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?

 

[sardar]

I can provide some insight into the applications of the acceleration four-vector mentioned in the WP article and the book by Tsamparlis.

One of the applications of the acceleration four-vector is in the study of particle physics. In particular, the annihilation of antiprotons involves the acceleration of these particles before they collide and annihilate with their corresponding particles, leading to the production of new particles. The acceleration four-vector helps in understanding the dynamics of this process and predicting the outcome of the annihilation.

The resonance of strange particles is another application of the acceleration four-vector. Strange particles, such as kaons and pions, have a short lifetime and decay into other particles. The acceleration four-vector can be used to study the decay of these particles and determine their properties, such as their mass and decay rate.

The radiation of an accelerated charge is also a well-known application of the acceleration four-vector. When a charged particle is accelerated, it emits electromagnetic radiation, which can be described using the acceleration four-vector. This application is particularly important in understanding high-energy particle accelerators and the radiation emitted by particles in these machines.

It is worth noting that the acceleration four-vector is a concept in classical mechanics and can be applied to quantum-mechanical systems as well. While Newton's laws do not hold exactly in quantum mechanics, the concept of acceleration can still be used to describe the dynamics of particles in quantum systems. The book by Tsamparlis may discuss the application of the acceleration four-vector in quantum-mechanical systems in a more general sense, rather than specifically discussing the first two applications mentioned in the WP article.

In conclusion, the acceleration four-vector has various applications in different branches of physics, including particle physics, classical mechanics, and quantum mechanics. Its usefulness lies in its ability to describe the dynamics of accelerated particles and predict the outcomes of various processes involving acceleration.