@Andrew:

Why you don't take the time and read the first chapters of a reasonable quantum mechanics textbook (unfortunately I don't know the newer ones to give advice, the old L. Schiff is very good).

If you are ready with the free particle and of the harmonic oscillator you know that what you express by 'energy and momentum are quantized variables' is probably a misconception: for a free particle there is nothing discrete with energy and momentum. Only a binding force-field (e.g. in the harmonic oscillator) lets discrete energy values arise, with momentum things are similar.

Whether the dimension of a quantity is 'elementary' or a combined one is a matter of human convention and not of Nature.

None of the above.

@Andrew:

Why you don't take the time and read the first chapters of a reasonable quantum mechanics textbook (unfortunately I don't know the newer ones to give advice, the old L. Schiff is very good).

If you are ready with the free particle and of the harmonic oscillator you know that what you express by 'energy and momentum are quantized variables' is probably a misconception: for a free particle there is nothing discrete with energy and momentum. Only a binding force-field (e.g. in the harmonic oscillator) lets discrete energy values arise, with momentum things are similar.

Whether the dimension of a quantity is 'elementary' or a combined one is a matter of human convention and not of Nature.

"for a free particle there is nothing discrete with energy and momentum"

I am not sure, but how can one be sure that such statements are correct: after all, we don't have the experimental means for verifying them, i.e. we don't have continuous measurement devices. ;--)

Lev

The presence of quantisation is reflected in the quanta meaning discrete energy packages that are emitted by molecules vibrating; this is an example of the HO as mentioned by Ulrich Munze.

Like in a string there also the allowed motion is quantized so nothing new, as long as boundary conditions are present. In this case the string can not move at the two ends

Lev,

please don't fall into your old misconception to see a fundamental difference between a continuous measurement and one that gives 4 valid decimal digits (and in the follower model will give 5 valid decimal digits, ...).

Ulrich,

There are no continuous measurement devices!

It is our models that are continuous. As Riemann mentioned, we simply postulate them to be continuous.

Now, suppose I will call your bluff and will ask for the *proof* of continuity?

By the way, even Hilbert conceded this.

Lev,

again you puzzle me with the problem how an educated person can (with obvious self-confidence) utter such nonsense. If you speak of 'proof of continuity' you speak about mathematics, a realm to which measurements definitively not belong.

When mathematical notions are nevertheless used profitably in physics, this is since the notion of idealization that connects reality and mathematics gets normally absorbed by scientificly inclined children during school age and normally is not a matter of discussion between mature scientists.

If you would look up in some physics book the methods that are available to determine the kinetic energy of an electron 'in flight' you would see how pointless the question of continuity is. If someone would give a list of energies and assert that an electron could only have kinetic energies from this list, one could disproof this easily unless the list would be sufficiently dense to be empiricly identical to the continuum.

Ulrich:

"If you speak of 'proof of continuity' you speak about mathematics, a realm to which measurements definitively not belong. "

No, I do not speak "about mathematics" at all: I'm educated as a mathematician. In mathematics we simply *postulate* some things. But these are just abstract postulates. By referring to "proof", I was talking about experimental proof and wanted you to realize that such is not going to come.

Moreover, some calculations can be confirmed, for example, even for up to 7 or 9 decimal places, but this only says that the model is useful for such approximations, no more and no less. It does not mean that the underlying reality is of continuous nature, which is a very, very different statement. Approximations are one thing but we don't really know what they mean (except as numeric approximations go). Ptolemaic (epicycles) model was also approximately OK, but so what. In fact, knowing what we know now, it is practically impossible for the continuity postulate to be confirmed (from 'physical' point of view).

Already in the first half of the last century such great physicists as Einstein and Schrodinger questioned the continuity postulate. Certainly, in the 21st century we are, finally, entitled to seriously question its physical legitimacy, especially in light of the indeterminacy relations.

I still cannot get over how lightly you dismissed (in my question discussion) the following very perceptive and relevant observation by a leading physicist of the last century:

"If you envisage the development of physics in the last half-century, you get the impression that the discontinuous aspect of nature has been forced upon us very much against our will. We seemed to feel quite happy with the continuum. Max Planck was seriously frightened by the idea of a discontinuous exchange of energy ... Twenty-five years later the inventors of wave mechanics indulged for some time in the fond hope that they have paved the way of return to a classical continuous description, but again the hope was deceptive. Nature herself seemed to reject continuous description …

The observed facts (about particles and light and all sorts of radiation and their mutual interaction) appear to be repugnant to the classical ideal of continuous description in space and time. ... So the facts of observation are irreconcilable with a continuous description in space and time " (Schrödinger, 1951)

But we have been through this several times to no avail, and I should probably stop paying serious attention to such things, except in this case I felt sorry for Andrew. ;--)

@Ulrich,

I understand and accept the QM argument about resonance between harmonic oscillators underlying quantization of energy. But the predicate to that QM argument is the prior existence of those discrete harmonic oscillators. That is what I am on about.

Can such discrete harmonic oscillators as we see in the standard particle model arise from a continuum of mass, time and length. I suspect this is the point @Lev was making (correct me if I am wrong) Or instead, do such stable discrete and identical harmonic oscillators as we observe in each electron arise from an underlying natural discreteness in one of the units?

Andrew

I do not understand in your last mail:

"such stable discrete and identical harmonic oscillators as we observe in each lectron"

a harmonic oscillator is a system in which a force is exerted on particle that is comparable to that has its analogon in classical mechanincs of that of an oscillator-spring; as Ulrich mentions, please consult a textbook on QM.

Andrew Correction

The keyboard was too slow in the previous entry

A harmonic oscillator is a system in which an EXTYERNAL force is exerted (on a particle) that has its analogon in classical mechanincs of an oscillator-spring. This is not an intrisical phenomenon

@Harry,

My response was purely in reference to Ulrich's raising of the subject about harmonic oscillators and was poorly worded due to a misguided attempt not to be too verbose.

