juanrga

What do you mean by "fundamental"? Contrary to "applied"? Reductionist? By definition Science cannot provide a theory of everything.

This is a discussion about scientific states (physical, chemical, biological...) which is not usual in textbook and other resources (an exception seems to be quantum mechanics textbooks, which devote some space to discuss what is a quantum state). Among material not covered in basic textbooks and encyclopedias I would emphasize that I introduce a hierarchical description of states first developed by Joel Keizer; a rejection of the "Bayesian interpretation of physics" over the basis of recent advances in statistical dynamics; and the proposal for substituting the term "physical states of matter" by the more adequate and precise term "phase of matter" (I include a link to a NASA page that is already using the new terminology). I also emphasize that p in thermodynamics state (T,p,N) is the pressure of the system (many textbooks got this wrong and claim that p is the pressure of surrounds). Educated comments, doubts, and suggestions to include material are welcomed.

I believed that titles/headings such as "Dark matter theory challenged by gassy galaxies result" would be self-explicative. Some parts of the body of the news are not accurate and do no reflect what the studies show. For instance, it is misleading to say that MOND predicted the relationship better than dark matter, because the dark matter model makes no predictions and because the dark matter model cannot fit the data. From the PRL paper: The author, in the quote that you reproduce, is not suggesting that dark matter works for clusters. He is really saying that there exist observational uncertainties regarding clusters. He says in the paper: The second link reports additional difficulties with the dark matter model. The second link quotes to Frenck stating his belief that CDM would be substituted by WDM to avoid the difficulties reported. The problem is that WDM presents other difficulties over the CDM. For instance, the observed abundance of dwarf galaxies cannot be explained within LWDM models.

Yes, everyone in this thread besides you. And my replies to some of them contained phrases as "No. I have just said the contrary." Other of those posters wrote (about the same link that you are using now to defend your point): "Baez doesn't make a lot of sense to me"... I explained to another poster that that speed is the norm of the velocity, and that velocity is a three-vector not a four-vector. And so on. Therefore, I am not going to accept your argument by evident reasons. In my above demonstration of that the speed of light is globally c, I only forgot to say that I am using the standard four-velocity. Therefore v is the standard velocity and |v| the standard speed. I am so accustomed to use standards that I do not always emphasize it in my writings. I ignored "the most important part" of your last post by reasons explained in the last part of my #67. A discussion of equations of motion, clocks, etc. in general relativity is given in the section "The physical interpretation of the equations of point mechanics. Standard equations of motion. Standard simultaneity" found in Möller's classic textbook. Also relevant is the section "Propagation of light signals. Fermat's principle". In both sections Möller computes the standard velocity and speed of a light particle. He uses another notation but his equation [math]\hat{w} = |\hat{\mathbf{w}}| = c[/math] is the equivalent of my last equation, |v| = c, in the demonstration #67. Of course, Möller says the same in words: This result was waited in pure physical terms because v, the standard velocity, is a gauge-invariant three-vector.

Thank you for the correction!

Where in my post did you read that [math]\tau[/math] is proper time? Some authors write [math]\tau[/math] other write [math]\lambda[/math], and others use another notation. I think that I explained what is each term. This link was discussed before in this thread. Just after the Einstein's quote Baez adds, in the same paragraph, "but a more modern interpretation is that the speed of light is constant in general relativity." About your other quote, Baez adds near the end of his page: "Finally, we come to the conclusion that the speed of light is not only observed to be constant; in the light of well tested theories of physics, it does not even make any sense to say that it varies." Some people claims that the speed of light varies. I have just computed the speed and obtained that it is a constant.

There are not evidence. The link that you cite is open to several objections. Who wrote the section "Alternative black hole models" seems to believe that a gravastar is another model of black hole, but the link to gravastars correctly emphasize that a gravastar is "an alternative to the black hole". This has nothing to see with what I said.

When I alluded to the particle in a box model I only said was the simplest possible quantum model, not that was complete or always valid. Even for linear conjugated polyenes this model of electronic structure is a crude one.

Measuring is the comparison of the property in the system with the property in a reference system (unit). Any property Q can be written as Q = {Q}[Q] where {Q} is the number of times that the reference (the unit) is contained in the property of the system. For example, the metre is the SI unit for length and it is given by a reference system held in Paris.

