In order to understand the nature of motion, it is first necessary to confront yet another fallacious concept in physics called continuity (infinite divisibility). It is a concept that scientists, especially mathematicians, hopelessly cling to in spite of its being blatantly illogical.
This belief has led to the introduction of the theory of general relativity which postulates a geometric solution to the phenomenon of gravity and introduced such harmful concepts as the existence of a space-time continuum (note 1) and the curvature of said space-time.
Truth is, continuity is wrong simply because it leads to an infinite regress. Nature is discrete and, as a result, particles move in discrete steps, i.e., their positions change from one discrete value to another. Discreteness means that there exist only discrete positional properties and that things like lines, circles, curves, surfaces, angles, etc... are all abstract concepts. The old debate between Euclidian and non-Euclidian geometries about whether or not parallel lines meet becomes immediately pointless (not to mention stupid) since both wrongly assume the existence of lines and other continuous structures.
That depends on either Corpuscular or Wave approach applied for the consideration.
The same old song.
Additionally it turned out that elementary particles are hardly "balls" or corpuscles. Even if we imagine the corpuscles as finite objects, there is no reason not to describe the field(s) around them as continuous. I know that there are speculations on the quantization of space and time as well - it is beyond my undeerstanding, I am a poor chemist. Anyway in the "micro -world" neither corpuscles nor the space around them behave as we imagine form our macroscopic experience.
I think that only mean values can be continuous. Mainly, because mean values do not exist or, at least, need not exist in the real world. For instance, the average height of a population can be 1.70ms; in spite of nobody is of 1.70ms in height. The mean position of a particle can change continuously; however its real positions are discrete. Recall that only mean values are observable.
If infinity cannot be reached, the same impossibility lies in infinitely small measures.
@MAA: This is a mix of questions. First of all we should arrive at "NATURE is discrete or not". I am not a mathematics or physics student, but from philosophical point of view, in nature, nothing is separate & distinct(discrete), but every thing is very much interconnected and dynamic. Mother nature is dynamic and supreme, It takes care of itself. If we disturb it, we have to bear the results. Then, so much so said, how a particle could be discrete?
Every new littlest particle we found has rules, its existence with rules implies an structure, and a behavior. For that every new littlest "thing" is discrete, but this capability to "found" another littlest "thing" can be infinite. (Another new named thing is discrete. To be out the random is discrete).
We are always in the middle... It's an intelligent position... (art)
It was Descartes that gave us the continuum, and Newton that gave it relevance to physics (space and time). It was Lagrange who gave us the discrete (the degree of freedom) and Leibniz who gave it relevance to physics, and therefore a very real shame Leibniz lived before Lagrange and could not quite have the right mathematical context to express his idea (energy).
I highly recommend reading "Energy - The subtle concept" (Jennifer Coopersmith) that explores the history of all this.
The Lagrangian view lives on in Quantum Mechanics, the Descartes view in General Relativity, and to date, never the two shall meet. We have been arguing in circles around these points since the end of the 18th century, and I am not going there (again) in this thread!
There is a correct and proven answer to this dilemma, published in highly respected journals in various forms over the last 100 years, but it is much more fun and educational to reinvent the wheel by deducing it for yourself.
Silence contains noise but not vice verse. Nothing contains everything but not vice verse. Atom is all vacuum except the core Thus nothing dominates over things ,viz matter. We humans appear as continuous from top to bottom but we too are mostly empty. Thus, discreteness is dispersed with with dominant 'nothing'. Large diameter circle too appears as straight line, as little straight lines joined together in atomic level vision! What we see or infer is thus subjectively relative to something we compare it with. Numbers are all a game of just two, 0 and 1. That is all.Surety appears unscientific and perhaps is what dominates science and so-called rationality.
It shows in a fascinating manner how does deeper worldview (i.e. metaphysical ideas) permeate our scientific understanding. The above view is typical for the Indian worldview where "nothingness" is a central concept. Thank you for the note!
On the necessity of RE-look approach.:_
Before one gets into the authenticity of an approach or assumption which has been proved and accepted so far, many basics questions should be raised as the present scientific world is going on like a relay race namely passing the baton of acquired knowledge from one researcher to another and actually in many cases the final goal is not really visible. Accidentally by this process one can stumble on newer findings that one really has not imagined, because the universe and Nature is wonderful everywhere.
If we look at many engineering applications the main fundamentals and the design which actually matters or cognizable is macroscopic and the principle with which it works can be practically described and the parameters required for product realization in many cases is global using mean values. In all these there are underlying philosophy with which it functions.
Now when the physics of all these engineering inventions are probed deeper so as to go into the roots of the problem, the mathematical analogies, derivations, assumptions can be skillfully and even truthfully done within the framework that mathematics will allow and the end result matching with the global parameters.There could be many more approaches which also could give the same result but may not be easily accepted i.e, first cum first serve approach. By this statement no offense is meant to the scientific community as there is nothing like propriety rights in a scientific pursuit.
