4 Simple Improvements in 4D Math = Unified Theory

[zankipu]

gimana bisa dapatkan angka main..singapur

[BagarozziBoi]

i'd like to see your quaternion derivatives defined with epsilon-delta level of rigour...

[RubenHogenhout]

A pitty I am not allowed by u-tube to give the determinant of the matrices.

Don t know why not.

[RubenHogenhout]

test reactie

[slowvan]

Great job, However I really agree with Tom VanAckers math and not using inverses. Zero being a real number.

[sweetser]

@slowvan zero is a number. Zero is the identity element for addition: a + 0 = a. Multiplicative inverses are everywhere, particularly calculus. Good luck in your studies.

[goldmosaic]

a long time ago when you were doing physics stand upcomedy i was listening i am still listening. good work keep it up

[sweetser]

@goldmosaic Will do. May have made some progress in understanding gluons, hadrons, mesons, and baryons like today :-) Will have to see if the details pan out.

[CavinPhil]

The bet is as stupid as the ideas !

[patilan420]

and it makes sence. in breef, they claim, that the space and time are ANISOTROPIC, due to the equations and to the experimental data, talking about "perpendicular" instead of "paralel" worlds, and that in our limited perspective we notice this only when we take a look at very heavy or very distant objects. So it seems that 4-degree equations are the key to 4-dimentional physics.

[sweetser]

@patilan420 Time is a scalar quantity that gets paired with 3D space, a 3-vector quantity. I have been able to use two multiplication rules to derive field equations, one being exactly the Maxwell equations, the other being for gravity. I have no ideas what it would mean to make the scalar time have 4 different dimensions. Good luck in your studies.

[patilan420]

Yesthey are using "quaternions" and hypercomplex numbers,

they don't work on "strings", but they claim, that time has also 4 different dimentins.

basicly they are a groop of mathematitions, trying to "wake up" their physisit coleigs, by bringing new math in the field.

They claim that to understand 4D world we nead the hypercomplex equations and that is enough to include all the forms of the field in single theory AND to explain the quasars and the cosmic background radiation

[patilan420]

I'm not a matemathition, and the only thing I got from your video is that you are french.

But I'm curious, and I watch videos about math and physics and even red some books.

So there are other people, who studied 4D-math, and they explain it better for dummies

There are some russian scientists, who studied the equations of Finsler, Berwald and Moor and are trying to bring them in to the physics and into the public. Watch this:

youtube.com/watch?v=aro5pAQU90­Q

at 7:23 to 9:52

[sweetser]

@patilan420 Sorry, but I do not speak Russian. Looks like at one point, they are using quaternions, and at another, are using hypercomplex numbers (but they may call them a different name). Unless one works on strings, everyone else works with time and 3D space.

[jupytr1]

If I'm understanding you, what have there is not a "4-d Jordan division algebra" in fact it is not even an algebra at all. The flaw in your _algebra_ is subtle although it can be simply demonstrated. Let A=(0,1,1,1) and B=(1,1,2,3) in the "California" representation. Both A and B have inverses and A dose not equal - B but A+B has no inverse and dose not seem to be an element in the _algebra_ .Thus you do not have a true binary operation AXA->A as required to form an Algebra over a field.

[sweetser]

@jupytr1 I have a subtle objection to your subtle complaint. I _specifically_ excluded your example of A+B, which is (t-x-y+z)=0. The _same_ thing happens with quaternions. Let A=(1,2,3,4) which has an inverse, and B=(-1,-2,-3,-4) which has a different inverse, but A+B does not seem to be an element in the quaternion division algebra. Ah, but A = -B, and you specifically excluded that case. Why? So you would not have the "problem" that this one has.

[jupytr1]

@sweetser Doug, is C= (1,2,3,4) an element of the California numbers? Is C congruent to zero?

[sweetser]

@jupytr1 No C is not an element of the California numbers because 1 - 2 - 3 + 4 = 0. All eigenvalues of the California matrix representation that are equal to zero are not elements of the California numbers. C is an eigenvalue that equals zero which may be more precise than saying congruent to zero. The complete collection is:

1: t + x + y + z = 0

2: t - x - y + z = 0

3: t - x + y - z = 0

4: t + x - y - z = 0

So for example D=(1, 3, 4, 2) is not a California number by rule 3:.

