A Tripolation

You're using it completely incorrect in this instance. And by what assumption are you basing your logic on? It is the assumption that a god must obey our laws that we have discovered. If there truly was an omnipotent deity, he would transcend all logic and order and could do anything he darn well pleased.

I have heard mention of this, but I never quite understood. Perhaps you can explain it for me. Does "phase velocity" also fall under this category? What is meant by "closing speed"? Am I correct in thinking about it the same way they tell you to think about a giant pair of scissors closing in space at the speed of c? The tips will be moving at "superluminal" speeds but they are just arbitrary points?

I assume you mean what happens if all of the mass in a human being were suddenly, and inexplicably, converted to energy per the mass/energy equivalence principal? Nuclear reactions aren't the same as matter-antimatter annihilation reactions. Nuclear chain reactions are the result of the fusing or fission of an atom. For example, in fusion, Hydrogen atoms are forced together to create Helium atoms (and some other stuff). The release of electromagnetic radiation is a by-product. No. The "energy" would expand radially away. Most likely in the form of an explosion.

By no means am I an expert, but I do intend to go to grad school for astrophysics, so this is of particular interest to me. I have a few questions. 1. Why are you assuming that the main reason for the redness of the galaxy is entirely due to the redshift of light? 2. It seems more plausible to me that these galaxies are missing stages of galactic evolution. As far as I know, there are many open questions regarding protogalaxies - specifically with regards as to why there was a certain varying density in some areas instead of a uniform distribution. 3. The Big Bang model is our most complete model of spacetime expansion. If these galaxies are so far away that their light has been traveling for more than the 14 billion years posited by the BB model, why would that render the entire theory false?

I agree with your entire post, iNow. But I do feel that some atheists behave quite religiously. It is also stated in your link: That seems an awful lot to me like an atheist that is proselytizing and, ergo, follows a belief system of non-belief.

It's not that you can only observe a single characteristic at a time. You just have a negative correlation among what you observe. This is most notable in the Uncertainty Principle with position and momentum, or the time coordinate and energy. It may also be helpful to view it in terms of de Broglie wavelengths. This is where every particle can be modeled as a wave. By restricting the delta(x) of a particle (the area it inhabits) you are localizing it, and you lose a lot of the certainty with which you can measure its momenta, as you are shortening the wave patterns. If you increase the area, you can get a definable wave (a lot of momentum certainty), but then again, you are no longer able to say with certainty where this particle resides in delta(x). Does that help?

It seems an awful lot like you're restricting intelligence to the kind of intelligence that humans have, and not the kind that animals have. You can make a correct choice about something with which you have had years of experience dealing with, ie, buses. But what if some advanced race were to show you what the Grand Unifying Theory looked like and asked you to identify what each of the terms meant? You wouldn't have a clue. You would not be able to make any sort of decision backed by logic whatsoever. Going by your reasoning, these beings could deem you as "unintelligent".

You would run into energy problems here. Altering your object that is orbiting at high speeds would make this method inefficient. Also, as Schrodinger's Hat pointed out, the gravitational slingshot can only be used three times (I actually thought it would only work once). This speed will not be near enough to the speed of light to help at all. Well, yes. This was established by Einstein in his Special Theory of Relativity. When you do a lorentz transformation, you will notice an effect called "time dilation". This is what Hawking meant. It isn't really traveling backwards in time at all. It simply means that time is passing slowly, much more slowly if you're around the speed of light, than it would be for other people who are in relative rest.

I know a lot of people, myself included, that wouldn't be able to consistently and correctly select the appropriate solution from a list of available choices on a quantum mechanics test. Does that mean that they are not intelligent?

QFT. While we do need to keep food/energy production local to America, I think we ought to be focusing on creating more technologically advanced sectors of business. Most people do not see this, however. They just talk about the loss of jobs, which is bad, sure, but they do not talk about ways to create jobs for the FUTURE world. A world that will most decidedly be governed by computers and renewable energy.

