Epsilon Pi's ideas on coordinate independence

[Epsilon Pi]

Tensors, a reason of great schism in physics?

Yes, this application of that aristotelian principle, you have described so well, where the third is excluded and as so uncertainty is the reason why there won`t be a quantum gravitation theory, and a reason why physical laws must not be expressed in terms of tensors. Is this not, as a matter of fact, one of the reasons of the great schism in physics?

Regards

EP

A "tensor" is a generalization of a "vector". The crucial point about tensors (as well as vectors) is that they change "homogeneously" under change of coordinates. Specifically, if a tensor is all zeroes in one coordinate system then it is zero in all possible coordinate systems. That means that if the equation A= B (where A and B are coordinates) is true in one coordinate system (A= B is the same as A-B=0) then it is true in any coordinate system. Since (obviously) a physical law does not depend upon an (arbitrary) choice of coordinates system, it follows that physical laws must be expressed in terms of tensors.

 

[chroot]

Epsilon Pi,

Ummmm... what?

- Warren

 

[jcsd]

Yes, this application of that aristotelian principle, you have described so well, where the third is excluded and as so uncertainty is the reason why there won`t be a quantum gravitation theory, and a reason why physical laws must not be expressed in terms of tensors. Is this not, as a matter of fact, one of the reasons of the great schism in physics?

Regards

EP

Yes good point, but one would find that if you leaned mpore towards the Socratean ideal of sticking your foot up your nose, it (your foot) would not be of a tensorial nature.

Physical laws must be expressed in terms of tensors (if a physical law cannot be expressed in terms of tensors you should expect it to be incomplete) as you cannot expect the laws of physics to be dependnt on the choice of coordinate system.

 

[Epsilon Pi]

Why so many paradoxes in physics?

Hi Warren and others,

Yes, reality is not simple but complex(not necessarely complicated), and any intent to linearize it will take us to paradoxes such as those ones Hawking is now correcting regarding black holes. How is it that at atomic level matter cannot colapse, but it can at large? How is it that a fundamental principle such that of conservation of energy is violated, and we still think everything is ok?

Regards

Edgar

 

[chroot]

Epsilon Pi,

Per physicsforums.com guidlines, you must refrain from posting non-mainstream theories to the general forums. Such posts are welcome only in the Theory Development forum.

Black holes and the conservation of energy are simply not topics relevant to the definition of a tensor.

- Warren

 

[Epsilon Pi]

Reducing geometry to algebra?

Coordinate systems?, or as I call it, reducing geometry to algebra, must they be represented by using a tool based just in the so-called "real numbers"? Has not Roger Penrose pointed out the fact that complex numbers are fundamental in understading the physical world?

Regards

EP

Yes good point, but one would find that if you leaned mpore towards the Socratean ideal of sticking your foot up your nose, it (your foot) would not be of a tensorial nature.

Physical laws must be expressed in terms of tensors (if a physical law cannot be expressed in terms of tensors you should expect it to be incomplete) as you cannot expect the laws of physics to be dependnt on the choice of coordinate system.

 

[jcsd]

Where does complex numbers come into it? they would onl;y bew relevant if you were sticking your foot in your ear.

Sure geometry is just a tool, but the physics must be indepednt of the tool, just like, for example, the physics of a star must be indepednt of the telescope you use to look at it.

 

[Epsilon Pi]

Thank you!

My apologies Warren, and thank you for splitting off Epsilon Pi's responses to a new thread in Theory Development. I hope we can now make some criticisms of that mathematics called Tensor Analysis from which General Relativity and as so black holes were derived

Regards

Ep

Epsilon Pi,

Per physicsforums.com guidlines, you must refrain from posting non-mainstream theories to the general forums. Such posts are welcome only in the Theory Development forum.

Black holes and the conservation of energy are simply not topics relevant to the definition of a tensor.

- Warren

 

[Epsilon Pi]

Is reality simple or complex?

Are you not making physics dependent on a tool such as Tensor Analysis with the generalization of the so-called coordinates systems? where they come from? Are not they an invention of the human mind? why should we make an absolute of that invention?

Should we not ask ourselves about the fundamental structure of reality? Is it simple or complex? If it is complex as we already known by QM, should we not use a complex tool, I mean complex numbers, to represent that physical reality?

Regards

EP

Where does complex numbers come into it? they would onl;y bew relevant if you were sticking your foot in your ear.

