# Is there such thing as an absolute measurement?

Hacker Jack
To want to know the exact quantity of an object whether it be it's length, width, weight etc... Doesn't an absolute measurement only exist in the math/our human Minds. Then go down to quantum scales and that gets even harder because from what point do we even measure from if there is no exact point (I think). Hopefully this is considered mainstream. Thanks in advance.

Staff Emeritus
Relatively speaking, yes, give or take.

ProfuselyQuarky, berkeman, DaveC426913 and 2 others
Mentor
Does the charge of an ion expressed in units of elementary charge count as absolute?

AlexCaledin
Staff Emeritus
2021 Award
I have six pennies in my hand. Is six absolute?

berkeman, Astronuc and etotheipi
Gold Member
I have six pennies in my hand. Is six absolute?
Yes. But is counting measurement? You only have 3 pairs of pennies.

Gold Member
You have somewhere between 5 and 7 pennies.

When you count to 5 you still have more uncounted but so you up the count to 6..
When you get to 6, you may have some more uncounted, but are unsure.
when you get to 7, there definitely is no penny, so you backtrack by 1 to 6.
Is that the last penny, you are unsure, so you backtrack once more to 5
Now some pennies left over so you count up, to 6
Is that the last penny, not sure, so count up to 7.
And so on...
you are always hovering between 5 and 7, forever, and ever,

Yes. But is counting measurement? You only have 3 pairs of pennies.

Huh?

You have somewhere between 5 and 7 pennies.

When you count to 5 you still have more uncounted but so you up the count to 6..
When you get to 6, you may have some more uncounted, but are unsure.
when you get to 7, there definitely is no penny, so you backtrack by 1 to 6.
Is that the last penny, you are unsure, so you backtrack once more to 5
Now some pennies left over so you count up, to 6
Is that the last penny, not sure, so count up to 7.
And so on...
you are always hovering between 5 and 7, forever, and ever,

What?

Klystron
Gold Member
Huh?

What?
When you count you have to look ahead - and count 1 after the amount there actually.
Certainly that comes natural to a person trained in counting.

The backtracking all the way to to 5 does seem kind of iffy, though.
More likely, one is hovering between 6 and 7 , with a mean of 6.5.

When you count you have to look ahead - and count 1 after the amount there actually.
Certainly that comes natural to a person trained in counting.

The backtracking all the way to to 5 does seem kind of iffy, though.
More likely, one is hovering between 6 and 7 , with a mean of 6.5.

No, that's absurd. The most basic operation is incrementation; you start at zero, with all the pennies on one side of the table, and each time you move one across to the other side of the table you increment the total by one. You can count by scratching a line in the table each time you move a penny, or whatever.

Why the heck would you increment the total a further time, to 7, when you have no pennies left to move across to the other side of the table?

Klystron and Dale
Gold Member
how did you know there were no more pennies left to move, you checked, which is one more count.

it might be abstract,;
but if you take a ruler marked off in inches, and measure a line length, one will write down the length as being 6 ± 0.5. it's not 5 .5 and its not 6.5, but somewhere in between. A measurement is actually counting.

Gold Member
You have somewhere between 5 and 7 pennies.

When you count to 5 you still have more uncounted but so you up the count to 6..
When you get to 6, you may have some more uncounted, but are unsure.
when you get to 7, there definitely is no penny, so you backtrack by 1 to 6.
Is that the last penny, you are unsure, so you backtrack once more to 5
Now some pennies left over so you count up, to 6
Is that the last penny, not sure, so count up to 7.
And so on...
you are always hovering between 5 and 7, forever, and ever,
Yup, you've nailed the math of counting. But, perhaps measurement requires counting AND the definition of what you are counting. It's not really that useful if I tell you the weight of a machine I'm shipping is 83. OTOH, you could bet that two of them would be 166, or 2 machines. "2 machines" contains useful information; I'm not sure "166" is that helpful.

256bits
how did you know there were no more pennies left to move, you checked, which is one more count.