This matter gets further complicated when the physics of matter in the atomic level is discussed and has a bearing with the creation of the Universe. Just as life mechanism in any living being is being understood and misunderstood, similarly particle physics is to the material world.
Hence there is every reason to look int basic assumptions on approved practices, and question them and is not re-inventing the wheel or can be called old stories.
All assumptions based on geometry , continuum, singularities, infiniteness, orderliness etc are man made for his convenience to arrive finally a tangible result which should be measurable in the global scale.
Continuum is an excellent description of Nature at the level of classical physics, including Einstein's GTR. Quantum Physics provides us well-defined limits to the accuracy of our observation, and also a way to quantize fields, which is how some of the elementary particles emerge. I don't understand what's the question (or the problem) here.
Readers of "The Ten Assumptions of Science" and "The Scientific Worldview " know about the philosophical choices required to distinguish between determinism (science) and indeterminism (religion). They know that the debate between those two worldviews is interminable. That is because fundamental assumptions always have opposites, and in the end neither is completely provable. To do science properly, however, we must choose the correct fundamental assumptions before proceeding.
Ahmad’s age-old question about whether particles are discrete or not is interesting in that it serves as a nice illustration of how assumptive choice affects conclusions. The choice here is between infinity and finity. It is obvious that no one can ever prove which is correct. No one can go to the edge of the universe to get a yes or no on infinity; no one will ever find the smallest particle. One may have difficulty in imagining how the universe could have an end to it. Would there be dragons there? If matter exists in one place, would it not exist in every place? One may have difficulty imagining a partless particle. Is matter a solid crème-pie filling of some sort? At the Progressive Science Institute, we use the Eighth Assumption of Science, infinity (The universe is infinite, both in the microcosmic and macrocosmic directions) to confront the Big Bang Theory and to resolve the multitude of paradoxes and contradictions in today’s physics and cosmology.
Like Ahmad, most scientists assume finity. That is why the Big Bang Theory and Finite Particle Theory are so popular. Of course, any hint of the infinite must be “illogical” for those who consciously or subconsciously assume finity despite the endless variety we see all around us. Finity, however, poses many contradictions, some of which were pointed out by Ahmad. In the effort to save that assumption, scientists have proposed extra-Euclidean dimensions and geometrical and other mathematical solutions for understanding natural phenomena. Sorry Ahmad, but Einstein’s space-time concept was ultimately used, not to propose an infinite regress, but to do just the opposite: stuff the entire universe into a finite pre-Copernican bundle.
To do that, Einstein had to objectify motion. This was his most important philosophical error (Borchardt, 2011). Although critical of relativity, Ahmad does the same thing: “Nature is discrete and, as a result, particles move in discrete steps, i.e., their positions change from one discrete value to another.” This would be a surprise to Newton and to anyone who has studied inertia, in which an object travels through space in a continuous fashion per the First Law of Motion. No energy inputs are required. For motion to occur in discrete steps, an object would require discrete collisions per the Second Law of Motion. Energy exchange would be required for each deceleration/acceleration step. Discrete material objects have xyz dimensions and location with respect to other objects. Motion does not have dimensions; like time, it is not “part” of the universe. It is what those parts do. The adjectives “discrete” or “continuous” do not apply to motion.
I have to agree with Ahmad that the continuity assumed in various abstractions is purely idealistic. Those are study aids, not real objects. How then do the adjectives “discrete” or “continuous” apply to real objects? In combination with infinity we use the Tenth Assumption of Science, Interconnection (All things are interconnected, that is, between any two objects exist other objects that transmit matter and motion). Thus, we know that the smooth, continuous surface of an object really is composed of discrete particles. Ahmad and I would not agree on the question of what is between those discrete particles. It is either something or nothing. One who assumes infinity would choose something; one who assumes finity would choose nothing.
The concept of nothing, however, is an idealization, just like the concept of solid matter. Empty space and solid matter are ideals, neither of which exists in nature. Everything that exists has the characteristics of both. Even as interconnection approaches infinity, there must be “empty space” for those intervening objects to transmit motion. Subdivision always produces what we call matter and empty space, ad infinitum.
Ahmad would say that it is “illogical” to assume infinity. True, for the cosmogonist that switch would amount to a revolution in thought, but it is no more difficult than believing the universe exploded out of nothing. As we showed in our latest book (Puetz and Borchardt, 20111), the logical replacement for the Big Bang Theory is Infinite Universe Theory, the culmination of what Copernicus only started.
Borchardt, Glenn, 2004, The ten assumptions of science: Toward a new scientific worldview ( http://www.scientificphilosophy.com/assumptions.html
): Lincoln, NE, iUniverse, 125 p.
