One of the challenges of modern physics is the astounding role of mathematics in physics. So that some physicists claim that physics is lost in mathematics.
https://blogs.scientificamerican.com/observations/quantum-monism-could-save-the-soul-of-physics/
What is your opinion?
Dear Sydney Ernest Grimm
"I am not "nervous" about the relation between modern physics en mathematics." I am not nervous too.
The problem is not the difficulty or simply of understanding of physics,
Mathematics of physics is formed on the physical principles
These principles need to be reviewed. Including massless photon is an assumption only. Please see:
The Greatest Unsolved Mystery in Physics
https://www.researchgate.net/publication/330366766_The_Greatest_Unsolved_Mystery_in_Physics
Dear Hossein,
Yes, physics is lost in mathematics (see my attached little memoir).
God Bless,
Denny
Dear Hossein,
Yes, physics is lost in mathematics (see my attached little memoir).
God Bless,
Denny
Dear Sydney Ernest Grimm
"I am not "nervous" about the relation between modern physics en mathematics." I am not nervous too.
The problem is not the difficulty or simply of understanding of physics,
Mathematics of physics is formed on the physical principles
These principles need to be reviewed. Including massless photon is an assumption only. Please see:
The Greatest Unsolved Mystery in Physics
https://www.researchgate.net/publication/330366766_The_Greatest_Unsolved_Mystery_in_Physics
Dear Dennis P. Allen Jr.
Thank you for the link, I will read it.
Best Regards
Sabine's book is not the general view of physics people. But she has raised some issues. For example, I think fine tuning does occur in the universe. Negative feedback loops have been used by engineers for process control and the same could be what the universe is doing. Also, beauty should be part of physics.
I also suggest the commonly accepted math does not accurately reflect physics. For example, what is meant by the equal ( "=") sign 1. the sameness of the numbers 2. a transformation or mapping 3. a cause-effect relation. just because the numbers match doesn't mean equivalent processes are happening.
Yes. As human being can never discover( every thing )in the Universe. This lies in the definition of our creator God.
The majority of the universe is not yet known and therefore we do not know what it is and how to describe it. As a new phenomena of the universe is suspected amd identified to exist, the more new mathematics is created or further properties of the existing mathematical equations are added. This relationship between mathematics and the physical universe is always a need of necessity, not of luxury.
I think that if you want to build a house, you first need to gather the needed tools. The question of whether physics gets lost in mathematics suggests that alternatively, physics could be what? "More intuitive"?
Taking this to an extreme, a few years ago a high school student expressed to me that he wanted to understand physics without having to learn calculus. Not an easy task! Even classical physics becomes rather mysterious. Without calculus, you have to take too many laws as a matter of faith.
More likely, new math needs to be developed, for physics to continue to solve the mysteries of the universe.
Dear Albert
I agree with you, in fact, physics without math is no longer knowledge and will be part of philosophy. Like what was before Newton. But mathematics is not physics.
Mathematics of physics is formed on the physical principles.
Dear Hossein,
You might be interested in this latest paper on neurolinguistics that correlates the latest experimental discoveries about the neocortex, including an experiment that locates the seat of mathematical thinking in areas of the brain different from those that are the seat of verbal thinking, and its relation to physical reality:
https://doi.org/10.4236/ce.2019.102028
Best Regards, André
Mathematics was a handyman for the king natural science until Albert Einstein. Now this handyman has taken contol over the kingdom. But equipped only with a hammer, this handyman considers any problem of the kingdom as a nail and acts accordingly!
In more sophisticated words, mathematics has become an alienation of man since the turn of the 20th century. A condition in which a creation of man (for his own need) in course of history and at a certain stage of its development; goes out of his control and becomes an alien as if coming from outside; and like a Frankenstein Monster sets itself to haunt and contol its very creator! We see this in Religion, the Nation States, Monopoly Capital, Media Technology etc.; - all products of man's creation, but now control the life of man himself!
