Is a Mathematical Definition of Observation Possible? by Daniel Wagner Fonteles Alves

Hi Daniel,

I enjoyed your essay, your insight, and your acknowledgment of the challenges that lay ahead. Your recognition that GR and QM cannot (and will not) be united is correct, something is either missing in our tool kit, i.e. mathematics or our core theories are incorrect; I believe it to be a case of both.

As a graduate student in physics your approach is correct in looking and developing alternatives. You have your career in front of you and should now digest all that is available to you. Please remember that many physical theories are based on assumptions and depending on where an author of said assumption is ranked on the who-is-who list of physics, places that assumption as fact or fiction. Physics

Please study my very short essay, engage your supervisors and try and answer it - it may make a difference to your career.

All the best and good luck with the competition - Anton

Hi Daniel - the above post is by me - regards Antob

Dear Daniel,

Great approach to the subject. I like the idea of using the measurement problem and you've used this well. Also nice diagrams.

Perhaps you'd find some common ground with my essay, if you get a chance to read.

Best wishes for the contest!

Antony

Dear Daniel,

very interesting essay. I think our point of view is very similar (or as Pauli express it in a letter to Heisenberg: boring agreement).

Maybe you will also find my essay inetresting.

Her I describe a concrete (topological) realization of your idea.

All the best for you

and good luck for the contest

Torsten

Olà, Daniel,

I like your central point that one should define measurement in terms of Prof. William Lawvere's "semantic functor". I appreciate that the limitations of space kept your exposition of the semantic functor to a minimum, although I would have liked to see more of those details, perhaps at the expense of the mathematical details of the examples you presented at the beginning of the essay. Perhaps in this way it would have been clearer how this definition of observation could be applied to the measurement problem, that is, that the Hermitian operator associated with measurement is not unitary or, otherwise put, why the wave function seems to "collapse". Your examples in Section 3 concentrated on aspects of Newtonian and Einsteinian mechanics, which were of course good inspirations for the Category Theory approach, but I would have liked to see the idea applied more directly to the question you started with.

In any case, the essay flowed nicely, first pointing out the main problems to be solved, and then presented the start of a possible solution. Although Category Theory is occasionally used in physics, it would be nice to see a wider application, as you propose.

All the best with your exams Daniel - look forward to discussions next week!

Best wishes,

Antony

Hi Daniel

It is nice to read you again. You are presenting an excellent entry. The last year we have a discussion about absolute and relative issues. Now that I read your essay, I have some points that I'd like to discuss and clarify. I could notice some conceptions in your essay that reflect what I think are misunderstandings of the actual Newton's view about space, time and motion. So, I'd like to open a discussion about this.

You say: Positions, by their own definition, are always expressed in relation to something and the q_i(t) are expressed in relation to absolute space. But since absolute space cannot be observed, how could this theory be tested?

However, instead of creating a theory where only observable data (relative distances) appear, Einstein still used invisible coordinate systems by presupposing a spacetime manifold.

There are several issues I could see here. First we need to make clear one thing. Newton held that space was a substance and that celestial bodies were connected by a material medium (Descartes' ether). So, for Newton space was not emptiness as many people still believe. Newton had a similar vision of space as Descartes but he realized that Descartes' view was so complicated to model mathematically and so he decided get rid of the ether in his formulation of gravitation (non fingo hypothesis). In this sense, he left his theory with an empty space mathematically represented by Euclidean geometry. Euclidean geometry represents the notion of an EMPTY STATIC CONTAINER from which Newton distinguished two concepts: Absolute and relative. He was aware that for practical purposes, what we measure with our instruments are relative motions relative spaces and relatives times, but behind these relative quantities there was also true motion, true space and true time. So, contrary to what most people erroneously believe, Newton was also a relativist. Newtonian mechanics is relativistic, why? Because all spatial quantities are defined relative to a system of reference --the exception is of course time. Which is assume to be equal for all frames. There are an infinite set of frames of references, among these we can find space itself as the absolute frame (space as substance not as an empty container). This is truly relativism because Newtonian mechanics doesn't exclude the absolute system of reference as special relativity (SR) does. So, if you have understood this, then you should understand that the quantities q_i(t) are not measured relative to absolute space but relative to a system of reference. Now, the fact that absolute space cannot be observed doesn't mean that it doesn't exist. And this depends on what is our notion of space. For Newton space was the substance mediating between objects (in the contemporary view, we call it field). For this reason Newtons' notion of space is called among philosophers of science SUSTANCIALISM. A different conception was due to Leibniz. He held that the notion of place and position arise from the configuration of objects. According to him, space was no other thing that a mesh of relationships created by the relative position of bodies (objects embedded in what thing?). In philosophy this view is called relationalism. So relationalism and relativism are not the same thing. Newton was absolutist and at the same time relativist but not relationalist.