Borchardt, Glenn, 2007, The scientific worldview: Beyond Newton and Einstein ( http://www.scientificphilosophy.com/The%20Scientific%20Worldview.html
): Lincoln, NE, iUniverse, 411 p.
Borchardt, Glenn, 2011, Einstein's most important philosophical error, in Proceedings of the Natural Philosophy Alliance, 18th Conference of the NPA, 6-9 July, 2011 ( http://www.worldsci.org/pdf/abstracts/abstracts_5991.pdf
), College Park, MD, Natural Philosophy Alliance, Mt. Airy, MD, p. 64-68.
Puetz, Stephen J., and Borchardt, Glenn, 2011, Universal cycle theory: Neomechanics of the hierarchically infinite universe: Denver, Outskirts Press ( www.universalcycletheory.com ), 626 p.
The concept of particle appears in mechanics as a consequence of the observation that the universe we perceive can (possibly) be analized into individual objects. From this comes the idea of the motion of an object "as a whole" that has its simplest representation in terms of three functions of time. Is this a sound concept? It depends on the answer to a question: is our universe a single entity or a collection of entities? Suppose the answer is: the universe is a single entity and the concept of particle is unsound, then we will never be able to describe the universe. In that worst case the concept of particle is justified, at least, as an analytical tool, on an empirical basis. That concept of particle is the one used by Tycho Brahe; Kepler; Galileo; Newton; and the list goes on and on. That idea has been applied successfully to navigate on Earth and in outer space; and to design and build the machines that make this civilization viable.
Sometimes we expect too much of science, and, in general, of our ability to describe the world, like if we were the last word in evolution: a sort of mortal gods. Most probably we are not the best thinking machines the universe can evolve. Most probably there are questions we will never answer. I observe a regression from heliocentrism to anthropocentrism.
Science is good, fun, and all you want, but it isn't and, probably, will never be perfect.
Tapio,
The part under discussion is that the "the degrees of freedom" remains stubbornly a required and axiomatic discrete.number, and the existence of this discrete number is needed in QM to quantize the fields to produce the particles. So the particle must be in a sense discrete, even though in the field description it is all part of a continuum system wave-function. This dilemma lies at the heart of the incompatibility between QM and GR, which I will explain as follows:
Mathematically, QM is solved as a discrete sum of wave-functions, whereas the interpretation of it is made as though it is not (only the system wave-function) and it works correctly when you do this because of the action of Hamiltonian mechanics.
But here is the point: It is not in general possible to take a generalized continuum theory without ANY discreteness in it and define a process internal to that theory that causes it to break up into a well defined sum of functions without first also imposing boundary conditions. And the universe has no boundary conditions that we know of (but more particularly the principle of general relativity also requires there be none). So there is a conflict.
So we bypass this conflict by first making the assumption that it CAN be broken up into discrete functions in this fashion, and this is what QM does using the a-priori defining of the degrees of freedom required for the answer, Since QM also agrees with Natural observations it follows there must also be something discrete going on in Nature, and this is in conflict with GR, like it or not because GR is a continuum theory through and through without boundary conditions!
As I alluded to in my original answer, this dilemma actually has an obvious and proven answer (much like, by analogy, the twins paradox is not really a paradox at all) But you will not accept that answer until you work it out for yourself, so I am not going to give it!
There is nothing wrong with the continuity. And talking about motion where's the problem with it? Surely there is discreteness with certain properties of certain particles but I fail to see any problem with that.
The modern mostly accepted theoretical physics concept is - particles are singularities of a universal vacuum field structure, being antropomorphically interpreted as "discrete" creations like particles etc. The physics science problem mainly consists in understanding this universal vacuum field structure, being nowadays presented by means of a Weinberg-Salam Standard Model etc.
Kimmo.
if you just do particle problems, or just do gravity problems, then you are right , no problem at all.
But in their current field theory formulation, GR denies boundary conditions, and QM requires boundary conditions and at some point in physics at high energy and small scale, the two are going to conflict. But both theories are correct to the limits of our empirical knowledge.
@Andrew
Optimal solution would be a model which includes them both. I have been working on that for a while (with extremely promising results).
There are already now several candidate theories of quantum gravity, but since I'm not an expert in this field I cannot comment the details. However, from all we know about field theories the existence of gravitons, i.e. gravity interaction-mediating bosons, is pretty much a certainty and awaits experimental verification. Thus, in this sense gravity should be no different from the other fundamental forces.
Kimmo,
Yes hence the "obvious" answer I alluded to earlier - when you see it, you know it, and once you know it, there is no going back.
As a reader of history in physics, I see all the signs of the next physics evolution on its way in the next few years. I hesitate to call it a revolution because unlike the early 20th century, this is more about a synthesis of known correct ideas, than an explanation of new observations. Nonetheless, it will make all the existing issues of dark matter and energy and inflation that are hard to explain quite easy - these will be viewed as a storm in a teacup and the great John A Wheeler will be proved completely correct in his most famous quotes.