No, it's because I looked and observed that there were no more pennies on that side of the table? The counting was implemented operationally by scratching the table each time I moved a penny, so if I only have 6 pennies to move across, I never make a "7th count".

but if you take a ruler marked off in inches, and measure a line length, one will write down the length as being 6 ± 0.5. it's not 5 .5 and its not 6.5, but somewhere in between. A measurement is actually counting.

That's completely different, that's uncertainty! The measured length of the line can be taken to be a random variable, and the value of a measurement is taken from a distribution. Then the measured value must be quoted with some measure of uncertainty, e.g. a standard deviation, which reflects the limitations of the measuring apparatus.

The difference with pennies is that the measured value is taken from the integers, whilst for lengths it's from the rationals (which are themselves dense in the reals). To both quantities you might assign an uncertainty, although probably not for the pennies if you're only dealing with small numbers.

Yup, you've nailed the math of counting. But, perhaps measurement requires counting AND the definition of what you are counting. It's not really that useful if I tell you the weight of a machine I'm shipping is 83. OTOH, you could bet that two of them would be 166, or 2 machines. "2 machines" contains useful information; I'm not sure "166" is that helpful.

Well, obviously! That was sort of my point. You can look at it in two ways:

- either, you're measuring two different quantities: ##n_1 = ## the number of pennies, and ##n_2 = ## the number of pairs of pennies.
- or you're measuring the same quantity, the "amount" of pennies, but expressing the measured value in terms of two different sets of units. In this case the measured value in a certain unit scales inversely to the size of the unit.

In other words, what @Vanadium 50 said was completely precise, because he was measuring the number of pennies, and not the number of pairs of pennies, which is a different quantity.

256bits and DaveE
Gold Member
In other words, what @Vanadium 50 said was completely precise, because he was measuring the number of pennies, and not the number of pairs of pennies.
Yes exactly. Precisely 6 pennies. Precisely 3 pairs. But not 6, and not 3.

etotheipi
Gold Member
It's a bit hilarious, if you think about it. A forum where a bunch of STEM types, mostly with college degrees, are discussing the kindergarten exercise of how many apples are in the fruit bowl. We all know everything about this question. We are all correct.

I'm not a huge philosophy fan, but It seems pointless even in that realm.

Hamiltonian, 256bits and jim mcnamara
Gold Member
how did you know there were no more pennies left to move, you checked, which is one more count.
No. Checking is not part of the counting.

Code:
while (uncounted_pennies > 0 {
movePenny();
}

movePenny(){
uncounted_pennies = uncounted_pennies - 1;
counted_pennies = counted_pennies + 1;
}

The check (the "while") is not where the counting occurs.
The counting occurs when you actually move a penny.

(While this is written out as pseudocode, it's just as valid logic in wetware as it is in hardware.)

Klystron and etotheipi
It's a bit hilarious, if you think about it. A forum where a bunch of STEM types, mostly with college degrees, are discussing the kindergarten exercise of how many apples are in the fruit bowl. We all know everything about this question. We are all correct.

Well, Terence Tao - one of the greatest living mathematicians - spent the first 15 or so pages of "Analysis I" explaining how to count.

256bits
Gold Member
2021 Award
Q: Bob had 25 candy bars and ate 20 of them. What does Bob have now?

nomadreid, AppleDan, jedishrfu and 2 others
Gold Member
2021 Award
you are always hovering between 5 and 7, forever, and ever,
Ridiculous. @Vanadium 50 does not hover. He has 6 pennies and he don't need no damn hovering !

Gold Member
A foot long ruler is exactly 12 inches long.

Technically, that's a definition, but it's just as easily a measurement.

Try measuring a foot long ruler in inches. Keep going to more accuracy* until/unless you start to see a discrepancy.

*or is it precision? I can never remember which is which...

Gold Member
Q: Bob had 25 candy bars and ate 20 of them. What does Bob have now?
I have two beans, then I add two more beans. What does that make?

Baldrick:
A very small casserole.

From Blackadder II by Richard Curtis and Ben Elton

nomadreid, jedishrfu, jbunniii and 4 others
Gold Member
A foot long ruler is exactly 12 inches long.