Sure geometry is just a tool, but the physics must be indepednt of the tool, just like, for example, the physics of a star must be indepednt of the telescope you use to look at it.

 

[homology]

My apologies Warren, and thank you for splitting off Epsilon Pi's responses to a new thread in Theory Development. I hope we can now make some criticisms of that mathematics called Tensor Analysis from which General Relativity and as so black holes were derived

Tensor analysis is, as is mathematics a consistent theory, rather beyond reproach (ignoring any possible foundation questions). Furthermore General Relativity is not derived from tensor analysis.

 

[Epsilon Pi]

Another version of GTH?

How is that? haven't you read the original paper "The foundation of the General Theory of Relativity? or do you know another version of GTR, if you do, please let me know

Regards

EP

Tensor analysis is, as is mathematics a consistent theory, rather beyond reproach (ignoring any possible foundation questions). Furthermore General Relativity is not derived from tensor analysis.

 

[Epsilon Pi]

What does it mean?

"The fundamental idea of this general theory of covariants is the following: - Let certain things ("tensors") be defined with respect to any system of co-ordinates by a number of functions of the co-ordinates, called the "components" of the tensor." The Principle of Relativity, pag, 121. Dover P.Inc.
If this does not mean that tensor analysis is the main mathematical tool in which GTR is based, then what does it mean?

Regards

EP

Tensor analysis is, as is mathematics a consistent theory, rather beyond reproach (ignoring any possible foundation questions). Furthermore General Relativity is not derived from tensor analysis.

 

[e(ho0n3]

As homology pointed out, GTR is not "derived" from tensor analysis. Tensor analysis is a "tool" that Einstein used (and had to learn as he was developing his theory if I remember correctly) to develop his ideas. Einstein used high school algebra as a "tool" do develop STR. This doesn't mean the STR is derived from high school algebra.

 

[Epsilon Pi]

a good mathrmatical tool must not reflect physical reality?

If a tool is going to be useful to represent physical reality there must be a closed association between the two, and as is shown in that original paper mentioned written by Einstein, it would have been impossible for him to get GTR without it, so how can you say its main conclusions were not derived from that tool?

Regards

EP

As homology pointed out, GTR is not "derived" from tensor analysis. Tensor analysis is a "tool" that Einstein used (and had to learn as he was developing his theory if I remember correctly) to develop his ideas. Einstein used high school algebra as a "tool" do develop STR. This doesn't mean the STR is derived from high school algebra.

 

[homology]

If a tool is going to be useful to represent physical reality there must be a closed association between the two, and as is shown in that original paper mentioned written by Einstein, it would have been impossible for him to get GTR without it, so how can you say its main conclusions were not derived from that tool?

The mathematics of the physics doesn't have to have any particular association with reality. For example, what reality would Hilbert space have with a chemical reaction?

I would also hesitate against saying that it would have been "impossible" for Einstein to get GR without tensors. Its an unprovable statement.

Furthermore, again, there is nothing in tensor analysis as an area of mathematics that implies the physical theory of GR. You have to add other assumptions, not necessary to tensor analysis.

Kevin

 

[Epsilon Pi]

Idealism in physical science?

Hi Kevin,

Your first paragraph is precisely one of the reasons why we have had such a great tendency to especulation and idealism in that field of science that should not: physics; no, I think that the mathematics of physics and its symbolism must in a certain sense reflects its profound dual structure, just as in QM, a complex expression solved the duality of the wave-particle problem.

The main problem with Einstein is that he did not use complex numbers; it is well known that the quadratic differential element introduced by Minskownki, as another interpretation of special relativity was obtained from complex numbers, but Einstein generalized that QDE, by using tensor analysis, i.e., just the magnitud of that QDE, and here he had his great drawback. As a matter of fact I have prepared a paper where this is proved that I hope will be read by all those interested.

Tensor analysis was the tool Einstein used to express his idea of "formulation generally covariant laws...as...all the components in the new system vanish, if they all vanish in the original system", and as so all his GRT became quite dependent on that tool...this is a fact you cannot disprove.

Regards

EP

The mathematics of the physics doesn't have to have any particular association with reality. For example, what reality would Hilbert space have with a chemical reaction?

I would also hesitate against saying that it would have been "impossible" for Einstein to get GR without tensors. Its an unprovable statement.

Furthermore, again, there is nothing in tensor analysis as an area of mathematics that implies the physical theory of GR. You have to add other assumptions, not necessary to tensor analysis.

