However, what if A's is 2.000000009 seconds and B's is 2.0000000000000009 seconds? This imperciptible difference will compound over time and after, may be millions of years, A and B will be out of sync. — TheMadFool

You misunderstand: it's the difference between periods which must be constant to show that both pendulums swing at a regular interval. The actual frequencies of the pendulum swings - which do not at all have to match - are irrelevant.

Another thing is the assumption (is there a physics law for this?) that the pendulum swing will remain constant — TheMadFool

What are you talking about? The comparison of the pendulums is made in order to asses that constancy. There's no 'assumption' made. Pause and think before you type, please.

You misunderstand: it's the difference between periods which must be constant to show that both pendulums swing at a regular interval. — StreetlightX

Why complicate the issue by going a step further than you need to. If I can see the pendulum swinging in sync why calculate the difference?

What are you talking about? — StreetlightX

The assumption is that the pendulum takes the same time for every swing (regularity). How can we confirm this? I can think of two ways of doing this:

1. Depend on some physical law that proves it

2. Using another time piece to confirm it

Both 1 and 2 lead to the chicken and egg problem.

. If I can see the pendulum swinging in sync why calculate the difference? — TheMadFool

Because difference is all that matters when trying to determine regularity. I should not have spoken of synchronicity, which seems to have misled you. Although if difference = 0 and stays as 0 (your pendulums are in sync), then your pendulums have regular swings.

Nope. We need the single best process that could be used at any time and any place. Radioactive decay would be that. Or some similar "free" quantum process. — apokrisis

So how would you decisively determine that radioactive decay is "the single best process" without comparing it to a number of different clocks. Or is this just a bias that you hold?

What alternative did you have in mind? Chinese water clock?

I never heard of the Chinese water clock, perhaps it's one possibility.

Maybe a sundial then. That would obviously work any time, any place.

Another possibility, the more the better. The ancient people made a clock of the moon, the sun, every planet, and the "fixed" constellations. That's what was required to determine the nature of the solar system.

Another thing is the assumption (is there a physics law for this?) that the pendulum swing will remain constant. — TheMadFool

It is not constant. Ever notice all the complexity of the pendulum on a grandfather clock, with all those bars made of different metals? It's not just decorative. It is an attempt to cancel out the normal variations in the period of that pendulum which would significantly reduce the accuracy of the clock.

The standard of time was the average length of a day, with a second being defined as a 86400th of that. I say average length because the day is about a minute longer in December than it is in June.
It would have been more accurate to slice up the time of one rotation (about 1436 minutes) since that doesn't vary significantly over the year, but nobody had a use for hours defined that way.

Anyway, we know that standard is reasonably stable since it would require incredible force to alter that rotation rate. OK, said force does exist, and we have leap-seconds to compensate. Eventually the day will be long enough that we need more than one leap second each day. Scientific definition of a second will diverge more significantly from a clock second, the former corresponding to a day length back when it was first accurately known, and the latter being a function of whatever the current average day-length is.

We need the single best process that could be used at any time and any place. Radioactive decay would be that. — apokrisis

Multiple posts that radioactive decay makes a good clock. It is unpredictable, uncaused and makes a crappy clock. Radioactive dating is accurate to no better than several percent. It serves where no other methods are available, but accuracy is hardly it's forte.

Anyway, we know that standard is reasonably stable since it would require incredible force to alter that rotation rate. OK, said force does exist, and we have leap-seconds to compensate. — noAxioms

But to know this we would have to rely on another clock, say A, and to check A we need another clock B...ad infinitum.

Anyway, we know that standard is reasonably stable since it would require incredible force to alter that rotation rate. — noAxioms

But to know this we would have to rely on another clock, say A, and to check A we need another clock B...ad infinitum. — TheMadFool

No clock was used to verify this. Clocks were made to sync to this. The day verifies the clock, not the other way around.
For the length of the day to be significantly variable would require a complete rewrite of the most basic physics. The Earth rotation is regular because of the complete lack of significant force to alter it.

That is what I was saying (in the bold) in my post.

The day verifies the clock, not the other way around. — noAxioms

Yes but what verifies the day?

Hah. Yes you are right. Complete brain fart to call it radioactive decay. I was meaning the radiative decay of electron transitions in atomic clocks.

Yes but what verifies the day? — TheMadFool

But to know this we would have to rely on another clock, say A, and to check A we need another clock B...ad infinitum. — TheMadFool

No. No clock is needed to know this.
The average length of the day is the arbitrary standard. There is nothing against which it needs to be verified.

The kind of time we're talking about isn't some phenomenological or lived time, it's temporal duration. So:

Ways of measuring duration - decided by convention. Using convenient periodic phenomena in nature and engineering (days, moons, clocks, pendulums, oscillations of a hydrogen atom).

