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.

 

[Astronuc]

Relatively speaking, yes, give or take.

 

[Borek]

Does the charge of an ion expressed in units of elementary charge count as absolute?

 

[Vanadium 50]

I have six pennies in my hand. Is six absolute?

 

[DaveE]

I have six pennies in my hand. Is six absolute?

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

 

[256bits]

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,

 

[etotheipi]

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?

 

[256bits]

Huh?
What?

Think about it.
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.

 

[etotheipi]

Think about it.
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?

 

[256bits]

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.

 

[DaveE]

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.

 

[etotheipi]

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.

 

[DaveE]

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.

 

[DaveE]

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.

 

[DaveC426913]

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.

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.)

 

[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.

 

[phinds]

Third grade math problem:
Q: Bob had 25 candy bars and ate 20 of them. What does Bob have now?
A: Third grade answer: Diabetes. Bob has diabetes now.

 

[phinds]

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 !

 

[DaveC426913]

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...

 

[DrGreg]

Third grade math problem:
Q: Bob had 25 candy bars and ate 20 of them. What does Bob have now?
A: Third grade answer: Diabetes. Bob has diabetes now.

Blackadder:
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

 

[256bits]

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?

 

[DaveE]

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.

 

[DaveC426913]

Didn't the foot long ruler length change depending upon who was king?

Perhaps the inch changed along with it...

 

[Astronuc]

I have six pennies in my hand. Is six absolute?

Exactly, my dear Watson. Cheerio. Pip pip.

 

[Dale]

Temporarily closed for review, but don’t hold your breath.

 

[Nugatory]

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”.

 

[berkeman]

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.

 

[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.

 

[Vanadium 50]

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.

 

[256bits]

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 -

 

[collinsmark]

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.

 

[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.

 

[Ibix]

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.

 

[collinsmark]

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.

 

[Vanadium 50]

As mentioned before, the speed of light is defined, not measured. You can't measure it any more than you can measure the transition frequency between the two ground state hyperfine levels of cesium. That defines the second, so the only possible outcome is exactly 9192631770 Hz.

There are quantities that are discrete and quantities that are continuous. Continuous quantities usually are measured within a range, and are most often expressed as a central value and an error bar.

Discrete quantities are most often determined by the C-word which must not be mentioned. But there are other examples. Gold at STP either has a FCC structure or it does not. Venus either has moons or does not. Radium is either radioactive, or it is not. These are discrete. (One can also ask related questions on continuous quantities, such as "what is the lattice spacing of gold at STP", but that doesn't change the fact that there are questions whose answers are discrete.)

 

[nuuskur]

Naively speaking, no, because we're always measuring relative to something. Mathematically speaking the question should be formulated as "Definition for absolute measurement" and then proceed to find examples or giving arguments why there are none.

 

[Hacker Jack]

Can't wrap my head around the fact that the speed of light is just defined but not measured. So you are saying a thing called photon or light that exists in reality like an object with mass moves from one point in space to another point and it is simply defined without some form of measurement. So how then do we even know that it has moved 299 792 458 metres in 1 second without measuring of some sort. And how can you be sure that is exactly the distance it traveled even with experiment when there are no perfect tools in existence.

 

[etotheipi]

It's just semantics, nothing deep. It's just because now the metre is defined as how far a photon moves in a vacuum in exactly 1/299792458 seconds!

 

[Hacker Jack]

But how can you know that without some sort of measurement. How can you know that the photon moved that much of a distance at specific time without measuring something.

 

[Ibix]

But how can you know that without some sort of measurement. How can you know that the photon moved that much of a distance at specific time without measuring something.

We define 1m that way. Then we get a very accurate clock and see how far light travels in the specified time. So we measure time, and use this process to define a distance measure.

Of course, the 299792458 number is picked so that 1m (by this modern definition) is very very close to the length of the rod we used to use to define the metre. That was deliberate, so that only metrology nerds needed to worry about the change.

 

[Hacker Jack]

But experiment with clock is not perfect so result of speed of light from experiment not perfect. But we just accept it as theory says?

