There doesn't seem to be a law that cleary demonstrates true regularity of any physical process. Every clock is imperfect. All we've done is postponed the event when our clocks will accumulate enough error to be noticeable. While this may be acceptable in living im the seconds, minutes, hours, days, months or years, we can't ignore it in doing science where accuracy is vital.

You're always going to have measurement error in experiments. 5.4*10^-17 error in a second is ridiculously precise. As the optical lattice clock paper noted at the end - this level of precision allows all kinds of new experiments. The need for no measurement error to demonstrate anything through experiment has the opposite effect than 'accuracy is vital for the progress of science', since it completely undermines every single experiment ever done.

The physical process has to be regular. In my OP I mentioned how this is ''less'' of a problem with other quantities like length, mass, volume because we have a standard whose state has been specified. With time it's different because we can never be sure of the regularity of a time piece. We can't be 100% certain that one period of a cesium atom takes the same time as the next. — TheMadFool

In the case of the atomic clock, there is no regular process. The clock is tuned to a constant of a physical system, and the second is thus DEFINED. The only "regularity" is that all the atoms have the same physical property, which, since we know they are indistinguishable, is a non-issue.

They ran for a period of a month, and they got out of phase by 2.8 x 10^-17 seconds. That doesn't mean it's only proven to be stable for a month. Quite the contrary, the error is so low in a month that it's negligible. — fdrake

Right, for a period of one month, the error was negligible. This means that the physical activity remained very stable for that one month period. It has been proven to be constant for a month. How do we know that in 10, 100, or 1000 years, that activity will not change?

In the case of the atomic clock, there is no regular process. The clock is tuned to a constant of a physical system, and the second is thus DEFINED. The only "regularity" is that all the atoms have the same physical property, which, since we know they are indistinguishable, is a non-issue. — tom

Regularity is critical in all measurements. Consider a student's ruler. If the centimeter markings are spaced differently (the should be spaced the exact same length) then the ruler is "broken". Similarly, if the seconds ticked off by a clock are of different "lengths" then time measurement would be pointless.

You're always going to have measurement error in experiments. 5.4*10^-17 error in a second is ridiculously precise. As the optical lattice clock paper noted at the end - this level of precision allows all kinds of new experiments. The need for no measurement error to demonstrate anything through experiment has the opposite effect than 'accuracy is vital for the progress of science', since it completely undermines every single experiment ever done. — fdrake

Yes, perfection in measurement is impossible. Length units like cm, m are also imperfect but the issue with time is slightly different.

With length, we can take an object, specify the temperature, its composition and other parameters and then define the unit of length (as was done before the metric system assumed its present form). We can then easily check all rulers to this particular length.

Time, on the other hand, is slightly different. A unit like second can only be defined with periodic change that has to be regular, just like for length. But, without a time piece that is already regular we can't determine if the periodic phenomena we're using to measure time with is regular or not. See...?

Don't you see the distinction between:

The clock only ran for a month, so the error is at least a month.
The clock ran for a month and had an error of 5.4*10^-17 in that period.

What allows the extrapolation of the error - and thus statements like '1 second in 100 million years' - is that the clock had a certain error which accrued over a month. The measurement error precisely gives 'how much it changes over time'. If the clock degraded, then the error would change. The degradation would occur in the instruments of measurements - what tracks which quantum state the clock is in, not in the oscillations between two quantum states; the latter is understood variation anyway (like variations due to gravity).

Time, on the other hand, is slightly different. A unit like second can only be defined with periodic change that has to be regular, just like for length. But, without a time piece that is already regular we can't determine if the periodic phenomena we're using to measure time with is regular or not. See...?

Ok, how do you account for the ability to assign measurement errors to clocks? What does your skepticism actually do?

We can't know the length of an object is regular either.

Regularity is critical in all measurements. Consider a student's ruler. If the centimeter markings are spaced differently (the should be spaced the exact same length) then the ruler is "broken". Similarly, if the seconds ticked off by a clock are of different "lengths" then time measurement would be pointless. — TheMadFool

The SI unit of length is defined in terms of time.

The SI unit of time is defined in terms of a property of matter.

