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Humans are time-beings. They are laid in time, their consciousness is one of things-in-time. In Kant's transcendental philosophy time is a pure form of sensuous intuition. But if we think of time as a physical concept, then we may stick to two different views about its nature - dynamic and static one. The first regards the "flow" of time as a real process. The world exists only in the "present" moment. The other view regards all states from the history of an object to be equally real, i.e. the flow of time is mind-dependent. Only the static view of time can treat the twin (or the clocks) paradox in a non-contradictory way. But an unexpected peculiarity comes to the fore, concerning the conscious grasp of the moment of the encounter of the twins. It invites the option Kant's transcendental conception to be revisited.
Humans are time-beings. They are laid in time, their consciousness is one of things-in-time. In Kant's transcendental philosophy time is a pure form of sensuous institution. Intellectual intuition (behind phenomena in our experience) lies beyond our cognitive capacity. Time is a priori condition for the total human experience, and thus everything that could be given to us is already temporal, existing in time.
But if one thinks of time as a physical concept, or from the standpoint of some realist philosophy, then one usually sticks to two different views about its nature - dynamic and static one. The dynamic view regards the flow of time as a real process. The world exists only in the "present" moment and evolves through time. The past events do not exist already, and the future ones do not exist yet. The dynamic view has been enriched and transformed nowadays into different A-theories of time.1 Each of them keeps its basic idea about the flow of time, and usually makes use of a tensed vocabulary, pretending to express the so called A-properties of time (like "pastness", "presentness", and "futurity").
The central claim of the static view of time is that time does not flow by itself. It regards all states from the history of an object to be equally real, and thus makes no ontological difference among the past, the present, and the future. The flow of time is mind-dependent, but not an objective process, valid for all observers. Although past, present and future events are equally real, we perceive them to be consecutive. The static view is nowadays the conceptual core of the different B-theories of time.2
The static view pretends to be consistent with the ontology of Einstein's theory of relativity.3 One of my aims here is to defend this pretension by giving meaning to the familiar Twin Paradox, or Clocks Paradox, from the point of view of the two mentioned conceptions about time flow. My second aim is to make then some relevant comments concerning the perception of time, or the awareness of objects in time.
Let us suppose that the one of two identical twins, symbolized by А, remains on Earth, while the other - B - undertakes a space voyage with a rocket ship moving very fast. He reaches a goal point G (some planet around a distant star), and returns to Earth to see his brother again (see fig.1). Denoting the space-time point of departure with D, and the space-time point of the meeting of the twins with M, let us further suppose that the elapsed time for twin A, who remained on Earth, is ∆tA = 10 years. It is well known then, that the respective time interval (between the same points D and M) for twin B will be ∆tB < ∆tA. If the speed of B's rocket is great enough,4 it could be the case, that when B returns to Earth, the time that has passed for him is twice smaller than his brother's, i.e. ∆tB = 5 years. Thus, when the twins meet
in M the one who traveled, B, will be 5 years younger than his brother twin A.
But why B should be younger than A? The answer seems to be clear: because B's world line DGM, along which his proper time is being measured, is twice shorter than A's - DM'M. The world lines of A and B, represented on fig.1, bear just an opposite impression, but this is due to the fact that on the two-dimensional sheet of paper - an Euclidean plain - a situation is depicted which occurs in the four-dimensional pseudo-Euclidean space..5
Now, if the dynamic view of time flow were correct, then A and B either could not meet together in M, or, the only possibility for this is the assumption that the time for B flows just twice slower than that of A.
According to the dynamic view, the twins have real existence only in the moment "now". Their physical presence is realized by their 3-dimensional bodies changing in time. But if so, after 5 years B will exist in M, and will not be able to meet his brother, since for the same period of time A will be found to be in the point M' - the middle of his world line DM.
So the different degree of 'agings' of the two twins is fully compatible with the principle of relativity, when the theory is generalized sufficiently to apply to accelerated frames of reference.6
The theory could be "generalized sufficiently", of course, but it has already become clear that there is no need for doing this. Because the effect of the Clocks Paradox will remain the same, even if no accelerated frames of reference are involved. This could be proved by considering the so called three-clocks version of the paradox. In this version only inertial (not accelerated) clocks participate in the thought experiment.7 Thus it becomes clear that the acceleration plays no part in the assumed slowing down of the time flux of the space traveler B. This assumption has to be rejected. So, if we still remain within the dynamic view of time, we must concede that the twins will not meet in M. In order to explain their meeting, we must turn to the alternative, or the static view of time.
According to this view, the meeting of the twins in the space-time point M is possible, since they both have an actual presence along their four-dimensional world lines DM'M and DGM. The twins exist not as separate bodily segments, corresponding to different moments of time, but as four-dimensional world lines (channels). To this effect the static view is the adequate one. The reason for the different degrees of aging of the twins lies in the fact that the route of B through the four-dimensional pseudo-Euclidean space between points D and M is twice shorter than the respective route of A between these same points.
But what will happen when the twins see each other in M, provided that, because of the rejection of the dynamic view, the flow of time must be considered as mind-dependent along the individual world line (the individual history) of each traveler?
