Students in college have a full schedule. Classical physics is no longer used in research -- it says that mass is conserved, time is absolute, there is no laser possible, quantum levels do not exist, and the hypothesis of continuity is true.
Mass is only conserved as an illusion, its value changes according to E0=mc2, and binding energy.
(Talks here about "mass is conserved" is even helpful -- it helps define what mass is not, and after the atomic bomb 75+ years ago, is just posturing. Life is a school; everyone helps, the noise defines what is a signal.)
The false expectations of classical physics end up creating bad intuitions and wasting time. Time to deprecate it, after 100+ years.
Students can save time and get correct intuitions by going directly to the Euler-Lagrange (E-L) equation, while getting no false results.
The E-L equation allows one to study F=ma (i.e., Newtonian mechanics) for more complex systems (e.g., double-pendulum, atoms, and black-holes), prepare on-ramps for Special Relativity and Quantum Mechanics, and get ready for future studies in electromagnetism -- such as diamagnetism, laser, and other quantum mechanical effects (e.g., in diamagnetism, materials placed in a magnetic field become weakly magnetized in a direction opposite to that of the applied field).
For example, students do not learn at first how to subtract a LARGER number from a SMALLER number (e.g., 3 - 5 = -2) -- it is just forbidden to so. But that happens in 1st grade! As students progress, there is no space to repeat incomplete or wrong stuff.
Classical physics, likewise, has no place in college, no space, and it is not to be used later! Then, modern physics can be taught correctly from the E-L equation, which the student had time to master earlier -- in F=ma (Newtonian mechanics), for example.
The E-L equation works in physics research as a general formalism and is not restricted to 3D + 1D curves, but full 4D. Classical mechanics is history, not science. It should be phased out of high-school also, because not everyone attends college.
In all instances where one thinks that classical mechanics can be used, even of a simple spring and mass, one can use the E-L equation, and get easily further insights. For example, what is the influence of the mass of the spring itself? This case (with and without a massless spring) is solved simply using the E-L equation in [1].
A proposal is presented and validated at my homepage. This work [1] further shows that the E-L equation gives the correct answers compared to F=ma (Newtonian mechanics), and beyond. There is no reason to retain classical mechanics or classical physics (e.g., classical EM).
[1] https://www.amazon.com/dp/B07ZX1Z1J8
All: Yes to the above, and my solution using the Euler-Lagrange Equation is shown in Appendix C of https://www.amazon.com/dp/B07ZX1Z1J8 as verified by Prof. Cheney of PCC for the mass of the spring itself (m) versus the value (M) of the mass that hangs on the spring.
This means the effective inertial mass of the spring is one third of the mass of the spring, but the effective gravitational mass of the spring is one half of the mass of the spring. These calculations assume that the spring constant does not depend on the spring’s length. This is not the case for real springs.
For small values of M/m, the displacement is not so large as to cause elastic deformation, where the spring does not return to its original length after the load is removed. In larger values of M/m, the effective inertial mass of the spring itself becomes smaller, eventually even reaching negative values, again due to the spring not returning to its original length.
Dr. Ed, this is very nice question.
The Text books should be reconsider to new version, and put every old science that belong to more than fifty years old out the book, including Mr. Albert Einstein.
Dear Ed,
Remember that Einstein's relativity had to use and redefine classical concepts, also remember that Quantum Mechanics is a house of cards and that the standard model fails to predict anything. Remember also that in the last 100 years nothing relevant has been discovered not preceded by some technical or technological improvement.
In my opinion the concepts of classical physics are more necessary than ever
Dear Ed
I think classical theory should be introduced as a special case of quantum and Relativistic physics.
Regards
N Das
ND and all: In the same way that classical physics does not exist in Nature (hence, it should not be studied, at least not in college), a classical wave does not exist in Nature, and cannot be used in elementary fashion.
A classical wave is nothing but an approximation to a large number of quantum waves, when one can ignore phase. But if we are going to study elementary "particles" as in the so-called Standard Model, classical waves (as well as F=ma) have no place, they just do not come up.
