1. Can quantum mechanics and relativity exist side by side?

2. What do you think of Gödel's Incompleteness Theorem?

1. Yes, or so I've been told.

2. I'm not sure... to my limited understanding, it really doesn't say much at all. It appears to me to be pointing out a special case of a type of proposition that can't be proved by the axioms of a system.
I say: so what? The type of proposition is artificial and self-referential, and seems functionally useless. It seems to me to be analogous to the case of self-referential paradoxes (eg "This statement is false.") Yes, such statements/propositions exist. Yes, they are an anomaly in the system. No, it doesn't functionally affect the system.

I could be wrong, of course. I'm no mathemetician.

<i>1. Can quantum mechanics and relativity exist side by side?</i>

Yes. Many quantum theories have relativity built in.

<i>2. What do you think of Gödel's Incompleteness Theorem?</i>

An impressive and important result.

Originally posted by Electric Jaguar
1. Can quantum mechanics and relativity exist side by side?
well that depends on what you mean? first of all, are you talking about special relativity, or general relativity?

if you are talking about special relativity, then yes. there are lots of relativistic quantum theories, QED being an excellent example. QED is possibly the most successful physical theory ever.

if you mean general relativity (which is OK, many workers in the field of quantum gravity use relativity to mean only general relativity), then the answer is a qualified "no". that is to say, general relativity, and quantum theory, as currently formulated, cannot exist side by side.

nevertheless, we know that quantum theory and general relativity are both correct approaches to describing nature. we know nature exists, so we all believe in our hearts that there is a quantum theory of gravity, we just don t know what it is yet. just because we haven t written it, doesn t mean that we won t find it some day.


2. What do you think of Gödel's Incompleteness Theorem?

at first i found it disturbing. after a while, i started to think it is natural. there are limits to the power of human logic, i think.

I'm unfamiliar with (read: know absolutely nothing about) general relativity. I'm also unfamiliar with quantum mechanics, which made the first question pretty much silly for me to ask. "QED? That which has been determined!"... right, I'll assume it's something to do with electrodynamics.

Originally posted by lethe
at first i found it disturbing. after a while, i started to think it is natural. there are limits to the power of human logic, i think.
I still find it disturbing. I plan on doing lots of drugs, like acid, so that it remains disturbing. Although, it does seem to clear up why paradoxes exist, I suppose - also, it puts a serious damper on any ideas that we might, one day, be able to synthesize human life (I consider this a good thing).