There are literally scores of different interpretations of quantum mechanics.

Suppose I came up with a new one, never seen before. How would I develop it? How would I publish it?
Let me know if you’ve seen this before.

A not-so-well-known paradox associated with infinity is this:

“In infinity odd or even? ∞ = ∞ + 1 so if infinity is even then it is odd and if it is odd then it is even.”

I know one, and only one, sensible way out of that paradox, and that way relies on a set of infinite numbers called Robinson’s hyperreals. Infinity in Robinson’s hyperreals is written ω, and ω ≠ ω + 1. So, how does ω escape the paradox? It escapes the paradox as follows.

ω exists as a superposition of two states (odd, even). You are free to choose whether ω is odd or even but once chosen that choice remains fixed for the remainder of the calculation. So if you choose ω to be even then ω + 1 is odd and ω + 2 is even. If you choose ω to be odd then ω + 1 is even and ω + 2 is odd.

¿Do you see the analogy with quantum mechanics, a property exists in a superposition of states until observed, and once observed its value is frozen.

The analogy is more than just a renaming. Infinite numbers play a fundamental role in the action of renormalisation in quantum mechanics.

mollwollfumble said:

There are literally scores of different interpretations of quantum mechanics.

Suppose I came up with a new one, never seen before. How would I develop it? How would I publish it?
Let me know if you’ve seen this before.

A not-so-well-known paradox associated with infinity is this:

“In infinity odd or even? ∞ = ∞ + 1 so if infinity is even then it is odd and if it is odd then it is even.”

I know one, and only one, sensible way out of that paradox, and that way relies on a set of infinite numbers called Robinson’s hyperreals. Infinity in Robinson’s hyperreals is written ω, and ω ≠ ω + 1. So, how does ω escape the paradox? It escapes the paradox as follows.

ω exists as a superposition of two states (odd, even). You are free to choose whether ω is odd or even but once chosen that choice remains fixed for the remainder of the calculation. So if you choose ω to be even then ω + 1 is odd and ω + 2 is even. If you choose ω to be odd then ω + 1 is even and ω + 2 is odd.

¿Do you see the analogy with quantum mechanics, a property exists in a superposition of states until observed, and once observed its value is frozen.

The analogy is more than just a renaming. Infinite numbers play a fundamental role in the action of renormalisation in quantum mechanics.

Surely the answer to the question:
“is infinity odd or even”
is no.

The Rev Dodgson said:

mollwollfumble said:

There are literally scores of different interpretations of quantum mechanics.

Suppose I came up with a new one, never seen before. How would I develop it? How would I publish it?
Let me know if you’ve seen this before.

A not-so-well-known paradox associated with infinity is this:

“In infinity odd or even? ∞ = ∞ + 1 so if infinity is even then it is odd and if it is odd then it is even.”

I know one, and only one, sensible way out of that paradox, and that way relies on a set of infinite numbers called Robinson’s hyperreals. Infinity in Robinson’s hyperreals is written ω, and ω ≠ ω + 1. So, how does ω escape the paradox? It escapes the paradox as follows.

ω exists as a superposition of two states (odd, even). You are free to choose whether ω is odd or even but once chosen that choice remains fixed for the remainder of the calculation. So if you choose ω to be even then ω + 1 is odd and ω + 2 is even. If you choose ω to be odd then ω + 1 is even and ω + 2 is odd.

¿Do you see the analogy with quantum mechanics, a property exists in a superposition of states until observed, and once observed its value is frozen.

The analogy is more than just a renaming. Infinite numbers play a fundamental role in the action of renormalisation in quantum mechanics.

Surely the answer to the question:
“is infinity odd or even”
is no.

Makes sense.

And while we are talking quantum, why is “observation” still treated as being something special, rather than just an interaction where we know the outcome?

The Rev Dodgson said:

mollwollfumble said:

There are literally scores of different interpretations of quantum mechanics.

Suppose I came up with a new one, never seen before. How would I develop it? How would I publish it?
Let me know if you’ve seen this before.

A not-so-well-known paradox associated with infinity is this:

“In infinity odd or even? ∞ = ∞ + 1 so if infinity is even then it is odd and if it is odd then it is even.”

