I first thought of a mechanical watch being used to assess the speed of its inner mechanism and then realized that any regularly repeating system could serve as such a timing mechanism

So if we take the orbit of the moon ,can it be used to assess the speed of particular movements ,say on the earth?

Can it tell usat what ,say Trump tells lies?(events "within" the mechanism)

Can it measure the speed of coronal euptions in the Sun ?("external" events)

It seems to me that,if we choose a different regularly repeating timing mechanism-say Mercury around the Sun then there will be different measurements for the same events and there will have to be a transformation to make them agree.

That seems like a preamble to what I wanted to ask ,which is "Can a clock measure the rate of its own internal movements or do we need a second timing mechanism to do that?"

Are all measurements of time relative and never absolute?

1 hour ago, geordief said:

That seems like a preamble to what I wanted to ask ,which is "Can a clock measure the rate of its own internal movements or do we need a second timing mechanism to do that?"

Are all measurements of time relative and never absolute?

Relative. All clock measurements are as compared to another clock.

As an example, a pendulum clock ticks at some rate, but the length of the arm can vary (on purpose, or owing to e.g. temperature changes) so the only way to tell is by comparing to another clock, preferably with different/smaller sources of error.

There’s no absolute measurement, no “truth” that we compare it to, no perfect clock. There’s a standard, but all measurements have errors. So nobody really knows what time it is (but some care); the time is what we decide it is - by agreement, these days.

Same thing applies to length - you can’t use a ruler to tell if that ruler has expanded or contracted - or any quantity we measure

32 minutes ago, swansont said:

Relative. All clock measurements are as compared to another clock.

As an example, a pendulum clock ticks at some rate, but the length of the arm can vary (on purpose, or owing to e.g. temperature changes) so the only way to tell is by comparing to another clock, preferably with different/smaller sources of error.

There’s no absolute measurement, no “truth” that we compare it to, no perfect clock. There’s a standard, but all measurements have errors. So nobody really knows what time it is (but some care); the time is what we decide it is - by agreement, these days.

Same thing applies to length - you can’t use a ruler to tell if that ruler has expanded or contracted - or any quantity we measure

So we can't even measure absolute time elapsed in our own frame other than to an approximation?(unsurprising perhaps)

Is it an interesting (or true) observation that a "clock" cannot "time itself?"

There are two kinds of measurements in Physics.
One is termed 'absolute' and temperature would be an example; there is a zero point and all measurements are all related only to that.
The other is 'gauge' which is a relational measurement depending on how you measure; a bird on a 15000V line does not get electrocuted, as the bird itself would measure 0V.

And you do have an interest in relativity and are quite familiar with it, so you are aware that time, distance and speeds are all relative, and interlinked by Galilean and Special Relativity.

Time is 'kept' by measurement of repeating changes, so, to measure the accuracy of the 'repeating changes' of your clock, you need another standard which measures repeating changes, and you can set T=0 whenever you want.

3 hours ago, geordief said:

regularly repeating system could serve as such a timing mechanism

This is a key statement.

'regularly repeating'

How do you know it is regularly repeating ? What do you even mean by this ?

An 'absolute measurement' that MigL did not mention is 'count' : There is a count of two atoms of hydrogen in a water molecule and one atom of oxygen.

But I regard any 'regular repeat' as a bit like the squares or lines printed on graph paper.

We use these, assuming that each square or each line is identically spaced on the paper, without thinking about it.

Similarly we think of a 'regular event such as a clock tick ( all clocks have this in one way or another) as being identical whith every other tick of that clock.

What is needed is something like how a toolmaker prepares a 'straight edge' or a flat surface and tests it for 'truth'.

When such an object is machined, they are made in threes not twos.

This way irregularities in one cannot build up with matching irregularities in another because both have to individual also test agains the third member.

For timing it may be possible to extend this idea to something like the old TV line and frame scan and frame rate.

I don't know, I would have to think about that, ideas are welcome.