What allows the extrapolation of the error - and thus statements like '1 second in 100 million years' - is that the clock had a certain error which accrued over a month. The measurement error precisely gives 'how much it changes over time'. — fdrake

The measurement error does not give "how much it changes over time". It gives how much it changed over one specific month of time. To conclude that it gives how much the change will be in a million years from now, is faulty logic, because all the possible variables are not known. It's like saying that if something doesn't change in a day, then it will be the same for a hundred years. But we do not know what could happen in the future, to change the rate of the activity which is being measured today.

The conclusion requires the premise that the activity which is being measured for that month will continue to be, as it was for that month, for a hundred million years. And this is an unproven premise, therefore unsound.

There doesn't seem to be a law that cleary demonstrates true regularity of any physical process. — TheMadFool

Yes there is such a law, and it is used in the articles linked. They've demonstrated the accuracy of some clock to X digits, and not by using a more accurate one.
You seem to just want to deny any answer to your query. So what's your purpose in asking then?

The laws of physics have been shown to operate over all observed parts of the universe - and thus back in time more than that. It isn't a stretch to assume if no one destroys the clock or the measuring mechanism, or turns it off, that the process operating within it that measures time will have that error rate.

The laws of physics have been shown to operate over all observed parts of the universe - and thus back in time more than that. — fdrake

You should read some material by physicist Lee Smolin, specifically "Time Reborn". The laws of physics have been proven to be reliable only in the human environment, under very specific controlled experimental conditions. And this represents a very miniscule part of the overall spatial and temporal expanse of the universe. There is no reason why we should believe that our laws are applicable in these distant regions.

It isn't a stretch to assume if no one destroys the clock or the measuring mechanism, or turns it off, that the process operating within it that measures time will have that error rate. — fdrake

Yes it is a stretch. From one month to 100 million years is a huge stretch, 1200 million times. By that same stretch the height of my body could circle the earth about fifty times.

Yes there is such a law, and it is used in the articles linked. They've demonstrated the accuracy of some clock to X digits, and not by using a more accurate one.
You seem to just want to deny any answer to your query. So what's your purpose in asking then? — noAxioms

My problem with the existence of a law that demonstrates the regularity of a periodic process is that time, space, and other physical quantities are more fundamental than any law of nature. First comes measurement, whether time, mass, volume, distance, etc., and only then can relationships between these quantities can be seen.

My physics isn't that good but look at the wikipedia article on the pendulum. The period, supposed to be regular, T = 2pi[(L/g)^0.5] where L = length of the pendulum and g is acceleration due to gravity. As you can see before we can derive this law, we need to know T, L and g. In other words, we already need a clock to measure time (T). How do we know that that clock is keeping accurate time?

The SI unit of time is defined in terms of a property of matter. — tom

Can you have a look at my reply to noAxioms.

How does the argument go then?

My problem with the existence of a law that demonstrates the regularity of a periodic process is that time, space, and other physical quantities are more fundamental than any law of nature. First comes measurement, whether time, mass, volume, distance, etc., and only then can relationships between these quantities can be seen. — TheMadFool

That is quite a startling claim given that the relationships between mass and energy, energy and wavelength, mass and velocity, length and velocity, time and velocity, ... ... (I could go on and on) were all discovered in Theory before any measurement or reason for measurement could be conceived.

So no, it is always theory first.

My physics isn't that good but look at the wikipedia article on the pendulum. The period, supposed to be regular, T = 2pi[(L/g)^0.5] where L = length of the pendulum and g is acceleration due to gravity. As you can see before we can derive this law, we need to know T, L and g. In other words, we already need a clock to measure time (T). How do we know that that clock is keeping accurate time? — TheMadFool

You do not need to know what T, L and g are. L and g can take any values, and we can still calculate T. If such a physical system existed, it would provide a perfect clock. All we would need to do is measure g and use that to DEFINE L and T. But of course, no such physical system exists.

But atomic transitions do exist, and the energy of transition can be measured. Because theory tells us the relationship between energy and frequency, and that transitions are induced in atoms when subjected to EM radiation of that frequency, we may DEFINE the second via that frequency.

