DQW

There is no flaw in that argument. It is something that has been known for centuries, and there's ABSOLUTELY nothing new or revolutionary about it. But in the Newtonian framework, you only have a temporal oscillation in the gravitational field - the field here changes with time, and so does the field out there. In the framework of Relativity, you have a real wave that oscillates in space and time. The aplitude out here is different from the amplitude out there, and the wave has a finite wavelength. To have a wave, you need a finite propagation velocity. In the Newtonian framework, gravity propagates instantaneously (with infinite wavelength - so it's not a wave).

I would recommend Vector Analysis, by Murray Spiegel. It deals extensively with vector calculus and finishes up with tensor analysis.

There are two books I'd recommend for the OP : 1. Alice in Quantumland, by Gilmore : read excerpt here http://www.amazon.com/gp/reader/0387914951/ref=sib_rdr_ex/002-0451815-3564041?%5Fencoding=UTF8&p=S00H&j=0#reader-page 2. Mr Tompkins in Paperback, by Gamow : read blurb here http://www.amazon.com/gp/reader/0521447712/ref=sib_rdr_bc/002-0451815-3564041?%5Fencoding=UTF8&p=S05U&j=0#reader-page

If you change the atom to make it something it is not, how do you expect it to retain its original properties ?

maxwell, I congratulate you on your decision to go back to school. I second ku's recommendation on Stewart - that is an excellent text ! Online courses : This one is not bad - though at times, it lacks continuity (no pun intended ) http://www.ugrad.math.ubc.ca/coursedoc/math100/index.html This page is nice for an additional reference, but not a primary text http://www.math.ttu.edu/~williams/etcalc/online.html An excellent page for vector/multivariable Calculus http://math.etsu.edu/MultiCalc/contents.htm A compliation of online resources for calculus http://www.unixl.com/dir/maths_and_engineering/calculus/

But it does veer from mainstream when you suggest that : (i) the understanding of the electroweak interaction as provided by the standard model is suspect, (ii) that any of the present formulations of QM could be done away with by applying the Newtonian formulation to microscopic objects, (iii) that SR & GR are redundant to Newtonian gravitation, (iv) that Boltzmann statistics is a scandal, and that all physical laws obey time inversion symmetry, (v) that the Feynman(-Wheeler) formulation of QED is its only renormalized formulation, etc.

I'm sorry Meta, but I think my time here is better spent helping those that are new to science and discussing mainstream physics, than debating your personal ideas, at the end of which I may only feel regret, if you show me that, for instance, the error in the "center of mass theorem" is of order 1 part in 10^23.

Yes, if you choose, you can represent atoms (as well as cans of soup or lampshades) as 4-dimensional objects in 4-d space-time. The choice of the number of dimensions you want to use is entirely yours. These dimensions are your own creation, and you use as many dimensions as you need to fully describe the system of interest. However, the electrons have very little to do with the need for a time co-ordinate, in the case of an stable, isolated atom. For one thing, according to QM, electrons do not really "revolve" around the nucleus. Electrons exist in probability clouds that are described by a quantity called the wavefunction, whose square (actually the square of its length) tells you the probability of finding the electron at a particular location and a particular time. Now, the wavefunction of an electron in a stable atom is known to be "time-independent", meaning that the probablity of finding an electron at a certain place is always the same, and does not change with time. While this does not mean that there are no effects of revolution, it does mean that you will not find any property of the stable atom changing with time (sort of making the time co-ordinate useless). It is only when you have interacting atoms that you begin to see time-dependence.

The flaw in the calculation above is merely in poor wording and a complete disregard to stating assumptions. The rule that n = real depth / apparent depth is only an approximate rule. It is valid only when you are looking almost vertically (normally) through the interface, and hence i and r are assumed to be very small angles. In this limiting case, A is very close to P, and hence : [math] AI \approx PI~;~~AO \approx PO [/math] But to call the triangles similar is just ridiculous !!

Primarygun, The quoted solution is not trying to prove that n = real depth/apparent depth. It is determining (although incorrectly, as pointed out) the real depth, given the apparent change in depth, and assuming that n= r.d./a.d. = 1.70 Do you want the correct solution to the problem (of determining the real depth) or a correct derivation of the fact that n = r.d./a.d. ? Or both ?

Those are actual pictures taken by a scanning tunneling microscope. They are not computer generated images; they are not predictions. I am not trying to deceive folks here by showing one thing and calling it another. Do visit the linked website. It's quite fascinating, what they've been able to image, over at the IBM Labs ! Okay, lets !

