Planck's constant is joules x second.

However, the second can be time dilated from an external reference frame's point of view and seemingly extended.

Following this logic.

Would an external reference frame see Planck's constant, hence the uncertainty principle, as changed or increased in a time dilated environment?


1 Answer 1


In the current understanding, units are defined in terms of constants of nature, Planck's among them, not the other way around. For example, the definition of second reads '... setting the fixed numerical value of the cesium frequency $\Delta \nu_{Cs},$ the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, in 9192 631 770, when expressed in the unit of Hz (hertz), equal to 1/s'. So, in the same reference frame we see how many transitions there are and that gives the duration of a given phenomena in seconds, but we define everything else in terms of fundamental constants. That is, they are the true constants and our units are just relations among them. See for example:


However, time dilation and Lorentz transformations have to be considered when applied to uncertainty principle considerations. For example, in very relativistic situations a particle is associated with a resonance, a peak in the probability amplitude at a certain energy, the value of energy for this peak is related to the mass of the associated particle and the width of such resonance (a $\Delta E$) is related to the lifetime of the particle (a $\Delta \tau$). Thus, the reference frame in which you measure both quantities matters and the values depend on the reference frame, but the uncertainty remains in all of them.


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