When we think of time we think of it as just one thing, the ticking of the clock. But time has a number of properties and not all of them vary together, nor are all of the properties of time necessarily continuously present. Some properties can be at zero, null, indeterminate or absent altogether.
Let’s start with an example of a property that has actually been dropped from the concept of time, that of ‘Cyclic Time’. Jump back even a few hundred years and this would not only have been considered a natural property of time but an essential or even fundamental property. Everything in the ancient observable world is cyclic.
Indeed, ‘Simple Harmonic Motion’ is still one of the cornerstones of physics and SHM is seen throughout the physical world. SHM can not exist independently of time, but time can exist without SHM as far as we can tell.
If we can drop SHM from time simply because time can exist without it then what of the other properties that time can live without, at least under some conditions?
At the quantum scale when considering single quantum events we note that there are no components of entropy present. The test for the absence of this property is a hypothetical video of a single interaction or an animation based on the data: could we or anyone else tell if the video clip was being played forward or backward? If not then the entropy property is absent. But what of a spatial extension that contains nothing above the quantum scale? Time is still present in the form of spacetime ~ space isn’t completely flat anywhere so the bit of curvature present needs the temporal dimension to describe it. But there is no entropy. Even the virtual particle, the quantum noise, can proceed in either direction.
So there we have two examples of where entropy, and therefore the arrow of time and even the time line are not present. As with cyclic time, each of those concepts can not exist independently of time, that is, entropy can not proceed independently of time.
The interval is another example, as is change and relative time. So what property of time is essential? There must be at least one property of time present for time to be said to be present, but it doesn’t matter which one. A photon can flit across the universe without accumulating an interval of any duration at all, so change can occur without a local interval.
In our usual experience, all the properties of time, including the cyclic component, are present and so it is an effort to imagine time without even one of the properties. As we probe into the physical world, some properties can be dropped or minimised but no property is always present in all conditions, the closest would be relative time as the observer’s clock ticks on regardless of any philosophical musings and so is readily compared to all other clocks in real and hypothetical conditions.
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