I Trouble understanding the SI definition of 1 second

[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.

 

[Orodruin]

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.

 

[BvU]

http://www.leapsecond.com/history/1958-PhysRev-v1-n3-Markowitz-Hall-Essen-Parry.pdf
says it's about the transition $$(4,0)-(3,0)$$
And it's not about electron orbits changing but about coupling of magnetic field from electron orbits with magnetic field from nuclear spin.

https://chem.libretexts.org/Bookshe...e_and_Hyperfine_Structure/Hyperfine_Structure

 

[vcsharp2003]

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?

 

[Orodruin]

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]

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

 

[vcsharp2003]

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.

 

[Orodruin]

@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.

 

[Orodruin]

Why would it decide to emit radiation?

Because the constituents interact with the electromagnetic field and this transition is possible.

 

[vcsharp2003]

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.

 

[hutchphd]

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?

 

[vcsharp2003]

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.

 

[haruspex]

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?

 

[hutchphd]

http://gisweb.massey.ac.nz/topic/we...asure frequency,that mankind has yet achieved.

 

[vcsharp2003]

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.

 

[vcsharp2003]

http://gisweb.massey.ac.nz/topic/webreferencesites/gps/usnavy/cesium.html#:~:text=Today, cesium clocks measure frequency,that mankind has yet achieved.

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.

 

[DrClaude]

@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.

 

[DrClaude]

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.

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.

 

[vcsharp2003]

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.

 

[Orodruin]

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.

 

[Alatorre]

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]

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?

 

[vcsharp2003]

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.

 

[vcsharp2003]

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.

 

[Orodruin]

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.

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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).

 

[vcsharp2003]

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]"

 

[Alatorre]

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

Here is the link to the original cesium fountain.
https://www.nist.gov/pml/time-and-frequency-division/time-realization/primary-standard-nist-f1

Here is the new time standard:
https://www.nist.gov/video/nist-lau... new atomic,and frequency standard since 1999.

cheers

 

[jbriggs444]

The authors won't lie or distort facts based on target audience.

Perhaps a trip to https://en.wikipedia.org/wiki/Lie-to-children is in order.

 

[PeterDonis]

Thread closed for moderation.

 

[PeterDonis]

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.

 

[pbuk]

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.

 

[PeterDonis]

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.

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.

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.

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.

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.

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.

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.

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.

 

[PeterDonis]

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.

 

[Orodruin]

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.

 

[hutchphd]

With apologies

 

[sophiecentaur]

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?

As far as I understand, this is all about resonance. When in the presence of EM radiation of the right frequency, an atom will absorb and then emit that frequency. This is much the same as with a quartz crystal (but not in the quantum domain). Most transitions are not particularly well defined; in general, the f in the hf is not easily reproduced accurately enough. The particular transition that's chosen for the standard is easy to use (practical reasons) and to reproduce accurately. This is a general principle for choosing any standard for a unit. The atoms can be kept in an environment that gives a consistent value of energy change between the two chosen states. There are many possible choices for standards; this particular one has been chosen.

 

[PeterDonis]

As far as I understand, this is all about resonance. When in the presence of EM radiation of the right frequency, an atom will absorb and then emit that frequency.

More precisely, the cesium clocks that are used as time standards to define the SI second at places like the NIST have cesium atoms that are put in a cavity that contains EM radiation, and then allowed to fall back out of the cavity to see if they emit EM radiation. If they emit EM radiation, it means they must have absorbed it while they were in the cavity; and if the frequency of the EM radiation in the cavity is tuned just right, it will maximize the emission of EM radiation by the cesium atoms when they fall out of the cavity--i.e., the EM radiation in the cavity is in resonance with the desired hyperfine transition frequency that defines the SI second.

More here:

https://www.nist.gov/news-events/news/1999/12/nist-f1-cesium-fountain-clock

 

[haruspex]

This is wrong. First, conservation of energy is related to the invariance of physical laws under time translation (Noether's theorem).

Does that make it wrong to say the conservation law is based on experiment rather than theory? Noether's theorem says it is equivalent to the assumption that the laws are invariant under time translation, not that either is necessarily true.

 

[PeterDonis]

Does that make it wrong to say the conservation law is based on experiment rather than theory? Noether's theorem says it is equivalent to the assumption that the laws are invariant under time translation, not that either is necessarily true.

Noether's theorem, as a mathematical theorem, is of course based on the assumption of time translation symmetry, since that is a premise of the theorem.

But it can be tested by experiment whether or not a particular physical system actually has time translation symmetry, so it can be tested by experiment whether Noether's theorem, the mathematical theorem, is actually true of our physical world: just test to see whether the "energy" the theorem defines is in fact conserved if, and only if, the physical system being tested has time translation symmetry. (Note that the definition of "energy" that is used in the theorem, in itself does not require time translation symmetry; only the proof that it is conserved does.)

