This is important, because it is impossible to understand what is going on in the clock itself if we don't see that velocity is a quantity that can be measured directly.
Historically speaking, the reason velocity got thought of as a ratio between length of a process and time is that Galileo discovered the law of falling bodies (that they all fall at the rate of 32 feet per square second) by timing the balls he was letting roll down an inclined plane--as the story, at least, has it, by singing a tune, since timepieces in his day didn't measure time as accurately as musical tunes did. He found (a) that all of them fell at the same rate, whatever their weight, and (b) that the farther they fell, the faster they fell, so that if they fell two feet the first second, they fell four the second, nine the third, and so on. Hence, the rate of their fall was learned in terms of the time it took them to fall a certain distance; and we have thought of "rate" in these terms ever since.
But if you look at why he was singing his tune or why you would use a clock for this purpose, you find, first of all, that the tune had a regular beat, and the clock has regular ticks (even if they're so close together in electronic clocks that we couldn't hear them). Secondly, you find a definite progression of these beats or ticks so that you can count them. In a clock, of course, they begin to repeat like the number system (they actually come from the Babylonian 12-based numbers) to make them easy to count.
The tune, we can now see, was a clock. With a clock, you have a process which you can "set" to "begin" at any point you wish, and "end" at any point you wish, since this kind of process is actually a series of smaller ones added together that you can count, and it keeps going as long as you want.
Of course, you have to have the "clicks" of the clock be closer together than the process you want to measure, because in between the clicks, the clock is useless. You can't use an hourglass to time a three-minute egg, because the hourglass takes an hour for the sand to fall through, and so its "clicks" are an hour apart). Since we now measure processes so accurately, we have to have atomic clocks, which are clicking at an astounding frequency.
At any rate, when you are "timing" something, you "start" your clock (i.e. note where it is) at the beginning of the process, and "stop" it when the process you are trying to measure stops. You then note--what? Something about the process in terms of the length of the clock's process.
Now what you know about the clock's process is that it has a regular series of "clicks"; if its mechanism works irregularly, it is useless as a clock. But what does this "regular" mean? Simply that the velocity of the clock's process is constant. It doesn't really matter what the velocity is; in fact, since it is a series of processes that begin and end, added together, in one sense it isn't really a process at all. The point is that the "process" has to have what is known to be a constant velocity, even if the actual speed it has is irrelevant.
And as sand timers show, clocks can be actual processes, as long as they are (a) constant, and (b) have beginning and end-points that can be matched with the process you are "timing." It is just that regularly spaced "clicks" that are close together allow you to time more things than processes like falling sand (which works as a timer because sand has the characteristic of having grains all the same size, so that a given number fit through the constriction at once).
So timing is actually comparing two processes, and measuring one against the length of the other. Now since both processes have both length and velocity, let us see what the comparison looks like:
Lc/Vc = lm/vm
What this says is that the ratio between the length of the clock's process and its velocity will be the same as the ratio between the two quantities of the measured process. But since the velocity of the clock's process is a constant, it can be ignored in the calculation, and you can express the ratio between the two quantities of the measured process in terms solely of the length of the clock's process.
That is, we have to agree on our "units of time" and compare our clocks so that what registers an hour of length on your clock will register an hour of length on mine. This is easy enough if the velocities are constant; we just adjust the length. For instance, 60 ticks on your grandfather's clock will be the equivalent of 300 ticks of my watch or perhaps 3 million ticks of your very accurate chronograph; we just make the numbers roll over at the proper number of ticks so that all of them say that this particular length is "five minutes."
Once this is done, then we need not bother any more with the velocity of the clock's process, and it's length then becomes the "time" which measures the ratio between the length and the velocity of other processes--which quantities, as I said, are independent of one another; but the ratio between them will relate to the length of this standard process.
