29. K Calculus (#5/6): Criticism on the derivation of length contraction by Hermann Bondi
Hello. Now this is the fifth post about K Calculus. The previous post is for writing this post. We will talk about the derivation of the correct relativistic length by K Calculus in the 5th and 6th post.
The K Calculus method being introduced is simple and powerful. It is a way to draw most of the conclusions of special theory of relativity. Moreover, it draws all conclusions from common sense.
Hermann Bondi and David Bohm
David Bohm introduces K Calculus in his book in detail.
 |
| Figure 1. David Bohm's book |
There is one important difference between the two books. Hermann Bondi used this method to derive length contraction. But David Bohm did not derive length contractions in his book.
 |
| Figure 2. Hermann Bondi와 David Bohm |
David Bohm has argued for hidden variable theory as an interpretation of odd quantum mechanical phenomena. He thought because mankind does not know what is on the back of the essence. He judged what was hidden behind the phenomenon as a "hidden variable."
So David Bohm has been criticized today for being mistaken for quantum mechanics. From this, we can think of David Spring as a very cautious person. He did not want to judge anything he did not know. Because of this tendency, he expressed his opinion on quantum mechanics as a "hidden variable theory".
Why did not David Bohm use K Calculus to induce length contraction? I guess, the reason is simple. This is probably because Hermann Bondi's method of inducing length contraction is incomplete. He just kept his honor by passing over the unclear logic.
David Bohm refers to length contractions in some of his books, but it is just lightly handled. I personally respect David Bohm in this respect. Today, even though criticized for the problem of quantum mechanics, his academic prudence is admired.
Some reasons for length contraction
There are several things that claim length contraction is right:
2. Roy Weinstein's derivation of length contraction from Lorentz transformation
4. Derivation of Hermann Bondi by K Calculus
There are several such things as evidence of length contraction. If you have more, please leave a comment. Let's take a look. Null phenomenon of Michelson-Morley experiment! This is never a proof of length contraction. The Michelson-Morley experiment does not prove length contraction, and the length contraction hypothesis has been created to ensure that the results of the Michelson-Morley experiment are consistent.
It is the length contraction hypothesis that modified the nature so that the results of the Michelson-Morley experiments fit human reason. This is the fact that history shows, and it is a fact that everyone acknowledges. It is difficult to claim that the Michelson-Morley experiment is evidence of length contraction.
And I have mentioned several times that the phenomenon of sea surface arrival of muon particles is not evidence of length contraction, but evidence of length expansion. If you are interested, follow the link to see the detailed description.
The next is proof of length contraction through Lorentz transformation. This is the way Roy Weinstein proposed in 1960. He showed his derivation process to Einstein and Gamov. And Weinstein writes that they got their consent in his paper.
Since then, most textbooks have used this Roy Weinstein's proof. Logically Roy W. Stein's error is so obvious. We will look at this later.
What is left is a method of inducing length contraction by the K calculus of Hermann Bondi. The logical contradiction of this method is obvious. Let's take a look at the way Hermann Bondi's derivation. And then let's see what's wrong.
Derivation of length contraction of Hermann Bondi
We cannot fail to observe rules of relativity and rules of spacetime diagrams. Violation of these rules will cause problems immediately. First, let's look at how Hermann Bondi derive to length contractions.
 |
| Figure 3. Derivation of Length contraction by Hermann bondi |
John fires light first at t1 to measure both ends of the ruler at the same time, and then fires at time t2. Then a world line like the picture is formed. Then the following expression is established.
Using the relationship of k, we can see that the following equation holds true.
Light emitted at t1 passes through James at kt1, and light received at t4 passes through James at t4/k. At this time, the length of the person James measures is called L. The time difference is 2L when light passes through it, then reflects it, and receives back light again. If so, the following expression holds true.
In James' s system, John measures the length of a ruler as follows: (1/2)(t4 - t1) and the near end is (1/2)(t3 - t2).
