If different elementary particles are at highly different relative velocities, how can it be said that an atom or larger mass is in its own frame?

[CrypticFish]

I'll try to keep this concise:

Elementary particles have very different relative velocities, with quarks and gluons moving at or near C, and electrons being much slower (eg sometimes ~0.7% C). With this in mind, an atom or larger mass is typically considered to be in its own reference frame, despite its components being at very different relative velocities. Why is this?

For example, a human does not perceive any time dilation or length contraction between the particles of their own body. Is this because the experience of a larger mass is more or less the average of its component particles? Would it be true that if a quark or electron could perceive the world, there would be a high degree of difference to how it perceives the world compared to a human that can be attributed to relativity, in essence, experiencing a significantly different degree of length contraction, time dilation, and events that seem simultaneous to us may not be simultaneous to the particle, etc? 

[Genady]

When a massive body is considered "in its own reference frame" it means in a frame where its momentum is 0.

[exchemist]

54 minutes ago, CrypticFish said:

I'll try to keep this concise:

Elementary particles have very different relative velocities, with quarks and gluons moving at or near C, and electrons being much slower (eg sometimes ~0.7% C). With this in mind, an atom or larger mass is typically considered to be in its own reference frame, despite its components being at very different relative velocities. Why is this?

For example, a human does not perceive any time dilation or length contraction between the particles of their own body. Is this because the experience of a larger mass is more or less the average of its component particles? Would it be true that if a quark or electron could perceive the world, there would be a high degree of difference to how it perceives the world compared to a human that can be attributed to relativity, in essence, experiencing a significantly different degree of length contraction, time dilation, and events that seem simultaneous to us may not be simultaneous to the particle, etc? 

In an atom, the nucleus does not move much relative to the reference frame of the molecule it is part of, and the electrons' wave-particle behaviour is modelled successfully in most cases by Schrödinger's equation which is non-relativistic.  (There are exceptions with the electrons in some heavy elements with very high nuclear charge, for which relativistic treatment is needed. Famously, the colour of gold is accounted for by this.) So actually relativity does not come into biochemistry that much (unless you are a purist who demands that particle "spin" be  treated ab initio rather than as a given feature.)

Where do you get 0.7c from, for the electron? In an atom one can't really speak of the electron's velocity (Heisenberg etc), so that sounds a bit dodgy to me. 

 

[Genady]

1 hour ago, CrypticFish said:

a high degree of difference to how it perceives the world compared to a human that can be attributed to relativity, in essence, experiencing a significantly different degree of length contraction, time dilation, and events that seem simultaneous to us may not be simultaneous to the particle, etc? 

They are differences between reference frames, and they exist regardless of there being or not anything to perceive them.

[CrypticFish]

3 hours ago, Genady said:

When a massive body is considered "in its own reference frame" it means in a frame where its momentum is 0.

To clarify, what I am getting at is that I am a bit confused on how an atom or larger body can be said to have a momentum of 0 and thus be in its own reference frame when it's components do not have a momentum of zero. Obviously, functionally, a larger mass can be considered as being in its own reference frame that can be compared to other reference frames. Just confused on how it works out on the tiniest level.

 

2 hours ago, Genady said:

They are differences between reference frames, and they exist regardless of there being or not anything to perceive them.

Just used perception for simplifications sake. Ultimately I'm trying to get at a comparison of the frame of a fundamental particle and the frame of a larger mass, i.e the timing of events, their relative position and the difference in these traits between frames (and ultimately if I am correct in saying the components of a larger mass exist in a significantly different frame to a larger mass).

[Genady]

11 minutes ago, CrypticFish said:

To clarify, what I am getting at is that I am a bit confused on how an atom or larger body can be said to have a momentum of 0 and thus be in its own reference frame when it's components do not have a momentum of zero. Obviously, functionally, a larger mass can be considered as being in its own reference frame that can be compared to other reference frames. Just confused on how it works out on the tiniest level.

 

Just used perception for simplifications sake. Ultimately I'm trying to get at a comparison of the frame of a fundamental particle and the frame of a larger mass, i.e the timing of events, their relative position and the difference in these traits between frames (and ultimately if I am correct in saying the components of a larger mass exist in a significantly different frame to a larger mass).

You can consider any system of moving components in any reference frame. In any frame, the momentum of the system is a sum of momenta of the components. In some frame, this sum is 0. This is the "system's own" frame.

[exchemist]

17 minutes ago, CrypticFish said:

To clarify, what I am getting at is that I am a bit confused on how an atom or larger body can be said to have a momentum of 0 and thus be in its own reference frame when it's components do not have a momentum of zero. Obviously, functionally, a larger mass can be considered as being in its own reference frame that can be compared to other reference frames. Just confused on how it works out on the tiniest level.

 

Just used perception for simplifications sake. Ultimately I'm trying to get at a comparison of the frame of a fundamental particle and the frame of a larger mass, i.e the timing of events, their relative position and the difference in these traits between frames (and ultimately if I am correct in saying the components of a larger mass exist in a significantly different frame to a larger mass).

You can in principle choose anything, of any size, and consider it either from the point of view of its own frame of reference or that of one of its components (if it is a composite entity) , depending on what you are trying to do. In the case of an atom, one would normally take the frame of reference of the nucleus as the reference frame of the atom, as that is quite pointlike for most purposes and happens to be where the centre of mass is  - and the centre of any electric field, in the case of an ion. The electron is problematic, as it has neither defined position nor a defined path of motion. 

 

Edited July 10, 2023 by exchemist

[CrypticFish]

3 hours ago, exchemist said:

Where do you get 0.7c from, for the electron? In an atom one can't really speak of the electron's velocity (Heisenberg etc), so that sounds a bit dodgy to me. 

