DrRocket

OK, let's drop the straw man and address the question from a different perspective. Please explain the reason or reasons why you believe in God. Please be clear as to the concept of God that relates to those reasons.

Absolutely. All you need to do is be accepted into a graduate program. But you should know that in the sciences, unlike engineering the master's degree is not normally a degree that is sought. Quite frankly it is often a consolation prize for those who don't make it to the Ph.D. The point is that you are more likely to get into a program if your objective is a Ph.D. It will be helpful if you have impressed your Physics professors while pursuing your B.S. in engineering. It is not at all unusual to obtain a graduate degree in a discipline that is related to but different than that of your B.S. or even M.S.

You have submitted at least an abstract to the conference, and your advisors, who are undoubtedly with communication with others in the field, know of your findings. The bombshell is already out. All that you need to do is present your results and the data and logic supporting it in a cogent manner. If you are correct, then your result is a major result in your field (whatever it is), and it will be recognized as such. Being correct counts for more than any number of opinions and any amount of ruffled feathers. Don't let Marat's "ghost story" frighten you. Appel and Haken announced their solution to the four color theorem at a conference in 1976. I don't know what was said by the audience at that conference, but I do know that combinatorists at my institution were intrigued and impressed by their technique of reducing the problem to a large but finite number of cases that could be checked by computer. Their complete proof, including microfiche, was published in the Illinois Journal of Mathematics, a prestigious journal, in 1977. Because their result was the first major theorem the proof of which involved computers, there was some controversy. Mathematicians, me included, prefer proofs that can be understood without recourse to checking so many cases that a computer is required. However, combinatorial theorems can simply require such methods. The reputation of Appel and Haken was never in doubt. Their reduction of the 4-color theorem to a finite number of cases, even a huge finite number, remains an impressive accomplishment.

This is rather obvious. Since you have a predilection for posting trivial problems and have yet to produce anything resembling an elegant or insightful argument, you have an opportunity to redeem yourself. Produce one -- say six lines or less. No cheating by copying a solution from any of the other forums in which you have posted the same problem.

bold added I would tend to agree with the exception of the last sentence. I do not equate religion with established, organized churches. I think that your points apply to the latter, but not the former. A friend sums up the position of the local dominant superstition as the "100-10 plan". 100% church attendance + !0% tithing equals salvation. This puts in concrete form your observations about the misplaced priorities of many organized churches. I have a great deal more regard for religion than for churches. I have more regard for church members than for the hierarchy. On the other hand I do have some physical evidence that some clergy have a tie to the Almighty.. In my younger days I used to attend a Presbyterian Sunday school whenever my parents forced me to go. Then a friend talked to me and I saw the light -- and joined the Baptist softball and basketball teams. I often rode to the games with the preacher. Anyone who drives like that and survives has a direct line to God.

Then go for it. But recognize that a good PhD from a reputable school is a full-time undertaking. I have seen it done part time, but was underwhelmed by what I perceived as the quality. I have seen really good work done by a PhD candidate nearing 60, so age by itself is not a big issue in my view.

That depends on who is doing the accepting. There is no universal definition of "mass". Tolman argued for relativistic mass. Rest mass occurs naturally in many applications. Invariant mass is convenient in considering systems of particles. Mass,. though a common term, is really not a cut-and-dried concept. (BTW aftewr a recent thread on this topic I had a discussion on this very topic with a local, and well known, high-energy physicist. There is no single definition within the community.) You are right that "gravitational pull" does not increase with relativistic mass. Spacetime curvature is invariant -- it is a tensor -- and that is what determines "gravitational pull". If gravity increased with speed, everything would look like a black hole to a photon, and it would be awfully dark around here.