All that said, I think most experimental tests of "conservation of energy" are actually not testing for the Noether's theorem version of that, but are testing for something different. See the last part of post #32.

 

[Orodruin]

Noether's theorem, as a mathematical theorem, is of course based on the assumption of time translation symmetry, since that is a premise of the theorem.

No. Just if the conserved quantity is energy. Noether’s theorem generally relates conservation laws to continuous symmetries, whether they are rotations, translations, time invariance, field transformations or something else.

 

[PeterDonis]

Just if the conserved quantity is energy.

Yes, I meant my post to only apply to that case.

 

[profbuxton]

Greetings,
From my reading of the above explanation, am I right in understanding that the particular atom and frequencies are so chosen because they closely match our previous definition of a second and are extremely stable or do we now have to completely "recalibrate" our second to match the new definition.
I quess the same applies to our "newer" definitions of the speed of light etc.

 

[PeterDonis]

the particular atom and frequencies are so chosen because they closely match our previous definition of a second

Only if you think that the number 9192631770 counts as "closely matching". AFAIK the particular atomic transition used was chosen because it was the easiest to measure to a very high degree of accuracy, not because it was any better at matching the old definition of the second.

do we now have to completely "recalibrate" our second to match the new definition.

No. The new second is the same period of time as the old second, to within the accuracy of the two measurements involved (a fraction of the Earth's tropical year--old definition--vs. a particular number of cycles of a given frequency of radiation--new definition). The new definition was chosen because (a) it can be measured more accurately so it can serve as a better time standard, and (b) it allows the meter to be defined in terms of the second by fixing the value of the speed of light in SI units, reducing the number of independent measurement standards that need to be maintained. (Since the new SI second definition was adopted, other units have also been redefined in terms of it--I believe that since the redefinition of the kilogram in terms of a fixed value for Planck's constant and the SI second, there are no other independent standards remaining.)

 

[Orodruin]

Only if you think that the number 9192631770 counts as "closely matching". AFAIK the particular atomic transition used was chosen because it was the easiest to measure to a very high degree of accuracy, not because it was any better at matching the old definition of the second.

I’m not sure this was the question. Yes, the atom was choosen because it can be measured precisely and easily, but the frequency of radiation of the transition (1/9192631770 Hz) was chosen such that the new definition matches the previous one within experimental error.

 

[PeterDonis]

the frequency of radiation of the transition (1/9192631770 Hz) was chosen such that the new definition matches the previous one within experimental error.

Yes, agreed; but choosing another atom would not make it any harder to match the previous definition. It would just mean a different many-digit number would appear in the new definition.

 

[DrClaude]

More precisely, the cesium clocks that are used as time standards to define the SI second at places like the NIST have cesium atoms that are put in a cavity that contains EM radiation, and then allowed to fall back out of the cavity to see if they emit EM radiation. If they emit EM radiation, it means they must have absorbed it while they were in the cavity; and if the frequency of the EM radiation in the cavity is tuned just right, it will maximize the emission of EM radiation by the cesium atoms when they fall out of the cavity--i.e., the EM radiation in the cavity is in resonance with the desired hyperfine transition frequency that defines the SI second.

This is actually incorrect. Emission is never measured, it is rather the number of atoms that have made the transition.

 

[DrClaude]

For what it is worth, the days of caesium being the reference for the definition of the second are counted (pun intended). It is no longer the atom allowing the highest precision. The future standard will probably be based on an ion instead of a neutral atom, using much higher optical frequencies (rather than microwave as in the case of caesium).

 

[sophiecentaur]

This is actually incorrect. Emission is never measured, it is rather the number of atoms that have made the transition.

That sounds to me exactly like an absorption measurement. Apart from using moreu precise conditions, it is much the same as optical and microwave spectrographic astronomy which identifies the presence of resonant structures. In a time standard cell there are plenty of the right atoms present and the pressure, temperature and levels of EM are adjusted to standard values.

 

[PeterDonis]

This is actually incorrect. Emission is never measured, it is rather the number of atoms that have made the transition.

The number of atoms that have made the transition is measured by the intensity of EM radiation emitted from those atoms and hitting the detector, correct?

 

[DrClaude]

The number of atoms that have made the transition is measured by the intensity of EM radiation emitted from those atoms and hitting the detector, correct?

No, it is absorption spectroscopy. They shine a laser to make a transition from the $F=4$ state to an excited state, and measure the amount of absorbed light.

I am not experimentalist, but I think that measuring emission would be very difficult. Spontaneous emission will be isotrope, so you would only collect a small fraction of the light, and then there is also the question of the timing of the emission. Also, that would require detecting microwaves, much more difficult than the IR (852 nm) light used for absorption spectroscopy.