Well, I'm confused by you response. Have you actually watched the video and understood it?
Quote (1.56):
"Interestingly enough, just giving a name to the solution of this one equation ( i equals to the square root of -) and adding it to the set of real numbers turns out to be sufficient to make all algebraic equations solvable..."
It's a hack!
AND at 5.34 she states about complex numbers"... that's not the case, they're not necessary and as long as you ignore quantum mechanics you can think of complex numbers as a tool and you have no reason to think they physically exist".
It's a hack!
Sabine makes the point that complex numbers are not real and that math can do without them, only that it would be cumbersome. And she goes on to argue that even for quantum mechanics this is true (5.47 - 6.55). The only reason why i shows up in the Schrödinger equation is that it beautifully represent a wave function, including sine and cosine.
She finally speaks out her doubt about this new paper that says complex number are real.
In any space including vector spaces any mathematical operation should not violate symmetry, what works in a positive plane should work in a negative plain in the same way (After all, everything is relative, what is negative for you is positive in the eye of someone looking from the opposite direction). So squaring negative numbers should have the same result i.e. a mirrored effect as the same operation in the positive plain. After all negative numbers in a vector space are just directions, real absolute values but in the opposite direction of positive numbers. If the minus sign in front of a negative number would have been recognized as an operator and not a property of the number itself, we would not need the hack of complex numbers to be able to just do that, square negative numbers. And it's all because vector spaces have no real absolute coordinates in space but have their origin in 0. And why is that a problem? In the real world an oscillation would occur round a given point and no direction around that point is 'negative', only the angle changes relatively around a given point. By convention, in verctor spaces we use minus signs and plus signs, but what if we used indices for direction instead? (4left,3up, sorry can't make indices in this text), 4 left squared would result in 16 left, just like 4 right squared would make 16 right. Mirror perfect. Look mom, no complex numbers!
It's so simple, why is this so confusing?
It is so ironic, Maixent refers to the Dunning-Kruger effect and obviously means the writer sits at the infamous peak at the start of the curve. Apparently he thinks of himself as sitting at the end of the curve, but if you can't see mathematics is flawed in many ways and still results in many paradoxes, you're simply only blindly following what you've been taught and have no clue as to how it all came to be and where we are now.
Take the simple statements:
12 / 12 = 1
and
12 * 1 = 12
Are these true? Are they reversible?
Well ONLY in specific cases. Consider slicing a pizza in 12. What do you get? Twelve SLICES of pizza. The Pizza is gone. (I was to take a cow as example but found it cruel...) Is it reversible? no. Twelve slices of pizza form a collection of slices, never a pizza. You can apply this thought experiment on any object.
Why is math not typed like programming languages? Then it would be clear which calculations are reversible and which are not? A pizza can become slices, but slices can't become a pizza. A cow can become a hamburger, but a pile of hamburgers won't ever make up a cow. In physics, this is quite a big deal. Why do some scientists think the math allows for travel back in time? Because they fail to see math is flawed in this respect, it does not take into account the law of causality AND that the previous state of the universe is not preserved, once it is gone, it is gone, unlike a calculation you make on a sheet of paper, that you can reverse and trace back. (by the way, going back in time means that ALL particles in the universe should trace their steps back, so you wouldn't know if this would happen or has ever happened since your memory would be reversed too. And another thing, any new state of the universe is unique and random, there will never be the same state again, in an infinite universe there are infinite possibilities, so every possibility will only ever occur once, within the boundaries of causality of course. And so a reverse of time would return to a very specific, well defined state (order!) and that would take quite some organisation, and that violates the second law of thermodynamics).
Why do scientist 'believe' there are more dimensions than we can observe, only to make string theory a plausible theory? Just because they can, mathematically! They take a vector notation and add more numbers to it. Simple! And then they just argue that these dimensions are so teeny-tiny that they are 'hidden' in our observable three dimensions (Oh, no, wait, they can also be large dimensions in a 'brane world'...). Now that's drivel! What is a 'dimension'? Are suddenly we supporting the idea of 'higher dimensions' like spiritual or religious people? A dimension is 'sizeless' it is actually the same as 'direction' (up, down, left , right, to, fro). You can't just add directions in space just because your vector notation allows for it and argue that because math allows it, it is plausible! And can you imagine, a curled up Calabi Yau manifold, a very complex shape with six extra dimensions in every Planck pixel, in the entire universe? Who makes them and makes them all the same?
Are you amused? Wanna hear some more drivel? What about the idea we are living in a simulation? Seriously? Come on, some scientists really argue about it! Well here's a thought experiment for you:
Consider a stream of photons that come from a distant star and hit your eyes as you look up. How come they form a sharp pinpoint like image on your retina of that star far away and not a blurry shape? Because they all follow the EXACT same path. Now imagine the calculation for only one photon of this trajectory. The exact position of this photon must be stored AND updated with endless precision (no, not rounded tot some decimal point because with every updated position this would introduce a tiny error that would add up to a huge one. And this position must be updated every 5,391 24(27) × 10−44 s (Planck time), taking into account the gravitational pull of ALL particles in the universe (in other words, the exact bending of spacetime in every location) AND the expansion of the universe so not only it's position but also it's wavelength (energy) AND the updated position of all observers (Yes, we all look at the same star, no matter where we are and can verify it is there). What kind of computer would be able to do that for one f*ing particle, let alone a stream of particles with the EXACT same result? I rest my case.
These are the same mathe-magicians that talk about the 'multiverse' because they can't get their grip on the collapse of a wave function (in the famous double slit experiment). There is really nothing weird about a wave function that collapses and no, it has nothing to do with observers. A photon (wave or package of energy) hits a surface, the energy is absorbed by one electron that jumps to a higher state and so the energy is transferred into another state. As long as it is on it's way, it's wave function is smeared out but as soon as it is absorbed the wave function is just gone because the energy has been transferred into the electron. Another wave function, another story. No observers required. If it is a light sensitive plate, you can choose to look at the results afterwards (or after some minutes, hours, years) but you can also choose to not look at all. The wave function collapsed anyway. And you know what, that wave function? Was actually the wave function OF THE SPECIFIC EXPERIMENT not of the particle. The particle is oblivious of how many slits there are, but the number and size of slits define the result of the experiment. The probability of where the energy will be absorbed on the screen is determined by the experiment, the exact setting of it and the number of slits, not by the particle(s). Yes the particle has a wave function, but as soon as it hits the slits of the experiment, the wave function is altered. How hard can it be! Is the result probabilistic? Yes, to a certain degree, within the altered wave function AFTER the slits. Where and when did the wave function collapse? First as soon as the particle(s) passes the slits and then as it hits the screen and it's energy is absorbed by an electron. The experiment does not only SHOW the wave function it also DEFINES (or alters) the wave function of the particles.
But hey, you've already stopped reading, thinking it's all drivel. So I will stop now. Still hope you had fun reading it and learned not to take yourself so seriously. After all we're just 'lonely and only animals with fancy shoes'.
