Each time a new class of lasers was allowed to produce shorter light pulses, people were wondering whether a time quantization would be observed. The smallest possible quantization is Planck's time 10^-44 s. Some nuclear resonances have been reported having an energy width suggesting a Fourier transform limited duration of 10¨-26s.
The question cannot really be answered unless the question 'what is time?' is answered first.
Once that one is convincingly dealt with, then the answer as to whether time is quantized will either answer itself, or turn out to be largely meaningless (for instance, if it turns out that time is not fundamental but, say, an epiphenomenon which reflects something else entirely, but which 'precipitates' as time under a specific narrow set of conditions & parameters - or environment.)
Hi Charles, I would be interested in reading the nuclear resonance source papers you are referring to above. The quantization of time is a hypothesized idea which as far as I know does not yet have any experimental support one way or the other. There was some talk about quantization of highly redshifted values of galaxies which is similar to placing the time scale of the redshift under an extreme magnification, but as far as I know that never went anywhere. This is one place that experimentally we are not yet to the point that any effects due to quantization would yet be observable.
IF time quantization does occur at a scale 18 orders of magnitude above the expected Planck scale, that would be a very interesting and unexpected result.
I think that time is quantized because i think that time cannot be defined without movement. The measured time can only be defined as a multiple of a period of a periodic movement. Thus it is by essence quantized.
Time is a special motion by which any motion is measured. So time is the motion or the change which is infered by the memory. If the motion is quantized, so does the time. Yes, I didn't give the answer because I do not know if the motion is always discrete under any time scales.
@ Tehini, Lin and Johann. Why do you consider motion to be quantized?
@ Robert. I am sorry the nuclear resonance is a 30 years ago reading. I forgot the reference. Yes of course that would be exciting finding quantization far above Planck's limit.
@Mohammad. I don't think so. Think about the band structure of a material, the energy states are quantized on a very small scale but with no effect on a macroscopic scale. Zeno's paradox is void, it only asesses that Zeno did not understand that series might have a finite limit. To his excuse this has only been fully understood at the end of the XIXth century.
Charles, if the nuclear resonance paper is 30 years old then it is clear that result didn't have the time quantization implications you mentioned. I was thinking you might be referring to something from the Higgs run or the recent CERN ISOLDE experiment. My bet is that we are several generations away from any type of experiment that would even begin to have a chance of showing a time/space quantization effect.
Until then there are many interesting areas of research that will be hit first including a characterization of gravity at small distances (possibly showing greater dimensionality than 4 to our universe), high density compression of matter at extremely small scales (currently being worked on for the sustainable fusion initiative), and the development of real high temperature superconductors. The fact that the standard model has been completed (for currently attainable energy levels) only tells us that we have the big picture down reasonably accurately, but there are still lots of directions to continue to explore long before we reach the planck scale.
@Robert. Sorry for confusing you. I only tried to give the shortest duration of a physical event know of as an illustration.
@Johann. Thank you. I understand your point.
Charles, to my understanding it is not much quantization of time, as a certain time scale (so called Plank time (tau_P = sqrt ( hbar G / c^2 ~ 0.54 x 10-43 s ), where G is the gravitational constant) beyond which our regular (3+1)-dimension physics isn't adequate any more. The Planck time is widely regarded as the time-scale of the birth-flash of the Big Bang, as well as an elementary ‘grain’ or ‘pixel’ of time within which our “regular” physics of four-dimensional space+time breaks down into much greater number of dimensions hypothesized by the superstring theory (for more or less popular explanation of superstrings one can read Greene's book, "The elegant universe" ). A related Planck energy is E_P ~ 1.2 × 10^16 TeV. Beyond this time and energy scales our understanding of time+space becomes a little fuzzy.
About nuclear resonance data mentioned by you -- well, it could've been some mis-interpretation or some other "mis-"; but I doubt 10^-26 s number very much.
How far we can reach these days with our time-measurements one can look at my brief review in Nature, -- ""The long and the short of it... Time: how much of the cosmological time-scale do we control and use?":
http://psi.ece.jhu.edu/~kaplan/PUBL/AEK.pubs/114.pdf
or its extension in "Optics and Photonics News" --
" In the middle of no-when: the long and short of time":
http://psi.ece.jhu.edu/~kaplan/PUBL/AEK.pubs/119.pdf
(hope you'll have a lot of fun reading it:-); there are some predictions too)
and finally, for a detailed report with a lot of references -- in my paper "Beyond attoseconds"
http://psi.ece.jhu.edu/~kaplan/PUBL/AEK.pubs/132.pdf
Those papers can be found on this web-site too, but I simply don't know how to give their links (this site needs a bit of improvement...)
Numbers, briefly: as of right now, we are able to reach pulses to ~ 0.2 femtosecond = 200 attoseconds (1 as = 10^-18 s); here we are at the time-roots of atomic physics (it takes an electron 150 attoseconds to go around proton at the ground state of a Hydrogen atom). Proposals have been published on how we can go into zeptoseconds (10^-21 s -- it is a scale of nuclear fast processes), and even yoctoseconds (three orders of magnitude down, gluon-quark plasma...).
Zs and Ys are way beyond horizon at this point, but even after we reach them and CONTROL them, we'll be still almost 20 orders of magnitude short of Planck's time. When/if we get to that, we will be able to launch a new Universe (or destroy ours...)
The question cannot really be answered unless the question 'what is time?' is answered first.
Once that one is convincingly dealt with, then the answer as to whether time is quantized will either answer itself, or turn out to be largely meaningless (for instance, if it turns out that time is not fundamental but, say, an epiphenomenon which reflects something else entirely, but which 'precipitates' as time under a specific narrow set of conditions & parameters - or environment.)
Time is a co-ordinate, no more sense in talking of its quantisation than in talking of space quantisation. Its measurement across space is described by (special) relativity.
Max, what an odd answer ? There is much sense in exploring whether the weft of space is quantized. In particular, it is the most promising area of research in trying to explain why the speed of light takes on the particular value it does.
I think, It is not just a question of time alone. We must try to understand, Is 4 dimensional Space-Time quantized. Which means all the three possibilities: Space alone is quantized, Space-Time is quantized and Time alone is quantized.
The lack of success in quantising fields (ie. equating force fields to particles) implies physics should return to conceiving reality as a combination of particles and fields http://crisisinphysics.wordpress.com/2012/01/01/the-higgs-after-einsteins-unified-field-theory/ . ' Quantising' space-time adds still more problems. The speed of light of course varies according to the matter and energy-density of the non-empty medium in 'space' .