Classical waves are also a fiction, they do not exist in Nature. They are human made, like the complex numbers. There are alternatives, not every intelligent sentient species, including as we may find in extraterrestrial or AI, need to use them.
Contradictions exist classically with classical waves as well, such as one cannot define the frequency exactly unless the classical wave is infinite, which does NOT exist in Nature (nothing is infinite).
All: Classical physics is no longer used in research. This, alone, should be enough to block it in college -- it creates bad intuitions and wastes time.
Classical physics is against SR and QM, and prevents GR and the SM to be modified as quickly as possible to agree with QM. SR already agrees with QM since Dirac, predictive of Quantum Field Theory (QFT).
For example, no one talks seriously about "particles" for a long time now -- a so-called "particle" is seen today as an excitation in a field, fields that fill the entire Universe, in QFT.
AB: What you say can be done in high school. For example, students do not learn at first how to subtract a LARGER number from a SMALLER number (e.g., 3 - 5 = -2) -- it is just forbidden to so. But that happens in 1st grade!
As students progress, there is no space to repeat incomplete stuff. Classical physics, likewise, has no place in college, no space, and it is not to be used later! Then, modern physics can be taught correctly from the Euler-Lagrange equation, which the student had time to master earlier -- in Newtonian mechanics, for example.
All: For examples how the lack of current physics understanding is unfortunately promoted by classical physics, mass is not conserved (although it is invariant), and time is not an independent running parameter or absolute.
Therefore, particles do not exist in Nature and Particle Physics is outdated. The only thing that exists in Nature is quantum waves, studied in QM and QFT for example. Classical waves do not exist either.
One of our mistake is, we think that Space is just holder and it goes to infinite, but we should consider space as a substance, because it is the Space that makes WAVE by TEMERATURE . Not to mention that when we are talking about Quantum Wave, we are talking about wave inside of atom.
Science proved that atom does not exist without Temperature, therefore Space of atom is making quantum mechanics wave.
The classical physics, spacetime, GTR, STR and the rest..all outdated, we have to study how an atom create this phenomenon of wave inside of atom
Ed, everything is connected together in this universe. atom to molecules, molecules to cells and bacteria, and bacteria to a larger entity like us. all our five sense are working with wave function of duality, therefore atoms are creating these wave (very soon the scientists will find it that space of an atom is creating this wave function for atom to communicate with electron) in other hand it is not electromagnetic in atom. As matter of fact, I am discussing this situation with one of a experimental scientists in this regard. The wave in atom for communication is never been mention, if they prove this phenomenon, atom consider as complete intelligent element (entity) of universe. Wave in atom is not CP.
JV: You write, "very soon the scientists will find it that space of an atom is creating this wave function for atom to communicate with electron."
This is the kind of lay guessing game that we definitely need to avoid in Physics, and in natural sciences. It is also against the RG ToS. Please delete.
No one should talk without at least some intersubjective evidence, preferably with objective evidence, that anyone else can test.
It is at the basis of the scientific method. Science is not magic or hear-say either. This is not politics, nor humanities. Nature is the final arbiter here, not humans or even possible extraterrestrials...
Ed, I just Copy Right this "ATOMS ARE SMART" for smartness it needs communication tool, the only tool that universe providing us, it is duality "Wave" Get some of my articles here in RG or academia.edu .
Todays text books are outdated and need to be modify. Here on example.
Article Gravity is an Internal Force
This article is telling, Gravity is internal. the description of gravity is, the force to govern electron is gravity, and this function is done by Wave function in the atom, NOT electromagnetism .
Even the Lagrangian is squarely grounded on classical mechanics.
The fact that teaching classical physics at entry level progressively went out of fashion is precisely the reason why most theoreticians currently are unable to relate electromagnetism to the concept of mass.
