LOST IN MATH... AND MEASUREMENTS by Israel Perez

Dear Israel,

I indeed meant that the actual density is not the same "thing" as its mathematical representation. In models of the density, the model is commonly only an approximation of the real density, due to all sorts of approximations that are necessary for being able to calculate a result. E.g. the exchange-correlation functional of an interacting many-particle system can only be approximated, e.g. by assuming the local density approximation, etc. So the model density is not even numerically identical with the actual density.

I only said this as I see this as being a problem in foundational physics. In general relativity there is a curved spacetime, but this is just a mathematical representation. And what is, in quantum field theory, the field PSI(x,y,z,t)? Why assume that this is a physical field? Historically, this field has only been created in order to describe experimental results.

Another question is what is meant with "exists". In what sense does the number 5 exist? I think it means that we have a formalized manner of using the symbol "5".

Israel

I have answered your post on my page.

Regards ________________ John-Erik

Israel

See my page

John-Erik

Yes, OK, "mind" is physical. And so are feelings.

But I meant: why assume that our mathematical representations exist "out there"?

See my page

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Dear Israel,

Thanks for this essay, whose main point cannot be stressed enough - indeed even Einstein did not appreciate it, especially in his later life. An interesting and polemical analysis in this direction is also contained in Sabine Hossenfelder's book Lost in Math. As you say, it is all about balancing physics, math and measurement, Newton understood this! Best wishes, Klaas Landsman

Dear Israel,

Your enjoyable essay makes a very good case for more ontological reasoning in physics, rather than just remaining lost in the maths wilderness, where we have been stuck for decades in many areas of physics.

My particular areas of interest are particle physics, time and the aether. By complete chance, back in 2002, I discovered a new preon theory, which I have named gimli theory. You quote Feynman "It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong." Gimli theory works and gives consistent outcomes that agree with experiment.

The point here is that a reductionist theory that works (agrees with experiments) can give new structural insights into the world of particles, and these insights can lead to a dismantling of much of the patchwork of quantum field theories of the Standard Model. Gimli theory is not based on heavy mathematics at all, yet it can provide many answers to big questions because of its ontology.

My grumble is that mainstream physics journals do not want any "maverick" theories challenging the status quo, unless put forward by a Nobel laureate, and even then it may still be difficult. New physics theories heavy in math tend to be only read by the few in the clique, and are often beyond the grasp of philosophers of physics.

You state that physical understanding is crucial to make headway; otherwise we might continue to be lost in math and measurements. I fully agree with you!

As my entry is my first ever FQXI essay, I tried to stick to examples of undecidability, computability and unpredictability, in my considerations of a TOE, although I do wander on to the philosophical time topic of presentism which I currently endorse.

I am currently reading your 2012 FQXI essay "The preferred system of Reference Reloaded" which is a brilliant essay. It is a pity that I have only just discovered FQXI, partially due to me working in almost total (physics) isolation for the last twenty years developing my 'structural' theories of space, time, aether and particles. The advantages of being a hermit (not visiting physics forums) is that you can keep ideas pure during development. Of course, one needs good reference material to work with from the start.

Good luck with your essay and 'may physical theoretical frameworks come into prominence'! (ie. may the force be with you)

Lockie Cresswell

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2 posts

Regards ________________ John-Erik

When I burn my fingers then I conclude that I have touched something external, yes.

Dear Israel,

I enjoyed reading your essay.

It does propose various claims with which I would tend to disagree but in any case they are well argued for.

I have some questions/ comments if I may:

-You said that "For if science is not about truth, then scientific activity becomes meaningless and in that case I should not be writing this essay". What if science is about unravelling "facets" of the truth rather than some absolute one way of looking at the world? Would that still make it meaningless?

- In your well-thought diverse examples to show that mathematics alone is not enough and ampliative principles from physics are necessary, I would more than agree with you.

But I thought that the way it was phrased was somehow unfair to the practice of mathematics. When solving an equation, an actual mathematician would ask in what space we are looking for the solutions. In the case of the degree 2 polynomial equation for the radius of a quantum dot, physics compels us to search for solutions in the set of positive real numbers. With regards to the particle in a box problem, I would argue the same. Although I totally agree with the main message, the mathematics problem that should be posed is that we are looking for a wave function psi(x) that satisfies the time-independent Schrodinger equation, hard boundary conditions at the walls and is normalised. If one chooses n=0, the last condition is not fulfilled since the wave function is identically zero everywhere. It is not that we decide to discard it for the sake of it, it just not satisfies the properties of a wave function.

- Of course we can also come back to the while discussion on relativity of motion later on :) .

I would be happy to know your thoughts on the questions/comments above.