Folks, you keep talking about time quantization in the context of (3+1)D world. But at the Planck's scale (in particular Plank's time scale), the world has much more dimensions (see briefly my earlier comment), from 10 to 26 dimensions, depending of whom you are talking about:-), and none of them can now be identified specifically with "time". Besides, it is not a sort of "classical" quantization; in the field of superstrings they don't talk about "time quanta", it is a completely different game down there.
I thank you all very much for the nice discussion that has developed.
@Alexander. The 10^-26s is not a time measurement but the potential duration of an event which energy spectrum is large enough to accomodate it.
@Charles; right, I understood that. My problem was/is that when you translate that into energy scale (E ~ hbar / (DELTA t)), you'd come up with the energy being enormously huge for a low-level nuclear resonances; my calcs gave me roughly ~10^2 TeV = 10^5 Mev, whereas the lowest nuclear resonances happen at a few MeV's. In general, of course we always have to remember about that above relationship connecting time and energy scales, but there is no reason to be awestruck by that energy. In cosmology physics, they are able to see (rare) events of particles arriving from the space that have energies comparable in order of magnitude to Planck energy (10^16 TeV)... In the best accelerators they are getting multi-terra eV's, let alone the colliding beams where you can look at gamma^2 *mc^2 energies...
The 10 or 26 dimensions to 'space' are mathematical fictions. The real world has 3 space dimensions, even 4-D space-time is a convenient mathematical trick (which also misleads, cf. exchange of space and time in a 'black hole'). My answer to abstruse mathematics is - get real!
@Max :
> The real world has 3 space dimensions...
And how do you know that?:-)
... the collective scientific process of observation, experiment and theorising has validated 3 space dimensions. In comparison, stating the world "has" many more space dimensions at the Planck scale or other is speculative, remote from experiment, so does not justify the positive "has".
Consider this: a sistem periodic in time means that, through Fourier transform it has a quantized frequency spectrum and thus, through the Planck constant, a quantized enrgy spectrum. If the period is T the enegy spectrum is E_n = h n v = h n / T, similarly to avi rating string. In my published paper I have dimosntrated that quantum mechanics can be equivalently derived by assuming that nature can be described in terms of elementary cycles (elementary particles + wave-particle duality). The idea was also suggested by de Broglie in terms of "periodic phenomena asscoated to every particle" That is, quantum mechanics is the manifestation of this elementary cycles. It is easy to see that the time scales of this periodicity is the Compton time of the particles. For an electron this is of the order of 10^-21 s. This time scale is to small to be observed with ordinary clocks so that these cyclic dinamics can be only described statistically. Remarkably this description turns out to be mathematically equivalent to ordinary quantum mechanics in both the canonical and Feynman formulation and it is derived from classical relativistic dynamics.
Why quantize time when the quantized varible is the energy, that is its conjugate variable? Quantum mechanics means that the time flow can be decomposed in elementary cycles.
Please read my refered papers.
Article Elementary spacetime cycles
See also
Article On the intrinsically cyclic nature of space-time in elementa...
You may like or not this description, but note that, if mathematics is not an opinion, this established interpretation of quantum mechanics, mathematically equivalent to ordinary quantum mechanics, clearly represents an important breakthrough. Its validity is certified by several peer reviewed publications in leading scientific journals of physics such as Ann. Phys., Europhys. Lett. and Found. Phys. Ignore certified results is not a fair way to do physics.
The quantization of energy does not mean time is also quantized. This may be due to time is not as simple as one may be imagined. Its a dynamical variable not as space variables which can be considered as static variables. So there are momentum and space quantization, but nevertheless time is not quantized in spite of energy quantization.
Dolce,
Could the maximal spatial scale of the universe be related to the smallest spatial scale and correspondingly is the smallest time scale of the universe related to its largest time scale? There are a numbers of evidences sudgesting that space is cyclical in the sense that when we get at the scale of the whole universe we end up at the scale of the smallest.
To Sadeem Fadhil@
I like your reasonings concerening the quantization of canonical variables of the phase space, as the momentum and spatial variable. In particular, one easily obtains the well uncertaincy Heisenberg condition that |ΔpΔq|≥ℏ/2. In modern and classical QM manuals there is very formally and amusably extended this inequaluty to |ΔEΔt|≥ℏ/2 , where t∈R is the temporal variable and E means the corresponding energy of the quantum state. But the latter can be, on the whole, derived ONLY from a virtual quantization of the time variable... But this fact of in these manuals is not mentioned and not explained, but very often used in different reasonings and argumenttions. Do you consider, this time-energy quantization is really existing, or this is a misleading thread owing to the fake anlogy used?
Sincerely regards!
Louis,
It would be more interesting to consider that the a maximal scale of the universe would determine the smallest value of the momentum quanta (by Fourier transform), similarly for the life time of a perfectly cyclic universe would determine the smallest energy quanta (notice however that the photon, being massless, can have zero energy and momentum, i.e. infinite wavelength and temporal period). Moreover, as the universe is composed by particles and every particles is a "periodic phenomenon" (see de Broglie) it follows the fascinating idea that the universe is ergodic (or chaotic), as a combination of periodic phenomena with not rational period is an ergodic system. Thus the universe can "return" arbitrarily close to its original configuration and "start" a slightly different evolution with respect our universe.
Another fascinating description has been used to describe my work in a physics blog:
"By the way, the 'esoteric' types here might want to look up the 'Elementary Cycles' interpretation of QM, wherein elementary particles are small worlds in themselves, each obeying deterministic cyclical behavior, and only looking 'random' because we sample them at different times in their (eternal recurrence) cycles:
Quote:
Eternal return (also known as "eternal recurrence") is a concept that the universe has been recurring, and will continue to recur, in a self-similar form an infinite number of times across infinite time or space. The concept is found in Indian philosophy and in ancient Egypt and was subsequently taken up by the Pythagoreans and Stoics. With the decline of antiquity and the spread of Christianity, the concept fell into disuse in the Western world, though Friedrich Nietzsche resurrected it as a thought experiment to argue for amor fati.
http://www.google.com/search?q=eleme...interpretation
The papers by Donatello Dolce would be typical: http://arxiv.org/abs/1206.1140
We interpret the relativistic quantum behavior of elementary particles in terms of elementary cycles. This represents a generalization of the de Broglie hypothesis of intrinsically "periodic phenomenon", also known as "de Broglie internal clock". Similarly to a "particle in a box" or to a "vibrating string", the constraint of intrinsic periodicity represents a semi-classical quantization condition, with remarkable formal correspondence to ordinary relativistic quantum mechanics. In this formalism the retarded local variations of four-momentum characterizing relativistic interactions can be equivalently expressed in terms of retarded local modulations of de Broglie space-time periodicity, revealing a geometrodynamical nature of gauge interaction.