P.S. Read a recent article by Freeman Dyson : http://publications.ias.edu/sites/default/files/poincare2012.pdf
@Prykarpatski
The arguments in this paper are of the kind that, in my humble, opinion, diminish the credibility of those thought experiments. "The second mass is constrained by a system of mechanical linkages and springs to follow the movement of the first mass and cancels the fields generated by the first mass." What kind of mechanical linkages and springs can be used to follow the movement of atomic particles? Those thought experiments are all the time referring to contrivances that cannot exist in our universe but then, when we ask for the position of an electron when it is not observed we are told that our question doesn't make sense, because the electron will not have a position unless that position is measured.
The "double slit" experiment is one of those thought experiments, where this kind of contrivances are introduced: a screen that cannot be penetrated by electrons, when we all recognize that most matter in this universe is made of atoms and therefore the space occupied by a body is mostly empty.
Every experiment I recognize starts as a thought experiment but then the experiment must be performed as described to be useful. A thought experiment is not but a disguised hypothesis: it must pass the test of an actual lab in order to be taken seriously. Unfortunately those gedanken experiments are everywhere in our science nowadays!
Going back to the question, the axiom of continuity can be proved consistent with the system of Dedekind Cuts. Furthermore, a model of the rational numbers can be build from the system of integers and, as a consequence, we can reformulate everything as if we were counting instead of measuring. It will be harder to understand, but we can, in principle.
It depends on your accuracy: if you see a 'particle' from a relative to its dimensions big distance away, you can treat it as a point entity. If you go 'closer', then you can treat it as a wave with de Broglie's wave length. If you want to go deeper, probably you have to treat it as a vibrating chord (string) or membrane.
A lot thanks to all colleagues for your nice answers and efforts by which I am able to understand the actual answer / phenomenon.
I think that special theory of relativity is the best tool to know the discrete nature of particle Physics.
@Mohammad Ayaz Ahmad
Mohammad, You are right, but it is necesary to remember that SRT still is linked with serious problems of describing many particle systems, as well as with those of finding an adequate physical explanation of the particle mass, radiation force etc. within the relativistic electrodynamics and its relationship with the energy and so on...
Regards!
Just to make it clear that STR is probably the best tested physical theory because there are many devices (such as satellites) whose operation depends on the validity of the STR. Rumours about the "failing" of STR are strongly exaggerated, to use a famous quote :). Actually, such claims are crank science: http://en.wikipedia.org/wiki/Special_relativity
http://en.wikipedia.org/wiki/Test_theories_of_special_relativity
I feel that any physical boundaries including space should be stretched where the relative time is within the limits of with whatever the particular engineering application from the Earth point of view calls for. That is Earthly space physics with the limits of Sun and the Moon. Beyond it namely the Deep space physics and the matters related to it can be discussed in different and varying ways depending on the location of the observer. What is past, present, and future for us can be as one event to a equidistant observer far away. Space, matter and time and all being interrelated and matter assuming huge variations and manifestations, it is impossible at least for the time being to follow any of the single uniform codes that have been devised so far.
@Tapio
Dear Tapio, sorry for the aside comment! I would much wonder if You were written down physicall sensible relativistic Dirac type equations for two electrons... and also explained both the classical/relativistic radiation phenomenon and the well known relativistic energy-mass Bridgman-Brillouin paradox (described in the Brillouin's honest book "Relativity reexamined" ( AP, NY 1970) ... Any way, I strongly support the classical medieval motto that "The tea will not become sweeter by means of stirring it!'...
@Anatolij
I don't understand what is the point that you're trying to make here. I can treat interacting particles with an appropriate Hamiltonian, and a two-particle problem is always analytically solvable (in principle). I don't know (and I have never heard) of the "relativistic paradox" that you mention. The only paradoxes I know of are not real but based on incomplete understanding and/or incorrect interpretation of STR.
Physics is governed by conceptual models that are then put in a Mathematical shape for further growth of the postulated theory. Maths does not rule physical concepts that are generated on physical observational facts or conjectures. Gravitational field is like entropy or temperature has also baffled me a bit. Gravity is already an anomaly as it does not unite with the other three known physical fields. Does it generate itself purely from space and time and how? Local inhomogeneity in space and time can well generate mass and energy but normally both these maintain homogeneity.
Comments made by have disappeared from the website!!!
Narendra Nath
@Tapio
OK, dear Tapio Ala-Nissila - read a book by L. Brillouin... Nothing happened, I am not familiar too with many facts in modern science... Yet I am trying to get aware of many of them ... simultaneously not "stirring the tea" ...-:) It is ok!
Regards.
@Nath
You wrote: "Local inhomogeneity in space and time can well generate mass and energy but normally both these maintain homogeneity."...