As far as can see, Mach, Barbour and you can be classified as relationalist, because you consider that what mediates between bodies is not space. Einstein tried to follow Mach and Leibniz but as you point out he only came up with another kind of INVISIBLE FLEXIBLE CONTAINER, i.e. a more complex version of Euclidean space (pseudo Riemannian manifold).

You: It is a strange coincidence the fact that it turns out that no physical process actually depends on absolute position and absolute velocity.

My argument to refute this is based on the measurement of the one-way speed of light (OWSL). Einstein proposed that the OWSL was isotropic in all frames of reference. However, we have realized that no experiment can measure it, experiments only measure the two-way speed of light. Despite this, it is necessary, for purposes of consistency, to assume in any theory that, in at least one frame of reference, the OWSL is isotropic. This means that despite that instruments don't measure OWSL we assume that the OWSL is isotropic. Thus, despite that we cannot measure absolute quantities we have to assume for purposes of consistency that object not only move relative to another object but also relative to the background of space (or vacuum). According to your arguments, you and Barbour reject space because you consider that it is superfluous and redundant. I agree that it can be superfluous but when you denied the absolute space we arrive at logical contradictions (such as the twin paradox in SR, please see Daryl Janzen essay for a deep discussion of this topic, perhaps you will realized how paradoxical SR is)

When you say that we have a configuration of particles I have to ask you: in what physical thing do you think those particles are embedded? What is the physical thing that mediates between those particles?

In relation to your formulation, you introduce a parameter of change called gamma. My question is: what is the physical meaning of gamma? In practice, how is this parameter measured? As far as I can see, this formulation is an attempt to get rid of the notion of time, but in this attempt you have to introduce a new parameter. In this sense, I only see an exchange of one parameter (t) for another (gamma).

Finally, I'd like to invite you to read my essay and leave some comments. There I discuss about Wheeler's dream and propose a potential way to get out of the present crisis in physics. I'll be looking forward to hearing any comments you may have.

Regards

Israel

Daniel,

I suggest we use Einstein and Wheeler etc's method. Visualise it fully first, and only then worry about the mathematics.

'Detection', 'channelling', 'processing' 'measurement' and 'observation' are indeed defined in detail including all EM interactions and implications. The orbital angular momentum of spin is the key, as is assigning the correct 'datum' frame for computing (processing) the output's 'speed' and 'frequency' from time and the state information of the modulated wavefunction (essentially wavelength lambda) channelled to the processor.

Now lets ignore commutativity etc, because this is where your principle concluding assumption comes in; That if something is invisible it 'does not exist'. Worth testing. But is it correct? or if not, irrelevant? If we study it I suggest we find 'NO' in both cases! But there is a 'save'.

Lets consider light propagating through another inertial system ('frame'). Is it visible? Of course not. The only light we can ever 'see' is light which has interacted with our own lens. So what do we 'see if we see a light pulse in a light box/clock, ot cloud chamber. If we see anything we see the light emitted by particles in the chamber. A different light!! Now envisage this; If we drive quickly past the chamber, does the apparent propagation speed change? Yes. Does the real propagations speed change. No!! It's just an optical illusion. Shocked?

So what about the light emitted BY the particles. That ALSO propagates at c of course, and when it meets our lens is re-scattered to c in the lens frame. So the lens (and channel) frame is the reference frame for computing speed and thus frequency.

And here is the 'save' for you. When computing frequency for Doppler shifts, if we use a poorly evolved processor we may mistakenly use the 'invisible' lights propagation rest frame (before it meets so is detected by the observers lens). Then we have the total confusion we have now.

But if we use the lambda/lambda formula for Doppler shift between media, as used in astronomy and optics but not in theoretical physics for some reason, then it can all make sense again.

But that also then requires some different assumptions to those that most use, not just you. But it's worth it as ALL can then make sense.

My essay should help explain this quite fundamental re-appraisal needed. Did you understand how the 'optical illusion' worked?

Hi Daniel

Thank you for your reply. I'm glad you had understood my main points. From your replies I could see that you are aware of the actual Newton's view and as you mention you are simply working out the relationalism approach because you think that this approach is more "economical" than Newton's. That's fine, it is nice to explore some roads.

