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  • Post #41

The new formalism suggests that any object has to be approached in light of its *generative* structure, i.e. in light of the event structure associated with its generation. So from that point of view, the meter stick has not appeared suddenly out of nowhere, but has some 'formative' history that can be associated with it. To simplify things, the generative structure we associate with it is the same as specified by the Peano axioms for natural numbers (after all, how else can you approach the meter stick?) .

In this case, although the event *structure* is the same, their spatial instantiations (for the two observers) could be different.

Lev,

Concerning your surprising question:

"Who said that “the meter stick constitutes a class of simultaneous events”?

I think you yourself can answer it by trying to give a definition of a spatially extended 3D object (even in pre-relativistic physics) when its existence in time is taken into account. Or you can recognize this definition, which is almost explicitly used in any textbook on special relativity when length contraction is derived by employing the Lorentz transformations.

I would suggest that you first state clearly what is the dimensionality of the world according to relativity and of the meter stick. Statements like "the meter stick has not appeared suddenly out of nowhere, but has some ‘formative’ history that can be associated with it" mean nothing, if the most relevant question is not answered. When you address that question you will realize that you have been placing new and confusing labels on well-established concepts:

"although the event *structure* is the same, their spatial instantiations (for the two observers) could be different."

Just compare:

"Although the worldtube of the meter stick is the same, the instantaneous spaces of the observers A and B intersect the worldtube at different places and A and B regard the two resulting 3D cross-sections of the worldtube as their 3D meter sticks."

I hope you now see that your statement above makes no sense in a 3D world. I would like to ask you to analyze this point carefully before replying.

From your essay and what you have just written I have the feeling that you have been doing one of the things I wanted to warn the younger generation of physicists not to do - overestimation of the predictive power of mathematics in physics. Any effort to find a novel approach deserves compliments and should be regarded as a brilliant endeavor. But two things should be constantly kept in mind - (i) a physical model comes first, and (ii) mathematics should not be confused with physics.

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  • Post #43

Dear Vesselin,

I can see now clearly that we will not be able to progress in our discussion (as I actually anticipated in my post of Oct 8.), since you are constantly referring to "well-established concepts" and some orthodox views as representing patent on 'reality'. (By the way, I don't believe that physics has a satisfactory "definition of a spatially extended 3D object".)

As to your last statement:

"But two things should be constantly kept in mind - (i) a physical model comes first, and (ii) mathematics should not be confused with physics."

I can only say (together with almost all greatest physicists) that one should not separate completely the physics from the formal language it relies on, since the latter becomes an integral part of physics. In addition, as Leonardo da Vinci suggested, "Theory is the general; experiments are the soldiers."

It also appears to me that what you prefer to call "physical models" are those closer to a mechanistic view of realty.

Finally, I just want to mention that I suggested to you to view the meter stick and observer A and the meter stick and observer B as two pairs of interacting processes, where each process should is viewed as comprised of a stream of events, which appears to me to be a reasonable candidate for a "physical model".

Best wishes,

--Lev

Dear Lev,

If you travel west in Canada and happen to stop in Montreal, we could meet and continue this discussion since we appear to have drastically different views on how one should do physics (of course, the ultimate proof of whose view is the correct one is what each of us will achieve in science).

I should tell you, however, that I will friendly not allow you:

(i) to continue to avoid answering the central question in this discussion - what is the dimensionality of the world according to relativity;

(ii) to make claims based on not proper reading of what we discuss - e.g. what you wrote: "what you prefer to call “physical models” are those closer to a mechanistic view of realty" (which is not true at all).

And I will be also glad to discuss in detail what you "say (together with almost all greatest physicists) that one should not separate completely the physics from the formal language it relies on". Statements like this might be used to justify attempts to present mathematical theories of unproven physical hypotheses as physics, especially if one thinks that the theory is more important than the experiment.

Best wishes and hope to see you in Montreal,

Vesselin

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  • Post #45

Vesselin,

Alright, since this is also the main thrust of your and many other essays, I will take up your suggestion to discuss the relationship between physics and its formal language (that will also address your (ii) ).

Let me begin by asking you: How do you separate physics from the formal language it uses? Please give me one 'purely physical' fact separated from all the 'formalities'.

4 days later

Dear Lev,

I agreed with you that on this forum we could not resolve the differences between the two main existing views on the role of mathematics in physics. But since that issue is of extreme importance for the advancement of physics I proposed to continue the discussion if you come to Montreal (given the fact that you live in Canada).

That is why I do not understand why you wrote "I will take up your suggestion to discuss..." The other thing I do not understand is how you could ask me a question, whereas you have been repeatedly refusing to answer a question I asked - a question that would have helped you realize that your claim "time is not a dimension" contradicts the experiments, which confirmed the kinematic relativistic effects.

Despite that I will answer your question by giving you one of the examples I discuss in a course I teach (and that will be my last post on this issue). Since we already mentioned it, take for instance length contraction - mathematics is the same but physics is different. There are at least two possible physical interpretations - the widely accepted Minkowski's explanation or the still alive deformation explanation (the initial Lorentz-FitzGerald contraction); next month in Paris there will be a talk on the second interpretation.

Let me put it another way - you measure (experimentally) length contraction (as in the muon experiment in the muon reference frame) and some claim that this experimental fact could have two different physical interpretations described by the same mathematics.

