juanrga

I forgot the squares, but I have corrected it now. Thank you. You won a vote!

This is a difficult question. Time is, in essence, the evolution parameter of Universe as a whole. Magueijo's ideas are incorrect and outdated. As many others, he is not aware of the difference between the time associated to the generator of time translations K and the x^0 in 4D-spacetime.

[math]\rho \equiv \sqrt{(T^{00})^2 - (T^{i0})^2}[/math] Convention summation and c=1

The underlying findings are interesting but the NS covering is too sensationalist for me

That singularity is merely indicating that general relativity (a classical theory) breaks and ceases to be applicable. This is not something special of general relativity. Each theory has a range of applicability. There is not singularity when quantum effects are taken into account.

Momentum p is not given by mv for massless particles. There is not problem with a particle having m=0 and nonzero p

This is a well-known result, which involves no use of infinitesimals, but ordinary algebra http://en.wikipedia.org/wiki/0.999...#Digit_manipulation

[math] \frac{1}{0} = ? [/math] if and only if [math] 0 \cdot ? = 1 [/math] Now any real number ? multiplied by zero gives zero and no number solves the equation [math] 0 \cdot ? = 1 [/math]. Conclusion: the division of one by zero is not defined.

Time travel is not theoretically possible. All studies about time travel that I know ignore fundamental theories as thermodynamics or quantum theory. Deterministic chaos theory says nothing about time travel, but non-deterministic chaos theory predicts that the evolution of the universe is irreversible. The same about time travel to future. Once one includes the physics of irreversibility, time travel is prohibited. Therein Ilya Prigogine famous phrase: "Future is not given".

The speed limit of c refers to the ordinary velocity of a body moving in spacetime. The cosmological speed of expansion is not related with an ordinary velocity but it is the rate of metric 'creation' of space itself and can be larger than c without violating any known law.

Living organisms are a beautiful example of dissipative structures.

Yes. Precisely the classical limit of a quantum theory is the limit when [math]\hbar \rightarrow 0[/math].

Loschmidt's paradox is not the only reason which the second law of thermodynamics is in conflict with the time-reversibility of mechanics. The solution to this paradox is that the time symmetry of mechanics is an approximated symmetry valid only for certain simple situations. Universe is not described by a group, but by a semigroup with a well-defined arrow of time. Time-symmetry is recovered only under certain approximations. A non-technical explanation is given in the well-known book The End of Certainty, which summarizes recent research advances. A set of references can be found in Prigogine webpage. Complementary non-technical presentations about recent advances in understanding irreversibility are given here and here.

The boundary between chemistry and physics is fuzzy and both disciplines overlap Nuclear chemistry is a branch of chemistry that overlaps with nuclear physics. From modern nuclear chemistry:

Thank you for taking a quote from a closed thread and use it for sharing your wise point that [math]\Psi[/math] is a variable. Although I will ignore you and continue to consider that [math]\Psi[/math] is a function. But thanks again. When I wrote that he was warned in "another forum" I did mean one of those in the menu Forums (above between the Homepage link and the Members link). Evidently, I did not mean that you as moderator would eliminate insults and nasty behaviour in forums outside SFN, but in any case thank you by the clarification. It was very helpful! Thank you for your very informative post and the "appeal to authority", although your sources do not represent any real authority. As you wrote in the OP, those sources say you that the state of a quantum system is given by a wavefunction [math]\Psi(x,t)[/math]. In more advanced and rigorous literature we rewrite this as [math]\Psi(x;t)[/math], and next we generalize this formalism [math]\Psi(x;t) \rigtharrow \hat{\sigma}(x;t)[/math] to a broad kind of quantum systems beyond those considered in your "trustworthy sources". Following your explicit desire I will not explain why advanced and rigorous references write [math]\Psi(x;t)[/math] instead of the outdated [math]\Psi(x,t)[/math] that you can still find in many sources. I will not give the references (are not at the undergrad level evidently) and I will not explain the differences between both functions, neither why the outdated form is mathematically incorrect and physically nonsensical. I have just deleted my vote from your poll giving you and other participants in this forum more freedom to share your thoughts. Thank you again. After reading this, I have stopped from watching this thread.