[jupytr1]

@sweetser Then the California numbers are not closed under addition and therefore not an algebra since (0,1,1,1)+(1,1,2,3)=C. (0,1,1,1) and (1,1,2,3) are two Calf. numbers whose sum is not.

[sweetser]

@jupytr1 Quaternions are closed under addition even if A+B=0 where B = -A. Zero is the element of the algebra that does not have an inverse. Same rule applies to the Calif. numbers (rule 1:). Why? Because A+B=0 where B = -A is another way to write 0. The same logic holds for rule 1 of the Calif. numbers. Rules 2:-4: are a generalization, B != -A. You have found another way to write 2:. If quaternions are closed under addition even though A+B does not have an inverse, the so are Calif. numbers.

[jupytr1]

@sweetser Zero is a quaternion. No matter what two quaternions you add together you get another quaternion, that's called closure. On the other hand, i gave you a simple example of two Calf. numbers, A and B whose sum is C. According to you, and I quote, "No C is not an element of the California numbers.." If C is not a Calf. number, the Calf. numbers are not closed. At first, what I thought you were referring to was a quotient space between the Calf. and their eigenvalues, but wasn't sure

[sweetser]

@jupytr1 I am missing enough formal math training to say what I mean (for example, I don't know how to use the phrase "quotient space" properly in a sentence). I can live with these observations: the inverse of the Calif. numbers involves the eigenvalues (and I don't appreciate all the implications of that statement itself). An inverse does not exist if an eigenvalue is zero, and does exist if all eigenvalues are non-zero.

[qwAirGear]

You have me tempted to see exactly how your algebra finds a hole in the Frobenius theorem on division algebras.

Other than that...though I'm sold on nothing along the lines of unification in physics, it's nice to know that at least some people, even if ones not in the mainstream, are still interested in experimental results.

[sweetser]

@qwAirGear There is no hole in Frobenius' theorem. Instead, I dodge it. The fundamental theorem of algebra assumes that i^2 = -1. For hypercomplex numbers, i^2 = +1. Math jocks then go off on the properties of ideals, but that too might have an assumption about i^2. I may have to say something like "on this particular support, there is always an inverse", yet not claim it is a division algebra (math jocks are picky). It is vital for calculus that an inverse always exists.

[goldmosaic]

thankyou, i have followed you for some time. Remember your comedic version, i acctually downloaded it and studdied it. fantastic that sombody took that lane.

[eternal000sunshine]

Thankyou very much too. Im not a math person but I know youre on to something. Youve simplified all that complex physics into a game of cards where there are four suits and 64 cards .Seems like this quaterion stuff was taken out of physics for a reason by the universities all those years ago since Newton. So im wondering how physics would have been different today if it was left in. ... anyway keep up your interesting thought experiments my good friend.

[sweetser]

They do teach quaternions back in Junior High math classes, but NEVER EVER call it that. Vectors in 3D are quaternions: the div, grad, curl, cross, dot, and cross product. Q's insist on the relationships between these math thingies. The accounting system used in physics is sloppy, that is all. Nature keeps track of everything correctly by using the same system throughout.

Quaternions are not enough, one needs that even representation. That is radical - two ways to multiply.

Enjoy your studies.

[ShallowThoughts]

I watched for the naked lady.

[translation314]

great idea to argue this on youtube, it helps bring discussion to a wider forum

[egeneral27]

omg!! dude seriously, i thought you were bill gates!!!

[scepticalchymist]

I think if it works, let there be an arbitrary amount of dimensions. There is no need to visualize it, if the outcome of its presence in some form or the other can be calculated.

I find quaternions intriguing insofar they represent rather 3+1 dimensions than 4 (a 3+1 reducible subgroup to 4D), but I never understood the reason for this behaviour really. Ok, it has to have something to do with the quaternions used for the description of 3D rotations (vectorial axis and scalar rotation angle).

