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**Author Michael A. Popov**: *on* 10/4/12 at 13:10pm UTC, wrote Sergei, Thank You - I suspect a kind of web-sophistication in the form of...

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**Benjamin Dribus**: *on* 10/2/12 at 19:15pm UTC, wrote Dear Michael, As promised, I have just finished reading your essay! Quite...

**Christian Corda**: *on* 10/2/12 at 16:27pm UTC, wrote Dear Michael, An good Essay, where you raise interesting issues. I am...

**Author Michael A. Popov**: *on* 10/1/12 at 11:38am UTC, wrote Cao Hai, Your statement "Mathematics is the "logical inference" of who to...

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**Hoang Hai**: *on* 9/29/12 at 16:56pm UTC, wrote Thank you Popov Very happy to be your answer, even though we do not have...

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Questioning the Foundations Essay Contest (2012)
[back]

TOPIC: Which of Our Basic Mathematical Assumptions in Physics Are Wrong? by Michael Alexeevich Popov [refresh]

TOPIC: Which of Our Basic Mathematical Assumptions in Physics Are Wrong? by Michael Alexeevich Popov [refresh]

Pure Physics is not Pure Mathematics. In comparison with mathematicians, physicists agree to simplify mathematics because in some cases it " naturally" arises from physical experience. Hence,some basic mathematical assumptions are defined as Wrong ( or not sufficiently realistic ) statements in physical sciences. In this context we can develop even the whole comparative theory of physical - mathematical differences from this point of view. In order to show this kind of anthropic comparative studies let us consider merely two the most sensitive passages of Relativistic Physics. Passage 1: Einstein physical theory loci in space. Passage 2: Einstein's Time as a new kind of complex number.

Oxford based anthropologist and cryptanalist ( quantum immune cryptography )

Hello, Michael!

Very deep thoughts. Excellent! But mathematics and physics ontologically unfounded science. (See Sukhotin "Philosophy of Mathematics"). You have not investigated the problem of the foundations of mathematics? Sincerely, Vladimir Rogozhin

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Very deep thoughts. Excellent! But mathematics and physics ontologically unfounded science. (See Sukhotin "Philosophy of Mathematics"). You have not investigated the problem of the foundations of mathematics? Sincerely, Vladimir Rogozhin

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Dear Vladimir,

Thank You. I suppose that human research tradition based on entangled co-existence of Mathematics and Physics has sufficient foundation and very long history.Practical wisdom or Philosophy of such sort of evolving bi- tradition is open problem,connected with foundations of mathematics,indeed.

However, we may await that any future X-ontology cannot change nature of human mathematics as well as nature of human physics.

Physics is Physics, and Mathematics is Mathematics.

Thank You. I suppose that human research tradition based on entangled co-existence of Mathematics and Physics has sufficient foundation and very long history.Practical wisdom or Philosophy of such sort of evolving bi- tradition is open problem,connected with foundations of mathematics,indeed.

However, we may await that any future X-ontology cannot change nature of human mathematics as well as nature of human physics.

Physics is Physics, and Mathematics is Mathematics.

Dear Michael,

I read your essay; the relation between physics and mathematics, especially at the foundational level, is a very interesting topic. Your essay raises some questions, though.

First a comment: on page 2, you wrote: "In Pure Mathematics real number may be regarded as the measure of a displacement." Actually, no. In pure mathematics, a real number is usually regarded as a...

view entire post

I read your essay; the relation between physics and mathematics, especially at the foundational level, is a very interesting topic. Your essay raises some questions, though.

First a comment: on page 2, you wrote: "In Pure Mathematics real number may be regarded as the measure of a displacement." Actually, no. In pure mathematics, a real number is usually regarded as a...

view entire post

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Dear Marcoen,

Thank You for questions.

1. Real numbers MAY Be regarded as the measure of a length, it May Be regarded as the mark of a point and it May be regarded as the measure of a displacement or change of position on the line ( complex numbers case ).