Unfortunately, general and complete undergrad textbooks such as "University Physics" by Sears, Zemansky and Young, or "Physics" by Halliday and Resnick, that were used in giving undergrad students a general knowledge of all aspects of fundamental physics, particularly in preparing them to smoothly transit from classical continuous processes to quantum and relativistic physics, progressively went out of fashion to be replaced by textbooks that barely skim over the classical concepts that were directly extrapolated from the classical equations that were established by the major discoverers of the past from physical experiments that they actually carried out, and that constitute a pool of mutually converging conclusions about electromagnetic energy whose neglect can only lead to a lessening of our understanding of physical reality.
All: Classical mechanics say that mass is conserved, time is absolute, there is no laser possible, and quantum levels do not exist. The Euler-Lagrange (E-L) equation says otherwise, in all the above and other counts in Nature, while giving no false results.
Which one is right is now plain to see for the researcher. The E-L equation works in physics research as a general formalism and is not restricted to 3D + 1T. Classical mechanics is history, not science.
RMJ and all: In all instances where one thinks that classical mechanics can be used, even of a simple spring and mass, one can use the E-L equation, and get easily further insights. For example, what is the influence of the mass of the spring itself?
BTW, this case (with and without a massless spring) is solved simply using the E-L equation at https://www.amazon.com/dp/B07ZX1Z1J8
All: Yes to the above, and my solution using the Euler-Lagrange Equation is shown in Appendix C of https://www.amazon.com/dp/B07ZX1Z1J8 as verified by Prof. Cheney of PCC for the mass of the spring itself (m) versus the value (M) of the mass that hangs on the spring.
This means the effective inertial mass of the spring is one third of the mass of the spring, but the effective gravitational mass of the spring is one half of the mass of the spring. These calculations assume that the spring constant does not depend on the spring’s length. This is not the case for real springs.
For small values of M/m, the displacement is not so large as to cause elastic deformation, where the spring does not return to its original length after the load is removed. In larger values of M/m, the effective inertial mass of the spring itself becomes smaller, eventually even reaching negative values, again due to the spring not returning to its original length.
All: The reference shows that this work also aims to describe how, in many, and probably most, physical situations, this newer method using the E-L equation, is shown to be superior to using F = ma, and applies where the Newtonian model does not, such as inside atoms or near black holes, further providing a generally simpler route to answers, and requiring less steps.
Again, for simple problems in Newtonian mechanics, the E-L equation is not necessary but remains more insightful and uses no vectors.
If your teaching students to be calculators, go buy a computer instead-its cheaper.
If you want to nurture thinkers and perhaps a creator of next innovation advancement, they need to study how Newton did it, what data he had and how he put it all together - classical mechanics.
Besides, E-L and atoms etc, have many problems - NOT settled science. Perhaps a good dose of Newton would help.
ED
depends on your initial postulates and definitions. The light is a wave nonsense would have been avoided if science stayed with Newton.
JH: It all depends on Nature, where we live and work. Not on imagination.
Mass can be converted to energy (e.g., atomic bomb) in a closed system -- by using mass into binding energy and/or mc2. Time is arbitrary -- not absolute. Classical physics represents a wrong universe, it is not even a hypothesis worthy entertaining in physics, maths, humanism, or in life.
I just read lectures, which are something similar.
https://www.researchgate.net/project/Lectures-on-Mechanics-and-field-theory-in-Russian
But these lectures for 2nd year students.
They have Mechanics at 1st year as 1st term of General Physics course.
Nevertheless sometimes the culture of physical thinking is insufficient.
MGI and all: The lectures in Russian you pointed to, only apply to classical mechanics and they say so -- the treatment is non-relativistic. It does not correlate with Nature, where special relativity (in the Minkowski formulation) must be used.
And in any relativistic theory, particle number need not be conserved, since the relativistic dispersion relation in SR, that E2 = c2p2 + m2c4, implies that energy can be converted into particles and vice versa. This requires a multi-particle framework.
But classical mechanics for students in first-year teaches them that mass is conserved, particle number is conserved, time is absolute, continuity and particles exist, quantum levels do not appear, and infinitesimals exist, all of which have to be debunked later on in the second-year or even in graduate courses, for great suffering to the students, professors, confusion, and loss of time. They also give the wrong intuition, which guides the students to make even more mistakes.
