Perhaps one of the questions for observers, like us who can ask questions, is why the Hilbert space of QM is complex? Maybe it is just because complex numbers are useful when describing waves, and there's that dang Schroedinger wavefunction, and deBroglie matter waves. But the same complex 2-vectors equally describe spin states (spin states have a wavelike nature??), electron spin is either parallel or antiparallel to the direction of motion. Or it's in a superposition of both. Which is why, if you have an incoming beam of electrons they're described by a mixed state, one which has equally probable outcomes for measurement. There are two more directions apart from the one defined by electron motion (i.e. linear momentum). If the electron isn't "moving", how many ways can the spin be in superposition? What's different when the superposition of spin states spans a pair of electrons? The math just "changes gear" so you have 4-vectors (otherwise called tensor products).
Finally, I certainly can (post the math that goes along with and supports this idea). Thanks for your patience. You are brilliant, and I want to be clear on this: so was Minkowski, and so was his student Hilbert. That being said, they are only wrong by a tiny fraction of a conceptual amount. At first, at any rate. I will explain, without the pseudoscience this time. That didn't come off as a bad imitation of a fictional villain like Baal on SG-1, I hope.
Yes, it is because of the wavelike nature of QM entities. You need to be able to specify both an amplitude and a phase angle at all points in space and time, so complex numbers are your answer. I don't think it is any more mysterious than that.
On the other hand, the Uncertainty Principle can be described by a pair of functions on the unit circle. These just have to take the sine and cosine functions to the upper half plane. Well of course, then you might as well use the complex plane, what the hey?
Planck, Bourne, Schroedinger, Pauli, et al were brilliant also. This tiny conceptual mod does not require throwing away any of QM or QFT theories either. Someone else will likely figure out a way to actually incorporate it into the math, even if I cannot do so. I'll try and show you where it needs to fit.
What do we mean by a classical measurement? It's some information from a classical device, which is: something usually in the solid state, containing a large number of particles (a molar amount) which can 'detect' single particles. A detector screen in particle diffraction for instance, 'detects' particle-like dots in a 2d pattern, that you can produce dots one at a time is a 'detection' of particle-like particles. An interference pattern indicates wavelike particles, so in diffraction you get information about both, over time. You could have a single row of detectors (a screen with a small height), discarding most of the information to get a good enough sample, i.e. you apply a statistical principle of measurement. Which says, any large enough sample will show interference if it's present, but single-particle statistics only need a large enough detector (since, you could arrange for a single detector to scan across the diffracted pattern). Measurement is assumed to 'absorb' the particle, in the sense its position and momentum following the instant of measurement are undefined. What is a quantum measurement then? It's an exchange of quantum information, which is an abuse of terminology because information is classical, like the bits that my computer transmits to this server. But I guess you have to call it something.
Ancient Greek geometry is "classical". Euclidean geometry is "classical". Shannon's information theory is not something I would characterize as "classical". It is still as cutting edge as it gets, and my career in technology depended rather heavily on it.
Please Register or Log in to view the hidden image! Minkowski defined a spacetime interval thus: Please Register or Log in to view the hidden image! Which explicitly references a proportion for the temporal or tensor component: Please Register or Log in to view the hidden image! And implicit in the idea for inclusion of this time component of Minkowski's spacetime interval is this: Please Register or Log in to view the hidden image! You will notice that delta t appearing inthe denominator of this last expression for the TEMPORAL nature of speed of light may be made as small as you like; vanishingly small, in fact. And when you have done this, you have divided by zero. And what you have also done when that happens is to trash the component of this expression which is responsible for holding the most important principle of physics; the conservation of energy. The conservation of energy normally would simply fall out of the ideas that: the bound energy that is a particle or collection of subatomic parts of matter or antimatter persists in TIME, from INSTANT to INSTANT, because or something faster than light propagates, i.e. entanglement, and the unbound energy that is an ENTANGLED photon propagating in free space at c persists in TIME, from INSTANT to INSTANT because it was produced by means of accelerating particles possessing both electric charge and ENTANGLEMENT. Persistence in time for energy IS the conservation of energy, and we have demonstrated an aspect of this that lies outside of the framework provided by Special Relativity. Entanglement is FTL, and is responsible for the conservation of both forms of energy commemorated in Einstein's most famous relation, E=mc^2. It is not possible for it to exist within the framework of the invariant speed of light, NOR ANY VELOCITY, invariant or otherwise, set to be proportional to time itself, or an instant of time. Entanglement does not trash conservation of energy even though it is instantaneous, because no net bulk bound or unbound energy is actually transferred by means of an entanglement spin flip.
There is no FTL, there is only interactions between particles. I think you have a somewhat tangled understanding of entanglement and measurement. When we control interactions, we control the entanglements, we can use it like a resource so it must be real. But then it means an electron in a hydrogen atom is entangled with a proton--the one it's interacting with. Measuring any entanglement between a proton and an electron, or why you can or can't says something about what it is and isn't. But it isn't about conserving energy and momentum if measurements are post-interaction, in the same way measurements which are separated in space and time aren't about conserving energy in a separate interaction between particles (how could they be?)
