(Affective past / Affective future / Right now)
In this section, Feynman
discusses three regions of space-time graph, namely, affective past, affective future, and right now.
1. Affective past:
“Therefore region 2 is sometimes called the affective past, or
affecting past; it is the locus of all events which can affect point O
in any way (Feynman et al., 1963, section 17–3 Past, present, and future).”
According to Feynman, region 2 is sometimes called the affective past
(or affecting past) because it is the locus of all events which can affect
point O. Phrased differently, all points of region 2 are in the “past”
of O, and anything that happens in this region could affect O.
Physics teachers should add that in region 2 (t < 0), the space-time interval between two events O and Q can be expressed as x2 < c2t2 and the square of the time-like interval (Ds)2 is greater than zero. This means that the two events, O and Q, are related causally and they are capable of interacting physically.
For example, an observer initially at event Q
could move to the position of event O
before O occurs. In other words, the
observer at Q can influence O (e.g., a transfer of energy) and the
two events are separated by a time-like interval that can be causally related.
Feynman elaborates an interesting physical relationship from region 2
(past) to the point O (here and now):
a physical object or a signal may move from a point in region 2 to the event O
at a speed that is less than the speed of light. For example, an object at Q
can move to O at a certain speed less than c, so if this object was
in a space ship and moving, it would be located at a point in the past (or
region 2). Physics teachers could explain that the principle of causality in
special relativity is related to the second postulate. That is, two events O and Q can interact physically, but it occurs while no physical signal
can move faster than c. Furthermore, based
on the principle of causality, the cause must
precede its effect is consistently observed by all inertial observers.
2.
Affective future:
“So this is the
world whose future can be affected by us, and we may call that the affective
future (Feynman et al., 1963, section 17–3 Past, present, and future).”
Feynman explains that region 3 is a region which we can affect from O,
for example, we can “hit” things by shooting “bullets” out at speeds less than c.
These include spatial points whose future can be affected by us, and he names
this region as affective future. We may add that in region 3 (t > 0), the space-time
interval between two events O and A
(a point in affective future) can be expressed as x2 < c2t2 and the square of the interval (Ds)2 is also time-like. In addition, if the
interval is time-like, i.e., (Ds)2 >
0, then tA > tO remains the same in every inertial frame. This is in contrast to quantum causality in which the causal order of
events is not always fixed whereby instantaneous movement is assumed possible.
One may hope Feynman to discuss the principle of causality. Interestingly,
the principle of causality as “an effect
cannot occur before its cause” is related to the temporal order of events. In Bridgman’s (1927) words, “[i]t
appears then, that the fundamental postulate of relativity (that the form of natural laws is the same in all
reference systems) demands that the temporal order of events causally connected
be the same in all reference systems (p. 87).” Furthermore, the light postulate has the
implication that no object or signal can move faster than the speed of light
from the perspective of inertial observers. This restriction of speed also
makes an assumption about the temporal order
of causally connected events (Bridgman, 1927).
3. Right
now:
“What we mean by
‘right now’ is a mysterious thing which we cannot define and we cannot affect,
but it can affect us later… (Feynman et al., 1963, section 17–3 Past, present, and future).”
Feynman says
that the interesting thing about region 1 (the remaining region of space-time)
is that we can neither affect it now from O, nor can it affect us
now at O, because nothing can move faster than the speed of
light. If the sun is exploding “now,” it takes eight minutes for the signal or
energy to reach us, and it cannot possibly affect us earlier. However, Feynman
did not clearly specify region 1 as “right now,” but it is named by some
physicists as “elsewhere” (Thorton & Marion, 2004), “causal present” (Rindler, 2003), or “present” (Resnick, 1968). Generally
speaking, O and R are separated by
a space-time interval that is space-like, i.e., (Ds)2 < 0. The separation between the two events is such that c2t2 < x2 whereby the influence between two events is limited by the speed of
light.
Feynman describes
right now as a mysterious thing which
we cannot define and affect, but it can affect us later if we had done
something far enough in the past. When we look at the star Alpha Centauri, we are
seeing the light from the star that was emitted four years ago; we may wonder
whether the star still exists “now.” In essence, two events that are separated by a space-like interval (e.g., Alpha Centauri
is four light-years away from us) have no absolute time sequence. The “now” is
dependent on the reference frame of an inertial observer, that is, the problem
of simultaneity is not a unique thing has been elucidated by Einstein. More
important, each event in region 1 may be identified as simultaneous with O (here and now) in a certain inertial
frame.
Questions for discussion:
1. How would you
define the region of affective past?
2. How would you define the region of affective
future?
3. How would you define the region of now
(or elsewhere)?
The moral of the lesson: two events that are separated by a time-like
interval have the same temporal order, and this is different from two events that are separated by space-like intervals
that have no absolute order of time.
References:
1. Bridgman, P. W.
(1927). The Logic of Modern Physics. New York: Macmillan.
2. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and
heat. Reading, MA: Addison-Wesley.
3. Resnick, R.
(1968). Introduction to Special
Relativity. New York: Wiley.
4. Rindler, W. (2003). Relativity: special, general,
and cosmological. Oxford: Oxford University Press.
5. Thornton, S. T. & Marion, J. B. (2004). Classical Dynamics of Particles and Systems
(5th Edition). Belmont, CA: Thomson Learning-Brooks/Cole.
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