The wave-particle myth arose in during the development of QM, when the subject was being developed and was not still understood. That myth has been completely eliminated from any modern and rigorous treatment of the subject. Although it persists in some circles. An electron is not sometimes a particle sometimes a wave as some believe. Chemists and physicists define the electron as a particle not as "sometimes a particle sometimes a wave". Links to the CERN and to the official definition of electron by the American Chemical Society were given, quotes from textbooks were given... Those are the facts and those facts will not disappear by you ignoring them and insulting to others. Regarding physics forums, I kindly asked one moderator (in a personal message) to close the account. And I am considering to do the same here because it is a waste of time to debate with people who do not know the most elementary stuff but still pretend to be experts: Questionposter is an excellent example of this, but he is not the only. My posts usually include reasoning, advanced details, citations to academic references, quotes and links. And I agree that this seems to be uncommon among posters here. It is curious that you appeal to "some sort of imaginary competition", because this is exactly the impression I get when I read the replies of other posters. Some of them systematically change what others wrote and then reply just to try to submit some post giving them the impression that they are winning that "imaginary competition". Whereas other posters pick some unrelated stuff from Wikipedia and post it in their reply, giving them the impression that they are not still out of the "imaginary competition"... Several people have noticed, in public way and several times, the silly behaviour of those other posters, but this seems to be the first time that you write something to one of them. Moreover, this is the second time that 'Royston uses ad hominem and insults against me. If my memory does not fail he was warned by a moderator in another forum. Although I was warmly received when I joined the forum, I am seriously considering if I will continue here or not. Regards.

Two complained because the link did not work for them, but next I gave a snapshot from the link. Read what I wrote, it is so simple like that.

I have given it several times. Several posters noticed it. You can search it by yourself instead asking me again. You would read what I wrote, instead making such ridiculous questions.

There is a precise definition. It was given. The existence of several (philosophical) interpretations of quantum mechanics is not the same than your claim "there's like 10 variations of quantum mechanics". I will merely quote an excellent advice that other poster wrote to you:

Where in the chapter "1.1 Mechanics of a Particle" of Goldstein's classic textbook you find that a classical particle must be zero-dimensional? I do not find necessary to introduce such requirement in the concept of particle. Precisely the concept of "classical electron radius" was obtained in classical physics. Of course, I am not saying that this classical model was realistic. The next is not clear for me. Do you consider a massless object a particle? This is not true. As Cohen-Tannoudji states in his textbook on QM: There are many more examples of quantum systems whose state is not described by a wavefunction. In the double slit experiment, what is measured is the position of the particles (plural), the particles are always detected (we know that the particles are there). Next is the typical sequence of such one experiment. (a) is the detector when only eleven electrons were used. (e) is the detector when the experiment is repeated with thousand of electrons: There exists an old interpretation of QFT, where particles are excitations of a field. But there is a problem or two... First, a field is not observable, by definition. It makes no sense to select as basic building blocks of nature non-observable stuff. What one detects in experiments as those made at CERN are particles never fields. Second, the model of fields is based in many approximations (infinite N, harmonics, free fields...). Third, it is possible to explain all the phenomena associated to QED without fields. This is the no-fields approach to QED, sometimes named the action-at-a-distance-approach. This is my favourite approach. Today field theory is considered an effective theory, not a fundamental theory. Therefore, another reason for which is not reliable to associate the concept of particle to the field is that a field is not fundamental. I do not know what do you mean by "still requires a wave and particle description". I do not know a single experiment in physics, chemistry, biology, astronomy, cosmology... which cannot be explained by the known theories of particles. In fact this fact is the reason for which S. Weinberg and other Nobel winners use the Wigner definition of particle. As the CERN emphasizes in its own website: By "everything" they mean everything known up to now.

psi is not a variable and its physical interpretation is well-known. Born was awarded a Nobel Prize for physics for giving the interpretation of psi. Because the Schrödinger equation is not a wave equation. This is more evident when we work with the generalized Dirac formalism of quantum mechanics [math]i\hbar \frac{d |\Psi\rangle}{dt} = \hat{H} |\Psi\rangle[/math] No. Quantum chromodynamics is only the QFT of the strong interactions and involves particles such as quarks and gluons. This theory does not explain the behaviour and interactions of particles such as electrons and photons, for instance.

