Epsilon Pi's ideas on imaginary numbers

[quantumdude]

What about the Pendulum as an open dynamic system? There you have a table that can be validated with what is observed. Please note its deduction is obtained under the same roof, in which I obtained the SWE, and those equations associated with the LTG and gravitational fields, I can present later specially for the sake of this discussion.

OK, at this point I'm going to have to ask you what you mean by "under the same roof". I interpreted it in the context of our previous discussion, meaning that if the Lorentz transformation is true, then the Schrodinger equation cannot be true.

And what is "LTG"?

1. The the SWE is a complex equation, that is a fact; a complex equation describing the behavior of an entity such as the electron, again it is not a quantitative matter.

Of course, I know that the Schrodinger equation is complex. I have solved it many times. But what you have consistently failed to understand is that the Schrodinger equation is complex because of:

1. The rules of quantization: p-->-igrad and E-->i(∂/∂t) and...
2. The nonrelativistic[/color] Hamiltonian: H=p²/2m+v.

The Klein-Gordon equation uses #1, and rejects #2. That is because we know for a fact that #2 is wrong. The Schrodinger equation is complex because it makes use of a deficient conception of space and time. If relativity had been developed a century earlier, the Schrodinger equation would not exist.

2. From your point of view, which is of course of modern physics, there is not a complex equation for describing the fundamental equations of physics, and I say, yes, there is. Up to know I have presented two examples, but will you pay attention if I present the others two, I mean, that of the LTG, and those describing the behavior of gravitational fields?

I did not say that there is not a complex equation to describe the fundamental equations of physics. I am saying that those equations need not be complex, just for the sake of being complex. If they turn out complex (as in the case of Schrodinger), then so be it. If not, then so be it.

And by the way, I am curious to know if you have yet looked up the the Dirac equation. There you have a complex wave equation that is also Lorentz covariant.

If I have a better way to represent things why should I look to one that has even been qualified, not precisely by me , as cumbersome?

All you have are severe misunderstandings of relativity, quantum theory, and how they relate to each other.

Yes, of course, we can put them, and this a complex mathematical assertion. I have already done it, and if this thread is not locked before, I will present it in here. But please note this will not be a TOE, but a complex mathematical methodology to see the whole thing, we are talking about, under a same roof.

Once again: You'll have to say what you mean by "under the same roof".

I was thinking that you mean by it what you were saying before, which is that it is possible to have the Galilean transformation and be consistent with relativity, which is of course false.

 

[Epsilon Pi]

First of all, I want to thank you for your criticism and time, but let's go to the point!

OK, at this point I'm going to have to ask you what you mean by "under the same roof". I interpreted it in the context of our previous discussion, meaning that if the Lorentz transformation is true, then the Schrodinger equation cannot be true.

And what is "LTG"?

This answer I will give you this next week mathematically in the next paper promised, but is not the LTG, that group of equations that not only make Maxwell's equations invariant, but that additionally can take us to the equivalence of mass-energy and the variation of mass with velocity?

Of course, I know that the Schrodinger equation is complex. I have solved it many times. But what you have consistently failed to understand is that the Schrodinger equation is complex because of:

1. The rules of quantization: p-->-igrad and E-->i(∂/∂t) and...
2. The nonrelativistic[/color] Hamiltonian: H=p²/2m+v.

The Klein-Gordon equation uses #1, and rejects #2. That is because we know for a fact that #2 is wrong. The Schrodinger equation is complex because it makes use of a deficient conception of space and time. If relativity had been developed a century earlier, the Schrodinger equation would not exist.

Thank you! this is the clearest and consistent objection I have received! But here is where I think I can offer a different point of view that needs sort of "paradigm shift" which I think is the most difficult thing to accomplish, so I really don't make myself much illusions. All that I really expect is to obtain a hearing, by someone as you, that really knows what he is talking about.
Again this objection cannot be answered without the next paper.

I did not say that there is not a complex equation to describe the fundamental equations of physics. I am saying that those equations need not be complex, just for the sake of being complex. If they turn out complex (as in the case of Schrodinger), then so be it. If not, then so be it.

And by the way, I am curious to know if you have yet looked up the the Dirac equation. There you have a complex wave equation that is also Lorentz covariant.