Units of measuring duration - again decided by convention. Can be made to equate a previously conventional measure of time (quantities proportional to seconds with the same dimension) and a physical phenomenon (oscillations of a hydrogen atom).

Duration - something real that is measured. Time constrained to a start and finish.

Time - the indefinite continued progress of existence and events in the past, present, and future regarded as a whole (thanks Google).

The central concept here is periodicity, or the propensity for something to repeat with high regularity. Regularity of measurements - oscillations in phase, periodic phenomena. Corrections can be made to account for small irregularities in the oscillations OR in terms of conventional measurements of duration (years -> leap years, errors in atomic clocks).

There is absolutely nothing mysterious here. It isn't philosophy, it's well established engineering and mathematics.

There is absolutely nothing mysterious here. It isn't philosophy, it's well established engineering and mathematics. — fdrake

Well hardly. Time remains physics biggest problem really.

The central concept here is periodicity, or the propensity for something to repeat with high regularity. Regularity of measurements - oscillations in phase, periodic phenomena. — fdrake

Note how these are all spatialised concepts of time. Whether it is the rotation of a clock hand or the rotation that is a periodic sine wave, it is is about repeating a round trip locally. Time is measured by the how long it takes to complete a repetitive motion. Going around in a little circle zeros the clock to make a cycle. The hand travels forever and winds back up crossing the same spot.

A problem with spatialised time is that it inherits the symmetry of spatial dimensionality. It makes no difference whether the clock hand rotates clockwise of counterclockwise. And yet time has an arrow that points in a direction. Spatialised clocks can’t measure that essential quality of actual temporal duration - the fact that the symmetry is broken.

But there is the other angle we could employ to measure time. And that would be in terms of energy, or entropy. A thermometer could measure time as falling temperature.

And indeed that is how we now measure the age of the universe. We read it off in terms of the average temperature of the cosmic background radiation.

The cosmic time is currently 2.725 degrees kelvin.

The standard of time was the average length of a day, with a second being defined as a 86400th of that. I say average length because the day is about a minute longer in December than it is in June. — noAxioms

OK, if I suppose that the standard is the day, I need to define the day empirically. I can't say that it is the time until the sun appears at the same place on the horizon again, because each day the sun is in a slightly different position. I believe this is why TheMadFool says we have to refer to another clock. I think that clock would be the year.

But to know this we would have to rely on another clock, say A, and to check A we need another clock B...ad infinitum. — TheMadFool

I don't think we need to keep going to more clocks ad infinitum, because we can synchronize a number of clocks, and make the necessary adjustments. After a full year, we can follow the sun's positioning on the horizon, and determine what NoAxioms calls "the average length of the day". Then the day is no longer the real standard, the year is, because the average length of the day is determined in relation to the year. Of course there is something called "the precession of the equinoxes", which may incline one to look for an even long period of time to determine the average length of a year. But there is no need to consider an infinite regress, as the time period of each of these standards gets longer and longer, until there is no need to go any further.

The average length of the day is the arbitrary standard. There is nothing against which it needs to be verified. — noAxioms

So the day gets verified by the year. It is the only way that we could produce an "average" length of day. We could go on to produce an average length of the year, but this would mean that we would need to place the year within an even longer cosmological time period. Right now, we just adjust with leap years as determined necessary.

Likewise, if we look to a shorter and shorter time period there would be a similar problem in inverse. The problem of the short time period cannot be so easily resolved though. The shorter the time period, the more difficult it is to find an activity to measure that period, and in theory we could assume a time period shorter than any activity. The problem of the short time period manifests in the uncertainty principle of the Fourier transform. You cannot claim to have certainty about the activity because the time period is too short, and you cannot claim to have certainty about the time period because the activity is too short. It's a conundrum.

No. No clock is needed to know this.
The average length of the day is the arbitrary standard. There is nothing against which it needs to be verified. — noAxioms

Why? How do we know that the length of the day is going to be constant, as is required? Is there a physical law that proves that the day length is constant? And how do we know that?

I don't think we need to keep going to more clocks ad infinitum, because we can synchronize a number of clocks, and make the necessary adjustments. — Metaphysician Undercover

We need to. For example we need to check all rulers/scales to the standard definition of a meter or a foot. In the case of length we don't have to worry because we can ensure regularity (each 1 foot = next 1 foot) satisfactorily.

However, when it comes to time, this can't be done without using another time piece to check the standard being used. In fact I think we do this. All time on a computer is checked against a clock in a server somewhere.

We need to. For example we need to check all rulers/scales to the standard definition of a meter or a foot. In the case of length we don't have to worry because we can ensure regularity (each 1 foot = next 1 foot) satisfactorily. — TheMadFool

This doesn't imply infinite regress though. What it implies is that we can never be absolutely certain about the length of any time period. This is because at the time when we start to measure a time period all previous time periods have gone past, so we cannot directly compare one time period to another, like we can compare the length of two physical objects. We can place one ruler beside another to see if they are the same.

