What analysis and what point?
OK as I said I’m not the expert.
But then you say:
Here it sounds as if you are not sure how it works and I never suggested it might be a sphere.
Well it should be or if it is not then something is wrong – IMHO- tell somebody who has just had his car smashed by inertial forces “well sorry your car is all bent up but we have no way to understand the forces that caused all that destruction” Blame Newton not Einstien.
To get back to “it is not an inertial factor”
Lets see what I understand about Cs133. It has mass so the bits that make up the nucleus, the protons and neutrons have mass and even the electrons have a small amount of mass. The nucleus is emitting a radio wave at a frequency of 9,192,631,770 Hz.
( Getting my information in a cursory manner from : http://hyperphysics.phy-astr.gsu.edu/hbase/acloc.html)
According to the information source above the hyperfine emission comes from an interaction between a lone distant electron and the nucleus (& the dimensions are given for the nucleus and it doesn’t matter if it's round or shaped like a unicorn). It is a dynamic system. It moves – it’s some sort of an engine that produces these electromagnetic waves. You say the mass of the parts have no effect on the emission? It seems to me that if there is any movement involved in the hyperfine emission then the mass/weight of the parts must come into the equation.
Look at it from a GR (or SR?) perspective and with the principle of equivalence gravity and inertia can be interchanged so if the intensity gravitational field effects the clock - proven,of course – then why can’t we postulate that if the inertial mass of the clock changes then its rate will change?
None of this is accurate. A nucleus is not an engine - it does not produce energy. In addition, "dynamic" and "it moves" are not synonyms.
A "state space" within which a dynamic system evolves need not involve three dimensional locations.
The hyperfine interaction is between the magnetic moment of the nucleus, which is a constant, and the electrons in the atom. The transition frequency should be a know function of electron mass.
I realize there it isn't possible to pin down shape of the nucleus or where any bits are at any one time but is there movement or rotation in the nucleus?
I have heard that "spin" is actually spin with angular momentum and other that say it is "intrinsic" (whatever that means) and doesn't connote any movement.
They're both right. The spin of a subatomic particle is indeed angular momentum, and it doesn't connote any movement or physical rotation. "Intrinsic" just means that nothing you do the particle will change its spin.
Since the frequency of the radiation associated with that transition (as opposed to the "transition frequency") is a defined constant, whatever it is a function of, it is a constant function.
Not sure how what "works"? Do you mean that the nucleus has a magnetic moment and an angular momentum? You measure those two quantities and don't get values of zero for either one. Is that what you mean by "how it works"?
And I agree that you never suggested it was a sphere.
As I told you, it's not about the physics, it's about the meaning of a word. Inertia. Inertial forces are not the same thing as inertia, their values don't even have the same units.
When cars collide, by the way, they get smashed by electromagnetic forces.
Inertial forces never ever smash a car. They are strain free. They occur in non inertial frames, and can be made arbitrarily large by choosing appropriate coordinates. Cars don’t get smashed or not if you choose a different coordinate system.
All clocks have mass, so they all have inertia. So what do you mean by “inertial factor”? Do you merely mean that it has inertia? If so then it is a fairly trivial statement that doesn’t describe much about clocks. Do you mean something more?
Clocks have inertia. Cars have color. Color is not the operating principle of a car. Are you simply stating that clocks have inertia or are you trying to say that inertia is the operating principle for all clocks? Are you merely saying the equivalent of “all cars have a color factor”.
"Transition frequency may refer to: A measure of the high-frequency operating characteristics of a transistor, usually symbolized as f. A characteristic of spectral lines. The frequency at which changes in the hyperfine structure of atoms occur. Turnover frequency in enzymology."
Seems to match my usage? Did I miss a memo?
The frequency of the radiation corresponding to the hyperfine transition in the ground state of the cesium atom is not the rate at which changes in the hyperfine structure of atoms occur.
Hyper fine structure is a property observed in spectral lines of an atom. This has zip to do with the rate of transition. Not all transitions need be to the ground state. It's an RF spectral line.
Fair enough. I mis-read your reference to "frequency at which" as "frequency with which".
So if the mass of the electron changes (in my imaginary world) does the transition frequency change?
That depends on how* the mass changes. Specifically, does the mass change in a way that also changes the fine structure constant (or other dimensionless constants) or does it change in a way that they do not change? The measurable transition frequency depends on the dimensionless constants like the fine structure constant.