Technically, that's a definition, but it's just as easily a measurement.

Try measuring a foot long ruler in inches. Keep going to more accuracy* until/unless you start to see a discrepancy.

*or is it precision? I can never remember which is which...
Didn't the foot long ruler length change depending upon who was king?

Gold Member
Well, Terence Tao - one of the greatest living mathematicians - spent the first 15 or so pages of "Analysis I" explaining how to count.
Exactly why I switched to engineering after my first Algebra class.

Gold Member
Didn't the foot long ruler length change depending upon who was king?
Perhaps the inch changed along with it...

Staff Emeritus
I have six pennies in my hand. Is six absolute?
Exactly, my dear Watson. Cheerio. Pip pip.

Klystron
Mentor
2021 Award
Temporarily closed for review, but don’t hold your breath.

Klystron, berkeman, jim mcnamara and 2 others
Mentor
Doesn't an absolute measurement only exist in the math/our human Minds.
Somehow this thread has drifted from the initial question into a long digression about counting. So in an effort to get back to the topic...

A scientific result presented as a “measurement” is always presented as a range. For example, the mass of the neutron (straight from Wikipedia) is ##1.67492749804(95)\times 10^{-27}## kilograms; the parenthesized 95 is the uncertainty.

So the answer is to the question is “No one has ever said there might be such a thing”.

Mentor
After an extended Mentor discussion, the thread is re-opened on the condition that "counting" of discrete objects is not relevant in the discussion about mearurements of continuous objects/events. Thank you for your cooperation.

hmmm27
Hacker Jack
Does that apply for the speed of light as well. We are all told that the speed of light is exactly 299 792 458 m/s but does that come with a percentage error/uncertainty (not sure what to call it woops) in the experiments.

Staff Emeritus
2021 Award
Drat. That will get us back into counting territory. The speed of light is an exact conversion, not a measurement. It is like there being exactly 12 inches in a foot.

Gold Member
Drat. That will get us back into counting territory. The speed of light is an exact conversion, not a measurement. It is like there being exactly 12 inches in a foot.
I don't think there is any way out, for any measurement, at least I cannot think of any that is not of a comparison of a particular object, directly or indirectly, to a set and agreed upon standard. The uncertainty of measurement would be how well you can - I can't say it -

Homework Helper
Gold Member
To want to know the exact quantity of an object whether it be it's length, width, weight etc... Doesn't an absolute measurement only exist in the math/our human Minds. Then go down to quantum scales and that gets even harder because from what point do we even measure from if there is no exact point (I think). Hopefully this is considered mainstream. Thanks in advance.
The closest thing to an "absolute measurement" like quantity I can think of off the top of my head is our current practical method of time keeping.

Some background before we discuss the practical stuff:

Before I get into the practical, let me briefly mention the theoretical. By our current definition of the second, 1 second is now defined as the time it takes a Cesium-133 atom at the ground state to oscillate exactly 9,192,631,770 times. Now we're back into counting. But let's not dwell on the counting part.

More to the point, if you have an atomic clock near a dense mountain it will tick slower than one away from dense mountains, all else being the same (elevation etc.) due to gravitational time dilation. Similarly, if you have an atomic clock at a higher elevation it will tick slightly faster, also due to gravitational time dilation. And yes, these atomic clocks are so incredibly "accurate" (so to speak -- more on that in a moment), that they can detect small changes due to relativistic effects. The point here is that even with incredibly accurate atomic clocks, they will measure time slightly differently depending on such things as their locations and speeds.

And even with relativistic effects aside, a given atomic clock is not perfect and will have uncertainty and variation due to thermal effects (it's not possible for the cesium-133 to reach absolute zero), if for no other reason. And then there's the inherent uncertainty at the quantum level. So theoretically speaking, even our atomic clocks are not perfect.

So that's all I have to say about the theoretical. Things get a little different once we start talking about the practical.

Practical aspects of time keeping:

Presently, the International Bureau of Weights and Measures combines the output of about 400 atomic clocks in 69 laboratories scattered around the globe, to form International Atomic Time (TAI). That, together with possible leap-seconds based on variations in Earth's rotation, is used for form Universal Coordinated Time (UTC).

