juanrga

Absolute zero is unreachable (third law of thermodynamics) in our universe and I do not know how dissipation would work in an hypothetical universe without third law. Do you? Average temperature of outer space is about 3 kelvin. If you move the Earth to a place without Sun or similar source of heat. It would achieve about 10-100 kelvins in 102 days or something as that. Earth would not achieve 3 kelvin due to internal heat. Of course in geological scales of time, volcanoes and other geological stuff would finally stop and then Earth would achieve equilibrium with outer space.

The photon is its own antiparticle (photon has no charge and the inverse of 0 is -0 which is zero again). Therefore you are asking about photon-photon collision. In QED, two photons can annihilate to give an electron plus and anti-electron (positron) [math]\gamma + \gamma \rightarrow e^{-} + e^{+}[/math] Two photons can also collide to give two photons [math]\gamma + \gamma \rightarrow \gamma + \gamma[/math] Both photon-photon collisions and annihilations are observed in current high energy particle accelerators, although in indirect ways. There are plans to build photon-photon colliders (also named gamma-gamma colliders).

This idea is named the free lunch cosmology. It is a plausible speculation. Yes, although it seems that the original idea was by Pascual Jordan.

And this singularity has been taken by some to mean that time was born with the Big bang. However, that model of the Big bang is classical. It is based in extrapolating backward in time the approximated equations of general relativity. Near the Big bang, gravity is so intense that quantum gravity effects cannot be neglected and general relativity is a bad approximation. When quantum gravity effects are taken into account, you find that there was no initial singularity and that times flowed just fine.

There are some rumours that they will announce the discovering of the Higgs boson. But no outsider knows for sure.

First, as the Wikipedia link emphasizes there is not such paradox in the sense of a logical contradiction. A complete description of the twins can be made in general relativity, but it can be also treated with special relativity, which deals only with inertial frames (constant velocity) and where spacetime does not bend but is flat . This would convince you that the twin behaviour has nothing to do with acceleration or mass. (Moreover, mass in general relativity is a fixed quantity denoted by [math]m[/math]: See A no nonsense introduction to general relativity). The difference in ages can be shown using special relativity, and its expression for time-dilation factor [math]\sqrt{1 - v^2/c^2}[/math]. Time goes slow for moving objects [math]v \neq 0[/math] than for objects at rest [math]v=0[/math]. Suppose that Ann stays at home and Bob rockets away at 3/5 light speed. Introduce [math]v=3/5 c[/math] in the above special relativistic formula and you get a time dilation of 80% for Bob. Bob lets 4 years pass. Bob returns at 3/5 light speed (time dilation is again 80% for him), taking another 4 years. Ann thinks 10 years have passed according to her clock, and both Ann and Bob agree that Bob is two years younger (10 years * 80% = 8 years).

My original premise was: And I supported my claims by giving link to Gell-Mann interview explaining how his work was considered crackpot and by giving some examples of Nobel awarded works rejected by reputable journals. There are many more. I also cited a specific example of a Nobel awarded work which was published in a unrefereed monograph, because journals rejected it. I have also explained that works, initially rejected, can be published latter when the topic is mainstream or when initial resistance to novel ideas vanish. In fact, when a topic becomes mainstream enough specialized reputable journal are born for it. For instance journals on quantum chemistry did not exist 70 years ago. I note you did not answered my question about chaos theory.

In a sense photons can interact with photons electromagnetically, although not directly. A small tutorial to two photon physics is http://www.hep.ucl.ac.uk/~opal/gammagamma/gg-tutorial.html

If you wait enough time the revolutionary correct claims become mainstream and publication is easy. I remark again that Newton and Gell-Mann were both considered crackpots. Today both are considered geniuses. Denis Gabor (Nobel Prize in Physics, 1971) had to wait 11 years before his initially rejected work in the field of experimental/applied physics was finally published. The largest time span I know was in chemistry, where one very important work was published 25 years after it was initially submitted! And regarding Physiology or Medicine, Burnet's work was rejected by the reputable journals up to a point that Burnet published his observations in an unrefereed monograph entitled "The production of antibodies". The discovery reported in the second edition of the monograph was awarded with a share of the 1960 Nobel Prize in Physiology or Medicine. Regarding theoretical physics, you can easily publish a paper in chaos in a reputable journal today, but do you know what was the reception of journals when chaos theory was being developed? I have received a rejection letter from one of those two journal and reading it was a pleasure: I already knew that my work was correct because I discussed with a pair of experts before, but politeness and sincerity of this rejection letter still captivates me.

