Applications of the acceleration four-vector

[bcrowell]

Does anyone have any favorite applications of the acceleration four-vector?

More specifically, the WP article "four-acceleration," http://en.wikipedia.org/wiki/Four-acceleration (possibly written by former PF member CH), says, "Four-acceleration has applications in areas such as the annihilation of antiprotons, resonance of strange particles and radiation of an accelerated charge," with a reference to a book by Tsamparlis. The Tsamparlis is expensive, and I've only looked at it through Amazon's "look inside" keyhole. The acceleration vector is discussed in section 7.2. This section lists the same three applications as the WP article, but doesn't actually discuss any of them. I was able to find a discussion of the radiation application in section 13.16, but couldn't find any discussion of the first two, which seem explicitly quantum-mechanical. Anyone have any idea what the heck Tsamparlis had in mind there? It seems a little implausible to me that acceleration would be of any use in discussing a quantum-mechanical process, since Newton's laws hold in quantum mechanics only on the average.

 

[Bill_K]

Does anyone have any favorite applications of the acceleration four-vector?

Thomas precession. (See my blog.)

 

[Bill_K]

Ben, Tsamparlis' book is downloadable from elsewhere on the web, and turns out to contain a pretty detailed discussion of relativistic kinematics. He's also witten this supplementary http://extras.springer.com/2010/978-3-642-03836-5/140396_1_En_ESM.pdf.

But nothing further in either one about the two QM applications.

 

[George Jones]

Does anyone have any favorite applications of the acceleration four-vector?

The Sagnac effect, which is discussed in detail in (which I now have)

https://www.amazon.com/dp/3642372759/?tag=pfamazon01-20

http://www.springer.com/physics/the...+computational+physics/book/978-3-642-37275-9

I have just ordered (actually, my wife did, but she has yet to realize this ) this new, comprehensive, advanced book on special relativity. From the content (check the above links for more details), this seems to be an amazing book. Some of the material can be transferred wholesale to frames in general relativity.

1 Minkowski Spacetime
2 Worldlines and Proper Time
3 Observers
4 Kinematics 1
5 Kinematics 2
6 Lorentz Group
7 Lorentz Group as a Lie Group
8 Inertial Observers and Poincare Group
9 Energy and Momentum
10 Angular Momentum
11 Principle of Least Action
12 Accelerated Observers
13 Rotating Observers
14 Tensors and Alternate Forms
15 Fields on Spacetime
16 Integration in Spacetime
17 Electromagnetic Field
18 Maxwell Equations
19 Energy–Momentum Tensor
20 Energy–Momentum of the Electromagnetic Field
21 Relativistic Hydrodynamics
22 What About Relativistic Gravitation?

More specifically, the WP article "four-acceleration," http://en.wikipedia.org/wiki/Four-acceleration (possibly written by former PF member CH), says, "Four-acceleration has applications in areas such as the annihilation of antiprotons

In a relativistic cyclotron?