But not all students have to go through this intellectual "hazing" ritual! They learn the Euler-Lagrange (E-L) equation in first-year, and Newtonian mechanics using the E-L equation. There is no confusion as they advance. In Norway, for example.
Physics, maths, and engineering demand faster advance. We should not repeat a culture of classical physical thinking -- that is itself insufficient.
For example, there is only one case of photon interference in the two-slit experiment, and that is the case that is often neglected -- the quantum case.
All: A photon is not to be described in classical mechanics, which is useless in EM -- essentially a QM effect.
The physical model of a photon is given as a vibration of the field, and follows QFT.
The photon is not made of neutrinos, or whatever, that also have mass. A single photon, as all experiments show, has no mass. Two or more photons, in a many-body-relativistic-QM a.k.a. a QFT, can have mass -- and that is straightforward to calculate.
QFT is a good approach for describing both old "particle physics" (nothing is a particle in Nature) and statistical physics systems, because in both cases we are interested in (relatively) long-distance or macroscopic properties.
The rest you can see at (recommended, with a good list of books also):
https://sites.krieger.jhu.edu/jared-kaplan/files/2016/05/QFTNotes.pdf
No, Physics is based on concepts, you can only build these based on macroscopic stuff readily visualized, like mass, pendulums, waves and so on. You cannot teach otherwise.
Energy, linear and angular momentum are conserved in both realms.
All: Mass is only conserved as an illusion, its value changes according to E0=mc2, and binding energy. It is against the RG ToS to use this space to deny it. Life is a school; everyone helps, the noise defines what is a signal.
(Talking here that "mass is conserved" is even helpful -- it helps define how mass is understood now (not conserved) ... and we are after the atomic bomb 75+ years ago. It is just posturing.)
Science is an edifice, defined by "NOT YET FALSE" instead of "YES" -- and herein lies its strength. Not by affirming a "YES" that would reveal soon to be false, pretending to be monolithic and right as well as the "party line", but by subjecting all affirmations to comparison with Nature in "NOT YET FALSE". If one compares wrongly, or the affirmation itself is wrong, it will eventually be replaced. No matter who said what. In physics, the final arbiter is Nature.
And Nature has deprecated classical physics. It should not be used anymore.
Thierry
I basically agree, photons do not conserve number as temperature changes
and have more to do with waves. Particle in this case has more to do with phenomenology when they are absorbed by matter, it is just a kind of image.
However I cannot digest Eds idea that there are no particles, in the case of massive particles.
Energy rather than mass is conserved (properly interpretated). Mass conservation is used in some engineering situations where you can exclude certain physical processes.
Thierry
Your post is a bit confusing, but I take it that you mean that the speed of light c is determined by properties of the medium, same as other waves.
However I cannot see what this has to do with E=mcc . This m is simply the mass of some object.(the dynamical mass), responsive to gravity.
All: I'd like to remind here that everyone helps, even contrarians. The noise helps define the signal. We want to keep free-speech here, which has been invaluable since Greek times, and denial of authority comes with it -- because trust (different from confidence, not all languages have it) does not come from authority (Michael Polanyi). So, everyone helps, everyone is a participant.
All: A Nobel prize scientist once told that he never wrote a paper that was not rejected first. Peer-review is the first barrier that creates quality in any work, be it science or art.
Classical physics faced peer-review long ago. And lost. Search the relevant journals, peer-review helped us understand its irrelevance.
We need to research what is new and important. Not to discuss what is known to not work.
It is still good to know that in daily life we rely on Brainwashed and non peer review Engineering principles every time we cross a bridge or get in a car.
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All: In software, we can use both rationals and irrationals, not so-called "infinitesimals". And we can only measure and produce finite rationals. So, with proper math, we can produce and measure 4/3 = 1.333333....
This was the basis of the Fast Fourier Transform (FFT) used in physics, and that shows one thing (of several) that is wrong with classical physics: assumed continuity.
The FFT is an algorithm for transforming a function of time into a function of frequency, much faster than the discrete Fourier Transform (DFT) can. There is no numerical difference between a DFT and a FFT, otherwise. They both compute exactly the same thing.
