juanrga

Time is the evolution parameter of the universe.

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.

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 [math]\omega[/math] the frequency.

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 You and him seem confused by the outdated concept of relativistic mass (which varied with the observer), but precisely due to this variation with the system of reference it could not be considered a property of the object under study: i.e. was not the mass of the object.

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.

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, movement is defined with respect to time [math]x=x(t)[/math], [math]v=v(t)[/math]...

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.

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 states are also different: Fermi-Dirac distribution describes fermions and the Bose-Einstein distribution describes bosons. Yes. kinetic theory of gases is a subset of statistical mechanics. One often speak of the kinetic regime or kinetic branch of statistical mechanics.

To add to swansont reply, without EM could not even exist atoms!

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}}{dt}[/math] only when momentum is given by [math]\mathbf{p} = m \mathbf{v}[/math] and the mass is constant [math]dm/dt=0[/math]. Otherwise multiplying mass by the acceleration does not give the real force [math]\mathbf{F}[/math]. Therefore your intuitions are not correct.

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).

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.

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 dynamical laws postulated since the 60s to describe collapse are all nonlinear... First I would like to link to the computer who discovered Newtonian laws by itself before replying about Adam http://www.wired.com/wiredscience/2009/04/newtonai/ About what Adam did/does I will simply quote the Science paper cited before: Tested hypothesis are the laws and theorems associated to the underlying formal systems. The physicists concept of law is not the only possible in science, biology and chemistry have their own laws.

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 new laws and theorems... The Automation of Science 2009: Science 324(5923), 85–89. King, Ross D.; Rowland, Jem; Oliver, Stephen G.; Young, Michael; Aubrey, Wayne; Byrne, Emma; Liakata, Maria; Markham, Magdalena; Pir, Pinar; Soldatova, Larisa N.; Sparkes, Andrew; Whelan, Kenneth E.; Clare, Amanda.

The physical interpretation of rest energy [math]E_0=mc^2[/math] is not very different from that for the Newtonian kinetic energy [math]E_\mathrm{N}=1/2 m v^2[/math]. Consider a free massive particle moving at [math]v=c\sqrt{2}[/math]. Then its Newtonian kinetic energy is [math]E_\mathrm{N} = mc^2[/math]. The first expression of above says you that a free mass at rest has an energy [math]E_0[/math]. The second says that a moving free mass has a Newtonian energy [math]E_\mathrm{N}[/math]. In this particular case both are [math]mc^2[/math]. The total energy of a free massive particle is given by [math]E = E_0 + E_\mathrm{N} + \cdots [/math], where the dots denote post-Newtonian corrections. No. The expression [math]E=mc^2[/math] is only valid for a free massive particle at rest. Thus, it is not valid for a massless particle such as the photon, for which [math]E=pc[/math]. Thus, the photon has an energy value but it has not mass: [math]m=0[/math].

No. As explained in quantum mechanics textbooks experiments are compatible with both realism and locality. Quotations from textbooks can be given if required... The chemistry behind mathematicians' brains is the same than that behind the rest of us. They are affected by the same drugs, chemicals... Moreover there is not "absolute mathematical truths" in our modern understanding of maths.

I am one. I did not tweet since Christmas, but I will start again in brief. My username is self-evident.

To add a little to swansont reply. Pions are composite particles and precisely by this reason pions are associated to a reducible representation.

There is no need to reinvent the wheel... http://www.scienceforums.net/topic/72113-time-is-it-reversible/#entry729283 In the first place, the dotted lines are technically representing anti-photons, not photons (although the photon is its own antiparticle this distinction is needed for a correct interpretation of the diagram, see below). In the second place, that diagram is a representation of an electron-photon scattering e- + y = e- + y Third, the electron travelling backward is not real but a formal representation of the real positron travelling forward. Moreover, this is a virtual particle not a real particle, that is why it is in the middle of the diagram, being immediately absorbed to satisfy conservation laws.

No. quarks are only one of the irreducible representations associated to the known zoo of elementary particles and the interactions involving quarks are limited as well No. Ballentine textbook on QM explain very well why a particle cannot be associated to a wave packet.

Already Newton differentiated both concepts of time: Real or absolute time (often denoted by [math]\tau[/math] in the literature although I prefer [math]t[/math]) is the evolution parameter that synchronizes particle correlations. Relative or apparent time (often denoted by [math]t[/math] in the literature although I prefer [math]x^0[/math]) is obtained from reading a clock. Usual notation in relativistic dynamics: [math]t = t(\tau)[/math] But I dislike that notation and prefer my own notation which reads: [math]x^0 = x^0(t)[/math]. I.e. I denote by [math]t[/math] what they denote by [math]\tau[/math]. I prefer to use [math]\tau[/math] for proper time... use the notation that you prefer. An alternative naming for the relative concept of time is operational time, because it is defined in terms of an operational procedure. Einstein always confounded both concepts of time, but modern physics does not confound them any more thanks to the recent works of Stueckelberg, Feynman, Schwinger, Horwitz, Piron, and others: http://en.wikipedia.org/wiki/Relativistic_dynamics In that link absolute time is named "invariant evolution parameter" whereas relative time is named "coordinate time". Notice that it is [math]x^0[/math] which can be reversed (e.g. Stuckelberg/Feynman interpretation of antiparticles as particle travelling backward in 'time'), but real time cannot be inverted ("arrow of time"). This is why you cannot travel backward in real time [math]t[/math] and change the history of universe doing that Nazi’s will won neither you can turn every single cell in every single living creature in cancerous and damaged. Time cannot be confused with matter (matter is a physical system with properties such as energy and momentum defined at a given instant in time). If all interactions between matter ceased and all expansion within the universe stopped then time, real time, will continue to flow whereas it is [math]x^0[/math], apparent time, which will be stopped, somehow as stooping a clock with your hands does not mean that you have stopped the flow of time.

The modern definition of mass is given as [math]m \equiv \frac{\sqrt{E^2 - p^2 c^2}}{c^2}[/math] For a photon [math]E_\gamma = pc[/math] therefore [math]m_\gamma=0[/math] and this is the well-known result that photons [math]\gamma[/math] are massless particles. Applying the definition for an electron we obtain the well-known value for [math]m_e[/math] reported below Note that the value [math]9.10939\times10^{-31} \mathrm{kg}[/math] that you give for the electron is inaccurate in its last figure. It is [math]9.10938\times10^{-31} \mathrm{kg}[/math] because the figures beyond the 8 are 291(40) and this is less than 500... The last recommended value for electron mass is found in the next table of constants http://juanrga.com/en/knowledge/scientific-constants.html

The statistical interpretation interprets the 'principle' (really a theorem) in terms of the standard deviations associated to a large series of measurements on system(s) prepared in the same way. This minimalist interpretation is closer to what one really makes in the laboratory and avoids all the Copenhagen's philosophy about what they imagine that happens prior to measurement or between measurements. A rather good discussion is given in http://statintquant.net/siq/siqse2.html

The E in the above formula is not the total energy but is lacking the potential energy. The total energy of a charged particle at rest in an external electric field is not mc2