# Time and measurement relation to displacement

Is there any other way to measure time without using any type of periodic motion. I think it's a no. A clock is essentially a periodic motion in which we measure some type of periodic displacement. I can't imagine any physical measurement that doesn't use the displacement at its core and since displacement and momentum are conjugate variables one can say that every measurement is in some form a momentum transfer. So a clock is just a reference for periodic displacement.

Is there any other way to measure time or any other physical parameter without using displacement?

Edit

The entropy is a statistical phenomenon.

Am asking it at fundamental level: Let's say in this universe there are only balls (indestructible) and reflector walls. how would someone measure time (regarding observer as omnipotent) and out of the two particle system.

And kindly give an elaborate way to measure time assuming that rate of change (is a fundamental constant) and cannot change in any way. Like burning rate of candle is not constant and can vary a lot , statistical phenomenon can't give you arbitrarily accurate time.

• Displacement doesn't have to be periodic. You can probably measure the time by the linear displacement galaxies have as they recede from us for example.
– Amit
Commented Mar 22, 2023 at 21:25
• How exactly can we measure time by linear displacement of galaxies? Commented Mar 23, 2023 at 4:24
• @Pradyumam - one example: en.wikipedia.org/wiki/Star_clock
– Amit
Commented Mar 23, 2023 at 6:05
• This example employs periodic motion of earth. Commented Mar 23, 2023 at 14:41
• The point is that you can define your time unit based on known linear velocity. Throw an object into deep space. Supposing you know its velocity and can keep track of the object, you can define time units to be equal displacement units observed. No periodicity required.
– Amit
Commented Mar 23, 2023 at 15:01

One way is:

"...The unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s$$^{−1}$$"

which measures oscillations of the electromagnetic field.

• but when you say transition isn't it a form of momentum transfer which can be seen through it's conjugate variable Commented Mar 22, 2023 at 20:37
• @Pradyuman No, the clock is actually the radiation field. The clock (the radiation field) is used to drive Cs transitions only to check that it is running at the right frequency. So the actual clock is the oscillating electric field in the radiation field. I think you would agree that oscillation of an electric field does not correspond to a physical displacement. Though it is a periodic oscillation nonetheless. Commented Mar 24, 2023 at 2:52

Any physical phenomenon that changes in a predictable way over time will do. They don't have to be periodic.

Some examples: a particle moving without any forces applying to it travels in a straight line at a constant speed. The distance travelled is proportional to time. A particle falling under gravity, the square root of the distance it falls is proportional to time. Radiocarbon dating measures the amount of Carbon-14 that has not yet decayed, giving the age of historic artefacts. We use the red shift in the colour of starlight to tell how long the light from distant galaxies has been travelling towards us. The rate at which organic materials rot is often a fairly universal biological constant, allowing forensics to determine how long a body has been dead for. Chemical reactions like the rate at which paper or plastic go yellow gives you an idea of how old it is. The rate at which a hot body in cold surroundings cools allows the temperature to tell you the time since it started cooling, again with well-known applications in forensics. Early clocks used processes like a candle burning down, sand falling through a hole, or water dripping to measure time. And you can tell roughly how old somebody is by looking at their size, skin, and hair colour. Are they a teenager, twenties, forties, sixties? Often you can tell to within a few years.

None of these involve periodic motions. Periodic motions are often best for the most precise and accurate methods of measuring time, as it then just becomes a matter of counting. But there are lots of other ways.

• How do you predict that way, (calibration) Commented Mar 23, 2023 at 3:58

Periodic events are "events separated in time at regular intervals." I think not only are these the only possible measurement of time – they are the definition of time itself. Assigning a number $$t=5$$ to an event is shorthand for saying "5 equal intervals of some periodic event have transpired since a particular reference event."

It seems to me it would be impossible to assign a number $$t$$ to events in our environment without a repeatable periodic set of events – just as it would be impossible to assign a spatial location to any objects or events without a common "measuring stick."

Now, saying any periodic event must comprise some form of spatial displacement, I do not think is necessary. Take a pulsar that emits a light signal at regular intervals from the same location.