Hence, time is not something "out there" at all; it is not something "primitive" "within which" things happen. It is a very sophisticated concept which involves comparing processes and their quantities and ignoring the velocity of the standard process (the clock) in order to use its length as a kind of measuring-stick for the ratio between the quantities of other processes.
It is not, therefore, surprising that primitive cultures, who have felt no particular need to compare the quantities of processes, have no sense of time, or a very fuzzy one. Of course, their "standard process," generally speaking, is the day, the month, and the year; and during the day there are the divisions of forenoon, noon, and afternoon, which in an agricultural or hunting culture, do well enough for practically all purposes. It isn't that they're stupid, or that they haven't "discovered the reality of time." It's that the only processes they're interested in comparing are so slow that measurement in terms of days and months is all that is needed.
But what, then, is time?
The time of a given process is the ratio between its length and its velocity.
Time as that which measures processes is the length of a process with a standard, constant velocity, used to measure the time (in the previous sense) of another process.
Physicists make this same distinction, and use the capital T to indicate the "internal time" or "period" of a process, and the lower-case t to indicate the time that is measured by a clock.
But now that we have seen what the clock is doing as a measuring instrument and what it is measuring, we can say some things about time.
Conclusion 11: Time is not real.
Time is no more real than the sameness among all red objects is a real connection between them. In the first place, the time within a given process is not real, because the length of the process does not depend on or determine its velocity. You can go very quickly or slowly from Cincinnati to Dayton without changing the distance at all; and you can travel any distance at 55 miles an hour. It just happens that the particular process you are interested in has this particular distance and this particular velocity.
And since the time measured by clocks is a comparison of these ratios, really, then obviously this is just another mental relation and does not correspond to any real connection between things. It just happens, for instance, that if you are traveling between Cincinnati and Dayton at 55 miles an hour (we have no other term for the velocity), then your clock will register that an hour has passed; that is, that your clock's process is such that the little hand has passed from the 3 to the 4.
And this analysis of time makes sense in terms of physics. It used to be thought that time was something "primitive," against which everything else could be measured; but Einstein showed that this was not so, even in the Special Theory of Relativity. There, he demonstrated that even "absolute simultaneity" was a meaningless term; if two people were moving with respect to each other, then events observed to be "simultaneous" to one would not be simultaneous to the other observer--and nobody was privileged, so that he saw the "real time" when they happened.
The reason for this is that the conveying of the information to each observer is a process, which, of course, has its own length and velocity. Einstein's assumption is that the velocity of light through space is for any observer the same as for any other one; hence, differences in length light travels will involve different travel-times for the light. Naturally, then, if one observer is at rest with respect to two events, while the other is moving toward one of them, then the one moving will not see them as at the same time if the one at rest with respect to them does. Einstein's point is that you can't pick either of them as the "correct" one, or the one who is "really" at rest.
This is not at all surprising if time is the way you compare processes outside you with the process that is going on in your clock. Time in that sense is a way of observing, not a "something" that is measured, really; what is measured is the process, but in its relation to your standard process.
It is for this same reason, as Einstein pointed out, if you are moving with respect to me and I look at your clock and mine and we both read exactly twelve o'clock, and then I look a half hour later (by my clock) at your clock (now at a different distance from me), your clock will read less than twelve thirty. But by the same token, you, looking at my clock at the time when yours says twelve thirty will (because of the same difference in transmission-distances) will read my clock as saying less than twelve thirty. Both clocks are going slower than each other. This makes sense if you try to figure it out; it's just that the time-lag of the transmission of information goes both ways.
Hence, time cannot be a "something" that is measured by clocks; it is simply a way of observing the ratio between the length and velocity of another process in terms of a standard process. And the result, as both of Einstein's Relativity Theories shows, is that if you try to "fix up" what the clocks say to compensate for the relative movement of the "reference frames," especially when you try to take acceleration into account, you come up with some very complicated mathematics indeed. But the processes are still what they are; and it was this "invariance" that Einstein kept constant as he tried to show what a given process or movement would look like from the point of view of various reference-frames in motion with respect to it and each other.
