DrRocket

It is not just a question of material, but also largely of design. What are you trying to do ?

I have no idea what it is that you have been watching or reading, but you have described nothing that even vaguely represents the holographic principle proposed by 'tHooft. What you describe is some sort of New Age tripe, if indeed it is an accurate description of anything at all. Whatever it is, it is is not physics. The History Channel is a very poor source for any scientific topic. Much sensationalism. Little accuracy or gravitas. Bohm started out as a rather mainstream physicist. His book on quantum mechanics (available as a Dover edition) was written during that early period. He later moved a bit farther out on the fringe and introduced a "Bohmian" interpreteation of quantum mechanics that is taken much less seriously, and has largely faded into obscurity and out of current QM texts. It is a valid interpreetation of quantum mechanics, but hardly the only valid interpretation of quantum mechanics. http://plato.stanfor...ntries/qm-bohm/ http://en.wikipedia....hmian_mechanics Adherents of the pilot wave interpretation tend to be rather dogmatic, and fail to recognize that interpretations that produce the same measurable predictions are in fact equivalent.

One can, and should, use the "epsilon-delta definition" to prove each of the lemmas that I suggested. Breaking the problem down to the fundamental parts can, and often does, illuminate what is important and makes the proofs easier to formulate and understand. You can go after the problem directly, but you risk losing the forest for the trees amidst some messy algebra.

That depends on what you intend to do with them. They have a place, but are not good substitutes for the standard text books. There is a reason that classic textbooks are classics. Texts writen by real experts, who have deep understanding, tend to be the most clear and insightful.

What were you drinking when the show aired ?

Probably the easiest and most instructive way to proceed is to prove a series of lemmas 1. Inversion, the function f defined by f(x)= 1/x is continous except at 0. 2. The fulnction f defined by f(x) = x is continuous everywhere. 2. If f and g are continuous so is the product [math] f \times g [/math] 3. If f and g are continyous so is composition [math] f \circ g[/math]

There is no convention regarding square roots of complex numbers as there is for square roots of positive real numbers (i.e. the square root is taken to be the the positive one in most cases), so the square root of i is not well-defined and either (1 + i)/√2 or (-1 - i)/√2 are roots that fit the bill.

I know of but one way to make a perpetual motion machine usiing a permanent magnet. 1. Take one small permanent magnet. 2. Place a drop of cyanoacrylate on the magnet. 3. Press the magnet with the super glue drop on mother-in-law's lip. 4. Maintain light pressure for about 20 seconds.

The only thing that I can imagine that is even vaguely relevant here is that gravity, like any vector field that is radially symmetrical, can be expected to decrease in "flux density" like [math]\frac{1}{r^2}[/math] in three dimensions and this is simply because the surface area of a 2-sphere is [math] 4 \pi r^2[/math].

Your question has NOTHING to do with any branch of science, including physics.

In a nutshell the "cosmic speed limit" is the logical consequence of the two fundamental axioms of special relativity: 1) the speed of light is the same in all inertial reference frames and 2) the laws of physics are the same in all inertial reference frames. It turns out that if you assume that anything propagates at some speed, say x, in all inertial reference frames and if you assume axiom 2 then you can deduce the Lorentz transformations with "x" playing the role of "c". "x" is then the "cosmic speed limit". There can be only one such value. One then notes the experimental fact that the speed of light is the same in all inertial reference frames to conclude that x=c. That is the mathematics behind special relativiity. There is no division by 0 involved. If want to go through this in detail a good reference is Introduction to Special Relativity by Wolfgang Rindler. Then the criticism is for both you and Baez. Your quote is both out-of-context and misleading. What Baez (and Bunn) are attempting to do (I think poorly) is provide a pop-sci explanation of the Einstetin field equations of general relativity. That equation in simplest form is simply [math] E + g \Lambda = \dfrac {8 \pi G}{c^4} T[/math] where [math]E[/math] is the Einstein curvature tensor [math]g[/math] is the metric tensor [math]G[/math] is Newton's universal gravitational constant and [math]T[/math] is the stress-energy tensor. This tensor equation is equavilent to a set of 10 coupled non-linear partial differential equations and to refere to it in the singular as "Einstein's equation" is itself a bit misleading. Baez and Bunn are attempting to explain this very complicated set of equations in extremely simple terms -- to my mind a gross oversimplification, given that the stress energy tensor includes ALL non-gravitational forms of energy. Moreover their statements are, as I said originally, nonsensical hand waving. A spherical ball of test particles, is itself a vague notion, and if initially at rest would stay at rest so the remainder of the paragraph is just more hand waving, as is the notion of changes in shape in terms of "orders in time". Quoting someone who is waving his hands wildly on a subject that you don't understand yourself is not a good strategy. If you want to understand general relativity and the Einstein field equations read a good book. Gravitation by Misner, Thorne and Wheeler is a standard reference. Yvonne Choquet-Bruhat's General Relativity and the Einstein Equations is another excellent book. Those authors are experts in general relativity. Baez is not. The down side is that these books are the real thing and require an investment in time to study them as well as the mathematical background to be able to comprehend their message.

