I was looking at a discussion about simultaneous causation and something that came up was that all physical processes take time. So nothing can truly be simultaneous.
And yet, we have philosophers treating some instances of causation as simultaneous.
How can this be? Is there something I'm missing here?
http://onlinelibrary.wiley.com/doi/10.1111/1467-9213.00331/abstract
First of all in mathematical physics we are treating idealizations of the world out there. There has been a continuous debate from antiquity as to what is meant by a continuum. Is it punctual, that is, made from points, or is there more? In classical geometry, as done by Euclid, he allows for points on lines, but Euclid is silent as to whether lines are exactly all of the points on the line. His geometry is synthetic. Descartes actually took that step (which paved the way for calculus). His geometry is analytic.
Certainly the most common notion treats the continuum as made up of points. For example, the calculus as envisaged by Newton and Leibniz does this. But already by then Leibniz declared the necessity for a analysis situs.
This was eventually formalized as topology. Over and above the idealization of the continuum as a set of points, one explicitly says how they cohere. It was also noticed that then one could actually do away with the notion of points altogether and just have the notion of cohesiveness (the theory of locales).
When you have a theory that has no points then in a precise sense it is meaningless to ask for exact simultaneity. But what this actually means is that one must expand on what one can mean by this in this new context.
While there has been a motion in Physics to atomize nature, from the atoms of matter, to quanta of energy and conjecturally spacetime, there also has been an opposite motion in which these atoms as point particles are seen to be problematic. Hence wave-particle duality (aka wavicles!), string and brane theory.
So far I've discussed the simultaneity in the small, which appears to be what you're asking about, but as a couple of the other posters have pointed out, there are problems with the simultaneity in the large as elucidated by Einstein in his special relativity theory. The laws of motion that we instinctively take for granted and formalized by Galileo are not correct. There is an absolute speed, the speed of light. Now speed as a formal concept ties together time and space, so how these are actually related must be modified. This was Einstein's accomplishment. Whereas the older paradigm treated space and time as essentially independent (so there were two notions of simultaneity - one for time and the other for space), he showed that they must be treated together (so there is a single notion of simultaneity using the idea of relativistic distance which combines information about both space and time).
It turns out we can keep the old idea of simultaneity when we are talking about events that are at the same location of space, but we cannot if they aren't. We must then use the relativistic notion.
Expanding upon Joseph's comment:
Special relativity rules out the possibility of absolute simultaneity. Read from the wikipedia page:
The theory of relativity postulates a maximum rate of transmission of information as the speed of light, and one consequence is that simultaneity at separated locations always is relative to the observer.
This SEP article also has relevant information at section 2.4.
Einstein had his own views on how we should treat our ordinary concept of simultaneity in light of special relativity. It certainly can't be (if we speak truly) that we are using the notion of absolute simultaneity. He wrote in a early paper that whether two events in distinct spatial locations were simultaneous has no definite answer and should be settled by convention. Whether special relativity is compatible with a non-conventional analysis of simultaneity is a matter of debate (see here for more discussion).
Taking a look at the paper you cite, they are fairly upfront that they are assuming classical physics. While this might be bad form for a physicist, it makes good sense within the context of the debate they are engaged in. Their thesis is NOT "since time actually has such and such a structure this view of causation is correct". Rather, they're stating something conditional in form.
Also, it is worth noting that for most everyday events, the differences between Newtonian and Relativistic are not too important. Newtonian mechanics approximates its more accurate relativistic counterpart when dealing with slow moving (i.e., low speed compared to the speed of light) medium sized objects (see the section on "limits of validity"). Most of the instances of causation we, as philosophers, are interested in analyzing are these everyday occurrences where pretending that classical physics is correct won't steer us too wrong. Since it is a simpler theory that is easier to understand and draw conclusions from, the hope is that it is still accurate enough to provide material for an accurate analysis of (everyday) causation.
Whitehead argues in Part II of Process and Reality that to accept simultaneities in the universe would violate the Ontological Principle which is an inflexible or categoreal presupposition of his speculative metaphysics.
He writes: “According to the classical ‘uniquely serial’ view of time, two contemporary actual entities define the same actual world. According to the modern view no two actual entities define the same actual world. Actual entities are called ‘contemporary’ when neither belongs to the ‘given’ actual world de¬fined by the other. The differences between the actual worlds of a pair of contemporary entities, which are in a certain sense ‘neighbours,’ are negligible for most human purposes. Thus the difference between the ‘classical’ and the ‘relativity’ view of time only rarely has any important relevance. I shall always adopt the relativity view; for one reason, because it seems better to accord with the general philosophical doctrine of relativity which is presupposed in the philosophy of organism; and for another reason, because with rare exceptions the classical doctrine can be looked on as a special case of the relativity doctrine—a case which does not seem to accord with experimental evidence. In other words, the classical view seems to limit a general philosophical doctrine; it is the larger assumption; and its consequences, taken in conjunction with other scientific principles, seem to be false” (PR, 65-66).
This takes place in the section where he also argues quite powerfully that "atomicity" and "continuity" are both consistent with universal relativity. So much for Zeno's paradox! I believe this is a definitive response. Without going into the significant differences between Einstein’s and Whitehead’s theories of relativity, they agree in principle that the simultaneity of actual entities is metaphysically baseless. If two entities did share the same ‘time-system’ then the universe would be deficient in novelty and fail to be creative—the ultimate category of Whitehead’s philosophy of organism. No entity’s world is simultaneous with another’s and that includes God on this account.
Thanks for asking this question!
For simultaneous events in different spatial locations see other replies. But consider two colliding bodies: don't they reach the collision location simultaneously? The two events at the same location must happen simultaneously in order for the third event (collision) to come into existence.
Basically if you get down to it, no, because the smaller and smaller you get in a period of time, time means nothing, but on a scale of seconds to nanoseconds, yes there is.