2 hours ago, geordief said:

So we can't even measure absolute time elapsed in our own frame other than to an approximation?(unsurprising perhaps)

It’s the scale of the approximation that’s relevant. Clocks today can measure and disseminate at around the tens of picoseconds level. One always tends to lead the other, from a technology standpoint - making a really precise measurement doesn’t mean a lot if you can’t tell anyone about it, i.e. the dissemination adds a significant amount of error to it (e.g. telling time to a nanosecond but your communication method is limited to a microsecond) - so there tends to be a focus on the lagging technology. During the latter half of my time at USNO there was a push to develop high-precision transfer over fiber-optic networks by labs around the world, to keep up with advances in the clocks. Prior to that it was improving satellite transfer methods using GPS signals.

Time intervals/differences, if they are short enough, can be measured to even higher precision (clock vs stopwatch)

2 hours ago, geordief said:

Is it an interesting (or true) observation that a "clock" cannot "time itself?"

It’s true. Interesting to some, sure. To those in timing/metrology, it’s more obvious.

1 hour ago, MigL said:

One is termed 'absolute' and temperature would be an example; there is a zero point and all measurements are all related only to that.

That’s a scale, though, and not a measurement. You would do a measurement with a thermometer or some other device, and that device would never be exact, nor could you be sure the value you measure is correct without calibration, which is a comparison to a standard.

50 minutes ago, studiot said:

An 'absolute measurement' that MigL did not mention is 'count' : There is a count of two atoms of hydrogen in a water molecule and one atom of oxygen.

Yes. That’s a special category, and while you can have counting errors, you’re not really comparing it to anything.

5 hours ago, swansont said:

Yes. That’s a special category, and while you can have counting errors, you’re not really comparing it to anything.

Isn't that why it is called absolute ?

14 minutes ago, studiot said:

Isn't that why it is called absolute ?

It’s why IMO it’s not a measurement.

8 minutes ago, swansont said:

It’s why IMO it’s not a measurement.

So If I put a quantity of marbles in a bag and my friend counts them it is not a measurement of how many ?

12 hours ago, studiot said:

So If I put a quantity of marbles in a bag and my friend counts them it is not a measurement of how many ?

No, not in a scientific sense

“Measurement is defined as the process of comparison of an unknown quantity with a known or standard quantity.”

Also there’s got to be units, that can be expressed in SI terms

https://en.wikipedia.org/wiki/Measurement

see also https://en.wikipedia.org/wiki/Metrology

19 hours ago, studiot said:

So If I put a quantity of marbles in a bag and my friend counts them it is not a measurement of how many ?

May we say that a measurement is an injection from a set of observations to a countable subset of \(\mathbb{R}\), and this injection may be composed of many linked injections?

If so, then it might appear that it is time that is the outlier, not count.

3 hours ago, Xerxes said:

May we say that a measurement is an injection from a set of observations to a countable subset of R, and this injection may be composed of many linked injections?

If so, then it might appear that it is time that is the outlier, not count.

How does time differ from the measurement of any other quantity in science that has SI units?

What if:

We measure time with constant notion and get some errors due to not factoring into density of time..?

11 hours ago, swansont said:

No, not in a scientific sense

“Measurement is defined as the process of comparison of an unknown quantity with a known or standard quantity.”

Also there’s got to be units, that can be expressed in SI terms

I'm afraid we are going to have to agree to differ on this matter.

There are certainly quantities, investigatable by and measureble by Science that have no units at all.

I was going to work my bag of marbels into some of these by noting that if some of the marbels are blue and the rest red we can calculate the % blue marbles in the bag.

This leads on to many quantities of interest that have no units and or are defined by ratios/fractions/percentages.

This includes one of the odlest determinations in scientific History by one Archimedes of Syracuse.

That is the question of purity.

Was the crown 100% gold ?

The we have the quantity angle which has no units

As does refractive index.

Count of course is different again because the integers are not continuous, unlike say sini/sinr.