Please explain your thought more clearly and Do it!
Sincerely, regards!
To help, uncertainity relations based on conjugate quantities like space and momentum (mass) and time (conjugate energy ) provides one the support for such ideas. During earliest period of BIG BANG only such things actually could have happened.
Narenda,
Cannot get around the basic dilemma that GR field theory axiomatically denies boundary conditions, and QM field theory axiomatically requires them. At some point in these theories this conflict is unavoidable. As I have already stated, the correct and scientific resolution of this dilemma is working through academia now and will be apparent to all in the next few years.
One example of new ideas that might solve all these issues:
http://www.nature.com/news/simulations-back-up-theory-that-universe-is-a-hologram-1.14328
@Narendra Nath
Dear Narendra, you wrote: "...uncertainity relations based on conjugate quantities like space and momentum (mass) and time (conjugate energy) provides one the support for such ideas."
I would be happy if you performed and sent me a derivation of the uncertainty relation for the " time -conjugate energy" ... I will award you for $1000!
Sincerely,
regards!
Here's a simple derivation: http://math.ucr.edu/home/baez/uncertainty.html. Where should I send my bank info for your deposit?
Are we gamblers in this site to earn money from one another. Please take me as a quitter! The Uncertainty relations are not equations for proof. Their indirect proof lies in the Special Theory of Relativity where these help one lead to the famous Mass Energy relation , E = Mc2. I am sure we have learned such things in our College Physics!I like you, Anatol and allow you to dislike me fully. After all we all need people who dislike us . They help us grow and appreciate 'opposing ' view points. Where is the finality in sciences, it is all relative truths, subject to modification as new expts and ideas come in!
@Tapio Ala-Nissila ·
Dear Tapio, I appreciate your "proof"-joke you attached, yet sorry I meant before the physically sensible and math-rigorous proof, not a joke! For your formal interest in the question posed above I can for sure pay on your account 1 cent, not more -:)!
P.S. Concerning the Mandelstam-Tamm "derivation", it is nothing more than a vain speculation on the topic... To the regret.
Regards!
@Narendra Nath
Your are in the main right, and we really need to freely discuss and accept or not accept different explanations, yet we also need like and accept each other as unique sources of all notions and ideas of the surrounding world and the universe ! As I am trying always to do!
Sincerely, regards!
Anatolij, i am for complete freedom of thought for an individual. Actions however need to conform to the norms of the society we live in. Results of actions come automatically but at the right time.I am a happy person being a good friend of persons like you. Best wishes
@Narendra Nath
Dear Narendra, with my cordial respect to You I am really happy too!
One has so much really interesting and exciting physics problems to discuss, to understand and to cope with... -:)
Season's greetings!
Dear Professor Anatolij Prykarpatski
A lot of thanks for season greeting!
The particles may be discrete , but all the participants are discreet and considerate..
Best wishes.
Happy hollidays my dear RG friends! Wish You better and healty next year!
Anatolij, coming back to the uncertainty relation: the simple proof that can be found in any elementary QM textbook is rigorous for non-relativistic QM - it does not assume anything about the wave function, either. What more do you want? Maybe Santa Claus can bring you the answer that you want :).
Merry Christmas and Happy New Year!
I wish a nice Night, "Noche Buena", and a very happy and hopeful 2014 !!
FELIZ NAVIDAD !
Look forward to meet in the Happy New Year. Particles are discrete or not, does it really matter!
@Tapio Ala-Nissila
Dear Tapio, please say honestly - would you prefer to know the truth or to get money? I am sorry to remind once more that the physical "proof-jokes" are not taken for granted as a rigorous proof... Why? The reply is very simple - It does not exist. I guess this line of the discourse is closed, as there is nothing more to discuss.
Sincerely, cordial regrads and wishes Merry Chrismas and Happy New Year!
All the best!
A.
@Narendra Nath
I congratulate up to Narendra for his nice sentence : "Particles are discrete or not, does it really matter!" Yes, they really EXIST, and it is SO MUCH, that exist still we!...
Cordial regards!!
First, things need to exist in our minds. Then, the same get projected outside. WE see and believe and what we don't see, we also believe! Long live our cordiality!!
@barkatram
This is illustrated more simply in the emphasis on pi, an unreal number because it repeats infinitely, and phi, or 1.6, the golden mean, where, when practicing a state of gratitude, for all species, both humans and animals, where the heart hits this frequency and jumps octaves, a state of sync only explained by intelligent design matrices revealed by math in the limitations on cosmic rays.. Dr. Wood, my mentor, derived Maxwells's equations of electricity and magnetism for himself and found that two of the three roots had been taken out of the texts. These being zero and the square root of minus one. However, if you accept my premise that there was no big bang, only an ongoing song of life itself manifested in music, such as Bode's Law, where every planet out from mars is one octave further from the sun, then we as co-creators and shapers of reality as a holofield of experiential matter and Galois polynomials separate every member of a species from every other species and individual manifestation, then the one song amkes sense and miracles are once more the natural way of being, as in ancients' times, where dolphin and human in love did rhyme...
