[cardguy]

Why does Pi appear in the equation underpinning his Genereal Theory of Realtivity?

Not the famous E=mc2 equation. But the real one...



Sean Carroll has the answer.

http://www.preposterousuniverse.com/blog...in-and-pi/

[RexImperator]

Makes me (kinda) miss school. Classical physics always seemed so straightforward compared to quantum mechanics.

[cardguy]

One of the highlights of my life was when we were taught about particle accelerators.

My Dad was actually my physics teacher - which is pretty weird. But it is what it is.

Anyway - I should ask him about this again - but last time I did I don;t think he recalled what I was getting at.

It was some ingenious calculation - where by moving around the different constants in the relevent equation - it meant that the larger diameter of a particle accelerator was - the faster the particles inside would go.

No extra energy was needed - it just came as a natural consequence of making the radius of the circle they travelled in bigger. Which is why CERN has a radius of 4.5km.

It was a really simple and ingenious discovery. And was a simple hack which opened the way for scientists to accelerate particles to much higher speeds and for very little extra effort.

I think the guy who discovered this won a Nobel Prize for figuring this out.

Anyway - that is as much as I can recall. Does it ring any bells with anyone else? I would love to check out the exact details again. And unfortunately - the whole thing is a bit too convoluted to find easily through a search on Google.

The whole thing was a lovely piece of ingenious thinking. And reminded me of the delight I get from learning a sneaky new magic trick (I'm a magician).

[RexImperator]

Not claiming I know the answer but isn't it all just a result of the curvature of the particle path as related to the strength of the magnetic field? It's a cross-product, or in other words, magnetic fields always cause acceleration at a right angle to the velocity (direction of travel).

[Architekt]

Pi is a geometrical constant. It pops up everywhere in the derivation of physical equations

[Parlay44]

Anytime you see Pi in an equation it means it's a periodic or repeating function like a Sine wave.
It makes sense since you're talking about the speed of light. Light is a wave so you have to describe
it mathematically in terms of Pi.

[RexImperator]

This is actually the more interesting relation between geometry and general relativity (which is what I thought the thread was going to be about):

http://www.daviddarling.info/encyclopedi...metry.html

[ElBorrachoInfamoso]

Probably because somewhere in the derivation, he assumed a perfectly spherical volume.

[spalex]

Because something in there is round.

That's my guess.

[Ensam]

(04-28-2014 07:43 PM)cardguy Wrote:  

One of the highlights of my life was when we were taught about particle accelerators.

My Dad was actually my physics teacher - which is pretty weird. But it is what it is.

Anyway - I should ask him about this again - but last time I did I don;t think he recalled what I was getting at.

It was some ingenious calculation - where by moving around the different constants in the relevent equation - it meant that the larger diameter of a particle accelerator was - the faster the particles inside would go.

No extra energy was needed - it just came as a natural consequence of making the radius of the circle they travelled in bigger. Which is why CERN has a radius of 4.5km.

It was a really simple and ingenious discovery. And was a simple hack which opened the way for scientists to accelerate particles to much higher speeds and for very little extra effort.

I think the guy who discovered this won a Nobel Prize for figuring this out.

Anyway - that is as much as I can recall. Does it ring any bells with anyone else? I would love to check out the exact details again. And unfortunately - the whole thing is a bit too convoluted to find easily through a search on Google.

The whole thing was a lovely piece of ingenious thinking. And reminded me of the delight I get from learning a sneaky new magic trick (I'm a magician).

I believe you're referring to Ernest Lawrence.
http://en.wikipedia.org/wiki/Ernest_Orlando_Lawrence

Linear accelerators are the most efficient because they have an infinite radius of curvature, but they also have to be very long in order to achieve any kind of energy. The round particle accelerators gain an advantage because they can cycle the same particles around over and over again effectively creating an infinitely long accelerator. However each time the particles path is altered they lose energy (in the form of synchrotron radiation). The total momentum change per revolution is the same regardless of diameter, but the energy loss per unit length of circumference goes down as radius goes up.

If you're curious why physical laws always tend to look the same when they're written down I highly recommend you watch Feynman's Character of Physical Law lecture series.

[RexImperator]

Good call Ensam.

http://www.aip.org/history/lawrence/epa.htm

Quote:

A few quick calculations showed that such a device might capitalize on the laws of electrodynamics. The centripetal acceleration of a charged particle in a perpendicular magnetic field B is evB/c, where e is the charge, v the particle's velocity, and c the velocity of light. The mechanical centrifugal force on the particle is mv2/r, where m is the mass and r the radius of its orbit. Balancing the two forces for a stable orbit yields what is now known as the cyclotron equation: v/r = eB/mc.

Lawrence was surprised to find that the frequency of rotation of a particle is independent of the radius of the orbit: f = v/2(pi)r= eB/2(pi)mc, with r disappearing from the equation. The circular method would thus allow an electric field alternating at a constant frequency to kick particles to ever higher energies. As their velocities increased so did the radius of their orbit. Each rotation would take the same amount of time, keeping the particles in step with the alternating field as they spiralled outward.

Cardguy, if the story was about Lawrence, then that page should ring a bell.

However, a cyclotron is actually a different kind of accelerator than what they have at CERN. They are much much smaller. (They can fit inside a room.)

[Ensam]

Actually my explanation isn't exactly correct - it's been about ten years since I worked around particle accelerators - but the jist is about right.

[cardguy]

Thanks guys - the Cyclotron is what I had in mind.

It is rare you see an ingenious discovery in physics like that which you can actually understand! :-)