2.Indeed, each of real numbers can be represented in terms of a ( signed ) infinite dicimal expansion. However, when Einstein uses Pythagorean exactness in his statements in pure physics, we can make comparison with Pure Mathematics.36^2 + 8^2 + 3^2 = 37^2, but there is no such odd^2 + odd^2 + z^2 = s^2 even in nature. In order to represent the same idea in real numbers you simply must change the sense and a form of equation.

As is known, Pythagoras theorem is basic valid assumption of Relativity.

3.Idea of a new kind of complex number (inspired by Einstein's physics) was developed by R.Penrose in his theory of twistors.The basic twistor is four -complex - dimensional object of the type Z# = ( Z, Z',Z'',Z''') where Zs are four complex components.Following Penrose, the twistor co - ordinates Z,Z',Z'',Z''' together with their complex conjugates ( vectors) Z,Z',Z'',Z''' can be used in place of the usual Einstein x,y,z,t and their canonical conjugates. In fact, anything that can be written in normal Minkowsky spacetime can be written in the terms of twistors.

My comparison with pure math of complex numbers may suggest that it cannot satisfy pure mathematical justification of a new kind of complex numbers.Moreover,there is pure mathematical Pontrigain theorem on limited generalizations of complex numbers which could be used also as argument.

best regards, Michael

Thank You for questions.

1. Real numbers MAY Be regarded as the measure of a length, it May Be regarded as the mark of a point and it May be regarded as the measure of a displacement or change of position on the line ( complex numbers case ).

2.Indeed, each of real numbers can be represented in terms of a ( signed ) infinite dicimal expansion. However, when Einstein uses Pythagorean exactness in his statements in pure physics, we can make comparison with Pure Mathematics.36^2 + 8^2 + 3^2 = 37^2, but there is no such odd^2 + odd^2 + z^2 = s^2 even in nature. In order to represent the same idea in real numbers you simply must change the sense and a form of equation.

As is known, Pythagoras theorem is basic valid assumption of Relativity.

3.Idea of a new kind of complex number (inspired by Einstein's physics) was developed by R.Penrose in his theory of twistors.The basic twistor is four -complex - dimensional object of the type Z# = ( Z, Z',Z'',Z''') where Zs are four complex components.Following Penrose, the twistor co - ordinates Z,Z',Z'',Z''' together with their complex conjugates ( vectors) Z,Z',Z'',Z''' can be used in place of the usual Einstein x,y,z,t and their canonical conjugates. In fact, anything that can be written in normal Minkowsky spacetime can be written in the terms of twistors.

My comparison with pure math of complex numbers may suggest that it cannot satisfy pure mathematical justification of a new kind of complex numbers.Moreover,there is pure mathematical Pontrigain theorem on limited generalizations of complex numbers which could be used also as argument.

best regards, Michael

Dear

Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regards !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regards !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Dear Hoang,

If I understand your questions you try to connect Einstein's equivalentness ( of inertial and gravitational mass ) with Higgs boson by some kind of philosophical definitions. I suppose that mathematically speaking, however, there is some technical problem here, connected with "unknownness" of Higgs-like complex scalar algebra...?

" No fundamental scalar fields have been observed in nature..."?

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If I understand your questions you try to connect Einstein's equivalentness ( of inertial and gravitational mass ) with Higgs boson by some kind of philosophical definitions. I suppose that mathematically speaking, however, there is some technical problem here, connected with "unknownness" of Higgs-like complex scalar algebra...?

" No fundamental scalar fields have been observed in nature..."?

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Dear Popov

Thank for your feedback.

Perhaps it is the lack of Higg: why is " No fundamental scalar fields have been observed in nature..." ?

For your essay:

In my opinion: Mathematics is just a tool, it's a technical, it was born from the "logical inference" of us.

So it can not be "wrong", the assumption of Mathematics is the "logical inference" of who to use of mathematics, that is "conscious of Physics " of us.

Very happy to discuss with you.

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Thank for your feedback.

Perhaps it is the lack of Higg: why is " No fundamental scalar fields have been observed in nature..." ?

For your essay:

In my opinion: Mathematics is just a tool, it's a technical, it was born from the "logical inference" of us.