Andi, your comment assumes human being as primary in the universe. Humans have neither created anything new in this universe that did not exist alraedy, We have only munipulated what exists already here. Big Bang or no Big bang is difficult to find experimentally as we need to do precise experiments for earliest of times in cosmology and these are far being possible with present technology on Earth!
Global picture is one thing which we actually see. Going into the details in the particle levels and understanding is another thing which is also exciting and has a lot of intuitory knowledge imbedded and can be substantiated by experiments. But trying to construct the global issues from the particle level can also be done in various ways,but the picture so built up with lot of mathematics and gimmicks will yield a totally new picture which will always be virtual as we should understand we are not the Creator behind these.
….> But trying to construct the global issues from the particle level can also be done in various ways,but the picture so built up with lot of mathematics and gimmicks will yield a totally new picture which will always be virtual as we should understand we are not the Creator behind these…..
Best wishes to Stefan to construct further pictures using Geometry, a beautiful part of Mathematics. In fact nature itself shows the geometry of structures through the cosmos we see from Earth. It may look the same from any other planet in our solar system except for some minor displacements. It makes us wonder weather we can ever escape from our solar syatem with a hope to return back too!
Dear All, I am very much thankful to all of you, by which I have understood a lot of in about the discrete nature or particle and Particle physics.
HAPPY NEW YEAR, 2014!
Almighty God blessed you all prosperity, health and all beautiful wishes!
Dear Mohammad,
Many thanks and mutually beautiful wishes to you and all around!
A tiny question subject to this blog is still left, so - Is the particle discrete or not? What have, in reality, we understood about the particle nature?...
Cordial regards!
Dear Professor Anatolij
Yes, the particle is discrete in nature.
Dear Mohammed,
Thank you for the very interesting question you posed , and the very interesting answers.
Wishes,
Panagiotis Stefanides
Yet.... what is, in reality, inderstood under the term "discrete" , when we say "the particle is discrete in nature"? Some space-time singularity with well specified locus data, or ... something else?
Sincerely,
Anatolij.
Nature is neither discrete nor continuous, these are concepts that are imposed for the sake of our attempts to understand. On the other hand nature is both discrete and continuous if both concepts have appeared in order to come to some kind of understanding. After all, our understanding is part of nature itself.
Time passes.
Is it not most logical to consider a basis of different kinds of time increment?
I like Hindu philosophy very much, I found it very logical in its fluidity and in its marriage with language. The three central `Gods' in Hinduism are Brahma, Vishnu, and Shiva: The creator, the preserver, and the destroyer. Strangely (or not so strangely..) in quantum stochastic calculus (QSC) we use a fundamental basis of time increments: creation, preservation, and annihilation. And these increments of time are given in the general context of creating, preserving, or annihilating information. Both discrete and continuous preservation is considered. Further, algebraically, all of these time increments may be realized as components of a single general time increment: the quantum stochastic increment of time.
Interestingly, this algebra of time increments is hyperbolic: as a matrix algebra it is represented in Minkowski space.
Continuity is only useful abstraction but very much useful for a lot of practical targets.
Dear Mohammad,
About your question, yes understand the nature of motion, it is first necessary to confront yet another fallacious concept in physics called continuity (infinite divisibility) but I suggest you то read below this paper maybe something will be in addition to your question.
Best regards,
Julijana
What is a Discrete Particle Size Distribution? - Brookhaven
www.brookhaveninstruments.com/.../What%20is%20a%20Discrete%20P...
particle size and size distribution, the main fea- tures of the ... Cumulative UndersizeDiscrete Distribution ... son is simple: The size classes are not all equal.
Dear JulijanaT.
A lot thanks for your kind reply and to share few time on the question.
Thank you for voting up. I believe your question is very profound and important for real scientists.
Dear Mohammad,
Thank you for voting up. I believe your question is very profound and important for real physicians.
Dear Mohammad, I do not know how I helped but I do not have an adequate response, and so I see things like you, many are not doing Physics,
Please see below link of paper,
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&ved=0CC8QFjAB&url=http%3A%2F%2Fwww.brookhaveninstruments.com%2Fpdf%2FWhat%2520is%2520a%2520Discrete%2520Particle%2520Size%2520Distribution%2520May%25202011.pdf&ei=rrzgUsWrJ4bLtQbk6IDICg&usg=AFQjCNEfMSAPEhuZ2lR-HWuK43b02kI5Fw
regards,
Julijana
Dear Valery Abramov
A lot of thanks for kind effort and admire.
I think that if one is to fully understand the suggestions of discreteness in nature one must understand the role of the measurement apparatus in extracting the data from which statements about reality are made. One must be clear that the inference from measurement can only provide us with information about how nature is responding to the particular apparatus taking the measurement.