So with time we always have a medium between the two time periods which are being compared, and this medium is a physical activity. When a physical activity proves itself to be very regular compared to other physical activities, we use it as that medium, through which we compare one time period to another.

However, when it comes to time, this can't be done without using another time piece to check the standard being used. In fact I think we do this. All time on a computer is checked against a clock in a server somewhere. — TheMadFool

The special theory of relativity describes the difficulties involved with comparing one physical activity to another. It proposes a resolution which assumes that each moving thing has a passing of time which is proper to it, and different from other moving things. Instead of assuming an independent, and absolute passing of time, the passing of time is dependent on the activity of the object. Each object, depending on its motion has a passing of time inherent to itself. I believe that GPS systems operate on relativity theory so they always need to re-synchronize their clocks, due to our inability to reconcile motions in an absolute way.

Some physicists, like Lee Smolin for example, propose an independent passing of time. This means that the passing of time is something itself real, and independent from the movement of objects. Then he can question whether the passing of time itself is something which remains consistent over a long period of time. But I think that to get any productive results in this line of inquiry, we need an explanation, or a description of what the passing of time is. So this is where speculation is needed.

Is there a physical law that proves that the day length is constant? And how do we know that? — TheMadFool

It is reasonably constant, and the Newton's laws of motion (the first two mostly) say this. This is not proof, just a very successful set of laws that make good predictions. Come up with different laws that do as well but make the day length much more variable, and then you can introduce doubt.

I say 'reasonably' constant. When precision was needed, the second was eventually redefined against something even more regular (the caesium vibrations). Each day is longer than the same day last year, a trend that will continue (assuming other variables stay nearly the same) until the day and month are the same length. Over long times, the day length is anything but stable, ranging from around 10 to 1500 hours. But it has been consistently 24 hours for the very short duration of humans measuring it, and that consistency is what made it our arbitrary standard of time.

It is reasonably constant, and the Newton's laws of motion (the first two mostly) say this. This is not proof, just a very successful set of laws that make good predictions. Come up with different laws that do as well but make the day length much more variable, and then you can introduce doubt. — noAxioms

Thanks. I was thinking too that there's some physics law that proves some physical durations are fixed and constant. I remember in high school I read something about the pendulum's period depending on g (acceleration due to gravity) and L (the length of the pendulum). However, I don't think this really solves the problem because quantification comes first in physics and time is a quantity. In other words, we need to possess accurate instruments before we can discover the quantiative laws of nature. Anyway, what's amazing is how, even with inaccurate clocks, science has ''discovered'' so many physical laws.

Now, here's something that I just thought of...

If you'll agree with me that time measurement isn't as accurate as we think then could it be that all the laws of nature we've discovered so far are wrong? They're just approximations at best and completely bogus at worst. What if there are no laws of nature and all the patterns we see in nature (at least those dependent on time) are simply illusions created by our failure to measure time accurately?

What it implies is that we can never be absolutely certain about the length of any time period. — Metaphysician Undercover

Yes. Please read above. Sorry can't reply to you separately.

I remember in high school I read something about the pendulum's period depending on g (acceleration due to gravity) and L (the length of the pendulum). — TheMadFool

This is true of weight pendulums like the one in a grandfather clock. Such clocks run slow on the moon for instance. There is a mass-pendulum in my watch, and in a typical 400-day clock. Those stay pretty accurate on the moon. Similarly your weight is dependent on G, but your mass is not.

However, I don't think this really solves the problem because quantification comes first in physics and time is a quantity. In other words, we need to possess accurate instruments before we can discover the quantiative laws of nature.

Right. So they know the length of the day was stable (plus/minus 30 seconds), so eventually they needed to build an instrument that said the same value day after day. The hourglass was not accurate enough. Oddly, it was the train and boat people, not the scientists, that drove the technology for the first accurate clocks. Train folks needed it to prevent crashes, and the boat people needed it for navigation. Science had little use for that sort of accuracy back in those days. They worked out F=MA without need of it.

Now, here's something that I just thought of...

If you'll agree with me that time measurement isn't as accurate as we think then could it be that all the laws of nature we've discovered so far are wrong?

The laws we know result in models that give relatively accurate predictions, and are not something that is wrong or right. If you want to posit different laws, you are welcome to do so, but if they make worse predictions, they're less useful laws.

They're just approximations at best and completely bogus at worst. What if there are no laws of nature and all the patterns we see in nature (at least those dependent on time) are simply illusions created by our failure to measure time accurately?

If there are no laws, then there is no time to measure inaccurately. The statement is thus incoherent, You're asking that if there is no map, is the territory an illusion? What if I have a completely bogus map that has no correspondence to the territory, and yet the nonsense map gets me where I want to go every single time? How bogus is the map then? Seems to be what you're asking.

