Checking the Positional Invariance of Planck's Consant Using GPS 41
gzipped_tar writes "Whether the fundamental constants really stay the same is always a question worth asking. In particular, the constancy of Planck's Constant is something that cannot be simply ignored, owing to its universal importance in linking the quantum and classical pictures of our world. Using publicly available GPS data and terrestrial clocks, researchers form the California State University were able to verify that the value of h indeed stays the same across different positions in the vicinity of our Earth. Their result says the local position invariance of h is satisfied within a limit of 0.007. The paper is published in the journal Physical Review Letters (abstract), and a free-to-read preprint is available on arXiv. In short: by the well-known formula E = h * f, a hypothetical variation on h induces changes in f, the transition frequency that keeps the time in atomic clocks, both on earth and aboard the satellites. When taking account of other time variations, such as general relativistic time dilation, and assuming the invariance of E (atomic transition energy) on physical grounds, we can figure out an upper bound on the variation of h reflected in the measured variation in f."
Fix (Score:3, Informative)
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Checking the Positional Invariance of Planck's Constant Using GPS
Re:Very large limits (Score:4, Informative)
Given that h is very small (1e-15, 1e-34 or 1e-27 depending on units), a limit of .007 seems rather large.
Considering NIST in Washington, NRC in Ottawa, NPL in London, and METAS in Berne (all national metrology labs) have directly measured h to within 300 parts in a billion (1E9), this is an unusual report. Those results are within a relative limit of 0.0000003.
Planck's constant cannot be measured with only a GPS or atomic clock, so this is at best some comparative result.
Re:Very large limits (Score:4, Informative)
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.