blah-Man…
We’ll get you there, don’t worry.
You are worrying right now about the roots of science. This is an epistemological (that’s the word you were looking for) game rather than a practical one. Also, you have the justification a bit backwards. Science doesn’t pick and choose which observations justify itself. It uses all observations to come up with theories and the BEST theories suggest further tests that would falsify themselves.
Let’s consider the development of quantum mechanics and HUP. It was really all instigated, you see, by the condundrum of the blackbody spectrum. The thermodynamical relationship of a blackbody radiating energy blows up as you approach zero energy. That is, there should be an infinite number of low frequency, high wavelength photons pouring out at us from everything if classical physics is right. We can measure such things and find them not to be true. What Planck found was that if you allow for quantum states that the photons have to be in (in other words, there is NOT a continuum of states), then you will necessarily get a spectrum that agrees with observation.
Okay, but Planck didn’t know WHY this was the case. Before we get to the next point, we have to mention some things about wave-particle duality. This was discovered pretty much independent of quantum mechanics. It had actually been a war of sorts back when Newton was around. Newton thought light was a particle, the French thought light was a wave. Ultimately the French won by using interference patterns of light to show that they couldn’t be particles, for how could a particle interfere with itself? (Temember this, it’ll come in handy later.) Now comes the photoelectric effect. This effect was measured in the 19th Century and found that light actually carried momentum. How does a WAVE that is massless carry momentum? Very confusing! Furthermore, de Broglie showed that if a wave like light could carry momentum, than any PARTICLE that carried momentum could be shown to be a kind of wave. Huh? Confusing!
So here’s problem number two: the atom. An electron spinning around a nucleus should give off radiation if it is in a classical E&M system. This would imply it looses momentum and goes spiralling in toward the center. In fact, if you calculate classicaly the age of an atom using this idea, you’ll find that atoms can’t exist for very long at all. They just degenerate! What’s the resolution to this? Again, the Bohr atom relies on the quantization of electrons in so-called orbitals. If the electrons are only allowed to be in places where they don’t destructively interefere with their waves. But electrons are particles, you say. Rightly so, but remember de Broglie? He gave us this wonderful way of making anything with momentum (including electrons) into waves. So it seems that Bohr was onto something.
Okay, so now we have to deal with Schrondinger. All of these facts were known about the world, but they didn’t seem to go together. That is, until Schrondiger decided to write down a peculiar wave equation that had as solutions both the Blackbody Spectrum and the Bohr Atom (with some minor additions that actually make the model BETTER than Bohr’s). Since you claim to be math-phobic, I’m not going to write down the equation (you can look it up for yourself if you wish). However, it deals with the following concepts: Wavefunctions; a system of states (think HARMONIC reasonances) for a given waveparticle (remember that waveparticle duality again), and operators; mathematical manipulations of the states that give you a property of the system you are looking at. Observables (that is anything you can measure) are a particular kind of operator that acts on a state to give you… not an answer, but a whole slew of answers that are each assigned a probability. This is the weird thing about having “states” instead of objects: you can measure one time and get one answer, and then you can measure another time the same wavefunction and get a different answer. Remember the problem of getting particles to interfere with themselves? Well, it’s no longer a problem because if they are in more than one state they can add and subtract to give you the peaks and valleys of an interference patter, even though you thought all along that the thing was a particle! In fact, there is no such thing as “particles” or “waves” in quantum mechanics. They are grouped together under one catagory: waveparticle.
A DIRECT consequence of this formalism is the Heisenberg Uncertainty Principle. Why? Well, it happens that both position and momentum are operators (as they are observable). Whenver you have two different operators, it is fair to ask the question, does it matter which order I operate in? In other words, if can I multiply first and then add or can I add and then multiply and does it make a difference. Sometimes the answer is “yes, it makes a difference” and sometimes the answer is “no, it makes no difference”. For the case of the position and momentum operators the answer is, “yes, it makes a difference.”
In other words, there is no way for you to measure the position and the momentum at the same time and get an arbitrarily good measurement on both. Scientists have been dreaming up ways around the uncertainty principle for ever, and EVERY SINGLE TIME IT IS TESTED, it has been found to hold true. Likewise, Scientists have been dreaming up ways to get around wave particle duality. You may have heard of Young’s Double Slit Experiment? Done with electrons,. it is a pefect example of how it is impossible to divorce quantum mechanics from observation.
You ask the question, what is all this math based on? The truth of the matter is it was based upon fundamental observed properties of the universe. It would be so much NICER if the universe didn’t behave quantum mechanically, but we just don’t see it doing that. Perhaps someday, in the future, someone will come up with a better theory that will incorporate all that quantum mechanics explains and do an even better job. Until that day, QM is the best we got.
You mention being worried about the “contrived” nature of science. You’re going to have to explain your worries better than that. To some extent, all of science is contrived. We see something, and we try to quantify it. Then we look for relationships between the quantities. We postulate a relationship that suggests other observations we can make. We go and make those observations. Sometimes we find, to our delight, that the observations confirm the postulate (the hypothesis). This happens with every relevant observation ever made and you have a theory. Sometimes it doesn’t work out and it’s back to the drawing board. Your mentioning of the Higgs Boson and the Cosmological Constant (dark energy: which, by the by, has direct consequences on Hawking Radiation) are two theories that are currently under considerable scrutiny. They both predict very particular things about what we SHOULD see if we look in the right place. Scientists are racing to look in those places to either confirm or deny these theories. Both of them stand up to the scrutiny that they explain all previous observations. (Did I say all? Yep, I mean all that are recognized as valid by the scientific community. If you wish to argue with the tests of validity or why the community gets to decide, that’s another thread.) We may find them to be lacking or wrong in some way, in which case it’s back to the drawing board. They are contrived ideas only from the standpoint that they are directly related to what we observed and not necessarily DEDUCED from axiomatic expressions (the way math is deduced). However, they have to be rigorous (you can’t have in your theory that 2+2=1.e5) and consistent. If you think that the scientific process in general is flawed, you’d probably be best to jump on one of the other threads that discuss this topic.
Okay, that just about does it. Hope this has opened a few more windows. Keep pushing if it doesn’t.
) . Hawking gives 3 possibilities for Hawking radition: 1: The Particle Anti-Particle forming right next to the Event Horrizon. 2: Quantum Tunneling Effect (I agree with this one) 3: I dont really rember this one but it was unusual.