The FFT works by requiring a power of two length for the transform. It also splits the process into cascading groups of 2 (that's why it is also called a radix-2 FFT). There are patterns for when the sine and cosine are at 1.0, and multiplication is then not needed. A huge saving in time!
Now, of importance here, the Fourier Transform (FT) returns a representation of a signal as a superposition of sinusoids for a "continuous" range of frequencies. That is OK with classical physics (that considers a step-less continuity in frequency) but wrong in Nature (where everything is quantum in frequency) and mind (which is not infinite).
The hypothesis of "continuity" does not exist in Nature nor mind, so the FT creates artifacts in frequency, and when going back in time. One of these artifacts is current-day QM, where there would exist a "particle-wave" entity (the quantum itself). But the simultaneous appearance of wave and particle aspects no longer can be defended in QM, although it could be entertained in classical physics.
Quantum field theory (QFT) has dispelled that notion, showing that only quantum waves exist in Nature, not particles, and not classical waves (FT, DFT), nor continuity.
There is only one (not two or even three) case of photon interference in the two-slit experiment, and that is the case that is often neglected -- the quantum wave case. See the two-slit experiment at low-intensity, for example at: https://www.youtube.com/watch?v=GzbKb59my3U
There is a lot to do with the continuity of a wave function
in the quantum also, I simply do not get such arguments, even though some knowledge or experties is exhibited.
Everyone knows the limitation of measurement, to a finite number of digits. It does not mean that the concept of continuity cannot be usefully used. If you like there is quasi continuity. Limitation of measurement comes from the aparatus itself or from basic physics reasons.
QFT does not dispell imaginary problems.
In fact quantum waves and continuity concepts go together,
so I question the very logic in this Ed post.
Unfortunately teachers who would start from QM in Collage courses of Physics are essentially unknown.
Just revise the Physics course structure in any university.
Leave research to researchers, they do as they please.
All: By deprecating classical physics, students can save time and get correct intuitions by going directly to the Euler-Lagrange (E-L) equation, while getting no false results.
The E-L equation allows one to study Newtonian mechanics for more complex systems, prepare on-ramps for Special Relativity and Quantum Mechanics, and get ready for future studies in electromagnetism -- such as diamagnetism, laser, and other quantum mechanical effects to follow.
Well, now you talk about EL applied to Newton...that is Classical stuff (your unmentionable)
You go
Newton....> Lagrange.....> Hamilton
all Classical, all basically equivalent.(ie. see Goldstein)
All: As pointed out by Janusz Pudykiewicz , the University of Oslo offers the course FYS3120 to undergraduates, which fulfills the requirements of this question and allows the students to understand the Euler-Lagrange equation as an introduction to Newtonian mechanics (not classical physics) and electromagnetism, with SR according to Minkowski. This includes:
This course gives an introduction to analytical mechanics with an emphasis on Lagrange-Hamilton formalism and the action concept. Further, the course contains a thorough introduction to Einstein’s special relativity using four-vector formalism. This is used to give a covariant (independent of reference frame) description of mechanics and electromagnetism, including Maxwell’s equations.
and is further at:
https://www.uio.no/studier/emner/matnat/fys/FYS3120/index-eng.html
This course can be followed easily, just after Thermodynamics in community college, and this has been done with an A grade outcome.
ADMINISTRATIVE NOTICE: As the manager of this thread, RG gives me management tools, not all public. As a reminder, it is easy to deal with fantasy and nonsense posters in this thread:
1. They talk against known science, such as quantum mechanics and special relativity; they defend classical physics, Heaviside operators and gravitomagnetism, and other outdated views. Mass is not conserved, time is not absolute, and the laser exists.
2. They say they can calculate what no one can, in mathematics and physics.
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If this happens, you can treat these messages as they are, personal ads, and skip them, reducing noise with known fantasy or nonsense posters.
Now, who thinks that Euler Lagrange does not belong to the
Classical period of mathematics-Physics?
That Newtonian Mechanics is not Classical or rational mechanics?