I did a bit of background reading on Smolin. From what I understand he advocates the view that the laws of physics change over time. I'm sympathetic with this view, since the different regimes of energy distribution at different stages of the universe's development give rise to markedly different topologies of physical law. By this I mean, at the start of the universe there is theorised to be a unification of the electroweak, gravitational and strong forces, and spatio-temporal variations in the ambient levels of energy unfold a universe with distinct forces and distinct length-scales for their activity.

However, the universe will still be in the same regime of energy distribution for billions of years, and there is no good reason to believe that the laws will change in this time. The mere possibility of the laws changing evidently does not impede scientific discovery and theory-forming over the different stages of the universe's chronology. I had a similar discussion with Rich once, the accuracy of measuring red-shift in photons coming to Earth gives excellent evidence of the constancy of universe over very large time scales.

Indeed, approximately 10^14-(13.8 * 10 ^ 9) = 10^13 years need to occur in order for the regime of distribution of energy to change in any meaningful way. That's 1000 times longer than the current age of the universe...

Any account of the study of physical phenomena must allow for the ability of physics to probe the beginning and the end of the universe, the near instantaneous (10^-18 of a second) to the universal (10^100 years) time scales with reasoned argument and mathematical precision. It must also allow the ability to assign errors and upper/lower bounds to these predictions and measurements.

If your metaphysical speculation is inconsistent with the sheer scope of our ability to study the universe, so much the worse for your metaphysical speculation.

Edit: another way of thinking about it - the contingency of physical law doesn't do anything to the laws revealed, other than requiring accounts for their formation and end. (and thus replacement by other laws)

Edit 2: and why would the process of measurement embodied by the optical lattice or caesium clok change anyway?

How does the argument go then? — fdrake

Which argument? The argument is yours. You are claiming that by watching something for a month, you can say something about it which will be true in 100 million years from now. If you think that this is really the case, then show me your argument.

However, the universe will still be in the same regime of energy distribution for billions of years, and there is no good reason to believe that the laws will change in this time. — fdrake

OK, I see you've made an argument now. However, I do not believe that cosmologists currently have an adequate understanding of the "regime of energy distribution" of the universe. That's why they posit "dark energy". And your argument is based on this unsound premise. Therefore there really is good reason to believe that the laws will change in this time. We will change our descriptive laws as we come to know the universe better, especially things like spatial expansion. We will have to change the laws in order to account for this new understanding, and it is likely that we will come to realize that what we say about an activity for a month right now, will not be the same concerning that activity in 100 million years.

What scientists believe about dark energy has absolutely no bearing on whether the laws of the universe will change in a given time period. Coming to know more about the laws of the universe may reveal the reason for all the 'missing matter', but this novel disclosure has no bearing on whether the laws will change - only what the laws are believed/known to be. With that in mind:

Can you make a positive argument that the laws of the universe will change within 100 million years? Can you establish that the measurement process going on inside an atomic clock or an optical lattice clock will degrade? When will it degrade? How will it degrade?

Also, it just doesn't follow that since an estimate of something was derived from a month's work of science that any error measurement derived from it is curtailed to a month. Such a temporal localisation of knowledge removes the validity of all measurements, not just temporal ones. You read a thermometer - the thermometer's measurement is only observed now - therefore we don't know what temperature it is when we look away.

What scientists believe about dark energy has absolutely no bearing on whether the laws of the universe will change in a given time period. Coming to know more about the laws of the universe may reveal the reason for all the 'missing matter', but this novel disclosure has no bearing on whether the laws will change - only what the laws are believed/known to be. With that in mind: — fdrake

This is contrary to your stated argument though. You stated that the laws of physics will not change because the universe will be "in the same regime of energy distribution for billions of years". The existence of dark energy is very clear evidence that such a claim cannot be justified. And if it cannot be justified that the universe will be in the same regime of energy distribution for an extended period of time, then, that the laws of physics will not change, likewise is not justified.

Can you make a positive argument that the laws of the universe will change within 100 million years? Can you establish that the measurement process going on inside an atomic clock or an optical lattice clock will degrade? When will it degrade? How will it degrade? — fdrake

You seem to misunderstand my argument. I am not arguing that a change will happen, I am arguing that it is possible, because that is all that is necessary to discredit your insistence that these activities will stay the same for 100 million years. Your claim is that such a change is impossible, because if you recognized it as possible you would not insist that these activities would necessarily stay the same for 100 million years.