At best an apparatus is fully understood in the context of a theory regarding a collection of properties, and then any disturbance of these properties may be used to infer compatible properties of nature.
For example, one may consider such properties as those of the electromagnetic field - which serves as an apparatus. Then any disturbances detected in this field may be regarded as interaction points. A structure in nature is regarded as that which the field is interacting with. This structure has ultimately been inferred from the only truth in science: measurement data.
For example, a pollen grain moves randomly, thus randomly moving particles are inferred in order to explain the observation. This observation is data.
Ultimately, we are all making observations. Scientists often regard their apparatus as the thing doing the observing. The data obtained, either directly as a human being or from the measurement apparatus, is always subject to interpretation. This cannot be avoided. In the case of laboratory apparatus the interpretation of the data is determined by the theory that the scientist is using. Different parts of the data may fit different theories. In the end it is up to the scientist's own intuition to decide whether or not a theory is satisfactory. What's more, the scientist's opinion may change. One day this, another day that.
If one is to find a satisfactory theory of nature then it must account for the role of the scientist too. If a scientist detaches his/her self from the science then that is like neglecting the role of the apparatus in the process of measurement. I appreciate that this is unsatisfactory, for a scientist attempts to be objective. But if one is to be truly objective then one must simply observe without interaction, or measure without measurement.
I apologise for this long message, but what I am trying to say is that any measurement is subjective. The very reason why a measurement apparatus is set up is to try and collect data about a particular way in which the world is being considered. The most objective form of measurement would be to simply live life without judgement, without trying to answer any particular questions. Particular questions have particular answers, and these answers raise more questions about interpretation.
But for the purposes of science we may attempt to build a general theory of measurement. That is a master equation that describes the process by which data is generated from measurements. We need not assume the existence of lines, but only an order relation on the measurements that are taken. But we do assume mathematical structures like functions, variables, and so on. But what is science without mathematics? What is an apparatus without the logics form which it was conceived?
I appreciate any time spent reading this, too long yet incomplete, opinion.
kind regards
@Mohammad, I have followed your thread from the early beginning. This is my first response which might be interested to people who follow this thread. Find out how we recreated the famous CERN particle physics laboratory at the Science Museum!
http://www.youtube.com/watch?v=ya3H5wDn9ag&utm_campaign=Marketing%3A+January+Lates+eflyer&utm_medium=email&utm_source=SCM+Group
Dear Matthew Brown and Ljubomir Jacić
I am very much happy to see your kind help and efforts which you made for me and now I am understand the mystery of the question.
thanking you
Dear Dr. Mohammad Ayaz Ahmad,
Particle is considered as body whose spatial extent, internal motion and structure are irrelevant hence no matter considered as discrete or not.
Particle is defined as abody that you can not describbe it as discrete or not because it is similar to atom .
Sun's energy heating up closed chamber of gaseous molecules, particle theory assumed as continuous gives meaningful results. The way the energy reaches all along from its source to the given matter is a long story ranging from discrete to continuous. . All phenomenon discussed are meaningful within a control volume which can be well understood be it small or big and within the grasp of an individual observer. When the human mind expands with the right intuition the picture becomes clearer and mathematically described. If not there can be weird hypotheses which is woven beautifully by the craft of mathematics., then we also see illusions which seem to be real.
I'm glad to be of some help Mohammad.
An additional note, that some may find interesting, regarding time:
One may deduce an intrinsic quantization of time in which there are only two degrees of freedom. These are past and future. In the context of information the past is regarded as the output domain of all information. This is where our data lives. Complimenting this comes the general assertion of a domain that is the source of all information, the future, the general domain from which the data is taken from.
For example, if one observes an old artefact, then prior to the observation of that artefact the considered observation is in the future until the observation takes place. Once the observation has taken place it is an element of the past.
The fact that the artefact may be regarded as an object possessing history makes no difference to one's observation of it being in the future.
One may take the above as definitions of `past' and `future'. i.e. future is defined as the domain of potential observations/measurements, and the past as the domain actual observations/measurements.
There is two very interesting things to note from this consideration:
I) past is not transformed into future, but instead future is transformed into past.
ii) When this is formulated mathematically we essentially have a future indicator (1,0) say, mapped to a past indicator (0,1). This may be irreversibly achieved by the action of the matrix
01
00
on the future row (1,0). However, and this is the interesting thing, this is the matrix algebra representation of the continuous differential increment dt. (That means that if dt is understood precisely as an element of an algebra where it satisfies the very particular conditions that it is non-zero but its square is zero (as is assumed in calculus), then it has the above matrix form.)
This does not mean that time is continuous, and it does not mean that time is discrete. It simply asserts that the matrix representation of continuous differential calculus (which is unique up to rotation) is the same as a logical formulization of basic observation: the transition of potential to actual.