I'm a student as well and I'm not studying the field you wish to pursue. I'd just like to take the time to tell you that it would be very difficult for you to get into a school like Caltech. Also, there are many other fine public universities that would net you a good education. You needn't attend the "best of the best" type schools.

mississippichem was saying that a photon's energy is defined by its wavelength. That doesn't mean it's soley dependent on upon it. Think about units here. Wavelengths are defined by meters. Energy is joules. A statement that e=v just doesn't make any sense.

I haven't seen any direct link between my use of a calculator and and my ability, or lack thereof, to use eigenvectors to solve for systems of DE's. We aren't allowed to use calculators on tests. So why would being dependent on one be beneficial to me? I think that they have helped me to understand how to solve more advanced mathematics.

As your velocity increases, the energy of the system increases, but none of the rest of this or its implications is correct.

Then how do you explain muon decay?

The Earth orbits in part because, like you guessed, it has a velocity perpendicular to the pull of the sun. Now where did this initial velocity come from? It has to do with when the Solar System formed. Planetary systems form out of the same clouds that form stars. When nebulas collapse due to gravity, a protostar forms at the center, and then is surrounded by what is known as a "protoplanetary disk". Eventually through a lot of mechanisms like accretion and the removal of the disk, you get small planet-like objects. These protoplanets continue to grow in size as they accumulate more and more matter. Now back to your question. These protoplanets are now spinning because the original gas/dust cloud was spinning, even if ever so slightly. Due to the law of conservation of angular momentum, these bodies spin faster and faster as they contract. And before you know it, you have spinning planets and such. I think this is accurate. I welcome any corrections of my simplification of planetary system formation by the more knowledgeable members.

Or...you know, since the Judeo-Christian God is omnipotent and all...he could've NOT murdered the babies and alleviated their suffering anyways. Anyways, this whole topic is far-removed from the OP. There's no point pursuing it. And there are many threads here about the questionable morality of the OT God.

Oh, ok. I must've skipped that bit.

Math_Struggles, you do realize that [math]Ax = \lambda Bx[/math] is the formula for an eigenvalue, from which you can then obtain an eigenvector, correct?

Based on this quote and this post, it seems that you have a problem with calculators. Not to deviate too far from the OP, but I don't understand this. I see a calculator as a tool. And like any tool, it can be used to create or destroy. I'm good at "plugging and chugging", but I struggle with abstract math. I often use a calculator or a program like Mathematica to obtain a final result. Once I do this, I'm able to think, "Now how did they get this?" and work backwards to a solution. It may not be the most elegant way to go about doing math. However, I find that it helps me to see how different techniques may be applied in different situations. It taught me to make substitutions that seem outright ridiculous at first. So in this way, I feel that calculators are vital to students. I do not think they are indicative of "lack of thought", as it were.

He may be. But if you read the Bible, you will find a God that commits many atrocities and evils.

Alright. That makes sense to me. And I can read the math in that connotation now. So the only way to discern this to look at the tables? There are no manipulations of any sort that I can implement that will show me a general function yields it's own general function as a solution to the Laplace transform? I haven't learned much about Fourier transforms. I don't quite understand what you're saying here. We want to modify the coefficient to be 1 so that it has no impact on our [math]f(t) = f(s)[/math], correct? We are only now covering eigenfunctions. What is an eigenfunction of an operator? I have never even used Hilbert spaces before, so I don't think I can use those to solve this problem. Thanks for the help, by the way. Also, could a mod delete the post above? My browser seems to have oddly submitted the edit.

I'm having difficulty understanding what this problem is asking of me. "Does the Laplace transform have a fixed point? Is there a function [math]f(t)[/math] defined on [math] 0 < t < \infty [/math], such that [math] \int_{0}^{\infty} f(t)e^{-st} dt = f(s) [/math] There is an extra condition that [math]f[/math] is not identically 0." I can use Laplace transforms as a general rule, but I do not quite understand what they mean mathematically. This question seems to be addressing that mathematical meaning, if I'm reading it correctly. How should I go about starting this problem? What do I need to understand to solve this? Thanks.

No. But it can't be ruled out because of the appalling "science" that its proponents implement.