Dear Albert,
Calculus allows defining spatial and temporal action ranges, the stable equilibrium states in which matter is stabilized at all levels would be better described in my view with resonance equations that already exist, or should not be that difficult to establish.
Best Regards, André
No. The math is OK as long as it explains the experimental data. Our lack is on what is behind the math! Things like “cloud of probability” or using dark matter as if it is real just loose understanding
André, I'm not sure I understand your point. The "resonance equations" I know about also require calculus, no? Resonance, expressed as first, or higher order, differential equations.
Anyway, I am in total agreement with Hossein. If math of physics is not the main tool used, then physics would devolve into philosophy. Which is not physics.
In most of the theoretic aspects of Physical Sciences,
Mathematics is the journey (analytics + numerics); Physics is the goal (illations + conclusions).
We, of course, often get too much tired and lost in the broad-long journey itself; leaving behind almost no interest and energy for the narrow-focused goal.
Dear Albert,
I also totally agree with Hossein that mathematics is the right tool to study our physical environment. From what I understand, it is in fact the idealized collectively understandable language that was developed over time, that allows us to describe and measure the processes and objects we perceive in the real environment.
Math as such being a language has no natural boundaries. It is up to us to harness it with the true boundaries that we detect in nature.
You wrote: "I'm not sure I understand your point. The "resonance equations" I know about also require calculus, no? Resonance, expressed as first, or higher order, differential equations."
What I mean is that every least action system, from the submicroscopic to the astronomic seem to be stabilized into some sort of resonance state.
The 3 scatterable elementary charged quarks inside protons and neutrons seem to be stabilized into some stable least action electromagnetic resonance state.
The electron in the hydrogen atom seems to be stabilized into some least action resonance state. In fact, this is what de Broglie concluded almost a hundred years ago, which is what inspired Schrödinger to define the wave equation to describe it.
Unfortunately, this line of reasoning was almost immediately sidetracked and left unexplored as Heisenberg's statistical method gained almost immediate popularity. A recall of these events is put in perspective at the beginning of this paper:
https://doi.org/10.4236/jmp.2018.95067
I see a resonance volume visited by the trajectory of an electron in free motion due to its Zitterbewegung.
Skipping a few levels, even in the Solar system, such resonance states can be identified. The planets seem captive in stable least action resonance states at mean distances from the Sun, mean distances between precise stable minimal and maximal axial distances (perihelion and aphelion) from the Sun, within which each planet's orbit can be circumscribed, defining a volume of space, a volume that can evolve into rather complex shapes for bodies that have satellites, that induce interference beat patterns that modify the otherwise regular volumes that would be visited by a body without satellite.
The Solar system captive in a resonance volume about the center of our galaxy, etc.
I see the potential of an integrated system of interconnected wave equations defining all resonance volumes from the bottom up. Seems to me that we may even have the math already to develop it.
I don't know if this makes any sort of sense to you.
Best Regards, André
Dear Albert
I agree with you on:"If math of physics is not the main tool used, then physics would devolve into philosophy. Which is not physics."
Dear Sydney Ernest Grimm
We are not seeing the world out of it. We are a small part of the world that we live in. Also, no picture covers all the landscape, the physical events are not in our minds, and we will process our personal phenomena in mind that usually are far from the reality.
We describe a personal phenomenon, it will bring judgment and the others are compared with the phenomenon itself. In discussion, a common phenomenon will be created that is closer to reality. The history of science shows that even a common human phenomenon isn’t all reality. Physicists in order to make the joint phenomenon close together and prevent dispersion of votes and results used mathematical models.
Therefore physicists used mathematics to describe reality. Kelvin said: "When you can measure what you are speaking about, and express it in numbers, you know something about it".
