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About juanrga

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  1. I have just updated my profile

  2. Time is the evolution parameter of the universe.
  3. We can go smaller, it is called the sub-Planck regime or scale, and it is studied by the sub-Planck physics. The math works fine, and there is no need to even mention a TOE when working at such scales.
  4. For instance via Compton scattering, the photon changes its momentum [math]p_\gamma \to p_{\gamma'}[/math] due to collision with an electron at rest. The electron final momentum [math]p_{e^-}[/math] is the difference between the final and the initial momenta of the photon (the law of conservation of total momentum holds) [math]p_\gamma - p_{\gamma'} = p_{e^-}[/math] The Newtonian expression [math]p=mv[/math] is only valid for a massive free particle moving at non-relativistic speed. The photon is both massless and relativistic. For a photon [math]p_\gamma=h\omega/c[/math] with [ma
  5. Who said or insinuated such thing? Precisely on the leading textbooks on general relativity (that by Misner, Thorne, and Wheeler) is titled Gravitation. Untrue, we can differentiate both and denote mass by "m" and energy by "E" as in the expression [math]E = \sqrt{m^2 c^4 + p^2c^2}[/math] No, mass is an relativistic invariant. E.g. the mass of an electron [math]m_e[/math] which you can find in a table of scientific constants is the same for any observer. You and him seem confused by the outdated concept of relativistic mass (which varied with the observer), but preci
  6. There is not proof that Planck time was the smallest unit of time. It is just a speculation. Because stuff is made of matter and this has a discrete structure. You cannot divide an atom infinitely.
  7. Effectively "before time" is a meaningless expression, but physics documentaries have to lack rigour specially those dealing with speculative topics such as cosmology beyond the standard model. Some cosmological models introduce a concept of time before the Big Bang. As the Nobel laureate Prigogine likes to say "time precedes existence" by "existence" he means Big Bang energy-matter. In these models, the Big Bang is a kind of phase transition from a previous quantum vacuum. http://www.timeshighereducation.co.uk/108305.article No, time is not a measurement for movement. In fact
  8. The energy of a photon is given by [math]E=pc[/math], thus photons with different momentum will have different energy. This is similar to what happen with 1000 kg cars. Their energy is given by [math]E=(1/2000) p^2[/math], thus cars with different momentum will have different energy.
  9. It is an extension of mechanics that considers statistical effects (deviations on the evolution and behaviour of systems prepared initially in the same state) in mechanical systems. Yes, the deviations are not deterministic and thus have to be described in probabilistic terms; i.e. which is the probability that the system will do "this". Are not different statistical mechanics but different statistics or more correctly different distributions. Fermions and bosons have different requirements regarding their quantum mechanical state and thus their quantum statistical mechanics
  10. To add to swansont reply, without EM could not even exist atoms!
  11. The definition of mechanical work is [math]W = \int \mathbf{F} d\mathbf{x}[/math] which is valid for both variable and constant forces. Therein [math]\mathbf{F} = \mathbf{F}(\mathbf{x})[/math]. Using [math]\mathbf{x} = \mathbf{x}(t)[/math] and the definition of velocity [math]\mathbf{v} = d\mathbf{x}/dt[/math] [math]W = \int \mathbf{F}(\mathbf{x}) d\mathbf{x} = \int \mathbf{F}(t) \mathbf{v} dt \neq \int \mathbf{F}(t) dt[/math] Regarding the second question, the expression [math]\mathbf{F} = m \mathbf{a}[/math] is obtained from [math]\mathbf{F} = \frac{d \mathbf{p}}{
  12. Depends. If the mass is a simple particle or a rigid body the answer is yes. If the body is not rigid then the answer is "no" if the force is by contact. There is a small delay between the application of the contact force and the motion of the centre of mass. The answer is again yes for non-contact forces (e.g. gravity).
  13. Because science is accumulative and one of the requirements of a new theory is that it must explain what is already known. Electrons are pointlike particles. Their spin is quantum and not due to motion around an axis.
  14. No. As explained in any QM textbook there are two possible evolutions of a given quantum system and each evolution is described by a different postulate of quantum mechanics: Schrödinger postulate vs von Neumann postulate. Evidently the latter is not reducible to the former (something already proven by von Neumann in his foundational papers) because otherwise you would not need two postulates. In von Neuman's own words: Bassi and Ghirardi just verify that the evolution associated to the von Neumann postulate is nonlinear. Something which has been known for many decades; this is why the dyn
  15. I wrote "textbooks", which is plural. But the above textbook is specially good because addresses, in a direct way, some of the more typical misunderstandings of quantum mechanics. The same link that you gave mentions the measurements: There is no theorem that proves him wrong. He does not say that I am wrong. He simply states his personal opinion (he emphasizes "I do") and next writes: Indeed! But "less sympathetic" is not the correct term used by critics including myself. He is just wrong. Adam is a well-known example of a robot scientist inventing
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