the problem of infinite divisibility and how QE sheds some light. QE = quantum entanglement A quanta of energy is considered the smallest possible energy "unit" in the universe. note to readers: the below is hypothetical and could have errors .......of various kinds i have asked this to be moved to philosophy section i think -- the quanta cannot be the "last stop" because that would make quantum mechanics very rigid/limited. it may be the last stop within our understanding of time and space but not within the larger laws/fabric of universe the phrase "problem of infinite divisibility" does not exist in any literature, its simply been coined to give a name to the argument below: Could there be events/changes that require less than a quanta? perhaps one or more of the below: - a photon transferring its energy to two other photons (..like a billiards ball striking two other balls)...where the total energy transferred was just 1 quantum....this quanta must however now must be split into two between the two entangled photons - a change in spin of a photon that requires less than a quanta of energy - a change in momentum or position that requires less than a quanta of energy - a split of a single path into two, or more, paths - even if its a single quanta....its still spread over (though infinitesimally small) time and space..... - or consider a quanta of energy/momentum applied to a photon....the back part of the photon will have slightly more energy (compression) than the front part.......because the quanta cannot be considered perfectly rigid.....however quantum entanglement provide some clues in our quest to resolve this ...... Quantum Mechanics, and the phenomena of quantum entanglement, fits in neatly by giving us some clues about the nature of reality (specially at the sub-atomic level) and telling us that our understanding of discrete, continuous is incomplete
thanks sigma.alpha i went through Zeno's paradoxes just now and its seems they are different. also Zeno's paradoxes are resolvable without having to make use of quantum mechanics. I am saying/hypothesizing that the issue presented above can be resolved only via quantum mechanics (and phenomena like quantum entanglement)... i.e. there are things beyond the quanta, beyond the smallest unit of energy/particle and quantum mechanics is giving us some hints/clues.
There will be much more knowledgeable posters, but i i think i can help with some of the questions. With respect to the observed world, QM is certainly limited in explaining the observed world, almost incomprehensible. Why? The so-called universe isn't made out of classical 'stuff', what makes you think it has to be certain way, instead of the other? By definition no(unless new physics is discovered not similar to QM and its postulates and constants). I will await to see if somebody will bring up virtual particles and their contribution. Correct me if i am wrong, but the word quantum doesn't mean much of anything in physics(beyond just a label for minimum quantity). The energy of a photon(or other particles) is represented by its momentum in eV and photons at certain frequences are more energetic and can easily penetrate solids. If you are asking if there is a smaller unit of energy than Planck's constant(4.135667516(91)×10−15 eV·s) i belive the answer is no. I don't consider this the most noteworthy problem as pretty much everyone recognizes that our understanding of everything is incomplete but the topic is certainly interesting.
How? I am not aware of any experiement that challenges Planck's constant. To the contrary, it seems to be one of the most solid things in physics and is the basis of all known physics. Edit: On a more phislosophical note, i don't believe motion can take place without quantization(even in principle), so your comparision to Zeno's paradox is justified(if you are questioning it, and not making bold claims).
....Zeno's argument is based on the assumption that you can infinitely divide space.... ....What they realized was that a purely mathematical solution was not sufficient: the paradoxes not only question abstract mathematics, but also the nature of physical reality. So what they sought was an argument not only that Zeno posed no threat to the mathematics of infinity but also that that mathematics correctly describes objects, time and space. The idea that a mathematical law—say Newton's law of universal gravity—may or may not correctly describe things is familiar, but some aspects of the mathematics of infinity—the nature of the continuum, definition of infinite sums and so on—seem so basic that it may be hard to see at first that they too apply contingently. But surely they do: nothing guarantees a priori that space has the structure of the continuum, or even that parts of space add up according to Cauchy's definition.....
no bold claims at all....because I realize i am on slippy/hazy/grey/imaginative area...:) i mean.....smaller than quanta in a different form..... for example take quantum entanglement.......it's as if it's showing us a deeper reality that the laws (for example of conservation of mass-energy) can "travel" instantaneously...and it has to be that way.....the law is valid at any point in time-space...as if its a-priori to time-space.... also on a separate note - maybe at the quanta level...position-momentum are same thing......you only need one of them to fully describe all about the particle.....
oh thanks Sigma.alpha...... thanks for boosting my self-esteem.....so I am thinking what Zeno thought many centuries ago...not bad not bad....