Best wishes,

Vesselin

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  • Post #47

Dear Vesselin Petkov,

Lev Goldfarb pointed us to the Ontology of Spacetime and in particular your contribution "Is There an Alternative to the Block Universe?

I appreciate you giving a lot of historical background: St. Augustinus already understood that there is no present between past and future. Presentism goes back at least to Aristotele who considered the world only real at the very moment. Let me ask why and what did he, what do we mean with real or existent?

If I am looking back, then I am looking at definitely existing influences only from the past, the closer the more relevant. Mostly it does not matter much if my temporal distance is a little bit shifted.

Likewise a plan of mine for next year is uncertain rather independently from the exact datum right now. It is a question of reasonable fuzziness if I say I am just doing something instead of nonsensically strict speaking "I will continue to do so within the next nanosecond".

Time is often seen as related to the natural numbers. This was surprising to me because every natural number is positive. Do all natural numbers exist?

While it is unlikely that someone else already wrote the following number

63812048449901753396ß255010733067ß43356854256798425674586727586724357982,

I do not follow Dedekind who claimed having created a new number. To me any natural number is just a stop of Archimede's endless procedure n

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  • Post #48

Vesselin,

My apology, I misunderstood you when you suggested

And I will be also glad to discuss in detail what you "say (together with almost all greatest physicists) that one should not separate completely the physics from the formal language it relies on".

However, you missed the main point: I have not at all refused to answer the question you asked. (I am assuming that you are referring to your "(ii) what is the dimensionality of the world according to relativity").

Please note that this question fits well within the issue I have pointed out. First, the very concept of dimensionality is not a physical but mathematical concept. Second, when I suggested that time is not a dimension, the proper way to understand this statement is through its formal content (again, dimension is a mathematical concept!).

Third, I believe that *fundamentally different* 'physical' interpretation can arise only when the existing formalism is not adequate.

Once more, there are hardly any physical concepts that we understand, and recognizing that, modern physicists have openly adopted funny terminology (e.g. quarks, color, etc.). Moreover, practically all classical physical concepts are of 'mechanistic' origin, including mass, energy, etc. I am actually surprised that you seem to be unaware of the fact that during the last century we have learned that spoken languages, including physical terminology, cannot deal adequately with the 'physical reality' (without heavy reliance on the formal concepts).

Again, best wishes,

--Lev

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  • Post #49

By the way, I'm not denying the role of 'physical' intuition, but even that is not separated from some formal content.

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  • Post #50

Sorry for my mistake:

I forgot that the larger or smaller sign is not tolerated here. So possibly an important idea of me got lost.

Let me try, recall and continue: ... n results from m+1. While Cantor's naive set theory has been based on a firm set or "block" of "all" natural numbers, I cannot confirm any necessity to assume a largest natural number. The natural numbers cannot be completely set but they are to be considered endless. One can biject the numbers 1,2,3,... to the numbers 2,3,4,...

Incidentally, Cantor ignored this impossibility to freeze the natural numbers in his proofs, in particular in DA2.

Laymen understand, as already did Spinoza, that the pseudo-quality "infinity" can neither be enlarged nor exhausted. Nonetheless, it is often reasonable to use "infinity" like a block.

What about countability, I argue, any set of natural numbers is countable but "the" set of "all" natural numbers is something qualitatively quite different and uncountable.

The block universe is imagined to extend in space from - infinity to + infinity in three orthogonal directions. Isn't this a considerable enlargement when compared to the just positive natural numbers? If one considers space with respect to a point belonging to a particular object, then one can use the always positive distance to all other points of space.

Such individualized space might be considered like a block that is open-ended.

I could agree that there are two likewise unilaterally infinite "blocks" of time: Past time and future time.

Would such consideration contradict

a) Einstein 1905

b) Minkowski 1908

c) neither E nor M?

Regards,

Eckard

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  • Post #51

Dear Lev Goldfarb,

I am not sure whether or not the notion dimension is only a mathematical concept if mathematics is understood as did Hilbert who supported Cantor's paradise.

Georg Cantor came to the same silly result as already Albert of Saxony (1316-1390). He wrote: "Je le vois, mais je ne le crois pas" (I see it, however I cannot believe it).

Concerning Vesselin Petkov's argumentation, I dislike that he concludes that 4D must be correct because otherwise the theory of relativity was wrong. I would prefer always concluding the other way round. Petkov reminds me of Palmstroem who concluded that his dead was an illusion.

Regards,

Eckard

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  • Post #52

Eckard,

It's interesting: actually it was within mathematics that measurement business started several thousand years ago, and so math was there before physics. ;-)

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  • Post #53

Eckard,

You say:

"I am not sure whether or not the notion dimension is only a mathematical concept".

What could possibly be the 'physical' concept of dimension?

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  • Post #54

I forgot to add my name to the previous post.

5 days later

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  • Post #55

Dear Lev,

Ancient mathematics arose from applications. Geometry was related to engineering and strictly separated from profane use of numbers for administration. Aristoteles (384-322) added metaphysics including the notion infinity after (meta) physics.

I do not know who introduced the notion dimension (lat. dimensio = measurement; extension). I just read papers by G. Cantor who obviously referred to the traditional three dimensions of space.

The worrying diversity of mathematical dimensions were fabricated later.

According to current opinion among physicists, the question 3D or 4D relates to whether or not one is ready to accept silly consequences of anticipatory physics. Common sense tells us that fatalisms is bad.

Regards,

Eckard

2 months later
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