Comments on: Hardy’s Paradox, or The Economist is Dismal at Science

By: Stephen

Stephen — Fri, 25 Nov 2011 20:30:12 +0000

Oh hm, I’m not sure. Possibly!

By: zaybu

zaybu — Tue, 22 Nov 2011 11:26:32 +0000

Could the probability of -1 be reinterpreted as particles/anti-particles? This is what Dirac did when he worked on his famous eponymous equation.

By: Chasethebear

Chasethebear — Sun, 16 Jan 2011 12:54:57 +0000

Thanks for confirming Stephen. None of us knows enough. If you happen to have a math question, I would be happy to apply myself to it. But I probably would be lacking in the math you are likely to need information about.

By: Stephen

Stephen — Thu, 13 Jan 2011 15:11:11 +0000

Your paraphrase sounds spot on. I’m glad my post helped!

By: Chasethebear

Chasethebear — Thu, 13 Jan 2011 14:35:04 +0000

Thanks Stephen, your exposition is far more understandable than any I have read. Please let me test my understanding by paraphrasing you:
QM theory holds that sometimes both fans end up with Pepsis. If we think back to how this can be, we can logically state the following proposition:
Either: A] Fans meet and fight Or: B] Fans don’t meet and fight
But if A] is true then neither fans gets any drink, hence they don’t end up with Pepsis.
If B] is true, both fans end up with Cokes, and again they don’t end up with Pepsis.
So logically the QM predicted outcome is impossible. But QM believers counter this by saying that we need not consider any proposition for which there is no observation. We did observe that both fans having Pepsis, but we can’t argue back from this to a period before the observation took place. (Or possibly they would counter by saying you can’t measure individual’s paths and their shared path at the same time.)
But, in any case, Lundeen and Steinberg have shown is some sort of statistical manner of getting around the QM taboos, a kind of low quality “squinting”, in which you must make many observations. This is a technical matter that I accept here, though of course I can’t understand it in detail.
Finally, in your last table, you consider all possible outcomes for both fans. The sum of all possibilities must be 1, but the sum of the first three possibilities is 2. The last probability must be -1, which it is. But conventional probabilities theory posits that no probability can be less than zero.
This appears to be another paradox, but evidently the rules of conventional probability do no hold when we deal with weak measurement.

Again, thanks for guiding me through some difficult terrain. I am not a physicist but a mathematician interested in consciousness. I was lead to Hardy’s Paradox in pursuit of some ideas of David Mermin that link consciousness to QM via the “Ithaca Convention”. Mermin seems to regard the human body as another scientific instrument but a very special one. Ultimately, the scientist must observe his scientific instruments with another scientific instrument, namely his own body. It is the poorly understood “weirdness” of this latter instrument that lead to the paradoxes of QM and of consciousness

By: Stephen

Stephen — Wed, 01 Apr 2009 22:11:09 +0000

That should be “blue”. I’ve fixed it.

By: Limax

Limax — Wed, 01 Apr 2009 21:57:06 +0000

I’m still trying to figure out the white hallway.

By: Jonathan Creekmore

Jonathan Creekmore — Tue, 31 Mar 2009 19:48:52 +0000

All of this is making me want to go back and tackle Road to Reality by Roger Penrose. I have taken one or two classes that kind of touched quantum mechanics, but I have always wanted to dig deeper into it.

By: Morgan

Morgan — Tue, 31 Mar 2009 16:48:09 +0000

Not weird, wyrd.