Joseph Loscalzo "Can Scientific Quality Be Quantified?" Circulation, [Online]
available;
http://circ.ahajournals.org/content/123/9/947.full
Scientific theories do not show the laws of nature, but are our understanding of physical phenomena to explain the nature and closeness of the common phenomena to the dominating rules of nature. So no theory is perfect, even if expressed with mathematical formulas.
Dear John,
Since any resonance phenomenon involves by structure some cyclic process or processes, it if can be mathematically established that quantum entanglement involves such processes, then this needs to be investigated.
Best Regards, André
Dear Sydney
This is not the essence of science, it shows the human disability and scientific theories.
You wrote: " do we want to replicate reality in our theories? If we can why no? But we cannot. I think our effort should be in this direction. For this reason, we always seek a better theory.
You wrote: "In fact, we want a true conceptual model to understand reality." What can we do other than modeling?
Dear Sydney,
You raised many interesting points. I have comments for each of them.
You wrote: " If a mathematician is trying to “develop” a new theory it is always about reality (like philosophy is about reality). Not only because it is senseless to design rules that have no purpose."
I completely agree with this.
You wrote: "In the past meta-physicists have discussed the problem and concluded that we can only think about what exist in our universe (that’s not only matter, e.g. a scientific culture is real too)."
I don't think that his is true at all. We can think of anything that emerges from any set of parameters that we assume true, whether confirmed or not. This is the actual playground of science-fiction and fantasy. For example, the Star Trek series assumes that teleportation is real. This doesn't mean that it is, nor that it will be possible any time in the future. The same for time travel, parallel universes in which anything can be imagined to exist.
You wrote: " So what is the difference between physics and mathematics? There is no difference is we realize that math has no “theory of math”. Just like theoretical physics has no TOE (theory of everything), mathematics has no TOM. If we want to discuss the influence of math in theoretical physics we have to understand that math - at the moment - is not much more than a box full of “conceptual tools”. Like physics at the moment is not much more than a box full of "experiments and models"."
There is no need for any theory of math, just like there is no need for a theory of French, English, or Russian. Mathematics is nothing less or more than a language that can be used to describe physical process or anything else we care to describe with it.
When used in correlation with real values abstracted from our environment, it allows us to take control and exploit the actual processes that it allows measuring. All of our technology is built on such developments.
You wrote: " Suppose someone publish a TOM. How do we know it is the right one? We cannot judge the TOM if the concept doesn’t fit physical reality. And what about someone who publish a TOE? Is it possible to describe the underlying structure of the basic quantum fields without a mathematical description of the metrical rules that not only create the phenomena but the basic laws and constants too?"
Again, there is no need for a "theory" of math, since it is only a language. Just as for any language, what can be established is how it evolved to the state it has now reached. For example, recent (2016) experiments with fMRI by Amalric and Dehaene just confirmed that the mathematical engrams develop in the brains of people who learn math in specific areas of the neocortex, and that high level mathematicians actually think by means of these mathematical algorithms, just like non-mathematicians think by means of the words of verbal languages:
https://doi.org/10.1073/pnas.1603205113
You wrote: " The only way to solve the problem is to understand mathematics and physics (and philosophy) without “domain walls” between the two branches of science. Besides that, physics is empiric science. So if we take empiricism serious we have to conclude that most of the amount of theoretical papers we publish must be absurd because there are no assignable results."
I think the issue simply is to come to terms with the idea that math is only a language. With this in retrospect, all of its descriptive power can be put to full use to harness empirical information that we abstract from our environment.
I don't think that electric motors that were developed from correctly mathematized electromagnetic understanding are absurd. It seems to me that any further level of correctly mathematized understanding of our environment is likely to beget more such useful applications.
Best Regards, André
Dear Colleagues and Friends,
I think all of us agree with me that Physics could be copiously categorized into the three specialisms as:
(a) Conceptual Physics,
(b) Mathematical Physics, and
(c) Experimental Physics.