*how meaning the details about the other changes that might be associated, not the mechanism of change
The interaction Hamiltonian which determines the frequencies of transition depends on the magnetic moments which depend on particle mass. Everything changes if ##\hbar## changes as well. These are all observed to be constant as far as I've heard.
Why does this even matter? The mass of an electron is fixed.
Torog, I appreciate your thinking, and then questions following on how we might define a clock. This is a good thread to help at least some of us attempt to properly anchor the roots of time itself.
First, I should correct my previous assertion (below) that all clocks rely on angular momentum... not certifiably true. It arose from a different, also unmentionable personal idea.
DrGreg properly rejected my reasoning on a surviving earlier post and I hereby acknowledge he is correct; strictly angular momentum cannot be the charred key we seek here. My bad.
I find of particular interest what Sorcerer and Dale have discussed above in posts #68 & #69. While I struggle to understand the abstract math symbols of Noether's Theorem, I think I do recognized the conceptual value of, "the principle of least action", as partially worded in this first paragraph. This paragraph seems very much along the lines of Occam's Razor, or as Maupertuis supposedly felt, that "Nature is thrifty in all its actions".
It seems that the ultimate object of science is to simplify whatever processes and observances of Nature that we can. For instance, we might strongly suspect Mother Nature is lazy, that she accomplishes her vocation in the simplest manner possible... and when sufficiently 'cooked', these actions should boil down to fundamental principles... in other words the very charred essence of what we seek. I really like the simplicity of conservation of energy idea for this and other reasons.
Prior to the conservation of energy posts, I was tempted to come back and suggest that, since all classical clocks seem to at least rely on non-erratic motion events, that perhaps conserved general momentums (not just angular) were still the key. Even a candle flame, water or sand must move non-erratically to usefully differentiate the increments as a clock. But 'conservation of energy' seems a much better key now that it has emerged from the soot... because 'conservation of energy' allows not just conserving momentum, but storing that momentum for reuse as counter-momentum if we wish. Clocks commonly work by stored energy and each burst is measurably the same as last. As food for thought, it seems perhaps an escapement loop principle somehow regulates them all.
In a non-classical view, regarding quantum behavior of atoms when remarks on motion were given by Mister T, I am still not so sure I can draw an obvious conclusion that there is an obvious discernible atomic counterpart to classic laws of motion, but that is just me. In my quantum fog, it seems we should only know either the position of the 'tiny' hands or the rate, but not both at the same time. Yet atoms furnish us a great timepiece, apparently by rate alone. It is like a blind man that can hear, and use, the precise tick-tock but need not see the position of the hands to tell time.
But then conservation of energy was brought up. Ok, I know energy transcends both mechanical and quantum. This is better. Just "hearing" the tick-tock of an atom is the process of periodic electromagnetic energy escaping, enough as to form a useful timepiece, particle position notwithstanding. The electromagnetic energy will escape and tell us time until it runs out, or ceases to be applied, like any other clock. Perhaps someone could explain if both atomic and mechanical share a comparable hidden escapement mechanism to not release their energy nearly all at once. Seems maybe worth a Nobel Prize... unless it's been done.
It is still not so clear to me why 'drilling down' would not succeed, why Nature would suddenly abandon her simplicity right at the bottom of the hole. It's difficult to leave Einstein's side and not share his desperate want to discover why random motion seemingly rules so non-erratically at the core. How can something so random as the ghostly gears of an atom be our best clock? Perhaps we will only really know the atomic mechanism in a heuristic mechanical sense, if or when Einstein's dice ever reveal their secret. Quantum gravity heck; what is quantum time? Non sequor...
It seems a thread like this, where there is not a specific single answer to cite, elicits more opinions that border on speculation. The safer route seems to be saying not much, which I've tried to avoid. I hope I am ok today.
To be upfront, I was the (or a) guilty party in earlier setting foot outside the rules box and got a time-out. I apologize, my zeal to somehow add insight occasionally precedes my head. My uncited previous post, especially about cosmology, was removed and I deserved it. I do very much continue to appreciate the tedious behind-the-scenes work done here by Mentors even when it turns out I'm the rascal gone Beagle Boy. So thanks, Mentors.
And thankfully Torog's worthy clock thread was not locked on my account.
This is just what I was trying to understand. The stability of the electronic clock is at least partially based on the fact that the mass is fixed.
I would like to say more but it is not a subject for this forum.
@Torog you didn’t answer any of my requests for clarification on this topic.
Separate names with a comma.