What do clocks measure?

Question

I recently asked a question about the measurement of time, and it has become apparent that I'm really asking a set of related questions, the premises of which need to be shored up and articulated clearly, particularly against the context of processes in nuclear physics.

It appears these questions cannot be put without utmost precision.

Focussing on just one aspect of the problem for now, I asserted that clocks measure the rate of a physical process that takes place in space as well as "time", rather than measuring "time" directly and indepdendently. Adapting someone else's apt turn-of-phrase which I've stumbled over, a clock is not like a gas meter through which quantities of pure time flow.

I assume this is an uncontentious assertion, that clocks are all physically measuring rates - of something or other.

We are accustomed to the idea of clocks that keep time poorly - those that measure time at a variable rate, at the "wrong" rate, or even stop working. When this occurs, we merely consider them to be "bad clocks" - we do not consider the "passage of time" to have been impugned by the vagaries of how a particular clock operates.

However, with atomic clocks, there seems to be a widespread belief that the "rate" of the clock is physically constant and invariable.

For sure, the conversion rate between the caesium standard and the "second" is defined to be constant - but that does not establish the physical constancy of the process which the atomic clock measures. Rather, it simply asserts that whatever the variability in the rate, so too that variability will be reflected in the definition of each "second".

This was the problem with the 19th century mill owners, who defined a "full day" as a certain period on the face of the clock - and by controlling the clock, manipulating it's workings, and affecting it's rate, they could extend the amount of time that was actually contained within a "full day" at the mill.

There are, of course, a category of experimental results which are capable of establishing the fact that the caesium standard is physically variable. All the experiments done in relativity, for example, where atomic clocks go on a journey or undergo a change in their gravitational environment, and come back with different readings. I doubt that I need to rehearse the names of specific experiments to anybody here.

In the comments in my previous question, I referred to how in the 19th century, physicists were accustomed to the notion that a pendulum swing was not a physical constant. Temperature, friction, "resonant coupling", all sorts of physical variables could affect it - and there were a series of innovations designed to correct for them. But they never lost sight of the fact that these variables were present, and if the clock rate varied, it was owing to the effects of some or another physical variable, and not to any change in the "passage of time".

But I note that in the physics of relativity nowadays, physicists don't seem to talk about "clocks slowing down" (or indeed speeding up, as they can do). Instead, they talk about "time slowing down".

In other words, there has been a shift in reasoning from classical times, in which clocks were expected to be subject to physical variables, to the modern conception in which the rate of an atomic process is held to be a physical constant. Since the rate is held to be constant, then if the clock reading varies, it is then attributable to a change in "the passage of time itself", rather than a mere change in the rate of the process being measured.

Why has there been this shift in reasoning, and what experimental evidence justifies treating the rate of any physical process as constant? Or is it not experimentally justified, but instead merely represents a difference in taste (compared to the classical physicists) in how a clock measurement is interpreted?

Answer 1

I think I see the heart of your question. It has nothing to do with relativity in fact. Let me attempt to rephrase.

In the past (say 1700’s) we had pendulum clocks to keep time. We said that every tick of the clock was one second. However, sailors at the time realized that if you put a pendulum clock on a boat it would run "fast" or "slow" because the rocking of the boat or temperature variations would alter the physics of the pendulum. How could they tell it was running fast or slow? They could bring the clock back to Greenwich where it was originally set and notice that their clock ticked 100,000 times whereas the Greenwich clock ticked 120,000 times. This was easily explained by what happened to the clock belonging to the sailors on the boat.

Now, your concern is that when people talk about atomic clocks (the modern day "standard" for time-keeping) they do not mention deleterious effects such as "rocking of the boat" that may cause the atomic clocks to run fast or slow. Your concern is that the atomic clock might be undergoing "rocking" but we just sweep it under the rug and just say that "time" is running fast or slow. The question is why the shift in attitude? Previously we recognized physical mechanisms that could alter how the clock runs and admitted they make the clock worse, but now we just cover it up by saying time is running fast or slow. What gives?

I hope the above was an accurate restatement of your question. Let me now provide my answer.

