Hi again bogz,
I've always seen E=mc^2 where m is one number.
Yes, that is because this is one of the SCALAR (non-vector/tensor) forms of Relativity. We are simply treating both mass and the speed of light as scalar numbers. However, in the full tensor form of Relativity, Einstein defines the
stress-energy tensor as a 4x4 tensor which takes the Newtonian (3x3) concept of stress and generalizes it to handle the concepts of stress, momentum, and energy all in one tensor.
Can you use I=ms^3 where m is one number also?
If my theory works-out, the answer will be yes, but just as in using a scalar form of a full tensor equation, you will lose accuracy of the full "field theory" effects explained by the tensor forms. But don't ask how my equation can be used in a scalar form yet!
I wish to complete the 3x3x3 tensor field equations first, and then the scalar forms will fall-out naturally once the tensor form is verified as correct.
Also, could you explain a little what the matrix for m would look like in E=mc^2 like you did with the topic of "stress" in the tensor thread?
OK, but I must first remind you that this is getting into my theory about how we need to take a different view of Mass and Matter so that we can "improve" Einstein's equations further. That being said, we can make a very direct analogy between the 3x3 stress tensor matrix and the manner in which I believe Matter needs to be treated as a 3x3 tensor, and Mass as a 3-dimensional vector.
If we consider that Mass is really a 3-D vector quantity just as Space is, then we would represent the Mass vector as M(x,y,z) with components Mx, My, and Mz. These components would correspond to the "orthogonal" elements of Mass that are associated with charge polarity (positive, neutral, negative).
Now, I have also defined Matter as different from Mass in my theory in that I define Matter as being the time-derivative of Mass. At the macroscopic level we typically call this the mass flow rate in fluid dynamics. However, it is my contention (and our investigations into subatomic particles have supported this view) that these particles of Mass are not static with respect to Time. They are always changing....or oscillating, if you will. And in my theory it is Matter, not Mass, that is the "m" term in Einstein's E = mc^2 equation. Now let's draw the analogy betweeen Matter as a tensor and the stress tensor:
For stress, we said its units align with pressure, in that we have Force per unit Area (F/A). Well, in the case of Matter we have Mass per unit Time (M/T). And you might remember that my theory also wishes to treat Time as a 3-D vector as well (T-past, T-present, T-future).
So, just like we had nine elements of the stress tensor matrix, and we designated each element of the matrix with two subscripts, we can do the same thing for Matter. So this would result in what I call:
_____The Matter Tensor Matrix______
{Matter(x-x)___Matter(x-y)___Matter(x-z)}
{Matter(y-x)___Matter(y-y)___Matter(y-z)}
{Matter(z-x)___Matter(z-y)___Matter(z-z)}
In this tensor matrix, the first subscript corresponds to the specific charge polarities of Mass associated with this Matter. The second subscript corresponds to the specific vector component of Time (past, present, future).
Now, if this tensor treatment of Matter "works out" as I move forward, this is going to mean something very speific with respect to the SpaceTime metric (c^2) portion of Einstein's equation. In order for the Matter tensor to multiply properly with "c^2", this means that "c^2" must at least be a 3-D vector, and it could quite possibly be a 3x3 tensor quantity just like Matter. How these two terms multiply together, and how their result (Energy) is measured with respect to dimensionality is dependent upon which indices of the Matter tensor (above) and the SpaceTime vector or tensor are covariant indices vs. contravariant indices. This is a more advanced topic in tensors that I have not dealt with yet in the "Vector & Tensor Fundamentals" thread.
RMT