The value of mass is not being redefined. But the concept of mass being a fundamental property is reviewed.

Mass is assumed to be fundamental physical property. The reason for this is obvious. It is something our senses can directly observe through either a mass's weight or the effort it takes to move an object, or impart a velocity. Mass is an unchanging property, conserved through many physical processes. This view was changed with special relativity. The only time mass is lost is when a corresponding amount of energy was released. The conservation of mass-energy replaced the separate concepts of conservation of mass and the conservation of energy. This effect of interchangeable mass and energy is used in high-energy physics but is ignored in our everyday environment.

There is another law of conservation that is required when doing mechanics, conservation of momentum. It is somewhat variable because the same amount of momentum can be found in either a small mass with a high velocity or a large mass with a low velocity. The amount of energy is different between the first example and the next. The exception to this case occurs with elementary particles that are massless. The photon is one of these particles. In this case a photon with twice the energy has twice the momentum, E=cp. If this law could be applied to all particles it would greatly simplify particle physics. Unfortunately, a particle with rest mass can have a variable amount of momentum, just like our everyday experience would tell us. A thought experiment is useful in potentially changing this view.

First, what is a particle? For example a massless particle, like a photon, has momentum and travels with a velocity of c. Now if a massless particle could travel in a direction that wasn't x, y or z, what would it look like? A direction that isn't x, y or z leaves one with a hyperspace dimension, one of the curled up superstring dimensions. Now this assumes superstring theories are correct. Additional spatial dimensions exist but are curled into a very short length. What does a photon look like when it is traveling down this tiny dimension. Even though it has a velocity of c, in normal space, it looks like it is standing still, unmoving, like a particle with mass. It has momentum, a very large amount of momentum if it is constrained to a very small dimension. One requirement imposed from quantum theory is that this momentum has an integer or half integer multiple of h divided by the length of this tiny dimension. If it could be shown that this momentum is directly proportional to a particle's rest mass, then a particle could be shown as a type of photon traveling in curled up dimension. This photon has some quantized amount of momentum in a hyperspace dimension and a variable amount in normal space, i.e. x direction. The combined vector velocity is still c. This is similar to a particle that was traveling with a velocity of .707c in the x direction and .707c in the y direction. A photon with some hyperspace velocity vector would look like a particle that is moving with a velocity of .707c in the x direction, 0c in the z and y direction. Now this is only useful if the mechanics of this experiment agreed with the energies, velocities and rest mass as calculated in special relativity. Below is shown how starting with special relativity's equation relativistic mass, the conservation of momentum in hyperspace, is derived.

One nice thing about this thought experiment is that the location of the particle still has a fundamental lack of point location. The photon has a location that extends the length of the tiny dimension. It isn't a point particle. There are no vacuum energy densities going to infinity.

The vector addition of momentum and the special relativity equations for relativistic mass are identical. This is shown:

Define:

m_total = m(v) ; The relativistic mass of a particle.

p_total = m_total c ; This states the total amount of momentum of a particle is its relativistic mass times the speed of light.

p_e = m_e c ; This is the rest momentum of an electron, if one assumes an electron is a photon like carrier of momentum moving at velocity c along a superstring dimension.

p_x = m_total v; This is the classical momentum of a particle.

 Note: p_x= m_x c. This is not used here but is included to show equation symmetry.

So vector addition of momentum is not new, but when shown this way it implies something new. That a particle's velocity value along x is just the dot product between the total momentum vector and the vector x. The conservation of momentum can explain the conservation of mass-energy. This simplification occurs only because hyperspace dimensions are considered equivalent in all respects to normal spatial dimensions except for their subatomic size. The small size is what allows for momentum quantization, which equates to rest mass quantization.

The equation m=p_total/c is ideal for finding the total or relativistic mass for particles with a rest mass, m₀=p₀/c. E=cp_total is used for a particles total energy if it has no rest momentum.

A new physical law is postulated: All known particles are elements of momentum moving at a velocity c.

Two pieces of physics have been unified: conservation of momentum and conservation of mass energy. A reason for fixed particle masses has been suggested. A couple of physics puzzle pieces are joined.

This concept is important so here is another attempt at stating exactly the same thing as above.

In detail: The rest mass for an electron is m_e. This gives it a rest momentum value, p_e=m_ec. Finding the amount of energy to get an electron to a velocity of 0.5c is the equivalent to adding some momentum along a vector p_x to get p_x equal to 0.5p_total. The total momentum is p_total = (p_e² + p_x²)^1/2, the vector sum of p_e and p_x . Solving for p_e shows its equals .8660 of p_total. P_total= p_e / .866. This result is identical to m(v)= m₀.

One result of using momentum formulas is that it shows that mass is not a fundamental property. Momentum is fundamental. For quantum physics, momentum, p and dimension, x are fundamental. (Note: this x implies all dimensions, normal and hyperspace ones, it is different from above where x referred specifically to a normal space dimension. Historical use of x in both of these cases may lead to some confusion. It is hoped that the context they are used makes it clear if x is a general dimension or the normal space dimension.) In fact, special and general relativity effects will be shown to derive from quantum physics. Lorentz contraction and a mass's effect of curving space, creating gravity, are basically the same things. Both effects derive from x p = n h / 2 .

 A new physical law is postulated: All known particles are elements of momentum moving at a velocity c. This is the result of extending a quantum theory formula for massless particles to all particles, p=h/2l . The new postulate is known to be true for photons. They have no mass, move at the speed of light and have momentum. At first, the new postulate seems to be untrue for particles with a rest mass. The momentum associated with a particle has a value directly related to the particle's velocity. This statement seems true because the present definition of momentum, p, includes only the three normal spatial dimensions, x, y, z. This new postulate applies for p traveling along all dimensions, including hyperspace ones. The value of a particle's momentum in hyperspace, its rest momentum, is just a particle's mass times the speed of light, p=m₀c. This extension is based on special relativity and uses SR equation for mass. One example of this: To add some relativistic mass, some kinetic energy is added. This is mathematically equivalent to adding some normal space momentum orthogonal to a particle's rest momentum vector.