The arrow of time (3): what is it, actually?

No, but honestly: what is meant by the term `the arrow of time’? I cannot get my head around it, unfortunately. This seemingly puts me in an unenviable minority position, enhanced by my obvious ignorance of relevant theories in modern physics.

My problem is this: If we do not know at all what time is, then how can we determine that there is an arrow of time?

As an illustration, let us look at the second law of thermodynamics, as related to the arrow of time via entropy (quote from wikipedia: entropy (arrow of time)):

Entropy is the only quantity in the physical sciences (apart from certain rare interactions in particle physics; see below) that requires a particular direction for time, sometimes called an arrow of time. As one goes “forward” in time, the second law of thermodynamics says, the entropy of an isolated system can increase, but not decrease. Hence, from one perspective, entropy measurement is a way of distinguishing the past from the future. However in thermodynamic systems that are not closed, entropy can decrease with time: many systems, including living systems, reduce local entropy at the expense of an environmental increase, resulting in a net increase in entropy. Examples of such systems and phenomena include the formation of typical crystals, the workings of a refrigerator and living organisms.

Entropy, like temperature, is an abstract concept, yet, like temperature, everyone has an intuitive sense of the effects of entropy. Watching a movie, it is usually easy to determine whether it is being run forward or in reverse. When run in reverse, broken glasses spontaneously reassemble, smoke goes down a chimney, wood “unburns”, cooling the environment and ice “unmelts” warming the environment. No physical laws are broken in the reverse movie except the second law of thermodynamics, which reflects the time-asymmetry of entropy. An intuitive understanding of the irreversibility of certain physical phenomena (and subsequent creation of entropy) allows one to make this determination.

By contrast, all physical processes occurring at the microscopic level, such as mechanics, do not pick out an arrow of time. Going forward in time, an atom might move to the left, whereas going backward in time the same atom might move to the right; the behavior of the atom is not qualitatively different in either case. It would, however, be an astronomically improbable event if a macroscopic amount of gas that originally filled a container evenly spontaneously shrunk to occupy only half the container.

In previous posts I already conjectured a similar view on time and entropy, perhaps a bit more radical: ΔTime \approx ΔEntropy.

The above conjecture is vague and needs improvement, the gist is that entropy and time are cut from the same cloth. But as I said I am rather hampered by my overwhelming ignorance of modern physics.

Still, it seems to me that what is usually called `the arrow of time’ depends on an experimentally unconfirmed ideal view of time as an independent and qualitatively different dimension (an `objective clock’ or perhaps `subjective clock’ which runs independently of other physical processes/attributes, at least on the nanoscale; precisely here might lie the difficulty in reconciling quantum mechanics with general relativity).

One should read at this point the Stanford Encyclopedia of Philosophy entry on time, to hopefully help gain some insight in what I’m trying to say.

[Also I think I remember a vivid related portraying of time by Kurt Vonnegut in Slaughterhouse-Five (I read this over 30 years ago, so inaccuracy is inevitable). As I remember this portraying, time is similar to the other dimensions, which leads to all things existing in four equivalent dimensions…only our human consciousness is like a train which moves in a certain fixed direction. And from that train we can only look out through a very narrow window (the present), hence we see the landscape pass us by in a more or less linear time fashion, moment after moment. If we would be able to break free from the train, then our sensation of time would be radically changed.]

If I may, let me put forward an aphorism which I discovered through my telescope on a meteorite made of antimatter :-). It perhaps illustrates my thoughts on a possible reversal of time: namely that time could well be a phenomenon produced by our consciousness, in other words an anthropomorphic artefact:

We anti-time humans have no memory to speak of, alas!, and can only rely on our often patchy foresight of our future


About fwaaldijk

mathematician (foundations & topology in constructive mathematics) and visual artist
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