What we want is equation (4). Here, Hermann Bondi omits the intermediate process and explains the equation (9), but we will take a closer look at the induction process. (T2 - t1) = (t4 - t3) because (t1 + t4) = (t2 + t3). Summarizing the inside of the equation (4), the following equation is obtained.
(T2 - t1) = (t4 - t3) is substituted for (1/2) [2(t4 - t3)] and this is (t4 - t3). So the following expression holds true. Therefore, the relation '(4) = (t4-t3) = (t2-t1)' holds. Then, in the equation (2), multiply both sides by k and summarize for t4.
The first thing we want to save is equation (5). We confirmed that equation (5) is the same as equation (7).
(4) equation = (t4-t3) = (t2-t1) '.
Put the following k value in equation (9) and summarize the equation.
Then you get the following expression.
So Hermann Bondi led Fitzgerald's length contraction formula. Here is a summary of how Hermann Bondi derive to length contraction. Did you find something strange?
Hermann Bondi's objective equations and the final concluded equations
Hermann Bondi started with equation (5) and concluded with equation (10). Let's take a closer look at the equation (5).
 |
| Figure 4. Equation from Hermann Bondi |
The first equation bondi seeks is (5). And (t4-t3) and (t2-t1) in the time axis are essentially the same as in equation (5) because c is set to 1.
Since Hermann Bondi computes c with 1, time and space units do not matter. Therefore, in Fig. 4, equation (5), (t4-t3) and (t2-t1), the three red bars are all the same. Therefore, this corresponds to the proper time and proper length. So, if you write down the final derivation by Hermann Bondi, it is like the following expression.
Equation (11) is the final conclusion of Hermann Bondi. How does this equation show the Lorenz-Fitzgerald contraction? This equation is not an expression of length contraction, but an equation of length expansion. It is normal that L should come to the left and write as equation (12).
Analysis of the length contraction derivation of Hermann Bondi
Let's take a look at the book of Hermann Bondi. If there is something different from what I have shown, what is different is the name of the person who appears.
John----Alfred
James---Brain
 |
| Figure 5. Illustration of Hermann Bondi |
Bondi says (t4 / k)-kt1 is clearly 2L.
 |
| Figure 6. Description of Hermann Bondi |
I'll ask you a question here. Is 2L a "proper length"? Or is it "Observed Length" or "Running Length"? Let's show all the lengths that appear here.
 |
| Figure 7. Types of lengths that appear in Hermann Bondi's description |
.
.
.
.
It is a proper length. Equation (5) is also proper length, t4-t3 is proper length, and t2-t1 is proper length.
 |
| Figure 8. (a) proper length and proper time: Since c is 1, they are the same here. (b) 2 × proper time and path of light: the path of light is oblique but the proper time is vertical, which is the same as that of Hermann Bondi. Therefore, the length of the Bondi is its inherent length. |
Hermann Bondi started with (5) and concluded with (10).
 |
Figure 9. Overall outline of derivation of length contraction by Hermann Bondi |
Hermann Bondi says that his book has led to length contractions, as in the following (19).
Apparently, Hermann Bondi derives the equation from the proper length.
Should we write L on the left side of (10) or write Lo? If you put L on the left side, it becomes a totally illogical expression. The equation itself does not hold. Hermann Bondi apparently originated from a proper length, so if you put the observed length on the left, it will of course be an equation like this. Bondi tried to leave it ambiguously by not writing the left side, but the following equations are so obvious.
Since we were looking for L, L must be:
This is an apparent length expansion. In the end, Hermann Bondi did not prove length contraction, but proved length expansion.
"The equation derived by Hermann Bondi is
not a length contraction but a length expansion."
How did David Bohm think about this situation? Of course, he would not have liked Hermann Bondi's proof of length contraction. Therefore, he was able to defend his honor by omitting this part in his book.
Comments
Post a Comment