**Hyperbolic observers and the principle of equivalence**

(posted: 2016-09-26 * minor corrections to the 2014-12 text)

After a brief summary of relativistic kinematics, we proceed along the following lines:

- first, we study the motion of a mass point subjected to a constant proper acceleration a0 and thereby establish the kinematic equations of the so-called hyperbolic motion
- then, we construct a whole (non-inertial) reference frame from a 3-dimensional array of these points, all subjected to some constant accelerated motion
- the next step is to use Einstein's equivalence principle to transpose the obtained results from the uniformly accelerated frame to some other frame, this one being stationary in a static gravitational field filling all space
- we finally use our simplistic model to draw some conclusions and make some wild speculations about the expansion of the Universe and the origin of its very large structure.

*Keywords:* special relativity, principle of equivalence,
accelerated reference frame, Universe expansion

Right-click to download: HyperObs.pdf (105 pages, 850 kB)

**Revolving observers and the principle of equivalence**

(posted: 2016-09-26)

We imagine a space station having the shape of a gigantic flat disk uniformly rotating around its axis. After a brief introduction of some mathematical concepts, we then proceed to study

- the non-Euclidean nature of the geometry on board the rotating station
- the various attemps by its inhabitants to define some concept of time that would enable them to establish a chronological order for the events they can observe
- the properties of the space-time they are living in
- the way the disk residents would describe the trajectories of bodies and of light signals passing over their habitat
- the principle of equivalence and the conclusions to which it leads to.

We investigate this problem working our way within the framework of special relativity and not by using the full mathematical apparatus of general relativity. Nevertheless, some important concepts of general relativity are being introduced along the way.

This text, together with the one on hyperbolic observers, is aimed at providing a transition from special relativity to general relativity.

*Keywords:* special relativity, principle of equivalence,
rotating reference frame, rotating disk

Right-click to download: RevolObs.pdf (95 pages, 692 kB)

**On the nature of entropy in statistical mechanics**

(posted: 2009-09-30)

*Abstract: *

An ideal monoatomic gas is initially confined to the left half portion of a box made of thermally insulating walls by a median partition, also thermally insulating. This partition is then removed and the gas is now free to expand throughout the whole volume of the container. This desribes a rather familiar thought experiment and one can easily find, in many textbooks, the calculations of the configurational entropy increase caused by the removal of the partition, but only the affirmation (with no mathematical argument) that replacing it would not reduce the entropy of the system.

In this paper, we show quantitatively that the number of microstates accessible to the system does increase when the median partition is removed but that it actually decreases when the partition is replaced. Since, in statistical physics, we usually define the entropy S of a system as S = k ln W where W is the number of its accessible microstates and since the considered system is isolated, it seems that the process of replacing the median partition is in conflict with the second law of thermodynamics.

We can solve this paradox by showing that, for ordinary gases, the decrease of entropy caused by replacing the partition is totally negligible. However, we might instead want the second law to be strictly exact and the variation DS never to be negative, no matter the precision with which it is being estimated. We might also want the second law to be extendable to very small systems, even to "gases" of only a very few particles. With such ideas, we will be led to reinterpret entropy as a variable characterizing not the system in itself but the manner in which its representative statistical ensemble has been prepared. As a consequence, entropy would no longer be a state variable of the system. This would even open the possibility that a physical system could become more orderly without decreasing its entropy.

*Keywords:* statistical mechanics, entropy, second law of
thermodynamics

Right-click to download: OnEntropy.pdf (18 pages, 226 kB)

**Outline for a knowledge processor**

(posted: 2011-11-21)

This short text just gives a general draft on how a knowledge processor could be made.

*Keywords:* knowledge processing, artificial intelligence

Right-click to download: KnowProc.pdf (2 pages, 62 kB)

**Who is the cat in the mirror?**

(posted: 2011-11-21)

In this short text, it is argued that, if given enough time to familiarize themselves with a mirror, most cats will probably be able to recognize their own images.

*Keywords:* ethology, animal behavior, cats, self-awareness

Right-click to download: CatInMirror.pdf (3 pages, 125 kB)

aratel@vif.com