# Trouble understanding the SI definition of 1 second

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• vcsharp2003
In summary, the SI definition of the unit of time is based on the duration of 9192631770 periods of the radiation emitted when an electron in a caesium 133 atom transitions between two hyperfine levels of the ground state. This transition is caused by the interaction between the nuclear and electron spin, and the specific transition mentioned in the 1958 PRL paper is from the (4,0) to (3,0) states. The electron does not "decide" to emit radiation, but rather it is allowed by the physics of the constituents interacting with the electromagnetic field. The higher energy states are unstable, which contributes to the electron falling to a lower energy state.
vcsharp2003
Homework Statement:: The SI definition of unit of time says the following.
"The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom."
Relevant Equations:: None

I know an atom has protons and neutrons in its nucleus and electrons orbiting around it. When an electrons jumps (i.e. transitions) from a higher orbit/sub-orbit to a lower orbit/sub-orbit then energy in the form of radiation is released and this emitted radiation would have a certain frequency/time-period. So, my guess is that an orbiting electron is changing or transitioning to a lower energy orbit/sub-orbit to release the radiation that is the basis of definition of unit of time. But, I am not getting the exact meaning of "two hyperfine levels of the ground state" and therefore cannot decide what orbits/sub-orbits are being referred to by the transition.

Maybe hyperfine level means azimuthal quantum number that are denoted by s,p,d,f etc. sub-orbitals of main orbital.
Ground state meaning would the the original configuration when no electrons have been disturbed from their existing orbits and sub-orbits.

Also, Caesium-133 isotope element is composed of 55 protons, 78 neutrons, and 55 electrons with an electron configuration of 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 5s2 5p6 6s1

Maybe the outermost electron i.e. 6s1 is jumping to a higher level 6p1 due to energy absorption and then its jumping back from 6p1 to 6s1, which is what causes release of radiation that is being referred to in the SI unit of time definition.

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Delta2
This is pretty well described on the Wikipedia page: https://en.wikipedia.org/wiki/Caesium_standard

In short: Both states are 6s1 states. They differ in energy due to the interaction between nuclear and electron spin, leading to a hyperfine splitting.

dextercioby, hutchphd and BvU
Orodruin said:
They differ in energy due to the interaction between nuclear and electron spin, leading to a hyperfine splitting.
So, is hyperfine referring to different energy states of an electron while staying in the same orbit and sub-orbit?

vcsharp2003 said:
So, is hyperfine referring to different energy states of an electron while staying in the same orbit and sub-orbit?
Yes. Hyperfine splittings in general are due to nuclear-electron multipole interactions that break the symmetry that otherwise implies that the states are degenerate.

BvU and vcsharp2003
@Orodruin :
can you clarify why the authors of the 1958 PRL refer to the transition as (4,0)-(3,0) ?

Orodruin said:
Yes. Hyperfine splittings in general are due to nuclear-electron multipole interactions that break the symmetry that otherwise implies that the states are degenerate.
And I have another doubt. Why would an electron in caesium-133 undergo a transition of hyperfine states from a higher to a lower energy state, so as to emit energy? I think there is really no definite answer to this question in today's science. I know if energy is absorbed then electron(s) could jump to higher energy states, but if it emits radiation then this jump could be from higher to lower levels. Why would it decide to emit radiation?

Perhaps, all excited states are unstable according to observations and that is why electron goes back to its original lower energy configuration.

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Dale
BvU said:
@Orodruin :
can you clarify why the authors of the 1958 PRL refer to the transition as (4,0)-(3,0) ?
That would be the total spin depending on whether the nuclear and electron spins align or anti-align.

BvU
vcsharp2003 said:
Why would it decide to emit radiation?
Because the constituents interact with the electromagnetic field and this transition is possible.

