Witty Rejoinder said:

mollwollfumble said:

mollwollfumble said:

Thanks. I needed that.

We thought your breakthrough might have caused a stroke with your genius going to the grave unheralded.

Nearly. I’ve been wondering if it’s the first sign of madness.

The solution to QM is, “Bohr was right, and Heisenberg made at least three mistakes”.

OK, a bit of background. You know i’ve done some work on infinite numbers. Last week i happened to notice an analogy between how Robinson’s hyperreal numbers can exist with multiple values at the same time and how quantum mechanics states can exist with multiple values at the same time, and that both can “collapse” to a single value.

So i read through a book on different interpretations of quantum mechanics on the web, how they can be categorised into four main categories etc. By the end i’d come to the conclusion that an interpretation of QM based on hyperreal numbers, if it exists, would have to be identical to Bohr’s. Which, given that Bohr’s is the most popular interpretation of QM, came as something of a revelation.

Heisenberg is the other author of the Copenhagen interpretation. His three mistakes that i spotted were:

• The Heisenberg cut – a length scale dividing small quantum phenomena from large ckassical phenomena.
• The von Neuman projection – a mechanism for collapsing the wave function.
• The measurement in Heisenberg’s scheme starts the moment the particles are created but only becomes available later.

The hyperreal interpretation could potentially overcome two of the three objections that Einstein had to the Copenhagen interpretation. Some philosophical problems that have dogged the Copenhagen interpretation still remain, however. Particularly “what is an observer”.

No other interpretation that i’ve seen so far comes close to a match. Not the ensemble, transactional, many worlds or hidden variable interpretations for starters. Not the neo-Copenhagen interpretation, either.

Given that “anything good is 1% inspiration and 99% perspiration” i’ll never see this through to the end.

The timeline is interesting. Hyperreal numbers were initially invented by Hahn in 1907. Rutherford didn’t discover that atoms had a nucleus until 1911.

On the other hand, reading Bohr’s first hand description of his view of how quantum mechanics works http://www.informationphilosopher.com/solutions/scientists/bohr/quantum_postulate.html

is … difficult to understand.

That’s not the way to proceed. Perhaps I can find the complete equations of quantum mechanics in pre-Dirac notation somewhere.

> Heisenberg is the other author of the Copenhagen interpretation. His three mistakes that i spotted were:

• The Heisenberg cut – a length scale dividing small quantum phenomena from large classical phenomena.
• The von Neumann projection – a mechanism for collapsing the wave function.
• The measurement in Heisenberg’s scheme starts the moment the particles are created but only becomes available later.

Some of Heisenberg, rather than Bohr’s, philosophy has come down to us in common speech.

Not: “Collapse of the wave function”
But: “Selection from a probability distribution”

Of the Uncertainty Principle
Not: “You cannot measure something without disturbing it”
But: “A wave packet contains a mix of wavelengths. The smaller the wave packet (position), the more uncertain it’s wavelength”

Dang it, haven’t disproved it yet.

Hyperreals are based on infinite sequences.
So are Hilbert spaces, which are at the heart of QM.

In both cases operations on the sequence is term by term, and both are linear and commutative.

The only real difference so far is that Hilbert spaces require the sequences to be at least weakly convergent. Hyperreals also allows some divergent sequences.

I’m not qualified to assess these ideas.

Bubblecar said:

I’m not qualified to assess these ideas.

That’s the problem. It looks like I have a heck of a lot of hard work to do even before anyone qualified to assess these ideas would bother to look at it.

I’ve failed to prove myself wrong three times already.

If everything good is 99% perspiration, then i’ve got a heck of a lot of perspiring still to do.

Anyone know the best quantum physics textbook written between 1928 and 1938? Between when Bohr completed the mathematics and Dirac changed all the notation.

Um, perhaps the key lies in making a vector space that contains Hilbert space.

Ie. Allowing an L2 norm that is infinite as well as “weakly converging” to a finite number.

mollwollfumble said:

Um, perhaps the key lies in making a vector space that contains Hilbert space.

Ie. Allowing an L2 norm that is infinite as well as “weakly converging” to a finite number.

Have you tried applying a Reiman Lagrangian?

Witty Rejoinder said:

mollwollfumble said:

Um, perhaps the key lies in making a vector space that contains Hilbert space.

Ie. Allowing an L2 norm that is infinite as well as “weakly converging” to a finite number.

Have you tried applying a Reiman Lagrangian?

No, would that help?

Dang it. Not one of Robinson’s original books/papers on non-standard analysis and hyperreal numbers is on the web.

I need to find the one about how to factorise infinite numbers.

mollwollfumble said:

Dang it. Not one of Robinson’s original books/papers on non-standard analysis and hyperreal numbers is on the web.

I need to find the one about how to factorise infinite numbers.

Went looking for it today in uni library. Didn’t find it.

mollwollfumble said:

mollwollfumble said:

Dang it. Not one of Robinson’s original books/papers on non-standard analysis and hyperreal numbers is on the web.

I need to find the one about how to factorise infinite numbers.

Went looking for it today in uni library. Didn’t find it.

How about defining your infinity as the product of an infinite increasing sequence of numbers starting from 1.

Then every number would be a factor of infinity.

The Rev Dodgson said:

mollwollfumble said:

mollwollfumble said:

Dang it. Not one of Robinson’s original books/papers on non-standard analysis and hyperreal numbers is on the web.

I need to find the one about how to factorise infinite numbers.

Went looking for it today in uni library. Didn’t find it.

How about defining your infinity as the product of an infinite increasing sequence of numbers starting from 1.

Then every number would be a factor of infinity.

Yes. That is done. But not for every infinite number.

I found one book today that said that many infinite numbers are prime. But it didn’t go into detail, unfortunately, just stated it.

mollwollfumble said:

The Rev Dodgson said:

mollwollfumble said:

Went looking for it today in uni library. Didn’t find it.

How about defining your infinity as the product of an infinite increasing sequence of numbers starting from 1.

Then every number would be a factor of infinity.

Yes. That is done. But not for every infinite number.

I found one book today that said that many infinite numbers are prime. But it didn’t go into detail, unfortunately, just stated it.

Presumably there are infinitely many prime infinite numbers.

But don’t take any notice of me, I really don’t get this approach.

i tried to pretend there was a largest prime number

I’ve disproved my new hypothesis. Bye.

mollwollfumble said:

I’ve disproved my new hypothesis. Bye.

back to the drawing board.