There is an intrinsic ability for an electron to allow the system it is part of to produce quantized energy packets (such as around the proton in an hydrogen atom). I did not mean to imply the values of these energy levels were intrinsic in the electron; they are of course intrinsic to the system or environment in which the electron finds itself.

The point I was making was that such systems that quantize energy require discrete particles to be present, and my question concerns the ability of a continuum state of mass, time and length to generate such discrete long lived particles with identical properties throughout time and space.

Andrew

My response is to the harmonic oscillator whihc has a beautiful analogon in the oscillation of the two atoms in a di-atomic molecule. This vibration can be calculated on the basis of QM (only) and is quantized and also the molecule absorbs and emits radiation in a quatized manner.

This for me shows the beauty of QM

Lev,

You want me to realize that an experimental proof for the non-existence of gaps in the values of kinetic energy of freely moving electrons is not going to come. The missing of such a proof is no problem at all. Is there a proof for the missing of angels?

If such gaps would be detected this would be a sensation. It would be 'new physics' from a direction from which no physicist expected something new.

Andrew, what do you mean by >? I don't see such oscillators.

@Ulrich,

Yes Harry pointed that mistake out already and I have admitted poor/wrong wording - see my reply to Harry

@Andrew,

you are right that the existence of stable particles, and their properties such as masses, charges, spins, and magnetic moments, so far largely withstood our understanding.

Good physics text emphasize this lack of knowledge. When trying to learn a bit of modern molecular biology during the last years I got the impression that in this field it is normal to mention only these problems for which solutions are already known. So physics seems to be a bit more open in this respect.

Ulrich, the old Leonard Schiff book is indeed a great foundational text on QM, the Merzbacher and the Cohen-Tannoudji are pretty good as well.

One oft-overlooked reason for quantization is simply ... geometry, more precisely the existence of end-points.

Whenever the environment within which some phenomenon takes place is not infinite, the end points (or walls) can give rise to systems of standing waves, with peaks and troughs. These peaks and troughs in turn can in turn give rise to quantization of some system attributes.

Schrödinger's equation is really a form of standing wave equation

Ulrich,:

"You want me to realize that an experimental proof for the non-existence of gaps in the values of kinetic energy of freely moving electrons is not going to come."

I'm not an expert, but isn't it true that we don't have adequate instruments to be able to detect any such possible gaps?

Chris

Also called boundary conditions, confinements

Lev,

in high resolution mass spectrometers even very small deviations from expected flight behavior of ions would become apparent. To build such a device, 10 times the normal size and much better protected against outer influences could be a research proposal for 'energy gap hunting'. Although this would be much less expensive than a large particle collider, one would build such a machine only if one has a non-negligible chance for finding something interesting.

Harry, 'boundary conditions' can be infinite .... although yes, it sounds like a misnomer .... :-))

Ulrich:

1. "you are right that the existence of stable particles, and their properties such as masses, charges, spins, and magnetic moments, so far largely withstood our understanding."

Not a minor list, by any stretch of imagination. ;--)

2. "one would build such a machine only if one has a non-negligible chance for finding something interesting."

And who is to estimate the "chance"? If the chance is so incredibly negligible, would you bet the life of your family on it? ;--))

Of course you! Of course not!

Sorry, I don't believe in the childish bets in science like, for example, that of Hawking with Preskill, when one does not risk any serious consequences. ;--)

Science requires and deserve different kind of commitment.

Lev,

if you mean to need experimental input, as Harry and I unisono stated already, you have to come up with a propoasal. This has to convince at least one experimental physicist so that she/he is willing to work out an experiment along your lines. Further you have to convince an institution to provide funding. Nothing in this agenda is childish.

Of coarse your propoasal has primarily to convince you. In thinking in this direction you will, no doubt, experience that hardly anything is more difficult than working out a relevant question to Nature for which the answer is not yet known. There are no limits to the required commitment.

Ulrich,

I'm a bit surprised: Is it that difficult for a *good* experimental physicist to identify the nature of the required experiment given the structured event hypothesis?

Do you mean to say that we don't have a clue how to investigate the micro-nature of a free particle's trajectory?

Lev,

we tend to be in a circle again. As I tried to point out, there are no structured events in the orthodox understanding of particle trajectories. If you stipulate such entities you better have an idea what kind of experimentally accessible phenomena can be expected from them. I think in fact that a 'good' physicist would be needed since part of his task had to be to absorb your ideas and to transform them into something testable. Actually I think that you would need a miraculous physicist to achieve this task.

To be sure, what an orthodox physicist would understand as the micro-nature of a free particle trajectory is considered clarified by the theory of quantum electrodynamics (for electrons) and the results are well known to provide the best agreement between theory and experiment known so far in physics.

Just to be sure: Do you mean to say that a good (probably young) experimental physicist cannot at all approach a particle's trajectory as an 'new' phenomenon to be investigated (independent of how theoreticians treat it)?

Chris

Thanks to you I started to (re)study Merzbacher for the boundary conditions. I notice now that he provides excellent insight in the basis. An anecdote: after 40 years not using it I got rid of it last year (also of Schiff and another author I do not recall): but the book is on the WEB for FREE. As a matter of fact in those former days I was less interested in the intro because for the tests we had to know the first 3 wave-functions of the various simple systems, like the HO hydrogen atom, by head, including the recurrence formulae

Lev,

of course a physicist can approach everything. That he will find anything not yet known is not guaranteed. For some phenomena it is highly improbable.

In the case of particle trajectories the situation is that generations of experimenters did their best to ask any question they could come up with. Did you come across Stern-Gerlach experiments? This give an impression of the non-triviality of some approaches.

Especially with particle trajectories one has to note that the primary statement of quantum mechanics is 'there are no particle trajectories'. From the basic notions of quantum theory it is a rather subtle deduction (originally done by Heisenberg) to explain track formation in cloud chambers, and related devices.

Here we come back to Harry's proposal, the double slit: There is definitivly no single trajectory that connects the particle in front of the slits with the same particle after passage of the slits.

Lev / Ulrich

The interference phenomenon is seen daily in an electron-microscope studying a nano-crystal that acts as a multislit

Interestingly, someone voted down my answer re boundaries.