Will 'string theory' turn out to be really due a restatement of the Eternal Verities? In these theories, QM itself becomes a semi-classical approximation (not unlike WKB or Bohr-Sommerfeld conditions [see also, the Theory of Metals]). Nice."
Dolce,
Very interesting. De Broglie is the first that came up with hidden variable quantum theory (pilot-wave theory) which was later re-invented by Bohm and which is now developed by Hiley. Is the internal clock hypothesis intrinsic to pilot-wave theory?
I think Chris Radford's recent answer may be about as good an answer as will be posted.
Permit to make a statement from a different, perhaps useful perspective. By taking a non-traditional approach - based in part on emphasizing inter-particle quantum interactions (and not necessarily assuming much about space time) - I develop theory that people may be interpret as suggesting that meaningful physics occurs at length scales at least as small at 10^(-100) meters. My work indicates meaning for the Planck length, but not in terms of a 'frothiness' or 'quantization' of space time. To the extent this work reflects nature, people may want to consider questions of 'quantizing time' as referring to time intervals smaller than ones previously considered.
The work is based on isotropic harmonic oscillators, not on traditional bases leading to the Standard Model. The work seems to lead easily to a unification of quantum gravity and electromagnetism and to well-defined candidate characterizations of dark matter and dark energy. The work may lead to a catalog of basic Standard Model particles.
For anyone interested, I attach a copy of material about my research.
Brassard,
the interpretation must not be confused with the de Broglie Bohm interpretation. It has no hidden variables as the quantization is given by introducing an assumtpion of periodicity so that the particle is like a particle in a box. In de Broglie Bohm there is not such an internal clock description. A pure quantum system (zero temperature and no interactions), say an elementary particle, is perfectly cyclic, that is is a clock. This is the nornal state of quantum mechanics as in classical meccanic the perfect state is the uniform motion (Newton's first principle). Such a periodicity in time, through Fourier transform and according to De Broglie and Planck imples a quantized energy soectrum E_n = n h / T. However, as in ordinary classical mechanics there is friction, in ordinary system there is thermal noise which destroy this perfect coherence, whereas interactions, i.e. variations of energy, implies modulations of periodicity. It is easy tonshow, see my papers, that in the classical limit (small momentum w.r.t. the rest energy) this extremely fast periodicity reproduces exactly the particle behavior. So there is not pilot wave and particles as in de Broglie Bohm. Roughtly speaking the hidden variable is time which however cannot be integrated out, the flow of time can be decomposed in terms of elementaryncycles. The resulting mathematics is perfectlynequivalent to ordinary quantum mechanics, and the validity of demonstrations has been certivied bybseveral peer reviewers.
To Anatolij Prykarpatski
Thank you for your interest in my answer. I agree with that time energy uncertainty relation may be an indication of time energy quantization, but this is not an indication of quantization of time as a variable. but its an indication of certain periodicity of frequency (which is reciprocally related to time) that is adopted by certain particle during its movement. Of course periodicity does not mean quantization.
Sadeem Fadhil@ and all others too
Thanks for your reflection concerning the time-energy quantization. Really, it is from the operator (quantizations rule!) poit of view an open and bad discussed problem in the modern physics.... Your "oscillatory" way of thinkking of the time vatiable is very promising as in general, there is no time measuring possibility if one has no true oscillatory physical process! But its relationship with quantization is really both hidden and obscured... But why not?
Fadhil and Prykarpaski,
it is a mathematical fact that the condition of periodicity can be used as quantization condition. There are many well known examples, but it is sufficient to think to the fact that the constraint of periodicity is a boundary condition. If we impose periodic boundary conditions to a particle, we have a system similar to a particle in a box, the quantized spectrum is the harmonics of a vibrating string. I have proven that by imposing to a particle its de Broglie Planck periodicity (i.e. the natural periodicity observed for elementary particles) the result is mathematically equivalent in all its fundamental aspects to ordinary QM in both the canonical and Feynman formulations. This logically means (A-> B and B->C thus A-> C) that every quantum phenomena can be consistently reinterpreted in term of intrinsic periodicity.
The resulting description is neither obscured nor hidden (expecially if compared with the numerouses paradoxes of ordinary QM). Indeed it is base on (semi-) classical relativistic physics (e.g. without relaxing the classic variational principle). Every elementary particle is described as a vibrating string whose harmonics coincide with its quantum excitations. This is an extremely natural description of nature since Pythagoras (in opposition to the attempt to justify an unnatural description of nature of recent high energy physics). Also the resulting description of time flow is extremely natural, as the time evolution of every system can be decomposed in (modulations of ) elementary cycles of time, and the description of time in terms of cycles is essentially what we do every day when we fix an events in our agenda or when we use a stopwatch, etc. Moreover it is common in many philosophies.
Please read my peer reviewed papers
Article Elementary spacetime cycles
Dear Anatolij
Time oscillation can be related easily to quantiazation by assuming delta t is repeated
in certain interval which according to uncertainty principal will make delta E has certain values (quantized) values.
Dear Docle
thank you for your nice discussion , but I just want to ask that is time oscillation is consistent with Minikoski space time , don't you think it needs modification ?
Dear Fadhil,
By considering the relativistic modulations of periodicity everything works in a wonderful way. The point is that relativity concerns about the differential structure of spacetime but it doesn't say nothing about the boundary conditions of spacetime. On the other hand quantum mechanics is characterized by boundary conditions (e.g. particle in a box, etc). This means that relativistic quantum mechanics can be derived in a geometrodynamical (unified) way from relativity by playing with boundary conditions in relativistic theories. In particular, if the boundary conditions (e.g. periodicity) are introduced in a consistent way (variational principle at the boundary) they do not violate the relativistic symmetry of the theory. For instance you can assume a periodic phenomenon such as a clock or a photon emitted by a source. Relativity tell you how its periodicity is modulated by boost (see relativistic Doppler effect) or in a gravitational field (see gravitational red shift or time dilatation). This can be easily described by the fact that the variation of the energy due to interaction or Lorentz transformation corresponds to modulation of time periodicity T according to de Broglie Planck relation E = h / T. From a mathematical point of view it turns out that the temporal-spatial recurrence of a particle is a contravariant (tangent) four-vector.
For instance the harmonic energy spectrum E_n = n h / T associated to a periodicity T in a given reference frame, denoted by p, by considering Lorentz transformations and that the spatial periodicity fixes the momentum p = h / L, one gets the energy spectrum prescribed by ordinary second quantization for a particles: E_n(p) = n \sqrt{m^2 c^4 + p^2 c^2}. Even more amazing is the fact that by thinking of particles interactions are periodicity modulations, and considering that the local modulations can be encoded in local deformations of the spacetime metric, one obtains a geometrodynamical description of gauge interactions as for gravitational interactions. That is one get a common (unified) description of gauge and gravitational interactions.
