B Can elementary particles truly be at rest in an E field?

[nmsurobert]

I'm working on E fields and particles in E fields, and I was wondering if particles are ever truly accelerated from rest. I did some reading on how accelerators work and cathode tubes, but it seems that particles are always in some type of motion. Is this just a thing for introductory level physics. Similar to "frictionless surface" type problems?

 

[A.T.]

... it seems that particles are always in some type of motion. ...

Motion is relative. They are at rest in some reference frame.

 

[ZapperZ]

I'm working on E fields and particles in E fields, and I was wondering if particles are ever truly accelerated from rest. I did some reading on how accelerators work and cathode tubes, but it seems that particles are always in some type of motion. Is this just a thing for introductory level physics. Similar to "frictionless surface" type problems?

When something comes off with, say 2 eV of energy, and it is then accelerated to 10's, even 100's or 1000's of MeV, do you think that 2 eV initial energy has any significance when compared to making the approximation of it being initially "at rest"? Do you also consider the gravity from Alpha Centauri when calculating forces on a bridge?

Zz.

 

[Herman Trivilino]

I'm working on E fields and particles in E fields, and I was wondering if particles are ever truly accelerated from rest.

There's no such thing as truly at rest. A lot of time and expense has been spent over the centuries searching for physical evidence of the concept, and nothing has been found. Moreover, the consequences have been thoroughly worked out theoretically and have withstood very extensive experimental testing.

No matter how precise and how developed your experimental efforts become, there is always going to be some experimental uncertainty, so one might quibble that. But as @ZapperZ points out, that can easily be made negligible.

 

[olgerm]

Only particles that have (rest)mass can be in rest.

 

[Henryk]

With laser cooling, atoms were slowed down to the energy of the order of 20 neV!

 

[sophiecentaur]

With laser cooling, atoms were slowed down to the energy of the order of 20 neV!

But only in a particular reference frame.

 

[nmsurobert]

awesome. thank you guys. sometime I have these random questions and its hard to find answers to them.

 

[mfb]

But only in a particular reference frame.

It's a thermal energy, it is in the center of mass frame of the gas.

 

[vanhees71]

With laser cooling, atoms were slowed down to the energy of the order of 20 neV!

However you should note that "elementary particles" cannot be described as classical point particles anymore, because you need quantum theory, and being "at rest" is impossible due to the Heisenberg uncertatinty relation $\Delta x \Delta p_x \geq \hbar/2$. If the atom is in an energy eigenstate in the trap neither position nor momentum are determined and their probability distribution obey for sure the uncertainty relation. Even in the ground state the particles are never at rest!

 

[Henryk]

However you should note that "elementary particles" cannot be described as classical point particles anymore, because you need quantum theory, and being "at rest" is impossible due to the Heisenberg uncertatinty relation ΔxΔpx≥ℏ/2ΔxΔpx≥ℏ/2\Delta x \Delta p_x \geq \hbar/2. If the atom is in an energy eigenstate in the trap neither position nor momentum are determined and their probability distribution obey for sure the uncertainty relation

Let's get some numbers, shall we?. Take, for example, cesium atoms, atomic mass 133 = $2.2085^{-27}$ kg. At the energy of 20 neV = $3.2 \cdot 10^{-27}$. Substitute that into $p^2 = 2 E \cdot m$ and we get $p^2 = 1.413^{-53}$.
Now, in the laser cooling experiment, the atoms are confined, that means the average momentum is zero. Therefore, $<\Delta p^2> = p^2$. I.e. $\Delta p = 3.76^{-27}$ That allows us to calculate $\Delta x = \frac 12 \hbar / \Delta p$. Plug in the numbers and you get something like 14 nm!. Now, that is a billion times smaller than the space in which the atoms are confined in laser cooling experiments.
Yeah, THEORETICALLY no particle is at rest, but PRACTICALLY, a particle in a space that you can see with your eyes can have energy very close to rest.

 

[vanhees71]

Sure, at some point the classical approximation gets right. It's a question of accuracy needed to describe the situation. In your case a resolution of 14 nm is enough, and the classical particle picture accurate enough.