Orodruin said:
Because the constituents interact with the electromagnetic field and this transition is possible.
But, also the fact that higher energy states are unstable may contribute to this happening.

vcsharp2003 said:
Why would it decide to emit radiation?
It doesn't "decide" anything. If allowed by the physics ,the event will occur. Why do the atoms in a lightbulb (LED or Tungsten filament) "decide" to emit light?

hutchphd said:
It doesn't "decide" anything. If allowed by the physics ,the event will occur. Why do the atoms in a lightbulb (LED or Tungsten filament) "decide" to emit light?
Still something must nudge the electron to fall to a lower state. Just because a specific path is available doesn't mean that the specific path will be taken.

vcsharp2003 said:
Still something must nudge the electron to fall to a lower state. Just because a specific path is available doesn't mean that the specific path will be taken.
Radioactive decay does not need anything to nudge it, so why would an electron falling to a lower state?

Orodruin
haruspex said:
Radioactive decay does not need anything to nudge it, so why would an electron falling to a lower state?
So, it seems that electrons falling to lower state is just a matter of scientific observations like principle of energy conservation is simply what has been scientifically observed and not something that we can derive in Physics unlike principle of conservation of momentum that we can derive from Newton's second law. Beyond observations of electron in an atom through scientific experiments and may be a mathematical model derived scientifically to model electron transition, its impossible to explain why it happens. We just need to accept it when dealing with Quantum Physics unlike Classical Physics.

hutchphd said:
The above link speaks of energy being absorbed, whereas I was thinking in terms of energy being emitted when I saw that definition of SI unit of time. That makes it easier, since now I don't need to bother about why an electron jumps back from higher energy state to its original ground state.

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BvU said:
@Orodruin :
can you clarify why the authors of the 1958 PRL refer to the transition as (4,0)-(3,0) ?
That's
$$\ket{F = 4, M_F=0} \rightarrow \ket{F = 3, M_F=0}$$
where ##F = I + J## the total angular momentum of the atom (##J## is the angular momentum of the electrons and ##I## the nuclear spin), and ##M_F## its projection on the z-axis.

For cesium-133 ##I= 7/2##, while the ground state 6s1 electronic configuration has ##J=1/2##, leading to the hyperfine doublet ##F=3## and ##F=4##.

The definition is based on the ##M_F=0## sublevels because, to first order, they are not affected by magnetic fields.

dextercioby and hutchphd
vcsharp2003 said:
So, it seems that electrons falling to lower state is just a matter of scientific observations like principle of energy conservation is simply what has been scientifically observed and not something that we can derive in Physics unlike principle of conservation of momentum that we can derive from Newton's second law. Beyond observations of electron in an atom through scientific experiments and may be a mathematical model derived scientifically to model electron transition, its impossible to explain why it happens. We just need to accept it when dealing with Quantum Physics unlike Classical Physics.
This is wrong. First, conservation of energy is related to the invariance of physical laws under time translation (Noether's theorem). Likewise, the theory describing the coupling between the atom and the electromagnetic field, quantum electrodynamics, shows how the probability of an atom transitioning from an excited state to the ground state + emitted photon increases with time.

vcsharp2003 said:
The above link speaks of energy being absorbed, whereas I was thinking in terms of energy being emitted when I saw that definition of SI unit of time. That makes it easier, since now I don't need to bother about why an electron jumps back from higher energy state to its original ground state.
The definition of the second does refer to absorption or emission, only to the frequency of the photons associated to the transition between the hyperfine levels. Modern atomic clocks using caesium ("caesium fountain clocks") start with atoms in the excited ##F=4## state.

Orodruin
DrClaude said:
This is wrong. First, conservation of energy is related to the invariance of physical laws under time translation (Noether's theorem).
My knowledge is limited unlike yours, since I have learned from various books that law of conservation of energy has never been violated and its therefore accepted due to this observation.

Noerther's theorem that you quoted appears to talk of scenarios with conservative forces, whereas law of conservation of energy is also true when there are non-conservative forces.

vcsharp2003 said:
My knowledge is limited unlike yours, since I have learned from various books that law of conservation of energy has never been violated and its therefore accepted due to this observation.
Any physical theory is subject to experimental scrutiny. Noether’s theorem states that if there is time translation invariance, then energy is conserved. If you find energy non-conservation then either there is no time translation invariance or classical mechanics is wrong.