I know one, and only one, sensible way out of that paradox, and that way relies on a set of infinite numbers called Robinson’s hyperreals. Infinity in Robinson’s hyperreals is written ω, and ω ≠ ω + 1. So, how does ω escape the paradox? It escapes the paradox as follows.

ω exists as a superposition of two states (odd, even). You are free to choose whether ω is odd or even but once chosen that choice remains fixed for the remainder of the calculation. So if you choose ω to be even then ω + 1 is odd and ω + 2 is even. If you choose ω to be odd then ω + 1 is even and ω + 2 is odd.

¿Do you see the analogy with quantum mechanics, a property exists in a superposition of states until observed, and once observed its value is frozen.

The analogy is more than just a renaming. Infinite numbers play a fundamental role in the action of renormalisation in quantum mechanics.

Surely the answer to the question:
“is infinity odd or even”
is no.

Incorrect. Consider four valued logic.
A, B, neither, both.
Hyperreal numbers says both. And that makes sense in the context of quantum mechanics.

The Rev Dodgson said:

mollwollfumble said:

There are literally scores of different interpretations of quantum mechanics.

Suppose I came up with a new one, never seen before. How would I develop it? How would I publish it?
Let me know if you’ve seen this before.

A not-so-well-known paradox associated with infinity is this:

“In infinity odd or even? ∞ = ∞ + 1 so if infinity is even then it is odd and if it is odd then it is even.”

I know one, and only one, sensible way out of that paradox, and that way relies on a set of infinite numbers called Robinson’s hyperreals. Infinity in Robinson’s hyperreals is written ω, and ω ≠ ω + 1. So, how does ω escape the paradox? It escapes the paradox as follows.

ω exists as a superposition of two states (odd, even). You are free to choose whether ω is odd or even but once chosen that choice remains fixed for the remainder of the calculation. So if you choose ω to be even then ω + 1 is odd and ω + 2 is even. If you choose ω to be odd then ω + 1 is even and ω + 2 is odd.

¿Do you see the analogy with quantum mechanics, a property exists in a superposition of states until observed, and once observed its value is frozen.

The analogy is more than just a renaming. Infinite numbers play a fundamental role in the action of renormalisation in quantum mechanics.

Surely the answer to the question:
“is infinity odd or even”
is no.

Oh, I should have said, the paradox is more subtle than that. A “no” answer is what leads to an impossible outcome.

> And while we are talking quantum, why is “observation” still treated as being something special, rather than just an interaction where we know the outcome?

Tell me when you know the outcome of an observation before making the observation?

In a deterministic non-chaotic environment perhaps. Not even in GR when it comes to the crunch, because the constitutive equations are purely based on observation.

mollwollfumble said:

The Rev Dodgson said:

mollwollfumble said:

There are literally scores of different interpretations of quantum mechanics.

Suppose I came up with a new one, never seen before. How would I develop it? How would I publish it?
Let me know if you’ve seen this before.

A not-so-well-known paradox associated with infinity is this:

“In infinity odd or even? ∞ = ∞ + 1 so if infinity is even then it is odd and if it is odd then it is even.”

I know one, and only one, sensible way out of that paradox, and that way relies on a set of infinite numbers called Robinson’s hyperreals. Infinity in Robinson’s hyperreals is written ω, and ω ≠ ω + 1. So, how does ω escape the paradox? It escapes the paradox as follows.

ω exists as a superposition of two states (odd, even). You are free to choose whether ω is odd or even but once chosen that choice remains fixed for the remainder of the calculation. So if you choose ω to be even then ω + 1 is odd and ω + 2 is even. If you choose ω to be odd then ω + 1 is even and ω + 2 is odd.

¿Do you see the analogy with quantum mechanics, a property exists in a superposition of states until observed, and once observed its value is frozen.

The analogy is more than just a renaming. Infinite numbers play a fundamental role in the action of renormalisation in quantum mechanics.

Surely the answer to the question:
“is infinity odd or even”
is no.

Incorrect. Consider four valued logic.
A, B, neither, both.
Hyperreal numbers says both. And that makes sense in the context of quantum mechanics.

