I am a very forgiving person. We are all flawed and need forgiveness many times throughout our lives. If I wasn't forgiving, how could I expect forgiveness?
on DoctorDick ( and I pray that Dr. Stafford will forgive me for saying this) is that 'when he agrees with your criticism, he does not respond'.
This is true to a certain extent; however, if I feel it is an important point I will usually tell the person I agree. And sometimes I do not respond even when I disagree because I have lost my patience. Particularly with Harv!
As an example, he has never responded to my claim that his first and all subsequent use of the delta function is his derivation equals zero because his summation excludes the points where it is nonzero.
He did say that the integral over the summation may be nonzero because different values of xi may be equal. But he expressly made every value of xi unique using unknowable data earlier in his exposition.
I thought I had responded to that but perhaps I did not make myself clear. Or maybe you are right and I didn't respond. At any rate, a response is required.
I think you missed the point of my proof. What I proved was that there always existed a set of "unknowable" data which could constrain the "knowable" data to any specific set desired, no matter how arbitrary the set was.
In my proof, I took the most extreme case. Remember, psi is to be a function which is to generate the probability of the specific distribution of xi. The absolute most extreme case is the case where "the rule of the universe" is to constrain all the xi (all the knowable data) to a specific set of discrete numbers for each and every observation (total absence of uncertainty of any kind - you have to understand that we are talking about constraining psi here, not about what actual measurements we get for the results of our experiments).
Even in this case, which is clearly beyond reason, the relation F=0 is capable of enforcing the rule if F is written as a sum over delta functions of separation: i.e., I can simply state the rule to be F=0 and essentially transform the correct (real???) rule (absolutely any rule you can conceive of) into being exactly equivalent to an appropriate selection of unknowable data.
"Can" and "will" are significantly different concepts. The point of the proof was to assure that absolutely any rule may be expressed by F=0 where F is a sum over Dirac functions. Now, if you look at equ(1.20) you will specifically see that (in my presentation) I work with F*psi. The only case where the circumstance discussed in the proof would arise is when psi yields exactly one set of discreet results, in which case psi is not continuous but is rather a descrete set of infinite spikes. If psi is a continuous function, clearly the probability of a specific discreet set goes to zero even if they are in the same place (xi=xj) thus the product F*psi will be zero even though the delta functions blow up! So there is no constraint to disallow xi=xj. The circumstance is very analogous to what happens when you integrate over f(x)dx .
Secondly, read carefully the paragraph following equ(2.4). As I point out in that paragraph, no constraint has been placed on the data that they cannot have the same value. Again, my earlier proof merely showed that even if the results of our calculation of the probability had to yield a discreet collection of numbers the F I have designed would suffice. In essence no constraint on overlap of the data whatsoever has been enforced. Since I introduced the tau axis in order to keep the knowable data separate, I have to come up with some additional scheme to keep the knowable data separate (otherwise the introduction of tau fails its purpose). That is the reason I have to make psi of the knowable data asymmetric.
However, I also think that he is on to something even though the math is not rigorous,
I think my math is quite rigorous. When you find it not rigorous, I suspect you are misinterpreting something somewhere.
the results may be correct- something like an emergent solution. Some solutions are correct even though their derivation is incorrect. We just have not found the right way to derive it. Hall in the Journal of Physics (in an April 2002 issue) found a correct way to derive Schroedingers equation from Fishers sample probability theory (1925), which is roughly what Dick is doing- how do you predict the accuracy of statistics for a population when you have only small samples of that population.
Somehow I doubt he is doing what I am doing, otherwise he would also show Dirac's equation, Maxwell's equations, Special Relativity and General relativity to be inevitable outcome of the same relations because they follow in a very straight forward manner from my work.
So I find Dick's analysis and conclusions to be inspired but not rigorous.
I think you are getting very close to following what I am doing. Stick with me and maybe I can get you over the hump. Show me what you think is not rigorous and I will try to assist you.
I'm having fun; how about you --Dick