I believe count is recently officially included in SI to allow for the n in such Physics as PV =nRT.

4 hours ago, Xerxes said:

May we say that a measurement is an injection from a set of observations to a countable subset of R, and this injection may be composed of many linked injections?

If so, then it might appear that it is time that is the outlier, not count.

We think that time is continuous not granular so needs a continuous number system to represent its flow or whatever.

But otherwise yes I agree your mapping would be good.

19 minutes ago, tylers100 said:

What if:

We measure time with constant notion and get some errors due to not factoring into density of time..?

Would you like to clarify this ?

Note I already pointed out that the only clocks I know of (perhaps swansont can offer some that are actuoully continuous such as ephemeris time ?) measure time in discrete 'ticks' that we believe the time interval between any sequential pair of ticks is identical to any other.

15 hours ago, studiot said:

I'm afraid we are going to have to agree to differ on this matter.

There are certainly quantities, investigatable by and measureble by Science that have no units at all.

I was going to work my bag of marbels into some of these by noting that if some of the marbels are blue and the rest red we can calculate the % blue marbles in the bag.

This leads on to many quantities of interest that have no units and or are defined by ratios/fractions/percentages.

This includes one of the odlest determinations in scientific History by one Archimedes of Syracuse.

That is the question of purity.

Was the crown 100% gold ?

The we have the quantity angle which has no units

As does refractive index.

Count of course is different again because the integers are not continuous, unlike say sini/sinr.

I believe count is recently officially included in SI to allow for the n in such Physics as PV =nRT.

We think that time is continuous not granular so needs a continuous number system to represent its flow or whatever.

But otherwise yes I agree your mapping would be good.

Would you like to clarify this ?

Note I already pointed out that the only clocks I know of (perhaps swansont can offer some that are actuoully continuous such as ephemeris time ?) measure time in discrete 'ticks' that we believe the time interval between any sequential pair of ticks is identical to any other.

Not Sure Exactly

I'm a bit not sure too about what I said in regard to density of time.

Maybe Gravity

Maybe it was something from my learning and doing thought-experiment with the gravity, density is part of it. So, maybe the density word and its meaning connected with time by myself to define time dilation or time speeding up (e.g. "time flies") as part of subjectively experience but not sure about objective though.

Scaling to Factor Density Maybe

Constant ruler measurement and constant time, but scaling to factor density in.

TBH

TBH, I'm still learning about physics and mathematics but still not sure what I'm talking about, but approximation to best can do.

16 hours ago, studiot said:

This leads on to many quantities of interest that have no units and or are defined by ratios/fractions/percentages.

This includes one of the odlest determinations in scientific History by one Archimedes of Syracuse.

That is the question of purity.

Was the crown 100% gold ?

The we have the quantity angle which has no units

As does refractive index.

Ratios involve quantities that have units, which is where the uncertainty arises.

On 12/13/2025 at 10:46 PM, studiot said:

We think that time is continuous not granular so needs a continuous number system to represent its flow or whatever.

Right. By a "continuous number system" I assume you mean a complete number system. Which would include \(\mathbb{R}\) but not include a countable subset, as I had claimed.

So my question is this (and it's not rhetorical!); if time is continuous, as I beleive the spectra of some QM operators also are, and if the rational numbers are not sufficient to describe continuous phenomena, what meaning can be attached to a measurement of, say, \(e\) or \(\sqrt{2}\) or, for that matter, of \(\pi\) which as you say is a ratio, not a measurement, which would have to included in a complete subset of the Reals

Edited December 15Dec 15 by Xerxes

5 hours ago, Xerxes said:

Right. By a "continuous number system" I assume you mean a complete number system. Which would include R but not include a countable subset, as I had claimed.

So my question is this (and it's not rhetorical!); if time is continuous, as I beleive the spectra of some QM operators also are, and if the rational numbers are not sufficient to describe continuous phenomena, what meaning can be attached to a measurement of, say, e or 2–√ or, for that matter, of π which as you say is a ratio, not a measurement, which would have to included in a complete subset of the Reals

Yes complete is perhaps more basic that continuous, though both rely on limits and convergence for their definition.

