2.1.1 The assumption

Now let us discuss the assumption we made about the limit of energy density that spacetime can take. To do this we will look at the reason why waves propagate and we will start from the easiest, that is a rope.
Everyone knows that if we start to oscillate one end of a rope the waves propagate through the rope to reach the other end which in turn oscillates in the same manner. When we oscillate one end of the rope, all we do is to oscillate around a middle point, and from there all other points along the rope are pulled by the preceding point and start to oscillate as well. Therefore there is an interaction between all points along the rope, that makes all points to oscillate around the same middle point.
The same observation can be done with water waves, molecules of water, that cannot be pulled apart at liquid temperature, pull other molecules to oscillates around a middle point that is the level of the water in the tank or the sea level if we are thinking at waves in the sea.
Now let us look at sound waves. Sound waves propagate through a medium (let it be air)because molecules of air are pushed and pulled by areas of high and low pressure. Hence the pressure of a section area or shell inside the wave oscillates around a value of pressure that stands in the middle between the high and the low pressure.
In the same way, waves of electricity propagate through a copper wire. Areas of high voltage with many electrons push electrons towards areas of low voltage with very few electrons and vice versa.


A small section area (or volume) inside the wire (see Figure 2.3) will alternate moments of many electrons with moments with few electrons, with a frequency equal to the frequency of the traveling wave. The number of electrons in the section area depends on the voltage applied to the wire.
Therefore, in order to propagate, waves need a tendency towards an average or middle value, or even better they need some sort of potential/internal energy that is stored in the medium they travel. This energy gets released to the neighboring section areas making the wave travel along the medium.
Electromagnetic waves behave in the same way, the only difference is that each spherical shell or section area vary in the intensity of electromagnetic field even if they do not have a medium.
Many system have the natural tendency towards increasing disorder, the measure of this disorder is called entropy. Consider a thermally insulated box divided by a partition into two compartments each having volume V (Figure 2.4). Initially one compartment contains n moles of an ideal gas at temperature T, and the other compartment is evacuated. The system has the ability to do work, hence has energy. We then break the partition, and the gas expands to fill both compartments spreading like a sound wave.
For this initial state the heat Q = 0, the work W = 0, and the change in internal energy DU = 0. Therefore, because it is an ideal gas DT = 0. In order to obtain an isothermal expansion from V to 2V at temperature T, heat must be supplied to keep the internal energy constant. The gas does work during this substitute expansion, the total heat supplied equals to the total work, which is:


If we did not supply the system with heat, the final state would have a lower internal energy than the initial condition. So it seems that this tendency towards "disorder" is in fact a tendency towards a lower energy state of the whole system. All hot objects tend to cool down eventually to 0K if not heat is supplied, and so is air pressure, it will tend to zero if molecules are left free in space.
The system just described is not very different from the section area described for sound and electric waves above, hence waves need some sort of energy stored in the medium in order to propagate. This energy gets released as the system tends to go towards a more natural state or "disorder". For an isolated systems the work done during this process can be in the form of heat, while for waves the work done on other particles (by collision or repulsion/attraction) makes the wave travel along the medium.
So it seems that in general free energy tends to zero and if this was not the case, than waves would not propagate. In conclusion, we can say that if energy in free spacetime has the tendency to zero. As a consequence it is not so crazy assume that spacetime must also have an upper limit of energy density that it can take, otherwise there would be no reason for this tendency to exist at all.
In fact this would explain the repulsive and the attractive force of molecular bonds. The attractive force would be the electric force and the repulsive force would be the limit of energy density that spacetime can take, which behaves like a spring pushing outwards when two atoms get too close.












Fig 2.3 - High frequency electric signal propagating through a copper wire. Single electrons oscillates around a fixed point. In the same way a section area along the wire will alternate moments of many and few electrons with the same frequency of the traveling wave.

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