Motion is either continuous or not. Either way, it is a simply remarkable thing.
Continuous: There is no first or last motion. All that is moving has moved and will move. Nothing is moving that has not already been in motion; and all in motion will be in motion. Motion is always between two terms. Trying to find a motion that has not been moving is like trying to find the next real number after 2, or the last real number before 2.
Discrete: no moving subject moves, for there is no subject, just as there is not one moving subject on a shelf of books where each book is annihilated one after the other. Strictly, there would be no “after” since this presupposes one thing that holds itself in the same way before and after.In fact, this would be a denial of motion.
Observation confirms the idea that motion is continuous. Observations can be more or less elaborate, but we are still speaking about something we are observing.
But if motion is continuous, and is therefore always between two terms, then the existence of motion requires the existence of its terms. What kind of temporal existence do they have? If the terms do not exist now, there cannot now be motion; but if the terms exist now, then how are they before and after in time, which is the only way we are interested in them? We easily imagine time lines, but time can’t be a line. In fact, a time line is as much a contradiction as square circle! it requires that something be at all at once (like a line) which by definition cannot be at once (temporal succession).
But if a time line is a contradiction, how is motion- as temporal- possible? Better yet, what is necessary if motion exists?
Just Thomism 
John said,
November 24, 2009 at 6:24 am
(I may have sent this already)
Your questions about continuity in time are equally applicable to continuity in space. Perhaps the right question is: what sort of spatio-temporal existence do two boundaries have? My own view is that, other than the entirely abstract idea of the two ends of a length, the only meaningful boundaries are particles (inhomogeneities in spacetime).
Systems of particles can become distributed in the dimensions available to them and this creates “becoming”, the direction of change. My own view, and that of many physicists, is that there are more than 4 dimensions for arranging objects. Some people confuse “becoming” with “dimensional time”: becoming applies to all dimensions in spacetime – objects move to “become” – but it is unusual to talk of the how breadth, length and depth are “timelike”.
Why is dimensional time “timelike”? Once we go beyond an attosecond or so along the time axis there is no communication between the 3D spaces at each instant (at attosecond intervals the 3D spaces undergo qm interference). This separation between hyperplanes is probably what leads us to assign “becoming” to the time dimension.
See: http://newempiricism.blogspot.com/2009/02/mctaggarts-unreality-of-time.html
http://en.wikibooks.org/wiki/Special_Relativity/Spacetime#The_modern_approach_to_special_relativity
http://de.scientificcommons.org/20590327 attosecond double slit
James Chastek said,
November 24, 2009 at 9:17 am
Thanks for the links. WordPress sent you to spam for them, which is why your comment took time to post. Liked your blog, FWIW.
This post is about motion, which can be considered either in a spatial way or in a temporal way. Here is my claim: motion depends on its terms to exist, and if motion is both temporal and spatial, it depends on spatial and temporal terms. Spatial terms involve no great difficulty so far as what is before and after in space can be present at once; but temporal terms present something of a difficulty, since the before and after of time cannot be present all at once. How can something be moving now, and therefore depend on terms now, and yet have terms that can’t be present now?
The way I am considering motion takes as its point of departure the continuous character of motion in its quantitative and temporal aspects. Relativity simply takes this for granted, as does all physics so far as it presumes that the real number system can meaningfully deal with its measurements. I’m still in a sub-basement here, and so it is not clear how I will work in later developments in quantum theory and relativity. The details in the sub-basement will eventually need to be balanced against and sythesized with more developed theories, but it is, at present, no more clear how we will incorporate the ideas of sub-basement physics into quantum theory than it is clear how we will sythesize and unify relativity and quantum physics (or even how we will incorporate the various models of things within a single branch of quantum physics. Is there even one model of, say, the atom? Should we even seek one? Why assume there is one model for anything?)
I’m working on these topics, but vita brevis, ars longa.
John said,
November 25, 2009 at 1:25 pm
You say: “Spatial terms involve no great difficulty so far as what is before and after in space can be present at once; but temporal terms present something of a difficulty, since the before and after of time cannot be present all at once.”
What is simultaneous for one observer is not simultaneous for another who is in relative motion. The reason for this is “relativistic phase”, the way that two observer’s clocks get progressively de-synchronised along the direction of relative motion. In fact “phase” is the most fascinating discovery of relativity because it is direct evidence of the four dimensional nature of reality. The most famous philosophical reflection on phase is the Rietjik-Putnam Argument (the Andromeda Paradox) and I have provided a link to an article on this below.
