Abstract
The importance of language in physics has gained emphasis in recent times, on the one hand through Hilbert’s views that concern formalism and intuition applied for outer inquiry, and on the other hand through Brouwer’s point of view that concerns intuition applied for inner inquiry or, as I call, self-inquiry. It is to demonstrate the essence of such investigations, especially self-inquiry (inward intuition), I find it compelling to report that a careful analysis of Cauchy’s statements for the definition of derivative, as applied in physics, unveils the connection to the Heisenberg uncertainty principle as a condition for the failure of classical mechanics. Such logico-linguistic, or semantically driven, self-inquiry of physics can provide new insights to physicists in the pursuit of truth and reality, for example, in the context of Schroedinger equation. I point out an explicit dilemma that plagues the semantics of physics, as far as general relativity and quantum mechanics are concerned, which needs to be taken into account during any attempt to pen down a theory of “quantum gravity”.
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Notes
The words “inner inquiry” was used by Brouwer only once as far as I could find in the literature and that also without any specific demonstration or any further explication. I have referred to Brouwer’s works for citation purpose and only to point out that the role of intuition had been investigated earlier. However, as far as my understanding is concerned, this work has nothing to do with the literature related to intuitionistic mathematics.
The first axiom of geometry, as stated by Euclid (see p 153 of ref. [20]), reads as follows: “A point is that which has no part.”
In view of Kant’s statement I would like to emphasize that the word “intuition”, in this present discussion, must be taken as a substitute for “human intellect” which Brouwer wrote too in ref. [17]. The present discussion has a priori nothing to do with the specific literature associated with intuitionistic mathematics and intuitionistic logic.
An exception is ref. [10] which deals with self-inquiry that concerns logico-linguistic or semantic issues associate with the foundations of physics.
One can alternatively use the adjective “semantic” instead of “logico-linguistic” in the present context. However, I prefer “logico-linguistic” over “semantic” because the former coveys the meaning more explicitly. That is, the former is semantically simpler than the later.
One may possibly object to the use of c in the context of “non-relativistic” quantum mechanics. To refute such a possible objection I may assert that the measurement of c has nothing to do with the theories of relativity or quantum mechanics – it is an experimental fact. Now, according to EPR’s condition of completeness of a theory, every element of physical reality must have a counterpart in a physical theory and any physical quantity measured with certainty without disturbing the system (which is light) has a corresponding element in physical reality [25]. Therefore, if Schroedinger’s equations are believed to be the foundations of a physical theory, it is through EPR’s arguments that the involvement c is justified. Further, the expression “E = mc2” which I have used in (14) is just constructed through dimensional analysis.
This “slight modification” is the consideration of the word “mass” alongside the word “point” to form the word “point-mass”. Certainly a question can be raised whether such a modification is slight or not because, semantically, this modification leads to a contradiction. However, then it becomes a question regarding what one means by the word “mass” which can give rise to endless debates. When such debates arise regarding any theoretical aspect, then the experimental implementation of the debatable ideas lead to the settlement i.e. what becomes of importance is how we implement an idea or become operational with it. Certainly when experiment comes into question, then there is no place for debate that the words “point-mass” can be considered to be justified because we do perform experiments whose data are interpreted in terms of equations which have been written down based on the words “point-mass” and not just the word “point”.
Of course, here I have considered classical logic.
I may clarify here that red-shift and time delay experiments both are founded on the same equation. The interpretations are different. What I have questioned here is the theoretical explanation that we give to energy propagation along a single null geodesic. The word “energy” is important here because it is to explain this particular term, we need its relation to frequency. This is related to the quality of the light signal i.e. we are worried about the colour of the light signal. When we explain the gravitational time delay, we are not worried about the colour of the signal, but the time delay between emission and reception of the signal i.e. we only care about the quantity that we call “signal”. However, the light signal is always associated with some colour i.e. we can not completely isolate quality and quantity which a fact of the reality of our experience. It is only to interpret the qualitative aspect that we need the involvement of h, and hence quantum theory, within general relativity. Therefore, the logical clash arises when we try to look at the qualitative aspect of light propagation.
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Acknowledgments
The author is grateful to B. Juarez Aubry for offering critical remarks on an earlier version of this work.
Funding
This work has been supported by the Department of Science and Technology of the Government of India through the INSPIRE Faculty Fellowship, Grant no.- IFA18-PH208.
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Majhi, A. Cauchy’s Logico-Linguistic Slip, the Heisenberg Uncertainty Principle and a Semantic Dilemma Concerning “Quantum Gravity”. Int J Theor Phys 61, 55 (2022). https://doi.org/10.1007/s10773-022-05051-8
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DOI: https://doi.org/10.1007/s10773-022-05051-8