You: Why should they be embedded somewhere? When we open our eyes and observe the universe directly, all we see are particle separations Rij. So why don´t we do physics with this information only?...

As I understood, your argument is that only objects are observable and therefore what mediates between them can be disregarded in the formulation. I wished you had answered my second question, and I'd like to insist on it: what is the physical thing that mediates between bodies? My questions were aimed at make you understand that particles are moving in a substance and are not contained by an empty container. Can you see the epistemological difference between "empty container" and "substance" (Newton's view of space is not to be conceived as an "ethereal container" because aether is a substance and it cannot be a container)?

You: So why don´t we do physics with this information only?...

Because if we reject this substance as the absolute frame of reference we arrive at logical inconsistencies. Theories should be internally consistent and free of paradoxes.

You: Why our mathematical descriptions should depart from the accesible empirical experience?

I gave you the example of the OWSL to make you understand that despite that we do not have experimental access to measure it, we have to assume that in least one system of reference the OWSL MUST BE isotropic. What we measure is actually the two-way speed of light (Nature seems to conspire against us, she doesn't allow us to measure the OWSL). In this sense, the second postulate of SR DEPARTS FROM EMPIRICAL EVIDENCE but despite this, the isotropy of the OWSL has to be ASSUMED because of LOGICAL CONSISTENCY in the theory. Do you get it? This is why an absolute frame has to be assumed to avoid falling into logical contradictions. It is not a matter of redundancy as you put it but of logic. The speed of light is defined relative to that ethereal substance where all bodies are embedded not relative to an "observable" body. Particles not only move relative to one another but also relative to this substance. The example of translation that you mention in your essay is naive because you argue that since the configuration is the same and there is no way of distinguishing one configuration from the other, the background of space is superfluous. No! It is not superfluous because there is something mediating among the bodies. That something is a substance. You may say, that thing is a field... yes, but what is a field made of? Imagine for a moment that we have two charges separated by a distance r. What thing mediates between the charges? The answer is an electrical field. What is the electrical field made of? Energy, matter...? So you have to admit that this field is static and that it can be considered as preferred frame of reference to judge the motion of the charges, do you agree? So, Newton's substance can be seen, in modern terms, as an all pervading field, and all particles are embedded in this field. Particles are the result of exciting this field, particles are in fact excitations of this field. I hope you have understood the distinction.

Finally, with respect to gamma, I see no difference since in your formulation you require a parameter denoting change and in Newton's theory t, plays this role with the same meaning.

Well, I wish I have clarified some points. I'll be looking forward to your comments.

Best Regards

Israel

With respect to the twin paradox (as other paradoxes) is indeed a topic that we should address in a separate post.

Hi Daniel,

Very nice! I have Israel Perez to thank for directing me here.

The question you raise in your title is *very* important, and truly fundamental. Bravo on the choice, and on your careful reasoning.

I like your treatment of the semantic functor, and I want to suggest something that in my opinion shows where Barbour errs in his program to rehabilitate Mach's principle for a complete physical theory:

As you show in fig. 4, the naturally non-commutative relation between process and semantically identical process terminates at y; i.e., all arrows orient on the output of process x ----> y such that the mathematical description alpha ----> Beta becomes part of the process input. In fact, this is exactly how the Hilbert space mathematics of quantum mechanics functions and which justifies the "shut up and calculate" school of thought.

Let's alter the map such that x

Dang it. I've never seen this glitch before. I wrote directly into the message box; I don't have a copy.

Since I took an hour or so to compose the message, I won't be able to recreate it as I'd like in my now limited time. I'll do my best to get the gist across:

Let's alter the map such that the arrow x ----> y is reversed. We then see that the ouput y accepts input through x, alpha, Beta and recursive to x. This illustrates the difference between a continuous measurement function that includes a time parameter and the discrete Hilbert space measure that does not. The map is also now identical to the real projective plane, RPP -- a nonorientable surface -- such that observer orientation alone assures both a noncommutative result and continuous input-output by the free will hypothesis.

Reversing the arrow x

Aha! I get it now. The system won't accept my arrow drawing, oriented to the left. Continuing:

Reversing the arrow (y to x) implies the independence of language and meaning (the theme of a paper I contributed to the Karl Popper Centenary in 2002), such that meaning is identical to neither the process of computation nor to the formal language (mathematics), and is solely identified with physical event.

All best wishes in the contest, Daniel!

Tom

Daniel,

If given the time and the wits to evaluate over 120 more entries, I have a month to try. My seemingly whimsical title, "It's good to be the king," is serious about our subject.

Jim