That assumption is part of Zeno's argument, but additional (and rather suspect) assumptions are needed to actually make the argument work.
i tend to agree....however......quantization within time-space....time-space maybe be a part of a bigger reality discreteness might exit "within" time-space......and continuous....(like the wave-function?)...beyond...
What is the quantization of spacetime? It has to be one Planck times, right? As part of a worldline in GR. It's much less certain than you think that spacetime exists apriori that which you label wavefunctions. Your question is basically reducible to fields vs observed eigenvalues, and you'd have a hard time if you don't think of the 'entities' as anything more than events.
well on the pragmatic side.. continuous at least to 10-^{48} mt and maybe beyond, and maybe continuous. http://arxiv.org/PS_cache/arxiv/pdf/1106/1106.1068v1.pdf planck scale: 1.616 x 10-^{35} meters
great info....and nice article, except that its way over my head...however I am honored to be chatting with a bright physicist/person like you and others on this forums
good points Maui, still reading your posts......in the meantime....i am responding to the above to clarify..... i guess that.....quantum entanglement (and wave functions ?) might not be "effected" by time-space and exist "beyond/outside" it.....except when we try to measure/detect them....i.e. when we pull them "back" into time-space the relationship between the two entangled photons ...the various laws/phenomena behind it....might be hinting to something apriori time-space
thanks, anyway http://www.esa.int/esaSC/SEM5B34TBPG_index_0.html ...it has been shown how a quantum wavefunction can be measurably inﬂuenced by general relativistic eﬀects... Quantum Connectivity of Space-Time and Gravitationally Induced De-correlation of Entanglement http://arxiv.org/pdf/0809.1907v1.pdf ...in a curved spacetime using localized operators. We contrast the new formulation with the standard approach and ﬁnd observable diﬀerences for entangled states....
very interesting. thanks sigma.alpha. I have discarded my hypothesis. thanks for reducing the paths the mind (not photon) must travel. give the mind a month.....to digest...:) does this not strengthen the idea that the wave-functions are real ..... since a bend in space time.....effects them.....
Some of what you write represents some misconceptions about quantum mechanics that are common in popularized discussions. Quantum is a term that popularized and watered-down discussions of quantum mechanics often only incompletely explain. In the primary usage of the term, where for instance we learn that energy is quantized in units which are called "quanta," we must be more specific and explain that this is most often the case for systems which are bound states. So for example, the electrons in an atom exist in orbitals which have a discrete amount of energy relative to the unbound system. Photons which are emitted when an electron in an excited state decays to a lower energy state will be found to have a discrete spectrum (with a caveat that I will address below). However, the spectrum of free particles in quantum mechanics is not quantized: their energy and momentum lie in the continuous spectrum of values contrained by ##E = \sqrt{(pc)^2 + (m c^2)^2}##. Furthermore, even higher-order transitions between bound states involve a continuous spectrum of photons. For example, the 2s to 1s transition in hydrogen occurs at lowest order by the emission of two photons. Only the sum of their energies is quantized, ##E_1+E_2 = E_{2s} - E_{1s}##. There is a kinematic distribution of energies ##E_1,E_2## that is peaked around ##E_1=E_2##. The second use of the term quanta arises in quantum field theory, which is often itself called "second quantization." This notion of the term refers to particles states being discrete excitations of a classical field. For instance the photon in QFT is the "quantum" of the electromagnetic field. The excitations are quantized in the sense that a classical EM wave corresponds to a finite (though large) number of photons. However, in the free-particle case, the energy-momentum of these individual quanta are not themselves quantized and form a continuum. None of the above addresses any notion of minimal length. That is the realm of gravity and QM alone doesn't address the issue. The uncertainty principle allows us to probe infinitesimally small scales at the expense of having an infinite uncertainty in energy-momentum. Momentum conservation forbids a single photon from splitting into two photons without having a fourth object around to carry some momentum in the final state. If this object were present, it could carry a continuous amount of momentum away and the spectrum of final state photons would be continuously distributed. Only the sum of final state energies is required to equal the energy of the initial photon. And in the free particle case, the initial photon energy wasn't quantized to begin with for the reasons I gave earlier. Spin is quantized, even for free particles. How a change in spin translates to an amount of energy depends on the specific process being considered. Yes, as I've been clarifying, a change in momentum for a free particle corresponds to a continuous change in energy. It is hard to how entanglement sheds any light on this. Photons are point particles. They do not have a front or back part.