Kevin

 

[homology]

Why complex numbers? I don't see the need for them, where would they come up: imaginary coordinates? these wouldn't make any sense as they describe positions in space-time. Would the complex numbers show up in the metric, I think not other wise we could end up with imaginary lengths from the inner product so induced, again, doesn't make any sense. Would the complex numbers end up in the stress-energy tensor, and if so what would that mean?

I'm not sure what you beef is with either tensors, which is just an area of mathematics, or with general relativity, which within its proper domain has shown outstanding agreement with experiment. All one can do to "improve" upon it is merge it with quantum and no one person will do that alone.

Kevin

 

[Epsilon Pi]

How can you express the dual structure of reality?

Why complex numbers? Didn't you know what I said before about Minkowski interpretation of special relativity? That quadratic differential element of space he introduced and Einstein generalized by using Riemann geometry and tensor analysis was based on complex numbers.

The great prejudice we have had against them is precisely due to Descartes the one who first used the term imaginary numbers, an unfortunate term that has prevented his use in other ways, just as they are used in electrical engineering, where they are taken for real.

If we want to reflect the profound dual structure of physical reality, duality of space and time, duality of wave and particle, must not we use a symbolism that permits us to reflect it?

Regards

EP

Why complex numbers? I don't see the need for them, where would they come up: imaginary coordinates? these wouldn't make any sense as they describe positions in space-time. Would the complex numbers show up in the metric, I think not other wise we could end up with imaginary lengths from the inner product so induced, again, doesn't make any sense. Would the complex numbers end up in the stress-energy tensor, and if so what would that mean?

I'm not sure what you beef is with either tensors, which is just an area of mathematics, or with general relativity, which within its proper domain has shown outstanding agreement with experiment. All one can do to "improve" upon it is merge it with quantum and no one person will do that alone.

Kevin

 

[jcsd]

Why complex numbers? I don't see the need for them, where would they come up: imaginary coordinates? these wouldn't make any sense as they describe positions in space-time. Would the complex numbers show up in the metric, I think not other wise we could end up with imaginary lengths from the inner product so induced, again, doesn't make any sense. Would the complex numbers end up in the stress-energy tensor, and if so what would that mean?

I'm not sure what you beef is with either tensors, which is just an area of mathematics, or with general relativity, which within its proper domain has shown outstanding agreement with experiment. All one can do to "improve" upon it is merge it with quantum and no one person will do that alone.

Kevin

Though I've only done it with the minlowski metric (i.e. specil relativity) I assume it would work for all Lorentzian metrics.

If you have x⁰ = -ict and x¹ = x, etc. and treat the mertic qas Euclidean (from what I understand this what is done in Eclidean quantum gravity) you get perfectly consistent results as long as you rember you're orgianl defniitnion. You're always going to have imaginary intervals in spacetime anyway.

 

[homology]

The ict notation is no longer used in modern relativity. As far as I can see there's no need to use complex numbers.

I have no prejudice against them. I use them in quantum mechanics all the time. However, in its modern form, I don't see their need in GR.

Kevin

 

[jcsd]

The ict notation is no longer used in modern relativity. As far as I can see there's no need to use complex numbers.

I have no prejudice against them. I use them in quantum mechanics all the time. However, in its modern form, I don't see their need in GR.

Kevin

Yep, but you can use it is the point. AFAIK the idea or something simlair is used in Euclidean quantum gravity.

 

[Epsilon Pi]

Complex numbers fundamental for representing reality?

yes, Kevin, they don't use anymore the ict notation because they even talk about an "imaginary time", in their futile intent to make complex numbers of the same nature as the so-called "real numbers", a great flaw, IMO.

The great reason why they don't have a quantum mechanics theory of gravitation is due precisely because they, the GRT side, abandoned once and for all the use of complex numbers; these are fundamental for expressing the dual nature of reality

Regards

EP

The ict notation is no longer used in modern relativity. As far as I can see there's no need to use complex numbers.

I have no prejudice against them. I use them in quantum mechanics all the time. However, in its modern form, I don't see their need in GR.

Kevin

 

[Epsilon Pi]

Reducing time to space? a great flaw?

Why do you talk about two metrics?
That mathematical artifice you'r talking about is their flaw intent to reduce time to space, or else, as I like to say geometry to algebra.

Regards
EP

Though I've only done it with the minlowski metric (i.e. specil relativity) I assume it would work for all Lorentzian metrics.