Instead of voting down, it would be more constructive to explain your objections, even though it seems that the person who did so , did so not because of the content, but because of a comment I had made in another thread initiated by that person.

Ulrich: "Here we come back to Harry's proposal, the double slit: There is definitivly no single trajectory that connects the particle in front of the slits with the same particle after passage of the slits."

Agree, but then why is all this confusing talk in physics of "particles" and "trajectories"?

It appears that what physicists are covering up is that QM severely undermined the previous conceptual view provided by classical physics and yet has not offered any coherent new view that can replace the old one (numeric computations are irrelevant here). And instead of admitting this and the transitory nature of the present physics (as for example Einstein and Schrodinger did) physicists are trying to pretend that "that's the way things are and they are not going to get much better".

Andrew,

I forgot to reply directly to your question.

I suggest that "the underlying cause of quantisation of energy and momentum" are not "length, time or mass" but the underlying, event-based, structure of all processes in nature. The discreteness of "length, time or mass" and everything else is the manifestation of this underlying discreteness.

In a sense, one might 'blame' the nature 'time', but the time is simply embedded in the stream of events.

Lev,

The simple answer (for me) is that it is given in a very readable and intellectually satisfying form in the books which Chris and Harry mentioned: 'the Merzbacher' freely downloadable from the internet.

The more difficult one is that I try to explain it myself and harvest the benefit from the clarification that usually is the consequence of writing something down instead of merely thinking about it.

As an adressee I have also Andrew in mind whom I learned to know as an engineer deeply interested in the inner working of Nature.

Quantum mechanics has a more complex logical structure than any physical theory created before. This logic has a precise mirror image in a technical device we all are familiar with, the digital computer. The structures which matter here are RAM and CPU on one side and hard disc and display on the other side. We ignore the existence of debugger programs so that there is no way to tell what's going on in RAM and CPU unless our program contains I/O statements (here the O part matters) which write the values of selected variables (with names not only adresses) to a file which we can print out and read.

Quantum mechanics in its basic formalization has just these two structures.

1.A Hilbert space H which holds states (just as computational states in the computer) and a Hamiltonian (a selfajoint operator on H) that makes the states move (just as the CPU in the computer)

2. A set of observables (also selfadjoint operators on H) which, when aplied to a state, give a measurement result and change the state in a manner that an immediately following application of the same operator gives the same result. To let the file output of our computer work in a corresponding mode we have to change its output method a bit (we program in C++ and can define our own stream-output operator

Ulrich,

I'm not sure if you reread your last answer, but my immediate reaction to it is: it is quite confusing.

I suspect the reason you don't see this confusion and the minds you mentioned at the end see it has to do with their ability to compare the resulting picture of reality with what one would *accept* as reasonable. You simply accept the reality the current theory suggests, while some of us do not for the reason stated.

That indicates to me that you do not have sufficiently strong 'criteria' what you would accept as "reasonable" (which could be discussed separately).

For example, for some reason you think that the computer analogy gives you some comfort. First, the analogy itself is somewhat dubious. But much more importantly, one must not take computer itself too seriously from a scientific point of view. It is just another gadget whose only importance has to do with some intimations it offers for the future, but by no means with its architecture or organization (the separation on programs, hardware, etc.). These are ephemeral. Von Neumann, who spent many years thinking about such issues also agrees with this in his last work "The Computer and the Brain" (see especially the last 10 -15 pages).

Let me try to reduce the above "reasonable" to a certain degree of simplicity and generality of the resulting view of "reality". There should be some simplicity thresholds which if the resulting view crosses the 'bell' of suspicion should ring. QM has crossed many such thresholds, which does not make it wrong (as far as the calculations go), but which puts it in the zone of transitory formalisms.

Of course, most science workers do not have such criteria bells ringing in their heads, and it is the resulting inertia which slows down the development of science during the transitional periods.

Lev

That "transitional period" has now lasted for almost a century. That is not transitional anymore and let me ask you a direct question on which I like an answer: did you study (textbooks of) quantum mechanics yourself?

Harry,

I have a long shelf of books on QM, including Sakurai, and as an undergrad I had a compulsory course at the Leningrad University on QM lectured and graded by the well-known Ludvig Faddeev.

Of course, I'm not a physicists by education. I'm a mathematician by education.

Harry: "That "transitional period" has now lasted for almost a century. That is not transitional anymore"

I know you need an excuse to keep your views intact ;--)

But as I have been repeating a zillion times (not that you care), this is an unusual transitory period which we have never seen before in the entire history, and this time nothing will escape unchanged, physics most of all.

-----------------------------------------------

Can I also ask you a simple question?

How difficult is it for you to accept the hypothetical possibility that almost everything you know in physics will change *unrecognizably* (for you) in 50 years?

Lev,

my intention was to prepare you in an hypothetical endeavour to find a physicist to help you with the experiments you believe to need. For this it can do no harm to know the orthodox view. You can't know how intensively I struggeled with understanding quantum mechanics and how many self-made alternatives I followed and still follow. It seems to be part of your nature that you know that your bells always ring right ... often in error, never in doubt!

Ulrich,

What you might be surprised to hear is that I have questioned and continue to question myself probably several orders of magnitude more often than you are. The reason you haven't seen it is that you have simply resigned to the orthodoxy (after much struggles which you admitted) and are not interested in the reasons why I propose such 'crazy' things. (The main reasons, of course, lie outside the present physics.)

So, I come to physicists with a crazy new discrete formalism around which some physical meat should to be put on. My intuitions are related to the formalism itself and how it is supposed to work, and the physics around it has to be put by some (young?) bright physicists. Obviously, I do not expect many retired physicists to get involved, but I didn't expect so much hostility (to put it mildly) ;--)

Unfortunately, we don't have many bright young physicists participating here. I guess it seems to be a general rule. May be, despite the Internet, we are still operating in the old mode, at least as far as serious discussions are concerned..

I really would have like to see more people participating here at RG, and not just a few, with much more intense and focused discussions. Well, we still somehow maintain that division between the scientific elites and the rank and file.