I understood you were making the claim that since the laws of the universe can possibly change. I'm not making the claim that it's impossible to change. I'm making the claim that they won't change in any meaningful way for 1000 times longer than the current age of the universe.

Why would you think that because it's possible for the universe's laws to change, that they will?

I understood you were making the claim that since the laws of the universe can possibly change. I'm not making the claim that it's impossible to change. I'm making the claim that they won't change in any meaningful way for 1000 times longer than the current age of the universe.

Why would you think that because it's possible for the universe's laws to change, that they will? — fdrake

Do you know what the "laws" of the universe are? These laws are the descriptions which human beings have made in their attempts to understand the universe. The laws are made by human beings, through inductive reasoning; they are generalities produced from observing regularities in nature. We describe the various activities which we recognize and understand in terms of laws. In the last three thousand years, the laws have changed dramatically, because our understanding of the universe has change dramatically. Between the time of Isaac Newton until now, the laws have changed substantially. Why would you ever claim that the laws will not change in a period of time 1000 times longer than the current age of the universe?

Why would you think that because it's possible for the universe's laws to change, that they will? — fdrake

As I said there is very much concerning the universe which we do not understand, spatial expansion, dark energy, and dark matter for example. When we start to get a better understanding of these aspects we will have to change the laws again.

Before Newton thought of ma=mg implies a=g, objects with little difference in air resistance fell in the same way. Before Schrodinger's equation, atoms were already probability clouds. Before the understanding of planetary accretion, the Earth formed. Reality behaves in a manner accordant with discovered physical laws because those laws describe what happens, and if they have errors - their description contradicts observation -, they are expanded, discarded or re-interpreted. The representation of a pattern in nature in scientific terms has a certain correspondence with what happens, because that's precisely what it means for something to be a physical law. They are discovered through human activity, that doesn't mean they are constrained to human activity.

The claim that the laws won't change in that time is based on 1) that the current understanding of things is basically correct and 2) that this current understanding entails that the universe will be much the same for that time period.

Even if science is wrong, that doesn't mean nature will change. Nature does not change to accommodate the beliefs of scientists. The scientific description of patterns in nature may change when previous descriptions are found incorrect or novel phenomena are studied.

You need to establish not only that the laws of nature can change - in the strong sense, that nature itself will change -, but that it will change in a manner that makes the error estimates for the optical clocks incorrect. As yet you've not. So tell me, why will the measurement process inside of the clocks change?

The claim that the laws won't change in that time is based on 1) that the current understanding of things is basically correct and 2) that this current understanding entails that the universe will be much the same for that time period. — fdrake

OK, then how do you make 1) consistent with dark energy and dark matter? These are enormous features of the universe which cosmologists admit that they do not understand. How can you say that the current understanding is correct, when the consequence of that understanding is the need to posit all of this mysterious substance?

Even if science is wrong, that doesn't mean nature will change. Nature does not change to accommodate the beliefs of scientists. The scientific description of patterns in nature may change when previous descriptions are found incorrect or novel phenomena are studied. — fdrake

If your claim is that the universe is the way that it is, regardless of how we understand it, then how is this relevant? What we are discussing is our capacity to measure the universe, specifically to measure time. So the fact that time is how time is, is irrelevant to our discussion of our efforts to measure time.

OK, then how do you make 1) consistent with dark energy and dark matter? These are enormous features of the universe which cosmologists admit that they do not understand. How can you say that the current understanding is correct, when the consequence of that understanding is the need to posit all of this mysterious substance?

Basically correct. If you want to talk about dark energy, you have to be able to accept solutions to Einstein's field equations as correct and the web of theory and experiment around them. Dark energy only makes sense as a concept on the background of the acceleration of the expansion of the universe; and is contained in a few explanations of it.

If your claim is that the universe is the way that it is, regardless of how we understand it, then how is this relevant? What we are discussing is our capacity to measure the universe, specifically to measure time. So the fact that time is how time is, is irrelevant to our discussion of our efforts to measure time.