The relativistic transformation of the elementary cycles of spacetime are described for instance in the attached peer-reviewed paper (published on Annals of Physics) or similar papers.
Article Gauge Interaction as Periodicity Modulation
Dear Dolce,
I apologize if I missed that piece of data in your prior posts, but what is the size of your time-quantum (let us call it (dt)_q)? or energy (dE)_q? Is it a Plank time? or anything else? in any case, what is it (say in terms or seconds, or perhaps of Plank time)?
Is it the same for the entire Universe, or it depends on an immediate environment? Are those time-cycles of yours synchronized with each other over the entire Universe (if they are, this would make the speed of their phase propagation being infinite...)
When two high-energy particles collide, is an individual time of each of them "ticking" with the same phase or it would be a random phase? What happens if their individual energies are much lower than (dE)_q?
Dear Kaplan,
if the energy quantum in a point q of an elementary system is (dE)_q, than the corresponding time cycles is (dt)_q = h / (dE)_q. The derivative notation that you have introduced is particularly efficient because (dt)_q transforms as a tangent vector. It is the analogous of the instantaneous periodic in a modulated signal, which typically is different from the period (that is the length of a complete recurrence).
Apart from these technical details, the magnitude of the periodicity introduced in my work is excactly defined by the above Planck de Broglie relation. In particular, since the mass is the rest energy of a particle (representing the lower value of the energy) this means that a particle has always a periodicity faster or equal (depending whether the particle is accelerated or at rest) to the Compton time. It is easy to see that, even considering an electron, this periodicity is of the order of 10^-21 s. If compared to the Cs atomic clock whose period is of the order of 10^-10 s, you see that for every tick of the atomic clock a the internal clock of an electron does a number of cycles of the order of the age of the universe expressed in year. Obviously, if you have such a fast dynamics and you can measure it with such a low resolution clock (try to describe annual cycles by comparing them with the age of the universe) you can only give a statistical description, just for a die rolling sufficiently fast with respect to eye time resolution. Heavier particles have faster periodicity.
*I have rigorously proven in detail that the statistical description of such fast relativistic cyclic dynamics is mathematically equivalently to ordinary quantum mechanics* (including Schrodinger equation, Hilbert space, commutation relation, Feynman path integral, etc). This can be summarized by saying that, assuming that God has infinite resolution in time, He has not fun "playing dice" as He can always predict the outcomes. My theory clearly points out a possible deterministic nature of quantum mechanics at time scales smaller that the de Broglie period.
The rest cycles are determined by the mass of the particle through the Compton relation T_tau = h / m c^2. By assuming that the mass of a particle and the fundamental constants are the same in any point of the universe at any 'time', the elementary cycles of equal particles are the same in every point of the universe. In my opinion this is a too strong hypothesis and if one consider our knowledges of the universe one could imagine to explain important cosmological phenomena in terms of variations of reference time cycles....
When two particles collide their cycles varies in order to satisfy the conservation of the energy (and momentum). For instance, E_1i + E_2i = E_1f + E_2f means that the reciprocal of the time periods is conserved T^-1_1i +T^-1_2i = T^-1_1f + T^-1_2f. The detail of the interaction may depend by the phase interference, and this is well described by the Feynman path integral of QED which can be directly derived in terms of classical cyclic dynamics as shown in my papers, e.g. 1110.0315.
The energy quantum of a massive particle cannot be smaller that its energy as E(p) \geq m c^2. However the massless particles can have zero energy quanta. This is because massless particles have infinite Compton time, that is the ticks of massless particles can have infinite duration (see description of black body radiation in my papers and the related transition between classical limit and quantum limit corresponding respectively to long and short periodicities).
I hope these answers give you some more element to understand the idea of elementary cycles.
Article Compact Time and Determinism for Bosons
@Dolce: 10^-21 s is a reachable time; it is what we called "zeptosecond" in our PRL paper with P. Shkolnikov, and it is a nuclear time-scale (and QED time-scale), it belongs to the energy domain 1 - 10 Mev (1 Mev ~ 2 m_e c^2); it was even proposed how it can be reached by petawatt or terrawatt lasers using electrons. Anyway, since strong nuclear resonances are well studied, I don't remember anything suggesting any enigmatic effect unexplained by the existing theories.
@Kaplan as far I knew the modern experimental resolution in time was of the order of the attosecond (10^-18 s), though Catillon et.al. have been able to indirectly see the zitterbewegung of the electron (10^-21 s) in 2008. The possibility that you are claming that the beyond zeptosecond precision can be reached is extremely exciting for me. This time resolution would mean to directly observe the underling dynamics of QED. According to my theoretical results this time scale would open a new frontier of physics, to finally be able to control quantum mechanics with unpredictable technological applications. It would be possible to imagine experiments to test some predictions of my work.
As I said my approach reproduces exactly (without fine tunings) quantum mechanics, but also shows that ordinary quantum mechanics emerges as a statistical description of extremely fast classical relativistic cyclic dynamics (similar to the statistical description of the outcomes of a die as I simplistically said in my previous post). Thus it is in agreement with the ordinary description of strong nuclear resonances, but it could go beyond this. One could see something beyond ordinary quantum description of nuclear interactions if only one knows where to look for, designing an ad hoc experiment. But it is necessary to have a precision better (a sufficiently stable zeptosecond clock) than the Compton time of the electron.
I have found your papers "Beyond Attoseconds" and "Lasetron: AProposedSourceofPowerfulNuclear-Time-ScaleElectromagneticBursts".
Please keep in touch.
the littlest space (distance) => the littlest time. (Depends of our measurement sensitivity. Is it?)
To the regret, no... The nature is not fitted for special human measurement facilities, it is Nature as it is, and is free of antropomorphic allusions!
Sincerely,
A.
If you fallow Bojowald's work ...you will get to the idea that it is !!
What is it, a Bojowald's work ??? Sorry for my stupidity...
Martin Bojowald is a theoretical physics researcher working in the field of Loop Quantum Gravity. Just take a look in the arXiv for his preprint papers or its book "Once Before Time".
Martin is one of the most talented young physicist.
@Ovidiu Racorean
Martin is one of the most talented young physicist.http://www.math.columbia.edu/~woit/wordpress/?p=3262
It is very interesting review what this book is about:
Not Even Wrong
"The cover of Bojowald’s book tells us about Loop Quantum Cosmology:
"Now the theory is poised to formulate hypotheses we can actually test."