As V. Petkov explains, in the ontological framework of the static view the phenomenon of time flux is mind-dependent. Under the notion "flow of time" we understand the permanent change of the events which are consecutively being illuminated by human consciousness, while being in the moment "now".8 So, we must concede that the flow of time for both of the twins is an identical process. At least, we have no reason to claim the opposite.
Five years since B's departure, the present moment (the moment "now") for A embraces the event M', while the present moment for B - the event M. Notwithstanding, the twins will certainly meet in M, in so far as twin A exists along his whole world line, and thus he will be available as a physical body in M, too. But this encounter will be quite strange. Because twin B meets his brother twin A not within his own present, but in a future moment of his conscious existence, which for B the meeting is grasped just in his personal moment "now". When twin A becomes aware of the meeting, i.e. when this event becomes his moment "now", he will meet B in a past moment of his conscious existence, because the moment "now" for B will be the event M" (see fig. 1).
The effect of the Clocks Paradox has been confirmed during lots of experiments with fast moving elementary particles. The realization of the Twin Paradox is beyond our technical reach for now. If V. Petkov is right in his contention, however, then one may pose the question whether such an experiment is worth carrying out on moral grounds. Anyhow, what I'm interested in here, is the plausibility of the contention.
Indeed, if we accept that the flow of time is mind-dependent (because the alternative view - the dynamic one - fails in its explanation), then we could hardly find any reason why the perception of time flux for every human being should not be the same. Everyone must have the same "mechanism" of permanent change of the moments "now" within his/her consciousness. (The more so this ought to hold true for identical twins.) To use a Kantian way of saying, normal individuals have identical sensuous intuitions. They organize the manifold elements of phenomena in an identical successive way, since time is a pure form of sensibility, common for every human being as a possibility of perception. So, this natural assumption, as it seems, speaks in favour of the contention under consideration.
How then twin A will experience the meeting in the event M, if his present moment of conscious awareness "has reached" the event M'?
Is it ever possible for humans to have sometimes even slight "impressions" of future events? "It is not for you to know times or seasons which Father has put in His own authority" (The Acts 1:7). It seems that we cannot have any direct perception out of our "time-crawling" consciousness, or at least this is not possible for all "standard" representatives of humankind.
An attempt at elucidating the curious contention of the non-coinciding present moments for the twins A and B in the event M, might be the consolatory claim that the experience of time is not a process which goes "hand in hand" with the concomitant physical, chemical and physiological processes. When we sleep for example, we certainly exist biologically, but the change of the moment "now" (when not dreaming) is unfelt. Yet we come into the present moment when fully awaken.
It seems that human perception of time has two components. The one is feeling of events as "happenings", i.e. as situations in which we are involved in some way or another, and to which we ascribe some value. This feeling could be, and is often psychologically dependent. We feel pleasant experiences to be transient and evasive, and unpleasant experiences to be long lasting, despite the equal clock intervals of time they may cover.
The other component underlies the first. It is an internal sense of changing objects, of objects having a beginning and an end, or a lasting presence, and to this effect it provides a time order. This second component bears the temporal grasping of things intrinsic to consciousness, and is identical for all human beings. By this differentiation I go back to Kant's transcendental notion of time. Its a priori status makes human temporal experience possible, but also allows time presentations to be related to human understanding. By giving meaning to something we can find ourselves to be in the unique epistemic position not only to say that we know it, but also that we know that we know it. Maybe it could be the case that similar "second order" reflections could save the twins from the considered unexpected surprise. They might be prepared for it by theoretically knowing it. If human beings have no intellectual intuition, they have at least the faculty for theoretical thinking at their disposal.
For the characteristics of those theories see for example Dainton, Barry, Time and Space. Acumen Publishing Limited, 2001, pp.1-26; The Monist, Vol.88 (July, 2005), N 3. General Topic: Time Travel.
For the characteristics of those theories see Dainton, B. Op. cit., ch. 3; The Monist, Vol.88 (July, 2005), N 3. General Topic: Time Travel.
Petkov, Vesselin, "Simultaneity, Conventionality and Existence", British Journal for the Philosophy of Science, 40 (1989), pp.69-76; Idem, Relativity and the Nature of Spacetime. Springer-Verlag Berlin Heidelberg, 2005, pp.142-147.
It could be easily calculated (by using the Lorentz transformations) that the speed of the rocket ship in this case must be about 261 thousand km/s.
The coordinate system is attached to the Earth - the straight line DM is its time axis.
Bohm, D., "Comment on the Paradox of the Twins", in: M. Čapek (ed.), The Concepts of Space and Time. Their Structure and Their Development. Reidel, Dordrecht, 1976, p.452.
Cf. Kroes, P., "The Clock Paradox, Or How to Get Rid of Absolute Time", Philosophy of Science, 50 (1983), pp.159-163; Petkov, V., Relativity and the Nature of Spacetime, p.144.
This intricate matter is considered in his Relativity and the Nature of Spacetime, pp.148-152.
(Prof. DSc. Anguel S. Stefanov works at the Institute for Philosophical Research, Bulgarian Academy of Sciences, Sofia, Bulgaria)