No problem with the Oslo course, follows a line often used in Rusia where Euler worked.
All fine, just do not denigrate Classical, or Maxwell, or continuous, or particles.
P.d.
In the Standfored encyclopedia dealing with QFT (your insistance) there is a long section dealing with the particle point of view.
There are variational principles in QM, not all specifically EL.
(Rare in basic QM)(More comon discussing fields- a la Goldstein)
For example minimize subject to the condition = constant. Using Lagrange multipliers you get
H psi> = lambda psi>
All: Classical historic period does not equal "classical physics"! Classical physics is now history, and can be used there -- not in science teaching nor research. The false expectations of classical physics end up creating bad intuitions and wasting time for students and professors. Time to deprecate it, after 100+ years. And continue listening to Bach.
Then explain to me why the Goldstein book is termed is termed Classical Mechanics. Or Jacksons Classical Electrodynamics.
According to you the Oslo course should never be taught!!
The first inkling of the quantum turned up with Planck at the turn of the century, near 1900.
Euler Lagrange was far earlier than this date, so is Newton
So what is taught today comes from the Classical era.(minus the quantum stuff)
JW: You can explain to yourself, why Goldstein's book Classical Mechanics, or Jackson's Classical Electrodynamics, should continued to be used by some, when proven wrong. And, according to me the Oslo course should be taught as soon as possible, maybe after Thermodynamics, as written.
JW: Nature proved, many times over, man proved with the explosion of an A-bomb 75 years ago as example of nuclear fusion, and the Sun proves every second with nuclear fission. Contrary to classical physics, mass is not conserved, time is not absolute, the laser exists, quantum levels exist, and the hypothesis of continuity is not true. Time to accept it -- classical physics is not an "approximation", it is just wrong.
Of course it is not all Classical. We have a mixture.
But Newton is still taught and so is Lagrangian mechanics
and Hamiltonian mechanics.
Do you think I live on another planet?
Hypothesis of continuity? Talking about math?
Continuity is just a math definition.
All: In the interest of being cordial, I will no longer repeat here that classical physics is a wrong theory. It is said in the question head, already.
The feeling is that, also, it would be better if we don't dispel rumors. When some people see a rumor refuted, contrarians could basically assume that it is possibly true. Let everyone decide. The question head is clear.
All: According to Teplitz, “The state of the classical electromagnetic theory reminds one of a house under construction that was abandoned by its working workmen upon receiving news of an approaching plague. The plague was in this case, of course, quantum theory.”
As cited in Electromagnetism: Paths to Research, by Doris Teplitz. Springer Verlag. See:
Preprint Maxwell Equations Excluded From Electromagnetism By Quantum Mechanics
JW and all: First, let me acknowledge that QFT may not be needed, one may do quite well just with QM ... until a certain point, then one needs to dress the QM with the corresponding QFT.
For example, how can one introduce spin? First, one can show that the spin–statistics connection can be derived in QM without relativity or QFT. Then, one can discuss path integrals for spin without using spinors. Finally, one can show how spin can be quantized in a path-integral approach, without introducing anti-commuting variables.
So, one sees that even though the standard methods of QFT are much more practical for actual calculations (e.g., in studying the quantum breaking of chiral symmetry; see quantum chromodynamics, the QFT of the strong interaction) a purely QM approach helps in understanding the meaning of the QFT concepts. But in QFT, particle number is no longer conserved (energy mass, so the number of electrons may change even in an isolated body), unitarity and causality can be imposed.
Likewise, one can study Newton's Second Law (F=ma) without introducing the variational principle on action and the Euler-Lagrange equation, although this is not even feasible in some actual calculations (e.g., to study the atom or a black-hole with F=ma). However, a purely Newtonian approach helps in understanding the meaning of the concepts in the Euler-Lagrange equation. Then, one can abandon the Newtonian approach, and introduce F=ma, special relativity, QM, and QFT, using the Euler-Lagrange equation in all cases. But mass is no longer conserved, time is no longer absolute, and the laser can be predicted and built. More things can be done too, such as MRI.