Time is mysterious. Duration in every day contexts is not. It isn't as if the mysteries of time impede interpretation and calibration of watches. That's the point I was making.

Science had little use for that sort of accuracy back in those days. — noAxioms

I guess we have acceptable limits of accuracy.

They worked out F=MA without need of it. — noAxioms

Really? I thought time was part of A (acceleration)? Were Newton's laws theoretically derived?

The laws we know result in models that give relatively accurate predictions, and are not something that is wrong or right. If you want to posit different laws, you are welcome to do so, but if they make worse predictions, they're less useful laws. — noAxioms

Let me illustrate what I mean.

Imagine a world with a radioactive element x that decays at the rate of 1 atom every true second.

Let's suppose we have a clock that is irregular too: one tick is supposed to be 1 second but actually tick1 = 1 second, tick 2 = 2 seconds, tick 3 = 1 second, tick 4 = 2 second and so on.

If we study the element x for 4 ticks (4 seconds by the defective clock) of the clock
6 atoms decayed because 6 true seconds have passed (1, 2, 1, 2)
Time passed by the clock = 4 seconds
Rate of decay = 6/4 = 1.5 atoms/second

But...

The actual time passed = 6 seconds ( 1, 2, 1, 2)
True rate of decay = 6/6 = 1 atom/second

If the defective clock is used universally then we will never notice the error.

What do you think? Thank you for your replies. I've learned a lot.

That's why we need to compare numerous physical activities to produce an accurate clock.

Science had little use for that sort of accuracy back in those days.
They worked out F=MA without need of it.
— noAxioms

Really? I thought time was part of A (acceleration)? Were Newton's laws theoretically derived? — TheMadFool

Without the precision required to navigate a boat. I didn't say it was done without time measurement.
Massive precision is needed only for more recent physics like the relativity experiments done a century ago.

Imagine a world with a radioactive element x that decays at the rate of 1 atom every true second.

Let's suppose we have a clock that is irregular too: one tick is supposed to be 1 second but actually tick1 = 1 second, tick 2 = 2 seconds, tick 3 = 1 second, tick 4 = 2 second and so on.

If we study the element x for 4 ticks (4 seconds by the defective clock) of the clock
6 atoms decayed because 6 true seconds have passed (1, 2, 1, 2)
Time passed by the clock = 4 seconds
Rate of decay = 6/4 = 1.5 atoms/second

But...

The actual time passed = 6 seconds ( 1, 2, 1, 2)
True rate of decay = 6/6 = 1 atom/second

If the defective clock is used universally then we will never notice the error.

What do you think? Thank you for your replies. I've learned a lot.

Sounds like you have the beginning of a competing set of laws in which time is defined alternatively. But it fails the falsification test.

I have two such samples. One of them does 6 ticks, and the other does 2. Next iteration, the former does 3 and the latter does 4. Clearly the radioactive samples are not measuring actual time since they're not matched.

My example used whole numbers and the error reveals itself quite easily but what if the time irregularity is in the nanoseconds or femtoseconds? Errors at such scales can be detected only over millions of years, right?

Look at the history of time measurement. Started with the sun, moon and earth - wasn't accurate enough. Then we moved to pendulums - wasn't accurate enough. Now we have atomic clocks - aren't perfect. Isn't this the infinite regress I'm suggesting here?

My example used whole numbers and the error reveals itself quite easily but what if the time irregularity is in the nanoseconds or femtoseconds? Errors at such scales can be detected only over millions of years, right? — TheMadFool

My counter example works fine with nanoseconds. The radioactive samples might tick every nanosecond and the example still holds. The two samples would not be in sync ever, and thus are not representative of actual time. The decays are random events, much in the same way that Earth rotations are not.

Look at the history of time measurement. Started with the sun, moon and earth - wasn't accurate enough. Then we moved to pendulums - wasn't accurate enough. Now we have atomic clocks - aren't perfect. Isn't this the infinite regress I'm suggesting here?

Sun movement is way more accurate than pendulums, but inaccurate in the long run. The day used to be a lot shorter.

I see no infinite regress, or even finite. Yes, some things are more regular than others, radioactive decay being probably at the low end of the scale. Such accuracy is not needed except to verify very fine differences. You apparently don't accept that. You seem to assert that time cannot be known without some insanely accurate device. But somebody said that a day is defined as the time from noon to noon on some arbitrary day in say 1900, and that's the standard, period, even if we don't know how to translate that value into Caesium vibrations (something even more stable than Earth) to twelve places until decades later.

but what if the time irregularity is in the nanoseconds or femtoseconds? — TheMadFool

I think you ask about what if the radioactive same ticked regularly. Then the decays would not be random events, but regular ones. All similar-rate samples would tick in sync. They don't. No way at all to predict when the next tick will come or which sample will yield the next tick.