Discourse of the physicist

Aproveitando uma pequena parada na estrada Rio/ São Paulo, entre duas caipirinhas, para traduzir este artigo ("Le discours du physicien") em Inglês.

Discourse of the physicist

- I cannot decently leave my last two articles (i.e.:"Méta-physique" and "mesurer") to the drawing board, without making a kind of synthesis, if only for my own use, in order to mark my path.

- Okay, but fast, then.

- Don’t worry, we’ll just philosophize.

We could start from the fact that we have no particular sense to apprehend time in itself: it is a way to represent a cerebral process of classification of information in the cortex, via the hypocampus (see "Perception du temps") and note that the scientist only confirms this difference between:

• what can be perceived as the "observable" in Mecha Q, and
• how to label our observations, or "measurements", in an elemental, countable chronological order.

- There is, however, relativity that marries the two...

- Indeed and we have seen that in other civilizations, the question of space/time has not experienced the same developments. In Japan, for example, we start from a kind of common concept, which supports as much as it separates the elements of discourse, Ma 間, for, at the Meiji era, and precisely with the intention of "understanding" Western science, to derive from it, our notions of time 時 間 and space 空 間.

In short, I have come to the conclusion that for us, Westerners here and now, the physicist’s discourse is developed on three modes :

• The "objective" mode ♧
• The "relational" mode ♢
• The "syntactic" mode ♡

I keep these labels very vague, which are found in other fields of experience, so as not to freeze us too much at the risk of discussing endlessly limits, and forgetting the essential...

- We still need a little more detail.

- So let us stick to this pattern, which I suggest as an epistem:

♧ Mode : (☯[∃][⚤]𓁝⇅𓁜[#]𓁝⊥𓁜[♲]𓁝⇆𓁜[∅]☯) 𓂀^♧

It will be the one where the physicist situates the object of his discourse, which he shares largely with the mathematician. This is why I use the Categorical language without too much force to specify this:

• [∃] Level at which is the final object of the Set category : singleton (*)
• [⚤] Level of discrete and 1^st order logic etc...
  • Time is originally the jump from the Imaginary boundary ☯[∃] to its representation [∃]↑[⚤]. This is Galileo measuring time by counting the pulsations of his heart.
• [#] Geometry level, and the concept of orthogonality ⊥.
  • Time is represented as an orthogonal dimension to those of spaces.
  • The space/time correspondence derives from Newton’s 1^st law or Galileo’s law of inertia.
• [♲] Einstein’s space/time relativity level, with a conservation law concerning the velocity of an object: v̅.v= c².
• [∅] Initial object level. For philosophical reasons, I kept the Set category empty object ∅. (see "Qui a tué Platon")

I would see it as a physicist’s answer to the Kantian question of a priori conditions of knowledge.

- Except that scientific theories can be verified by experience...

- We will put a slight reservation on this beautiful scientistist enthusiasm when we get to the mode ♡. But let’s continue.

♢ mode: ([∃]𓁝⇅𓁜[⚤]𓁝⇅𓁜[#]𓁝⊥𓁜[♲]𓁝⇆𓁜[∅]☯) 𓂀^♢

Upon reflection, physics (beyond the kinematics of the point in space that can be brought back to pure mathematics) begins when one is interested in the interactions between objects, and in their relative movements.

- In other words Newton’s 2^nd and 3^rd laws, followed by Lagrange etc...

- Exactly. The whole question will be to make the link between this relational mode ♢, and the previous objective mode ♧. It is in this mode that the discourse of the physicist differs from a more general discourse of the mathematician. And this bifurcation between the two will be marked by a specific choice of final object. Thereafter, I’ll just talk about mechanics, because historically it all started there.

• [∃] The level at which the final object will be the momentum p⃗=mv⃗.
  • To the initial singleton (*), which we represented by a "point" graphically in space, we match a point mass;
  • We link space and time by speed: v=dx/dt.
  • The operation corresponds to what we do in mathematics by going from singleton in[∃]^♧ to monoid •⟲ of the category of Graphs in [∃]^♢;
• [⚤] Discrete level. I haven’t talked about it too much, but there is a whole branch of "applied maths" that physicists use, concerning probabilities, thermodynamics etc., which doesn’t necessarily require continuity;
• [#] Continuity level. This is the flagship level of classical mechanics, and we have seen that the Lagrange equation deals with the transition [#]^♢↓[#]^♧; (cf. : α or "Entendement de 3^e espèce")
• [♲] Energy level:
  • Here is located the principle from which "derives" the final concept of momentum in [∃]^♢;
  • E=mc² is associated with v̅.v= c², and in the transition [♲]^♢↓[♲]^♧ the mass is "forgotten";
  • Potential energy/kinetic : equivalence in [♲] and orthogonality in  [#]^♢;
• [∅] The level where the initial empty object  ∅  is the source of energy E, like of everything else...

