The stochastic regeneration model of the Universe has implications for the meaning of mass and its relationship with electromagnetic radiation.
Mass may be generally understood to mean the amount of material in an object or entity. Mass is obviously a fundamental property, but it is one which is not verifiable by an independent observer, for instance, in the same way as acceleration. It must always depend on an additional factor for verification to give it what might in engineering be called a degree of freedom.

In the terminology developed in the previous papers, all measurements must take place in a part of the Universe which is not homogeneous through time. Non-homogeneity through time is therefore a given, if we are to make observations and measurements. Inside such a part of the Universe, cyclical change, say the period of an orbit or diurnal rotation, then allows the construction of a means of measuring the passage of time. With this 'clock' and any arbitrary standard of length an observer can measure acceleration.

Mass on the other hand is not independently verifiable, even in such a part of the Universe. An object may be seen to be suspended in space, but that does not allow an observer to determine whether it has mass or how much.

Mass is detected by the application of force. If the application of force results in acceleration, then the body has mass. Mass does not accelerate unless a force is applied. It is said to have inertia.

The same equation defines force. If a body accelerates, it is because of the application of a force. The force is defined as proportional to mass for a given acceleration, which can be measured independently. By extension, if a body is unable to move because, for instance, it is lying on a surface or otherwise restrained, force is still defined in terms of acceleration. It is the acceleration which the body would have, if it were not so constrained. The surface or the restraints in fact absorb the force, and transmit it to whatever is supporting or holding them in their turn.

The result is that mass is always defined in terms of a timeframe, the one in which its acceleration is measured. Or in other words, mass requires a time frame in which to make itself apparent. When this has been done once, there is a unit of mass against which all others can be measured by comparison.

The proposed model of the Timeless Universe suggests that the application of force means causing an entity having the property of mass to accelerate through the gravitational field which permeates the whole Universe at all times. In the absence of force the entity is held by the gravitational field; it has inertia. Force overcomes the interaction of mass with the gravitational field to produce acceleration i.e. it is a measure of the interaction.

Measurement of force cannot separate the mass from the effect of the field, simply because they interact. However, decomposition of the interaction in this way, suggests that the force required to cause acceleration may not increase linearly with acceleration. It becomes progressively more difficult to cause a body having mass to accelerate when it approaches the speed of light, to the point that this speed can never be reached. There is no reason to believe that the mass changes during the process, in the sense of the amount of material in the body, but rather that the interaction with the gravitational field requires ever increasing force to overcome its effects.

The form of the relationship of force to velocity may be understood as a rectangular hyperbola centred on the origin with velocity as the ordinate and force as the abscissa. As velocity approaches the speed of light, the slope dF/dV tends to infinity. Application of a force in the opposite sense gives the same effect in the opposite direction. We normally operate on a flat part of the curve near the origin where change is least.

The limits are those observed in experiments. Enormous amounts of energy are required to accelerate particles to anywhere near the speed of light. Photons on the other hand always travel at the speed of light in vacuo, which suggests that they have no mass. The corollary is that they also exert no force.

It is unlikely to be a coincidence that the same limiting velocity is reached both for mass and for light. We have already proposed that light should be considered as an interaction of a photon with an electromagnetic field which permeates the whole Universe isotropically, and imposes a maximum speed, the speed of light. Since the same limit applies mass, it suggests that they are different forms of interaction with the same field, which the model requires to fill the whole of the Universe isotropically i.e. it is a field with both electromagnetic and gravitational properties, which we detect through different interactions, one with light, another with mass.

Fundamental particles which have mass are homogeneous through time. Such particles agglomerate to form larger masses. Thus there is a minimum possible mass, a quantum of mass, and all masses are multiples of this quantum. If more than one type of fundamental particle has mass, and if it has a different mass, there will be a wider range of multiples of quantum mass levels available by agglomeration.

The kinetic energy of a body with mass m is ½mv^{2}. From the above argument it follows that the upper limit on the kinetic energy which a fundamental particle having the minimum quantum mass could attain, will be ½mc^{2}, where c is the velocity of light in absolute space. However, there remains the problem of observing velocities of masses approaching the speed of light. If force measures the interaction of a mass with a field, there may be implications for the interpretation of experiments which use accelerators to obtain information about particle masses.