DrRocket

Magnetic fields are typically measured in Teslas or Gauss, but electromagnetic fields are typically measured in terms of the electric field component, which is in volts/meter. The magnetic field then is determined by the permitivity of free space. A 10 Hz pulse is nearly a contradiction in terms. What I surmise that you mean is a square wave on which is superimposed a 10 Hz sinusoid. But you have failed to specify the desired pulse width which is the most important parameter or the rise and fall and times required to approximate the square wave, which will determine the actual high-frequency content of the signal. Electromagnetic fields are created by the time variation of currents, which is as important as the amplitude of the current. Amplitude of a true DC current determines a static magnetic field, which could just as well be obtained from a solid magnet. I know of no evidence whatever that there is any biological effect from a static magnetic field or any reason to think that there might be. In any case the field generated will not be uniform so you need to do a considerable amount of work to determine the field levels over the space in which you intend to place your plant or plants. Voltage has nothing whatever to do with the "electric potential of a wire" and in fact that phrase is nonsensical. Voltage is the difference in value of the potential function that determines a static electric field when measured at two points. EMF is the result of a line integral of the electric field over a specified path, and the value will in general depend on the path, since time-varying electric fields are not conservative. I suggest that you take a bit of time to learn the basics of electromagnetic theory and to figure out what biological phenomena you are really interested in studying. Any freshman physics text should help with the electromagnetics, Halliday and Resnick's book is one that would suffice. But more importantly you need to figure out what it is that interests you from the biological perspective. An experiment conceived in confusion and ignorance is doomed.

For a very readable treatment of the simplest case in the simplest setting one can read Mike Spivak's Calculus on Manifolds.

You have just discovered resonance. Now go read a introductory book on ordinary differential equations. Pay special attention to second order equations with constant coefficients. You might also want to watch this video.

That requires a rather lengthy discussion of the various concepts of dimension in topology, which goes well beyond the algebraic notion that applies to vectors spaces such as [math]\mathbb R^n[/math]. Hausdorff dimension is based on measure theory, which itself is a significant topic. The book Fractal Geometry, Mathematical Foundations and Applcations by Falconer gives a nice treatment in a single source. While not directly concerned with fractals (it predates the work of Mandelbrot bit quite a bit), you might also like Dimension Theory by Hurewicz and Wallman which is the classic treatment of dimension in topology. The point is that to really understand fractals requires quite a bit more than just the pop-sci treatments that are common. It is a subject that has received quite a bit of hype in popularizations, because of the pretty pictures. It is more than just the result of iterated functions (and less than what the hype would lead you to believe). You will have to decide for yourself if it is worth the effort.

There are lots of jobs for chemists. Drug companies are only one of the major industries that need chemists. If you want to do research a PhD is highly recommended. Many research jobs require one and it is a big plus for any research job.

A fractal is a topological space, not a function. By whatever definition you please, whatever "fractal" means to you it is not something that is at all smooth. The gamma and zeta functions are analytic on their domeains and meromorphic in the complex plane. That makes them very smooth indeed.

Vacuum energy, as in quantum electrodynamics, does indeed create a "negative pressure" which should translate into a positive cosmologcal constant (aka dark energy). This has essentially nothing to do with any ordinary measurements of vacuum pressure. Unfortunately the usual calculation results in over predicting the observed acceleration of expansion by about 120 orders of magnitude. That is a colossal error. The botom line is that nobody understands this or has any physical explanation for dark matter. Dark energy does have an effect on the galactic and smaller levels. It is just that the effect is dwarfed by gravity in regions in which matter is concentrated. The effect is miniscule. In regions of deep space where matter density is extremely tiny the effect of dark enrgy, though small locally, dominates. There s an awful lot of deep space out there.

I'll do it at my regular consulting rate.

Wrong,

General relativity is quite a bit more subtle than special relativity. Even with special relativity the heart of the theory is not "time dlation" or "length contraction" or other coordinate effects but rather the invariance of the spacetime interval as measured with the Minkowski metric. This carries over to general relativity, where you discover that special relativity is really just a local approximation to general relativity -- it is general relativity on the tangent space to the spacetime manifold. While this may not yet make sense to you, until it does you are not yet ready to seriously study general relativity. Any successful attempt to explain Einstein's concept of gravity must start with an understanding of the underlying theory, and that involves much more than any metaphor. In short, a metaphor is no substitute for understanding. You are right to not be satisfied with the cartoons that are "out there". But you are extremely naive to think that ANY metaphor will provide you with understanding. Difficult questions have simple, easy-to-understand, wrong answers. Rather than undertake something for which you do not yet have adequate background, you would be well advised to spend your time in obtaining a deep understanding of those subjects that are within your reach and in learning the necessary material to extend that reach. General relativity requires quite a lot of mathematics, in particular differential geometry. But you are in a position to study special relativity seriously, since that requires little more than elementary algebra (though linear algebra is needed for more advanced study of the geometry of Minkowski space). You are also almost certainly in a position to learn algebra and elementary calculus which is a necessary step in the study of the mathematics needed for general relativity.

The only thing that is clear is your propensity to pontificate on subjects about which you know absolutely nothing. In fact you know less than nothing as what you say is often wrong, but couched in buzz words designed to bamboozle neophytes. Matter most certainly will not always radiate away as gravity waves. Were that the case there would be no such thing as a stable particle.