If you had a very long spaceship and were able to walk from one end to the other whilst it was in motion you would be walking back and forth in the time dimension of those who you considered stationary.
So two spatially separated events have a doubtful simultaneity. What of temporally separated events? The quantum double slit experiments in the time domain suggest that events at two times can be simultaneously active at a point. If we move away from points to assemblages of events distributed in space then you only need to set the assemblage in thermal motion for attosecond differences in time to appear between the members as a result of time dilation. If the formula (speed of light times time difference) is used to convert seconds to metres then a nanosecond is 10 cm long. If you heat a gas its molecules become temporally out of phase with each other so almost any observation is really an observation of events that are at all different times, many times being present at once in any given observer frame that is used to examine the gas or any other system in thermal motion.
You say: “In fact, a time line is as much a contradiction as square circle! it requires that something be at all at once (like a line) which by definition cannot be at once (temporal succession).”
Surely this only applies to an observer who is a spacetime point. At a point in space and an instant in time. A spatial line cannot be observed except by transfers of data at separate times and so is as much of a contradiction as a timeline.
See Andromeda paradox
James Chastek said,
December 1, 2009 at 12:13 pm
John,
Since this thread has continued till now, I figure I ought to say something.
There are difficulties in co-ordinating different clocks, and (sometimes) telling what is moving and what isn’t (nothing in relativity tells me I can’t be certain my hand is moving when I move it), but I would have happily admitted this before you said it. Despite quoting me, you are not speaking to anything I actually said, you are simply changing the topic to another topic (determining simultaneity between observers) where relativity concerns are (admittedly) quite important. This other topic you are bringing up has a good number of difficulties even in itself, much less in trying to square it with other things we know about nature, and so it is not always fruitful to go charging off in to discussions about relativity as though we knew how to incorporate them into other notions we have of physical things. We don’t.
As for your last paragraph here, I think you are simply agreeing with what I said.
AT said,
November 29, 2009 at 4:40 am
I recall (hopefully correctly) from the Physics that time is the measure of motion and motion is the measure of time. But time is also the mind enumerating – which I take to mean counting – which is discrete: 1,2,3… which I also take to mean – no humans, no time (probably still a before and after – for angels).
So, there is no “time line”, at least until we stop counting. Secondly, the time of motion A is given by the motion of B – a clock. I can’t think of any way to intrinsically measure the time intrinsic to motion A (if there is such a thing).
I’m one of those who thinks the past doesn’t exist and the future doesn’t exist, so clearly I can’t accept any kind of “time line”, except as a fiction (or a memory). So, I think this also means that I can’t accept the notion of a “space-time interval”.
John said,
November 29, 2009 at 11:44 am
Yes, presentists reject relativity (and hence modern physics -QED and QCD are relativistic theories). See Presentism and the denial of mind.
AT said,
November 30, 2009 at 3:59 am
I didn’t know I was a “presentist” – however, one who doesn’t reject relativity or modern physics.
I thought I was an “Aristotelian” of sorts and don’t see that that is incompatible with modern physics. (Even though the future and the past are non-existent, time is continuous).
John said,
December 1, 2009 at 2:21 am
I am slightly puzzled, when you say “So, I think this also means that I can’t accept the notion of a “space-time interval”, as far as I can see this means that you are rejecting Relativity Theory and most of modern physics.
Since the widespread adoption of Minkowski’s postulate of a 4D universe in 1908 Relativity is physics in a four dimensional manifold of signature (—+) or (+++-). The “physical law” that Relativity expresses is a direct result of the symmetry of spacetime manifest as the invariance of the space-time interval between reference frames. The invariance at the heart of Relativity is known as “Lorentz invariance” and it is identical to the invariance of the space-time interval.
No spacetime interval equals no Relativity. (Google Lorentz invariance or Lorentz symmetry if you wish to confirm this).
It is symmetries and the consequent invariants that form the substance of the modern interpretation of a “physical law”. For instance, the conservation of linear momentum is due to the invariance of length under translations in a 3D space. See Noether’s first theorem. So, by rejecting the spacetime interval you are rejecting the whole of physics after 1908.