So it can not be "wrong", the assumption of Mathematics is the "logical inference" of who to use of mathematics, that is "conscious of Physics " of us.

Very happy to discuss with you.

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1. Higgs boson existence.

I suppose an existence of mathematical object ( called Higgs Boson ) as a consequence of

Conjecture( Goldstone - Higgs ( 1964 ))" Loretz - covariant field theories in which spontaneous breakdown of symmetry under an internal Lie group occurs contain zero-mass particle fields iff the conserved currents associated with the internal group are coupled to gauge fields ".

But, I cannot accept Higgs' simplification of true algebra of complex scalar in particle physics.Taking seriously.

2." Mathematics is just a tool".

I think, it is very popular and very naive error. Pure Mathematics is area of experimental science. Anybody can test that x^3 +y^3 = z^3 cannot exist in Nature( please test it, may be you can find counter-example,because following your assumption " numbers are merely abstractions","human subjectivity",etc) If math is "only language" you always can re-write such theorem in "suitable solvable" manner and you always can "find" solutions for any mathematical problem reduced to language paradox. Similar with Pythagoras theorem used by Einstein.If Math is just language,you always can re-write such sort of theorem for any numbers. But, without Pythagoras theorem Einstein theory cannot be formulated at all. Please test it.

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I suppose an existence of mathematical object ( called Higgs Boson ) as a consequence of

Conjecture( Goldstone - Higgs ( 1964 ))" Loretz - covariant field theories in which spontaneous breakdown of symmetry under an internal Lie group occurs contain zero-mass particle fields iff the conserved currents associated with the internal group are coupled to gauge fields ".

But, I cannot accept Higgs' simplification of true algebra of complex scalar in particle physics.Taking seriously.

2." Mathematics is just a tool".

I think, it is very popular and very naive error. Pure Mathematics is area of experimental science. Anybody can test that x^3 +y^3 = z^3 cannot exist in Nature( please test it, may be you can find counter-example,because following your assumption " numbers are merely abstractions","human subjectivity",etc) If math is "only language" you always can re-write such theorem in "suitable solvable" manner and you always can "find" solutions for any mathematical problem reduced to language paradox. Similar with Pythagoras theorem used by Einstein.If Math is just language,you always can re-write such sort of theorem for any numbers. But, without Pythagoras theorem Einstein theory cannot be formulated at all. Please test it.

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Thank you Popov

Very happy to be your answer, even though we do not have the same perspective.

I called the department of science do not need the ability to independent thinking or reasoning,and is a product born from a other scientific result is: a tool.

I agree with you about: "mathematical object ( called Higgs Boson ) as a consequence of Conjecture".

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Very happy to be your answer, even though we do not have the same perspective.

I called the department of science do not need the ability to independent thinking or reasoning,and is a product born from a other scientific result is: a tool.

I agree with you about: "mathematical object ( called Higgs Boson ) as a consequence of Conjecture".

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I agree with you about: "an existence of mathematical object (called Higgs Boson) as a consequence of Conjecture".

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Cao Hai,

Your statement "Mathematics is the "logical inference" of who to use of mathematics, that is "conscious of Physics " of us " is assuming that mathematics is something always and everwhere reducible to logical operations only due to logical axioms. However, if it is correct, we always can change logical system of axioms in order to prove that x^3 +y^3 = z^3 (I suggest that this consequence of Fermat theorem is impossible in any logical system of axioms as well as in Nature)because Nature has own mathematics and own "lovely" representations.It is easy to test in physical laboratory.

Generally,in contrast with popular philisophazing physics, Mathematics and Physics are different kinds of Experimental sciences used Computational and Physical experiments to understand Nature.

This means if you are physicist, it is natural to await that you can offer EXPERIMENT, but not philosophical hypothesis, in order to prove your version of the wrong physical assumption,indeed. Unfortunately, I am sorry, but I cannot find any manifestation of experimental physical thinking in the contest...