Evidently, the speed |v| is not the "magnitude of an object's four-velocity". [math]|\mathbf{v}| = \sqrt{v_iv^i} \neq \sqrt{v_\mu v^\mu}[/math] From the Wikipedia link... Velocity v is a "a three-dimensional vector".

Uh, the velocity is v and the speed, |v|, is only c for massless particles.

The four-velocity (check any textbook) is [math]v^\mu = \frac{dx^\mu}{d\tau}[/math] The velocity v is [math]v^i = \frac{dx^i}{d\tau}[/math] The speed is [math]|\mathbf{v}| = \sqrt{\mathbf{v}^2} = \sqrt{v_iv^i}= \sqrt{\gamma_{ij}v^iv^j}[/math] with [math]\gamma_{ij}[/math] the spatial metric. For Schwarzschild spacetime, the spatial metric tensor coincides with spatial part of the spacetime metric tensor [math]\gamma_{ij} = g_{ij}[/math]. [math]\gamma_{ij}v^iv^j = g_{ii} \left( \frac{dx^i}{d\tau} \right)^2[/math] Using the relation between [math]d\tau[/math] and [math]dt[/math] and the symmetries of the Schwarzschild metric [math]\gamma_{ij}v^iv^j = g_{ii}^2 \left( \frac{dx^i}{dt} \right)^2[/math] For a light signal [math]ds^2=0[/math] and using all we finally obtain [math]|\mathbf{v}| = \sqrt{g_{ii}^2 \left( \frac{dx^i}{dt} \right)^2} = \sqrt{c^2}[/math] which is the well-known result that the speed of light is always constant in general relativity and equals c. Some people defines the speed of light to be anything that they like and then obtain any result that they like, including unphysical results. Different people makes different mistakes and I am not going to revise all. Some people computes the (unphysical) speed associated to a fictitious flat-spacetime (light signals are moving in a curved spacetime) and then obtains an (unphysical) speed of light that varies with the gravitational field. Other people propose ad-hoc definitions of speed no compatible with the covariant equation of motion... EDIT: I have used bold face to emphasize the difference between four-velocity, velocity, and speed.

New observations are in contradiction with the dark matter model. Check for instance this recent ones http://www.bbc.co.uk...onment-12571965 http://www.bbc.co.uk...onment-14948730 Any search of dark matter made in last decades has not found anything. I am convinced that dark matter does not exist. That black holes could never form, is contrary to mainstream theory. That stellar black holes can form by collapse of remnant stellar masses above the Chandrasekhar limit (~3 solar masses) following novas and supernovas, is presently well accepted theory. What a stellar black hole really is inside its very small diameter (as small as 15 miles) may be debatable since it depends upon the black hole theoretical model(s) that are being discussed.// As said above, if one considers only GR, a black hole with its corresponding horizon can form. The problem is that GR is very far from being a final theory... When one considers effects beyond the scope of GR, one obtains that a black hole never forms. As said above even Hawking is starting to change his mind and now he writes: Hawking lost the bet about black holes, because he was ignoring several technical details; although some of us warned him that his work was science fiction. When one adds additional corrections to the GR model, one finally finds that black holes never form.

Dark matter is a mere hypothesis. Black holes are not counted as dark matter. Although GR predicts the formation of a black hole. The final result of a collapse is not clear when quantum gravity and other effects are considered. Several experts affirm that a black hole never form (and I recall that even Hawking is changing his mind about this). The hypothetical concept of dark matter is not well-defined and there is no theoretical model that can predict what happens in a collapse

In this case Einstein's answer to the OP question is "no, light has no mass", because Einstein explicitly embraced the modern concept of mass in 1948.

c = dr/dt and your 0 = dx^2 + dy^2 + dz^2 - (cdt)^2 are only valid in flat spacetimes. Consider two frames which are not Lorentz invariant ds2 = gab dxadxb = g'ab dx'adx'b for both the primed and the non-primed frames the speed of light is constant and equals c. A light signal sent from a frame to the other travels with speed c.

Once he did dream that could obtain one. He never got one, of course.

