Joy Christian wrote:gill1109 wrote:The even sub-algebra of the real Clifford algebra Cl(4, 0) is isomorphic to the real Clifford algebra Cl(0, 3), as you said yourself.

No, I never said that, either orally or in writing. That is your claim.

You said something that implies this immediately. From your RSOS paper:

Joy Christian wrote:In this higher dimensional space,

is then a unit vector,

(2.32)

and the corresponding algebraic representation space (2.31) is nothing but the eight-dimensional even sub-algebra of the

-dimensional Clifford algebra

.

You said that your 8-dimensional algebra is the even sub-algebra of

. Now please consult some standard textbooks or do the algebra yourself.

Alternatively, we can go directly to the nub of the matter. Fire up GAviewer and check that in

, (e1 e2 e3 e34)^2 = 1 (or do the algebra yourself). Note that e1e2e3e4 is an element of the even sub-algebra of

. Because (e1 e2 e3 e34)^2 - 1 = 0, it follows that (e1 e2 e3 e34 - 1)(e1 e2 e3 e34 + 1) = 0.

We have a pair of zero-divisors of the even sub-algebra of

: elements x = e1 e2 e3 e34 - 1, and y = e1 e2 e3 e34 = 1 such that xy = 0, but neither x nor y = 0.

If your algebra could be normed, it would mean that ||x|| ||y|| = 0, hence ||x|| = 0 or ||y|| = 0, hence x = 0 or y = 0, hence e1e2e3e4 = +/- 1.

Recently you also wrote

Joy Christian wrote:Quantum mechanics cannot predict individual event-by-event outcomes for any phenomena. A good example is the decay of a radioactive element. Quantum mechanics can only predict probabilities for such a phenomenon. It is a statistical theory. And, in my opinion, no theory, including classical mechanics, can predict individual event-by-event outcomes for complex phenomena such as the weather or an outcome of a coin toss.

That is also one standpoint which is fully consistent with Bell's theorem. As John Bell remarked, Niels Bohr would have found Bell's theorem uninteresting because he already knew that, it was exactly what he had been saying all the time.