shoemaker-Levy approached Jupiter. This comet, which has entered the Roche Limit, collapses into Jupiter by Jupiter's tidal gravity and collides with Jupiter in turn. If it collided with the planet, the earth would have faced a great disaster.

From this point on, fear of comets and meteorites began to become common to mankind. Before that, we imagined it, but it was the sight of many scientists on Earth at that time. Fear is amplified when you actually experience it. The figure below shows that the Shoemaker-Levi comet, which was approaching Jupiter, was disintegrated and destroyed by the tidal gravity of Jupiter.

Figure 5. Jupiter's tidal gravity destroyed Shoemaker-Levy 9 comet

The fragments hit Jupiter in turn. The picture below is a photograph that collapses and collides with Jupiter in turn. It is the lower part of Jupiter. The trail is much larger than the earth.

Figure 6. Shoemaker-Levi 9 comet collides with Jupiter

Jupiter's tidal gravity is this level, but in the case of the sun or black hole it will be beyond imagination. So the object approaching the singular point of the black hole is infinitely extended by the tidal gravity pulling up and down.

Tidal gravity of a black hole

   Tidal gravity near the singular point of a black hole leads to infinity. It should not happen, but if the astronaut falls to the black hole, it will look like the picture below. Time runs from bottom to top.

Figure 7. The figure of the astronaut falling down to the singular point of the black hole(imagination)

When an object approaches the singular point through the plane of the black hole, its length is infinitely increased by the tidal gravity of the singularity. And time seems to stop.

Perhaps no one would object to the fact that approaching the horizon of the black hole causes a time delay and is observed as if it were stopped. Do you agree that the length of the object also increases to infinity?

Whatever you think, it is the freedom of the readers. But many scholars in the world are claiming to be infinite. If you want to check, you can check through the book below.

Black Holes and Time Warps: Einstein's Outrageous Legacy

It is probably not possible to explain objects falling into black holes through the theory of length contraction. Even if it is possible, we will have to completely rewrite the current black hole theory. However, the theory of length expansion is quite natural and logical. Why do not you choose this easy path?

The object that falls into the singular point of a black hole is said to be infinitely increased in length by tidal gravity. Always be careful when infinity appears in science. I will ask you one question. Will the material extend to the end of the universe because of the increased length of infinity? Such a thing does not happen.

As objects A and B approach the singularities (as shown in Figure 8 below), even if the tidal gravity increases to infinity and the length of the object increases, it does not extend to the other end of the universe. In Figure 3 above, from the perspective of the astronaut, there is a force to pull upward. But from the third party's point of view, this is actually a downward force.

Thinking like this, it's simple. It is infinite as a ray, not a straight line. Mathematically, a straight line is infinite on both sides, but a ray is infinite in only one direction. Therefore, an object falling into a singular point will be infinitely long from that position to the singular point. In other words, it is infinite in one direction. In Figure 8 below, it is not infinite as B, but infinite as A.

 Figure 8. Length of the object falling to the singular point.
Even if it extends to infinity, it does not reach the end of the universe.

It is easy to think of how to measure time or measure length. Figure 9 below shows how to measure the length. The red path is the length of the object. This corresponds to twice the length of the object. And when you change the red path to straight, this is equal to the length of the blue. If red does not come back, you will not be able to measure time, and you feel like time has stopped. However, light is always moving at a constant speed.

Figure 9. Mechanism of infinitely extending length

In Figure 9 above, when the Lorentz parameter is infinite, the light is moving towards singular points. The light does not move to the opposite side of the singularity. Therefore, even if the length is increased to infinity, it does not happen to move to the opposite side of the universe.

And one thing to note is that the length in Figure 9 above is different from the actual length. Actual length should be measured in space-time, not space. The length in Figure 9 above does not indicate the length in space-time. If you really want to know the exact length, you need to look at the length in the space-time diagram below. Figure 10 below shows the two-dimensional space-time. If so, the mechanism of increasing length is as follows.

Figure 10. Construction diagram showing that the length of the object increases to infinity.
The angle between the two axes of the oblique coordinate system tapers until it meets the horizon.

In Figure 10 above, the length of the light path in red is exactly the same as the length of the light path in blue. And if you want to know the quantitative value of this, you can use k calculus. I will post about this later.