Have a care with this statement. What do you think the similarity of the classical oscillator equation is to the quantum wave equation? Furthermore are you aware that an oscillator and a wave are different things? What has to see what I said with your questions? I think the comments were clear enough. Again, what has this to see with what I said about the oscillators? You are not the only person allowed to input to this thread (although you have certainly input a great deal and merit thanks for that). Evidently, that is not the question. The question is what has to see what I wrote about oscillators with the above questions that you asked to me? Thanks! Three or four posters said to the OP that an electron does not orbit. If an electron does not orbit then, evidently, nobody can answer the OP question "what makes an electron orbit?". Nobody will offer to the OP an "obvious simple answer" as yours, because your "Earth orbits the Sun" answer is completely incorrect. You would speak by yourself. I gave the standard definition of particle and dozens of references supporting the well-known fact that an electron is an particle. Thousand of scientist agree on this definition. There is absolutely no known experiment or observation which cannot be explained by the current particle model. The definition of particle is based in scientific requirements. Particle physicists give a precise definition, which is well-tested in the lab. This is the same definition used by chemists when they claim, officially, that an electron is a particle. There is no reason for which a precise and well-tested definition would be substituted by an imprecise and nonsensical definition as "something that is wave-like". The link that you gave about quantum harmonic oscillators do not support your view, but uses the same quantum mechanics of particles that I am alluding to in my corrections to your posts. Maybe you missed this previous reply: The quantum harmonic oscillator was not derived to account of the nodal surfaces in atomic orbitals. Not even close!

Have a care with this statement. What do you think the similarity of the classical oscillator equation is to the quantum wave equation? Furthermore are you aware that an oscillator and a wave are different things? What has to see what I said with your questions? I think the comments were clear enough. You made 3 questions unrelated to what I wrote. Again, what has this to see with what I said about the oscillators?

Have a care with this statement. What do you think the similarity of the classical oscillator equation is to the quantum wave equation? Furthermore are you aware that an oscillator and a wave are different things? What has to see what I said with your questions? Evidently no. That your previous statement about duality and harmonic oscillators was (sorry) nonsense: For emphasizing that there is not mystery... It is a pure question of logic, physics, and math. A quantum particle is... a particle and not a wave. A cat is a cat and not an apple.

I have emphasized several times in this thread that a quantum particle is not a classical particle. It is evident that the quantum mechanics of particles was developed about 1930 because the classical mechanics of particles could not explain all the properties and the behaviour of particles as the electrons. I have given the particle physics definition of particle (both link and snapshot from textbook) and, of course, nowhere the definition alludes to classical particles. 'jaungra' already explained what is a particle, gave a precise definition of particle, gave dozens of references supporting his points, gave the physical properties that characterize a particle, gave a table of particles with their properties, and also explained to you that a particle is not a "little sphere". 'jaungra' does not need to do all that again. I could not agree more with the first comment about that video: This is all wrong. Duality has nothing to see with a quantum harmonic oscillator. A quantum harmonic oscillator is a kind of quantum system. A quantum oscillator is the quantum analogue of a classical oscillator. The same link that you give explains how to study the quantum oscillator starting from the "Hamiltonian of the particle", "where m is the particle's mass", and the the "first term in the Hamiltonian represents the kinetic energy of the particle", and solving H|Psi> = E|Psi> for the particle (I already wrote this equation before in this thread). Again, no mystery here. The quantum mechanics of particles continue working as well as it always did. Misunderstandings about quantum mechanics in the pop-culture (read again the comment in the youtube video) do not change the facts about quantum mechanics or about particle physics.