Checking the Positional Invariance of Planck's Consant Using GPS

The summary could have been clearer, but the 0.007 number isn't even remotely close to representing absolute error bounds. It's actually a scaled relative error--that is, the amount the ratio of Planck's constant at one position to the value at another position differs from 1, multiplied by a scale factor. That scale factor is somewhat complicated and depends on the speed of light as well as the gravitational field and velocity of measurement devices at each position. I don't know enough general relativity to explain the reasoning behind the particular scale factor chosen. Without that reasoning the quoted number is almost useless; perhaps someone else can provide it.

From the abstract:

The results indicate that h [Planck's constant] is invariant within a limit of |\beta_h| < 0.007, where \beta_h is a dimensionless parameter that represents the extent of LPI [local position invariance] violation.

[For those unfamiliar with TeX markup, \beta is just the Greek letter beta, and _ indicates a subscript.]

The paper defines \beta_h in equation (6):

LPI violations for h can be written as
? ? ? ? h_x/h_o = 1 + \beta_h \Delta U / c^2
where h_o is the locally measured value of h at reference point O, h_x is its locally measured value at x, and \beta_h is the parameter for Planck?s constant.

\Delta U had been defined just after equation (1):

The potential difference is \Delta U = U_x - U_o,
where U_i = \Phi_i - v_i^2 / 2, \Phi_i is the gravitational potential energy per unit mass and v_i is the clock?s velocity.

Source: http://rss.slashdot.org/~r/Slashdot/slashdotScience/~3/byO0xOdlaoA/checking-the-positional-invariance-of-plancks-consant-using-gps

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