Chapter II




"The poet only wants to stick his head in the heavens. It is the logical that demands to put the heavens on his head. And it’s his head that gets divided. "

- G. K. Chesterson -


      The former felt that the basic elements of matter were four: Air, Water, Earth and Fire. The atomists considered that matter was made of indivisible atoms. Today, it is said that matter consists of particles: protons, neutrons and electrons.  More recently, the physicists found that particles like protons and neutrons are made of even more elementary particles: the Quarks!

      How far reaches the indivisibility of matter? Does Nature have a limit? Or this division will extend forever into the infinity?

      The Mass is the key to solve this puzzle, and it is the missing link to establish a relationship between Quantum Physics and Relativity.

      To understand the Big Bang, the supposed beginning of the Universe, the physicists have to reconcile the two theories. However, General Relativity and Quantum Mechanics appear to be incompatible. The Theory of General Relativity does not fit in the exact moment of the Big Bang, when our Universe was still a newborn and this time is usually called by the Planck Time; and also does not fit in another time just before a Big Crunch, the physical state that may occur as one of the possible final destinations of our Universe, the death of the Cosmos!

      Another inevitable conflict and a particular case in which the General Relativity does not fit is inside a black-hole. In some particular stars the natural evolution consists in an unavoidable gravitational collapse of matter. Within these stars there is a huge density of matter confined in to a very small space. Due to the huge amounts of pressure, density, temperature which is supposed to exist in those physical state, it is expected that the structure of matter as we know, it will not have the slightest chance of survival. And the strong gravitational field will continue forcing a contraction and an inevitable collapse of all the matter and radiation in to the direction of a central point called singularity.

      These regions and situations are, in terms of physical behavior, simultaneously big and small, extended and very confined in to an astronomic and microscopic space-time region... and highly complex.

      And, indeed, we do not have a good theory that describes what happens inside a black-hole, and also for other physical states with similar conditions, as it is the moment of the Big Bang or the Big Crunch.

      And I quote: In these stages "The Gravity is strong. We need a Quantum Theory of Gravity, which does not exist yet. "- Frank Close.

      Attempts to combine Quantum Theory with the General Relativity equations transport us in to infinite solutions. If an equation has an infinite solution, the physicists conclude that this has no real meaning in a physical context; therefore, they assume that the equation must have a wrong formulation.

      Without a real solution, the physicists have not the slightest chance of knowing what is happening in these physical processes. Using a determinist concept, if we can’t understand what happened in the past, we can’t predict what will happen in the future.

     The Theory of Relativity is no longer valid for the Planck Time and the Quantum Theory also does not provide any solution for these micro-spaces of high energy. Both theories are in bankruptcy in these circumstances and in this particular regiions of space and time.

      The existence of a Quantum Theory for Gravity is logical and even necessary!

      Problems emerge right from the beginning, as soon as we try to proceed with a   quantization of Gravity. This obstacle seems to be insurmountable to us.

      If on the one hand the process of physics of particles act on a space-time background, absolute solid and rigid; by the other hand the General Relativity acts on a flexible and dynamic space-time stage.

      Considering the Electromagnetic Force, we know that the transmission and mediation of this force is limited to the minimum quantization of photons, and its energy can be summarized to Planck packages. For the Gravitational Force we still don’t know what is its mean of transmission, we haven’t got the slightest idea how this force takes place, what is its mediator particle, already denominated by Graviton, the mediator of the Gravitational Force, a particle that should be everywhere but hasn’t been detected yet; and also we have not found the unit basis, the minimum quantity of matter, the quantization of mass.

     This is where we are … at least this is what physicists think.

      I can tell you that today we haven’t reached much further than Einstein when he aspired for Unification!

      The research for a Quantum Theory of Gravity has become a gigantic puzzle and the biggest enigma of contemporary Physics...

      The equations are known to each other, some are usually friendly and there are others who disagree violently. When this happens, and two theories persist to get a major confrontation, it is normal that from there arises a third.

      The union can be born has a peaceful and unifying concept, the crisis can be an excellence time for creativity and new creation can be born from this state of chaos.

      It is often said that a new theory is always an extension of a previous theory ... but it does not need to be necessarily so. When we seek for the truth, we can find many truths in many things!

   In the Special Relativity, Gravity was not involved. In order to accomplish a correct theory, Einstein had to include Gravity and take into account all the effects of gravitational force.

      Two observational keys led him in to his new Theory of General Relativity:


1 .- The first observation relates gravitational mass of an object with its inertial mass.

2 .- A second observation shows  that gravitational field  effect can be simulated by an accelerating reference system, even in the absence of gravity.


      Now let us describe in detail on what this means:

      We say that the gravitational force is proportional to the mass of an object and we say that an object that reacts to the force of gravity is defined as having gravitational mass.