But it is possible that these complications are not necessary. Why, if velocities can be measured directly, and especially if clocks suppose that velocities can be measured (because otherwise how would you know that the clock's velocity is constant?), do you have to go through all this indirection to find the velocity of the process, which is what you were interested in in the first place? Just read the speedometer, and think in terms of "vels," not "miles per hour."
This won't always work, of course, especially with processes at a distance from oneself--which is where Einsteinian physics becomes relevant. Nevertheless, it is worth exploring a little, if only to get free of the mind-set that thinks that all processes have to be measured in terms of clocks.
I mentioned that acceleration was the quantity of the change of quantity of a process. Hence, a given process involving acceleration can be used to time itself, because obviously the lengths of the processes are the same, and the two velocities are what differ (the "average velocity" and the acceleration).
In terms of time, this is what velocity is:
v = dx/dt
where the "dx" and "dt" are the "zero" of length of the process and its time measured on a clock respectively (i.e. they are the "tendency" of the process to have a length at any point in the process)(1).
In terms of time, acceleration is this:
a = dv/dt
or in other words, the tendency of the velocity to increase or decrease at any point in the process. These "infinitesimals" behave like algebraic quantities, and so we can solve for dt, and get:
dt = dx/v = dv/a
And since this equation shows that the two fractions are equal to each other as well as to dt, then we can simply eliminate the dt, and we have got rid of the clock time, and have the two "internal times" of the same process now related to each other.
If we now bring the v's together on one side, we get:
a dx = v dv
and to perform a bit of the magic we promised a while back when talking about Newton's force equations, let us solve this for a, leaving it alone on the left side, so that we see what acceleration looks like in terms of v (the "average velocity") and dv (the tendency of the velocity to change at this point):
a = v dv/dx
Now then, taking Newton's equation for force:
F = m a
and substituting for a, we get:
F = m v dv/dx
and separating the variables, we have:
F dx = v dv
which is the differential form of Newton's energy equation, which integrates into the work equation:
F x = mv2/2
which we saw earlier. It can now be seen that all I did was eliminate the indirection of the clock, and relate the various quantities of the process to each other directly; and adding force and mass, Newton's energy equation fell out of it perfectly naturally.
Prediction: If clock-time were eliminated as an "independent variable" from physical equations, they would turn out to be simpler.
In order to get from real-world observations to the type of equation where you could eliminate clocks, you might have to do some fancy footwork; but once you got the process in relation to itself, as I have shown, the time only adds an unnecessary complication to the mathematics. And the preliminary steps to "get an equation into proper form" can be quite tricky, as any student of physics knows; so I am not proposing anything strange here.
I don't know how much clutter this would eliminate, because I am not a physicist; but the equation above (and certainly the logic above) indicates that there is a good deal that could be got rid of. And if in fact some enterprising physicist tries this business of thinking of acceleration in terms only of distance (length of process) and velocity and finds that the mathematics of physics shows more clearly what is going on, this would be a pretty good empirical verification that this philosophical view is on the right track.
And if you add to this thinking of the "distance" as the length of the process, meaning the difference in energy-levels, so that it is an amount of energy, this might get rid of some more detritus based on seventeenth-century philosophy.
It is quite possible that present-day physics, with its reference-frames and coordinate systems and its dependence on clock-time, is complicated because it is introducing the complications itself, not because what it is describing is complicated. After all, if you insist in looking at the dog in my back yard by looking into a mirror that is attached to a telescope that focuses on another mirror which is then attached to another telescope that undoes all that the first apparatus did, you are going to need funding to finance what could be achieved by just looking out the window.
I'm not pretending that all of present-day physics is smoke and mirrors; just that some of it may be. And if we care about what physics is describing and the facts it is getting at more than we care about "prestige," it is, I would think, at least worth a try to see if I am right.