That brings us to the gist of my point: For all practical purposes the length of a second is whatever time it takes for the TAI time to advance 1 second. That's the closest thing to a practical, commonly accepted, "absolute measurement" that exists in our world today. (At least the closest thing that I can think of.)

To pound home the point, if, hypothetically, for some weird reason, system of atomic clocks used to measure TAI time started ticking slower, then pretty much all official time as we know it -- GPS satellites, your cell phone's clock, your computer's clock, pretty much everything -- would soon synchronize up and would also start displaying time at a slower rate. (At least until UTC started manually playing around with leap-seconds, but that wouldn't change the official flow of time in-between leap seconds.) The unit of the second in SI units, which is also based on this, would change too, accordingly.

So for all practical purposes, the system of atomic clocks in TAI (or UTC if you want to include leap seconds) define the units of time. Sure, there are measurements and practical aspects involved, but that's about as close to an "absolute measurement" as you can get.

It gets a little weirder too.

The speed of light is no longer a measured quantity; it is now defined. The speed of light is, by definition, 299792458 meters per second. Exactly. No more; no less. One does not "measure" the speed of light anymore. It's defined. You just look up the number.

Instead, if you want to know how long an object is, you bring the object into the laboratory and measure the time it takes for light to pass from one end of the object to the other, multiply that time by the speed of light (299792458 m/s), and Bob's your uncle, you have the length.

This has some interesting implications. Going back to our hypothetical scenario where the atomic clocks in the TAI would slow down for some weird reason, it would also cause the official length of meter sticks to shrink grow.

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Hacker Jack
Hacker Jack
Please explain why it isn't measured and is instead 'defined'. How is it defined and how can you just define it without experimental results? Sorry if stupid question, I have little physics background.

Please explain why it isn't measured and is instead 'defined'. How is it defined and how can you just define it without experimental results? Sorry if stupid question, I have little physics background.
You can choose a standard "clock tick" and a rod of standard length, and then you can ask how many rod lengths does light travel in one clock tick. That's how you used to measure the speed of light before 2018.

But in 2018 we changed our definitions. Now, we don't have a standard rod. We still have a standard clock tick, and our standard rod is replaced by the statement that light travels exactly 299792458 units of distance in one clock tick. That defines the meter - it is 1/299792458 times the distance light travels in one second. But it also means that attempting to measure the speed of light is circular: "in one second, light travels 299792458 meters" means "in one second light travels 299792458 times the distance it travels in 1/299792458 of a second".

So in modern units the speed of light is a definition and our distance unit is derived from it.

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collinsmark
Homework Helper
Gold Member
Please explain why it isn't measured and is instead 'defined'. How is it defined and how can you just define it without experimental results? Sorry if stupid question, I have little physics background.
How is what defined?

If you're talking about the speed of light, it is now just defined as a number. No experimental results necessary. It's a physical constant and you just look up the number.

Length, on the other hand, is measured. You measure it by determining the amount of time it takes for light to pass from one location to another, then multiplying that time interval by the speed of light.

Time is the odd one out, since presently, our accepted systems of units of our science and technology use time as a fundamental basis.

"What is time?" You may ask. The best answer may be, "time is that which clocks measure." OK, sure, that sounds fine and dandy, but which clocks?

From a purely theoretical point of view it's just assumed that whatever clock is used for measuring time is accurate. From a slightly more practical (yet still theoretical), our commonly established units of time are based on the hyperfine level transitions of the unperturbed ground-state of the caesium-133 atom.

But from a purely practical point of view -- and this is where things get interesting IMHO -- the passage of time is measured by the International Bureau of Weights and Measures, combining the output of many atomic clocks, to form International Atomic Time (TAI). It's interesting in this particular case because any variations or inaccuracies in the measurement are folded into human kind's official records of the flow of time. It's the only situation I can think of where the measurements (variations, uncertainties, and all, folded in), for all practical purposes define the quantity rather than just report it.

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Staff Emeritus