      Similarly, a gravitational mass tells us the magnitude of the gravitational force that an object feels.

      Furthermore, the inertial mass tells us the speed and how fast an object can move in response to an external force.

      Inertia is a measure which reflects the resistance of an object to a change on its state of motion.

      For example, an object with twice the mass of another object will feel half the acceleration, when subjected to the same strength and therefore the object of greater mass will move more slowly. In other words, the greater the inertial mass of an object, the slowest it moves when subjected to the same strength.

      Take another practical example for this interaction:

      If we have a ball of lead and a ball of wood, we say that a ball of lead has a gravitational mass larger than the ball of wood. Therefore, we say that the ball of lead feels a force much stronger when exposed and subject to the force of Gravity, so the magnitude of their weight is bigger.

      Furthermore, the ball of lead has a higher inertial mass, this means that it will be slower to react to the external Gravity force.

      What this reflects is the following: the force that is applied to the ball of lead may be bigger, but nevertheless the speed of reaction is slower, or inferior, because it has a highest inertial mass; so, therefore, the acceleration is exactly the same as that gained by a wooden ball.

       Conclusion: different objects with different masses feel exactly the same gravitational acceleration. And this it is shown in the 2nd Law of Newton:


F = ma <=> a = F / m


           This ratio (F / m) is always proportional; once again, the acceleration experienced by the two objects is always the same.

      The acceleration is the only constant! ... Very interesting!

      The equivalence between inertial mass and gravitational mass suggests a deep relationship between these two apparently very different concept from reality. Several experiments were performed and repeated in various scenarios and the results are always the same:


Gravitational mass = Inertial Mass


      And this relation can only be explained in one way: if there is no distinction between these two concepts, of course!     

     Thus, we can establish as definition of Gravitational Mass mg:


mg = F / a


     And, besides, we can give another definition of inertial mass:


mi = F / a


     At first glance, there is no obvious reason for these two types of mass to be related. The gravitational mass is the capacity that an object has got to attract other, and is usually expressed in Newton's Gravity equation (Fg=G.m2/r2), relating the magnitude of gravitational force. The inertial mass is the one expressed in the second Newton's law of dynamics (F=ma), which relates the movement and speed.

     But the facts do not lie and experience proves that these two separate measures are usually confused and merge it into one.

     The conclusion can only be one:  that these concepts should be identical in their essence and therefore they can be interchangeable.

     Now for the 2nd point:

     To clarify a little better the relationship between gravitational field and acceleration of a reference system, we will show a practical and concrete example:

      When we are on board of a plane, just about to take off, we all can feel our own weight that push us down, but also an additional inertial force that makes us feel even heavier. This force arises when the plane starts to accelerate, reaching enough speed, the sufficient velocity to lift off. When the plane takes a constant speed, a cruise velocity, everything returns to normal and we feel only our own weight.

     The opposite effect can also occur: If the plane takes a free fall, in this new and accelerated reference system, we are without weight and we no longer feel the effects of gravitational force.

     With this experience we can also suggest that there is a deep connection between Gravity and accelerated reference systems, such that:


Gravity = acceleration


     Also these two concepts must have some complicity in its essence and can, therefore, be interchangeable.

     For those who have never traveled by plane, another similar example occurs on board of an elevator. In the particular case of free fall, we do not feel our own weight because we fall with the same acceleration as the elevator.

     Based on this type of observations Einstein concluded his Principle of Equivalence, summarizing:

     The definition between the masses of two objects is defined in Mechanics of two different ways: by the inverse reason of the accelerations that are communicated by a same force (Inertial Mass); and also by the direct reason of different forces that are applied in two distinct objects when exposed into the same gravitational field (Gravitational Mass).

     The equality and similarity of these two kinds of mass, identified by a very different method has not raised any issues or questions for the current physicist. However, Classical Mechanics does not give any explanation about this type of equality!

     Is it simply a gap?

     Is there a possibility that these equalities are trying to reflect the true nature of these concepts?

     A little reflection shows that this Principle of Equivalence is extended to the Principle of Relativity, which means that can be applied in to coordinated systems with non-uniform motion, accelerated systems, with relative movements in relation to each other.

     Let us see how:

     If we consider a system of inertia K, where all objects are sufficiently distant from each other, we could say that, on this system K, there isn’t any kind of acceleration, so everything remains at rest and all the particles remain at the same position.

     But if we consider another reference system K ', uniformly accelerated, moving with non-constant speed; from this point of view we could say that  all the masses of reference K have all equal and parallel acceleration;  we will consider that those particles are all moving away from the reference K ', and behave as if they were subject of a gravitational field! And yet, as if K’ did not have the initial acceleration considered!

     In other words, assume or accept that K' is at rest and that in hat region there is only a gravitational field, is the same as believing that K is the legitimate reference and that there is no gravitational field in K', and that this one is only accelerated!

