Tick-Tick

Slavoj Zizek, "Absolute Invariants in Physics and Society"

The Albanian prime minister Edi Rama told the following joke at an international conference: “Russia is considering unifying its time zones because there is a nine-hour difference between one side of the country and the other. Then the Russian Prime Minister went to Vladimir Putin and said: ‘There is a problem. My family was on vacation and I called them to say good night and it was morning and they were at the beach. I called Olaf Scholz to wish him a happy birthday, but he said they would be there the next day. I called Xi Jinping to wish him a Happy New Year, but he replied that they still had the old one…’ Putin replied: ‘Yes, it happened to me too. I called Yevgeny Prigozhin’s family to express my condolences, but his plane has not taken off yet.’” This joke brings us directly to our topic, namely the problem of simultaneity, in which Putin obviously thinks he lives in a block universe where the future (of the bomb exploding on Prigozhin’s plane) already exists now for him as a privileged observer.

It is well known how special relativity theory relativizes the notion of simultaneity of two events: “That no inherent meaning can be assigned to the simultaneity of distant events is the single most important lesson to be learned from relativity.”[i] The basic idea is clear: there is no absolute position in spacetime; every movement is a movement with regard to a certain observer; something moves with regard to the position of this observer. Since there are dozens of sites explaining the paradox this thesis involves, let’s quote a popular description of Einstein’s thought experiment consisting of a moving train with one observer midway in the train and another observer midway on the platform as the train moves past:

“A flash of light is given off at the center of the train just when the two observers pass each other. The observer on the train sees the front and back of the train at fixed distances away from the source of the light flash (since the front, back, and train observer are all in the same inertial frame). According to this observer, the light flashes reach the front and back of the train at precisely the same instant of time—that is, simultaneously. On the other hand, the observer on the platform sees the back of the train moving toward the point at which the flash was given off, and the front of the train moving away from it. This means that the light flash going toward the back of the train will have less distance to cover than the light flash going to the front. As the speed of light is finite, and the same in any direction relative to the platform (regardless of the motion of its source), the flashes will not strike the ends of the train simultaneously. /…/ For both observers, the speed at which the light traveled is constant, but the distance traveled (and thus the time consumed in covering the distance) varies depending on the relative motion of the observer.”

Can we then decide if one observer is right and the other wrong? The conclusion that imposes itself is that “neither one can be shown wrong, and that a simultaneity in one inertial frame need not be true outside that frame.”[ii] Sabina Hossenfelder draws the general ontological consequence of this paradox:

“the physics of Einstein’s special relativity does not allow us to constrain existence to merely a moment that we call ‘now.’ Once you agree that anything exists now elsewhere, even though you see it only later, you are forced to accept that everything in the universe exists now. This perplexing consequence of special relativity has been dubbed the block universe by physicists. In this block universe, the future, present, and past exist in the same way, it’s just that we do not experience them in the same way. And if all times exist similarly, then all our past selves – and grandparents – are alive the same way our present selves are.”[iii]

Let me quote also an explanatory passage by Sean Carroll: “for objects spatially distant from each other, there is no absolute simultaneity. A faraway event might be in the ‘future’ or in the ‘past’ of some nearby event, depending on one’s frame of reference. The slightly more slippery point is: therefore, if I want to attribute reality to all things ‘now,’ I have to attribute it to a set of faraway events that might be in the direct past or future of each other. And therefore, I pretty much have to attribute reality to the whole four-dimensional universe, including events in my own past and future.”[iv] The logical implication of this reasoning is that one cannot ask, independently of the observer’s frame, if an event A is in the past or future of an event B; it is neither. From the perspective of one observer, B can be slightly in the future of A, and from the perspective of another observer, it can be slightly in the past.