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Your statement "Mathematics is the "logical inference" of who to use of mathematics, that is "conscious of Physics " of us " is assuming that mathematics is something always and everwhere reducible to logical operations only due to logical axioms. However, if it is correct, we always can change logical system of axioms in order to prove that x^3 +y^3 = z^3 (I suggest that this consequence of Fermat theorem is impossible in any logical system of axioms as well as in Nature)because Nature has own mathematics and own "lovely" representations.It is easy to test in physical laboratory.

Generally,in contrast with popular philisophazing physics, Mathematics and Physics are different kinds of Experimental sciences used Computational and Physical experiments to understand Nature.

This means if you are physicist, it is natural to await that you can offer EXPERIMENT, but not philosophical hypothesis, in order to prove your version of the wrong physical assumption,indeed. Unfortunately, I am sorry, but I cannot find any manifestation of experimental physical thinking in the contest...

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Dear Michael,

An good Essay, where you raise interesting issues.

I am going to give you an high score.

Cheers,

Ch.

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An good Essay, where you raise interesting issues.

I am going to give you an high score.

Cheers,

Ch.

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Dear Michael,

As promised, I have just finished reading your essay! Quite interesting. A couple of thoughts:

1. It's certainly true (at least, in my opinion!) that not all mathematical constructs are useful or appropriate for describing physics, and it's also true that physicists have invented (or discovered, depending on your point of view) a lot of new mathematical ideas in an attempt to describe physics.

2. There are many connections between complex numbers and geometric ideas in spacetime physics (I see now that my answer to you over on my thread was mostly irrelevant to the point you were making). For example, special relativity in two dimensions can be described entirely in terms of complex numbers in the complex plane rather than two-dimensional Minkowski space.

As you point out, the fact that a minus sign appears in the last term of the expression describing the square of the relativistic displacement does associate an imaginary factor with the time variable.

In four-dimensional spacetime, there are also several other ways to think about complex numbers or generalizations of complex numbers. Quaternions, for instance, are generalization of the complex numbers in which there is one real unit 1 and three imaginary units i,j, and k, all of which are different but all of which have -1 as their square. Here is an article about expressing special relativity in terms of quaternions.

Another somewhat similar idea is Roger Penrose's twistor theory. In "twistor space," there are two plus signs and two minus signs rather than three plus signs and one minus sign as in Minkowski space.

Anyway, I thought you might find that interesting. Thanks for commenting on my thread. Take care,

Ben

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As promised, I have just finished reading your essay! Quite interesting. A couple of thoughts:

1. It's certainly true (at least, in my opinion!) that not all mathematical constructs are useful or appropriate for describing physics, and it's also true that physicists have invented (or discovered, depending on your point of view) a lot of new mathematical ideas in an attempt to describe physics.

2. There are many connections between complex numbers and geometric ideas in spacetime physics (I see now that my answer to you over on my thread was mostly irrelevant to the point you were making). For example, special relativity in two dimensions can be described entirely in terms of complex numbers in the complex plane rather than two-dimensional Minkowski space.

As you point out, the fact that a minus sign appears in the last term of the expression describing the square of the relativistic displacement does associate an imaginary factor with the time variable.

In four-dimensional spacetime, there are also several other ways to think about complex numbers or generalizations of complex numbers. Quaternions, for instance, are generalization of the complex numbers in which there is one real unit 1 and three imaginary units i,j, and k, all of which are different but all of which have -1 as their square. Here is an article about expressing special relativity in terms of quaternions.

Another somewhat similar idea is Roger Penrose's twistor theory. In "twistor space," there are two plus signs and two minus signs rather than three plus signs and one minus sign as in Minkowski space.

Anyway, I thought you might find that interesting. Thanks for commenting on my thread. Take care,

Ben

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If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is and was the quantity of people which gave you ratings. Then you have of points. After it anyone give you of points so you have of points and is the common quantity of the people which gave you ratings. At the same time you will have of points. From here, if you want to be R2 > R1 there must be: or or In other words if you want to increase rating of anyone you must give him more points then the participant`s rating was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

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Sergey Fedosin

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Sergei,

Thank You - I suspect a kind of web-sophistication in the form of non-cooperative game was also added.

Michael

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Thank You - I suspect a kind of web-sophistication in the form of non-cooperative game was also added.

Michael

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