This is sometimes named the free-lunch cosmology. It is an idea based in certain hypothetical models of quantum cosmology that assume that the total energy of universe is exactly zero. If the total energy is always zero then the creation of the universe would be a kind of transformation from something (preuniverse) with zero energy to something (universe) with zero energy (0 [math]\rightarrow[/math] 0). Some people goes beyond this speculation and claims that the universe was created out from 'nothing'. There is a popular book now about this, but is receiving very hard criticism (see this review). I find it all odd. First, the original premises are based in some incorrect quantum cosmological models (I do not agree that the total energy of the Universe is zero). Second by 'nothing' that people means systems as a quantum vacuum or something similar.

With advanced electron microscopes you could 'see' a big molecule, but not the structure of an atom because have not enough resolution.

The electronic structure of substance defines its visual properties when the difference between energy levels is in the range of visible spectrum. The substance absorbs certain wavelengths of white light, and we see what is left over. The particular wavelengths of light that a given substance absorbs determine the colour we perceive. Chemists are able to predict the colour of a substance before synthesizing it. The most simple quantum model to predict colour is the particle-in-a-box model.

Time is a physical quantity, it can be measured and has units. The International System of units uses the second as the basic unit for time.

Light does not have any mass because is made of photons which are massless particles http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/960731.html The massless property of light has been well-tested http://en.wikipedia.org/wiki/Photon#Experimental_checks_on_photon_mass As ACG52, timo, and DH reported before. Massless particles are also affected by gravity. If you want to go into the details, search the term "massless" in the next introduction to General Relativity and you will find the equation of motion for light signals.

Sorry Pete, but you are also completely wrong about this. I knew Rohrlich's work before you cited it here.

Evidently a new edition does not guarantee that everything in that edition is free of error or up-to-date. But the important part of my comment was that Rohrlich's is a good text and that he agrees with me. I add snapshots of relevant parts of the textbook cited by Pmb, including a relevant paragraph where Rohrlich criticizes Pmb definition of mass. Rohrlich uses a much more correct, well-defined, and consistent concept of mass, which is the same that I use. After saying you thanks, I explained to you why I do not need that outdated article. First, your above expressions are mutually inconsistent. As you write at the very start of your message you This means that your Pi is wrong unless you change m to mean rest-mass. But if you change m to mean "rest-mass" then your above p is lacking the [math]\gamma[/math] term. No matter what is your choice for m, both equations are mutually inconsistent. Second, Rohrlich denotes the canonical (four)momentum by the symbol [math]\Pi^\mu[/math] Third, Rorhlich denotes the four-momentum by [math]p^\mu[/math] The momentum p is the spatial component of the four-momentum [math]p^\mu[/math] [math]\mathbf{p} = m\mathbf{v} + (e/c)\mathbf{A}[/math] It must be remarked that Rorhlich is using a tau-parametrization [math]\mathbf{v} = \mathbf{v}(\tau)[/math] instead of the more usual t-parametrization, the relationship is [math]\mathbf{v}(\tau) = \gamma\mathbf{v}(t)[/math]. Other authors use a different notation. The term [math]mv^\mu[/math] is usually named the kinetic (four)momentum. The term "mechanical momentum" is a misnomer, although can be still found in the literature. Rohrlich also uses the term kinetic momentum as I do As I said above the kinetic momentum coincides with the momentum p only in absence of electromagnetic fields [math]\mathbf{p} - (e/c)\mathbf{A} = m\mathbf{v} [/math] Fourth, Rohrlich agrees with me on that the addition of [math]\gamma[/math] to the definition of mass is useless and only found in older literature. He uses the concept of "rest mass" (which is simply named mass in modern literature), Again both Rohrlich and me are in full agreement: I already wrote that Poincaré stresses model is an completely inconsistent and outdated model which was abandoned more than 100 years ago. After showing how Rohrlich is using the same concept of mass that I am using, let me cite the next article by Okun, where the concept of relativistic mass used by Pmb is rejected http://www.physicsto...isAuthorized=no Or just check Taylor & Wheeler (Spacetime Physics, 2nd Ed.): After stating why m is a better concept of mass. Let me simply add this letter by Einstein about the subject:

I never said that a global reference frame exists. In fact I have said that it does not exist!