Here find available in PDF a short essay that I wrote back in 2009, which was NOT submitted to the FQXi Essay Contest, on the theme “What’s Ultimately Possible in Physics?”.
It was not supposed to be “scientific” (by design, FQXi essays cannot really be, right?), just some personal thoughts.
I have just published a new Science-Fiction novel at Lulu.com, in English (finally!), and completely **FREE** for downloading as a PDF file.
Here it is:
This SF novel was written back in 2011, in the NaNoWriMo contest, a yearly challenge in which participants must write at least 50,000 words in just one month.
This version is the raw result of that challenge. It has not been further edited or corrected. It may contain typos, grammatical errors, stylistic oddities and things of that nature. This work was written continuously, everyday, and the plot was developed as I was writing. Evidently, some deep thought on the overall story was given, but the actual realization of is was done practically on-the-fly. You can check my writing statistics here:
A civilization specialized at an obscure procedure to obtain and control pockets of time distortions, spread out over their planet, unknowingly hold the key to the fate of their world and of its distant twin planet, the Earth.
I have recently been thinking about the “idea of this blog”, about its contents, scope, and audience, as contrasted to the time and energy that I have available to invest on it.
It is clear by now that I have not been able to blog here as frequently as I should, but this was somehow expected. Also, although I love writing, it seems that, as I age, it becomes more and more difficult for me to write, specially technical content, even if brief, as blog posts are supposed to be (at least, in this blog).
Another factor that is bothering me is: the subjects that I have chosen to blog about, although being my favorites, unfortunately are not related to what I am presently working on (professionally). As time passes, I feel more and more detached from those subjects, and when I do find time or energy to write about them, it seems to take me forever to remember what I once knew, to keep up with otherwise new information, or simply “get into” the matter. Time runs out soon and I have to turn myself to something else.
In addition, this blog has never achieved a good statistics, it is really very poor in that regard. I have had other blogs in the past and this one has – by far – the worst statistics on visits. It is even worse than my shutdown blogs, which still receive traffic. I presently have another blog, called Matemática Replay!, written in Portuguese for Brazilian (or Portuguese-spoken) mathematics students (fundamental and high school levels), which receives a very high traffic, even though it is not frequently updated as well. Yet, I feel much more motivated to write there because I know it is being useful for the students and teachers.
Do not get me wrong: I do not write blogs just to gain traffic or attention towards myself. Since I have started blogging, back in 2005 or so, my sole purpose has been to write useful content and to learn in the process. Of course, having a good traffic is important because then you have an idea that the time spent is turning into something useful to others. I also think it is very important to revert the knowledge that I have gained – however small – back to society. But is it really worth the effort if it is rarely accessed? If I have such a hard time writing and the resulting posts end up not as good as I would like them to be?
As I age, and yes I am getting old, I must be even more selective on how to spend my time and energy. For example, I have stopped commenting on other scientifically-oriented blogs because I came to understand that what I write is quite often misunderstood. I came to the conclusion that I do not write (at least, in English) as well as I thought. So it may be the case that the present blog does lack clarity or some other feature that otherwise would increase the number of interested people. Therefore it may be not only a question of content but also of form.
In summary, I am re-thinking about Toy Universes, how to make it a useful and interesting blog, how to make my writing worthy and better, given that I have such a difficult time with it. So this post is just a short note to eventual readers – and a reminder to myself – that this blog might suffer some changes in the future.
I am not sure what those will be, and when, but eventually they must come.
We continue our notes on Mach’s Principle (MP) and its various interpretations. Today we will briefly point out a sixth interpretation of MP of our list of 21, namely;
Mach Principle 6: “As induction of inertial forces by accelerated masses by analogy with electromagnetic induction.”
There is a formal analogy between the equations of electrodynamics, described by Maxwell’s equations, and the weak-field limit and slow motion approximation of Einstein’s General Relativity equations (GR). Such description is referred to as “gravitomagnetism“.