Lev

When you show that ETS describes the elementary properties better duality i would immediately accept it.

Next question: how does it describe the propagation of an electron through a multiple slit that leads to an observable pattern

Harry,

I'm sorry, with all due respect, why do you think I'm after *your* personal acceptance? ;--)

(Harry, let's face it, even if ETS is OK, you can't contribute to it, and I would be more interested in "convincing" someone who can.)

If ETS is out to lunch, it will not be "accepted", but if it is not, it will be accepted sooner or later.

But let's focus on the original question: is there any underlying "discreteness" that explains the discreteness of everything else?

Lev,

is there a chance that you will communicate how ETS may handle the double slit?

Harry and Ulrich,

I'm sorry, but I already did briefly mentioned it just several days ago in the discussion under my question.

Referring to figure 5 of my last essay http://www.cs.unb.ca/~goldfarb/FQXi_5.pdf , one of the possible explanations is this. Since the hypothetical photon or electron events may have multiple outgoing processes, the explanation might look similar to the conventional one: similar t the the Huygens *picture* of light propagation. But there are no "waves", which appear to be the convenient calculational figment of out fertile imagination. ;--)

Though mysterious looking I think quantimization is an appearance resulting from a universe so vast and old to be beyond the abilities of perceptual judgement abilities...a complex weave of distances and spaces aliken to the generation of patterns in a cloth by a weaving machine. The universe so old and vast that at a given point, the point of human witness/existence, things appear to fit the mathematics of a circle though all is always dynamically changing in analogy to the need to apply wisdom from learning and intuition for for survival understanding. The emergence of substance requires a familiarity based fitting of lengths and volumes of received energy and those of existing physical structure....motion that is directional from the conservation of momentum...continuity..such that the world is a special case, appears quantimized though quantum divisions are emerged, dynamic and change with time increments that are vast...are not absolute.

I discuss natural and sociological processess in "Logic, Nature and the Town Council"..

http://ssrn.com/abstract=1376065

also attached from RG below. The full view is sociological, involves a historical facet, and includes an ethic involving form, direction and physical contiguity, that is absent from scientific renditions

Article Logic, Nature and The Town Council

to add: imagine space in analogy to the mesh of a nylon stocking...at a given point distances will appear to be constant, but in a larger view distances in the weave will vary depending on the amount of stretch applied to an area to cover a given surface shape. I like the expression "fabric of space" but I think from there descriptions diverge from accurate interpretation. In Levs' description, trying to reconcile quantimaztion from generality, I think particles might engage each other only one at a time..to keep his interpretation, one then the other, then the other, the other interactions beyond view I still do not think add up to fill all spaces...the world is simply a special case, has assymmetry that is independent of parameters of perspective. This idea makes physics theory, not theory but parametric description of a present situation. Perhaps some of it is usefull but I do not we should go about tearing the trees apart to find the forest.

I'd like to point out something quite basic, which, unfortunately, not many scientists realize.

In basic science, to deal with such absolutely basic phenomenon as the encountered discreteness, it is absolutely absurd to try to "modify" the only basic formalism we have had so far -- the continuous formalism.

Formalisms have their structural logic which cannot be changed without destroying the integrity of that formalism. The problem we are facing now is that we have had to rely throughout our entire history on one basic formalism, which had worked more than miraculously up to this point when we encountered the underlying discreteness.

The reason Harry thinks that a hundred years is good enough is because he does not realizes the situation we might be in. Of course, before abandoning the only formalism that powerfully served us for millennia, we will invent various *very* ingenious ways how to avoid abandoning it, and we are very, very good at it. But in QM we are already, quite admittedly, stretching our credulity. This can only continue so far, and then we will simply have to admit to failure of our basic numeric formalism. Some of us prefer to do it earlier rather than later (because, following Einstein's metaphor, our scientific 'noses' simply cannot take it anymore). See also the above quote by Schrodinger.

Of course, no one can know now what the right new ("discrete") formalism is, but some of us do know that we *must* abandon now the ship---that was so powerful, comfortable, and served us so well--- to look for the one that can take us to new destinations we have barely though about before, not the least important of which is the nature of information in the Universe, including the mind.

On the other hand, I must also stress that without such radically new formalism, i.e. just by *talking* about various nice things, we will not advance anywhere. (This is another extreme which most people not trained formally fall for.) Science cannot operate relying on the spoken language, it is too unreliable.

Discreteness and continuity generally appear at the same time. For example the physical space is continuous, but has a discrete number of dimensions. When we deal with particles or events, it is exactly the same. The phase space is continuous with a finite number of dimensions.

We can't prove anything about Nature, we can only build models that happen to agree or disagree with observation, in the former case usually tentatively. If the model describes a continuous measurement, let it be, as long as it remains valid, even in restricted domain. Physics isn't mathematics.

Thank you all for your answers to date. The point of my original question was to promote discussion around the apparent dichotomy that although QM quantization emerges from a continuum system, it requires a discrete countable system of particles (i.e. state variables?) to do so, and that current theory does not seem to specify how to construct such discrete particles out of that very continuum (but it sure knows what to do with them once it has them!)

a) Are we comfortable that a continuum should be sufficient to create the standard particle model , if we are sufficiently clever to figure it out.

b) Is instead, a discreteness required somewhere in that continuum to achieve that feat of creation of the standard model?

c) It all does not matter. Let's just use the standard model, GR and QM, cosmological initial conditions and conclude that reconciliation is not achievable even in principle.

d) As of now, we just don't know.

In the absence of evidence/proof we always go in circles around intuition, ideas, and "educated guess work"; some wrong headed/misguided/out of context . This is not contrary to the scientific method which is about verifying and validating (or not) that intuition post facto; before the theory comes the hypothesis. As an engineer, I sure did not make a career out of unjustified intuition (that tends to break things and kill people), but I sure did make a career out of thinking apparently crazy thoughts that subsequently led through validation to nifty products that worked that nobody else had.

Can I finally make a plea for us all not to assume what others have and have not read. Regardless of the intention of such comments, it does not come over well in the reading thereof. By all means quote and refer to such works.