5 hours ago, Xerxes said:

e or 2–√ or, for that matter, of π which as you say is a ratio, not a measurement, which would have to included in a complete subset of the Reals

But I'm am not sure what led you to think I regard any of these as a ratio ?

On 12/13/2025 at 6:35 AM, swansont said:

“Measurement is defined as the process of comparison of an unknown quantity with a known or standard quantity.”

If I was standing, like a bird, on a 1500V cable ( without a ground, obviously ), what would I measure the voltage of the cable to be ?

On 12/14/2025 at 9:29 AM, tylers100 said:

I'm a bit not sure too about what I said in regard to density of time.

We have no clue what you mean by 'density' of time.
Are some clocks heavier than others ?

52 minutes ago, MigL said:

If I was standing, like a bird, on a 1500V cable ( without a ground, obviously ), what would I measure the voltage of the cable to be ?

Voltage is always measured with respect to something. It’s a potential difference. So you have not provided enough information to answer the question.

11 hours ago, swansont said:

Voltage is always measured with respect to something.

Exactly.
That is an example of a 'gauge'.

Something like temperature, on the other hand, is not a relative measurement.
We don't so much compare it to a scale, rather we assign a scale to it.

I would have thought the word 'absolute' would be fitting, but maybe not.
Nevertheless, there is a difference to a relational 'gauge' measurement.

33 minutes ago, MigL said:

Exactly.
That is an example of a 'gauge'.

Something like temperature, on the other hand, is not a relative measurement.
We don't so much compare it to a scale, rather we assign a scale to it.

I would have thought the word 'absolute' would be fitting, but maybe not.
Nevertheless, there is a difference to a relational 'gauge' measurement.

Can you measure temperature without a comparison?

Absolute vs gauge doesn’t matter in this context.

39 minutes ago, MigL said:

Exactly.
That is an example of a 'gauge'.

Something like temperature, on the other hand, is not a relative measurement.
We don't so much compare it to a scale, rather we assign a scale to it.

I would have thought the word 'absolute' would be fitting, but maybe not.
Nevertheless, there is a difference to a relational 'gauge' measurement.

20 hours ago, Xerxes said:

Right. By a "continuous number system" I assume you mean a complete number system. Which would include R but not include a countable subset, as I had claimed.

So my question is this (and it's not rhetorical!); if time is continuous, as I beleive the spectra of some QM operators also are, and if the rational numbers are not sufficient to describe continuous phenomena, what meaning can be attached to a measurement of, say, e or 2–√ or, for that matter, of π which as you say is a ratio, not a measurement, which would have to included in a complete subset of the Reals

11 hours ago, swansont said:

Voltage is always measured with respect to something. It’s a potential difference. So you have not provided enough information to answer the question.

Taking regard of the above points I would perhaps reconsider my comments since whilst I agree that many, if not most, measurements are made with reference to a standard, not all measurements are actually numeric.
And even when the output is a 'number' it maynot be a cardinal or ordinal but a number used as a label.

The Richter scale, the Beaufort scale the Mohr scale, the Atterberg scale. Lustre, Sheen come to mind.

So regarding measurements as injections is perhaps a bit over the top and certainly specefication of the set from which the numbers are drawn.

17 hours ago, MigL said:

If I was standing, like a bird, on a 1500V cable ( without a ground, obviously ), what would I measure the voltage of the cable to be ?

We have no clue what you mean by 'density' of time.
Are some clocks heavier than others ?

I don't know for fact, but I imagine some clocks would be surely heavier in some zones affected by different heights (e.g. gravity) and materials made.

3 hours ago, tylers100 said:

I don't know for fact, but I imagine some clocks would be surely heavier in some zones affected by different heights (e.g. gravity) and materials made.

clocks measure time, they are not time itself