1) First, the title of this post is "What do clocks measure?". You have suggested that clocks measure rates. I think this is incorrect. I believe that clocks measure a NUMBER of events. A pendulum clock measures how many times the pendulum reaches its right extremity. A quartz oscillator measures how many times its tines reache the extremities of their motion. An atomic clock measures how many times the electron wavefunction revolves around the nucleus*. What are rates then? Well, we have defined the second to be something like: Whenever the Cesium clock in Boulder ticks 9,192,631,770 times we say one second of time has passed. Thus, we can now say (based on the definition) that the Cesium clock ticks at a rate of 9,192,631,770 ticks per second. The fundamental measured quantity is a number of events, the defined quantity is a time, and the derived quantity is a rate.

2) Ok. But, just like on the boat, can't deleterious effects affect how quickly the Cesium clock ticks? That is, how much "time" it takes between two ticks might change if the Cesium clock is "rocking". How come I don't hear about that sort of thing? Well, you probably just haven't heard about that sort of thing because you aren't immersed in the field of precision measurement or atomic physics. Atomic physicists in fact worry about things that mess up the ticking rate of their atoms all of the time. Things that can mess up the ticking rate are electric/magnetic fields (cause atoms to tick faster or slower), collisions with other atoms etc. One problem with atomic clocks is that blackbody radiation emitted by the room temperature vacuum chamber in which the atoms reside causes the atoms to change their ticking frequency. Because of all of this it is recognized that the second is defined to be the amount of time it would take a Cesium atom to tick 9,192,631,770 times if it was at 0 K, in 0 magnetic field, in 0 electric field with no external influences. However, physicists realize that this is impossible to achieve in the lab. Nonetheless, there are technological benefits to attempting to do the best they can. So they perform a certain experiment and measure Cesium ticks in a particular way the best they can and report to the world whenever their cesium ticks. Physicists are continually trying to build better clocks that have lower uncertainties so that they can study ever more precise physics and explore new technologies.

3) If clocks can always have some error than what is the benefit to having clocks at all? Well, even though clocks are always wrong to some degree they are also right to some degree. For example, my friend can say to me: "Hey let's meet at the bowling alley after the quartz oscillator in MY watch ticks 34,875,329 times!" and even if he goes to his house (which he keeps at 65 F) and I go to my house (which I keep at 70 F) and drop MY watch in the sink (it is waterproof) I can still pull it out and have faith that once my watch ticks 34,875,329 times my friend’s watch will ALSO have ticked the same amount so I can get to the bowling alley and not annoy him by being 5,328 ticks late!**

The point of making better and better clocks is for humans to be able to have such faith in each other's time keeping devices on ever finer and finer time scales. For example, if the physicists at the atomic clock in Boulder, Colorado do a good job keeping their clock running (with minimal magnetic fields etc.) and the physicists at the atomic clock Paris France do a good job at their clock then the two parties can have faith that even after the passage of a long amount of time***** they will still have counted the same number of ticks of their clocks. This has practical implications when those clocks are used to synchronize different clocks all around the world including those used for satellite GPS and running the global stock markets, both of which rely on measuring very very small differences in time.

4) And another note reminding us of the sailors. Let's ask again how the sailors knew their clock was running fast or slow (other than seeing their crewmates kick the pendulum a few times). They would notice that the sun would not rise when they expected it to according to their clock or they would bring their clock to Greenwich and compare it there. In both cases they are comparing their clock to another oscillatory physical phenomenon. The key is that they are comparing their clock to a phenomenon which is more "stable"*** than the one on their ship. However, these two clocks are also of course susceptible to clock fluctuations. If the temperature changes in Greenwich that would affect their pendulum clock as well, just not as much as the smaller pendulum on the boat beset by the harsh maritime environment.

In addition to stability it is important that a clock standard can be recreated elsewhere and give the same results. That is illustrated by the presence of similar Cs atomic clocks around the world. The beauty is that, if you can control the environment well enough, a Cs atom in Boulder has the same ticking frequency as a Cs atom in Paris. If everyone can then synchronize to these and other clocks in the international system of atomic clocks then we can be confident that we can all agree on the time to a part in $10^{-16}$ or so and this can be useful technologically. As you have identified however, there IS a limit to how precise we can be. This is known and recognized and people are always working to improve this limit.

edit: One more note here. Since clocks measure number of events happening, and time is derived from that measurement, in some sense if the clock at Greenwich slows down or the atomic clock at Boulder slows down it is correct to say that time itself is slowing down because that it how time is defined. However, you are correct to point out that we must recognize this is happening because of undesirable physical effects in our apparatus. That is why we recognize that these clocks only have a finite level of precision and we recognize some level of uncertainty in definition/measurement of time. Building a better clock means pushing down this uncertainty.

