The relationship between geometry and energy for gravitational waves

By continuing the last post, we will talk a little about the sources of gravitational waves. Of course that the subject can be found in many other places, for example the wikipedia site. However, my hope is to add something besides the content at Wikipedia.

Well, we know that gravitational waves are predicted by the Einstein's general relativity. The main equation of the theory is called the "Einstein's equation" which is a tensor equation. We can see it below.

R_μν -g_μνR/2 = 8πGT_μν/3

Here, the R_μν and R terms are elements of geometry and the T_μν term represents elements of density of mass and energy; g_μν is the metric of space and the other terms are constants values.

As we can note we have geometry elements on left-side and matter elements on right-side. This equation shows a way of interacting the geometry of the universe (of a piece of it) and the distribution of mass (or matter, or energy) on the space-time. Thus, we will have just a space-time completely smooth if there is no matter in all space-time. From the moment that we have the presence of a small density of matter, the geometry of space-time is not smooth any more. What we need know more is that all space time geometry is defined by the metric.

Now if we want gravitational waves, which are deformations on the gravitational field (represented by the metric) we need to insert something else in the metric. We need just insert a small perturbation on it. Thus mathematically speaking, gravitational waves are a kind of perturbations on the space-time metric. By inserting  a perturbative term in the metric and by solving the Einstein equation it's possible to visualize gravitational waves.


So in order to visualize the solution for gravitational waves from the a certain massive body, we must insert in the Einstein equation the elements of geometry of the region where the body is localized and its distribution of matter (or energy). Some examples of possible sources of gravitational waves are black hole, extremely massive stars, and the main one, an inflationary period which took place in the first stages of our universe. I say main because gravitational waves that were generated in this special period can carry very important information about the first minutes or even seconds of the universe.

Gravitational waves, what is it?

Gravitational waves, what is it?

Recently the research on cosmology has touched a level of difficulty that just a few people are able to understand. However, the cosmology is almost entirely based in the theory of general relativity. So the understanding of some points from that theory can allow us to understand a little of "classical cosmology". Current cosmology deals with multi-universes and other things like that, that is, effects that arises when are put together quantum mechanics and general relativity.

Gravitational waves are a immediate consequence of the general relativity. They are obtained even just in the classical cosmology, although its source are quantum effects. To understand what are gravitational waves we can make use of a basic analogy. Assume an electric charge and also that we are in a inertial system of coordinates in relation to the charge. Then if we are watching the charge moving, it's well known from the electromagnetism that we will to observe a electric field. Now, if we are in a accelerated motion in relation to the charge, also is well established that we will note a magnetic field as well. What we know as electromagnetic waves are just deformations on this field, called electromagnetic field.

In a complete analogy, the gravitational waves are just deformations on the gravitational field, which is our old friend since Galileo and Newton. But we need to use the general relativity to realize that. Nevertheless, we can not to measure signal of gravitational waves in a direct way yet. That happens due to the fact that the intensity of the gravitation interaction is much lower than other interactions, for instance, electromagnetic interaction. 

In the next post, I'll expose some devices which are candidates to measure directly signal of gravitational waves. Before, however, I must to show some sources from these waves.

Any question, it will be a pleasure to discuss about it.

Two problems of exchange of knowledge

The sharing of knowledge is an important step which must be done if we wish that the world be more and more sociable. In this mechanism we have the exchange of knowledge between Professor  students in the University as well as between the "scientists" (Professor and students) and the society in general.
Of course, there are problems in all countries about it, even that it be different one of another.

I post here two little articles about this subject and I hope that they can be usefull for someone. One of them is about the exchange of knowledge between the scientists and the society and the another one is about the transfer of knowledge from Professor of physics to students of physics.

The first article, named  How to not Teach Physics shows the exchange that I have cited first, and the second exchange being discussed in the article named Social Media for Scientists Part 1: It's Our Job.

The link for the articles can be seen below:  

http://blogs.scientificamerican.com/science-sushi/2011/09/27/social-media-for-scientists-part-1-its-our-job/

http://dissidentvoice.org/2013/01/how-to-not-teach-physics/

Just as a comment, here in Brazil we have both problems deeply. The society in general does not care if you collide two protons at a accelerator or if you is capable of moving a metal arm with your mind. Of course, the magazines most popular are not doing their job right, what makes the situation worse.

By the other hand, we have good students of science in general, particulary in physics, but unfortunately they are not valued neither by companies nor government agencies.

An introduction on the concept of heat

The word “heat” is frequently present in the people life, for example, when we speak that the weather is hot: it is very hot today! However, few peoples understand the truly meaning of this word and how its concept was discussed along of the 18th century.

 In the beginning of the 18th century, there were two hypotheses about the origin of the heat. The hypothesis more accepted regarded the heat like indestructible substance “occupying the pores” of the bodies and that it would flow from a body “hot” to another “cold”. The scientist Lavoisier called this substance of "caloric". This hypothesis meant that the heat could be transferred from a body to another one, but the total amount of heat was conserved.

 The rival hypothesis, in which two authors was the philosophers Francis Bacon and Robert Hooke, explained the heat as being a minuscule motion of vibration of the particles of bodies. Both theories about the heat concept explained some everyday examples that there was in that century, like rub two kindling and feel both getting hot. Nevertheless, the caloric theory suffered a lot of difficulties in another examples, like we will mention below.

 According to first theory, the caloric was a substance that would occupy the pores of the bodies and because that it would have some weight that could be measured, at least in principle. In the 18th century already had methods for such measurement to be realized, even if the weight were so small. The scientist adventurer Benjamin Thomson realized the following experiment: he weighted a large piece of bronze and after that he pierced the piece of bronze in order to generate very heat by friction. With that he would expect that after piercing, the piece of bronze would be lighter than before. However, it was not what happened and thus he came to believe that the caloric was something not constant but an unlimited substance within the material. Therefore the caloric theory was discarded, leading other scientist at that time to defend the theory of heat as being a vibratory motion of the particles of bodies. 

In the 19th century, the scientist James Watt developed the steam machine, so showing that the heat could be converted to energy to put in moving from simple things to train. The steam machine definitely showed, together with some others experiments, that the heat is nothing more than a type of energy. Thus, if we use the concept of heat as being the vibratory motion of the particles of bodies we can say: the heat is, of course, a type of energy; however, it is an amount of energy that is being transferred from a body to another one. This transfer happens through of collisions of particles of a body with particles of another one. Therefore a hot body is a body with more vibratory motion than a cold body. 

Although nowadays the word “heat” is present in any discussion, it generated a great scientific and philosophic controversy in the 18th and 19th century. The concept of heat is very well established now, being extremely used by physicists and engineers

Just a phrase

The first column, actually a phrase only, it is about cosmology and its dark side as well as its inflationary period:

Dark matter, dark energy, and inflation... About the two first things, because we don't know almost nothing actually about these dark things, now the physicists are asking yourself about the dark side of the universe, arguing that changes in fundamental laws can be made. On the third thing, observations have shown that would be more likely an universe like ours emerge without a inflationary period than through one. It's likely many changes in coming years.