Ha! That equation is actually identical in form to SchrÃ¶dinger's wave equation so I have to whole-heartedly agree since from a physicist's perspective, even at the quantum level physics at non-linear scales boils down to that equation.

What can I say, nature is consistant. Whether dealing with quantum physics or engineering, if non-linearities can be ignored we use the same fundamental equations! :)

Very interesting jmb275. And I like to poetic way of saying this very much.

Yes, the more I learn, the more I'm impressed with how consistently the same set of equations come up in different fields. Perhaps we force this on our world, but I'd like to think that perhaps there's more to it than that.

This is why almost all current physics research focuses on cases where there are significant non-linearities. We have excellent mathematics for linear problems, but the non-linear problems are the ones that are in serious need of work.

Ha! That equation is actually identical in form to SchrÃ¶dinger's wave equation so I have to whole-heartedly agree since from a physicist's perspective, even at the quantum level physics at non-linear scales boils down to that equation.

ReplyDeleteWhat can I say, nature is consistant. Whether dealing with quantum physics or engineering, if non-linearities can be ignored we use the same fundamental equations! :)

Very interesting jmb275. And I like to poetic way of saying this very much.

Yes, the more I learn, the more I'm impressed with how consistently the same set of equations come up in different fields. Perhaps we force this on our world, but I'd like to think that perhaps there's more to it than that.

ReplyDeleteTurns out that vector spaces are very useful!

This is why almost all current physics research focuses on cases where there are significant non-linearities. We have excellent mathematics for linear problems, but the non-linear problems are the ones that are in serious need of work.

ReplyDelete