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As far as I am aware, frequency is the most accurate physical property we can currently measure. This has led us to very high standards of experimental verification of e.g QED predictions and the CMB spectrum.

EDIT: as is pointed out below, the second is a defined figure and time should not really be listed here. Please take measuring frequency as a distinct matter.

Out of pure curiosity, I am wondering what the next physical property, without involving energy or time, is it that we can measure most accurately?

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    $\begingroup$ The base unit of time, the second, is defined explicitly. $\endgroup$ – Kyle Kanos May 21 '15 at 16:42
  • $\begingroup$ Minor point, time is not a physical constant $\endgroup$ – Jim May 21 '15 at 16:43
  • $\begingroup$ One should probably distinguish between absolute and relative measurements. Ratios can usually be measured with much higher precision. An integer or even fractional frequency ratio, for instance, can be established with arbitrary precision (within the limits of the lifetime of the experiment, of course). Voltage and current ratios with relative errors down to the 1e-9 range and below can be made with almost trivial electronics equipment, a similar absolute precision requires the use of a quantum hall effect setup. As a consequence precision experiments are therefor trying to use ratios. $\endgroup$ – CuriousOne May 21 '15 at 17:15
  • $\begingroup$ @CuriousOne I can look it up, but I'm guessing it was something similar that Hulse Taylor did when measuring pulsars emissions years ago. I know they could not possibly have known the exact stellar masses to plug into equations. Maybe I am completely wrong here, I will check it anyway. Thanks $\endgroup$ – user81619 May 21 '15 at 19:12
  • $\begingroup$ Re @CuriousOne's remark, Ratios can usually be measured with much higher precision. Within a domain, I would agree. Across domains, that's still a bit of a struggle. An example within a domain is the ratio of the mass of a proton to that of an electron. This is known to a fairly high degree of precision (but not as well known as $g_e$ in zeldrege's answer). Examples of ratios that cross domains: The mass of a proton or the mass of the Sun in kilograms, both of which are ratios. The former hinges on Avogadro's number, while the latter hinges on $G$. $\endgroup$ – David Hammen May 21 '15 at 19:22
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You talk about time, but usually when I think "physical constant" I think of something more like $c$ or $\hbar$. Since we're increasingly using those kinds of constants to construct our units, it's a bit difficult to say how well they're measured--$c$ isn't measured, it's defined, for instance. For that reason, I think we ought to pick a dimensionless number. The best one I've found is the electron g-factor which is measured to within one part in $10^{-13}$. Note that the anomalous magnetic moment of the g-factor--the percentage difference from $g = 2$--is also the best-confirmed theoretical prediction in physics.

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  • $\begingroup$ Thank you for your answer. I do take your point regarding defined quantities and as far as I know, we can use the Planck length idea, energy...to define the most used constants, but does that not still leave measurement of G say. I should really have asked instead what is the nearest match of theoretical to experimental results, which I thought were the CMB results. Still learning how to ask questions properly $\endgroup$ – user81619 May 21 '15 at 18:56

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