I suppose that it would be emphasized that quantum entanglement does not involve any particle/signal moving faster than light. The FTL sometimes associated to quantum entanglement is only apparent "Since the underlying behaviour doesn't violate local causality or allow FTL". http://en.wikipedia.org/wiki/Faster-than-light#Quantum_mechanics

I know about 50 examples of Nobel laureates. And you would increase that figure at least on one order of magnitude if you count very important papers but that did not won a Nobel Prize. Some examples related to experimental and applied physics: In the year 1958 PAVEL ALEKSEYEVICH CHERENKOV, ILYA MIKHAILOVICH FRANK and IGOR YEVGENYEVICH TAMM shared the Nobel Prize in Physics "for the discovery and interpretation of the Cherenkov effect". However, their original manuscript entitled Visible radiation produced by electrons moving in a medium with velocities exceeding that of the light was turned down by Nature, "whose editors did not take the work seriously". Twice the Journal of Chemical Physics rejected in 1965 the key paper that led to the 1991 Nobel Prize in Chemistry so rightfully awarded to Richard R. Ernst. The editors claimed that the contents of originality were insufficient for publication in such journal. This article described the use of single, high energy pulses of radio waves containing all frequencies that would make atoms "flip" instead of a gradual sweep with a spectrum of radio waves that was in use previously. Klaus von Klitzing was awarded the 1985 Nobel Prize in Physics "for the discovery of the quantized Hall effect". However the original report initially submitted to the Physical Review Letters was returned. A share of the 1986 Nobel Prize in Chemistry was awarded to JOHN CHARLES POLANYI. According to the Nobel Press Release "The method which he has developed can be considered as a first step towards the present more sophisticated, but also more complicated, laser-based methods for the study of chemical reaction dynamics". His paper was rejected by Physical Review Letters. One half of the 1986 Nobel Prize in Physics was awarded to GERD BINNIG and HEINRICH ROHRER for developing the scanning tunnelling microscope. In their Nobel Lecture, they have spoken about being often told that they were addressing something that would "not have worked in principle". Actually, their first attempt to publish a letter describing the scanning tunnel microscope failed. Professor Nico García, a visiting scholar from the Universidad Autónoma de Madrid (Spain), intervened with his paternal remark, "that's a good sign". The 1996 Nobel Prize in Physics was awarded to DAVID MORRIS LEE, DOUGLAS DEAN OSHEROFF, and ROBERT COLEMAN RICHARDSON for the discovery of superfluid Helium. Their key paper was rejected by the reviewers of the journal Physical Review Letters. One reviewer argued that the system "cannot do what the authors are suggesting it does". The 2000 Nobel Prize in Physics was awarded to HERBERT KROEMER "for developing semiconductor heterostructures used in high-speed and opto-electronics". His paper was rejected by the journal Applied Physics Letters.

Your question is not clear to me. By definition a luxon particle always moves at the speed of light. And this is the fastest speed that any particle can travel. Check also this http://en.wikipedia.org/wiki/Tachyon In the standard model of physics plus general relativity "FTL interactions" are forbidden. Also no scientific measurement of "FTL interactions" has been made up to now. It is right that some few theorists are speculating about the possibility of "FTL interactions", but I do not know any consistent model. E.g. some years ago someone proposed a very speculative model with gravitational interactions propagating faster than light and claimed that his model was being confirmed by observations, but posterior analysis showed that observations were compatible with an ordinary model of gravitons travelling at the speed of light: c.

The source of the gravitational field is the stress-energy-momentum tensor (SEM). For massive particles this tensor is proportional to mass. For massless particles such as the photon this tensor is proportional to photon momentum. Gravitons are massless particles which are believed to be the quanta of the own gravitational field.