Same thing here. Either the hyperfine transition occurs or the theory is wrong.

vcsharp2003 said:
The above link speaks of energy being absorbed, whereas I was thinking in terms of energy being emitted when I saw that definition of SI unit of time. That makes it easier, since now I don't need to bother about why an electron jumps back from higher energy state to its original ground state.
Metrologist here. You have the right idea. There is an animated video of the current cesium fountain on the NIST website if it helps with understanding the theory.

Cheers

vcsharp2003
Alatorre said:
Metrologist here. You have the right idea. There is an animated video of the current cesium fountain on the NIST website if it helps with understanding the theory.

Cheers
Can you post the NIST website link so I can find this animation?

DrClaude said:
This is wrong. First, conservation of energy is related to the invariance of physical laws under time translation (Noether's theorem).
This is (as below) what I have come across at my level of high school Physics from the book Fundamentals of Physics by Halliday & Resnick (Jearl Walker), which a lot of students at my level follow and highly respect. I believe it's a good and very reliable book on Physics for high school and undergrads. Why the authors chose to not explain using Noether's theorem is not clear to me. That theorem probably preceded the authors' lifetimes by many decades.

DrClaude said:
The definition of the second does refer to absorption or emission, only to the frequency of the photons associated to the transition between the hyperfine levels.
You mean does not refer to absorption or emission.
Yes, that makes sense.

vcsharp2003 said:
This is (as below) what I have come across at my level of high school Physics from the book Fundamentals of Physics by Halliday & Resnick (Jearl Walker), which a lot of students at my level follow and highly respect. I believe it's a good and very reliable book on Physics for high school and undergrads. Why the authors chose to not explain using Noether's theorem is not clear to me. That theorem probably preceded the authors' lifetimes by many decades.

View attachment 300662
View attachment 300663
Physics books lie. This is not malicious or unintended but rather a question of placing reasoning at the level of the target audience.

As far as Noether’s theorem is concerned, it is a relatively advanced topic best covered in analytical mechanics through the Lagrangian formalism (or its corresponding symmetry statements in the Hamiltonian formalism).

pbuk
Orodruin said:
Physics books lie. This is not malicious or unintended but rather a question of placing reasoning at the level of the target audience.
Sorry, but I don't agree with you when you say that a book so well accepted for the last many decades all over the world is lying. For you that may be true. The authors won't lie or distort facts based on target audience. While I understand that numerical answers to some questions may be incorrect due to misprints in the book or something else, but lying about fundamental laws to students makes no sense to me.

This book and its authors have helped millions of students all over world and not just in US. It's too imaginary to me when someone says they are lying about Law of Conservation of Energy.

Following is how well regarded this book is as per https://en.wikipedia.org/wiki/Robert_Resnick.

"The book has been used widely and is considered to have revolutionized physics education. Now in its tenth edition in a five-volume set revised by Jearl Walker, and under the title Fundamentals of Physics, it is still highly regarded. It is noted for its clear standardized diagrams, very thorough but highly readable pedagogy, outlook into modern physics, and challenging, thought provoking problems. In 2002 the American Physical Society named the work the most outstanding introductory physics text of the 20th century.[3]"

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Moderator's note: Thread has been moved to Other Physics Topics. Some off topic posts have been deleted. All posters, please keep the discussion on topic.

Thread reopened.

jbriggs444
Orodruin said:
As far as Noether’s theorem is concerned, it is a relatively advanced topic best covered in analytical mechanics through the Lagrangian formalism (or its corresponding symmetry statements in the Hamiltonian formalism).
Absolutely. Conservation of energy is a concept that is introduced early in Physics (generally at the beginning of high school), and it will take you a long way - 1 or 2 years into college.