I don’t know what the benefits of hyperreal numbers might be, but I’m pretty sure they have nothing to do with quantum mechanics.

mollwollfumble said:

The Rev Dodgson said:

mollwollfumble said:

There are literally scores of different interpretations of quantum mechanics.

Suppose I came up with a new one, never seen before. How would I develop it? How would I publish it?
Let me know if you’ve seen this before.

A not-so-well-known paradox associated with infinity is this:

“In infinity odd or even? ∞ = ∞ + 1 so if infinity is even then it is odd and if it is odd then it is even.”

I know one, and only one, sensible way out of that paradox, and that way relies on a set of infinite numbers called Robinson’s hyperreals. Infinity in Robinson’s hyperreals is written ω, and ω ≠ ω + 1. So, how does ω escape the paradox? It escapes the paradox as follows.

ω exists as a superposition of two states (odd, even). You are free to choose whether ω is odd or even but once chosen that choice remains fixed for the remainder of the calculation. So if you choose ω to be even then ω + 1 is odd and ω + 2 is even. If you choose ω to be odd then ω + 1 is even and ω + 2 is odd.

¿Do you see the analogy with quantum mechanics, a property exists in a superposition of states until observed, and once observed its value is frozen.

The analogy is more than just a renaming. Infinite numbers play a fundamental role in the action of renormalisation in quantum mechanics.

Surely the answer to the question:
“is infinity odd or even”
is no.

Oh, I should have said, the paradox is more subtle than that. A “no” answer is what leads to an impossible outcome.

What is the impossible outcome of infinity being neither odd nor even?

mollwollfumble said:

> And while we are talking quantum, why is “observation” still treated as being something special, rather than just an interaction where we know the outcome?

Tell me when you know the outcome of an observation before making the observation?

In a deterministic non-chaotic environment perhaps. Not even in GR when it comes to the crunch, because the constitutive equations are purely based on observation.

I didn’t say we did know the outcome before the observation.

> What is the impossible outcome of infinity being neither odd nor even?

The paradox is set up to have a physical outcome. Think of it like schroedinger’s cat. If infinity is even then the cat is alive. If infinity is odd then the cat is dead.

If neither odd nor even then the cat is neither alive nor dead, which isn’t possible.

And no, a zombie cat would be both alive and dead, like schroedinger’s.

The Rev Dodgson said:

mollwollfumble said:

The Rev Dodgson said:

Surely the answer to the question:
“is infinity odd or even”
is no.

Incorrect. Consider four valued logic.
A, B, neither, both.
Hyperreal numbers says both. And that makes sense in the context of quantum mechanics.

I don’t know what the benefits of hyperreal numbers might be, but I’m pretty sure they have nothing to do with quantum mechanics.

Well you do agree that infinity has a lot to do with quantum mechanics. Feinman integrals tell us that an electron can travel out to infinity and back between sender and receiver. And quantum renormalisation wouldn’t work at all without infinity.

Hyperreal numbers are just the most rational way of handling infinity. The may be, probably are, identical to Hahn series, to Conway’s surreal numbers, to the Veronese continuum, and to du Bois-Reymond’s infinitary calculus. It’s just that the mathematics of hyperreal numbers has been followed further than that of the alternative descriptions.

Infinitesimals, the flipside of infinities, play a large role in calculus. And where would we be without calculus?

mollwollfumble said:

> What is the impossible outcome of infinity being neither odd nor even?

The paradox is set up to have a physical outcome. Think of it like schroedinger’s cat. If infinity is even then the cat is alive. If infinity is odd then the cat is dead.

If neither odd nor even then the cat is neither alive nor dead, which isn’t possible.

And no, a zombie cat would be both alive and dead, like schroedinger’s.

That doesn’t seem to answer the question.

If infinity is neither odd nor even, what is the impossible outcome of that?

As for Schroedinger’s cat, it is always either alive or dead, we just don’t know which until we look at it.

mollwollfumble said:

Well you do agree that infinity has a lot to do with quantum mechanics. Feinman integrals tell us that an electron can travel out to infinity and back between sender and receiver. And quantum renormalisation wouldn’t work at all without infinity.

Not really. Just a bit of mathematical trickery to get the model to work reasonably well.