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45,146 Views • 7 months ago • Click to toggle off description
Full video: • This "USELESS" Equation is The Mathematica... "How the theory of all matter comes from a useless equation"
This video explains why we have imaginary numbers in physics equations. They represent mathematics, not anything physical.
Views : 45,146
Genre: Science & Technology
License: Standard YouTube License
Uploaded At 7 months ago ^^
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RYD date created : 2025-04-16T22:35:49.00999Z
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77 Comments
Top Comments of this video!! :3
The i is not required. It is a convenience. Without it, there would be multiple equations that needed to be solved simultaneously.
93 | 4
i is basically just 90 degrees rotation into the complex plane. Perfect for wave functions literally. Calling it “imaginary” just creates confusion which is understandable. Once you know what i really is, it seems perfectly reasonable and normal for i to be here.
1 | 0
I think what’s so cool about complex numbers is that they’re such fundamental representations of what we can describe via other means. Want the angle given by a 2D matrix? Just use an arg(z) function! Want to describe 3D surfaces? Complex numbers!
And I think what makes it incredibly exciting is how rotation and modulos are baked into the system itself. Complex numbers are what give a real numerical basis for rotation, not just some fancy trick with trigonometry. It’s incredibly beautiful.
5 | 0
I would say it goes beyond mathematical convenience: complex fields with global symmetries have a conserved charge. Definitely represents something physical.
3 | 1
I love the subtitles.."Eye" instead of " i "
22 | 1
Actually both descriptions are equivalent so theres really no point in saying the i is "physical" or not. Just some kind of ontologic fear i guess. Btw some would say that only natural numbers exist.
1 | 0
That explanation felt both circular and open ended
6 | 0
Love this explanation!
1 | 0
Nah. The i isn't necessary. The equations describing the evolution of the square of psi don't need any i's in it by necessity. It is just a simple form. The complex numbers are just a nice way to put a phase in while always having an absolute value. A complex phase wave is always the same distance from the origin. That is mostly it, if you wanted to describe the function in Rn with real numbers you would need a different algebra and something like sums of trig functions in different directions to make up the components of the vector. When you take the square of a complex vector, you are just calculating an area associated with its length, doesn't matter whether it is complex or not. The math is simplified by unsing complex numbers thats all, the evolution of the probability distribution can be given by real functions for the imaginary and real components of the wavefunction. But then you need two coupled differential equations instead of one for complex variables. There is nothing special about quantum mechanics, it is just a janky interpretation of differential equations.
3 | 0
What if it is describing the negative part of the wave like in sound rarefraction and compression you get what im saying
2 | 0
I disagree that the i doesn't represent anything physical.
In Electrical Engineering, power has an i component that indirectly denotes inefficiency. In signals, the i represents a phase variance term. So it does have physical effects, but not in the "real" axis.
| 0
fun fact you can use a different convention for the gammas, s.t. gamma0 squared gives -1 and the i's completely disappear in the Majorana basis, there are thus entirely real solutions which describe the Majorana particles
2 | 0
No physical meaning?
Bivectors entered the chat
1 | 0
Hey Arvin! In my opinion, imaginary numbers represent something very real. Consider this analogy: I borrow money from my neighbor and promise to repay him with 25 square meters of farmland. That means my current land ownership is –25 m². If you think of this as a square area, the side length of my “land” would be 5i meters. People often make it more complicated than it is: i is just the square root of –1. That’s it. It shows up in real life - we just struggle to accept that we need a two-dimensional number space to represent it.
1 | 4
I thought i is required, but to certain extent it can be manouvered aroud with multiple equestrians.
All in all i is just as real as real numbers, that just so happens have 0 component coming with i. 1 + 0i.
1 | 2
Actually, the i rules the cyclic nature of the whole.
1 | 0
The i is lateral. If you are measuring in one direction (propagation) and the thing you measures rotates without losing momentum in the direction of propagation, you have a funny event to describe.
On the original line we are measuring, that has the primary answer we want (distance/frequency, etc) but we have this influence that we want to include that (in this case) doesn’t change the direction of the measure we wanted, the real measurement.
If we imagine another dimension, and measure the effect, we will find a non-zero answer on that imaginary dimension. That’s imaginary numbers — vey real, very unfortunately named
| 0
Ah...ah...ah ..AH... QUATERNIONS!!!!!
Oh, excuse me 😊
2 | 0
It’s like phasors we use to solve simple harmonic equations?
| 0
@ArvinAsh
7 months ago
Full video: https://youtu.be/CnBrbJVaecg "How the theory of all matter comes from a useless equation"
6 | 4