Of course I have looked up the Dirac equation, but my point is that I have found myself with another way to present things in which I really do not have that conflict as I will try to show in my next paper.

All you have are severe misunderstandings of relativity, quantum theory, and how they relate to each other.



Once again: You'll have to say what you mean by "under the same roof".

I was thinking that you mean by it what you were saying before, which is that it is possible to have the Galilean transformation and be consistent with relativity, which is of course false.

No, where did I talk about Galilean transformation consistent with SR or the LTG? I know this is quite impossible, as with GT, the velocity of light was not a constant. I know that SR was based on:
1. The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion.
2. Any ray of light moves in the "stationary" system of co-ordinates with the determined velocity c...
In a certain sense the first can be applied to GT, but not the second.

What you will find in my next paper is not certainly a deviation to the LTG, on the contrary that LTG will be put in another context even more general that this one of SR.

Did not the same Einstein have a real problem when trying to generalize its SR, or apply it to non-uniform motion of K' relatively to K.? Is it not true that this same problem is at the base of that incommpatibility between QM and GTR?

Best regards
EP

 

[quantumdude]

This answer I will give you this next week mathematically in the next paper promised, but is not the LTG, that group of equations that not only make Maxwell's equations invariant, but that additionally can take us to the equivalence of mass-energy and the variation of mass with velocity?

I take it that "LTG" stands for "Lorentz Transformation". Still don't know what the "G" is for.

If that is what you mean, then yes, the Lorentz Transformation is the coordinate transformation under which Maxwell's equations are valid.

Of course I have looked up the Dirac equation, but my point is that I have found myself with another way to present things in which I really do not have that conflict as I will try to show in my next paper.

What conflict?

No, where did I talk about Galilean transformation consistent with SR or the LTG? I know this is quite impossible, as with GT, the velocity of light was not a constant. I know that SR was based on:

You said that the Lorentz transformation can be derived nonrelativistically (whatever that means), and that the result would be that time would be decoupled from space. That is the Galilean Transformation, through and through. The fact is that there is no way to have the Lorentz Transformation and the decoupling of time and space.

Did not the same Einstein have a real problem when trying to generalize its SR, or apply it to non-uniform motion of K' relatively to K.? Is it not true that this same problem is at the base of that incommpatibility between QM and GTR?

No, GR and QFT are incompatible because of the singularities in GR. Nonuniform motion does not present a problem here. In fact, QM (not QFT) is compatible with GR. The problem arises when one graduates from the mechanical theory to the field theory.

But in any case, this is not really pertinent.

 

[Epsilon Pi]

Another way of coping physical reality

As I promised I am presenting the third paper:

The Lorentz Transformation Group from a non relativistic point of view

http://www.geocities.com/paterninaedgar/LTG.PDF

Abstract. The aim of this paper is to present the LTG under a more general and dynamic context than that of systems in uniform translatory motion, in which SR was conceived, in this way even that famous equation of the equivalence of mass-energy can be found in a more consistent and natural way; in a certain sense this approach can be considered a philosophical and semantic evolution of that work of Einstein though. Two main points must be recalled additionally: one has to do with the complex plane considered in this case sort of dynamical background; the other one has to do with the fact that the magnetic field is taken as the fundamental physical field, what is expressed in a proposed new order of Maxwell's equations.
Comments. 12 pages, 4 figures and equations.

I hope with this paper to have made clearer my position regarding this discussion as in it you will find in a most rigorous and mathematical way what I have been holding:
- under a same roof all the fundamental equations
- the LTG from a more general point of view
- no more conflicts, even if you want to preserve your point of view you can, but by time being you will not need it.

Regards and thank you for your time!
EP

I take it that "LTG" stands for "Lorentz Transformation". Still don't know what the "G" is for.

If that is what you mean, then yes, the Lorentz Transformation is the coordinate transformation under which Maxwell's equations are valid.



What conflict?



You said that the Lorentz transformation can be derived nonrelativistically (whatever that means), and that the result would be that time would be decoupled from space. That is the Galilean Transformation, through and through. The fact is that there is no way to have the Lorentz Transformation and the decoupling of time and space.



