"The true metaphysics of the square root negative 1 remains elusive." - C.F. Gauss

  • Wavefunctions and Probability Amplitudes:
    In quantum mechanics, wavefunctions (denoted by ψ) are complex-valued functions that describe the state of a quantum system. The square of the magnitude of the wavefunction ( |ψ|² ) gives the probability density of finding the system in a particular location or state. Using complex numbers allows for the inclusion of phase information, which is crucial for describing interference phenomena in quantum systems.

  • Linear Algebra and Superposition:
    Quantum systems are linear, meaning that any solution to the Schrödinger equation can be multiplied by a complex number, and any two solutions can be added together, and the result is still a solution. This allows for the concept of superposition, where a quantum system can exist in a combination of multiple states simultaneously.

  • Spin and Half-Integer Spin Particles:
    The spin of particles, a fundamental property in quantum mechanics, is often described using complex numbers. Half-integer spin particles (like electrons) require complex numbers for their rotation and other transformations.

  • Mathematical Convenience and Generalization:
    Complex numbers provide a more compact and convenient mathematical framework for describing quantum phenomena, including the evolution of quantum states over time. They also allow for the generalization of concepts from classical physics to the quantum realm.

  • Experiments Reveal Necessity:
    Recent experiments have shown that a quantum theory based on real numbers alone cannot fully reproduce experimental results, further solidifying the need for complex numbers in quantum mechanics.
 
IBDaMann said:
Exactly. Can you imagine a casino hiring a mathematician to compute odds and then complaining that imaginary numbers weren't used?
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Nope. Doesn't even take much of a mathematician to compute odds.
Although I will say that casinos attract two kinds of people: suckers, and mathematicians.
 
AProudLefty said:
  • Wavefunctions and Probability Amplitudes:
    In quantum mechanics, wavefunctions (denoted by ψ) are complex-valued functions that describe the state of a quantum system. The square of the magnitude of the wavefunction ( |ψ|² ) gives the probability density of finding the system in a particular location or state. Using complex numbers allows for the inclusion of phase information, which is crucial for describing interference phenomena in quantum systems.

  • Linear Algebra and Superposition:
    Quantum systems are linear, meaning that any solution to the Schrödinger equation can be multiplied by a complex number, and any two solutions can be added together, and the result is still a solution. This allows for the concept of superposition, where a quantum system can exist in a combination of multiple states simultaneously.

  • Spin and Half-Integer Spin Particles:
    The spin of particles, a fundamental property in quantum mechanics, is often described using complex numbers. Half-integer spin particles (like electrons) require complex numbers for their rotation and other transformations.

  • Mathematical Convenience and Generalization:
    Complex numbers provide a more compact and convenient mathematical framework for describing quantum phenomena, including the evolution of quantum states over time. They also allow for the generalization of concepts from classical physics to the quantum realm.

  • Experiments Reveal Necessity:
    Recent experiments have shown that a quantum theory based on real numbers alone cannot fully reproduce experimental results, further solidifying the need for complex numbers in quantum mechanics.
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Mindlessly cutting and pasting again random shit from somewhere? You don't even have any idea what you are posting!
 
Into the Night said:
Defense of what??
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Self-defense, as in defensiveness.

Into the Night said:
He has no point to defend.
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Exactly, but he has to appear as though he is "too smart for you, and too important to bother with you."

Into the Night said:
I've never seen him make one!
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Exactly. He just issues curt cryptic quips (did you notice my use of alliteration?) as a facade of participating in a value-added manner. Please recall his claims of having a degree in math as well as in science and in whatever else he has initiated discussions.

Into the Night said:
You must mean defense of his ego somehow. Well, his random posts certainly don't do that!
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Yep, that's what I mean. His greatest fear is the "Cypress Bane", i.e. that people will recognize someone else as the authority on some subject.
 
Into the Night said:
Mindlessly cutting and pasting again random shit from somewhere? You don't even have any idea what you are posting!
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Notice that he is a Cypress-lemming, presuming that everything Grok/Copilot/ChatGPT/Google/Quora spews is absolute truth, because it came from the internet. Notice that he is happy to cut-n-paste all of the intermixed errors that he doesn't even know he is grabbing as well. He believes that everything on the internet is true, and that his cutting-n-pasting will reflect vast knowledge on his part, and will thus command respect. He doesn't realize that the errors he posts guarantee that he is viewed as not knowing anything about what he is talking. Silly.
 
IBDaMann said:
Self-defense, as in defensiveness.


Exactly, but he has to appear as though he is "too smart for you, and too important to bother with you."


Exactly. He just issues curt cryptic quips (did you notice my use of alliteration?) as a facade of participating in a value-added manner. Please recall his claims of having a degree in math as well as in science and in whatever else he has initiated discussions.


Yep, that's what I mean. His greatest fear is the "Cypress Bane", i.e. that people will recognize someone else as the authority on some subject.
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It is clear you do not have any degree. Your misunderstanding of English proves that.
 
AProudLefty said:
It is clear you do not have any degree. Your misunderstanding of English proves that.
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I'm happy to acknowledge that I am an eight-year-old in the 3rd grade, that I have absolutely no credentials and that I can only point to math, science, logic and economics.

Absolutely happy to do it.

How are you bested by a 3rd-grader ... time and time again?
 
IBDaMann said:
Notice that he is a Cypress-lemming, presuming that everything Grok/Copilot/ChatGPT/Google/Quora spews is absolute truth, because it came from the internet. Notice that he is happy to cut-n-paste all of the intermixed errors that he doesn't even know he is grabbing as well. He believes that everything on the internet is true, and that his cutting-n-pasting will reflect vast knowledge on his part, and will thus command respect. He doesn't realize that the errors he posts guarantee that he is viewed as not knowing anything about what he is talking. Silly.
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I haven't posted anything that is beyond what somebody who took math in 11th grade couldn't intuitively grasp.

The fact you believe this knowledge could only come from sophisticated AI software programs is a comment on your level of education.
 
IBDaMann said:
I'm happy to acknowledge that I am an eight-year-old in the 3rd grade, that I have absolutely no credentials and that I can only point to math, science, logic and economics.

Absolutely happy to do it.

How are you bested by a 3rd-grader ... time and time again?
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You have demonstrated your lack of knowledge in mathematics and English.
 
Cypress said:
I haven't posted anything that is beyond what somebody who took math in 11th grade couldn't intuitively grasp.
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You post errors that any 11th-grader would avoid making. You insist that math errors are perfectly fine because you read it on the internet.
 
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