LOST IN MATH... AND MEASUREMENTS by Israel Perez

Noson Yanofsky

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

Israel Perez

Dear Noson

Thanks for reading my essay and leaving some comments. Indeed, I also mention Dirac in my essay in relation to antimatter and the negative solutions. My work stresses that physical understanding is very important. Unfortunately, in the last decades we have not worked much this understanding and instead we are betting on mathematical description. Thanks for sharing your story with your advisor, indeed, calculations are just a matter of quantifying.

Best Regards

Boris Egorov

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

Israel Perez

Dear Boris

Thank you for your comments. You say it very nice. Without understanding, it is pure mathematical philosophy. I will be looking forward to seeing your entry.

All the best

André Martins

Dear Izrael,

Interesting essay. The message mathematics is an amazingly useful tool but that we do need to talk about the real world is an important one. Indeed, claiming the universe is made of mathematics is pure untestable metaphysics, a claim quite beyond our abilities. At the very least, our current ones.

Best,

André

Israel Perez

Dear André

Thanks for your post and for reading my essay. Mathematical representation of physics can give us quantitative answers but poor qualitative ones. Certainly, we have to walk on solid ground when developing a theory.

Best Regards

Israel Perez

Dear Vesselin

Thanks for your comment. The etymology of the word science says it all: science=knowledge. But not any kind of knowledge but true knowledge, knowledge that can lead us understand as much as possible how the world works. We may deal with approaches to the truth and in that sense it might be convenient to use one or the other, however, the final goal of a scientist is to gain true knowledge that can be useful to tell reality from fiction.

Best Regards

Charles Sven

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

Israel Perez

Dear Charles

Thanks for reading my essay and commenting. My essay is about finding an equilibrium between our physical understanding and mathematical objects. In this work, I discuss a couple of instances where physical understanding sees things that math doesn't. However, the opposite is also true. Mathematical symmetry has predicted physical reality that our physical understanding was not able to foresee, for this reason both aspects are important. I will try to find some spare time to read your essay and leave some comments. Thanks again.

Best regards

Israel

Irek Defee

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

Israel Perez

Dear Irek

Thanks for your comments and reading my essay. For me metaphysics is an old term to describe aspects that are beyond the physical realm. But, accepting the existence of metaphysical entities implies the acceptance of a metaphysical world. I therefore, deny the existence of metaphysical entities along with that world, I only accept a physical world and ideas or abstractions as part of this world, after all, the process of thinking is also a physical process that demands energy consumption. So mathematics as a way our brain has for representing the world is quite acceptable. I guess, the success of applying math to physics comes from this physical essence. I will do my best to try to find some spare time to read your essay which sounds interesting.

Regards

Israel

Irek Defee

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

Kwame Bennett

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

Israel Perez

Dear Kwame

Thanks for reading my work. It would be interesting to read your essay. Please be patient, these days I have been quite busy with my academic activities, I'll do my best to read your work.

Good luck in the contest!

Israel

Luca Valeri

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

Israel Perez

Dear Luca,

Thanks a lot for reading my essay and leaving some comments. I am glad you like my essay. I am sorry I could not reply before, but I am overwhelm with my academic activities. The article from arxiv was published about 10 years ago, when I was still a graduate student. Some things have changed since then.

As for your first question the answer is: In their quote they are clearly excluding the absolute frame of reference which is also inertial. As for the second question the answer is: no! They say that Galilean relativity implies that there is no absolute frame of reference that should be preferred to other frames. In other words, they are denying absolute motion and embracing only relative motion as real phenomenon. This clearly contradicts Newton's theory. When we remove the absolute frame, there is no absolute motion; all motion becomes relative in the same sense of special relativity. But relativism is not the hearth of Newton's theory for this relies in absolute motion, absolute time, and absolute position. They are absolute because it is assumed that there is an absolute frame. It seems that many people do not see this distinction.

As for the third question: Since Galileo we know that the Earth rotates absolutely. Newton understood very well the distinction between absolute and relative motion. No physicist thinks that the universe rotates, for as we learned from Newton, we understand that the apparent motion of the stars in a day is due to the absolute rotation of the Earth.

I hope I have clarified your doubts, in any case please let me know. I will do my best to read your essay and comment on it.

Best Regards

Israel

Luca Valeri

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

Israel Perez

Dear Luca

Indeed, Galilean relativity is just a theorem derived from the laws. Newton was aware that absolute motion cannot be distinguished from relative one in inertial frames (this means that as long as we stay in inertial frames one cannot single out absolute motion, this is Galilean relativity). However, he claimed that it is possible to distinguish absolute motion from relative one by forces and accelerations. For this he envisioned the famous bucket experiment and some others. See Steven Weinberg discussion.

Cheers

Israel

David Jewson

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

Israel Perez

Dear David

I am happy you liked my essay, thanks for leaving some comments. As for your question, that situation has happened in the past with the helicentric and the geocentric models. Both models made similar mathematical predictions. Another example is Snell's law that can be derived assuming that light is a particle or a wave. Here we have two different physical understandings (interpretations) of the same phenomenon with the same math. In this case, we are still uncertain as to what light is, wave or particle or both. So, this means that there is a deep reality behind and more investigations are required to settle this matter. Maybe strings or solitons!

I will try to find some spare time to read your essay which seems interesting.

Regards

Israel

Alan Kadin

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

Israel Perez

Dear Dr. Kadin

Thanks for reading my essay and commenting. I am glad you found it interesting. I would not say that physical understanding and physical intuition are synonyms. Intuition means: the ability to understand something immediately from instinctive feeling, without the need for conscious reasoning. Since intuition is related to "instinctive feelings without conscious reasoning", I reject to accept them as synonyms. Physical understanding, as I conceive it, is an understanding with conscious reasoning, with a well-reasoned complex picture of a phenomenon in mind, based on scientific observations and a well founded theoretical framework (not necessarily a mathematical framework). For this reason, I do not name it physical intuition or common sense. For instance, in the example about the electron in a box, I argue that the option n=0 is physically meaningless because this implies that k=0, which means that there is no electron wave in the box. Another way to mathematically say this, is that the wavefunction must satisfy both the Schrodinger equation and the normalization condition. The latter must be 1 for the whole space interval where the electron is supposed to be. If the integral of the square of the wavefunction were zero, there would be no electron in the box; this result also occurs when k=0. To me this is not an intuitive understanding (based on instinct or without conscious reasoning) but rather a physical understanding.

Quantum computing is an exciting topic. I am also interested in discussing topics on quantum mechanics. Both quantum mechanics and general relativity have been widely exploited by a century and, according to Thomas Kuhn, they are both in decadence, I guess they have not much to say. We need new theories. I would be happy to see your view on these matters. Thanks for calling my attention.

Best Regards

Israel

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