I’m no sure exactly what that is supposed to mean, but it appears to be misleading hype, not corresponding to anything actually in the book. The text of the book itself wavers back and forth, sometimes explaining the overwhelming problems one faces if trying to extract some kind of prediction out of the LQC framework and emphasizing how speculative it all is, at other times expressing ungrounded optimism that somehow these problems will be overcome. It ends on an upbeat, hopeful note
Will we ever, with a precision that meets scientific standards, see the shape of the universe before the big bang? The answer to such questions remains open. We have a multitude of indications and mathematical models for what might have happened. A diverse set of results within quantum gravity has revealed different phenomena important for revealing what happened at the big bang. But for a reliable extrapolation, parameters would be required with a precision far out of reach of current measurement accuracies. This does not, however, mean that it is impossible to answer questions about the complete prehistory of the universe. Cosmology as well as theoretical investigations are currently moving forward and will result in unforeseen insights. Among them might well be experimentally confirmed knowledge of the universe before the big bang.
but I found nothing in the book to justify this optimism. The few allusions to specific attempts to find some relation to something observable are vague and suffer from the book’s nearly complete lack of any references to more technical sources of information."
and so on ...
Dear All,
Really, a lot nice views regarding the time quantization. I am agreed with all of you.
I think the theory of relativity has an important role in time quantization.
The big-bang understood as some time t=0 for the universe is scientific non-sense. Planck's time is an order of magnitude of the time-scale when physics does not work any more. The time t=0 will not be defined (or not) until gravitation and quantum mechanics have been unified.
Any mathematically dressed discourse on what happens before the big-bang is only meta-physics.
That does not prevent time to be quantized or not.
Charles,
Quote
Any mathematically dressed discourse on what happens before the big-bang is only meta-physics.
Unquote
This is deemed especially true since the the Bogdanov brothers' 'Avant le Big Bang' best-selling slapstick book. These guys' (and a few others') interventions have cast a pall of ill repute on all such studies.
Nevertheless it is still legitimate to
1- explore under what different scenarios a Big Bang can happen (e.g. Nikodem Poplawski , Tryon, Penrose, Bojowald scenarios, etc.) then
2- investigate what happens at infinite time after theoretical Big Bangs (also bearing in mind that infinite time within certain environments can turn out to be finite outside these environments) - and
3- extrapolate whether such scenarios can lead to other Big Bangs or to the birth of further universes, and
4- loop the loop, i.e. explore whether our own BB could have possibly arisen under such a scenario.
The challenge is then to devise testable hypotheses which would be equivalent to (at least some of the ) elements constitutive of such scenarios.
Finding testable hypotheses formally equivalent to hypotheses raised during the above scenario exploration is not trivial, nevertheless it is an area where there is interesting progress, see e.g. the interesting testable proof put forward recently by Martin Savage for the 'simulated universe' hypothesis, as well as the current attempts by Sean Carroll, Julian Barbour, and others, to devise tests for their own respective hypotheses - hypotheses which are not, per se and as are, directly testable.
Chris,
I fully agree. Speculative theories on any subject are not to be confused with meta-physics; as long as they look for ways to be falsified or verified. That was not my point, of course.
I think the present situation is comparable to the situation that occurred at the turn of the last century when people were desperately looking for a theory that would overcome the ultraviolet catastrophe in the black-body radiation problem.
Thank's for the point.
Does exist a minimum distance whose quantized the distance (space)?
In the mass, does exist a quantized distance for example between nucleus to orbits, or between two protons or proton-neutron?
Does exist a minimum impassable?
Dear Ana Maria,
yes, your opinion is very nice.
All these points one can understand with the prediction of Standard Model.
To @Ana Maria:
There exist in physics no a priori quantization of distance, time, and other quntities, whose evolution=dynamics (in time!) with respect to the full system Hamiltonian is not defined physically correctly, and under the condition that this description really has sense. The negative values of electron in hydrogen are quantized only owing to the special structure of the Hamiltonian operator, describing its dynamics in time via the Schredinger equation. In other cases speaking of the "quantization" of any other thing is senseless. There is in our world the only strange but real quantized quantity, - the minimal volume of the quantum phase space, I mean the well known quantity Δ:=(1/((2π)³))dp_{x}dp_{y}dp_{z}dxdydz=ℏ³, where ℏ equals the reduced Planck constant, a really nontrivial and unique quantum quantity still not well understood in physics...
What one can not say, for instance, about the Newton's gravity constant γ, which is supposed to change in time... Anyway, this constant is not yet explained also within the modern quantum gravity etc.
Below is an answer I posted 19 days ago that seems to have disappeared!
"Is time quantized? In other words, is there a fundamental unit of time that could not be divided into a briefer unit?
The brief answer to this question is, 'Nobody knows.' Certainly there is no experimental evidence in favor of such a minimal unit. On the other hand, there is no evidence against it, except that we have not yet found it. There are no well-worked-out physics theories incorporating a fundamental unit of time, and there are substantial obstacles to doing so in a way that is compatible with the principles of General Relativity. Recent work on a theory of quantum gravity in which gravity is represented using loops in space suggests that there might be a way to do something roughly along these lines--not involving a minimum unit of time but rather a minimum amount of area for any two-dimensional surface, a minimum volume for any three-dimensional region in space and perhaps also a minimum 'hypervolume' for any four-dimensional region of space-time."
---------------------------------------------------
John Baez, Scientific American.
The article describes three more answers to the question. Below is the link:
http://www.scientificamerican.com/article.cfm?id=is-time-quantized-in-othe
I think time is related directly to velocity so if its quantized then time is quantized. Until now the forbidden speeds are those larger than speed of light . I think its more presize to search for time limit than searching for time minimum.
Sim o tempo e quantizável e o numero indicado pela transformada de Fourier esta certo! agrego a resposta uma parte da teoria final que terminei a pouco de faser e la nao coloquei o valor do quantum de tempo mas eu o tenho se o senhor se interessar posso lhe mandar a equacao e explicacao. at. Jorge barcellos o testo esta escrito em PORTUGUES DO BRAZIL.
Physicists like T. D. Lee have speculated about discrete or quantized space-time to get cut-off scales so as to avoid field theoretic divergences while others like J. A. Wheeler have imagined space-time foam at Planck scales. There are no dearth of theoretical ideas. The problem is how to test these conjectures using do-able experiments.
According to me, the central mystery about time is, why does it flow? Why do we continuously evolve in the future direction?
To Patrick@
From the vector field-(dynamical system theory) point of view it is almost natural: the evolution of any object in the form dx/dt=F(t;x), x|_t=0 will always move ahead from t=t_0 to the time parameter t>t_0... if F(t;x) not equals at some point zero. What is important here that the time =evolurtion parameter is NOt interpreted here as an additional space dimension, even more, it could not be interpreted this way... contrary to the relativistic physics and General theory of gravity cases. I guess, this point is worthy of more detailed and thorough analysis in physics, if any... What I have observed many of modern statements in commonly used physics theories are of the type: NOT EVEN WRONG"...
