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Suppose a system with a gravitational field that emits a photon of frequency f. This photon will have an energy:
E = h x f where h is the Planck constant and f the frequency.
Although the photon lacks its own mass, the system that emits the photon loses a certain amount of mass m = h x f / C 2
The photon separates from the emitting system at the speed of light and we can not say that it accumulates potential energy because it lacks its own mass, it will never stop traveling at the speed of light, it will never stop and it will never return. However, as the photon separates against the gravitational field of the emitting system, it loses a certain amount of energy and consequently its frequency decreases; it shifts to red in the case of visible light.
After a certain time, the photon can be captured by another system and then its energy will be incorporated as a mass to it. But its frequency is no longer f, it is a lower frequency f', and therefore its energy is no longer E = hxf, but a smaller energy E'= hxf', so that the mass that is incorporated into the second system is a mass m'= hxf'/c2, which is a mass smaller than m.
What happens with that mass difference m'' = m - m', or with its equivalent energy, that the photon has left in its path? Where is that mass or that energy? Energy is neither created nor destroyed, it is only transformed, and given the equivalence between mass and energy we can speak in terms of mass and say that mass is neither created nor destroyed, only transformed, what has been transformed the energy lost by the photon? In what has the mass m'' lost by the photon been transformed?
That mass m'' (or its energy) has nothing to do with the first system, which lost a mass m but then neither gains nor loses mass no matter what happens with the photon. It also has nothing to do with the second system that captures the photon that gains a mass m', but nothing more. In any case, the second system would gain the mass of m and with it its potential energy, but this only adds one more question: What happens to m'' and what happens to the potential energy of m''?
We accept that energy does not disappear, is not created or destroyed, only transforms. It is then forced to accept that this energy, or that mass m'', has passed into space or has been incorporated into space. We could think that it has passed to the gravitational field that surrounds the emitting system, but it is a force field, so it cannot capture an energy. The lost energy can only have been incorporated into an energy field, but around the emitter system there is only space which implies that around a mass, and in general in any gravitational field, there is an associated energy field and that field has its Once as a support to the space itself, then it is the space that incorporates the lost energy.
Obviously, if space has incorporated a certain amount of energy with the passage of the photon, space has changed. But for an observer, that energy lost by the photon has literally disappeared and at the same time space has not changed at all with the passage of the photon. The most logical solution to explain this phenomenon is simply to think that space itself is a form of energy, or what is the same, that space itself is an energy field. Not that space "contains" a field, but that space itself is a field: that space is a third form of energy.
If we establish this hypothesis, what we should next ask ourselves is where does it come from or what is the origin of that field, and what is its relation to mass and the force of gravity.
VALUE OF THE PRIMARY FIELD
Regardless of the above considerations, the application of logic without concessions forces us to think that the presence of a mass modifies in some way the space that surrounds it, and that this modification has the structure of a field that depends on the mass itself and on the distance to it. This field relates or puts the masses in contact with each other and is the vehicle of the force of gravity.
Suppose two masses M1 and M2 located at a distance R. Each mass modifies around it the space that surrounds it and between the two there is a force of gravity Fg that depends both on the masses and their distance. If we accept that this force is not unique or directly produced by the masses, but is the result of the interaction of its two respective fields, they also have to depend on the masses and distance as well as their gravitational fields, although have a different formulation. The gravitational fields will be in this case secondary fields.
If each of the fields affects the other, we do not have to think that it does so at a specific point, or through the line that unites the two masses or the space that separates them: the strictly logical thing is that this interaction takes place in all the space, in the totality of the space that surrounds each mass. At first we do not know what the mechanism of this interaction is, but we know its result, the force of gravity between two masses M1 and M2 separated by a distance R equals:
Fg = G x M1 x M2 /R2 where G is the universal gravitation constant.
From this data and accepting that the action of gravity is the result of the interaction of two fields in the entire space, we can calculate the value of the field (whose nature we ignore in principle). The calculation is not simple but the result obtained yes. The field "d" that a mass M creates at a distance R in the space that surrounds it, has a value equal to:
d = 2 x G x M/R4 (Possibility B d = G x M/R 4)
Since the fundamental units of G are newtons per square meter divided by kilogram squared, the units of "d" are newtons divided by square meter and kilogram:
d is expressed as Newtons/square meters x kilogram.
This means that the field d is a force field, a field that has a certain force per square meter and kilogram.
But the field d is not altered if we express it in another way, multiplying its numerator and denominator by meters. In that case, d offers us another physical sense, since it would be expressed as:
d can also be expressed as Newtons x meter/cubic meters and per kilogram.
But Newtons per meter is a unit of energy, joules, and cubic meters is volume, then the field d represents a certain amount of energy per volume and kilogram.
If we now consider a constant d field (for example in a spherical crown around a mass M) and multiply the field d by the volume of that crown:
d x V = X joules/kilogram:
That is, what we get is a certain amount of joules per kilogram, but precisely joules per kilogram are the fundamental units of a potential energy field around a mass M.
Therefore, d is the primary field that we supposed to exist when we consider the potential energy, and when we separate m from M a distance R the potential energy of m is precisely equal to the product of the primary field d created by M, by the mass m and the volume R3. Then it is in that volume that the energy that we supply to me becomes and that apparently disappears. That energy has been inverted in the primary field of M, but since that field does not change because it only depends on M and R, what has increased is space. So to speak, a new R3 space has been created. The force of gravity is the one that opposes the creation of that space and causes it to recover its original state, returning then the accumulated energy, or what is the same, the potential energy.