Counting seconds of flexible duration...
On the prior page I suggested that every object in the universe has its own version of "now" separating its past from its future. I am a little uneasy about this idea. It seems a sort of disorderly way to run a universe. The existence of compound objects, like people for example, require complex interactions among a huge number of very small pieces. If each piece can only act in its "now" and those "nows" are not synchronized in some fashion it is hard for me to see how these interactions come about. Let's consider the simplest sort of interaction between a pair of idealzed objects. Picture two mirrors bouncing a pulse of light between them. A spacetime diagram of this situation is shown below.
Both time and distance in this diagram are expressed in meters. Suppose the mirrors are 1 meter apart so that the time between reflections is 1 meter. There are two conditions that must be met for a reflection to occur. The reflection must happen "now" for the reflecting mirror and it must happen when the photon reaches the reflecting mirror. The photon transit time between mirrors is fixed at 1 meter by the fixed speed of light. The speed of "now" up the time axis is also fixed by the speed of light. If "now" for the left mirror was different than "now" for the right mirror then the arrival of the photon at the right mirror would not coincide with "now" for that mirror. Under those conditions no reflection could occur. So it looks like the mirrors must agree on what time "now" is.
How about the photon's view of the above situation? According to the relativity principle, time stands still for objects moving at the speed of light so the emission of that photon from its source, all the reflections it undergoes and its ultimate absorption perhaps after the universe has aged a million years, all happen at the same time in the photon's reference frame. The interaction between a photon and a mirror can only happen "now" for both objects. I have been thinking about "now" as a vanishingly short instant in time separating the past from the future for an object. For a photon there is no past and future. All its existence consists of "now" so whenever a photon shows up it is always in its "now" thus photons are always eligible for interacting with an object in the object's "now". This turns out to be a fortunate accident of relativity since all interactions among the atoms in an object involve an exchange of photons and without this flexibility in photon interactions nothing would be as it now is.
If we accept that "now" must be the same for interacting objects, how far are we to take the idea of what constitutes an interaction? Distant stars are spitting out photons of visible light, among other things, and on a clear night, those photons may be absorbed in my eyes. The time of the absorption of the photon was obviously "now" for me and the flight time of the photon was fixed by the distance to the star and the speed of light, so the "now" in which the photon was emitted must have been synchronized with the "now" in my part of the universe back when the emission took place. In fact the whole universe is immersed in a bath of microwave photons that dates all the way back to around the time of the Big Bang, making it seems reasonable that the boundary between past and future called "now" should be synchronized throughout the universe. We still have not decided if "now" can be assigned a specific time coordinate.
On the page Pebbles and People, from another string, I mentioned that the material from which people are constructed has been around for roughly 13.7 thousand million years. It is only temporarily arranged into a person, or into a pebble for that matter. The building blocks for all atoms: neutrons, protons and electrons, have been around from almost the beginning of time, so in a certain sense you are roughly the same age as the universe. When we thought of time as universal and constant, an understandable error back when we were trying to measure acceleration with an ox cart and an hourglass, there was never any question that things created at the same time would always be the same age. With the our understanding of the relativity principle that changed.
Suppose there were twins, one that jumped on a space ship and traveled to a far place at a speed approaching that of light and returned to be reunited with the twin that remained behind. It has been well demonstrated that the traveling twin would be younger than the one who stayed home, possibly much younger depending on the length of his trip and the speed of his travel. He could even find that his twin's grandchildren were there to greet him. Now imagine a pair of very accurate clocks synchronized with great precision. Launch one of the clocks into space to orbit the planet and keep the other sitting on a shelf in the lab where they were synchronized. After ten years in orbit, retrieve the traveling clock and compare its reading with the stay-at-home clock.
Given the experience of the twins, you should expect the well traveled clock to be younger than the lab clock. In fact you find the opposite effect. The time elapsed on the lab clock is less than that on the orbiting clock. It turns out that the effect of gravitation in the lab slowed the passage of time as compared to the passage of time for the freely falling clock in orbit. This gravitational effect more than compensated for the high relative speed of the orbiting clock. The counterintuitive statements in this and the previous paragraph are predicted by the relativity principle and well verified by experiment.
The amount of time that has elapsed from the beginning of time to an object's current instant, the object's age, turns out to depend on an object's relativistic history. It is statistically extremely unlikely that any two of the large number of particles that make up a person, for example, have had identical experience with speed, acceleration and gravity since the beginning of time. Still they all must share the same current instant in order to interact successfully in forming the person, I must conclude that the current instant ("now") is somehow separate from the age of any particular object. In the case of the reunited hypothetical twins, it is no use to ask them when "now" is because they will give different answers in spite of their obvious sharing of the current instant.
There are only two possibilites that occur to me at the moment about when "now" is. First it may be that "now" is somehow "off the clock" so to speak, meaning that the current instant exists without reference to any time coordinate. I don't have a good grip on this notion and its ramifications. The second is that "now" might be the age of the universe, leaving the ages of individual objects to float. All the relativistic effects only slow the passage of time so the age of the universe is like an upper bound on the age of any of the objects in it. That seems to me to be a reasonable candidate for the time coordinate of the current instant even if objects could not agree on how long it took them to reach that instant, some having experienced seconds of different duration during their lifetime. I think it unseemly that the universe would stride into the future, leaving its contents to straggle along behind it.
Back on the page on Where is Now we concluded that there is a separate "now" for each object. Here we concluded that all these "now"s are in some way synchronized, possibly at the age of the universe. There is another aspect of "now" that I wonder about. If we consider the universe to be populated with events, such as "object found here", collisions between objects, emission and absorption of photons and so on. The nature of those events is radically different depending on whether they lie on the past side or the future side of "now". Future events may be influenced by past actions and the vast majority of possible future events do not happen at all. Those events that survive the passage of "now" are frozen into history and not subject to influence by future events. I think I will wait for another page to try to think through this mystery of time.