Vadim Matveev

2006-Feb-12, 08:06 PM

1) The common case of the relative motion

Let’s consider a long rod with a letter A on one of its ends and a letter B on its body.

The rod appears as follows:

A__________B__________

Let us mentally saw off the piece of the rod right so that we obtain the remainder of the rod limited by the letters A and B – such one:

А___________В

We shall name this remainder “remainder AB”.

Let us visualize that the remainder AB, moving in a certain inertial reference system K’ with a longitudinal velocity v, possesses the length L’.

It is clear that the proper length of the remainder AB (the length in the reference system K, in which the remainder AB rests) is equal to GL’, where G is the Lorentz coefficient (G>1). We can say that the longitudinal velocity and the length of the remainder AB are relative.

2) Another case of the relative motion

Let us suppose that the rod is manufactured from combustible material and the remainder of the rod is made not by the sawing, but by the fallowing way.

Let us assume that the end, which does not have the letter designation, is set on fire at a certain moment of time, and the rod begins rapidly to burn up to its complete combustion. During the combustion of the rod the process of combustion continuously moves toward the end A of the rod. At a certain moment of time the process of combustion reaches the letter B and for a moment the remainder with the letters A and B on its ends appears – such one:

A___________B*

The mark * at the end of the objects symbolically means the continuously burning of the end of the rod.

We shall name this remainder “remainder AB”.

It is clear in this case too that the proper length L of the remainder AB is equal to GL’ and the longitudinal velocity and the length of the remainder AB are relative.

3) A case against the relative motion and relative length of the remainder AB

Let us consider a long combustible rod with letters A and B on its body moving in an inertial reference system K’ with a longitudinal velocity v, moreover the rod is burning rapidly from two ends - thus:

* ___________А__________В__________*

Suppose that at a certain moment (simultaneously in the reference system K’) the processes of combustion reach the letters A and B and for a moment appears the remainder

*A___________B*

with letters A and B on its ends. The marks * at the ends of the objects symbolically mean the continuously burning of the ends of the rod.

We shall name this remainder “remainder AB”

The length of the remainder AB of the burning rod in the inertial reference system K’ is equal to L’.

Now answer a question.

How large is the own length of the remainder AB of the rod burning from two sides (case 3)?

In my opinion, the remainder AB has no own length, if we understand by it the length of the resting remainder AB. The proper length L of the remainder AB is not equal to GL’ The remainder AB cannot rest, because in the reference systems, where the rod burning from two ends rests (or moves with a speed, which is not equal to the above-mentioned speed v) the remainder AB can not be discovered. In my opinion the speed and the length of the remainder are relative in the first case, where the remainder AB does not burn and in the second case, where the remainder AB burns from one side, but in the third case, where the remainder AB burns from both sides they (the speed and the length) are absolute.

I think that everybody who understands the cause of the difference between the first two "correct" cases on the one hand and the "abnormal" third case on the other hand, will understand much more.

Let’s consider a long rod with a letter A on one of its ends and a letter B on its body.

The rod appears as follows:

A__________B__________

Let us mentally saw off the piece of the rod right so that we obtain the remainder of the rod limited by the letters A and B – such one:

А___________В

We shall name this remainder “remainder AB”.

Let us visualize that the remainder AB, moving in a certain inertial reference system K’ with a longitudinal velocity v, possesses the length L’.

It is clear that the proper length of the remainder AB (the length in the reference system K, in which the remainder AB rests) is equal to GL’, where G is the Lorentz coefficient (G>1). We can say that the longitudinal velocity and the length of the remainder AB are relative.

2) Another case of the relative motion

Let us suppose that the rod is manufactured from combustible material and the remainder of the rod is made not by the sawing, but by the fallowing way.

Let us assume that the end, which does not have the letter designation, is set on fire at a certain moment of time, and the rod begins rapidly to burn up to its complete combustion. During the combustion of the rod the process of combustion continuously moves toward the end A of the rod. At a certain moment of time the process of combustion reaches the letter B and for a moment the remainder with the letters A and B on its ends appears – such one:

A___________B*

The mark * at the end of the objects symbolically means the continuously burning of the end of the rod.

We shall name this remainder “remainder AB”.

It is clear in this case too that the proper length L of the remainder AB is equal to GL’ and the longitudinal velocity and the length of the remainder AB are relative.

3) A case against the relative motion and relative length of the remainder AB

Let us consider a long combustible rod with letters A and B on its body moving in an inertial reference system K’ with a longitudinal velocity v, moreover the rod is burning rapidly from two ends - thus:

* ___________А__________В__________*

Suppose that at a certain moment (simultaneously in the reference system K’) the processes of combustion reach the letters A and B and for a moment appears the remainder

*A___________B*

with letters A and B on its ends. The marks * at the ends of the objects symbolically mean the continuously burning of the ends of the rod.

We shall name this remainder “remainder AB”

The length of the remainder AB of the burning rod in the inertial reference system K’ is equal to L’.

Now answer a question.

How large is the own length of the remainder AB of the rod burning from two sides (case 3)?

In my opinion, the remainder AB has no own length, if we understand by it the length of the resting remainder AB. The proper length L of the remainder AB is not equal to GL’ The remainder AB cannot rest, because in the reference systems, where the rod burning from two ends rests (or moves with a speed, which is not equal to the above-mentioned speed v) the remainder AB can not be discovered. In my opinion the speed and the length of the remainder are relative in the first case, where the remainder AB does not burn and in the second case, where the remainder AB burns from one side, but in the third case, where the remainder AB burns from both sides they (the speed and the length) are absolute.

I think that everybody who understands the cause of the difference between the first two "correct" cases on the one hand and the "abnormal" third case on the other hand, will understand much more.