The basic logic that underlies these conclusions is clear: we see the explosion of a star which took place millions of years ago now (much later), so it exists now for us, but it existed millions of years ago for a putative observer who was near it when the explosion took place, so we have two now’s, ours and that of the putative observer. But I see some problems with the conclusion that “everything in the universe exists now,” the future, present, and past. Can we also say that we – who observe the explosion in our now – fully exist in the future for the putative observer who was close to the star? What if a contingent event that might have happened a mere half a million of years ago (measured by in our time) were to annihilate all life on our earth? Would it not be more logical to say that everything fully exists in its own now (which cannot be synchronized with my own now)?

In order to appear to multiple observes who perceive an event in different nows, it has to “really occur” at a moment simultaneous to an observer at the same place. In other words, can we really include future events or objects into this image? How can something appear “now” to an observer when this event didn’t even take place? It can on one condition: that we reduce time, the temporal flow, to the limitation that pertains to our subjective perception – a conclusion which is for me problematic. If future also exists now, if (our) future events are real in the same sense (our) present events are, then space has priority over time; the future and the past would be all real and present for an omnipotent observer able to see the entire block of past, present, and future. However, what if time is not just another dimension of space but a crack in space, an imperfection of space which is not just epistemological but ontological? That is, what if space is in itself, not just for our limited perception, imperfect, traversed by cracks?

Next point: what happens when we imagine faster-than-light travel (and information can travel faster than light when two particles are entangled, as recent experiments demonstrated)? It’s not that, in this case, the eternal Now becomes reality, everything co-existing simultaneously. Since we still have multiple observers, the question should be specified: how will an observer perceive an object which moves faster than light for another observer? Since the speed of light is the maximum speed in our spacetime, the conclusion that imposes itself is unavoidable: for the first observer, the object will move back in time.

The paradox of travelling back in time “can occur in special relativity when faster-than-light travel is possible, because an object that moves faster than light for one observer can look as if it’s going back in time for another observer. Thus, in special relativity, you always get both together: faster-than-light motion, and that opens the door to causality paradoxes.”[v] Do we not encounter a somewhat similar paradox at the spatial level where the conjecture imposes itself that “the inside of our elementary particles has a large volume”: “they might be bigger on the inside than they look from the outside. /…/ That’s because in general relativity we can curve our space-time so strongly that it’ll form bags figures. These bags can have a small surface area – i.e., look small from the outside – but have a large volume inside.”[vi] Recall the bag of Mary Poppins, an ordinary-size bag out of which she pulls many much larger objects… Something similar also happens in our daily experience: a small car appears from outside too tight for me to enter it, but once I do enter it, I may feel quite comfortable in it. An additional point: why mention just large-scale cases like how to walk to or from Andromeda? A problem arises already with my own body: am I simultaneous with/to myself, my own body? The basic lesson of the analysis of perception is that I do not immediately see what I see: I compose/construct the mess of my projections relying on my expectations about the future and then I project this construct forwards into the now. In short, what I experience as something here-and-now is sustained by a complex backward-and-forward movement.

Here is a simple and clear description of this paradox:

“We feel that we perceive events in the environment as they unfold in real-time. However, this intuitive view of perception is impossible to implement in the nervous system due to biological constraints such as neural transmission delays. /…/ at any given moment, instead of representing a single timepoint, perceptual mechanisms represent an entire timeline. On this timeline, predictive mechanisms predict ahead to compensate for delays in incoming sensory input, and reconstruction mechanisms retroactively revise perception when those predictions do not come true.”

However, after all these variations on the topic of relativity, one should conclude with the crucial point that Einstein’s special theory of relativity implies two absolutes. The first one, known to everybody, is the speed of light as the maximum speed in our material universe, independent of the movement of objects and observers within this universe. The second one, less known but much more interesting theoretically, is the absolute observable, the “space-time interval between events that all observers will agree on”:

“the two observers measured different spatial and temporal distances between the same two events but when they both (1) take the time interval, multiply it by the speed of light and then square it, (2) take the spatial distance between the events and square that, and (3) subtract the two numbers, then they get the same number. It is an absolute observable, the space-time interval between events that all observers will agree on.”

