1st 5 minutes audio sucks, but from the moment Sean begins his talk the audio didn't break down, although I've been listening at a 3rd volume. Otherwise this talk is in the same vein that Sean spoke at the Santa Fe Institute about 2 years ago, both are exceptional in helping those of us understand the difficulties we seem to create for ourselves in mathematics. Thank you Sean, and to the host's, for sharing your time and work, Sean is one of the best communicators in science and this has been great. Peace Q&A was great and really nice to see so many young people involved in solving the many questions we still have unanswered.
What a lucid and engaging lecture. Sean does important work presenting the history of these concepts & theories as well as persistent questions (and answers), making all accessible to a general audience. Bravo!
I would love to know the answer to this as it seems important to me in understanding the schrodinger equation. I'm an engineer and we use the number i, all the time, it's a way to get a mathematical shortcut to a more complicated solution if we had only used real numbers. However I've heard it said so many that the number i, as used in the shrodinger equation, is inherent and not the kind of shortcut or convenience that I normally use and I was genuinely surprised when Sean said that it's use in the Shrodinger equation is similarly just a convenience which can be avoided.
Wave oscillations of a sort are often most easily modeled with complex numbers because complex number multiplication does rotation. You can always get rid of the need for complex numbers by using a lot more sin and cos and doubling your number of dimensions, but if complex numbers fit more naturally, why do that? That said, complex numbers are only one way to conveniently model oscillations. There are other mathematical structures you can use, but they end up being equivalent to using complex numbers without additional convenience. There are some times in physics where using complex numbers gets tedious, and then other mathematical structures become more convenient, like quaternions or rotors or spinors. It’s about finding the structure that fits the problem naturally and matches conventions so that people can understand it.
Could all of reality just be a probability, a degree of fluctuation, the event horizon between a probability and a certainty, a duality of nature like a wave function, this weird semi/permeable phenomena of space where space within space can be larger than the space it’s contained in, making almost every probability an exotic state of non local localities and non interactive interactions. Also mention to constructive and destructive interference or decoherence in the double slit experiments, after reading Carl Jung, do we really understand entropy in a world of order and chaos, perspective or flavor for one is counter intuitive for the other, let’s just say things change in this crazy world and the order operators or chaos operators were in superposition or oscillatory states respectively, then you have nihilism, I feel like I begin to understand why Sean is bridging the gap.
I don’t understand what you are suggesting here. In the talk, Dr Carroll talks about how the Copenhagen Interpretation is not a well-defined theory, because it never defines what it means by a “measurement”. Reading your comment, I feel similarly, like there are a bunch of things you are saying without any precision or definitions, so that I can’t figure out what you are suggesting.
@@davidandrewthomasIn the standard interpretation ( the modern version of Copenhagen), measurement occurs when decoherence , i.e entanglement with a device/ the environment occurs ( similarly as the " splitting of the worlds" is defined in MWI). It is known that the "Heisenberg cut" in the standard interpretation is arbitrary: it doesn't alter the predictions of the theory ( in MWI they say that the "splitting" is a coarse grained notion, not precisely defined...). The "collapse of the Wavefunction" in the standard interpretation is not to be taken literally ( as in GRW, for example): In that case the Schrödinger equation is a mathematical function that gives amplitudes/ probabilities ( the Copenhagen -related versions of QM are fundamentally probabilistic. Stochasticity is built in). The same with Superposition: it is not to be taken literally . It's a consequence of the linearity of QM.
@@davidandrewthomas Both the textbook and the Everettian QM are mathematically equivalent ( provided that Everettians will find some adequate non-circular derivation of the Born Rule, or at least they'll postulate it as an extra axiom). If Copenhagen is not well defined mathematically, the same holds for MWI. The basic difference is that MW has all this extra ontological baggage, without avoiding irreducible randomness...
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The audio issues are disappointing. Looking forward to accurate captions being added.