Out of all (a)-(c), it is only (b), which deals with rigorous mathematical analyses. It widely relates all the specialized portions of Advanced Mathematics, such as mappings, relations, groups, rings, fields, Lie algebra, Hopf algebra, Painleve' analysis, etc. Despite that, it still better remains as a specialized Physics - the so-called "Mathematical Physics" in particular.
In addition, there exists a specialized section of Mathematics, which is termed as "Applied Mathematics", dealing formostly with the theoretical aspects of Physics exclusively. The most of the analytic techniques and formulae herein are pioneered by Physicists only. Thus, it clearly seems that "Mathematics" is a specialized naturalistic branch of "Physics" thereby tending to nullify the relevancy of the precast question that "whether Physics is lost in Mathematics".
With kind regards,
PK Karmakar
Department of Physics, Tezpur University, India
And going back to the original question, what makes physics different from fairy tales, is indeed the math. Without the math, it becomes merely someone's (most likely flawed) "intuition." I put that in quotes, because intuition changes with knowledge.
Something André said that I think I agree with:
For example, the Star Trek series assumes that teleportation is real. This doesn't mean that it is, nor that it will be possible any time in the future. The same for time travel, parallel universes in which anything can be imagined to exist.
True. Physics can certainly begin from premises that are not real in our sphere of knowledge, yet, that is. It doesn't mean that with the proper tools, those phenomena can never be explained, quantified, and put into daily use. All it means, before this happens, as that we did not know what we did not know.
Star Trek postulated personal communicators, long before they could exist in practice. Now they exist in practice. They are called cellular telephones. The crucial development there was cellular communications. However the spark that got that going could well have been pure imagination.
Star Trek postulated tricorders, which you could wave over a patient, sense what was wrong, and even possibly fix the medical problem. We now have smartphone apps that can measure glucose levels or take EKGs, and even transmit the data automatically to the doctor's office.
Teleportation could follow that same path, for all we know today. But not just by having people waxing eloquent about it. Some creative writer dreams something up, and real science can get to work and make it happen. Math is required.
Dear Sydney
In general, I agree with you that we both use different words for the same concepts.
Best Regards
Hossein
André Michaud
Resonance in the same way radios have resonance with the radio station the entangled particles share resonant frequencies.
In continuation with my previous answer, the following might be added.
We are gratefully proud of "Mathematics" for having been remaining ever associated with "Physics" as a vital expressive tool for decades.
Dear Sydney,
I absolutely do not underestimate the scientists from the past, contrary to the impression you seem to have.
You wrote "The problem is that any new idea is a combination (transformation) of existing ideas. That is exactly how our universe transforms reality on and on."
This is true only if the existing ideas proven right are considered.
For example, two existing ideas that contradict each other cannot both be right. Since there exists only one physical reality, if even one of them is right, then the other can only be wrong.
I observed that the community as a whole has lost sight of the fact that electrodynamics is grounded on Lorenz's interpretation of electromagnetism, that Maxwell disagreed with, and not on Maxwell's theory, which ended up in many sources asserting that electrodynamics is grounded on Maxwell's theory.
Which one is right? Confusion can only beget confusion.
LRC systems, for example, are in harmony with Maxwell's theory of mutual induction of the electric field and the magnetic field, not with Lorenz's interpretation that both fields max at the same time synchronously. Why doesn't this raise any question in the community?
The confusion is so deep that Lorenz's interpretation is confused with Maxwell theory.
Of course opinions do not matter indeed. Only confirmable facts matter. But misunderstanding physical facts or processes do matter because misunderstood premises can only lead to wrong conclusions.
I think that applied physics/mathematics does matter, because this is what has been proven to work, and that confirms the correctness of the underlying theories.
Given the confusion previously mentioned as to the grounding ideas about electromagnetism, I for one am not surprised at the never ending increase of scientific papers with minor importance, at least in electromagnetism.
Not surprised either in the quantum domain given that the line of research that de Broglie and Schrödinger started to explore was completely ignored and left unattended from the get go.