If you have x⁰ = -ict and x¹ = x, etc. and treat the mertic qas Euclidean (from what I understand this what is done in Eclidean quantum gravity) you get perfectly consistent results as long as you rember you're orgianl defniitnion. You're always going to have imaginary intervals in spacetime anyway.

 

[Epsilon Pi]

Physical science and Complex Thinking

Hi everyone,

For all those interested in the evolution of philosophy of science you can find in my profile a paper that was published in KJF, a philosophical forum; the corresponding URL, is

http://www.douglashospital.qc.ca/fdg/kjf/Complex%20Thinking.pdf

If you have any problem with pdf, I can send it to you, personally in html format

Thanks

EP

 

[Epsilon Pi]

The third included and complex numbers?

For all those interested, in my paper, Physics, Edgar Morin and Complex Thinking, presented in KJF, as I said down, there is another way of representing reality, where complex numbers are taken as that mathematical tool that definitevely by including the third, has the chance to be an ideal tool for representing the fundamental equations of physics, such as those of QM or the Schrodinger wave equation, the pendulum formula and its aproximation factor that can be validated with what is observed, the equations of special relativity, but also those of gravitational fields. This gives us another procedure of representing physical reality, in which the theoretical symbolism must be taken as a tool that must fit that reality it is representing. Would you use as an engineer a tool that does not fit reality?
The main advantage with this complex symbolism and the Basic Unit System concept introduced is that, the so-called "incommesurability of compiting paradigms", coined by Thomas S. Kuhn is overcome, and as so the great schism physics has lived since QM.

Regards

EP

Yes, this application of that aristotelian principle, you have described so well, where the third is excluded and as so uncertainty is the reason why there won`t be a quantum gravitation theory, and a reason why physical laws must not be expressed in terms of tensors. Is this not, as a matter of fact, one of the reasons of the great schism in physics?

Regards

Originally Posted by HallsofIvy
A "tensor" is a generalization of a "vector". The crucial point about tensors (as well as vectors) is that they change "homogeneously" under change of coordinates. Specifically, if a tensor is all zeroes in one coordinate system then it is zero in all possible coordinate systems. That means that if the equation A= B (where A and B are coordinates) is true in one coordinate system (A= B is the same as A-B=0) then it is true in any coordinate system. Since (obviously) a physical law does not depend upon an (arbitrary) choice of coordinates system, it follows that physical laws must be expressed in terms of tensors.

EP

 

[Epsilon Pi]

A principle the source of our problems?

Many posts have been written since this one was sent to a new section called "theory development", as I posted it initially in a section of "normal science", and I apologized to Warren for doing so well his job.
But what has become very clear to me since then, is that our main problem(something very, very wrong in modern science), is due to the same man that almost took Galileo at the beginning of our science to be burned: Aristotle and his principle of the third excluded.

Best regards to all

EP

Yes, this application of that aristotelian principle, you have described so well, where the third is excluded and as so uncertainty is the reason why there won`t be a quantum gravitation theory, and a reason why physical laws must not be expressed in terms of tensors. Is this not, as a matter of fact, one of the reasons of the great schism in physics?

Regards

EP

 

[HallsofIvy]

If a tool is going to be useful to represent physical reality there must be a closed association between the two, and as is shown in that original paper mentioned written by Einstein, it would have been impossible for him to get GTR without it, so how can you say its main conclusions were not derived from that tool?

Regards

EP

It certainly would be possible. Many modern physicists (and mathematicians) prefer to use "differential forms" instead of tensors.

 

[Epsilon Pi]

history is an irreversible process, isn't it?

Historically it was not the case with Einstein, history is an irreversible process, isn't it?. We must take into account the way Minkowski interpretation of Special Relativity influenced in Einstein, in developing his ideas on general relativity(see The Principle of Relativity, by Einstein at all, Dover P, Inc.1952,pag.119).
And it is quite right to use differential equations instead of tensors; if we take for granted that differential equations can be converted into "simple algebraic equations" because of that remarkable property of Euler relation to remain the same the change, i.e., with those mathematical processes that represent it: integration and differentiation, we then come across with a tool, an ideal to represent the isomorphic or covariant laws of nature.

Regards

EP

It certainly would be possible. Many modern physicists (and mathematicians) prefer to use "differential forms" instead of tensors.

 

[mathwonk]

thanks guys, this gave me a good laugh out loud.