Orbital Path Length Contraction: Explained by Relativity

[neilparker62]

Hi

Just wondering about the orbital path of a high speed particle - eg electron in orbit. Is it length contracted? Then how do we manage nλ=2.π.r ?

Neil

 

[mfb]

nλ=2πr comes from Bohr's model, this has been replaced by quantum mechanics about 90 years ago.
With relativistic quantum mechanics, it is no problem to find orbitals for electrons even around heavy nuclei, where relativistic effects are important. It is problematic to switch to the view of the electron (because it does not have a fixed velocity).

 

[bcrowell]

Length contraction is a description of a difference in an observation between two different frames of reference. We're not doing any measurements in a frame of reference moving along with the electron, so there is no reason to convert to or from that frame.

 

[jartsa]

Hi

Just wondering about the orbital path of a high speed particle - eg electron in orbit. Is it length contracted? Then how do we manage nλ=2.π.r ?

Neil

Orbital path is length contracted, and wavelengths are length contracted. So we don't have a radius, and we have many different lambdas.

So we write: d = n * sum of lambdas, where d is distance traveled when going around the path once.

d changes smoothly when speed changes smoothly.(I assumed this was a question about a high speed hydrogen atom)

 

[sardar]

Hi Neil,

Thank you for your question about orbital path length contraction and its explanation by relativity. This is a very interesting topic and one that has been studied extensively in the field of physics.

To answer your question, yes, the orbital path of a high-speed particle, such as an electron in orbit, is indeed length contracted. This is a consequence of Einstein's theory of special relativity, which states that the length of an object moving at high speeds will appear shorter to an observer than its actual length. This phenomenon is known as length contraction.

Now, you may be wondering how this relates to the equation nλ=2.π.r, which describes the relationship between the wavelength (λ) of a particle's orbit and its radius (r). This equation is derived from classical mechanics and does not take into account the effects of relativity. However, when we consider the orbital path length contraction, we can see that the actual path of the particle will appear shorter to an observer, and therefore the wavelength will also appear shorter. This means that the value of n in the equation will be larger, compensating for the shorter wavelength, and resulting in the same value for 2.π.r.

In other words, the equation still holds true in the context of relativity, but the values for n and λ will be different due to the effects of length contraction. This is just one example of how relativity can affect our understanding of physical phenomena.

I hope this helps to answer your question and sheds some light on the fascinating concept of orbital path length contraction. If you have any further questions, please don't hesitate to ask. Happy exploring!

Sincerely,