Regards.
Yes, the 'flow' of time is primary, based on the observed universe comprising matter in galaxies and other clumps evolving from a compact early epoch (perhaps not as dense as the hypothetical big-bang). It's an extension of Mach's principle - that matter on the universe-scale determines time as well as the non-rotating space frame. Relativistic physics and General theory of gravity should not be contrary, but rather have to be framed to be consistent with the flow of time.
Gentlemen in a previous post I put a small part of the final theory and she and 100% verifiable trough of mathematics since only 4 numbers with two fixed and two adjustable to reference one can convert any equation of the actual physical and subistituir constants by running equations simplifications and keeping the result equal to the original only with calculations between this 4 values! quantun the time and given weights following equation: sqr ((uo. & 0) cubed) worth 3.71140109 x10-26 seconds. already tested the exhaust theory and runs forever even at work behind this as I posted it derives relativity from quantum mechanics and rightfully time be quantized and that there is inertia!
Jorge Barcellos
Time is the equattion of physics is an abstraction. Real time cannot be abstracted because real time is ''change''. All that can be said, written, thought in any language including mathematics are abstraction about unchanging aspect of reality thus excluding ''change''. So real time, ''change'' will forever remain outside of what can be said including physics. It is interesting to note that ''galileo'' was the first to have parametrized time, the time of clock, for predicting movement with a fixed equation. It was the first time movement could enter the timeless realm of mathematics by spatializing time. But this spatialized time can capture the change that can be predicted but nothing else, not real change/time.
Dear Dr. Brassard.
I fully agree with you that time is an abstraction, and it has more cultural and cultures that do not realize the time! The work indicates that and that time is nothing more than the delay of transfer of information between two points in Euclidean space, and this delay and therefore quantizavel and time calculation in each string is a single quantum bit processor. Going beyond the demonstration that the equations univerço is a projection of wave interference or be a hologram, where brains and all around are all made of the same object that is a string. The projection of the string on is univerco as the permeability and permittivity of free space. I wish you a look at a small part of the work I posted past to dowload. and we can discuss the level that you want it!
Acts
Jorge Barcellos.
To some of collegues@
To the regret, I have to confees that I have understood nothing from the "word flow in time" above... It is too complicated! I could not catch and figure out any phisical sense within it. Sorry... Please, try to lay out the thoughts more clearly with more real physics, if it possible!
Regards!
Anatolij,
The variable ''t'' in the equations of physics is like any other variables. There is no special value of ''t' that is special in the sense of being the present moment, the ''Now''. When we experience time, we do not experience the future or the past but are stuck in the present time and everything happen now and when we speak that has happened we mean to say that it happened into a ''NOW' that do not exist anymore except by the traces it has left in the world and in our memory in the Now. In the equation of physics, there is no special now and a flow of time in the now, all location in time are equivalent and so exist simulteneiously into a block universe where nothing really happen.
To @Louis Brassard
yeh, thanks, I understand, I think, what you tried to explain, but the physics language is math, anf if we try to describe the surrounding nature by means of its tools, we need to adapt the way we figure out the phenomena models in terms of these math notions, and then What is the Time? Is it an evolution parameter fixing the changes in the world, or it is something else, which is still not caught by our level of understanding...That is a question, I mean.
Sincerely,
Anato.
Regards.
To Anatolij
Time is a challenger for the transfer of information between two points in Euclidean space and once processed faser becomes part of the global information of the universe, become irreversible. Ie is imposivel back in time but it is possible to reverse the twins paradox of Einstein. read my work and have posted brings matemacica the basis for this view of time, which is actually a vision of information theory. Since the equations show that the universe and massively parallel quantum computer
At.
Jorge Barcellos.
Nice, Jorge - It is new for me to tie the information as it is to the time change... I will think of and try to ponder into the matter ... if it is possible.
Regards!
How long is the "present"?
(I think it's not zero, it must be "something"). (In our brain can be more long because our memory and imagination whose can make it longer), but in reality, how long is it?
Sorry for the question.
The time of transformation of the future in past (immovable) is for me the present.
for Ana
The time has to be seen by two points of view:
Human time which is a creation of the brain, for without memory only exist this once so perceive the past because it is stored in memory which in turn is nothing more than a figure of interference of waves that belongs to the individual and this within the overall system memory.
The human memory and and made of frames every 125 ms and the correlation of these conditions generates the past as well as the analysis of them can predict the future ie all processes are local human creating the illusion of human time!
The second time and the arrow storm that has to do with the constant increase in speed of the particles inside the computer called the universe and seen as the traditional physical entropy increase. ve the actual physical speed of light constant as what to whom this within the universe and a true, since it is necessary to measure speed one meter and clock and observe the relativity equations to time dilation and contraction of the distance effects are resulting from the displacement speed of the object in relation to a benchmark and that the results derived constant ie creates the illusion of being fixed!
Read the work that I add where I show how to derive special relativity from quantum mechanics and better understood.
The work was finished the little Einstein's dream to unite all the physics in a set that describes all the physical and no odds how quantum mechanics in a deterministic but what made this possible was to understand that the one and only univerco holographic projection in which the human mind is part of the hologram and how facebook games!
The equations demonstration univerco closed one where the free strings vain a speed almost nil until the speed of light that the actual physical believes to be fixed.
Upon reaching the maximum speed the particle loops around the edge of the universe and returns to almost zero speed and arrow temporal contrary, ie as paul dirac predicts in his equations the antimatter and matter with a negative time.
This change of direction and made with a geometric figure of moebius loop and generates a parallel to this univerco made of antimatter that moves a distance of 1x10-15 meters of this structure on a brane stacked and interconnected.
That is the view of the big bang is not static and what one sees as the beginning and only vlta Zerktouni of a polarity to another matter!
I hope I have acid course but unfortunately I speak Portuguese and English and my bed so excuse any errors that use translater google
Jorge Barcellos
Hi, guys,
It is below a fantastic article! Enjoy and make a time to be quantized right now! -:)
Hi Anatolij.
Louis has put it much more eloquently and succinctly what I had tried to say in my previous posting. At the same time, one must realize if time was indeed stopping intermittently at discrete instants (!!) and then continuing its usual run, one could never detect this erratic behaviour, assuming that all dynamical variables continue from their older values when time had stopped. That brings one to an interesting speculation: if dynamlcal variables evolve not continuously but in quantum jumps, could it be because of local time flowing in a jerky manner?
Regards.