Best,

Fabien

Dear Israel,

Absolutely agree with "If science were not about true knowledge, it would be useless." Only several hours ago I had to address this same issue on my blog:

... such misconceptions are often caused by inadequate views on the nature of physical theories (e.g. one can hear "theories are just descriptions"). Perhaps, the saddest example of how such inadequate views can prevent even great scientists from making a discovery is Poincaré's failure to discover the spacetime structure of the world. He believed that our physical theories are only convenient descriptions of the world and therefore it is really a matter of convenience and our choice which theory we would use. As T. Damour stressed it, it was

"the sterility of Poincaré's scientific philosophy: complete and utter "conventionality" ... which stopped him from taking seriously, and developing as a physicist, the space-time structure which he was the first to discover."

Best wishes,

Vesselin

Dear Israel Perez,

I enjoyed reading your essay.

Your discussion of negative solutions was very thought provoking. I think it is worth pointing out that sometimes negative solutions should not be dismissed and

do have significant physical meaning. Dirac's finding of the positron comes to mind.

I wonder if all fake negative solutions would go away if we dealt with the right mathematics. For example, we always thing of the whole set of real numbers. Maybe we should do mathematics only with positive real numbers. We always deal with groups. Maybe we should deal with the less familiar monoids.

I also enjoyed you stressing the importance of understanding. I once humorously pointed out to my thesis advisor, Alex Heller, that

there are subatomic particles in nature that follow equations of motion

that human beings cannot solve. And even though humans do not know

where the particles will go, the particles seem to know exactly where to

go. Professor Heller responded by saying that this shows that science has

nothing to do with calculating or predicting. Calculations can be done by

computers. Predictions can be performed by subatomic particles. Science

is about understanding -- an ability only human beings possess.

Again, thanks for a great essay.

All the best,

Noson Yanofsky

Dear Izrael,

Your essay is very interesting. I completely agree with you that physical understanding is very important and in my essay I try to prove it on concrete examples. One mathematical model can have several interpretations and one physical phenomenon can be described by different mathematical models. The force of physics is in the possibility to combine different methods of cognition in order to find the correct solution. Without experiments and math physics is philosophy as it was at the very beginning. But without physical understanding and experimental confirmations physics can turn into mathematical philosophy.

I wish you good luck

Boris

Greetings Israel Perez

To respond to your last paragraph: "... that mathematical beauty is not enough to tell the whole story, and to achieve a solid knowledge we should work out a physical understanding. The history of physics has shown that physical understanding is crucial to make headway in this field; otherwise we might continue lost in math and measurements."

I must submit that math can and does obstruct -

especially when that math describes things not observed in real life that becomes the basis of physics - as in de Sitter's expanding space - Friedman's creation of the world from nothing - and Lemaître notation - "If the world has begun with a single quantum..." these all obscure applicable common 3D physics hiding the physics of the Big Bang.

It is proposed that any evidence describing the Big Bang is beyond science's reach and yet this essay of mine entered January 18th Common 3D Physics Depicts Universe Emerging From Chaos presents a plausible explanation with plenty of current replicable evidence describing 'Reality.' Check it out.

Regards

Charles Sven

Dear Israel,

Your essay is very interesting and well written. The relation of mathematics and physics is a fundamental issue. Tegmark is championing radical thesis that physics is mathematics. This of course sounds like a metaphysical belief but the "unreasonable effectiveness of mathematics" when applied to physics can not be just brushed away. Thinking along these lines I developed approach in which uncomputability is foundational, Theory of Everything has to be founded on it but in a very peculiar way. This is sketched in my essay.

Best regards,

Irek

Lovely Essay,

Checkout the long form version of my essay where I too compare the human brain to a supercomputer that is actively processing information about the physical universe

Please take a look at my essay A grand Introduction to Darwinian mechanic

https://fqxi.org/community/forum/topic/3549

Dear Israel,

what a refreshing essay. I usually do not consider to read an all-caps-title-essay, (Why did you do that?), but I'm glad I did. I think, I knew your name from your arxiv article on the physicist's view of the universe.

I like your approach to physics. As fascinating some of more modern information theoretic approaches to quantum foundations are, I miss the physics sometimes. It is so different to read the 'old ones' on foundational questions.

I have a few questions though. Where did Landau and Lifshitz exclude inertial frames? Didn't they just say, that between the inertial frames non is preferred?

Regarding the rotational motion, I did not know, that statement (2) is accepted as false by most physicist. How and when did this change come? I somehow missed that.

In my own investigations on time dependent symmetries (within quantum mechanics), I asked myself why does the translation symmetry remain a symmetry, if we make it time dependent and the rotational not. The answer I found was basically: For rotational symmetry to hold on subsystems the environment must be isotropic. Introducing a global time dependent rotation introduces a direction in the environment and hence breaks the isotropy. Group theoretical arguments where enough to show this.