     What this example means is that nothing can be concluded, therefore, in space there is no fixed reference point, there is not an absolute reference system for which we can make measurements and establish absolute physical facts.

     The Principle of Equivalence proposed by Einstein states that the laws of Physics in a Gravitational Field are exactly the same as in an Accelerated Reference System; establishing that we cannot make any distinction between both. In fact, we cannot do any kind of experience that confirms us, or let us know, in which situation we are.

     This immediately raises another question about the Universe:

     After all, where do we stand?

     Immersed in a huge gravitational field, or transported in a huge accelerated system? Since we can considered Gravity as a Natural Inertia and Inertia can also be considered like an Artificial Gravity.

      Interesting idea indeed!

     Another link to be taken into account as we try to reveal the mystery of matter, is the following:

     For a long time scientists have considered Mass and Energy as two different phenomenon. What science has taught us is that mass and energy are indestructible and that they both satisfy identical Laws of Conservation.

    Einstein, once again, had the vision to see that both mass and energy had exactly the same characteristics, curious as ever, noticed that both are contracted and expanded in similar factors, their properties were very similar. In all major aspects he concluded that Mass and Energy were indistinguishable, that inertial mass is simply latent energy. And with a final revelation he has shown us that mass could be destroyed and converted into energy and vice versa.

     And present us the Mass-Energy concept through his famous formula that we all already know:


E = m.c2


     The experimental and incontestable evidence of the demonstration of this formula is in the disintegration of radioactive elements and in the nuclear fusion of stars.

     But it should be noted that Einstein incorporated these two concepts in only one, introducing a new Principle of Conservation of Mass-Energy, or more simply, the Law of Conservation of Energy.

     From a practical point of view, about the Principle of Equivalence between mass and energy, this means that a material object can be transformed into pure motion; Kinetic Energy can be converted into mass and vice versa. What this means is that pure movement can be transformed into a pure solid object!

     If you notice well, this is truly amazing!

     Matter can be created only by spending motion … movement … energy? ... Very interesting!

     This transformation would only have to obey to the Law of Conservation of Energy.

     We say that Energy = Mass x Speed of Light squared, meaning that matter can be destroyed but it can also be created and transforming the equation, we have:


m = E / c2


     This is not a new formula, but with this equation we can see how false it was the belief of the past that considers that matter could not be created nor destroyed, and how false is the belief of today about the stability and quantization of matter, because this physical concept it is not even a fundamental property, but only apparent!

      Indeed, there is no Law of Conservation of Matter, what is always preserved, as far as we know, is the Energy!

     The only real quantities that are always conserved in collisions are the momentum (quantity of movement) and energy, which means, the theoretical conservation of mass.

     However, we aspire for the quantization of matter, but then we make a relationship between matter and energy; we admit that these two concepts are indistinguishable and the same. And now we separate the same concepts and relate Mass with Gravity and Energy with Field. So, after all, where are the differences and the similarities? I do not understand … is it possible that we are those who are imposing the differences?

     We could begin by clearly conclude that the mass of an object is a measure of its energy content. That the Mass is a form of Energy! That Mass is a manifestation of Energy in Motion!

     That would simplify many things! And this is what Einstein tells us, when we read his equation.

     Energy together with its component vector: momentum or amount of movement. Energy in motion, these two concepts go hand in hand together and both produce everything that exists! Everything is energy in motion ...

     Before finishing, let's see another analogy:

     If on one side, the inertia of an object depends on its energy content, such that:


m = E / c2


     And on the other hand, with a little help of quantum theory, we know that E = h.f, so the energy depends on frequency, and replacing our equation of inertial mass, is that:


m = h.f / c2


     Moreover, it’s also known that there is a relationship between mass and momentum (p=m.v), so that the equation of classical physics that relates these two quantities is:


m = p / v


     This equation says that the mass of an object is a measure of its speed and its momentum.

     And finally, by the famous Newton’s formula (F = m.a), it is known that the mass of an object is a measure of its acceleration, whose origin is in a mysterious force, supposedly Gravitational:


m = F / a


       I do not wish to add anything else to the concept of mass, because if we do so, we will start to get confused. Indeed, everything is already said:

     Basically what we have seen until now is that Mass can be described by several different equations, relating different concepts and different units of Physics, and that the matter may appear in a very diverse and versatile way!

     Unless the mass is not an innate characteristic, a fundamental unit, and essential concept; it follows very clearly that this mysterious reality and fact of Nature cannot be explained and described in an objective way!

     Therefore, trying to summarize ... all these versions of mass lead me into a question: Does mass have some kind of a multiple-personality syndrome or disorder?!

     Or is that all these relations and equations translate and hide its true physical meaning? ... Before we move forward to any kind of conclusion in our relation and definition of mass, perhaps we could ask for some help to Gravity ...