Making it interesting would be good. But this isn't interesting -- just parlor tricks. We have [math](ab)^{n-1} = a^{n-1} b^{n-1}, (ab)^n = a^n b^n, (ab)^{n+1} = a^{n+1} b^{n+1}, \forall a,b \in G[/math] and taking inverses [math](ab)^{1-n} = b^{1-n} a^{1-n}, (ab)^{-n} = b^{-n}n a^{-n}, (ab)^{-n-1} = b^{-n-1} a^{-n-1}, \forall a,b \in G[/math] So [math] ab = (ab)^n(ab)^{1-n} = a^nb^nb^{1-n}a^{1-n} = a^nba^{1-n}[/math] [math] ab = (ab)^{n+1}(ab)^{-n} = a^{n+1}b^{n+1}b^{-n}a^{-n} = a^{n+1}ba^{-n}[/math] Thus [math] a^nba^{1-n} = a^{n+1}ba^{-n}[/math] multiplying on the left by [math]a^{-n}[/math] and on the right by [math]a^n[/math] we have [math] ba=ab[/math] . QED As to the insufficiency of two of the three conditions, consider a non-abelian group [math]G[/math] of order n, for some n. The last two conditions are satisfied. since [math] a^n=1 \ \ \forall a \in G[/math] I am about through with this sort of thing.

All true. I find it easier to understand the implications of the discriminant by simply deriving the quadratic formula and factoring a general quadratic (nothing deep here) [math]ax^{2}+bx+c = a(x^2 + \frac {b}{a} x + \frac {c}{a})[/math] [math]= a (x^2 + \frac{b}{a} x + \frac {b^2}{4a^2} - \frac {b^2}{4a^2} + \frac {c}{a} )[/math] [math] =a([x+\frac {b}{2a}]^2 - \frac {b^2-4ac}{4a^2})[/math] [math] =a([x+\frac {b}{2a}]^2 - [\sqrt {\frac {b^2-4ac}{4a^2}}]^2)[/math] [math] =a( \{[x+\frac {b}{2a}] + [\sqrt {\frac {b^2-4ac}{4a^2}}]\} \{ [x+\frac {b}{2a}] - [\sqrt {\frac {b^2-4ac}{4a^2}}] \})[/math] [math] =a( \{[x +\frac {b}{2a}] + [\frac {\sqrt {b^2-4ac}}{2a}]\} \{ [x+\frac {b}{2a}] - [\frac {\sqrt{b^2-4ac}}{2a}] \})[/math] [math] =a( \{[x- [\frac {- b - \sqrt {b^2-4ac}}{2a}]\} \{ [x - [\frac { -b + \sqrt{b^2-4ac}}{2a}] \})[/math] The roots are thus seen to be [math] [\frac {- b - \sqrt {b^2-4ac}}{2a}][/math] and [math] [\frac { -b + \sqrt{b^2-4ac}}{2a}] [/math] with nature and multiplicity following from the character of [math] \sqrt {b^2-4ac}[/math] which is called the discriminant. The "quadratic formula" is just a way to avoid going through the tedium of completing the square and factoring quadratic polynomials repeatedly. The heart of the matter is a concrete realization of the fundamental theorem of algebra, realizing the general quadratic as a product of two first-order polynomials (and a constant). This may involve complex numbers and repeated roots, but it all falls out of the factorization.

[math]10\equiv 1mod(9)[/math] is the only observation needed. Everything else should be obvious to anyone who knows what a ring is. I flat do not believe Obelix. He has made exactly the same post elsewhere. The questions are trivial, about what one would expect in an introductory class. The "proof" that he offers is clumsy and lacking in insight. If he is not looking for help in a mathematics class, then he should be. I have had students lie before. My BS meter is fully functional.

I have seen it done, and done well. But it takes someone with an exceptional attitude and dedication to do it. If your motivation is a deep interest in your field then you have a good chance If your objective is simply career advancement, then probably not.

Check your PM box. If you have questions reply to the PM.

This your second post in multiple forums of a straightforward and elementary algebra problem (this one has literally a one line proof). It is rather obvious that this is a class assignment. You have not posted under "Homework Help" and are asking, not for help, but for a solution. This is called cheating. If anyone other than Obelix desires to see the simple proof, send me a PM.

Belief to be meaningful must be based on something deeper than "deciding to believe". I certainly know "religious" people who flaunt their "belief" so flagrantly that it casts doubt on whether they really believe or are simply to scared to state otherwise. As far as I am concerned there is a rather fine line between "deciding to believe" and hypocrisy. I value honesty. I think many religions do too. I know some moral atheists. I know some immoral priests, bishops and pastors. I know moral Christians, Budhists, and Muslims. I don't trust politicians no matter how many church services they attend. I have respect for those with genuine religious belief. I also have respect for those who genuinely do not believe. So long as they respect the right of the other side to their own belief. I have a friend who, nearing the end of life, has "confessed", become very religious, and completed a proselytizing mission for his church. I am, to say the least, a bit skeptical. He burned the candle from both ends, plus the middle, prior to his transformation. I would like to acquire the movie rights to his confession. Declarations of belief alone do not impress me.