In my own essay symmetry plays a prominent role and the question under which conditions measurements are well defined and so also concepts of the laws or properties of objects or systems. It would be a pleasure if you would find the time to read and give your opinion on my essay.

Best regards,

Luca

Dear Israel,

How interesting!

What would you say about situations where exactly the same maths describes two completely different physical interpretations? Would this not support your assertion that it's not just about the maths?

You may be interested in a couple of things that I have discovered and that are discussed in my essay.

First, if you imagine a world where all change travels at the same speed in an absolute space, then, clearly, that world would not be relative. However, it turns out that a clock that moves around in such a world will slow down, contract along it's direction of motion, and increase in mass, all in accordance with the equations of Special Relativity. The maths can, therefore, apply to both an absolute and a relative world.

Second, it is possible to use the maths of quantum electrodynamics (a quantum theory about photons and electrons) to describe a Universe made of just quantity, direction and change, and where photons and electrons don't actually exist at all. The maths, therefore applies both to a world with electrons and photons, and a world without them.

All the very best,

David

Dear Dr. Perez,

I enjoyed reading your essay, which argues that physical understanding (which is perhaps better known as physical intuition) may provide a better guide to promoting progress in physics than either abstract mathematics or experimental measurements.

I agree. I would take this argument a bit further, pointing out the importance of confirmation bias in the design and interpretation of complex experiments. We should not be trying to prove that a given theory is correct; rather, we should design experiments that could prove the theory incorrect.

In my own essay, "The Uncertain Future of Physics and Computing", I point out that the developing technology of quantum computing provides the first significant application of quantum entanglement, and therefore provides a major test of quantum foundations. But the experimental measurements thus far in quantum computing have been designed to confirm the orthodox theory, not to test it.

I predict that the entire technology of quantum computing will fail catastrophically within a few years. This may provide an opportunity for a reexamination of the foundations of quantum mechanics.

Alan Kadin

Dear Israel,

Thanks for your explanation. But does not Galilean relativity follow from Newtons law? Hence from the laws no absolute frame can be singled out. This does means, that Newton uses concepts and explanation, that go beyond, what the laws can express. But then how can these concepts like absolute space be defined and be understood.

Don't get me wrong. I can understand, that a theory might contain more, than just the formal language. There might also be the need of a meta language of how to apply the formal language. Sometime I am just puzzle how we can get an understanding of this language.

Luca

Dear Israel,

Thank you for your comments placed in my thread, they are valuable as I can see from them where my arguments should be clarified and sharpened to make them clear. I am replying here to reach you easier.

You write "I also support the view that we should develop a physical understanding to have a complete view of reality." This of course is fundamental issue. Position of the majority of physicists (put eloquently by Hossenfelder) is that there is physical reality which is something different or beyond math. It stems from long tradition of seeing physics as concerned with 'material' and also from our perception of the world in which reality bites but mathematical abstractions can not bite. Problems with this position is that mathematics is so 'unreasonably effective' and getting ever more abstract for the description of reality confirmed in experiments that this can not be treated anymore as a coincidence or invention of human mind.

I am not fully convinced about your examples for the argument how physical understanding have to be put on top of the mathematical one. The problem as I see it is that models and mathematics used in these case might be too simplified. For your example of the wave number of electron. It obviously assumes that electron is a wave but is it really? According to quantum field theory electron is field excitation and there are creation and anihilation operators, quantum vacuum, and so on. Thus there might be mathematics in the QFT which eliminates the need for such physical understanding. It would thus be enlightening to ask experts in the sizable area of 'Electron in QFT' what they think about this.

In general it be could that the need for any physical understanding is due to limited math models we have and not that math is just an imperfect tool for physics. It could then also be that any time we need the 'physical understanding' it points that underlying math theory is simply incomplete and insufficient.

That leads to the issue of relation of mathematics and physics which is the topic in my essay. The argument of Tegmark is rather thin, assuming all math structures exist. In my essay I am trying to derive arguments that the fundamental structure have to be uncomputable sequences which are intrinsically tied with nothingness. Symmetry requires then that infinite permutations groups have to act on these sequences and this gives rise to emerging mathematical structures, physics is one of them. From this, support for the Tegmark claim that all math structures 'exist' comes with addition that this will be very intermittent structures, just appearing and disappearing due to the action of permutation groups. Physics from this point will be exceptional in the sense of created by rare special group whose symmetry will be dissolving in a huge number of actions. Also from my elaborations it results what is the relation of infinities and real numbers to physics. Infinity is appearing only in the uncomputable substrate from which physics emerge, there is no need for infinity in the physics itself and real numbers are only emerging as apparent but they both are done there in the substrate. I have to prepare expanded version of the essay to make all this clear, there was too much compression and only now I am getting valuable comments.

Br,

Irek