Would I ever deny this ?! (In fact, I had a sneaking suspicion, you might be keeping tabs on me.) Yes, I was looking into that thread and a few others along those lines to see if someone had anything to say that was essentially contradictory to what I had just said. Also, I noticed a link you provided over there, which I can now look into - the computer I was using then did not have Acrobat Reader on it. And now, I shall read the rest of your post.

Tom, I've never come across the term "space-time" in QM, but that may just be from my limited knowledge. Also, I know that QM treats time very differently than it treats spatial displacement. For instance, time is handled as a parameter in (NR)QM, not a hermitian operator (or observable, unlike displacement). If you can have a hermitian time operator in (NR)QM that is one component of a (4-component) space-time operator, there must be a reason why this is not done (or is it ?). I do not know what such a reason may be (nor have I given it much thought), but to the best of my knowledge, this just doesn't exist in QM.

Most physical phenomena do not exhibit time reversal (T) symmetry. Counter-examples to your claim are : T-asymmetry in the (i) weak interaction, and (ii) second law of thermodynamics, and very possibly in (iii) the strong interaction as well (I'm not certain about this though). Any mechanical system with dissipation violates T-symmetry. This negates anything you've said based on this premise.

Hey, not so fast ! I'm not going to spend time here if all that follows are more unsubstantiated claims and rhetoric. Nor am I going to take the effort to prove Gauss' Law (which, according to the OP, should be wrong).

Pray, elaborate ! An "incomplete understanding" on whose part ? What is this illusion, and how does it come about ? And going a step further, what is the true speed of light, according to you ? "Phenomena" are detected or observed. "Quantities" are measured. "Phenomena" can not be measured.

Pauli Spin Matrices have nothing to do with a rotating diatomic molecule. So, this thread is basically saying : "QM and GR are fundamentally flawed/redundant. Everything follows naturally from Newtonian Mechanics." And in this "everything" you include electromagnetism as well, even though Newton knew nothing about the existence of such a thing as "a quantized charge" (not to say that he knew anything quantitative about charge itself).

Would you please prove this statement ? It seems you are suggesting that the treatment of the gravitational field due to a spherical mass (of uniform densty) as that due to a point particle of the same mass is only an approximation. There is enough proof for GR outside of detecting Gravity Waves.

There is no such thing as space-time in Non-Relativistic Quantum Mechanics.

This looks like a doable Dynamic Programming problem. Have a look into DP. Come back if you have questions. It's been ages since I solved a DP problem, but who knows, something might come back to me.

In the ground-frame (to an observer on the ground) : NOIn the car-frame (to an observer in the car) : YES

Sorry for the digression. I think we should get back to YT's questions on expansion.

http://www.almaden.ibm.com/vis/stm/gallery.html Xenon atoms on Nickel substrate : Iron atoms on Copper (a Quantum Corral) : Single Electron Spin measurement by Rugar et al, IBM-Almaden http://www.almaden.ibm.com/st/nanoscale_science/asms/mrfm/ The Nature article : http://domino.research.ibm.com/comm/pr.nsf/pages/rscd.nanoscale-picb.html/$FILE/single%20spin%20MRFM%20Nature%20article.pdf

No. Wrong again. Take a look at the STM Gallery at the website of IBM (Almaden) Labs. Not only have scientists looked at individual atoms, they have picked them up one by one and moved them around (into different shapes) to draw funny pictures and write words. Oh, scientists have also looked at individual electrons, by the way. Look into the MRFM measurement of a single electron spin by Rugar et al (sometime in the summer of last year). Not only is it possible, it's history. Empty of what ? It depends on what these particles are doing. If they are doing something important, it is quite surprising that we understand (and can predict) atomic properties so incredibly well without considering such particles. Also, something being small has ABSOLUTELY NOTHING to do with our ability to detect it. We have detected particles with ZERO size. What can be smaller ?

I'm only glad to yield the floor to those who are better informed. For now, I'd like to address one little question that YT asked : I'd rather let Martin handle this, but perhaps I can start something off, at least. YT : According to the standard model "everything is a vacuum" ! While that was worded thusly for effect, it is hardly untruthful. All matter is currently believed to be composed of fundamental particles (leptons, quarks) which are pointlike - they are 0-dimensional objects. So, essentially everything is just composed of these points and all else is just "the space between". So, given a certain volume of space, the probability that any randomly chosen point will contain matter is 0. This view no longer holds if you choose to view the mass being distributed, not in sharply peaked delta-"functions", but instead as scaled by the probability density. And when you ask if it is a 'vacuum' you might want to clarify what exactly you mean by that word.