AT said,
December 1, 2009 at 11:13 am
If the space-time interval is a measurement and doesn’t make any claims about past and future time existing “now” then I don’t have a problem with it.
It will take someone a lot smarter then I am to reconcile Aristotle/Aquinas with modern physics. Maybe Dr. Rizzi at info@iapweb.org. If I understand correctly what he said in Science Before Science we can’t take the discoveries of modern physics as metaphysics explanations.
John said,
December 6, 2009 at 3:19 am
Relativity places the space-time interval on the same footing as a spatial interval. The undergraduate examples such as the “pole-barn paradox'” show this clearly – in one reference frame the two ends of a pole are expressed by a pure space interval and in the other reference frame by a combination of space and time. (See Pole barn paradox)
Conscious experience (and physics) is going to be incomprehensible if we exist for no time at all. It is easier to explain awareness if we extend over a period of time because we would then coexist with both a statement and a question: ie: “I think I am” and “what did I just think?”. If I can hear whole words and see motions then that in itself is awareness.
The idea of “now” coexisting with “then” seems like a contradiction in terms but see the section on “the apparent paradox of two times being simultaneously present in “Time and Conscious Experience
James Chastek said,
December 6, 2009 at 7:55 am
Those paradoxes were wonderful. Great to see them all in one place.
I’m missing something in your argument. Your argument requires defending the following claim: relativity proves that the present is extended in one reference frame. I’ll concede every argument that shows some kind of “now extension” between reference frames, but I don’t see how that makes my present extended- which is the central claim you keep setting forth. You can appeal to other arguments to show that my present is extended, and they are not without force, but I don’t see how the science works in here.
John said,
December 7, 2009 at 10:43 am
I was using relativity to demonstrate the existence of the space-time interval. A direct demonstration of the existence of dimensional time requires experiments such as the qm double slit experiment in the time domain: Attosecond double slit in which an electron interferes with its historical self (cf: the energy-time version of the uncertainty principle – see Horwitz’s analysis of these experiments).
The essential point here is that dimensional time is theoretically predicted in physics and has been experimentally demonstrated.
AT said,
December 8, 2009 at 5:19 am
Of the experiment and the interpretation I can only say: interesting but not compelling. For one thing, the 500 as interval is dependent on the electron energy so I suspect it is not a purely time interval. (“Figure 4 also shows that each slit is, on closer inspection, a pair of slits and that the temporal separation of these sub-slits depends on the electron energy [21]. The experimental data must be considered to be a measurement
of the time difference of the two sub-slits, which is approximately 500 as.”)
James Chastek said,
December 7, 2009 at 2:14 pm
And this is what you are using to explain that the now is, what, several seconds long?
It’s my understanding that you are appealing to all this as some sort of way to explain how I hear the whole word “hello”. So is the “now” about as long as “hello”? Longer?
John said,
December 8, 2009 at 2:02 am
Yes, how do we explain whole words being present?
If I use a presentist model of time there should be no “specious” present because at each instant there is no motion and there are no other existent instants. (In presentism only the present instant, of no duration, exists.)
If I look and listen it seems evident to me that my conscious experience has a geometrical form that also involves time. I have described this experience in a Summary of New Empiricism. If you are interested in descriptions of phenomenal consciousness this might be worth a quick scan. The dimensional time within my experience does not seem dissimilar to the form of time in modern physical theory.
Of course, physical theory can be doubted or overinterpreted. You raised the implication that attoseconds in the double slit experiment may not be comparable with the seconds of time in conscious experience. The spatial double slit experiment also uses a tiny interval between the slits, in this case a spatial interval, but its results are nowadays extrapolated to the entire universe in quantum electrodynamics (QED). Incidently, QED is part of the Standard Model and is a merger of quantum physics and Special Relativity Theory in which dimensional time plays a crucial role. (Its a shame its not fully compatible with General Relativity). So the attoseconds in the temporal double slit have the same significance as the microns in the spatial double slit and the existence of interference in both shows that spacetime exists.
There is indeed a problem containing whole seconds in the mind. As I wrote in Presentism and the denial of mind: “The application of time extension to time intervals greater than a microsecond would seem to require Green’s time-like fifth dimension (Green 2002) to create an appropriate time dilation, the time-like nature of this dimension might be due to the continuous appearance of experience.”