To some this may sound like mathematical jargon, but I hope that that is not so.
Thank you for reading.
Dear Mohammad
Thank you very much for sharing me this question
In Physics, particles can be visualized by tiny bodies with zero size (when compared with surrounding). Particles can be located in space such that for certain time they can have their space coordinates, no more than one particle can occupy the same location at the same time, i. e. particles cannot be coincides. When we deal with what is known as rigid body (which is compose of a large number of tiny particles, we mean atoms), instead of saying; rigid body is compose of a number of particles which are tied together; we say that the integration of an infinitesimal volume element (dV) is exactly the volume of the rigid body (V).
Particles are discrete tiny bodies. If we seek for continues thing, an example is wave, waves are spread in space and time it cannot be located in a certain location at certain time.
I hope my answer is clear
Best regards
If you "found" what you are looking for... "This" is discrete.
Las particularidades son pellizcos del azar absoluto. (Random).
Dear Abdulghefar Faiq and beloved sister Ani
Your opinions are very nice. thank you for your kind attention and give me some valuable time in your busy schedule to write the comment on my question.
What is discrete today may become continuous & vice verse, it is all dependent on the measurement sensitivity and accuracy. Homogeneity and inhomogeneity also get affected in the same manner. Space and time are the concepts taken in science to describe and study Nature. We need to assume somethings that appear plausible for a particular study we undertake. We may change our same assumptions in a different situation. Simplicity and complexity decide what is reasonable. We live in a relative reality!
i do not understand the confusion between Faiq and Ana Maria above two comments!
There are a lot of interesting theories in physics. Matter exists as a state of energy, while waves of probability spread throughout the universe. Existence itself may exist as only the vibrations on microscopic, trans-dimensional strings. Here are some of the most interesting theories, to my mind, in modern physics (in no particular order, despite the enumeration).
The behaviour of all of these particles and forces is described with impeccable precision by the Standard Model, with one notable exception: gravity. For technical reasons, the gravitational force, the most familiar in our every day lives, has proven very difficult to describe microscopically.
I also wonder about the nature's evolution of gravitational force , followed by electromagnetic, nuclear strong and nuclear force in this sequence. Dark energy as well as dark matter are the terms used for unknowns and gravity is playing a duel role here, being attractive and repulsive both!
I am always having the doubt about the real depth of gravity. I feel it is felt more instantaneously than the speed of light, as we are talking of stars rotating about its central focus which are millions of light years away..Understanding the gravity of the problem is an age old saying and is literally very true.
Gravity has both the attraction and repulsion part, hence electromagnetic waves is the consequence to gravity evolution. Particles got later formed which must be dependent on the electromagnetic waves.
Metallic atoms are discrete and knowledge of it is useful to manipulate and change the metallic properties and even for identifying the global structure. In metals the atoms are confined while in space they are very mobile and the problem becomes very complex. Though particle is actually discrete , by what use it would be when a wandering particles motion is studied in a global context? But in the atomic level there is no doubt that a particle as a group of atoms is a particle and is to be studied discretely.
@Sundaresan Muthuswamy
The phenomenon and related physical essence interplay is well demonstrated by means of the classical Dirac delta-function expansion:
δ(x-t)=(1/(2π))∑_{n∈Z}e^{in(x-t)}, that is a strongly discrete point peculiarity in space can be understood as ... a set of plane waves in space..., which, under some conditions, can even be measured and some harmonics can be really observed.
That is a nice joke of Nature!
Sincerely, to all - regards!
Mathematics is the invention made by man. For he physical appearances of matter in the world it is not man made.Mathematics is better than physics in terms of purity because it is made from well laid rules has no bias or desire element in it. But all the same it is Natures gift to man who has a good mind and mathematics has been practiced from the very distant past. But the physical appearances of matter, the particle; is much beyond mathematics, miles away, a thing which is physically created and not manipulated; fairly or otherwise as done in mathematics. Strangely mathematics has the ability to create virtual images again true and untrue and man gets carried away by it too far.
Dear Professor Sundaresan Muthuswamy
Thank you for your kind effort. Yes I am fully agreed with your nice opinion.
@Sundaresan Muthuswamy
I understand your doubts, but ... believe that the Nature is not so malice and Her creation, a Man, thinks tracing the Nature ideas a true way saving their attraction : "The physical law should have mathematical beauty" (P.A.M. Dirac) ...
With best regards,
Anatolij.
@Anatolij Prykarpatski
I fully appreciate your valued views.My only emphases is that a knowledgeable man as an individual is indeed humble, but the collective wisdom of individuals reflected as a scientific outcome is sometimes not pure mathematics or physics as it has a consensus element which becomes the scientific Bible for the masses. Nature is kind and patient as it nurtures all of us no doubt, but it will not support any little untruth.
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