To Patrick: Yes, if time flow is changing discretely, assume, - what then does respond for the object velocity? It is not defined on the whole. Next, an interesting question I found in a student QM manual: if an electron in hydrogen atom jumps from the level E_1 to E_2 and a gamma quanta radiates, are these processes realized simultaneously or not? What is a time this process takes?
It is interesting that this time can be evaluated!...
Regards.
To Anatolij.
This time will be change of orbital multiple of, sqr ((uo. & 0) to high cubes) being equal to multiples of 3.71140109 x10-26 seconds.
However I should note that the computer has two communication channels a near instant what and where is the actions quantum and another that follows the equation of Maxwell to light speed, and this speed apparently fixed, but from the outside of the machine it is variable . eg in quantum entanglement communication is nearly instantaneous and also quantum tunneling.
Ana Maria,
How long is the present? Many philosophers such a William James , Bergson have phenomenally investigate this question. Mathematically the answer is clear, any time could possibly be a present which has no thickness. But phenomenally, the present is all there is and so is allways there. If all that exist, exist NOW then what is the past? The past is the structure of everything that exist in the NOW. The structure of everything is changing NOW and some of these changes are preserved in the NOW in terms of structure of the NOW. Fossils, geological strata, memories, galaxies, atoms everything has a structure that has been created into the NOW and is preserved in the NOW. The mathematical representation of a spatial dimension t is very very misleading. IF it were true nothing would exist in the now. The correct picture is to imagine a the transformation of a shape. All there is the shape in the now and the evolving structure of the shape capture the path of its transformation and so define the past in the now.
@Anatolij:
>if an electron in hydrogen atom jumps from the level E_1 to E_2 and a gamma
> quanta radiates, are these processes realized simultaneously or not? What
> is a time this process takes?
> It is interesting that this time can be evaluated!...
Anatolij, (1) "hydrogen atom jumps from the level E_1 to E_2 and a gamma quanta radiates," -- it is not a gamma quanta; the wavelength is about 675 angstroems (and energy is about 10.2 eV), which is in a far ultraviolet domain, even not a soft X-ray yet...
(2) the time of this so called "quantum jump" (there are experimental observation of such process for single atoms) is evaluated in a simple way: tau = 1 / (2 omega ) = hbar / [ 2 ( E_2 - E_1 )] ~ 0.2 femtosecond (1 fs= 10^-15 s) (this time domain is by now reachable by so called attosecond pulses). It is "simultaneous" only within that time interval -- simply because of the principle of uncertainty.
(3) and of course, it has nothing to do with "time quantization".
In general about the whole discussion -- well, it is fun to see how people can talk each other into all kind of off-the-wall things while knowing next to nothing about related physics (no, Anatolij, it is not about you...)
Louis@
Nice! Shape changing defines time flowing! It is so natural - as the mathematical isomorphism of structures. It is well known from the classical physics that if there had no any change in the ambient matter , there would have no time!
Regards!
I think we can say that present is the only existence. (Past is an human view, because we can remember). (Future is an human view, or resourse, because with acts or changes in the present we can obtain a diferent future- present-past fancied, because our presence, being, existence).
If we can be only in the present we can have not the limit of time...
To Alexander@
Thanks for your comprehensive comment, and all that about! Yet - can I kindly ask you to show-derive math-exactly the realtionship ΔEΔt≥ℏ, you just made use of? I have checked the Landau-Lifshitz "quantum mechanics" book..., But failed to find it there... Anyway, I have some doubts that such a derivation exists...(if Landau had omitted it!)
Regards!
to Anatolij
If we talk about traditional physical measures speaks louder than any equation and usually at this point and considered that an electron jumps instantly to be bombarded by a photon energy proper, but the measurement shows something else. this time and in the order of 20 attoseconds with an uncertainty of 5 attoseconds, not being applicable the principle of incertesa the beginning of time jumping. Article http://www.sciencemag.org/content/328/5986/1658
This brings up esperiment not have to access the article me an email and I send you.
About Heisenberg principle and the incertesa I follow the vision of the moon Einsten deicha not be it, because not only am looking at! And if someone analyze the work in the comments atachei understood that this principle only applies when you have a messenger that transmits information to the photons. since the particle interacting with the the same but it interferes with and possible measure and correct such interference as shown in this test. http://www.sciencemag.org/content/332/6034/1170.abstract
Ie has a lot of absolute truth is not so absolute and what I discovered is that the truth is much more subtle than you might imagine! If someone here knows the equation that defines the plank constant, the charge of the electron, the mass of the electron, and that makes possible to work with them algebraically in place of the values provided by NIST and the result of the calculations and simplifications is the same result. And lets understand where relativity by understanding these simple equations, I would love to discuss it in depth, but dicutir what has already been discussed million times between Einstein and Neils Born and not resulted in anything useful and then in a dead end road!
Relativity and quantum mechanics this right also but the two can not coexist are looking for matter, energy, time and space!
The output I found and treat it as information and this way I found the equations that describes what I quoted so well as quantum gravity and the rest is that both dreams, but if colleagues want to continue discussing an unsolved problem there have not nothing more to add!
Jorge Barcellos.
Violation of Heisenberg's Measurement-Disturbance Relationship by Weak Measurements
Lee Rozema, Ardavan Darabi, Dylan Mahler, Alex Hayat, Yasaman Soudagar, Aephraim Steinberg
Physical Review Letters
Vol.: 109 (10)
DOI: 10.1103/PhysRevLett.109.100404
Let me refocus the question.
There is no experimental evidence of time quantization.
But is there any physics principal that prevents time to be quantized ?
Time is a measurement tool of periods (including phases, intervals and cycles) between events or duration of events, processes or progressions within a time scale. It is also the instant dimension point of bifurcation from which any system (organization, scheme, organism, method, regularity and order), and any process, progression or knowledge splits, derives or develops towards new models, patterns or configurations.
Charles,
As often is the case in physics, experimental evidence can be in the eye of the beholder.
Edward Tryon, for instance, considers the Big Bang itself as evidence of time quantization in a prior matrix universe, where the Big Bang would be born of a quantum fluctuation - whereby a virtual particle could just happen to be occasionally so big that its Heisenberg conjugated duration of existence would need to be shorter than the time quantum for it to remain in the quantum foam: it cannot do so and gives rise to a big bang, i.e. the virtual particle becomes non-virtual.
The calculation of the upper boundary of the time quantum in that putative prior matrix universe is straightforward: plug the mass of our universe into Heisenberg's equation. (This yields a time quantum in the matrix universe of about 10 to the power minus 105 seconds.) Likewise, you can use Planck's time to calculate the mass of a Universe our universe could be the matrix universe of under a quantum fluctuation scenario (about one ten thousandth of a gram.)