Andrew: "QM quantization emerges from a continuum system"

Who said that? ;--))

Claude: "Discreteness and continuity generally appear at the same time."

"The phase space is continuous"

Such statements became very popular during the last half a century, but they lead to a great confusion, mainly because we have not had a single "discrete" formalism for modeling nature that could 'replace' the continuous one. So in that phrase the term "discrete" is simply a *negation* of "continuous", which is not helpful at all.

@Lev, @Chris

On the contrary I find the notion of boundary conditions (and yes they come in a remarkable variety of types so I am talking generally here) somewhat vital to this question. A function is defined on a continuum and has no boundary (at least as far as I understand the definition of a functional theory)

So the introduction of any boundary to get a solution seems something "additional" to the functional theory that we have imposed to suit the circumstance. A very grey area I think only resolved by considering each specific circumstance. But to me this lies at the heart of the unification problem (and yes one hundred and a bit years is too short a time to give up), so let me give you a couple of practical examples:

I note that as soon as you introduce an implied discreteness (or boundary) to a continuum (such as a Planck length for example) you run into the danger of changing the whole character of that continuum and any theory related to it, while still continuing to blithely believe in the continuum as underpinning the theory! I give you an example of this danger, and how it is avoided:

a) If the Planck length is an emergent property of the continuum (much like quantized energy packets are emergent properties of an electron in a potential (yes indeed I have read a QM book or two in my time ;-)) then it seems the concepts of a quantized measurement of length vs the reality of a continuum of length sit together quite well.

b) But you also see a lot of quite renowned people then dividing space up into Planck units, and talking about space coming in Planck sized bits, and strings and loops with Planck Length end points and such. I have a real problem with this, because you change the whole nature of the length unit from a continuum with cardinality Aleph 1 on the set of real numbers to one with cardinality Aleph 0 (the set of natural numbers). I can see no justification arising from existing theory to treat the Planck length in this second way. It seems to be a case of "lets try it and see what happens"

I note also that mass is a continuum in QM right up until the point you have to actually apply it to a measured wave function - and then it must take on a particular value to make sense of the circumstance. This is very much like imposing a boundary condition (and an empirical one at that!) on the QM theory. So is the mass of the electron an emergent property of the continuum? or does it arise from a discrete scale of mass?

So all possibilities (units continuum or unit discrete) should be considered in the research. The assumption of a continuum in mass,length and time with emergent quantized measurements is the status-quo but nobody in more than a hundred years has made progress to unification on this basis.

Plenty of research and time has been directed at possibilities arising from a discrete length unit - some quite interesting results but still to date with little to show for it on the unification front.

And yet when the only other two possible alternative unification strategies are proposed (either a discrete mass or time unit) as possible avenues of significant research, the theoretical physics community seem to run screaming in all directions but down those particular rabbit holes.

@Lev,

;-) Umm who said that? Yes I said that! (as my interpretation of the status-quo). I like to seed some of my sentences with provocative implied definitions. The intent is to make people actually think about the definitions and unspoken assumptions, but often it just reinforces peoples views of my untreatable ignorance and misunderstanding of matters (So do not feel too sorry for me. At my age being seen to be, or even actually being wrong or ignorant is not a limitation). I am not scared to be shown I am wrong - this is how we know to stop exploring the dead end and move on ... and if shown to be ignorant...well we have just learned something!

I was hoping to get a comment that "QM quantization emerges from a continuum system" showed a lack of understanding on my part. Then I could frame it side by side with comment that my assumption of discreteness also showed a lack of understanding, thereby completing the set and match by showing that both arguments for and against the continuum show ignorance. ;-)

I really do like your comment about not being able to tack a discrete formalism on to a continuum formalism. You have to start a discrete theory from scratch and work back up to show in the limit it all agrees with status-quo AND that the unification issues go away at the extremes. So far nobody has done that; but then again in a hundred years nobody has done it with the continuum approach either. My working hypothesis then is that either the continuum formalism is flawed in the extreme limit, OR it cannot be done by any formalism and nature is an eternal mystery. My personal time is spent on theories that have a discrete mass scale, and a continuum of time and length, since I am not yet prepared to accept that the universe cannot be understood, given the incredible track record that most of it HAS been understood.

In quantum field theory, the discrete particle number arises from the quantization of a continuous system. Each mode corresponding to an energy is described by a harmonic oscillator. That's not necessarily the best or the only way, but that shows there is no need of a primary discreteness.

A quantized variable means that its coniugate variable is periodic. For instance a vibrating string of lenght L implies a quantization of the wavenumber n/L. Through the Planck constant this implies a quantization of the momentum (the physical coniugate variable of space) k_n = n h / L. Similarly the quantization of the energy is an consequence of a periodicity in time. In my reviewed papers I have proven that quantum mechanics can be exactly derived by assuming that particles a vibrating strings with intrinsic periodicities. The mass (rest energy) is an proper time periodicity of Compton time T= h / m c^2. Please give a look to the publications in my RG page.

Claude: "In quantum field theory, the discrete particle number arises from the quantization of a continuous system."

Claude, let me tell you why I find physicists "funny".

I see the situation as follows.

Is the underlying "reality" discrete (in the sense we don't yet understand because we have never smelled such kinds of basic formalisms) or not?

(By the way, Einstein, Schrodinger and some other physicists suspected that the answer might be "yes".)

If the answer is "yes", it will not help to play the childish "discretization" game, because we are simply fooling ourselves by using the word and hoping to fool the nature: we can fool ourselves but not the nature. It appears that this is what is happening.

Of course, if the answer is "yes", at the beginning, we cannot expect to proceed with the development of the new physics at the usual pace. We have to be much more patient than we have been: first, we have to learn how to use the new "discrete" glasses and see nature through them. Our present mathematics cannot help us at all, and moreover we probably will have to start almost from the beginning.

Lev

You are as always fully evasive: we have asked you a physical question:

how does ETS deal with the double slit issue

You never give a quantitative answer and then play it on the person or remind us to keep to the original question.