Your argument so far has been based on an equivocation of the following: the beliefs of scientists and the practice which generates them; usually called science, and the phenomena they study; usually called nature. If a pattern is observed in nature, and it becomes sufficiently theorised and experimentally corroborated, it will be a scientific law. Note that nature behaved that way first, the scientists adjusted their beliefs and inquiries to track the phenomenon.

You want to have it so that the changes in the beliefs of scientists over the ages implies that nature itself has changed over that time. This is a simple category error. You keep attempting to justify the idea that assigning a small measurement error to an optical lattice clock is unjustified because the laws of nature possibly will change. Besides being an invalid argument - the laws of nature would have to change , not just possibly change, in order to invalidate the current error analysis of the clock, you're using the above equivocation to justify it.

You thus have to show that the laws of nature (read - how nature behaves) will change in a way that invalidates the error analysis of the clock within 100 million years.

It's very suspicious to me that something you could have understood by reading the papers thoroughly and researching the things you didn't know to enough standard to interpret the results, but now you're attempting to invalidate a particular error analysis of a clock by either the cosmological claim that the way nature operates will change in some time period or undermining the understanding that scientists have of reality in general. Engage the papers on their own terms, show that the laws of the universe will change (not will possibly change), or stop seeing nails because you have a hammer!

Basically correct. If you want to talk about dark energy, you have to be able to accept solutions to Einstein's field equations as correct and the web of theory and experiment around them. Dark energy only makes sense as a concept on the background of the acceleration of the expansion of the universe; and is contained in a few explanations of it. — fdrake

Your claim of "basically correct" is nothing more than an assertion. So you support your assertion that the measured activity of the caesium clock will be precisely the same in 100 million years, as it is today, with the assertion that the laws of the universe, as stated by human beings today, are "basically correct". What does "basically" mean here? Does it mean that some parts of our understanding may be incorrect, but the part which relates the activities of the caesium atom to a hundred million years of time passage, is precisely correct?

Your argument so far has been based on an equivocation of the following: the beliefs of scientists and the practice which generates them; usually called science, and the phenomena they study; usually called nature. If a pattern is observed in nature, and it becomes sufficiently theorised and experimentally corroborated, it will be a scientific law. Note that nature behaved that way first, the scientists adjusted their beliefs and inquiries to track the phenomenon. — fdrake

I don't see any support for your claim that I have equivocated. I see however that you have fallen victim to two distinct unsound premises. First, you assume that if an activity of nature has been observed, as following a pattern then the description of this activity is necessarily correct. Second, you believe that one can proceed without that firm (correct) understanding of the activity, just an understanding of the pattern, to claim that the pattern will remain the same for an extended period of time.

You want to have it so that the changes in the beliefs of scientists over the ages implies that nature itself has changed over that time. — fdrake

This is a misunderstanding. What I am saying is that changes in the beliefs of scientists, over time, indicate that what scientists belief at any particular time, is not the "correct" understanding. You claim that what scientists believe now, is all of a sudden "basically correct", despite the fact that this has never been the case in the past. On what principles do you claim such a change? This is totally inconsistent with what we have observed, the believes of the scientific community change. How do you support this claim, that scientist now have a correct understanding?

You keep attempting to justify the idea that assigning a small measurement error to an optical lattice clock is unjustified because the laws of nature possibly will change. Besides being an invalid argument - the laws of nature would have to change , not just possibly change, in order to invalidate the current error analysis of the clock, you're using the above equivocation to justify it. — fdrake

Now you are equivocating. What do you mean by "laws of nature" here? As I said already, "laws" refer to descriptions produced by human beings. We know the laws will change because we know that human beings do not have a complete and precise understanding of the universe. So it is not the case that the laws of nature will possibly change, it is the case that they will change.

You seem to be equivocating from the human descriptions to the activities described. But we are talking about the human descriptions here, the laws, and their accuracy. You are assuming that the description is necessarily correct. That's your first unsound premise.