Here we get the oft-ignored other side of relativity theory: the interval between two events can be formulated as a fact (a number) independent of all observers. However, the true paradox is that observers are not simply absent: each observer can arrive at the absolute interval not by ignoring his observations but by submitting them to the same mathematic procedure. First, you take the time interval between the two events as you perceive it (and this interval is not the same as the interval perceived by another observer) and submit it to the prescribed procedure; then, you take the spatial distance as you perceive it (and, again, this distance is not the same as the distance perceived by another observer) and square it; finally, you subtract the two numbers and you get a number which is the same for all observers… Nevertheless, since I am not a specialist in relativity theory, rather than dwelling on the details of the absolute observable (which I am also unable to do), I will shift to a homology which immediately strikes my eye here, a homology with two key antagonisms in our societies: class struggle and sexual difference.

Social classes are not an objective fact, they exist only as an effect of class struggle, which is why class difference is not a symbolic difference but the Real of an antagonism. As Lacan would have put it, there is no metalanguage in class struggle, no neutral way to describe it: every description of class struggle is already done from a position within class struggle. In other words, class struggle affects the very notion of class struggle: it appears in a different way to those at the bottom, exploited, and to those at the top. And the same goes for sexual difference: it also names an irreducible antagonism, which means that it appears in a different way to those who occupy the feminine position and to those who occupy the masculine position. However, in both cases, this “relativization” does not imply a relativistic subjectivization: there is an “absolute invariant” of class struggle as well as of sexual difference, and this invariant can be reached only through subjective perceptions and stances. In these two cases, of course, the “absolute invariant” cannot be determined as a number; it can only be specified as a basic antagonism that is in this case arrived at by way of identifying it as the common denominator, to which each of the two main class or sexual positions react.

In the case of sexual difference, Lacan has already shown the way in his “formulas of sexuation”: each sexual stance (masculine, feminine) is defined by its constitutive antagonism. The masculine stance is that of a universality based on its constitutive exception, and the feminine stance allows for no exception but remains thereby non-all. (In her classic analysis, Joan Copjec demonstrated how these two antagonisms repeat Kant’s “scandal of pure reason,” the couple of dynamic and mathematic antinomies of pure reason.) The absolute invariant is here the gap of the immanent impossibility of sexual rapport (Lacan’s “il n’y a pas de rapport sexuel“), and this non-rapport takes the form of two symbolic “contradictions” (universality with exception, non-all with no exception).

It is important to note how Lacan’s four formulas cut diagonally across two “logical” couples: instead of a universality without exception and a non-all set with an exception, we get a universality with exception and a non-all set with no exception, the underlying idea being that a universality is constituted only through an exception. This is why we should absolutely avoid reading the formulas in a vulgar “phallic” way: the phallic signifier as the exception that makes masculine totality, the surplus which sticks out, and the feminine set as “non-all,” with a gap (hole) in its midst which calls to be filled-in. What formulas of sexuation imply is precisely that the hole and the exception do not fit each other because they are one and the same thing in a different space (which is why, as Lacan put it, phallus is a signifier of a lack, while the hole is not an exception but comes as an excess).

And things are homologous in class struggle. The fact that class struggle logically precedes classes means that not only the rapport between classes is antagonistic (“il n’y a pas de rapport de classe”) but that the identity of each class is in itself antagonistic. The ruling class operates in a masculine mode; it is an exception which totalizes a society (which is why it perceives all other classes as a threat to social unity). It is, then, an exception in the well-known sense of an illegal element (violence out of law) which sustains the rule of law. The exploited class is non-all (dispersed, not totalized), and for this reason it has no exception to sustain its unity. When such an exception emerges (as in the guise of the Stalinist Party), it reintroduces the logic of class power. And, again, these two subjective stances are the two ways to deal with the “absolute invariant” of class antagonism that constitutes our societies.

Notes:

[i] David N. Mermin, It’s About Time, Princeton: Princeton University Press 2021, p. 9.

[ii] Op.cit.

[iii] Sabine Hossenfelder, Existential Physics, London: Atlantic Books 2023, p. 11.

[iv] Personal communication

[v] Op.cit., p. 177.

[vi] Op.cit., p. 181.