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Re: [Phys-L] Fwd: [PTSOS] spacetime simulator: flexible conduit?



Excellent points.

I just went back and reread the whole tape & darts article (http://www.av8n.com/physics/geodesics.htm) looking at the correctness of the analogy in various respects. It's good.

In fact, the only "non-win" side I see to the tape & darts is that it's not as cool as the marbles orbiting the mass on the trampoline. Watching the trampoline sink and the fabric adjust -- not just at the location of the heavy mass but also at various distances from the heavy mass -- is cool. Seeing marbles which used to roll in a straight line on the undeformed trampoline (yes, if it's horizontal) now follow paths that cause them to orbit the heavy mass is cool. Seeing an "Earth-Moon" system orbit the "Sun" is cool -- although I had serious doubts whether what we were actually seeing was an Earth-Moon type situation. Having the marbles keep on rolling on a variable surface has a much greater coolness factor than sticking tape down on a surface with a few discontinuities in surface orientation. (Now there's a place where the darts analogy is weak: pretty hard to make a gradually varying surface, you're limited to using a finite set of fixed darts.)

How could the "wow factor" be reinserted? On a shelf in the demo room we have a "constant velocity car" that trundles along at a pretty constant speed, and can climb small slopes because of its rubberized treads. I thought of putting in on a surface with darts, but they'd have to be larger than the car's wheelbase. No, in any case, the constant velocity idea is not true to GR or even Newtonian dynamics, so motion can't be reinserted into the dart demo that way.

The only way I can think of to make it an _animation_, is to video the process of laying down the tape, and remove the hands from the scene, or simply make a virtual animation of the whole thing. But I tend to return to virtual animations too readily, so I was hoping for a good real demo.

KC

-----Original Message-----
From: phys-l-bounces@mail.phys-l.org [mailto:phys-l-bounces@mail.phys-l.org] On Behalf Of John Denker
Sent: Tuesday, 17 July 2012 9:32 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] Fwd: [PTSOS] spacetime simulator: flexible conduit?

On 07/17/2012 05:52 PM, Ken Caviness wrote:

But I really doubt whether even 1% of the people notice or learn
incorrect physics from the non-fitting parts of the demo. It should
be taken only as an analogy: the heavy mass deforms the surface, it's
no longer flat, and marbles on the no-longer flat surface behave
differently! That much is shared by the demo and the actual theory.
As good as many analogies, I'd say.

We agree that all analogies are imperfect ... but I insist they are not all _equally_ imperfect.

Sometimes one analogy is apt in one respect while another is apt in another respect, such that taken together they tell far more of the story than either one separately. Ask yourself what goes in the middle of the following diagram, such that it is in some ways related to the set of blue things and in some ways related to the set of triangular things:
http://www.av8n.com/physics/img48/blue-triangle.png

One should never overreact *or* underreact to the imperfections of an analogy. Deciding which analogy to use, and how to use it, is sometimes not easy. It requires judgment.
a) Sometimes tricky tradeoffs must be made.
b) Sometimes not. Sometimes one analogy is Pareto superior to another.

One question that is almost always fair game is this: How much would it cost to come up with a better analogy?

In the present case, before you run off and spend time and money building a trampoline, consider how much better *and* cheaper it would be to stock up on masking tape plus a collection of suitable curved objects.

I suggest that students making geodesics using tape will actually learn something useful. They will learn about how geodesics actually behave. This has application to geography, navigation, and aviation (great circles), optics (Fermat's principle), classical physics (principle of least action), plus quantum mechanics ... as well as to general relativity.

The trampoline trick is deceptive. Virtually everything that the youtube video says about curved spacetime will have to be unlearned.
In contrast, none of the tape geodesic ideas will have to be unlearned.
Sure, there are imperfections in the tape model, but it is rather obvious what the imperfections are, so nobody is going to be deceived.

Not all analogies are equally imperfect!

The geodesic lesson (compared to the trampoline trick)
a) requires less cost and less laborious preparation;
b) has less downside in terms of deceptions and misconceptions; and
c) has more upside in terms of correct conceptions and applications.

Looks like a win/win/win to me.
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