5) There is a dimension of your question which does involve special relativity but I think that is in fact the less interesting point. In some sense we can say that relativistic effects are just another external effect that causes the clock to tick differently than the clock in Boulder. What if the clock in Boulder is experiencing special relativistic effects? Well, we can still compare it to the clock in Paris and get results good to some precision. Eventually, to build a better clock, perhaps such effects will need to be controlled. Some effects which limit atomic clocks (cause them to tick differently) now are: Atomic collisions, Blackbody radiation, the lasers used to measure the atoms, stray magnetic fields etc. Someone closer to the atomic clock field could do a better job than me at producing this list.

6) I highly recommend reading the popular science/history book "Longitude" by Dava Sobel about the need for and invention of precision chronometers for naval navigation in the 18th century to get a handle on practical reasons WHY we want a precise clock and what we mean by a precise clock. Perhaps after understanding some concrete real-world situations you will have a better view on some of your abstract questions.

edit2: 7) Important note on clock stability. When I say a clock is stable what do I mean? Well say I have two wristwatches built which were manufactured one after another on the assembly line. If I synchronize them today I can then watch them for a year and see how far off they get. If they get off by 30 seconds in a year then I can calculate a fractional discrepancy. $$ \frac{30 \text{ s}}{1 \text{ yr}}\approx 10^{−6} $$ I don't know which clock is more correct (accurate), but I know that they agree to a part per million. That is they have a relative stability of $10^{-6}$. Now the standard Cs atomic clocks are good to a part in $10^{16}$ or so if they are compared against eachother**** Again, we do not know which clock is more correct, but we can say that the atomic clocks are more stable than the wristwatches because they can agree with each other for a longer amount of time

*This is a bit of atomic physics here, but the atoms used in atomic clocks can be thought of as being exactly like pendulums. It is a system which is physically oscillating in space. This can be a topic for another question.

**Though as we all know, having an accurate watch is not a guarantee that one won't be late! Such a guarantee requires, in addition, a certain amount of personal responsibility!

***Where stability can be defined in a technical sense by comparing the ticking rate of one clock to a clock which is more physically controlled or by comparing the ticking rate of two clocks if there is no "better" clock around. See section 7)

****The most stable atomic clocks reported in fact use Sr and are accurate to a part in $10^{18}$ or so but these are not used as the official time standard. Perhaps in the future they will be.

*****Note that these clocks tick almost $10^{10}$ (ten trillion) times per second. At a stability of $10^{16}$ these clocks can run for over 10 days and not get off by one tick.

Answer 2

The parameter time is a concept derived by abstraction from physical observations. These observations show that different physical processes (at a location) exhibit a coherence which also can be repeated. For example, the number of swings of a pendulum or a balance wheel corresponds repeatedly to a good approximation to the emptying of a sand or water clock or to the daily passage of a star due to the rotation of the earth. This coherence is, of course, dependent on the accuracy of used devices or processes but the abstraction works pretty well that there exists a parameter $t$ called time that maintains an enduring and repeated relation between different physical processes. To use the concept of "rate" for a process is only a different way to use the concept of time because rate is just amount of change divided by time. This concept of an existing parameter $t$ governing all physical processes at a location has been extraordinarily successful and has been confirmed in all advances in accuracy of technical implementations to represent this parameter.

In my opinion, there has probably not been a shift in reasoning with respect to the possible influence of various physical conditions and errors on time keeping devices since the 19th century. And the abstract concept of time independent of time keeping devices exists since antiquity. Only the understanding of the used physical processes and the reduction of errors have increased enormously. This includes the discontinuance of the concept of an absolute time and the influence of gravity on it in the special and general theory of relativity.

Answer 3

There are many different types of clock that we make, that (relativistic effects aside) can be said to run with more-or-less constant time. A simple pendulum, for instance, has a period of approximately $$ T=2\pi\sqrt{l\over g} $$

A pendulum, of course, is not that great of a clock. As you have said, its "constant" time keeping can be frustrated in a number of ways. Most of these can be compensated for in one way or another, but in the end we don't expect a pendulum to keep perfect time. What we can do is figure out all these sources of error and quantify them- this gives us a statement like "this pendulum keeps time accurate up to one second per year."