Before going on to discuss movement, let me draw a conclusion which in itself is obvious, but has certainly caused confusion through the centuries:
Conclusion 12: God is not in time.
This, as I say, is obvious. Since God is an act in absolute equilibrium, then he does not have any "internal time," nor is it possible to time his act with any clock or compare it with processes that are going on.
The traditional name for God's act as not in time is "eternal." But you have to be careful here; because "eternal" is usually thought to mean "always," in the sense of "at all times," and God does not always exist, any more than glass is white because it is colorless. What "eternal" means is that time words do not apply to God. Note that the term "colorless" means that it is nonsense to ask, "What color is it?" If you say, "It is no color," then it is black, because black is the absence of color (within the category "color"; black is the "zero" of color, so to speak, not colorlessness. Similarly, if you say it is "all colors," then you would have to say it is white; but glass is not white. Nor is it any other color, even if you see colored objects through it; they don't color it at all (because color implies absorbing and re-radiating out different wave lengths of light, and light just passes through it "as is."
My point is that if you can understand what you mean by "colorless," you can understand the timelessness of eternity.
No time words apply to God--or to finite pure spirits, either. Hence, God does not always exist (just as glass is not white), God does not now exist (just as the glass is green because you see the green yard through it), God did not exist in the past or yesterday (for the same reason), he will not exist tomorrow or in the future, he does not never exist (just as glass is not black). To ask "When did God do X?" is to ask a meaningless question, analogous to "What color is freedom?"--since God's activity, of course, is simple existence, identical with himself, and so any act of God is eternal, because in fact it is the Eternal Act.
But some people ask, "Well, if time began with the Big Bang (it did), then what was God doing before this?" God wasn't doing anything "before" the first moment of time, because in the first place there is no "before" the first moment of time, and secondly God's act is not temporal at all.
But doesn't God now know what I'm going to be doing tomorrow? No. God does not know anything "now." God eternally knows (as we will see) what I am going to be doing tomorrow, but this doesn't mean he "always" knows it, or that he knows it "before" it happens. He knows it timelessly (This would be analogous to seeing something green through glass); and he knows it as it happens: that is, he knows it as happening when and how it happens; but he doesn't know it at the time when it happens, or before, or after; he knows it timelessly.
Furthermore, he eternally causes it to happen as the finite act which it is, which means that he eternally (timelessly) causes it to happen when it happens (i.e. as related to the other processes which it is in fact related to) and how it happens (e.g. as dependent on the finite causes it is dependent on). But of course, this can't mean that he "always" causes it to happen then, or that he caused it to happen "from 'way back before the beginning of things'"; his causality, like his knowledge, or like anything about him, can't be put into a time or a period.
The fact that the effects of his acts are temporal doesn't mean that his act of causing them has to be temporal, any more than the fact that the effects of his act are material means that the act of causing them has to be material. The cause, as we saw long ago, cannot be like its effect. The temporality of changing bodies is a characteristic they have because they are in process and finite, and there are more of them than one, and so the quantities of their processes can be matched up the way we match up their colors or shapes or other properties they have. But this does not imply anything with respect to the one who causes them to be the finite acts which they are.
Many of the arguments against God's existence are actually based on a confusion of eternity with "always" or "beforehand." I have hinted at some of them above, and have given the grounds for straightening out the confusion, which can be stated in this way, if you want an aphorism: "Eternity is to time as colorlessness is to color." If someone asks you, "Yes, but if God did this, he had to do it at some time, didn't he?" you answer, "If glass exists, it has to be some color, doesn't it?"(2)
Let me mention one difficulty that really bothers people, and show that it is based on the assumption that time is some kind of a reality, and that it contradicts itself.
People tend to say, "But how can God know the future? It hasn't happened yet; it doesn't exist." But we know the past, and in the sense that the future doesn't exist, the past doesn't either. Does it?