You are sounding slightly more balanced, but I dont really know...
I suspect that math people may not agree, analytic functions and continuity is fairly central.
Well, the number of electrons in a solid is constant, not the number of phonons.
(unless you rubb them off). Depends how you use number conservation, mass conservation, etc. Laws of conservation can be used if you watch out how you use them, what the situation is. For example momentum is conserved, AS LONG as there are no external forces.
Teplitz exagerates I think, enm is fairly self contained.
JW: But in QFT, particle number is no longer conserved (energy mass, so the number of electrons may change even in an isolated body), and unitarity and causality can be imposed. One needs to dress QM with the corresponding QFT (QED, QCD, QSM, etc.)
Teplitz did not exaggerate on EM, and his book is hard evidence from a serious publisher (Springer Verlag). QED is the QFT of EM. QED was the first QFT where full agreement between quantum mechanics and special relativity was achieved.
All: Unfortunately, I cannot repeat Charles Darwin, who said:
‘I am quite conscious that my speculations run quite beyond the bounds of true science.’
In letter to Asa Gray, 18 June [1857].
I am not making a speculation -- true science says that classical physics cannot be applied, even approximately, to the universe we know, and classical EM is part of this denial. This has been known for 100+ years.
Ed
Charles Darwin applies to you, hook, line and sinker.
Evidence is more important than theory.
JW: Evolution is not a theory as laypeople (and, apparently, you) understand the word, but science. Evolution is relentless, both in scientific theory and experiment, also with humans -- we are all at a simple step in a ladder. We all share the same amino-acids, for example, even plants, pointing to a common origin.
The Darwin quote means he is great enough to admit faults and mistakes, and all science is tentative.
Slight modification above.
All: Ramanujan never made, or thought he had made, a mistake in math. There are many other cases. People with a trustworthy connection to a "future" world, which is also a real world, have been an example in all countries. People who live hedonistically or anachronistically are known exceptions, like Edison who electrocuted humans and even elephants to "prove" that AC was "dangerous" -- an AC that his company did not sell and competed against with "his" DC.
As this paper shows, experiment and theory imply that unbounded fields, not bounded particles, are fundamental. It's important to clarify this issue because textbooks still teach a particles- and measurement-oriented interpretation that contributes to bewilderment among students and pseudoscience among the public. This article reviews classical and quantum fields, the two-slit experiment, rigorous theorems showing particles are inconsistent with relativistic quantum theory, and several phenomena showing particles are incompatible with quantum field theories.
See https://arxiv.org/ftp/arxiv/papers/1204/1204.4616.pdf
If this is so, Id rather keep particles and throw out QFT. Again evidence is more important than theory.
All: Classical physics, like general relativity, is based on continuity. Both have to be abandoned in favor of a QM description. The need for field-continuity in GR is evident from the very existence of the second-derivative -- which requires continuity.
Continuity is, however, not experimentally-valid in QM -- the quantum levels are not continuous; there is no 1/2 or fractional value, and so on. Thus, the GR idea that gravity would be the manifestation of a spacetime continuous curvature is certainly not experimentally-valid under QM. Yet, QM is experimentally-valid elsewhere, which motivates the work to use an experimentally-valid underlying topology that would represent a quantum field, albeit being represented by a real number in a dual space.
All: The physical model behind this approach to vibrations and quantum mechanics, as not tied only to the microscopic view, to an atomic view of matter that we find has further subdivisions, is the Euler-Lagrange equation, harking back to the Sturm-Liouville differential equation, but In Galois fields.
For a limited time, my home-page has two free full-text papers on it -- as offered through Amazon and Kindle books -- for any RG members, just for the asking, in PDF. Sent me please a PM, and I will send back. At least until June 30.
Ed Gerck : Just one thing: You say: classically quantum levels do not exist, ...
This is the best example that also you would need some classes in classical mechanics. Quantization is a natural phenomena of force free coupled rotating rigid masses:
See: Peter H. Richter: Die Theorie des Kreisels in Bildern, Fachbereich Physik und Institut für Dynamische Systeme Universität Bremen (1990)
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