Now, relativistic effects aside, atomic clocks are the "gold standard" of constant clocks. The time measured by two atomic clocks in the same reference frame, at the same altitude, is extremely consistent. Now, these clocks are still not perfect- there's slight drift due to experimental error. By the 1990s, however, this was less than a nanosecond per day, as shown by this graph of clock uncertainties, by NIST:

Now, to relativity. Why do we believe in time dilation? How do we know that it's not just atomic clocks changing frequency?

Ultimately, this comes down to the fact that special and general relativity work extremely well. Remember that, at the time relativity was developed, no time dilation effects had been measured, as no clock could measure time accurately enough to detect a deviation from the tiny effect of earth's gravity. Relativity predicted that time would dilate under certain effects, and when our clock technology caught up, we noticed that, indeed, everything that could be considered a clock acted exactly as relativity predicted.

Ultimately, time is a human construct. Let's say you get into a spacecraft traveling a significant fraction of the speed of light (let's say $\gamma=2$) and return to earth. Your atomic clock says you were traveling for 10 years. You've aged 10 years. The experience felt like 10 years. Your watch says the trip took 10 years. Your radioactive clock has gone through 10 years worth of half-lives. In relativity, you would just say the trip took 10 years of proper time. All of these would be reasonable definitions of time, and they all agree with one another.

You can, of course, make a new theory where time is absolute, and whatever NIST-F2 measures is absolute time, and it's just all processes that could be construed as a clock that change rate when you're not in Boulder, Colorado (which is where NIST-F2 is). This has a few problems:

• It makes it literally impossible to measure "time" anywhere outside of Boulder, Colorado
• It's extremely geocentric. Which is just kind of dissatisfying from a philosophical standpoint
• You are abandoning relativity, which means you now have to find different explanations for the many apparently disconnected phenomena that relativity explains. Consider the precession of the orbit of Mercury, for instance.
• If you can come up with a consistent theory (and note that I'm not asserting you can) that explains everything relativity does, it's certainly going to be more complicated. So what was the point?

Answer 4

The main reason for shift in reasoning has been better understanding/formulation of passage of time.

Yes, clocks measure rate of something or other.

The variables you refer to in classical sense, are design specific variable. You can design two pendulums almost identical but having slightly different friction. This is a design issue.

In case of atomic clocks, the design issues do not come into picture, or if they do, they are very different kind of design issues and once calibrated, the variation in these designs is probably nil. In a classical clock (pendulum), two clocks can not only have different friction to begin with, their friction can also vary differently with time. Hence the classical issues are considered true variable because they arise from the design and they can be measured.

Now in case of calibrated atomic clocks, design specific variables are supposed to be eliminated. So, how does the tick rate still varies? The tick rate can vary because of situations that are independent of the design issues. How you can detect this change in tick rate, is a different issue?

For example, you have an atomic clock at a fixed location on earth today and it ticks at one rate. A month later, earth itself moves say closer to couple of neighboring planets because of orbital circumstances. Now the same clock will tick at a different rate, but there is no way that you can detect this change in terms of design changes/corrections. All clocks, classical/atomic/good/bad will undergo that change in tick rate.

That is where relativity comes to help. It talks about frame of reference. Two different frames of reference have different tick rates. So, when earth moved closer to other planets, in effect frame of reference (counting gravity in) has changed and so did the tick rate. To detect this change, you have to measure it against tick rate in another frame of reference.

Two identical atomic clocks, one placed on equator and one on the pole at equal height from see level will tick at different rate. Two identical atomic clocks, placed at different heights from see level on same vertical line, will tick at different rate. These are not design specific differences, these are frame specific differences and while being in same frame of reference, you can not detect these changes, whatever you do.

So comparing with your temperature example, the change in temperature changes the frame of reference. If all processes are perfectly coordinated with temperature, you can not detect these changes as the temperature changes assuming you can not measure temperature itself and deduce that something changed.

The frame of reference defined in relativity, says that everything is perfectly coordinated in that frame - "laws of physics are equally valid in all inertial frames of references".

Answer 5

To answer your main two questions:

What do clocks measure?

Clocks count the number of times the same continuous sequence of events occur.

Since the rate is held to be constant, then if the clock reading varies, it is then attributable to a change in "the passage of time itself", rather than a mere change in the rate of the process being measured.

We shouldn't assume this. The continuous sequence of events a clock is counting may indeed change, making the clock inaccurate. So to account for this, physicists create a number of clocks using a different sequence of events, and then compare their readings. If the majority show the same reading within a certain error, then physicists can be increasingly confident that the sequence of events each clock is counting doesn't change either, making the clocks accurate.