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I asked this question of a physicist and he told me to ask a philosopher. If one was to observe a closed, isolated region of space under vacuum conditions, i.e. there are no particles in this region and none may enter into it. Also there are no fields (i.e. gravitational, electromagnetic, etc.) acting or existing on or in this region. The only interaction with this system is as an outside observer. Can this observer notice the passing of time? If so, how? And does the act of observation make the observer part of the system, since the observer is technically interacting with it? Currently we measure time by the movement of quantum mechanical particles, such as the molecules in a ticking clock; the vibrations of atoms; and the decay of radioactive isotopes. But could we perhaps, in this hypothetical system, justify using properties of space itself, such as quantum foam or the expansion of space (expanding universe), and, if so, how would we observe these features?

Thank you for your question. Let me touch it up just a bit: There are no gravitational fields in general relativity over and above the curvature of space(time). In the spirit of the question, I will assume that the spacetime geometry is unchanging. An observer might be able to notice the passing of time in lots of ways (e.g., from his own heartbeats or passing thoughts or wristwatch). I presume that the question is asking whether the observer could notice it on the basis of some observed changes in the region of space in question. I am inclined to think not. Nothing is changing there. If spacetime geometry were changing, then the passage of light through the region to us would betray the change to us. But the question stipulates that nothing passes through the region.

Was Zeno unfair toward Achilles in his paradox? Last week I was reading the Croatian edition of Bryan Magee’s “The Story of Philosophy” and he reminded me of Zeno’s famous “Achilles and the tortoise” paradox. Here is how the paradox goes (taken from Wikipedia): “In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 meters. If we suppose that each racer starts running at some constant speed (here instead of ‘one very fast and one very slow’ I would stick to the original: Achilles is twice time faster than the Tortoise), then after some finite time, Achilles will have run 100 meters, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, 50 meters. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever...

Dear Robert, You are right. The key to understanding the paradox is that although Achilles must complete an infinite number of tasks in order to catch up to the Tortoise, he can do so in a finite amount of time, since each successive task takes much less time than its predecessor (as you noted). Of course, today we understand how to add an infinite sequence of terms that converge to a finite quantity. But this wasn't well understood until millenia after Zeno -- and the logical foundations for doing so required Cauchy and Weierstrass in the nineteenth century. So we shouldn't be too hard on old Zeno. By the way, you might find it amusing to consider some more recent Zeno-like puzzles, such as the "New Zeno" discussed by Stephen Yablo in the journal ANALYSIS, vol 60 (April 2000).

If an arbitrary length of time is infinitesimal in comparison to infinity then it would seem then that it would be absurd to say that any length of time is long or short. So why then do some lengths of time such as a decade feel "long" where as other lengths of time such as a second feel "short"? Length and height are also relative to infinite length but in those cases judgments about how long or short something is can be determined by comparison to different objects but with duration their is no outside reference for comparison. (I hope that made sense.)

Granted, 10 years in comparison to infinity is as short as 10 seconds is in comparison to infinity. But it does not follow that 10 years and 10 seconds are equally long (or short). In comparison to any finite span of time, 10 years is longer than 10 seconds. The same applies to lengths and heights. I see no reason to say that there is no common reference for duration. The amount of time it takes for the earth to go once around the sun (or to spin once on its axis) is commonly used as a unit of duration.

How long is a instant? please answer!

Thank you for your question. The standard answer is that an instant lasts for no time at all. That is to say, the start of an instant and the end of an instance occur at exactly the same time. An instant is indivisible; it has no separate beginning, middle, or end. You might think of time as like a number line, with (for instance) zero as the time when you started reading this sentence and 1 as the time when you arrived at the end of it. Then each number between zero and 1 corresponds to an instant of time. None of those instants is any length of time at all. Of course, that an instant of time lasts for no time at all might lead you to wonder how a span of time lasting, say, for an hour could possibly consist of a bunch of instants each lasting for no time at all. This is closely related to some of the paradoxes first proposed by the Greek philosopher Zeno thousands of years ago. Bear in mind as well that between any two instants of time, there is another instant of time -- and, indeed,...

Say we could speed up matter and go further into time. I went and I saw my future self, no interaction, and I noticed that I had a finger missing or some dramatic change in my body since my present self. Could I dedicate my life to keeping my finger safe, or will it happen anyway?

I agree with Professor George's answer, but I would like to add one thing. Suppose you are a professor of English. You take a time-machine trip into the future and learn from a reliable source that you died in dramatic fashion: in the midst of teaching a Shakespeare class. You tend to get very excited while teaching Shakespeare, and you died from cardiac arrest while giving a spirited lecture. However, you do not learn anything about the date of your death. Then you travel back to 2005 and continue your life. When your department chair asks you what you would like to teach next year, it would be perfectly rational for you to say, "Anything but Shakespeare." By not teaching Shakespeare, you cannot change the future from what it will be. (Apparently, despite your determination never to teach Shakespeare again, you end up doing so, somehow, and die in the midst of it.) But by not teaching your Shakespeare class next year, you can make it true that you lived a longer life. It is no different from your...

If we are part of a 4-D spacetime, why do we experience past and present?

What we experience depends on what information about the world we receive and when we receive it. We receive information about the world through our senses, as when a ray of light arrives in one of our eyes from an event that occurred sometime in the past. (That light ray may have been launched by an event that occurred just a few millimicroseconds ago, or it might have come instead from an event in the very distant past, as when a ray of light emitted by stars many years ago enter our eyes as we look up at the sky at night. If the star is 100 light years away, then that ray of light was emitted 100 years ago.) Since we do not receive rays of light today from events that have not happened yet, we do not experience the future (yet!). Now light travels very quickly, as you know. The various rays of light that are arriving in my eyes right now, having previously bounced off of various objects in the room I'm in, all left those objects at very nearly the same moment. So those rays of light give...

After a discussion about time travel, I asked my high school science teacher, “How can we be sure time even exists? How do we know it’s a tangible thing that can be traveled through?” His simple reply was to say that time can be measured. Therefore, it exists. That answer was never enough. As I’ve grown older, I still believe that time doesn’t exist, because all it is, is a term used to describe the interaction between matter. As matter interacts, the physical world changes, thereby creating one’s perception of ‘time’. The more gravity one has, the slower matter interacts and the inverse. One can’t go back in time, because one can’t rewind all the infinite physical changes that have taken place. However, one can speed up the interactions. So, I pose you the same question. How can we be sure time exists?

Newton proposed that there is "absolute time", over and above the motions of clocks and pendulums and celestial bodies that (to some degree of accuracy) measure absolute time. Newton did so in the context of a scientific theory that aimed to account for some of our observations of the motions of material bodies. The tremendous success of his theory counted as good evidence for the existence of absolute time. Roughly the same situation exists today, except that our best current theories of how and why bodies do what they do fail to use Newtonian absolute time. Those theories (roughly, quantum mechanics and relativity theory) use other notions of time -- indeed, notions that are difficult to reconcile. Still, whatever evidence we have that time exists comes primarily from evidence for our best scientific theories, which use various concepts of time to characterize the universe. Now those theories might be mistaken, or the evidence for their accuracy might not constitute very strong evidence for what...