Yanniru,

This post makes it very clear that you have missed a central issue that all unknowable data must always be included.

***** Richard:
But here is my latest problem with your work. Your derivation seems to fail in the limit of high time resolution. We can always think of the data stream as happening at such high time resolution that in any one time interval, only one data point is obtained.
*****

Remember, all information about the Universe must come from this data stream and the entire collection of data must be included in the analysis. Sure, we can conceive of the universe as a single isolated entity but that isn't a very interesting picture!

***** Richard:
This is actually how quantum mechanical detection theory of light works.
*****

Now, just how the hell can "detection" take place with only one entity in existence? When you bring that time scale down to a time resolution where only one data point exists, all that equipment must be "unknowable". The continuity through time of all that junk is clearly an assumption! If you could simultaneously prove that both your photon and your detection equipment existed, you would be working with more than one data point!

***** Richard:
So in this limiting case Schroedinger's equation is not derived. Yet this limiting case is completely general. Your results could be obtained if you require a summation over a sufficiently long enough time to get high statistical probabilities.
*****

In the limiting picture where the Universe contains but one point, Schrodinger's equation is quite meaningless!

***** Richard:
Perhaps you can say that the entire psi pattern can come from the one data point plus unknowable data. But then I have to ask- why do you need even one data point.
*****

I don't! Not to derive the necessity of physics! But I have specifically left the issue open as it appears to me that it is possible that reality has some "knowable" characteristics!

***** Richard:
Your derivation would then work if all you had was unknowable data. The result is the interesting concept that the fundamental equation does not require any data. It is true even if we sense nothing at all, or know nothing at all. Maybe so.???
*****

Well, thank you for that! Yes, I claim fundamental physics is "true" as it is nothing more than a way of organizing data!
And I am sorry if I upset you with my comment to Paul.

Have fun -- Dick