1st 5 minutes audio sucks, but from the moment Sean begins his talk the audio didn't break down, although I've been listening at a 3rd volume. Otherwise this talk is in the same vein that Sean spoke at the Santa Fe Institute about 2 years ago, both are exceptional in helping those of us understand the difficulties we seem to create for ourselves in mathematics. Thank you Sean, and to the host's, for sharing your time and work, Sean is one of the best communicators in science and this has been great. Peace
Q&A was great and really nice to see so many young people involved in solving the many questions we still have unanswered.
What a lucid and engaging lecture. Sean does important work presenting the history of these concepts & theories as well as persistent questions (and answers), making all accessible to a general audience. Bravo!
Excellent lecture! But there are constant YT streaming audio issues at the beginning of each one!
I would love to know the answer to this as it seems important to me in understanding the schrodinger equation. I'm an engineer and we use the number i, all the time, it's a way to get a mathematical shortcut to a more complicated solution if we had only used real numbers. However I've heard it said so many that the number i, as used in the shrodinger equation, is inherent and not the kind of shortcut or convenience that I normally use and I was genuinely surprised when Sean said that it's use in the Shrodinger equation is similarly just a convenience which can be avoided.
Wave oscillations of a sort are often most easily modeled with complex numbers because complex number multiplication does rotation. You can always get rid of the need for complex numbers by using a lot more sin and cos and doubling your number of dimensions, but if complex numbers fit more naturally, why do that?
That said, complex numbers are only one way to conveniently model oscillations. There are other mathematical structures you can use, but they end up being equivalent to using complex numbers without additional convenience.
There are some times in physics where using complex numbers gets tedious, and then other mathematical structures become more convenient, like quaternions or rotors or spinors. It’s about finding the structure that fits the problem naturally and matches conventions so that people can understand it.
8:14 " Reality is a superposition...etc": This is true only if "superposition of different branches" is taken literally.
If not...
Audio is Terrible
Could all of reality just be a probability, a degree of fluctuation, the event horizon between a probability and a certainty, a duality of nature like a wave function, this weird semi/permeable phenomena of space where space within space can be larger than the space it’s contained in, making almost every probability an exotic state of non local localities and non interactive interactions. Also mention to constructive and destructive interference or decoherence in the double slit experiments, after reading Carl Jung, do we really understand entropy in a world of order and chaos, perspective or flavor for one is counter intuitive for the other, let’s just say things change in this crazy world and the order operators or chaos operators were in superposition or oscillatory states respectively, then you have nihilism, I feel like I begin to understand why Sean is bridging the gap.
I don’t understand what you are suggesting here.
In the talk, Dr Carroll talks about how the Copenhagen Interpretation is not a well-defined theory, because it never defines what it means by a “measurement”. Reading your comment, I feel similarly, like there are a bunch of things you are saying without any precision or definitions, so that I can’t figure out what you are suggesting.
@@davidandrewthomasIn the standard interpretation ( the modern version of Copenhagen), measurement occurs when decoherence , i.e entanglement with a device/ the environment occurs ( similarly as the " splitting of the worlds" is defined in MWI).
It is known that the "Heisenberg cut" in the standard interpretation is arbitrary: it doesn't alter the predictions of the theory ( in MWI they say that the "splitting" is a coarse grained notion, not precisely defined...).
The "collapse of the Wavefunction" in the standard interpretation is not to be taken literally ( as in GRW, for example):
In that case the Schrödinger equation is a mathematical function that gives amplitudes/ probabilities ( the Copenhagen -related versions of QM are fundamentally probabilistic.
Stochasticity is built in).
The same with Superposition: it is not to be taken literally . It's a consequence of the linearity of QM.
@@davidandrewthomas Both the textbook and the Everettian QM are mathematically equivalent ( provided that Everettians will find some adequate non-circular derivation of the Born Rule, or at least they'll postulate it as an extra axiom).
If Copenhagen is not well defined mathematically, the same holds for MWI.
The basic difference is that MW has all this extra ontological baggage, without avoiding irreducible randomness...