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Cuchulainn
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### Re: negative transition probability

Negative probability means that stochastic matrix and Markov chain theory breaks down. Not to mention the current underlying mathematics..
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Jean Piaget

ISayMoo
Posts: 2292
Joined: September 30th, 2015, 8:30 pm

### Re: negative transition probability

Wigner function is not a probability distribution, its values are not probabilities at all. Wigner function is just a different way of representing the wave function.

Cuchulainn
Posts: 61517
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### Re: negative transition probability

Wigner function is not a probability distribution, its values are not probabilities at all. Wigner function is just a different way of representing the wave function.
Did someone say that Wigner function was a negative probability?
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ISayMoo
Posts: 2292
Joined: September 30th, 2015, 8:30 pm

### Re: negative transition probability

Yes, Collector did: "why the negative probs in the Wigner quasi-prob-distribution?"

Cuchulainn
Posts: 61517
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### Re: negative transition probability

Yes, Collector did: "why the negative probs in the Wigner quasi-prob-distribution?"
Oh dear.
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Jean Piaget

Cuchulainn
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### Re: negative transition probability

REMARK [NEGATIVE PROBABILITIES]. A non-negative (linear) state can of course be Interpreted as a classical probability distribution on the set .

. Therefore, one could generally call the state parameter w(E) the ”probability” of the event E – accepting with this terminology ”negative probabilities” or ”probabilities exceeding 1” come into existence. The possibility of mathematical models for stochastic events on the basis of negative probabilities was already noted by Dirac [4] and Feynman [7].

This is the section where I stopped reading the article. I thinks if Feynman knew (or used) how integers (+, -) were constructed from the natural numbers (+) there might have been some hope, mathematically speaking.

Now it's "let's assume neg probs exist? Too much name dropping.
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Jean Piaget

Cuchulainn
Posts: 61517
Joined: July 16th, 2004, 7:38 am
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### Re: negative transition probability

Here is a discussion and critique (by John Baez?) from a mathematical perspective on negative probabilities. Worth a read
https://johncarlosbaez.wordpress.com/20 ... abilities/

Unsurprisingly, the clearest writing about negative probabilities that I’ve found is by Feynman:
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Every Time We Teach a Child Something, We Keep Him from Inventing It Himself
Jean Piaget

Cuchulainn
Posts: 61517
Joined: July 16th, 2004, 7:38 am
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### Re: negative transition probability

Qualitatively, we will encounter negative probabilities when σ is relatively small and the risk-free rate is relatively high.

FALSE (B*). The correct phrasing is

The binomial (CRR) method breaks down for convection-dominated problems. This leads to spurious (non-physical) solutions.  This is well-known in engineering.

//
You see meaningless negative numbers in this case. Major fault in logic and irresponsible to suddenly call them negative probabilities.

It is a culture-shock that people still believe in these things, like the tooth fairy.
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Jean Piaget

Collector
Posts: 4557
Joined: August 21st, 2001, 12:37 pm

### Re: negative transition probability

I submitted a paper recently where the reviewers got upset because I criticized the use of negative probabilities.

Why so positive to negative probabilities?

Cuchulainn
Posts: 61517
Joined: July 16th, 2004, 7:38 am
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### Re: negative transition probability

I submitted a paper recently where the reviewers got upset because I criticized the use of negative probabilities.

Why so positive to negative probabilities?
I just hope they apologised to you.
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Every Time We Teach a Child Something, We Keep Him from Inventing It Himself
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katastrofa
Posts: 8943
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: negative transition probability

A1: Do you remember the restaurant where we first met?
B: Yes, how could I forget! The one next to Piazza San Marco.
A2: It was actually in Rome.
B: Opss... you're name isn't Adam, is it?

A2 is a negative information from the point of view B. People use it for lying and deception or just being wrong

Collector
Posts: 4557
Joined: August 21st, 2001, 12:37 pm

### Re: negative transition probability

Are u describing the meeting of Rome-o and Juliet, or Adam and Eve? actually written by B!

Collector
Posts: 4557
Joined: August 21st, 2001, 12:37 pm

### Re: negative transition probability

"I just hope they apologised to you. "

Not yet, but you cannot have probabilities without time? so probably in the future?

katastrofa
Posts: 8943
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: negative transition probability

Are u describing the meeting of Rome-o and Juliet, or Adam and Eve? actually written by B!
Romuliet is a good example too: he thinks she's dead but she isn't, she thinks he isn't dead but he is, they are both dead. Negative information was what killed Romeo and Giulietta.

Collector
Posts: 4557
Joined: August 21st, 2001, 12:37 pm

### Re: negative transition probability

yes dead and alive, the immortal atoms, one of my favorites from Romeo and Juliet:

"Drawn with a team of little atomies
Athwart men's noses as they lie asleep"

"Who shut their coward gates on atomies"
Last edited by Collector on September 20th, 2018, 4:34 am, edited 1 time in total.

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