Length expansion in gravitational field

If the Lorentz contraction does not occur in the gravitational field, how does a reasonable length change in the gravitational field occur? Before we think about how the length will change, there is a topic we must surely see. What is the length, how to measure. You cannot measure with a ruler in the gravitational field. So here we will measure the length using light.

When the light clock falls, it calculates the total round trip time. Then multiply the round-trip time by the speed of light c and we can measure the desired length.

Figure 11. Photo-clock of The gravitational field

Now, let's drop the photo-clock, which is now oscillating up and down. In Figure 12 below, the blue path on the left shows the case where it has not yet fallen down and the red path on the right shows that it is falling at high speed in the gravitational field.

Figure 12. Principle of increasing time and length in gravitational field

When it is stopped, the time it takes to make a round trip to the light clock is the unit time. Let's say it's just a second. On the right is not a stop, but a photo-clock that falls. Of course, the length of the round trip becomes longer.

So comparing the proper time of blue, the proper length, and the moving time of red and the moving length, the length of one second observed during the fall becomes longer.  At this time, the speed of light is constant, so in order for light to travel more distantly, it is necessary to move longer. This is the time dilation the gravitational field. And the longer distance is of course the length expansion. Or just multiply the speed of light in time by c.

Now, if you compare the length of the blue path and the length of the red path in straight lines, you can see that the moving length of red is longer. Below is a comparison of the positions of length contraction theory and length expansion theory.

Figure 13. Comparison of length contraction and length expansion in black holes

In the case of length contraction theory, objects converge on the horizon, but in the case of length expansion, they do not converge but are drawn into the singularity through the horizon. It is now in good agreement with other theories about black holes.

According to length contraction theory, no object can pass through the horizon. All objects must converge on the horizon, not singularities. This clearly conflicts with other theories about the current black hole. If you have any questions about this, please refer to the previous post.

           The singularity of the black hole and the length contraction

And when the light travels, discontinuity sections should not exist. Therefore, observing the elliptical theorem and observing the path of light in the gravitational field, it is as follows.

Figure 14. Path of light seen by ellipticity theorem

In this way, we can explain that within the gravitational field we run at the speed of light without discontinuity. This is not possible with length contractions. In order to comply with the luminous flux invariant principle, a discontinuous section necessarily appears, and if the discontinuity section is eliminated, the light converges to a point, and it cannot move any further, and must eventually stop. This is a contradiction.

In this way, we can explain that light travels in the gravitational field without discontinuity. This is not possible with length contractions. In order to comply with the principle of invariant light speed, a discontinuous section necessarily appears, and if the discontinuity section is eliminated, the light converges to a point, and it cannot move any further, and must eventually stop. This is a contradiction.

Confrontation of black hole and length contraction

It is generally understood and accepted that when approaching a singular point past the horizon of a black hole, the length of the object is increased infinitely by tidal gravity. It's a bad idea to say that the length of an object is constant or even reduced while falling into a singularity. However, there is such a theory. It is the Lorenz-Fitzgerald length contraction theory.

Figure 15. Length contraction hypothesis contrary to various theories

Only the Lorenz-Fitzgerald length contraction theory is claimed to be contracted, and most of the rest of the theory says that it is increasing to infinity. Tidal gravity, singularity, and length expansion theory are interpreted in the same way.

The two figures below (Figure 16) show the length of an object falling into a black hole. The left shows the length change according to the length contraction theory, and the right shows the length variation as interpreted by the tidal gravity and the length expansion theory.

Figure 16. (a) Analysis of length contraction         (b) Analysis of length expansion

In the left figure (a), it is a mechanism that must be contracted as the gravity becomes stronger and the speed of the object gets faster. This was explained in detail in a previous post. If the length contraction is correct, it should be as shown on the left (a). The red circles on the left indicate the horizon of the black hole. On the horizon, the Lorentz factor becomes infinity and the length of the object converges to zero. Then all objects cannot pass through the horizon and must gather on the horizon. Therefore, the space inside the horizon should be empty.

However, the right figure (b) is the opposite. The closer the object is to the horizon, the longer the horizon becomes, and the length becomes infinite, eventually sucked into the singularity. The tide gravity and length expansion theory have the same prediction. However, the length contraction is the opposite.

What is left is your choice.

Length Expansion(Amazon books)