I should clarify I am just a layman by the way, so sorry if anything I say seems silly. 

The 0.7c thing mainly comes from the various sources I have seen recently which attribute some velocity to an electron, but you are right to say it probably doesn't have velocity in the traditional sense, I think the 0.7c thing comes from people attributing a traditional orbit to an electron on further reading. 

6 minutes ago, Genady said:

You can consider any system of moving components in any reference frame. In any frame, the momentum of the system is a sum of momenta of the components. In some frame, this sum is 0. This is the "system's own" frame.

Can you clarify on why the sum of momenta is zero in the local frame of a system? I interpret that as the total value of momentum equalling zero because momentum in any one direction is negated by momentum in the opposite direction thus it essentially averages out to zero. Or is it due to the components having equal relative velocity? 

3 minutes ago, exchemist said:

You can in principle choose anything, of any size, and consider it either from the point of view of its own frame of reference or that of one of its components (if it is a composite entity) , depending on what you are trying to do. In the case of an atom, one would normally take the frame of reference of the nucleus as the reference frame of the atom, as that is quite pointlike for most purposes and happens to be where the centre of mass is  - and the centre of any electric field, in the case of an ion. The electron is problematic, as it has neither defined position nor a defined path of motion. 

 

So am I being misguided in focusing too much on the relative velocity between quarks/gluons and electrons due to the lack of defined position or motion for an electron?

[Genady]

32 minutes ago, CrypticFish said:

the total value of momentum equalling zero because momentum in any one direction is negated by momentum in the opposite direction thus it essentially averages out to zero.

This is essentially correct. More generally, momentum is a 3-dimensional vector with a magnitude and a direction. When you sum several such vectors, you get a vector. In some frame, this final vector is 0. This is the frame we're talking about.

Edited July 10, 2023 by Genady

[exchemist]

1 hour ago, CrypticFish said:

I should clarify I am just a layman by the way, so sorry if anything I say seems silly. 

The 0.7c thing mainly comes from the various sources I have seen recently which attribute some velocity to an electron, but you are right to say it probably doesn't have velocity in the traditional sense, I think the 0.7c thing comes from people attributing a traditional orbit to an electron on further reading. 

Can you clarify on why the sum of momenta is zero in the local frame of a system? I interpret that as the total value of momentum equalling zero because momentum in any one direction is negated by momentum in the opposite direction thus it essentially averages out to zero. Or is it due to the components having equal relative velocity? 

So am I being misguided in focusing too much on the relative velocity between quarks/gluons and electrons due to the lack of defined position or motion for an electron?

There are real physicists on the forum who are better qualified than I on this but I think so, yes. As I say, the Schrödinger equation almost always works for electrons in the atom and that does not consider relativistic effects, which would not be so if the electron were treated as moving at a significant fraction of c.

To treat a case like gold in  terms of the Schrödinger equation, my understanding is one has to resort to "relativistic mass" to account for the observed absorption in the blue part of the spectrum that makes gold appear yellow, i.e. the electrons behave as if they are heavier due to effectively travelling at relativistic - though undefined - "speeds". But this explanation is not very rigorous (modern physics does not use the concept of relativistic mass any more). I'm sure the real physicists would do the whole thing over using other mathematics.

As for motion of quarks within the nucleus, that is out of my league.   

[Mordred]

The Klein Gordon equation is Lorentz invariant. So it's a useful choice where relativistic effects become involved. It modifies from the Schrodinger equation. QfT itself employs the Klein Gordon for this reason. However the Dirac equations are also Lorentz invariant. You can also use the Dirac equations for quarks though you would need the Gell Mann matrices rather than the gamma matrices. Both QED SU(2) and QCD SU(3) incorporate the Pauli matrices which are Hermitean and via the Pauli four momentum Lorentz invariant.

 

Edited July 10, 2023 by Mordred

[swansont]

3 hours ago, exchemist said:

To treat a case like gold in  terms of the Schrödinger equation, my understanding is one has to resort to "relativistic mass" to account for the observed absorption in the blue part of the spectrum that makes gold appear yellow, i.e. the electrons behave as if they are heavier due to effectively travelling at relativistic - though undefined - "speeds". But this explanation is not very rigorous (modern physics does not use the concept of relativistic mass any more). I'm sure the real physicists would do the whole thing over using other mathematics.

The whole relativistic mass explanation is a pop-sci retelling of the physics; the solutions to the equations are in terms of the energy, for which you get a correction in the relativistic case (and this is how the journal article I once looked up treated it). It’s in the pop-sci retelling they talk about relativistic mass, or take the kinetic energy and get a velocity.

[exchemist]

1 minute ago, swansont said:

The whole relativistic mass explanation is a pop-sci retelling of the physics; the solutions to the equations are in terms of the energy, for which you get a correction in the relativistic case (and this is how the journal article I once looked up treated it). It’s in the pop-sci retelling they talk about relativistic mass, or take the kinetic energy and get a velocity.

Is that on the basis of still using Schrödinger's equation, in which case I suppose you must mean some correction to the Hamiltonian (?) , or would it be on the basis of the Klein-Gordon equation, as @Mordred suggests.

[swansont]

I think it’s the use of K-G instead of Schrödinger

[exchemist]

3 minutes ago, swansont said:

I think it’s the use of K-G instead of Schrödinger

OK. I'm afraid the pop-sci version is all we got as chemists at university (e.g. in my copy of Cotton and Wliklnson's Inorganic Chemistry), since while we were familiar with the Schrödinger equation, the Klein-Gordon one would have been out of scope. I know just about enough to realise it's rather handwavy and unsatisfactory, but that's it.