Quantization http://en.wikipedia.org/wiki/Canonical_quantization

I gave a specific example. Read the thread. I never said or insinuate that. Read the thread. Nobody here "highjacked this thread" and no moderator said so. I wrote the correct quantum version of Newton second law and gave a link showing how the quantum version provides the correct classical limit via the Ehrenfest theorem. In fact, the equations for the quantum harmonic oscillator are well-known. You only need to substitute the value of the force F in the equations that I wrote in #18 (and repeated in #20) and you obtain [math]\frac{d \hat{p}}{d t} = -kx[/math] with harmonic constant [math]k = mw^2[/math] You can again check this equation online (although virtually any QM textbook gives this equation) http://en.wikipedia....tator_relations You and another poster claimed [math]{\partial \hat{p}}/{\partial t} = -kx[/math] but your equation is wrong. EDIT: I attach the image with the quantum equations from the Wiki link

The definition was [math]\hat{F}\equiv - \nabla \hat{H}[/math] (check your own #7). This is the same than [math]\hat{F}\Psi \equiv - (\nabla \hat{H}) \Psi[/math]. At the other hand, it is trivial to check that [math]\nabla \hat{H}\Psi = (\nabla \hat{H})\Psi + \hat{H} (\nabla \Psi)[/math] equals [math](\nabla \hat{H}) \Psi[/math] only when [math]\nabla \Psi = 0[/math]. Are you aware of the title of this thread? "Quantizing Newton laws". The quantum version of the classical Newtonian law is [math]d\hat{p}/dt = \hat{F}[/math] I wrote this expression two or three times before. Evidently [math]\hat{p}[/math] is an operator. I was not citing the Ehrenfest theorem, what I cited was the equation of motion [math]d\hat{p}/dt = \hat{F}[/math] and the well-known result [math]\partial\hat{p}/ \partial t = 0[/math]. Check my previous post. You can find both in the link given in my previous post. In fact the wikipedia page even devotes a footnote to explain why [math]\partial\hat{p}/ \partial t = 0[/math]. In general [math](\hat{A}\hat{B})f \neq \hat{A}(\hat{B}f)[/math]. In particular [math]\frac{\partial\hat{p}}{\partial t} = -i\hbar\frac{\partial}{\partial t} \left( \nabla \right) \neq -i\hbar \left( \frac{\partial^2}{\partial t\partial x},\frac{\partial^2}{\partial t\partial y},\frac{\partial^2}{\partial t\partial z} \right)[/math] The left hand side [math]\frac{\partial\hat{p}}{\partial t} = -i\hbar\frac{\partial}{\partial t} \nabla = 0[/math]. The right hand side [math]-i\hbar \left( \frac{\partial^2}{\partial t\partial x},\frac{\partial^2}{\partial t\partial y},\frac{\partial^2}{\partial t\partial z} \right) \neq 0[/math] Apart from the mistakes regarding operator associativity, algebra, derivatives, etc., you started from a wrong classical equation ([math]{\partial p}/{\partial t} = F[/math]) and wrote a wrong quantum equation ([math]{\partial \hat{p}}/{\partial t} = \hat{F}[/math]). In fact if you were to take averages on your wrong quantum equation you would obtain [math]\langle \frac{\partial \hat{p}}{\partial t} \rangle = \langle \hat{F} \rangle[/math] but as is well-known (check my posts or check the wikipedia [the equation just after "Suppose we wanted to know the instantaneous change in momentum [math]\hat{p}[/math]"]) [math]\langle \frac{\partial \hat{p}}{\partial t} \rangle = 0[/math] which means that you obtain the wrong result [math]0 = \langle \hat{F} \rangle = F[/math]. In short. The quantum Newton law is [math]\frac{d\hat{p}}{dt} = \hat{F}[/math] taking the classical limit (Eherenfest theorem) gives the well-known Newton law [math]\frac{dp}{dt} = F[/math]

I wrote more than that inequality. I wrote an important condition for the wavefunction and you quoted it in your first reply #15. Now you ignore that part of what I said. I already remarked in a previous post that the Newton law uses total derivatives. At least the OP already apologized by using partial derivatives in the notation: "It's a nasty habit". Evidently the partial derivative of momentum operator is zero with independence of F, because the expression is [math]\frac{d \hat{p}}{d t} = \hat{F}[/math] This is all well-known: http://en.wikipedia....renfest_theorem

My complaint was not about the definition. Read what I wrote. No. I did not wrote commutation of derivatives but something different. Read what I wrote. No your relation is not generally true. Associativity means [math]\hat{A} (\hat{B}\hat{C}) = (\hat{A} \hat{B})\hat{C}[/math] I merely computed the partial time derivative of the momentum. It is zero.

How is Stefan–Boltzmann law impossible? How can be incompatible with energy conservation law?

