Thursday April 20, 2017
The closer you look at reality, the weirder it tends to look, especially if you’re using the twin lenses of general relativity and quantum mechanics. It’s thanks to the latter that we can build ultra-accurate atomic clocks (like this one). One of the most interesting features of high precision atomic clocks, is that they can actually measure something called relativistic time dilation effects – but when you add quantum theory to the mix, it turns out that the more accurate a clock is, the less accurate clocks around it can be.
How does that work? Well, relativity assigns an idealized clock – a non-physical one – to every “worldline,” which refers to a timeline associated with a single observer, evolving in spacetime. However, as Einstein himself pointed out, not thinking of the clock as an actual physical object leaves some of the picture incomplete. Einstein wrote, ” One is struck [by the fact] that the theory [of special relativity]… introduces two kinds of physical things, i.e., (1) measuring rods and clocks, (2) all other things, e.g., the electromagnetic field, the material point, etc. This, in a certain sense, is inconsistent…”
Indeed. As it turns out, if you look at what goes on with actual physical clocks things get weird, and if you add quantum theory to the picture, things get even weirder.
Here’s what happens. In quantum mechanics, there is a little thing called Heisenberg’s uncertainty principle, which says (short version) you can’t know two complementary values of a physical system to an arbitrarily high level of precision. For our purposes, the better precision to which time is being measured by a clock, the more uncertainty there is with respect to the energy content of spacetime around the clock.
In general relativity, the energy content of a given region of spacetime can cause a clock in that region to slow down or speed up relative to an observer looking at that clock from another reference frame (technically, a “non co-moving frame of reference.”) This is a well known effect and you can actually measure time dilation effects with atomic clocks – a clock in orbit in a GPS satellite runs at a different rate than one on the Earth’s surface. Therefore, if there is uncertainty in energy content in a region of spacetime, there will be imprecision in how accurately a clock can run in that region.
Researchers at Penn State, publishing in the Proceedings Of The National Academy Of Sciences, say, ” We prove that, as a consequence of this fact, the time dilation of clocks evolving along nearby world lines is ill-defined.We show that this effect is already present in the weak gravity and slow velocities limit, in which the number of particles is conserved. Moreover, the effect leads to entanglement between nearby clocks, implying that there are fundamental limitations to the measurability of time as recorded by the clocks.” In their conclusion the authors state, “These results suggest that, in the accuracy regime where the gravitational effects of the clocks are relevant, time intervals along nearby world lines cannot be measured with arbitrary precision, even in principle.”
So basically, if you have been staying up nights hoping for a perfect clock, well, the entrance to the land of high precision horology has a new sign over the gate that says, “Abandon Hope, All Ye Who Enter Here.” To read a fairly accessible review of the article in question, check out this coverage from Pionic; if you would like to check out the original paper, it’s right here (chock-full of mass-energy equations, but there nonetheless).