[scepticalchymist]

When mankind learned about electromagnetism we were able to build so much technology out of it. When mankind will learn about gravity, I have no doubt, that controlling gravity will be the ultimate consequence.

[dougsweetser]

Good luck in your studies.

At this time, I do not how my specific proposal will lead to controlling gravity. In time it may be used to deal with problems we have in our understanding of how things work: non-zero mass in the standard model, the horizon and flatness issues in the big bang, velocity profiles in galaxies, and the accelerating universe. I would be happy getting the obscure math notation dead on for one of those problems, but have yet to do so.

[ev1Lsect]

The emphasis is understanding gravity, not "controlling" it.

[scepticalchymist]

But that means the same. If I understand something on the fundamental level I have, at least theoretically, the possibility to control it. There may, of course, practical reasons that prevent gaining control, e.g. enormous energy cost etc.

[scepticalchymist]

I am a chemist and interested in some of the math, too, but obscure notation and too less or too many symbols together with no pictures makes it no fun to read a math paper, even if one might be interested in the topic, when a different style of presentation were chosen. I also agree that if one finally understands gravity from a unified theory, that a lot of weird physics will pop out, and applications too, of course.

[scepticalchymist]

Nice ideas presented with the necessary math and a good portion of humour. I really agree that professional mathematicians should use more animations/visualizations/grap­hics to present their work. Nothing of the rigour is lost in a carefully designed graphic and it does help to understand things in a remarkable way, far more faster and ready memorizable. This is true especially for people on the fringe, interested in math from a non-expert viewpoint and without university degree in this field.

[sweetser]

You are correct if you say there are no 4 spatial dimensions, there are only 3 you can point at, a forth vector dimension is redundant. While doing all this pointing, you can see a clock move, which is time and is independent of the 3 spatial dimensions. Time has a different quality to it which is reflected in the mathematics of quaternions (time is a scalar). So I have seen the fourth dimension which is time.

[kinghingle]

@sweetser i would have considered density or colour a more pratical 4th dimention, rather than using time because that would just then be a series of 3d images in some kind of series, rather than a representation of an actual 4th dimenteion which a density or colour model would offer.

[sweetser]

@kinghingle In special relativity, space mixes with time in a well-defined mathematica way. Space does not mix with density or colour. Perhaps the problem is I should call this subject 3D+scalar. 4D implies they are all the same. That is not the case: space is not like time because one can point in the direction of space, but not so for time.

[kinghingle]

@sweetser ah understood

[ShallowThoughts]

@sweetser That's not true. I pointed in a direction of time once. (However, I was outcast from my social group for a negative month.)

[noobyfromhell]

I liked your video, even though I didn't understand a large chunk of it :D

[wresing]

I guess my question is about the relationship between math and physics. Or perhaps more broadly, the relation between logic and reality.

Know how some people want experimental confirmation? Even a thought experiment could help concretize a theory. Could you suggest a thought experiment or visualization that could clarify your ideas and their implications. A theory of the foundations of 4Dspace-time can't start with 4Dspace-time or even the concept of dimension. Perhaps its all fractal.

[wresing]

But why four? Why not work with arbitrary dimensional formulations that can derive the number of spacial and temporal dimensions? What about octurnians?

[sweetser]

A fair question given that pro physicists are wasting time in 10 and 11 dimensions. Physics is the study of change in spacetime. Calculus, the study of change, needs a mathematical field. The 3 finite dimensional, associative fields are the real numbers, the complex numbers, and the quaternions. Calculus cannot be done in arbitrary dimensions, only over these fields. For consistency, I think it must be done with these fields. Why 4? it all about math. I have yet to see a need for octonions.

[Quelch1]

You have a humor that is needed, when trying to give meaning to a point.

[tyrbolo]

I liked the part where he showed that there are things we haven't seen yet if E8 is right.

Doug you are mean to make the string theory math boys try to conform to the observable

universe...LOL

[sweetser]

It is Nature that is mean. She is both completely open and silent.

[dtman83]

Great video, I really enjoyed the humor in this one. I wish more people were as passionate as you.