Newton law does not use partial derivatives. Curious, because pressure is almost always denoted by p as in "pdV". [math]-\nabla H\Psi \neq \hat{F}\Psi[/math] unless [math]\nabla\Psi=0[/math] but then the left hand side of your Schrödinger equation is zero. First you use [math]\nabla (\frac{\partial }{\partial t}\Psi) = \frac{\partial }{\partial t}(\nabla\Psi)[/math] but latter you use [math]\frac{\partial }{\partial t}(\nabla \Psi) = (\frac{\partial }{\partial t}\nabla) \Psi[/math] which is incorrect. Indeed [math]\frac{\partial \hat{p}}{\partial t}=0[/math] The same link that you give states clearly that the relativistic generalization of the Newtonian law [math]\mathbf{f} = m \mathbf{a}[/math] is [math]F^\mu = m A^\mu[/math] The 3-projection is [math]\mathbf{F} = m \mathbf{A}[/math]

Well, his paper defined it as the gravitational 3-force. Don't shoot the messenger, this is why I asked the questions I did. I would say, should it be surprising that a force can have a christoffel symbol in it? I mean... after all, the Christoffel Symbol (is the gravitational field) in GR. (more) I have the geodesic equation written down somewhere, I was working by memory... but if you say so. The equation however will not describe massless particles, since the equation has M defined as a gravitational charge, or passive mass in other words. So yes, s would be the proper time interval. Here it is. You where right, it is not partial derivatives, but it does use proper time. http://en.wikipedia....ral_relativity) No shooting here, only a polite and impersonal remark about the non-existence of gravitational forces in GR. The christoffel symbols are not gravitational fields. The christoffel have no true physical meaning. The mass of the particle does not appear in the geodesic equation of motion by virtue of the equivalence principle. And no, s is not proper time if the particle is massless. The geodesic equation is the same but s is not proper time then.

It was already commented before that one cannot universally claim that eA is a field-like momentum. Since you insist on repeating the claim I will add more info. If one restricts himself to field electrodynamics, sure that eA is related to the field, but when one works with Wheeler-Feynman electrodynamics or with more advanced and recent formulations of electrodynamics the term eA is not related to any field because A is given as a functional of particles path. In the first place, the geodesic equation of motion does not use partial derivative but total derivatives [math]d/ds[/math]. In the second place, [math]s[/math] in the geodesic equation of motion cannot be proper time for massless particles. In the third place, pmb's [math]v^i[/math] cannot be derivative with respect to s, unless he is now using another notation than that he used before here when he tried to define kinetic momentum (e.g. in #3). In the fourth place, [math]m\Gamma_{ij}^{k}v^i v^j[/math] is not a gravitational force because it includes a Christoffel symbol! Gravitation is not a force in general relativity. In the fifth place, you are lacking a minus sign in one of the equations.

Electron attract to protons electromagnetically. In fact, the electromagnetic interaction is the main interaction that describes electronic structure in atoms and molecules. There are not forces F in the Schrödinger equation. Electrons in atoms are confined to specific levels because energy is quantized. Atoms absorb or emit quanta of energy when electrons jump from a given energy level to another. An electron in a stationary level in an atom is not "at specific distances from the nucleus". In fact, the electron does not have even a well-defined position. You cannot imagine an electron in an atom as a little billiard ball. It is all more sophisticated. The more common isotope of Hydrogen does not have neutrons. Effectively, quantum mechanical spin is different than classical spin. Quantum spin has nothing to see with electron rotating around an hypothetical axis. In fact recall that electrons are not little billiard balls! Quantum spin is a purely quantum effect that defines one of the fundamental properties of the electron (together with mass and charge). Spin 1/2 means that the magnitude of its projection is [math]s = \hbar/2[/math]. Note that 1/2 is only the projection of the spin, the magnitude of the total spin is [math]S=(\sqrt{3}/2) \hbar[/math]. Fermions have half-integer spin and verify the Fermi & Dirac statistics. Bosons have integer spin and verify the Bose & Einstein statistics. Fermions cannot occupy a particular quantum state at the same time. Bosons can be also 'intuitive'. Think on photons. Light is made of photons. You cannot say that bosons are inside fermions as the electron. Electrons and quarks are elementary particles, which means that in the Standard Model they are the ultimate building blocks of nature.

The standard gravity model says that antimatter falls in exactly the same manner as normal matter. Although some speculative models claim otherwise.

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