The pop-sci analogies often create as much confusion as enlightenment. 1. Space-time is static. Nothing moves through it. The spacetime manifold embodies all of space and all of time -- past, present and future. Movement of a body is reflected in the world line of that body, which is a curve in the spacetime manifold. It can roughly be said that the body moves through "space" but not through spacetime. Even that requires a bit of thought as there is no such thing as a global notion of "space" (nor of "time"), and you need to understand the real meaning of local charts (What physicists call coordinates). 2. Curvature in higher dimensions is something that is a bit difficult to portray, so what you see in pop-sci are cartoons that depict curvature of surfaces. To really understand what is going on in relativity you will have to invest the effort to understand how curvature is handled in (pseudo) Riemannian geometry -- i.e. understand what a metric and curvature tensor really are. There is no simple explanation, despite the pop-sci cartoons that you see, and talk of the number of degrees in a triangle. . 3. As noted in 1), mass does not affect spacetime. But you can consider so-called gravity waves as an effect on the curvature of space, and those are predicted to propagate at the speed of light. This effect is not particularly straightforward, as it involves the non-linear nature of the Einstein field equations and an effect of gravity itself on curvature. It is not straightforward because gravitational energy does not occur directly in the stress-energy tensor that determines curvature, but rather enters through non-linearities in the field equations. The bottom line is that if you are going to think deeply and seriously about general relativity you will have to go beyond the pop-sci analogies. Probably the best source for a rigorous exposition of general relativity is Gravitation by Misner, Thorne and Wheeler. Another excellent book is General Relativity and the Einstein Field Equations by Yvonne Choquet-Bruhat, but to read that one you should probably first read something like Analysis, Manifolds and Physics by Yvonne Choquet-Bruhat and Cecile Dewitt-Morettte. Or you can stick with the pop-sci explanations. But in that case many questions that arise will be the result of the confusion that naturally arises from over-simplified and misleading ideas, and they will not have answers that are comprehensible in the language in which the initial "explanation" was presented.

Yes, there is a generalization of the Nash embedding theorem that shows that any Lorentzian manifold can be embedded in a hyper-space of suitably high dimension so as to preserve the metric. But it is rather pointless to do that. You lose the flavor of spacetime as an intrinsic Lorentzian manifold and gain nothing in the process.

What in the world is that supposed to mean ? How would a "cosmological event" generate any number ? Physical events generate numbers with attendant units and you can make the bate number anything that you want by simply choosing the numbers appropriately. The exception are a very few fundamental constants (like the fine structue consytant) that occur as pure ratios and they are generally not integers at all.

no

correct

Then you realize that a fractal is a topological subslpace of [math]\mathbb R^n[/math] for which the Hausdorff dimensiion is strictly greater than the topological dimension. A fractal is not necessariy determined by a "formula". There are various ways of constructing fractals, usually involving some sort of limiting process. Wiki is not always the best reference. Try Fractal Geometry, Mathematical Foundations and Applcations by Falconer.

[math] KE = \gamma m_0 c^2 - m_0 c^2 [/math]

Pressure is part of the stress state of a material. Because liquids and gasses cannot support shear, it describes the stress state in such materials. The dimensions of stress are force per unit area. Force is not reflected directly in stress. Archiimedes principle is easily derived from Pascal's Principle. I leave to to you as and exercise to do just that. This results from simple principles of thermodynamics. You may not yet be ready for thermodynamics but if you feel that you are then you can read, for instance, Elements of Thermodynamics and Heat Transfer by Obert and Young. See Pascal's Principle Try reading a good book. You have asked the same question several times, all depending on Pascal's Principle. You can start by studying those questions and recognizing why they are the same. It is important to recognize that the laws of classical physics are all derivable from a very few basic principles. What you should learn in a good physics class is what the basic principles really are and how other useful results, like Pascal's Principle, are derived from them. To do that you have to become able to derive those results for yourself.

Fortunately is Maxwell's opinion, and not yours, that prevails.

That is a correctable condition. After you correct that condition it will be possible for you to understand what the Heisenberg principle really means. With regard to the complementary variables of position and momentum it means that if you have a large number of particles which start in the same quantum state and make measurements of position [math] x [/math] followed by momentum [math]p[/math] that the standard deviation of the positioin measurement [math]\sigma_x[/math] and the standard deviation of the momentum measurement [math]\sigma_p[/math] will satisfy the inequality [math] \sigma_x \sigma_p \ge \frac {\hbar}{2 }[/math] This is ultimately a statement about the failure of certain operators on a Hilbert space to commute and is related to the behavior of Fourier transforms. Quantum mechanics is an inherently abstract subject and to study it seriously requires and investment in the language in which it is formuated. That language is mathematics.

So then, please supply me one cubic meter of Joules.

Lee Smolin has suggested a lot of things.

How about earth, air, fire and water ?

Einstein went out of his way to seek help from Marcel Grossmann, who helped him with Riemannian geometry and tensor analysis. It was ony because Riemann had invented differential geometry that Einstein was vable to formulate genersal relativity. Einstein was vrather clear in acknowledging his debt to Riemann. Mathematics is the language of physics. If you do not understand the requisite mathematics you are effectively illiterate. That appplies to all of physics -- relativity, quantum theory, mechanics, electrodynamics, the whole enchilada. This is just plain wrong. It was specifically the application of differential geometry and tensor analysis that enabled Einstein to formulate general relativity. That is embodied in Einstein's notion of "general covariance" which in reality is just the coordinate-free formulation permitted by differential geometry. Because he initially lacked understanding of much of the mathematics necessary, he sought out help and learned the mathematics. Einstein's quote that "Imagination is more important" is widely misunderstood and quoted by the mathematically illiterate. It is true in the sense that imagination is the most important ingredient of good research. But imagination wihout an understanding of both existing theory and the tools of mathematics is useless and results in nothing but fantasy. Good researchers first come to understand the existing theory and the language, mathematics, in which it is expressed and only after establishing a solid foundation do they apply imagination to further the body of knowledge by means of disciplined research.