 

[etotheipi]

you don't measure definitions bro

 

[Hacker Jack]

Then what proof is there that light is certain speed in certain time if you don't measure. Can I define the speed of a car driving by and say that is certain speed it's going at. Science requires experiment to verify theory even though experiment always had uncertainty or percentage error whatever you call it. But guy mentioned accurate clock is used to measure so I guess that's that.

 

[russ_watters]

Can't wrap my head around the fact that the speed of light is just defined but not measured.

IMO, it's over-stated to say the speed of light can't be measured, and the history gives insight into this. The problem is accuracy/consistency. Any system of measurement has arbitrarily chosen units that need to be defined. Defining the length of a meter is different from measuring the distance to the sun. The distance to the sun is measured, whereas the length of a meter has to be defined...but if you really wanted to, you could define a distance scale using an approximate value of the distance to the sun; and we have. But the length of a meter doesn't have a physical manifestation absent human assignment. If you tried to measure the length of a meter, you'd really be doing that by comparing two different representations of the defined value.

There are of course devices for measuring the speed of light, that have the same problem as comparing two meter sticks. They use approximations of the defined units for things like length and time. But a century ago it was recognized that the speed of light was constant, so it makes more sense to use the speed of light as the measuring stick instead of the object being measured. Eventually it made sense/became necessary to make that the "meter stick".

 

[etotheipi]

Can I define the speed of a car driving by and say that is certain speed it's going at.

well no, the trick with the photon is that as far as known it always goes along in a vacuum at a constant speed (thought to coincide with the universal speed limit) and which is the same as measured by any inertial oberver. so light can be used to define a standard unit of proper length

speed of a car is not constrained to be constant, nor invariant. so it's silly to try and define a unit of length based on that

 

[Ibix]

Can I define the speed of a car driving by and say that is certain speed it's going at.

If you define a mile as "the distance my car goes in 2 minutes when my foot applies a certain pressure on the accelerator on a flat track in fourth gear on a windless day", then sure. Note that there's many caveats here that there aren't with light in a vacuum, which makes light speed a much more reliable measure. This car based one is nowhere near repeatable enough for metrologists, but it's not wrong in principle.

 

[PeroK]

Then what proof is there that light is certain speed in certain time if you don't measure. Can I define the speed of a car driving by and say that is certain speed it's going at. Science requires experiment to verify theory even though experiment always had uncertainty or percentage error whatever you call it. But guy mentioned accurate clock is used to measure so I guess that's that.

You can take a look at all the historical definitions of the metre here:

https://en.wikipedia.org/wiki/Metre#Timeline

You can't have everything done by measurement, because you can't get started. You can't measure something until you have a definition. You need a definition of the basic units.

The modern approach is to take the speed of light in vacuum as a basic unit, as it were, instead of defining the metre. That's ultimately a question of usefulness and practicality.

Using your car wouldn't be very practical or reliable - although, in the past, units have been dependent on who does the measuring. Horsepower must at one time been the power of an average horse. And "feet" would have been literally that and a measurement would depend on the size of your feet.

 

[f95toli]

You need to be a bit careful here.
In physics (well, metrology) an "absolute measurement" means a measurement where the result does not rely on a comparison to a reference. Or, in other words, you don't need any part of your measurement apparatus to be calibrated for you to get the correct result.
Absolute measurements a rare, but they do exist. An obvious example would be the realisations of the SI which for obvious reasons ideally should be absolute. A good example would be the quantum hall effect which is used to calibrate resistance standards.
Sometimes we do "bend the rules" a bit. It is quite common to call a measurement "absolute" if it only relies on one primary standard as a reference, usually time/frequency.
For example realisations of the Ampere using electron pumps are sometimes called "absolute" even though you need to have an frequency standard that is known to be accurate (say a hydrogen maser) for it to work.
If you know the frequency and you know that your pump only moves one electron at a time you have a "absolute" current standards where the output current is I=e*f. Once you have that current you can then use it to perform absolute measurements of other currents by using "nulling".

 

[WWGD]

The only thing that is arbitrary is the unit of measurement. Once that has been decided, agreed upon, the measurement is " absolute".

 

[jbriggs444]

Any system of measurement has arbitrarily chosen units that need to be defined.

If, for instance, one defined the meter as the distance between two particular scratches on a particular artifact then the measured distance between said scratches would naturally be one meter exactly, by definition.