♡ mode : ([∃]𓁝⇅𓁜[⚤]𓁝⇅𓁜[#]𓁝⊥𓁜[♲]𓁝⇆𓁜[∅]☯) 𓂀^♡

After being interested in the relationships between objects, we are now interested in the relationships between the Subject and the objects of his attention. It is here that the link between the Subject’s attention and intention is established. The best definition I can give of quantum mechanics is this:

It is the syntax of a discourse regarding the
measurement of the objects of our attention.

• [∃] The final object is the ih of the 2^nd Axiom of Quantum Mechanics or Schrödinger equation 
  ih∂/_∂tψ(r⃗,t)=Ĥψ(r⃗,t) or ihd/_dt|ψ(t)⟩=Ĥ|ψ(t)⟩ :
  • The discourse concerns a discrete "h" energy, when it pointed to the mass m in mode ♢;
  • The imaginary "i" indicates the direction of time, orthogonal to the 3 dimensions of space (i.e. : the temporal term ihd/_dt|ψ(t)⟩ is orthogonal to the spatial one Ĥ|ψ(t)⟩), when the speed v⃗ put them in relation in mode ♢;
  • It is also the switch between operators [x̂,p̂_x]= ih; connecting modes ♧ (i.e.: x̂) and ♢ (i.e.: p̂_x).
• [⚤] The space to describe quantum mechanics is C,
  • The "discrete" aspect of the measurement is that it can only be one of the eigenvalues of an observable  (3^rd Axiom of the Q meca).
  • An "object" is defined by a Complete Set of Commutent Observables (CSCO)
• [#] 1^st Mech Q Axiom : The space where:
  • The states of a system |ψ⟩ and
  • Actions  on the system
  • is a space of Hilbert E_H.
• [♲] This is the level at which discourse about equivalences and relations is set:
  • Expression of the operators Lagrangian L̂ , and Hamiltonian Ĥ;
  • Definition of the observable Â;
  • Measurement definition: ⟨ψ|Â|ψ⟩;
  • Expression of switches [Â,B̂] etc;
• [∅ ] level where we find as always our initial empty object ∅.

This gives more consistency to our general Imaginary map:

- But with a slight caveat, since we can go directly from ♡ to ♧...

- Indeed, we came to the conclusion that instead of a simple Moebius ribbon between the faces ♢ ♧ (the stage and backstage Alain Connes talks about), we had to link the 3 modes ♡ ♢ ♧ in this way:

Moebius 3 bands	cross section

Presentation that solves as many problems as it raises !

1/ The evidence:

1. By defining Meca Q as a syntax in ♡, it is quite easy to understand that classical mechanics, in ♢ , can be seen as a field of application of this syntax. This is the passage (...)𓂀^♡=>(...)𓂀^♢;
2. This allows us to understand the application of Meca Q to electricity as a passage of the same type, and should, without too much effort, serve as a framework for gauge theory;
3. The direct passage (...)𓂀^♡=>(...)𓂀^♧ leaves the field for observations in ♧ mode that would go beyond the framework of classical mechanics in ♢, typically, it would be the "spin".

2/ The aporia of the discourse:

The passage through an "encompassing" syntax to found the principles of physics that were elaborated prior to this formatting, brings us back to the discussion we have between "topos" and "sites" supporters. Without going back in detail on the subject (Note 1), we could perhaps situate here the difficulty of bringing together General Relativity and Quantum Mechanics.

- That is ambitious !

- You be the judge :

• The theory of relativity is above all an effort to reconcile space and time:
  • in [♲]^♧, with a "proper speed" v̅.v= c² which is the kept quantity;
  • in [#]^♧, in a curved Minkowski space;
  • The theory is situated in this zone of the Imaginary map: 

• Quantum mechanics postulates an absolute heterogeneity (or orthogonality) between space and time:
  • in  [∃]^♡ with "i" in ih as final object;
  • in [#]^♧ with a Hilbertian functional space (from where time is excluded);
  • The theory focuses "rather" in this area:

If you consider the overlapping areas, you fall back on the essential domain of expression of physics, namely levels [#]^♧ and [#]^♢, in green:

Where there is friction, if I may say so, precisely in the understanding of "time":

• Seen as a geometric "dimension" in relativity,
• Seen as simple variable of the discourse in Meca Q, not necessarily continuous. With a radical "orthogonality" to space, which makes it an "other" concept, exogenous.

I think that from this perspective, it is easier to organize our way of seeing the object and talking about it. After that, it is time to go back to reading Saunders Mac Lane !

- Not too soon !

Hari

Le 05/ 04/ 2023

PS : À la relecture de cette traduction, je m'aperçois avec horreur de ce que j'ai pu laisser passer, ce dont je m'excuse humblement : la caipirinha n'excuse pas tout !

Reminder

Note 1 :

See:

• The note  du 08/ 03 from Méta physique.
• 2eme-colloque-lysimaque-mathematique-et-psychanalyse-1-le-trois