I must admit I have never heard of "classical measurement" and have no idea what it might mean. Surely measurement is measurement? Nor have I any idea how you can have a "classical" device, as opposed to some other sort. I would have thought the term "classical" would relate only to theoretical models, not to acts or instruments of measurement.
My understanding is fine. A theory of spacetime that explicitly forbids FTL ENTANGLEMENT / SIMULTANAEITY like Minkowsky does is the conceptual roadblock here. Simultanaeity exists. It exists everywhere, in all inertial reference frames. Denial of this only occurs when you are gullible enough to think that light propagation is the basis of time itself, and to conceive of this idea using proportional math as your model is dividing by zero. It's as simple as that.
Since I also now understand that it was the way I presented these ideas initially that was causing many of my own (other, micellaneous) conceptual problems, I want to thank everyone here for giving me the opportunity to at length post something I think will be of lasting value. But that is not for me to decide. Your values are your own.
No, I do not think so. You do not say what "j" is, but in order that units and signs come into register, Minkowski set the temporal component of spacetime equal to \(ict\) so that \((ict+x+y+z)^2=-c^2t^2+x^2+y^2+z^2\,\,(i = \sqrt{-1})\), a Lorentz invariant Then you don't know what a "tensor component" is . Then you do not understand limits and the differential calculus - division by zero does NOT enter the picture. Moreover you may need to explain to we native English speakers what you mean by the "temporal nature of speed"
The terminology shows up in the quantum computation literature. The distinction is because of the quantum 'gate' paradigm, which uses quantum 'logic', which is not classical. And yes, measurement implies information, and information is something that requires energy to erase. That, believe it or not, is why quantum information (a misnomer if ever there was) is not classical. Use that black-box thing. A quantum gate is made out of classical stuff--lasers. mirrors, beamsplitters, the inputs and outputs are classical, but what happens between inputting and outputting can't be defined classically (you probably have seen that one before).
I see an extreme red shifted photon with a single wavelength spanning the known universe. An entangled photon near the source gets observed, and the entire waveform spanning the known universe instantly flips entanglement state at the same instant. Do you envision how different and strange this is compared to the relativity you were taught? Unbound energy persists in time only when it propagates at c (in this case, for a time interval spanning the age of the known universe, or light travel time that is equivalent). Distance means exactly nothing. Time dilates all the way, just as relativity predicts, and can do so ONLY BECAUSE time is not proportional to c. If it were (proportional to c), light literally could not propagate. It all makes perfect sense now.
I'm sorry, that's all a bit too vague for me to deal with. The redshifted photon, what do you mean you "see it spanning the entire universe"? This photon is entangled with another "at the source", can you explain that a bit more? Or just post a diagram that illustrates what you mean. maybe. I don't actually like the idea of "speed of entanglement", and the whole FTL drama. What is meant, I think, is the change in entanglement states when a measurement is made and the apparent speed of propagation of this change. I also think it's a problem which is based on our ignorance of the true nature of space and time--if we live in a four dimensional universe, why do we distinguish one dimension as being fundamentally different, how do we "spend" the symmetry?
As an electrical engineer (!) Dan has presumably used j as synonym for i preferred by physicists. Which makes his first formula in #88 explicitly erroneous. First term inside the sqrt should of course be just -ct² (using -+++ signature convention).
Ah OK, thanks. I presume then that a "quantum" as opposed to a "classical" device in this context would refer to a quantum computer or something, would it? However it still seems to me that the measurement itself is neither "classical nor "quantum". A measurement has to yield a value, surely? (But I admit I have avoided quantum computing like the plague, so I'd be interested to learn if even this old certainty is now under attack.Please Register or Log in to view the hidden image! )
When you are measuring EXACT physical distance dimensions of material objects in space, those ALWAYS depend on relative velocities. The Lorentz treatment of the subject is not exact either, depending heavily on the inertia of the roadbed itself, although I give it high marks for being able to salvage relative time dilations anyway. Anyone who looks at relative Lorentz length contractions and still be convinced they can do geometry must be living in a very static world. It is still possible to do physics with the concept of time, but only if you actually understand what that is. It is not something "proportional" to the propagation of light, or some concept untouchable simply because division by zero doen't work when you suffer from the aforementioned misconception. EITHER your measurement must be made very, very QUICK, or else whatever you are measuring must NOT BE MOVING AT ALL, relative to you or to your measuring device. If you have to move at all to make a measurement, or if the thing you are measuring has atomic structure as its makeup, that measurement CHANGES, and truth be told, the meter stick's dimensions change WITH WHATEVER YOU MEASURE. A gravity wave could even pass through the room while you are making your measurement, confounding absolute measurement in yet another dimension you could not be certain of without more than one gravity wave detector. This is why I argue so strongly that ancient greek Euclidean gemometry is the only "classic" tool used in early 21st century physics in the same way Euclid himself used it. It just doesn't get any more "classic" than that. Hilbert spaces still uses Euclidean geometry. You can evaluate the idea for yourself, but that modeling tool looks very "classical" to me.
Dunno why you have waffle on about concepts from relativity in every conceivable context. This is about quantum computing, which has sod-all to do with relativity. I'll wait for a reply from Arfa.