One can show that the angular momentum of a stationary mass-energy current, in the above-mentioned limit of GR, plays a similar role as the magnetic dipole moment of an equally stationary charge current. Therefore, similarly to electromagnetic induction, the orbital plane of a test body is dragged along the sense of rotation of a massive central body, the so-called “frame-dragging” phenomenon.
So the question is: how far such a result, intrinsically manifested in the equations of GR in the weak-field, slow motion limit, could be extended to a stronger principle? That is essentially MP #6.
The interested reader is referred to Ciufolini’s review article on Nature (subscription required), and his article in [Barb95] , page 386. A freely available paper of interest is also his arxiv review.
We continue our notes on Mach’s Principle (MP) and its various interpretations. Today we will briefly point out a fifth interpretation of MP of our list of 21, namely;
Mach Principle 5: “As the generation of inertial forces in any body accelerated with respect to distant masses”.
You can tell when a body is accelerated by the emergence of the so-called inertial forces acting on the body, which do not exist if the body is at rest or moving at constant velocity(*). The statement concerns the question of whether such inertial forces arise from the motion of the body with respect with distant bodies.
It is well-known that Newton’s bucket experiment shows that inertial forces inducing the concavity of the surface of water in the rotating bucket arise independently of whether the water is rotating with respect to the bucket. In other words, it indicates that inertial forces seem not to be related to motion relative to other bodies.
Mach, however, pointed out that we do not know whether the concavity of the surface of the water would arise if in the experiment the bucket’s walls were increased many orders in width! (A brilliant observation, by the way). In other words, that experiment may rule out the effect of nearby masses, but not necessarily the integrated effect of distant masses in the Universe. This is the point of MP # 5.
(*) …with respect to what… ? – you would certainly claim to add some reference against which you establish that a body is at rest or moving in constant velocity. According to Newton, the reference is, of course, the Absolute Space. In a Machian view, velocity can only make sense if measured relatively to other bodies, so one could say that the average motion of all bodies in the Universe makes such a reference frame. Today, one would use the Cosmic Microwave Background Radiation (CMBR) “rest frame”, that is, if a body does not move through the average CMBR, then it is “at rest”, and accordingly for a constant velocity movement. In any case, General Covariance extends the notion of inertial frames of reference, so that what is important is that the physical laws have the same mathematical form under arbitrary coordinate transformations. More on that later.
We continue our notes on Mach’s Principle (MP) and its various interpretations. Today we will discuss a fourth interpretation of MP of our list of 21, namely;
Mach Principle 4: “As a mechanical interaction of masses, in particular through as interactive Machian ‘kinetic energy’”.
That particular interpretation is not only interesting by itself, but also for its apparent historical origin. The above-mentioned ‘Machian kinetic energy’ is explained in the article by John D. Norton on pages 32-33 of [Barb95], from which my brief exposition is here based.
The idea emerges as a Machian hypothesis by its own essentially because it arises from a quote by Einstein in a 1913 paper, where he discussed “the hypothesis of the relativity of inertia” and cites an “ingenious pamphlet of the Viennese mathematician W. Hofmann”.
Essentially, Hofmann (1904) argued that the standard kinetic energy of a body of mass () was unsatisfactory, due to an intrinsic asymmetry: the kinetic energy of with respect to would not be the same as that of with respect to . This consideration would be a necessary outcome of the assumption of the relativity of inertia.
Therefore, in order to have a symmetric law for the kinetic energy, Hofmann proposed that
where is a constant and an undetermined function. The idea was: since the mass measured of a given particle should arise as a contribution of all masses in the Universe according to that law, then by an integration of all masses, that formula would have to converge to the usual formula for the kinetic energy.
Further work along that line was carried out by H. Reissner in 1914-15, but he cited Mach for the modified kinetic energy law, and Hofmann was not mentioned.
(Well, I was unsuccessful to find any further online references for W. Hofmann, either a bio or link to his “pamphlet”…)
For historical details, curiosities and references, the reader is referred to Norton’s article.