symmetric tensor

[AntonioLao]

Einstein’s symmetric metric tensor (g) of general relativity is a 4 by 4 matrix with 16 real elements. In the special case where the trace (sum of diagonal elements) is 2, its sum of squares of elements describes a general invariance for a linear Lorentz transformation. This is simply the spacetime interval ds known as the proper time for all inertial systems that are relatively motionless or uniformly moving with respect to each other. For non-inertial systems (e.g. accelerated systems) the metric tensor must contains at the least 1 nonzero off-diagonal element but for linear symmetry, the trace vanishes while for nonlinear symmetry the trace must remains nonzero. Both conditions of nonzero elements and nonlinearity can be satisfied by using singular symmetric Hadamard matrices.

The key advantage of using the latter is their increasing eigenvalues of their power factors. It is noted that g=I, where I is the identity matrix. g=g, g=I, g=g, g=g, and g=I. Clearly, these indicate that the nonlinear odd power transformations of g is an invariance but the even power transformations reduce them back to the identity matrix. All these describe a static, stationary, and no growth universe. On the other hand, the power factors of a Hadamard matrix, H are H=4H, H=16H, H=64H, H=256H, H=4096H, and H=16384H. All these accelerated exponential growths imply the usefulness of Hadamard matrices for describing the accelerated expansion of spacetime and also simultaneously satisfy the missing mass principle using the general invariance of Hadamard matrices representing a no background spacetime quantum.

[mkirkpatrick]

I just knew that HMs were in there somewhere,they are surely the building block
that will support fusion.




regards michael.

[AntonioLao]

I just knew that HMs were in there somewhere

Without HM there would be no quanta of spacetime and no squares of energy. Yesterday, I was trying to use HM to prove Riemann Hypothesis for the distribution of prime numbers along the positive real whole numbers line.

[mkirkpatrick]

Without HM there would be no quanta of spacetime and no squares of energy. Yesterday, I was trying to use HM to prove Riemann Hypothesis for the distribution of prime numbers along the positive real whole numbers line.

And did you?It seems that without HM nothing can occur?




regards michael.

[AntonioLao]

without HM nothing can occur

In binary number system 11, 111, 11111, and 1111111 are primes. By inductive reasoning the largest prime is an infinite binary number of 1111111111111111...

[Profpat]

Good thought Antonio, is it possible for a prime number to reach infinity?

[AntonioLao]

I can't prove it but infinity itself could be the largest prime 111111111... in binary numbers notation.

[Profpat]

Is there a " LARGEST " in infinity, since infinity never ends?

[AntonioLao]

infinity is the largest but i can't prove it.

[Profpat]

If you could Antonio, my guess would be, there would be a nice prize for you in Sweden.