Quantization often results from the ability of a system of given attributes to establish 'standing waves'. Nothing in principle prevents either time or space to be quantized, at least in dimensionally finite universes. It's less straightforward in dimensionally infinite universes, and it seems to also depend in non trivial ways on the particular spacetime signature.
for Charles.
His work with the limit superios harmonics of Fourier transforms agree with my calculations. Now out indirect methods will be pretty hard to prove by direct quantization metos time because humans need a messenger of information to be informed and this interferes with the messenger being measured on, being of the same order of magnitude as the entity to measure , hence arises the principle of uncertainty. However by mathematical methods that was possible and I used to prove and even inertia and so according to these equations is precisely the time to be quantized, and this allowed me to derive the theory of general relativity and quantum mechanics, I'm working on a new formalism for Einstein tensor representation of time to represent the space in 4 dimensions. The part that demonstrates how to derive special relativity from quantum mechanics this in an article posted shortly ago. To remove any doubt about the validity of this mathematical work he allowed me to convert all the equations, constants and forces the mathematical relations between four values, two fixed and two-adjusted inertial frame to be measured.To remove any doubt about the validity of this mathematical work he allowed me to convert all the equations, constants and forces the mathematical relations between four values, two fixed and two-adjusted inertial frame to be measured. Since the two values are fixed magnetic permeability and electrical permittivity of space. That according to the vision of the work I've done are the projection of the strings in the universe of matter, since these strings in my theory are quantum information processors of a qubit.
Examine the small part of the work that grossed and observed that the key to resolving the paradox of time and just find the equation that defines the starting plank finds the projection of the strings in the universe.
Jorge Barcellos.
In my job processing time information on this rope and given by the following equation Square root of the magnetic permeability multiplied by mermisividade electric cubed = square root ((uo. & 0) cubed) equals 3.71140109 x10-26 second. this value and the minimum length of the string calculation and agrees with its range of calculations. answer your other question the other hand am not aware of anything prohibiting the quantization of time. Would like you to look at my equations and send your opinion about possible errors, since the concept is complex and multidisciplinary but the calculations as simple as Einstein imagined what should be a final theory.
Grateful.
Jorge Barcellos.
Jorge@
I would like to pose once more a simple question: What are we speaking about, namely, what is understood under the term "time quantization"? Do you assume the existence of some operator and Hilbert space with respect to which this "quantization" can be realized as an observable quantity? Or the notion "quantization" means something else?
Regards!
To Anatolij.
The work I've done shows that the universe has five dimensions, with the 3 real Euclidean space. And two virtual consoles that teem physical and temporal interpretation. These two temporal dimensions is one time einstein regards the speed of light and the other has a speed almost infinite and represented in the Hilbert space as infinite ie instant. The space of Einstein treated the transfer of information, the photon being the bearer of this information, because everything that reaches the human brain needs a messenger, it's a vibe or electromagnetic compressive as in sound, The quantum mechanics works in my theory as a theory finite element where it approaches the final values for the interaction of the edges of the cell information processing. In quantum mechanics the way communication is a wave that spreads in 3 seconds time einstein within the entire universe would be the limits of the memory of a quantum computer that is what we call the universe. This wave velocity of quantum mechanics and quantum entanglement in view of particles that Einstein did not accept.
The quantization of time only applies to the space of Einstein as the level of quantum mechanics and the universe integrated and works as a point that is one dimension zero. The best representation of quantum and De broglie with the Schrodinger wave equations. and considering the universe as an array of points that have almost instant communication with each other (hence the infinite Hilbert space). observation in my work and the universe closed and finite in space but in time cyclic, and as a membrane that goes up to the edge and back to the opposite side and seen as a parallel universe of antimatter. I hope I was clear and I am berto any questions or criticizes based.
My work on this basis before quantum mechanics and relativity and allows both to explain and show how they relate including 4 simple equations derived from special relativity dirac constant.
I'm working on how to represent both in a theory extruded matrix integrated, but this does not affect in any way the current validity of both theories are correct within the limits which they propose to work.
I would like to analyze my work that has a complex concept but one very simple and mathematically verifiable and if I'm wrong please show me my mistakes. Thank you.
Jorge Barcellos
Another detail that I find interesting and enlightening Anatolij that both theories describe two communication channels of a computing machine and my theory on this is the best vision for the subject seen from the point of view of matter, energy, time and space. What I have analyzed and creating a formalism to have the two theories into one, because the work I did hardwaer describes the machine and its mathematical instructions, so I have equations for all forces and constants of physics traditional and these equations are deterministic giving resultador comparable measures nist better than one part in 10 million. Ie is a deterministic theory that describes quantum mechanics and relativity, but goes far beyond. greetings
Jorge Barcellos.
@Anatolij:
> can I kindly ask you to show-derive math-exactly the realtionship ΔEΔt≥ℏ,
> you just made use of? I have checked the Landau-Lifshitz "quantum mechanics"
> book..., But failed to find it there... Anyway, I have some doubts that such
> a derivation exists...(if Landau had omitted it!)
Anatolij,
(1) precisely speaking, it should read ΔEΔt≥ℏ/2 (notice ℏ/2, not ℏ).
(2) I don't know what should be called "derivation" in this case; it is more about properties of quantum operators, but in general uncertainty principle is sort of more or less trivial notion (and very common in many fields other than QM, e. g. in communication theory or diffraction theory). I guess QM was not part of your curriculum back in school time:-), but Landau & Lifshitz books are tough cookies anyway (I happened to go through almost all of them back in my school days...) What I can do in response to your request, is to attach for you here copies of a few pages from my notes for the course on "Basics of wave and quantum mechanics for engineers" that I teach at Johns Hopkins for many years.
(3) If you would be interested in further reading (other than L&L), here are the books that I usually recommend to my student as supplemental texts:
P. L. Hagelstein, S. D. Senturia, T. P. Orlando, Introductory Applied Quantum and Statistical Mechanics , Wiley, 2004; Also recommended: R. L. Libov, Introduction to Quantum Mechanics , Addison-Wesley, 1992; W. Greiner, Quantum Mechanics; Introduction , Springer, 1989.
@Chris. From what you say shall I understand that I must wait for gravitation and QM to be unifiée Belfort guettions an answer?
@ Anatolij. My question is quite general. In the present state of the gravitation theory time is not an observable, but we know this theory needs to be reformulated.
@ Jorge. I have much difficulty understanding your posts.
@ Alexander. You are right the uncertainty principle is a principle not the result of an experiment or the result of à demonstration.
@Chris. From what you say shall I understand that I must wait for gravitation and QM to be unified before getting an answer?
Sorry for the mess.
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