I mentioned electric motors because they are the proof that the underlying theory is right, and that research to further advance our knowledge stands a good chance of being fruitful if it is taken as a starting premise to integrate what new facts that have been confirmed since its invention, at least for all that concerns electromagnetism.
Best Regards, André
I disagree, Mathematics models and theories are used to explain the beauty of physics.
when you look at the small particles in side the atom and deal with its movement geometrically as spin movement or string movement you enjoy that.
Dear Omima Mohamed
This is an artistic and very beautiful attitude.
Is nature beautiful or does beauty create by math?
Dear Hossein,
From my observations, it is beauty that creates math.
We do not see beauty in an imperfectly spherical object, for example, but a perfect sphere immediately captures our attention by its perfection.
When considering an imperfectly drawn circle, for example, the idea that every point of its circumference can be at equal distances of its center cannot possibly emerge. But contrariwise, when visualizing a perfect circle long enough, this is a natural conclusion that will eventually become obvious, giving rise to the idea of the radius, which then leads to measuring how many times this invariant length can be applied as a unit to measure the circumference, and then you obtain your first mathematical equation C=2πr, and so on.
So mathematics can stem only from the perfect idealized geometric shapes that we generalized from observation of the imperfect shapes that we generally observe in our environment. We can then adapt these idealized mathematical concepts to describe and measure these imperfect objects in our environment.
Quote from page 398 of this paper, previously given in reference, titled "The Mechanics of Conceptual Thinking":
" All of these idealized geometric and mathematical concepts are of such perfection that their inherent esthetic beauty easily causes a loss of sight of the fact that they are virtual and do not directly reflect physical reality."
https://doi.org/10.4236/ce.2019.102028
But they can only be the actual origin of mathematics as a tool to measure our environment.
Best Regards, André
Dear Hossein,
I tend to agree (with a Yes to your question "Is physics lost in mathematics?"). Going back many years to when I was in middle school (when my mathematics teacher defined a Straight Line, as "the Shortest Distance between two points"), I felt that something really fishy was going on. The definition really did not make sense. One of the biggest mistakes in my life was that on that day, I failed to ask my teacher the obvious question - "How can you Draw, a Distance?". If I had asked that question, then not only myself, but the entire class of my fellow students would have learnt something more from the teacher's answer.
There has been a lot of theorizing going on in Physics and thought experiments. Which may sometimes be taken over by Researchers in Mathematics, and taken to the extreme. Then the interested parties may sell it to the media.
The only real problem is, on what data is this based? Are we going on to though experiments and Mathematics based on that, when we have not even conclusively established that the Data is "Rock Solid"? Or atleast there has been an honest attempt to verify the data and to minimize the mistakes in data gathering?
And how well can we trust our own senses? (eg. Rabbit - Duck Illusion)
https://upload.wikimedia.org/wikipedia/commons/1/1d/Kaninchen_und_Ente.svg
As far as Mathematics goes, it may have its own problems because today it can take a very long time for mistakes to be found in the Proofs.
Then there is also the case where mathematicians do Not agree with each other:
https://en.wikipedia.org/wiki/Foundations_of_mathematics#Foundational_crisis
The Most unfortunate thing today is that the Successful Academic is more respected than the True Scientist (who has very little time to publish all his/her work, since he/she is trying to build a Firm Foundation of evidence for the research.
Physics has a unique quality and strong natural identity, and hence, it is never lost in any form as yet known so far.
Nature is beautiful and math is a tool to formulate and interpret this beauty
Dear P. K. Karmakar
I agree with you that Physics has a unique quality and strong natural identity, but it is not all story, please see the followings:
Art Hobson, There are no particles, there are only fields, American Journal of Physics 81, 211 (2013);
https://doi.org/10.1119/1.4789885
Robert J. Sciamanda, THERE ARE NO PARTICLES, AND THERE ARE NO FIELDS, The fields of QFT are operators. American Journal of Physics 81, 645 (2013);
https://doi.org/10.1119/1.4812316
Dear Hossein Javadi ,
Thanks for response. Could you please clarify what you want to show and why?
