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In Andy Weir's "Project Hail Mary" protagonist Ryland Grace wakes up in an environment and with a few physics experiments timing falling objects he relatively quickly determines that he is on a spaceship with a rotational gravity system. He goes on to calculate more physical properties of his environment from this base information. It seems that the key to him learning about his environment was discovering a calibrated digital stopwatch.

My question is, assume you were not given a calibrated watch. Assume you are given no reference to time at all when you wake up in a strange environment. No visible sky, no sunrise or moon, and no clocks. You may assume but do not know that you are on earth (can that be discovered without space travel?), although you have at your disposal all of human scientific knowledge except radioisotope half-lives. I must grant that you also have some measure of length (perhaps you know your own height, at a minimum). Is it possible, by any means at all, given enough time, to determine the physics of your environment in known units, or are you condemned to creating all your physical measures anew? E.g, can you determine your local temperatures, barometric pressure, gravitational constant, planetary mass, velocities, etc. in known units?

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It can be done, thanks to the adjustments to the definitions of the SI units. In the past this would be impossible, because too many units (like the kilogram) were arbitrary. Of course, it is not easy. It will require a great deal of equipment that is far more expensive than a digital watch.

The second is defined relative to the hyper-fine transitions of Cesium. Putting together an atomic clock is far harder than just bringing a watch along, but in theory it can be done without existing units. Once you have that, the meter can be defined using the speed of light.

The kilogram is the hardest, but now that it is defined with respect to plank's constant, there are balances (such as the kibble balance) which can measure accurately enough to define the kilogram.

With those three, getting other units is comparatively easy. Without them, measurements will be impossible. At the most fundamental level, if the unit includes a dimension you can't measure (time, in the case of several quantities you asked for), you simply cannot measure it without a unit in that dimension.

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  • $\begingroup$ Excellent answer, but Two parts: I neglected to mention that inches of mercury or water would be simple to measure, thus if you had conversion tables, pressure could be had to within the accuracy that you know your own height, or whatever other accurate measure you know (clothing measurement, etc). I don't know if there may be a round-about way to derive time via a known pressure gradient (Fluid mechanics and Viscosity?) Another thought: A cesium clock I believe would need a pre-calibrated reference oscillator to sweep the 9,192,631,770 Hertz microwave spectrum. Does that change this answer? $\endgroup$
    – Vogon Poet
    Commented Jan 29, 2022 at 20:34
  • $\begingroup$ I may have solved my own problem... You know how to closely find 98.6F, you can create a pressure gauge w/ InHG or water; you know water viscosity at different temps & pressures. The time it takes water at a known temperature to move through a hole of known diameter with a known pressure differential can be measured without gravity. Derive the true second from this fluid xfer rate, then the other calculations follow. So the minimum information would be water properties and pressure conversion charts. Is this correct? $\endgroup$
    – Vogon Poet
    Commented Jan 29, 2022 at 20:46
  • $\begingroup$ Ugh. Nevermind... Knowing pressure with mercury or water requires known gravity. $\endgroup$
    – Vogon Poet
    Commented Jan 29, 2022 at 21:03
  • $\begingroup$ @VogonPoet Yes, its a pest trying to find these values without any knowns, like gravity. Of course, this is not too large of a surprise, given that it took us quite literally thousands of years to come up with non-relative measures. As for the clock, you do need an oscillator, but it does not have to be pre-calibrated. The caesium clock resonates at the specified frequency, creating a detectable change in energy. You look for that resonance, and that tells you when you're at the right frequency. (the devil, of course, is in the details there) $\endgroup$
    – Cort Ammon
    Commented Jan 29, 2022 at 23:32
  • $\begingroup$ And the solution, of course, is to have a time standard which doesn't depend on anything external in the new world. Perhaps something with springs whose oscillating frequency is well understood and uncorrelated with gravity. Or even better, a piece of quartz crystal and the mechanics to track its resonant frequency. As Douglas Adams put it: digital watches are a pretty neat idea. $\endgroup$
    – Cort Ammon
    Commented Jan 29, 2022 at 23:34

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