Don't be too quick to say, "Of course it doesn't." If the past doesn't exist, and the future doesn't either, then all that exists is the present. But when is the present? As soon as you name it, you are naming the past, which doesn't exist. If you pronounce the words "the present moment" then all that exists is the syllable you are pronouncing, not the phrase. You can't even say, "All that exists is the present" if all that exists is the present.
So to say that the past doesn't exist any more is to fall into the trap that Zeno fell into when he said that no body is moving because it's at rest at any point along its movement (and therefore at every one), and what's at rest isn't moving. To say that the past doesn't exist any more is to take the comparison of processes, especially the minute measurement of this comparison, as if it were "the real reality of everything" and to make the processes themselves "unreal," because of course a process doesn't occur if all that exists is the present; processes happen through time, not at a time. And all that "happening through time" really means is that from the point of view of some observer, their beginning points (instabilities) and end-points (equilibria) match.
Hence, the past exists. Of course it does; we know it does because we have experienced it and can distinguish it from what is imaginary. My wedding is a real event, not something I made up.
Well yes, but it's not happening now. Of course not. But the "nowness" or the "thenness" is a tag that belongs to it, not something absolute--like saying that it took place in Boston, not Cincinnati; it just matches it up with other processes than the ones that connect together now. That is, saying that it's not happening now doesn't make it unreal now, any more than saying that a wedding now happening in Boston is unreal because it's not taking place in Cincinnati, where I happen to be.
But the future doesn't exist. Of course it does. What I am going to be doing tomorrow is what in fact I will be doing tomorrow; and that is what is real. But I don't know what I am going to be doing tomorrow. So what? I don't remember what I did ten years ago on this date. Does that mean that what happened did not happen? Well yes, but I can control what happens tomorrow. So? I controlled what happened on my wedding day too. Does the fact that it happened mean that it had to happen that way? And does the fact that I will freely decide to skip breakfast tomorrow mean that it won't happen that way because it is free? What will happen will in fact happen as it in fact will happen, just as with any real event.
Well yes, but it hasn't happened, so it doesn't really exist--yet. True, it doesn't exist yet, any more than the past exists still. But that doesn't mean it doesn't exist. The time is a tag that is put on it, and putting the tag on it or not does not take it from what is real and put it into what is imaginary.
And in fact, as Einstein shows, what is future for one observer can be present for another and past for a third. We can even experience this in the everyday world. Everyone gets all excited about New Year's Day happening in Japan when it's still last year over here. When is New Year's Day, actually? Is it now New Year's because we get TV signals from Japan, and it's New Year's there here? Which of us is right? And the answer, of course, is Yes.
What I am saying is that future events do exist, and are not even future from some observers' point of view; and if that can happen even on earth for a few minutes or hours--if it happens at all--then this shows that the time is not something that makes something real or removes it from reality.
The point of all of this is that time is a way of observing events (processes); from which it follows that it is observer-dependent and not something real; and so we shouldn't confuse "happening at some time" with "being real."Next
1. It is this type of number that I was referring to as the "derivative" in the calculus, which is the particular 0/0 that is approached as a limit. The dx and dt are the "fudge factor" I mentioned, implying that the number isn't zero, but an "infinitesimal bit" beyond it, so that the fraction makes sense. But an "infinitesimal bit" is a contradiction in terms, as I showed. In my system the "dx" refers to the zero approached in distance, and the "dt" the zero approached in the time; or, at that point, it is the tendency to move (since at that point, of course, an actual movement is a contradiction, because movement is a process that goes between "points.") Remember, "a point in a process" is part of the path, not the act of the process, which goes constantly to the end and then stops. That's why Aristotle said that the solution to Zeno's paradoxes was to walk across the room.
2. So now it can be seen that Leibniz's "axiom" that "whatever happens, happens somewhere and somewhen" is true only if you define "happen" as "an act that begins" or a process. Spiritual acts do not happen "anywhere" or "anywhen."