Please explain what you have in mind.
Kind regards,
PK Karmakar
Dear P. K. Karmakar
It is good question, thank you.
Today, physics is in the mastering of mathematics. Especially in quantum mechanics, quantum field theory is described with mathematical formulas, without explaining what the fields themselves are made of. While CPH theory is first described by physical phenomena, then mathematical relations are formulated. For example:
Generalization of the Dirac’s Equation and Sea, 2016
https://www.researchgate.net/publication/303988070_Generalization_of_the_Dirac's_Equation_and_Sea
Dear @ Hossein Javadi ,
Thanks a lot for a nice response. Hope to receive similar cooperation in future too.
Kind regards,
PK Karmakar
Thanks to Hossein Javadi for initiating this discussion, and to the others who expressed their valuable views and opinions.
But does this discussion give us an idea of the (illusory) nature of Reality?
Or maybe mathematics has taken us too far.
For instance, when you see 7 data Points on an X-Y plot, how do you connect them?
Do you do it with a "Straight-line" or with a "Sign Curve" or with something else?
This is the simplest example I could think of, but how do we do it. Or when the 7 data becomes 70, when 70 becomes 700, we my think we are moving more and more to an accurate result.
But when will this stop, or Will it ever stop?
Thank you all great comments about the role of mathematics within physics. My agreement with "...... The Most unfortunate thing today is that the Successful Academic is more respected than the True Scientist (who has very little time to publish all his/her work, since he/she is trying to build a Firm Foundation of evidence for the research....." that Madanayake had especially since my experience was same having evaluators - editors+reviewers - not having critical original thinking appreciating progressive science; they particularly seem to have been caught all up with bureaucracy!!!!!
To resolve the complex aspects with mathematics having vagaries of mere mechanics without a logical reflective physics. my resolution was to configure metrix protocol that will take us out of logic to language, while set theory takes us from language to logic to mathematical proofs & further fomulations equaions. These are quite necessary since logic forms the basis of science with abstractions natural observations proving hypotheses experimentally & theoretically. However very important step will be configuring algorithms that will have coding with IT programming to verify & justify with experimental & natural unbiased observations & objectively terms to long time knowledge & understanding with the underpinnings of the consequential outcomes. We all should also have to comply with philosophical requirements, for example Popper's falsiability principle to explaining communicatively to laypersons. These are where metrix protocol plays logic intermediary. Now that we have theory of everything comprising many many equations, there are key missing models, that our team experimentally theoretically modeling, that will provide links to algorithmic problem solving to unravel physics operating paradoxical problems with natural solutions!!!!! More to come........
Yes I think so. There's no reason that I can see why everything seems to get more complicated as time goes on. The mathematics isolate a small few and as everyone knows very well the become more isolated and their efforts are part of the entropy of the universe, not forgotten, just misplaced where no-one knows where it is any more. The work gets more complicated but it doesn't change very much, and the mathematics remains somewhat the same, for too long, because it's just recycling for some reason that has never been clear. It doesn't have to be this way but this is the way it has remained far too long
Dann Passoja
I agree with you, thank you for comment.
Unfortunately, mathematics has so far dominated physics today which physics is an interpretation of the results of mathematical equations.
Any demarcation between the two closely related widely applied subjects - Physics and Mathematics - helps the growth of neither.
It could be seen that Physics and Mathematics are like the two sides (= 1, 2) of a regular coin (= Special Natural Science). If any of the sides is affected, the coin (= Special Natural Science) loses its economic worth.
Physics (= Side-1) + Mathematics (= Side-2) = Special Natural Science (= Coin).
- Badges
- Science topic
- Similar topics
- Mathematics