I will repeat this question every time you dodge the very concrete questions for ONE concrete example of how ETS works for a "simple" duality issue

Harry, didn't I suggest it qualitatively?

Or do you expect me to do the "calculations" when no details are available?

It appears that for some reason we are talking past each other.

But first, did you understand what I suggested?

By the way has Ulrich understood what I suggested?

Whether space is discrete or not can make a difference only if space is probed by waves of a wavelength similar in magnitude to the discretization length. For larger wavelength there is no difference in resuts and assuming lattices instead of continua is often more convenient from a technical point of view. All numerical simulations of quantum particles in potential wells to be found in the internet (also those authored by myself) are actually discrete models with lattices for both time and space. If the lattice-width are adjusted according to simple rules, the discrete structure is completely hidden.

What makes quantum phenomena possible is, as all physics books tell us in the first few sentences on the topic, the existence of a natural constant of dimension energy times time, Planck's h! Notice that h/(2*Pi) is the angular momentum of the electron around itself. That there is an angular momentum among the natural constants is perhaps the the strongest indication that quantum physics necessitates particles. Where else an elementary angular momentum could occur? In ether eddies, as considered in 19th century physics?

Here I have what you need courtesy of Enrico Scalas

Found this by chance at the entry here at RG under the heading double-slit

by Derek Abbott

http://www.hitachi.com/rd/portal/research/em/doubleslit.html

http://l-esperimento-piu-bello-della-fisica.bo.imm.cnr.it/english/index.html

Harry, you always insist on me answering your questions but you don't answer mine.

For how long this can go on? ;--)

How can we communicate? Should we?

I don't know how much you understand from what I say, and you insist on me following you prescriptions.

Harry are you prepared to learn something (conceptually) really new? ;--)

But thanks for the links!

Ulrich: "What makes quantum phenomena possible is, as all physics books tell us in the first few sentences on the topic, the existence of a natural constant of dimension energy times time, Planck's h!"

This is a numeric manifestation of some underlying "discrete" phenomenon.

Lev, I know that you know that, no doubt.

Your scetch of a double slit explanation does even not touch the problem. One needs to understand that

1. Downstreams the slits a intensity pattern is formed the fringe-distance of which depends on the slit distance so that the propagation process of the electron (or photon) necessarily probes both slits.

2. If soft particle detectors are installed to look at the electron in the slit plane,

the electron is always found in just one slit (never in both; of course we are discussing a low intensity situation in which we can be reasonably certain that at most one particle is in the device).

Even if the electrons were given ( a la Bell) in their source a program how to behave, this could hardly solve the problem. (Nevertheless Bohm's 'causal interpretation of quantum mechanics' has a solution, which, however makes my bells ring.)

Ulrich,

I forgot: What does happen when one puts "soft detectors" at both slits?

Lev, Can you not see these discrete letters in a continuum sentence at the same time? (By the way, parenthetically, time is not quantized in QM; see http://www.iep.utm.edu/requires/).

Cj, what are you talking about??? ;--)

The sentence is not "a continuum".

Lev,

of course you can't tell precisely yet. But I guess that any conceivable interaction process with lets one "soft particle detector" fire will have a significant probability to let also the second one fire. Notice that a process net that explaines 1. necessarily touches both slits. So you have to ask yourself whether your process in/process out logic can explain such a selective behavior. With some communication back and forth to non-spatial information pools ( as you envisage in your EPR pseudo-explanation) this should be no problem, but then your bells should ring loudly.

PS. To your forgotten question: Only one detector fires, the impact in the interference pattern plane does no longer match the pattern.

Ulrich,

I don't know yet what is being changed in the system when, let's say, a single detector (at the slit) is added. How much (which kind of) interaction is going on between the detector and the "particle"? I have to think about it.

By the way, how do such soft detectors interact with the "particle" in order to record it?

Lev, the sentence is a continuum in a paragraph, in a section, in a page, in a chapter, in a book, on the world wide web, in the universe, ad infinitum -- all at the same time, unless you decide to place your 'fun' (not) blinders on and stop at circularly round and round like a trapped pinball with out-of-context (or out-of-continuum) tautologies like among many this response of yours, "The sentence is not 'a continuum.' [sic.]" In that case, your thinking is nothing new or nothing more than the age-old turtle upon turtle upon turtle... uninsightful view of the universe that you then accusingly project onto false characterization/stereotyping of extremely patient colleagues.

I have in mind the situation considered in p. 7, particularly Fig.1-4, in the great book Feynman/Hibbs: Quantum Mechanics and Path Integrals. The soft detectors (non-destructive detectors, they don't absorb the electron) are light beams. If an eletron passes the beam and deflects a photon out of the beam (as seen by some photon detector) the electron is detected. It continues its flight to the interference plane. The scattering of light by free electrons is known as Compton effect.

Cj, thank you very much for your incredible patience!!!

Ulrich:"If an eletron passes the beam and deflects a photon out of the beam (as seen by some photon detector) the electron is detected. "

But how much do we understand about the interaction of the entire beam with the electron?

Lev, That also is the wrong conclusion to draw.

Lev,

we understand everything here (with the exception of your event streams of course). The Compton effect is among the easiest and best understood processes in particle physics. Also the beam, coherent or thermal, holds no problems.

Ulrich,

My problem is that the proposed representation is structural---each event has a particular structure and they have particular interconnections---so if the reality is like that and our detectors cannot record practically *any* of this structure, how much can I say on the basis of such detectors?

Lev,

thinking about this problem could perhaps show you that the prognostic power of your theory is zero. Or you continue to believe that a young and good experimental physicist will invent the detectors that allow to figure out what all these interconnections are ...

Ulrich: "thinking about this problem could perhaps show you that the prognostic power of your theory is zero."

I'm surprised at the shortsightedness of your statement.

First of all, ETS was originally developed for the needs of pattern recognition and this is where its "prognostic power" can be judged: it can produce class representations and the latter can be used for classification purposes.

Second, I have not talked of any "theory" (in a conventional sense), so I'm not sure about which "theory" you are talking about.