That is a very good book. But it is usually used at the junior/senior level as the text for a second course in linear algebra. It would take a very good freshman to gain much from it.

Abstract: Life is an inordinately complex unsolved puzzle. Despite significant theoretical progress, experimental anomalies, paradoxes, and enigmas have revealed paradigmatic limitations. Thus, the advancement of scientific understanding requires new models that resolve fundamental problems. Here, I present a theoretical framework that economically fits evidence accumulated from examinations of life. This theory is based upon a straightforward and non-mathematical core model and proposes unique yet empirically consistent explanations for major phenomena including, but not limited to, quantum gravity, phase transitions of water, why living systems are predominantly CHNOPS (carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulfur), homochirality of sugars and amino acids, homeoviscous adaptation, triplet code, and DNA mutations. The theoretical framework unifies the macrocosmic and microcosmic realms, validates predicted laws of nature, and solves the puzzle of the origin and evolution of cellular life in the universe. Bold added. This has all the earmarks of total bullshit.

There is no way to address this without knowing what mathematics you already know and what you will be studying during your first year. Generally one would expect that you will start out in some sort of calculus class. I recommend that you wait until you have an instructor to guide your study. Freshman calculus texts are notoriously bad. If you already have a reassonable grasp of elementary calculus, you might try reading Maxwell Rosenlicht's Introduction to Analysis. It is a good book, relatively easy reading, available as an inexpensive Dover reprint, and won't do any harm.

It is for you if you took that quote out of context and for Baez if that is essentially the complete content of what he wrote. You can quote Baez's bio all you want, but it does not really address the issue. I am acquainted with his background and work (and know his former dean personally). He is generally pretty good, but not infallible, and has a reputation more as an expositor than a researcher. Quoting "experts" is not a substitute for a critical reading of what they have written.

Not at all, and the answer is quite obvvious to anyone with an understanding of physics. To find ridiculous babble one need only read your posts.

Alaiin Aspect's experiment is a realization of the thought experiment proposed byEinstein, Poldalsky and Rosen. It is intimately related to Bell's inequality. It has absolutely nothing to do with the holographic principle -- which was first proposed by Gerard 'tHooft.

No. Black holes are merely a feature of spacetime. Spacetime is in fact static. It embodies all of space and all of time, but spacetime does not "change". What we observe are slices of spacetime, not the whole manifold. So as time progresses we see changes in the slices, but spacetime itself is fixed.

With the caveat that by "the same particle" one means a particle with the same quantum state. All such particles are, of course, perfectly identical. So whether the particles actually pierces the potential barrier or somehow an identical particles is created on the other side is immaterial. The point here, for the neophyte (and Swansont is not a neophyte) is that the quantum world is not some simple analog of the macroscopic world and the words we use and the stories we tell to understand it in classical terms are not completely accurate. That electron is not a little marble. This is one example why debates on "interpretations of quantum mechanics" (the words and stories) often get bogged down and one really should pay attention to the mathematics and the predictions that one can actually measure.

It is a function, but not "just another function". It is a particularly important function. A great deal of analysis depends on that function.

Likewise heat absorption "converts" energy to mass -- heat up a bucket of water and it will weight slightly more than it did when cold. This very quickly gets into subtleties with what one defines to be either mass or energy. The crux of [math]E=mc^2[/math] is that there is no clear cut distinction unless one demands by fiat that mass be rest mass.

The classification of such operators is the Stone-Von Neuman theorem which shows that they arise as irreducible unitary representations of the Heisenberg group. So one then finds interest in the representations of nilpotent Lie groups. A good book on that subject is Pukanzsky's Lecons sur les representations des groupe (if one can read simple French)

Experiments to attempt to detect gravitational waves from ANY source have been underway since the 1970's, with incrreasing levels of sophistication and sensitivity. To date no gravitational waves have been directly detected. The best evidence for gravitational waves, as predicted by general relativity, come from measurements of the orbital decay of binary star systems.

Primarily. And you don't have to guess. If you are speaking of patent rights or commercial rights of some kind, as opposed to credit for invention, then that is a different matter entirely. Generally any employer, including an academic institution, requires employees, as a condition of employment, to agree that any patent or commercial rights associated with an invention will be assigned to the employer. Nevertheless, a patent must, by law, be granted only to the actual inventor. The inventor then can, and with a typical employer/employee relationship, must, assign the patent rights to the employer. If the names on the patent application are not, in fact, those of actual inventors then the patent can be invalidated (I have seen this happen with big money involved). I don't know about PIs. I have never worked for another PI.

That rather depends on the idea, the discipline and the institution. When I was in academia, even as a graduate student in mathematics, my ideas were mine and published in my name alone. I do have engineering publications that were done in collaboration with others, but for projects in which I participated credit went to all participants. In that case there was actually a publication in which my appeared that I was not aware of until a third party called my attention to it (It turned out that I had done simulations that were of value in the paper and the group doing the writing was temporarily at another school).