You need to learn a lot of mathematics (calculus, ordinary differential equations, vector calculus, partial differential equations, Lagrangian mechanics) before you are ready to use Noether's theorem.

vcsharp2003 said:
I am not getting the exact meaning of "two hyperfine levels of the ground state"
As others have explained, It means that the state that is normally referred to as the "ground state" of the Cs-133 atom is actually two states with slightly different energies, because of the interaction between the single unpaired electron spin of the 6s electron and the spin of the nucleus. The difference between those two energies corresponds to a specific photon frequency.

vcsharp2003 said:
Perhaps, all excited states are unstable
Yes, this is correct. Since the electromagnetic field is always present, any atom in an excited state can interact with the electromagnetic field to emit a photon and drop to a lower energy state. This is called "spontaneous emission" and does not require any external "trigger" event to happen.

vcsharp2003 said:
also the fact that higher energy states are unstable may contribute to this happening.
The fact that excited states are unstable is the same thing as interaction with the electromagnetic field happening. See above.

vcsharp2003 said:
it seems that electrons falling to lower state is just a matter of scientific observations
It has certainly been observed, but you seem to be implying that we don't have a good theoretical understanding of it. That is not correct; the detailed theory of spontaneous emission was worked out decades ago.

vcsharp2003 said:
like principle of energy conservation is simply what has been scientifically observed and not something that we can derive in Physics unlike principle of conservation of momentum that we can derive from Newton's second law.
First, I think you mean Newton's third law here, not his second; that's the one that is equivalent to momentum conservation in Newtonian physics.

Second, as others have commented, energy conservation can be derived; the derivation uses Noether's theorem. So does the modern derivation of conservation of momentum; Newton's third law in the modern viewpoint is viewed as a consequence of conservation of momentum, not the other way around.

Also, the "energy" in the conservation law derived from Noether's theorem is not the only kind of conserved "energy" in physics. See further comments below.

vcsharp2003 said:
Beyond observations of electron in an atom through scientific experiments and may be a mathematical model derived scientifically to model electron transition, its impossible to explain why it happens.
This is not correct. See above.

vcsharp2003 said:
Noerther's theorem that you quoted appears to talk of scenarios with conservative forces
No, it applies, as @Orodruin said, whenever there is time translation symmetry.

vcsharp2003 said:
Why the authors chose to not explain using Noether's theorem is not clear to me.
Because they are talking about a different kind of "conservation of energy" from the one that Noether's theorem is about. The kind of "conservation of energy" that Halliday and Resnick are saying has been confirmed by many experiments deals with locally measured forms of energy, work done by one system on another, etc.; in relativity, this law is expressed as the divergence of the stress-energy tensor being zero. The conserved "energy" appearing in Noether's theorem when there is time translation symmetry is not the same thing; in relativity, it appears as a conserved quantity associated with a timelike Killing vector field in a region of spacetime, and might include components like "potential energy" in a gravitational field that are not locally measurable.

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vcsharp2003
Orodruin said:
Physics books lie.
I don't think this is a useful description in general, but in this particular case, I think it's incorrect regardless of one's attitude towards the general question involved (discussion of which is probably off topic for this thread). The "conservation of energy" Halliday and Resnick are talking about is not the kind embodied in Noether's theorem; it's the kind embodied in the divergence of the stress-energy tensor being zero. See my post #32 just now in response to the OP.

vcsharp2003
PeterDonis said:
I don't think this is a useful description in general, but in this particular case, I think it's incorrect regardless of one's attitude towards the general question involved (discussion of which is probably off topic for this thread). The "conservation of energy" Halliday and Resnick are talking about is not the kind embodied in Noether's theorem; it's the kind embodied in the divergence of the stress-energy tensor being zero. See my post #32 just now in response to the OP.
Well, I was making the statement a bit tongue-in-cheek and general. That physics textbooks do not generally tell the whole truth is to be expected since many times the intended audience is not prepared for that.

With apologies

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