Recent content by pnaj

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    Quantum Entanglement: Does Normalisation Matter?

    Hi xepma, We are assuming that |A\rangle is normalized. P.
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    Quantum Entanglement: Does Normalisation Matter?

    Hi once again, Yes - just noticed that - now I see why you said 'minor' mistake now ... it should just have read ...P(A, m) = |\langle m|A'\rangle|^2 = a_m^* a_m. But I still am having trouble following the logic in Prof. Susskind's lecture. So, we have: P(A, m) = a_m^* a_m. P(B, m) = b_m^*...
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    Quantum Entanglement: Does Normalisation Matter?

    Hi Fredrik Ah - maybe this is where the confusion lies. To calculate the probabilities I took the average value of the projection operator for m, which is a definition given in the course ... P(A, m) = \big(\sum \langle k|a_k^* \big) |m\rangle \langle m| \big(\sum a_n |n \rangle \big) =...
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    Quantum Entanglement: Does Normalisation Matter?

    Hi Fredrik, Thanks for answering - I think I understand. But shouldn't the superposition of |A> and |B> be normalised in the first place (before we apply the time evolution operator). P.
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    Quantum Entanglement: Does Normalisation Matter?

    I've been following the lectures given by Leonard Susskind on Quantum Entanglement. In Lecture 6, he describes a simplified version of the two-slit experiment so that we can use finite dimensional spaces to describe the system (which is all we've learned so far). He also uses what he calls...
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    ElementaryFunctions/Exp/06/GraphingOnTheComplexPlane

    Muzza, that is a really nice link. Thanks, Paul.
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    Why are there more irrational numbers than rational numbers?

    Ok, Matt, See you round ... and NateTG. P.
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    Why are there more irrational numbers than rational numbers?

    NateTG, Well I didn't want to open it all up again. But fair enough. The 'Jeez' post was actually directed at your previous post. I had already asked Matt to explain his comments and he hadn't responded yet. You interpreted it as if I was further questioning Matt's comments. On...
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    Why are there more irrational numbers than rational numbers?

    NateTg, Well all I can really say to that is: fair comment. Paul. P.S. NateTg ... if you really want me to list the misquotes, I will, but I'd rather not.
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    Why are there more irrational numbers than rational numbers?

    Matt, Thanks for your last post. I accept everything you say. As I said before, you've taught me a really good lesson in how NOT to answer questions. Hopefully, I won't be making the same mistake again. Paul.
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    Why are there more irrational numbers than rational numbers?

    Matt, I have acknowledged the mistakes I have made. I just will not acknowledge mistakes that have been made on my behalf. So far, according to you, I've been 'wrong', 'badly wrong' and then 'oh, perhaps not wrong'. Not once have you acknowledged that YOU misunderstood my first statement...
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    Why are there more irrational numbers than rational numbers?

    Hi Matt, You're right there! But I've shown quite clearly that both you and NateTG were wrong to insist that a 1-1 map is not sufficient to make a listing of the rationals. He has misquoted me on a number of occasions (and you have too, once). Now he assigns implications to me that I...
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    Why are there more irrational numbers than rational numbers?

    It wasn't my implication, whether or not that's how it's being read.
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    Why are there more irrational numbers than rational numbers?

    NateTG, I didn't see your last post until after my last one. Thanks for acknowledging the 'misread' bit. I appreciate it. But I have to come back because I'm afraid that you have 'put words in my mouth' again. You said ... The trouble is, I most certainly did NOT imply equality of...
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    Why are there more irrational numbers than rational numbers?

    Well, I've certainly learned a valuable lesson here.
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