Pretty much everyone expects that something like the chronology protection conjecture will be shown to be true. But it is not straightforward. Closed timelike curves do exist in some exotic solutions to the Einstein field equations. Gödel's lambda dust space, the Tipler cylinder and Kerr black holes have CTCs. On the other hand Hawking showed that if the weak energy condition holds then there are no CTCs. Quantum fields, as I understand it, generally do not conform to the weak energy condition (ajb chime in) so chronology protection may well not hold at the quantum level. There are Feynman diagrams that include non-causal branches. I have no idea if Thorne coined "closed timelike curves", but it is natural terminology for dealing with the geometry of a Lorentzian manifold. There is good reason to demand a mathematical proof based on general relativity. Odd things really do happen. When black hole solutions were first found, many physicists, Einstein included, did not believe that physical black holes would exist. One learns in physics by pushing the limits of what is known and investigating situations that might be termed "exotic". Exotic is not necessarily impossible. Any proof of the chronology protection conjecture will have to include some conditions that constrain the admissible solutions to the Einstein field equations. The known exotic solutions with CTCs serve to demonstrate that fact. General relativity alone is not enough. In a sense the deep problem is that causality appears to not strictly hold at the quantum level, but it seems to apply in "normal" macroscopic situations. So, where is line between the quantum world and the macroscopic world where causality kicks in ? This is well worth understanding.

There might be a way to produce such a [mathv[/math] without finding the eignvectors of [math]A[/math] but I don't see it. Good luck in your search.

It is considerably more complicated than that. To put numbers to it would require getting into propagation of stress waves in solids. I am not ready o break out the books and delve into that detail.

There is no such thing as gravity in flat spacetime. Gravitation is a manifestation of curvature.

Try again. [math] x^2+y^2 = 20[/math] does not describe a parabola.

[math] \frac{d}{dx} (2x-1)^{\frac{1}{2}} = (2x-1)^{\frac {-1}{2}}[/math] [math] \frac{d^2}{dx^2} (2x-1)^{\frac{1}{2}} = -(2x-1)^{\frac {-3}{2}}[/math] [math]\frac{d^3}{dx^3} (2x-1)^{\frac{1}{2}} = 3(2x-1)^{\frac {-5}{2}}[/math] . . . [math]\frac{d^n}{dx^n} (2x-1)^{\frac{1}{2}} = ( (-1)^{n}\displaystyle\prod_{k=0}^{n-1} (2k-1) )(2x-1)^{\frac {-2n+1}{2}} [/math]

What you fail to realize is that Gauss's concept of curvature, extended to higher dimensions by Riemann lies at the heart of Riemannian geometry. In turn Einstein utilized the work of Riemann in formulatng general relativity as a generally covariant theory of gravitation. Cosmology is based on general relativity. So the ONLY notion of curvature or of flatness that is germane to cosmology is that which comes from Riemannian geometry. You have two choices: 1). Learn and understand the concepts on which the theory is built. 2) Continue to babble incoherently making inane, irrelevant and nonsensical comments..

Draw yourself a graph of [math]x^2 + y^2 = 20 [/math] Also graph [math]y = 2x + p[/math] on he same axes for several values of p. An approach should then suggest itself.

I will thank you to cease and desist from mis-stating and mis-representing my opinion of Stephen Hawking or anyone else. That extends to my opinion regarding any currently speculative physical theories. You may be a retired psychologist, but I am quite confident that you are no more clairvoyant than anyone else. You may take whatever issue you feel capable of supporting with a concrete issue, but setting up a straw man by misrepresenting my opinions, which you very clearly do not grasp, is logically fallacious. What is truly an exaggeration is your opinion of the gravitas of your opinion. You would do well to first understand a theory before you criticize it.

It is a matter of communication and accepted definition. Choosing an unconventional meaning for standard terminology , without making a very visible exception to convention, is not reasonable. In other words, your personal definition is worse than worthless. It cultivates confusion.

Stating it is a whole lot easier than making it precise and proving it. http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html