No, GR and QFT are incompatible because of the singularities in GR. Nonuniform motion does not present a problem here. In fact, QM (not QFT) is compatible with GR. The problem arises when one graduates from the mechanical theory to the field theory.

But in any case, this is not really pertinent.

 

[quantumdude]

I read your third paper, and I find it extremely incomprehensible.

From page 3:

The metric we will use is a complex one based on Euler rotation and its associated basic unit system concept, where in this case, we will determine the state of an electromagnetic entity, represented as:

DS=|DS|e^iθ

I have no idea of what you mean by “metric” or “electromagnetic entity”, nor how your DS constitutes either of these.

From page 4:

DS=c dt+ i dSr

So now DS is no longer an electromagnetic entity, but a vector in the complex plane? Your use of language is quite obfuscating to say the least.

Also, what is “dSr”? Is it just “dx”? And what is “E” on the horizontal axis of Figure 2?

From page 5:

The second supposition is that the velocity of light is a constant in the universe.

Near as I can tell, this statement lacks meaning. Do you mean to reiterate Einstein’s speed of light postulate with this?

In regards to having two system rotating against each other, the condition they have a same frequency permits us to see them both as in sort of “merry-go-round”, what is expressed in that angle between the two systems; in the complex plane, sums, differences, integral, and derivative of a Bus of a given frequency…

If the two systems are rotating at the same frequency (as measured by the same person, I assume), then they are not “rotating against each other”. There is no relative motion at all between them.

And what is a “Bus”?

From page 6:

In this sense we deviate clearly from a relativistic conception of systems of coordinates, where time was just another space coordinate, or a generalization.

There’s nothing “clear” about any of this. But you are most definitely wrong about the status of time in SR. It is not just another spatial coordinate. If it were, the metric of SR would have a signature of 4 instead of 2. What is true is that space and time are coupled in Einstein’s theory, and guess what? They are coupled in your theory as well. You go on to show that this is the case in equations (4) and (5) on page 9.

We already know that here (edit: Lorentz covariance of physical laws) lies the great well-known incompatibility between SR-QM and GTR…In fact QM was dragged by SR to the point that the complex nature of the Schrodinger wave equation was by all means dropped out. In a complex equation we must have always in mind both, its magnitude and its phase; if we consider just one of them we are just making a rough simplification.”

This is chock full of errors.

1. Lorentz covariance is not the source of any incompatibility between QM and GTR. In fact, the trouble you believe exists between QM and GTR doesn’t even exist. The problem comes into play when QFT and GTR are merged, but it has nothing to do with covariance of physical laws. In fact, I already told you why they disagree, in this very thread.
2. QM was not dragged by SR. QM was merged with SR. And no one simply “dropped out” the complex nature of the Schrodinger equation to do it. I already explained to you that the complex nature of that particular equation is nothing more than an artifact of a deficient conception of spacetime, and of momentum-energy.
3. Complex equations (including the Schrodinger equation) do not have a magnitude or a phase. Their solutions do, and the solutions of the Klein-Gordon and Dirac equations are no different.
4. And there is no incompatibility between SR and GTR, so I don’t know why you would put them in opposite camps.

You seem to think that the KG equation is somehow deficient simply because it is not complex. But that’s not a problem with the KG equation, it’s a problem of your particular bias for complex quantities. And that bias is not justified in the least.

Now when your derivation started on page 7, I was about to throw this blasted paper in the garbage, because it is quite obvious that the whole argument starts out with inconsistent premises. But then, after a page and a half of mathematics, you conclude yourself that it leads to an absurdity. I certainly don’t disagree, but what is the point of going through that exercise?

Now, in the middle of page 8, we get to the real crux of the issue:

…we have an absurd that is solved by introducing the well-known relativistic factor as:

!

You are simply postulating what Einstien has deduced!

If you can’t see that the use of this factor is does not make your formalism fully relativistic, then there is nothing I can do to help you. Furthermore, you introduce it in such an unnatural, ad-hoc way that I cringe to call your work a “formalism” at all.

I’m afraid there’s not any merit to this work. The Admininstrators and Mentors agree, and they have been itching to close this thread down. And after reading your papers, I can see no reason not to.

So long,