We have proposed a new (structural) representational formalism, which has nothing to do with a typical physical theory. But, again, I can clearly see that after so much time you still don't know (don't want to know?) what a *representational formalism* is.

If you understood that much, you would not insist on immediately *seeing* what it can do for you: this is "childish". In fact, if I could show you this, then such "new" representational formalism would be a fancy rehash of the conventional one and wouldn't be needed at all.

Ulrich,

Just to have some clarity: Do you know what a representational formalism is?

Lev,

for me it is sufficient to have learned that a 'representational formalism' à la Lev Goldfarb is a body of thoughts that promises to provide a profound transformation of physics and that can provide not any reasonable argument to make this credible. It further has the power to make its founder believe to know the future of science, and endow him with unlimited self-confidence.

Ulrich, it's a pity that during all this time we have been discussing a structural representational formalism you didn't even once tried to get at least some idea what it's all about.

It's still a puzzle for me why would you want to *waste* all this time discussing something without trying to understand what it is about.

So no wonder you missperceived the importance of the *idea* of structural representation---independent of which form it would take, ETS or something else---for science in general and physics in particular.

Of course, for some reason, you didn't even try to understand why I'm suggesting that it is important. You just wanted to know "what it can do for you right now". If this is not shortsightedness, then I don't know what is.

@Ulrich,

OK I am convinced by your arguments that numerical simulations can usually be made to come arbitrarily close to a continuum equation solution at any defined level of precision that is required, and that from the point of view of the continuum equations, you cannot really work out if the underlying mechanism Nature uses to express that solution acts discretely or in the continuum without pushing the extreme limits.

My original question then becomes a more practical one, not directly related to the "truth" of how nature works: Do we need a discrete lattice in order to reconcile the theories of QM and GR with each other and with the observations of Cosmology and the Standard Particle Model.

I would suggest that history seems now against a reconciliation using continuum arguments. If lattice arguments also fail, then Nature is very mysterious indeed. Until someone does it, we just won't know.

I guess my main concern is that a lot of research is spent on lattice length/time options, while lattice mass options are being quietly ignored. My personal view and experience is that lattice mass approaches have a lot of demonstrable merit in the reconciliation of QM and GR concepts. For example they can be used to resolve the paradox of reference frame dependence of total system energy.

Lev,

if it is possible to read nearly all of your stuff (as far as cited by yourself as related to physics) and not getting some idea of what it's all about, then this probably happened.

Actually, I'm not interested in the first place why someone is suggesting something, if he is unable to show that the suggested adds to our understanding of some relevant problem.

From my time in industry I know that an inventor tends to promis more then he can actually bring to the table and that, in a sense, he is forced to behave that way. In your case this discrepancy ranges in the upper half of those I encountered in the past.

@William,

Agreed - a continuum reality cannot be proved not to be discrete;

But in the current continuum theory status-quo there remain the missing parts needed to address incompatibilities between QM and GR, and to use these theories to predict the Standard Particle Model observations, and Cosmological observations (COBE etc) I think we all accept there is unfinished business, just that we are uncertain what to do about it.

History is now not on the side of a continuum argument being able to achieve this resolution, given the brilliance of the multitude of people working on it for the last one hundred years. Not to be dismissive of new continuum approaches - just that the likelihood of success now I would rate as quite low.

But if a discrete lattice formula was to be found that simultaneously made sense of these issues, then a good case can be made that a discrete formulation is a more appropriate theory of reality than the continuum. Unfortunately numerical simulations usually derive their form from an underlying continuum equation; now we need to start more or less from scratch and work backwards to find a lattice formulation that agrees in the low energy density limit, and makes sense of the high density.

It may well be if such a solution is found (and I for one think we are within 20 years or so of having one), any attempt to translate it back into a continuum equation results in a continuum equation that makes no sense in the high energy limit! QED as far as reality is concerned. - we would then accept a discrete reality as somehow more consistent with what we know.

My rationale behind the question was to encourage physicists to continue the search, not to give up, and in particular not to ignore research into lattice solutions in mass that to date have been ignored. If in another 50 years we also do not find a lattice solution, then I think nature has more or less beaten us, and I will go back to my day job (which probably will be six feet under given my age!)

@Andrew:

in the standard model, masses don't come in as masses but as 'coupling constants' (all 'direct' masses are zero, which is the only option in the presence of local gauge symmetries). So, all approaches based on masses as primary parameters are much off the mainstream.

@William:

potentials never collapse, only the much more shaky wavefunctions do so.

@Lev, @Ulrich

I have absolutely no problem having somewhat off topic argy bargy as part of answer discussions, but really, you two should get married! ;-) That is a joke by the way.

The causes of mismatch between explanation and understanding are many and varied and often have little relevance to the logical validity or not of what is being said; and ResearchGate is an almost impossible forum to resolve these issues. It frustrates the heck out of me. I for one wish engineers, mathematicians and scientists could get together and agree on the terminology used for the same things, and for goodness sake, where a word in English has a common meaning, don't hijack it for a specialized meaning in a discipline. We should rise above elitism and confusion of common meaning.

However as long as you two are not angry at each other, I for one continue to read your posts with great interest! Both of you have made valuable points in this discussion.

Interesting question on quanta. Yes, I think that we have both (dual property of nature, particles and waves). As far as quanta, discretness, I believe mass is quantized, and there is a minimum quantum of mass and therefore of energy. Also of momentum, and angular momentum. Therefore space,length, must be quantized too. To me the only doubtful parameter is time. May be it just does not exists.......

Thanks for posing the question, Andrew. Like you I'm reading all of this with interest including the personal battles which I also wish were taken offline. Frankly I don't know the answer to your question and, as far as I know, no one does. At the moment I come down on the side of energy and spacetime being continuous but I've been closely following the answers to my post that posed that question and may change my mind. I'm not sure what it means but if you combine the two equations in your post and do some simple algebra who come up with E=mc^2. Is that just a coincidence or does it reveal some deeper truth. I don't know.

