Can a measurement be 100% accurate? What about counting things?

Question

I have never heard about any experiment performed which is 100% accurate (Sorry,if there is any).By the term accurate I mean measurements exactly equal to the theoretical value .Is it every time that an experiment performed is not accurate? Why is it so?

Answer 1

Some food for thought:

1. Accuracy vs. Precision.
   In everyday conversation the words Accuracy and precision are often mixed around quite a lot, but in science it is very important to keep these concepts separate. Accuracy refers to whether the statement is True or False, while precision is a measure of the statements detail.

   For example, if I were to say that my height was between 1 cm and 100 m this statement would be accurate (it is true), but it is very imprecise. I could also say my height is 1.234274721 cm — this statement is very precise (many significant figures) but is not accurate — I am much taller than 1 cm! Ideal measurements should be both accurate and reasonably precise. So that they tell us stuff that is both true and useful.

   I assume by your question you mean “100 % precise” and NOT “100 % accurate”, but I will try to answer both questions.

2. Can I be infinitely Precise with a measurement?
   No measurement is infinitely precise. There are many reasons for this. One fundamental reason is that an infinitely precise measurement of a quantity (say the temperature) would be some number T = 23.43284731..... that never, ever ends, so would require an infinite memory to store. There are other reasons such infinite precision is not possible (the finite temperature of the detector for example).

3. Can I be 100 % accurate with a measurement?
   See my statement above where I said my height was between 1 cm and 100 m. Is this measurement accurate? I think it is. What kind of odds would I give on this measurement being true? Very very good ones. But is it “100 %” accurate? What does this statement even mean? Is this the “%” that would be implied by the odds I would offer if I was gambling on this statement? Or is it the statistical chance of me being right (so if you got millions of copies of me the % that did not make a mistake and get it wrong).

4. How do we know the truth anyway?
   Accuracy just refers to whether a statement is true or false. To know if a statement is true you need to know not just the statement, but also the true state of the world. How do you know this? All we can really say for certain about the accuracy of a measurement is whether that measurement is consistent with other measurements or statements we believe to be true. We cannot access the objective truth directly for a comparison.

Answer 2

You're not right. For example, for every billiard ball sunk into the hole, the experiment result is 1. That is because

• The measurable object (the ball with diameter 57 mm) is big in relation to the resolution of the measurement instrument (our eyes with a resolution of ≈ 50 μm)
• The setup after some settling time is irreversible, the ball hangs firmly in the net.

But it is very easy to change the setup to get a result with less than 100% accuracy. You will be blindfolded. Or/and the room with the billiard and you will be revolved head-over.

So any experimental setup includes the measurement instrument and a stable over time final state. With which instrument for example could you measure the size of an electron? Or its position? The neutrino is not interacting - or only in very rare cases - with the electron, and the measurement of any deflection is much more difficult. Any photon interacts with the electron, changing its energy content. And the oscillating electric and magnetic field components interact with the electrons field in an unmanageable manner.

Perhaps you know, that the Copenhagen interpretation is so called because

quantum mechanics can only predict the probability distribution of a given measurement's possible results. The act of measurement affects the system, causing the set of probabilities to reduce to only one of the possible values immediately after the measurement.

Scientific progress is progressing in leaps and bounds, and with the increasing complexity of experiments, there is a certain likelihood that the boundaries of unknwledge will shift further.

Answer 3

That's so because I think the initial conditions and the conditions during the period the experiment is made are always changing and hence we have to take that into account.

During our experiment sometimes(most of the times), we have to take into account many real world problems which can be ignored in theory.

Moreover there are also situations when the instrument or the device limits the maximum possible accuracy achievable. In these cases we are not concerned about $100 \% $ accuracy because the result works just fine enough. However with the right tools, methods and conditions we can go arbitrarily close to $100 \% $ accuracy.

You'll notice that in the results, the numbers which aren't fully accurate or determined with certainty are usually marked with parenthesis "$()$".

However when we go down to the quantum scales which involve sub atomic particles, Heisenberg principle prohibits $100 \% $ accuracy even in theory. We should keep that in mind :-)