"Speed limit of light" analogy

[DaveC426913]

Thought of this while driving home from the lofters.

As if we need one more analogy for relativistic speed limits, but here goes...

Q: How is c a speed limit? Why can't we just go a little faster and exceed it?

A: Behold an analogy as to how geometry can limit movement, no matter how fast you go.

Think of one of those swing merry-go-rounds at the fair. Here's a small one:

(Those are Indestructible High-G Robot Child-Androids.)

The pole is exactly 2.99792458 metres tall, a value we will call p.
The Propulsion unit of the merry-go-round has complete freedom to increase or decrease the device's revolutions, but has no ability to directly affect its altitude.
As the IHGRCAs increase their revolutions, their altitude will approach p.
At 100revs, they will reach .99p.
At 200revs, they will reach .999p.
At 300revs, they will reach .9999p.
They can continually increase their revs without bound, yet their altitude will never reach p, merely asymptotically approach p. And no amount of revs will ever allow them to exceed p; the attempt is obviously preposterous.

So the limit of their altitude is dictated, not by some retarding factor, or by some inability to put more effort into it, but by the mere geometry between revs and altitude.

Clearly, this does not explain the physics of c as a speed limit - there will be more questions - but what it does do is get relativity students to start thinking about spacetime as a geometry. A big step, IMHO.

 

[Mentz114]

That is thought provoking. The harder you push the heavier it gets.

On a lighter note I was reminded of the centrifugal speed controller we used to have on our old steam cyclotron

 

[jerromyjon]

Beautiful analogy, I love it! Especially the relativistic mass aspect. Obviously the "mass" of a person on a swing doesn't really change.

 

[OCR]

On a lighter note I was reminded of the centrifugal speed controller we used to have on our old steam cyclotron

Lol... it was sometimes called a "flyball" governor.

And no amount of revs will ever allow them to exceed p; the attempt is obviously preposterous.

It is a good analogy...

 

[Orodruin]

Unfortunately, those child andriods could simply bring a big stone and once close to the horizontal throw it in the transversal direction. This would lead to oscillations around the minimum of the effective potential.

 

[Mentz114]

Unfortunately, those child andriods could simply bring a big stone and once close to the horizontal throw it in the transversal direction. This would lead to oscillations around the minimum of the effective potential.

This shows something else about relativity - a self-propelled body is not subject to the restriction and can develop an horizon. Although there are no coordinates in which light-speed is achieved, part of the universe has gone awol behind the horizon.

I don't know, maybe this is pushing the analogy too far.

 

[Noctisdark]

I loved that analogy, but a better way of thinking of it (without analogy) is the all fundamental interaction happen to be mediated at the speed of light (all bosons only move at the speed of light), if you are getting to c, you are not well interacting with the outer world, so you see times dilates and length contracts, you can never get to c because at that particular speed because you'll be "out of the universe" even your atoms don't interact with the universe, the only way they feel each other is by sending photons that move very fast to be aware of each other and interact, so if you reach c we can't feel you, but we do, that mean that it's impossible to get to c .

 

[Unified28]

I like the analogy. What is true about it is that regardless of the angular momentum there is a limit. However what is this limit? In this analogy it is due to that the direction of the force vector changes based on the height of the chairs. Where do the force vectors end up? It ends up pulling a string with infinite tolerance keeping it in place. So in terms of real space or space-time what really happens? Two infinitely large forces keeping each other in check? I could translate it into that it would be as fast as a wave can travel without breaking apart. But why do they not simply break apart then? If it cannot break apart, why is there a limit to its motion?

 

[PhanthomJay]

The analogy is interesting, in that without gravity, our child swings horizontally at exactly the height p, whereas also without Gravity, space time geometry is not curved. Gravity with a capital G...the Universe's mystery. Now if I knew what a 'lofter' was, I might head there to do some more thinking about this...

 

[DaveC426913]

The analogy is interesting, in that without gravity, our child swings horizontally at exactly the height p, whereas also without Gravity, space time geometry is not curved. Gravity with a capital G...the Universe's mystery.

That's the caveat. It does not model the physics, all it does is demonstrate a geomretical limit.

Now if I knew what a 'lofter' was, I might head there to do some more thinking about this...

Sailmaking and canvas. I am adding a set of handrails to my dodger.