Johan,

I guess, according to you, for some reason, Feynman, for example, wasn't educated properly enough:

"Newton thought that light was made up of particles---he called them "corpuscles"---and he was right . . . We know that light is made of particles because we can take a very sensitive instrument that makes clicks when light shines on it, and if the light gets dimmer, the clicks remain just as loud---there are just fewer of them. Thus light is something like raindrops---each little lump of light is called a photon---and if the light is all one color, all the "raindrops" are the same size.

I want to emphasize that light comes in this form---particles. It is very important to know that light behaves like particles, especially for those of you who have gone to school, where you were probably told something about light behaving like waves. I'm telling you the way it *does* behave---like particles." (Feynman, QED, 1985)

Lev,

continue to tell stories, about the future of science, about streams of events, about people, ... that's what you are really good at.

I hope that all such discussions (and quite *basic* disagreements, see Johan Prins above vs. Feynman) should illustrate to most people how far physicists are from a coherent view of Nature, and why we are poised at the threshold of unprecedented changes in science.

As I have already mentioned, I blame the increasing "mess" on the timidity and the indecision to begin to look for radically new "discrete" representational formalisms.

Ulrich,

Thank you.

I certainly don't think I'm good at telling any kind of "stories" (and honestly, I don't enjoy telling them). However, what else am I supposed to do when I'm, in fact, being accused of "brainwashing" the good people? ;--)

By the way, what are you "really good at"?

---------------------------------------------------------------

Sorry everyone, that was a distraction related to the *inevitable* clash of scientific temperaments (still educational, isn't it).

@Johan,

Thanks, it is accepted that energy is a continuum variable, and it is the QM system that makes it come out in discrete packets. At issue is the requirement of discrete particles in this QM system (an antenna in your terminology) to make that quantization happen - given that we have not yet managed to build those discrete particles out of the raw continuum.

This is why the standard particle model is an important third pillar of physics in addition to QM and GR. I would argue cosmological observations surrounding initial conditions rate as a fourth. With these four, we have encompassed all of theoretical physics I think - we now just have to make them play nice with each other.

A photon: is something like a particle a particle? It is just a leftover of imprecise English and hijacked word meanings. I would not read too much into calling it a wave or a particle or a packet of energy, or a wave-function or whatever. From the maths, we know what it is, and this defines it, not the word we use to call it.

Andrew,

You seem to be quite comfortable with many 'gods' in the pantheon (of physics): good for your friends and family but not so good for science. ;--)

Remember what Einstein taught all of us: (conceptual) unification, unification, and once again unification (or one 'god'). The underlying continuity cannot generate discreteness in the observed multifarious manner.

@Ulrich,

Ahh yes, precisely my point. Mass IS treated differently. It seems the closer we try to observe it, the more it just evaporates or morphs into something else. We look at a proton and say "aha! now that looks like a nice solid chunk of rest mass to get my empirical teeth into" - and the more we look, the less we find of it!

For those of you interested, Prof. Frank Wilczek http://web.mit.edu/physics/people/faculty/wilczek_frank.html has some pretty interesting and accessible things to say about most rest mass not being associated with the more fundamental particles at all, but rather with the interactions between them. In the quark view of the proton it is well established that most of the rest mass derives not from the quarks themselves, but the interactions between them.

In my view it is therefore a reasonable topic of research to extrapolate these observations to the point where all rest mass (rather than just most of it) arises from the local gauge interactions between particles , and not from the particles themselves. In other words the attempt to divide mass up into smaller and smaller equal chunks, could well result in a fundamental particle that is rest mass-less!. The corollary is that all rest mass is simply kinetic energy bound in place by the local gauge interactions, which sits very well with m=E/c^2, and it requires both quarks and electron are in a sense composite.

Now the question is; Do we try to build this hypothetical fundamental mass-less particle out of space-time or do we give it an axiomatic existence in its own right. In my own research I choose the latter approach, and this is what I mean about research involving explicit quantization of mass.

@Lev,

But seriously, I am well aware I responded to you saying you cannot tack a discrete formalism on to a continuum formalism, and then accepted Ulrich's argument that a continuum may have a discrete underpinning to the same arbitrary precision limit and we would not know.

What I meant by my comment to you is that you can't mix approaches within the one type of unit (such as length), because the discrete numerical equations and the continuum equations ARE different types of formulation and have no direct analytic transform from one symbolism to the other; they just happen to give the same answer to any given measurement precision at the end of the day

So you use the one that is easiest to use, and make sure you stick with that method and not swap back and forth during the analysis. It just seems to me that the people who take the Planck Length, and then divide scale up on this basis are trying to have a bet each way and ARE incorrectly mixing different methods.

So starting with discrete identical particles of mass, and a continuum of length and time, which may well then be solved by discrete lattice methods I do not find to be inconsistent at all, provided you do not use a result derived from a different historical formulation half way through.

An engineer uses the tools to hand. We do not look at something that works and say "I don't understand it therefore it does not work" , we take it apart and tinker with it until we know how it does work, and meanwhile people stand around watching you and say "but you broke it", or "Why did you hit your thumb with that hammer?" and other such statements of the bleeding obvious. Well tough, science is messy, and we make mistakes on the path to true understanding. I just happen to be brave and foolish by putting some of my messy tinkering out there in forums and am quite glad when someone like Ulrich points out what I have broken in the process.....

@Bill,

Yes I too am on the side of a continuum of space and time, and of energy (yes that is right Lev, I did say that, and whats more I mean it!)

So if I believe that, why did I post the question? Because the particles in the standard model from which quantization of the energy continuum arises are defined discretely! - you can count them! and how can this be? This is the real topic of discussion I hid away behind my benign and explicitly "ignorant" question, and I was curious to see who took me at my word, and who looked behind the scenes questioning the other built-in assumptions behind the textbook QM case studies.

Do not take my research goal of exploring explicit quantization of mass as also requiring energy must come in discrete amounts. It turns out the attempt to quantize mass leads to a single fundamental mass-less particle from which the composite quark and electron (might cross-fingers) be built. The mass appears in the interactions between these particles as bound up kinetic energy (the cause of potential!) - and energy is a continuum taking on particular values interpreted as rest mass according to how each standard model particle is built from the underlying fundamental units.