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

Cypress said:
Are imaginary numbers just a mathematical convenience or do they have a tangible reality?

Does quantum mechanics need imaginary numbers?

The square root of negative one doesn’t correspond to any physical quantity, but that doesn’t mean it has no place in the physical sciences. For example, putting an imaginary number in an exponent changes the behavior of the exponential from rapid growth or decay to a steady sinusoidal oscillation. The result is a useful description of the physics of waves.

In electromagnetism and most other fields of physics, imaginary numbers are merely a mathematical convenience. All the relevant phenomena can still be described using nothing but real numbers. Quantum mechanics is an exception: The observable quantities and probabilities are by necessity all real, but the underlying quantum states and governing equations involve imaginary numbers, and there’s no simple way to remove them. But are they just an artifact of the way the theory was written down, or do they really need to be there?

In their new theoretical work, Miguel Navascués of the Institute for Quantum Optics and Quantum Information in Vienna and colleagues shed some light on that question.1 They find that, subject to some postulates about how a quantum theory must be mathematically structured, no real-valued version of quantum theory can duplicate all the predictions of the familiar complex-valued formulation. Moreover, they designed an experimentally feasible test capable of ruling out real-valued quantum theories. In the time since their proposal was made public in January 2021, two groups carried out the experiment—and both found results in favor of standard complex-valued quantum theory.


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When we deal with antenna impedance, we get complex numbers like this: 5-j10 or 50 + j10, the J in this case is an imaginary number, and this is an example of mathematical convenience like you posted.
 
Daylight63 said:
LOL. Thank you for FINALLY confessing that all you do most of the time is quote other people in the hopes of making yourself look smarter.

That's a breakthrough for you.
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So you believe posters on JPP should post their own original experiments and theories on quantum physics? :laugh:

Perry, most of what we know we don’t know directly. We gain such knowledge through testimony, we read textbooks, listen to teachers and subject matter experts, we take classes, we read articles. None of us perform experiments or see the evidence and data directly for ourselves. It's hubris for you to believe JPP posters are going to be publishing their own original quantum mechanics theories.
 
Trumpet said:
When we deal with antenna impedance, we get complex numbers like this: 5-j10 or 50 + j10, the J in this case is an imaginary number, and this is an example of mathematical convenience like you posted.
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That's what I've heard, that for the most part complex numbers and i are a mathematical convenience, even a shortcut.
This article seems to be saying in the quantum world you literally have to use imaginary numbers, and you can't substitute real numbers in their place.
 
Cypress said:
That's what I've heard, that for the most part complex numbers and i are a mathematical convenience, even a shortcut.
This article seems to be saying in the quantum world you literally have to use imaginary numbers, and you can't substitute real numbers in their place.
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images

EVERYBODY! Cypress is holding forth on Quantum Mechanics! Let us all be amazed!​
 
Cypress said:
So you believe posters on JPP should post their own original experiments and theories on quantum physics? :laugh:
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No I think you should be honest with everyone and tell us why YOU posted about QM. We all know it's because you want to sound smarter than you actually are.

You don't know the first fucking thing about Quantum Mechanics. Now stop acting like you're something we can all tell you are not!

 
Trumpet said:
When we deal with antenna impedance, we get complex numbers like this: 5-j10 or 50 + j10, the J in this case is an imaginary number, and this is an example of mathematical convenience like you posted.
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Is it because impedance involves a wave carrier? I've heard that complex numbers are the easiest way to represent sinusoidal functions.
 
Daylight63 said:
You don't know the first fucking thing about Quantum Mechanics.
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Perry, the worst way to 'impress' girls, impress people at parties, or relatives at family reunions is to discuss math.

The real issue here is your festering resentment and imaginary grievances, chap!

Perry, there are only a few thousand people in North America who really understand quantum mechanics, and you are claiming that nobody else is allowed to read, discuss, or learn about it. :laugh:
 
Cypress said:
It's really funny how MAGA morons are always dissing the liberal arts and demanding everyone in college get STEM degrees, but then they cannot even cope with a thread about high school math and popular science journalism.
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Ok then. Splain to me how I can utilize the OP to a real life application.
Because I had no problem applying my STEM degree to a useful and profitable business.
 
Trumpet said:
When we deal with antenna impedance, we get complex numbers like this: 5-j10 or 50 + j10, the J in this case is an imaginary number, and this is an example of mathematical convenience like you posted.
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j is used in electrical and electronic engineering calculations as a substitute for i because the later is used as the symbol for current and that would confuse things if it were used.
 
Cypress said:
Perry, the worst way to 'impress' girls, impress people at parties, or relatives at family reunions is to discuss math.
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And it's also a great dodge to hide the fact that you really don't know the math we are talking about here. C'mon, man. You and I both know you know next to NOTHING about QM.

It's silly that you think you are going to fool anyone.

Cypress said:
The real issue here is your festering resentment and imaginary grievances, chap!
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Like your imaginary bete noirs on this forum? All you do is sit on here bitching with Doc about other posters when you aren't actively trying to "show off" like some stupid toddletr.



Cypress said:
and you are claiming that nobody else is allowed to read, discuss, or learn about it. :laugh:
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Why don't you GOOGLE it? LOLOLOLOLOLOLOLOLOL
 
Cypress said:
Are imaginary numbers just a mathematical convenience or do they have a tangible reality?

Does quantum mechanics need imaginary numbers?

The square root of negative one doesn’t correspond to any physical quantity, but that doesn’t mean it has no place in the physical sciences. For example, putting an imaginary number in an exponent changes the behavior of the exponential from rapid growth or decay to a steady sinusoidal oscillation. The result is a useful description of the physics of waves.

In electromagnetism and most other fields of physics, imaginary numbers are merely a mathematical convenience. All the relevant phenomena can still be described using nothing but real numbers. Quantum mechanics is an exception: The observable quantities and probabilities are by necessity all real, but the underlying quantum states and governing equations involve imaginary numbers, and there’s no simple way to remove them. But are they just an artifact of the way the theory was written down, or do they really need to be there?

In their new theoretical work, Miguel Navascués of the Institute for Quantum Optics and Quantum Information in Vienna and colleagues shed some light on that question.1 They find that, subject to some postulates about how a quantum theory must be mathematically structured, no real-valued version of quantum theory can duplicate all the predictions of the familiar complex-valued formulation. Moreover, they designed an experimentally feasible test capable of ruling out real-valued quantum theories. In the time since their proposal was made public in January 2021, two groups carried out the experiment—and both found results in favor of standard complex-valued quantum theory.


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Every Leap Goes into an Extra Dimension

From the very beginning, explanations of Postclassical phenomena required, but refused to consider, the existence of a fourth spatial dimension in order to conform to rationality. This imaginary number would be real in that underlying dimension.
 
Cypress said:
nobody else is allowed to read, discuss, or learn about it. :laugh:
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^^^^THis is rich coming from the guy who accuses EVERYONE and ANYONE who is smarter than him of "googling".

LOLOLOL.

Thanks, though, for confessing that all you do is frantically google these things so you can talk about them even though it's patently obvious you don't know the first fucking thing about ANY of this stuff.
 
Cypress said:
Yes, the fact you are always complaining about my threads means you cannot resist clicking on them and reading them.
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Go pop your ego balloon, Sybil.
Cypress said:
The topic here is high school math and a popular science article composed for interested laypersons. If the content doesn't interest you, or is beyond your capabilities, then don't pay attention to the thread.
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Nope. There is no topic. You are just posting random shit to post for the sake of posting.

Go pop you ego balloon.
 
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