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 You and him seem confused by the outdated concept of relativistic mass (which varied with the observer), but precisely due to this variation with the system of reference it could not be considered a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