You thus have to show that the laws of nature (read - how nature behaves) will change in a way that invalidates the error analysis of the clock within 100 million years. — fdrake

This is untrue. To make my argument I don't have to show anything about "how nature behaves". What I need to show is how human beings behave. We are discussing the human activity of measurement, not "how nature behaves". This is where you are loosing track of the argument, you assume the argument is about how nature behaves, not about how human beings behave. Human beings have demonstrated over and over again throughout history, that at one time they believe to have a correct, and accurate measuring device, only to find out later that it wasn't as accurate as they thought. This is especially true in the case of measuring time.

very suspicious to me that something you could have understood by reading the papers thoroughly and researching the things you didn't know to enough standard to interpret the results, but now you're attempting to invalidate a particular error analysis of a clock by either the cosmological claim that the way nature operates will change in some time period or undermining the understanding that scientists have of reality in general. Engage the papers on their own terms, show that the laws of the universe will change (not will possibly change), or stop seeing nails because you have a hammer! — fdrake

As I said the laws of the universe will change. Human knowledge of the universe is incomplete. Things such as spatial expansion, dark energy, and dark matter, provide undisputable evidence of this fact. Human knowledge of the universe is incomplete. If you are not ready to face this fact, then that is not my problem, it's yours.

Help me out a bit.

(1) Beliefs about nature and methods for deriving them are fallible.
(2) The laws of nature are non-necessary.
(3) The laws of nature can change.
(4) The laws of nature will change.
(5) The laws of nature only describe properties of thought.
(5) Measurement error is a property of human engagement with a phenomenon.
(6) Historically, ways of measuring time have been less accurate than described.
(7) Scientific beliefs can change.
(9) An observed pattern of nature cannot be assumed to arise or perpetuate in the controlled conditions which generate it.
(10) Scientific knowledge is incomplete.

Are all elements of your post.

Can you tell me how their combination entails:

(11) The measurement error analysis of the caesium-133 clock and the optical lattice clock are wrong.

?

Edit: if I've missed a vital element, please add it to the list!

Can you tell me how their combination entails:

(11) The measurement error analysis of the caesium-133 clock and the optical lattice clock are wrong. — fdrake

I didn't say that the measurement error analysis of the caesium-133 clock is wrong. I said your extrapolation is wrong. The measurement error is for a one month period. You extrapolate this to a 100 million year period. You base this extrapolation on the following principle: "the universe will still be in the same regime of energy distribution for billions of years". My argument is that the uncertainties involved with the concept of dark energy indicate that such a claim is unsound, and therefore your extrapolation is unprincipled.

Ok. If the measurement error analysis in the paper isn't wrong, that means the 1 second in 100 million years isn't wrong. Since that corresponds to an error rate of about 3 * 10 ^ -16, which was derived within the month. The unit of the error rate is in seconds per second... Take the reciprocal, voila!

Ok. If the measurement error analysis in the paper isn't wrong, that means the 1 second in 100 million years isn't wrong. Since that corresponds to an error rate of about 3 * 10 ^ -16, which was derived within the month, — fdrake

If, for the sake of argument, we accept your rash extrapolation into the future, then the implication is that the clock is accurate to 1 year in every 3.154e+15 years. I'm pretty sure there will be some changes in that time, and who wants a clock that's wrong by a whole year?

Would you be happy with 6*10^-16 seconds per 2 seconds? How about 9*10^-16 per 3? You can scale the error like that all you like, it still represents the same error rate. If you ran the clock for 3*10^15 years, of course you're going to get an error on it: what matters is that it's the same error as predicted by the analysis of the process.

Also, since you know the error rate, you know when it's going to have accumulated a second of error, so it can be re-calibrated. (subtract a second from the display, or a year from the display...)

If the measurement error analysis in the paper isn't wrong, that means the 1 second in 100 million years isn't wrong. Since that corresponds to an error rate of about 3 * 10 ^ -16, which was derived within the month. The unit of the error rate is in seconds per second... Take the reciprocal, voila! — fdrake

You don't seem to understand the issue fdrake. You haven't disclosed your principle of extrapolation, and this is what validates your extrapolation. Suppose I can eat one hot dog in thirty seconds. This is a rate of one hot dog per thirty seconds. You extrapolate and claim "therefore I can eat 120 hot dogs in one hour". Do you see the problem with this type of extrapolation? You need a principle whereby you can assert that the rate which was obtained in the short term will continue over the long term. Without that principle your extrapolation is just a baseless assertion.