17 Relativistic train paradox




Hello

    Today, I would like to take a look at the questions posted at https://physics.stackexchange.com/. The contents are as follows. There is an iron bridge. This bridge cannot withstand the weight of the entire train, but if it only has to support part of the train as shown in Figure 1 below, it can do it.


Figure 1. Non-relativistic consideration, if only a part of the train is on the iron bridge,
the iron bridge will not collapse


Therefore, when the train runs slowly, it is placed only on a part of the bridge, so the bridge does not collapse. (Click below to see the original.)


However, if the length contraction is correct, it will be as shown in Figure 2 below. The train is contracted, the entire train is placed on the bridge, and the bridge must collapse.

Figure 2. When the observer on the ground sees it,
the entire train has come up and the iron bridge must collapse
(Length contraction)



However, from the standpoint of the person on the train, the story is quite different. Inside the train, the length of the bridge is reduced, as shown in Figure 3, so that only part of the train is on the bridge. Then the iron bridge does not collapse.


Figure 3. When a person in a train observes,
only a part of the train is raised and does not collapse
(Length contraction)


For a person on the ground, the iron bridge must collapse, and the person in the train should not break the iron bridge. If so, does this bridge collapse? Will not it collapse? If both sides are right, this is a paradox. I think it would be called "train paradox." Do you have a solution to this problem?

.
.
.
.
.
.
.
If you think of this problem as a length expansion, the problem is solved easily. First of all, if a length expansion occurs from an observer on the ground, only a part of the train will be placed, and the bridge will not collapse.

Figure 4. When the observer on the ground sees it,
only a part of the train is raised and does not collapse
(Length expansion)

Now, let's look at it from the perspective of the observer in the train. The weight of the train did not change. However, the length of the orbitals of the atoms that make-up the iron bridge and the iron bridge increases. Therefore, the overlap of the orbitals of atoms constituting the iron bridge increases with the ratio of γ. Therefore, the strength of the bridge becomes stronger and the bridge does not collapse accordingly. Therefore, there is no paradox.



Figure 5. When a person in a train observes, the entire train is on an iron bridge, but the overlap of the orbitals of the iron atoms increases so that the bridge does not collapse


Lehgth Expansion(Amazon books)



















Comments

Post a Comment

Popular posts from this blog

06 Muon Paradox

Image
   Today, I would like to talk about the muon paradox. There are several subatomic particles that are smaller than atoms, such as a μ-meson. It is called a μ-meson, but it is abbreviated to muon. The lifetime of this muon is fixed. The proper lifetime of this particle is 2.2 μsec. It only survives for a very short moment, and then  it collapses into other particles. Cosmic-rays are constantly coming out of space due to the explosion of stars in the universe or the nuclear fusion reaction of the sun. At this time, the cosmic-ray and the earth's atmosphere react to create a muon. Muon's speed is near the speed of light when it falls to Earth. It drops at a rate of about 0.998c. However, even if it falls so fast, it cannot reach the ground because its life is short. If the muon has a lifetime of 2.2 μ sec and a speed of 0.998 c, the muon can run about 650 m from the point where it was created. The point where the usual muon occurs is about 10km above sea level. I
Read more

10 Rotating disc of black hole and Ehrenfest's paradox

Image
  Black holes are unusual in many ways. Thet have also has a spinning disc, a jet, a Schwartzchild radius, a horizon of events and singularities. But there is one thing that can not be explained in modern science or the theory of relativity. It is the rotating disc of a black hole. Black hole and Ehrenfest paradox   The speed at which materials rotate in the rotating disk of a black hole is almost as close as the speed of light. If so, all the materials must be decomposed and discarded by the Lorentz contraction. However, the rotating disk of a black hole certainly exists. It is definitely a contradiction. In fact, these are linked to the famous paradox of the Ehrenfest paradox. [1] Today, we will look at the Ehrenfest paradox. Fig. 1 Paul Ehrenfest Personally, I think Erlenpest paradox is the best of relativity's paradoxes. Other paradoxes seem to be a little simpler than this paradox. The list of people who studied this paradox is very extensive. Einstein
Read more

31. Ehrenfest Paradox 2: Does the length of a rotating circumference change?

Image
  We looked at the Ehrenfest paradox last time. There are two issues in the Ehrenfest paradox. The first assumes a disc made up of an ideal rigid body, but when rotated at relativistic speed, it ruptures. The second is that the perimeter of a rotating body is different from its length when it is stationary. In the last post I looked at the first issue, and this time I want to look at the second issue. For those who have not read the first part, I will briefly introduce this paradox. It is best to read the previous post. Below is a link to the first part. The Ehrenfest paradox part I Rotating disc and length contraction   In relativity, objects that run very fast are said to shrink in length. So the official name of this is Lorentz - Fitzgerald Length contraction. It is not 'Einstein's length contraction'. This was born regardless of the theory of relativity. Before the theory of relativity was published, several people experimented to detect ether, but the e
Read more