questionposter

Ok, I get that raising to the power of i would generate some expression based on the logical properties of logarythms and trigonometry, but I don't mean that, I want to know what your doing when you raise something to the power of an imaginary value. I don't mean "what happens when you raise e to the power of i pi or I guess other things on a polar graph?", I mean it in the same way as "why does 2^2=4?"

I think on my graphing calculator that I somehow accidentally did an intersection on an asymtote or the actual line that represents "undefined" and the calculator said "ERR: SINGULARITY". What does that mean?

Even though space time is naturally flat, there's a bunch of different curves in it and even enough in our local space to distort light in some way, so doesn't that mean euclidean space doesn't actually exist in the universe because there is no place where a completely straight line can be drawn?

I mean I get how the logic of logarithms work, I guess in this instance it generates complex numbers that are easily visible, but I mean just in general. What if I just say "[math]2^i[/math]"? What does that mean? What does i actually mean when I say " sinx+5=0 at (w/e)i"?

How can you raise something to the power of an imaginary number and get a real number? Every time I try to do it I get an error. Does it only work on a complex plane in some way? I mean I guess it get that it just happens, but, how does that actually work out?

So if you take two entangled particles and shoot a photon at one particle, will that particle really destroy the photon and have it re-appear on the other end comming out of the other particle? Because I think some nova or pbs program said that, and you'd think something like successful instantaneous materialization would make the headlines. I mean what they are saying has to be coming from somewhere, but it seems like a leap. How would you even measure that without destroying the entanglement?

That's actually pretty close, but that seems to deal with more parametric and polar equations, I was thinking more of actual functions.

So if you can draw a sine-wave as a circle, what about other types of sine-waves? Can you draw them as other shapes too? Or what about secant? Can you draw that as a shape? Is there some way I could add two circles and get a bigger circle?

Information isn't necessarily preserved through time, it get's destroyed and re-created, i.e. in the atomic world there is no past information you can use to accurately predict the future with. Whether or not something happens to be where it is or whether or not something will be perceived the specific way that it is, is chance. Things might seem deterministic because at large distances, probability is very minuscule, and there's also that at the large distances we see, we aren't just dealing with one atom, its gooplexes.

Wait, in helium the electrons are closer, but how much are they closer if they aren't half as much as hydrogen and why? Shouldn't the distance of the ground state electron(s) be somewhat exactly proportional to the amount of protons in the nucleus?

Everything is built from the atomic realm, so how could the classical realm be deterministic if the atomic realm isn't?

I thought electrons could appear inside hte nucleus without interacting with it? Shouldn't that technically be energy 0?

I'm still talking about specific instances where I specifically hear that merging black holes cause a gamma-ray burst, not the heating of the gas around them.

I'm familiar with resonance already, but I just don't get exactly how it works in the atomic world. Also, I know that steel and concrete are actually kind of flexible depending on their percent compositions, but how the hell does it do that? Did that Tesla death vibrator finally work?

Ok, I think I'm getting a picture that the energies are different, but because of the orbitals and the different numbers of electrons, some atoms are bigger than others. However, I'm still not completely sure whether or not any energy actually IS possible, just not within one system.

So if they don't have the same energy, couldn't an electron have any energy by going to different atoms? Also, then how much closer are electrons in helium than hydrogen?

But how could a ground state electron in an s orbital 1/2 the distance of hydrogen's s orbital from the nucleus have the same energy as one that is 1/3 the distance of hydrogen's ground state electron from the nucleus Or basically, if the atoms in helium are 1/2 the distance of hydrogen, how could they have the same energy as electrons in lithium which would have electrons 1/3 the distance of hydrogen?

Wait, how could the energies of electrons not be continuous then? Couldn't there just be a small and smaller fraction of energy that electrons could form hybrid orbtials with? Because you could have helium who's electrons are 1/2 the distance of hydrogen, and then lithium's who are 1/3 the distance of hydrogen and etc, and since there's no limit to how big a nucleus can actually be, could an electron actually posses any energy?

So could the nucleus of an atom be so big that its boundaries exceed the most probably location of its ground state electron? Like say we were able to fuse two uranium atoms together to make a really big nucleus...

The age of the universe should be bigger unless galaxies are traveling so fast away that it could make up for that .7 billion years difference, which I don't think they are.

I'm not talking about quasars or accretion disks though, I'm talking about more like a gamma-ray burst out of nowhere and then astronomers assuming its black holes merging. If it was a black hole feeding on gas, we would have seen it before.

So if you can pluck a string and not play it right, when the universe began, couldn't there have been electrons trying to vibrate at decimal energies that just couldn't sustain their existence due to this destructive interference?

Well, I don't know what to tell ya. Classically you would think electrons would be closer to a nucleus with more protons, but atoms don't operate on classical mechanics. Plus, in order to get a high degree in chemistry, you need to know some quantum mechanics. If a ground-state electron is closer to the nucleus then it shouldn't have the same energy, but it does. Actually, I think even swan corrected me on this. I said electrons in bigger nuclei are closer and even he said that's not right.

If black holes merge, how could that cause a gamma ray burst if light can't escape a black hole?

So someone predicts that all matter will radiate it's energy away in the form of gravitational waves? But since matter can't travel at the speed of light, wouldn't the gravitational waves from all matter hit matter everywhere else and and thus matter and the universe would continue to have lots of energy? In fact, gravitational waves like that from supernova and things like neutron stars and black holes merging would even trigger the birth of stars in local gases and nebulae.