Light, Space, Time and the Trombone

Sitting there at a high school concert this afternoon. Trombone player standing 10 feet from me. Gets a fellah thinking.

Spacecurve is usually depicted as something akin to this image.

Your average trombone has a bell that looks like this, or this.

Remarkably similar. Is there something about that shape that is common for a good reason? Does sound amplify in a way similar to the way that scientists believe that space bends?

I’m quite serious. I saw something that sure looked like something else. Is there an underlying elegance / commonality / reason for such a marked similarity?

Cartooniverse

There’s a reason trumpet (and trombne) bells are shaped the way they are – they make the output louder and affect the frequencies of the horn. There’s theory going back quite a ways on this:

Gravity wells are inverse-square law forces with inverse-radius potentials. I don’t think musical instrument bels have these shapes.

Bottom line: It’s a coincidence.

Okay then.

Actually, I think it is less than a meaningless coincidence. Spacetime isn’t curved like the instrument bell. It is just that the instrument bell is a familiar three dimensional item that illustrates what curved two dimensional spacetime looks like. Whenever you talk about the curvature of spacetime, you kind of need an additional dimension to illustrate it with a physical model. But taken as a three dimensional item in flat or practically flat three dimensional space, the instrument bell isn’t illustrating anything and has no relevance in discussing curved three dimensional space.

Only if you play them loud enough.