But in time, objects — or people — can travel only from the past to the present and then on to the future, but never from the future into the past.
This unidirectionality leads to many questions: Is the unidirectionality of time truly a universal rule? Are there any exceptions? If it is a rule, why? Why are the other directions not unidirectional? What would be the difference between an ‘object traveling backwards through time’ and ‘time itself running backwards’?
To borrow a bit of verificationist jargon, if it makes sense to say that certain events can’t happen, then those events — the events that can’t happen — need to be adequately described in a way that an observer could know what they are. If it makes sense to say that an object can’t move backwards through time — i.e., travel from the future to the past — then in order for this saying to make sense, the observer will need to be know what to look for, and when the observer doesn’t find what he’s looking for — when the observer sees no objects moving backwards through time — then the observer can confirm this saying: the saying will have been verified. But in order to confirm that no objects are moving backward through time, the observer will need to know what to look for: there will need to be a description of what it means for an object to move backward through time, and not simply any type of description, but rather specifically a description which can be compared to any bit of sense data, or compared to any bit perception; this comparison will yield one of two answers: either “yes, it’s an object moving backward through time,” or “no, it’s not an object moving backward through time.” Presumably, then, the answer will always be “no.”
The description which either does, or does not, match an observer’s experience, is necessary in order for the saying to have meaning. Rudolf Carnap famously wrote that “we conclude that there is no way of understanding any meaning without ultimate reference to ostensive definitions, and this means, in an obvious sense, reference to ‘experience’ or ‘possibility of verification’” and “the meaning of a proposition is the method of its verification.”
Carnap’s phrases became slogans for the verificationist school of thought.
For the notion of an object moving backward through time, there are many such potential descriptions, provided in print by science fiction writers, and on screen by science fiction films. Of course, some of those descriptions may be more useful than others. But there must be some description which answers the question: What does it look like for an object to move backward through time? If there is no description, then the observer has nothing with which to compare his observations.
But it seems more difficult to give meaning to the phrase “time itself moving backwards.” What would this mean? What would it look like? What description of “time moving backwards” would one give to an observer, to tell him what to look for?
If it were taken as axiomatic that time can’t run backwards, then to give that phrase meaning, the observer would examine various events to confirm that in none of them was time running backwards. What would the observer seek, and not find, in those events?
To say that “there are no purple flowers in the garden,” and to ensure that this saying has meaning, one would have to know what a purple flower looked like, so that when one looked in the garden, one could confirm that one did not find a purple flower.
Likewise, to give meaning to the utterance, “time can’t run backwards,” one would need to know what it would look like for time to run backwards, so that one could confirm that one did not see it.
Unless, that is, time actually can run backwards.
In aScientific American article, Martin Gardner details how some physicists attempt “to give an operational meaning to ‘backward time’” and do so “by imagining a world in which shuffling processes went backward, from disorder to order.”
One might imagine shuffling a deck of cards, and starting with 52 cards in a pile, in no discernable order. After shuffling them, one might find them arranged in a clear order, e.g., by rank and suit. This is improbable, of course — massively, overwhelmingly improbable.
Improbability can be overcome by iteration. If billions of men were shuffling billions of decks of cards, and did so endlessly for billions of years, then it is not so improbable that one day, a scrambled deck of cards would be neatly ordered after shuffling.
Similarly, the reader will be familiar with the story about monkeys and typewriters, which, if left to their task for enough time, would eventually type out an accurate copy of Shakespeare’s works.
Of course, nobody is organizing billions of card dealers or billions of monkeys. But the air in any room is filled with billions and trillions of gaseous molecules, each of which is constantly vibrating and moving about in a random or near-random fashion. Martin Gardner explains how one physicist viewed this:
Ludwig Boltzmann, the 19th-century Austrian physicist who was one of the founders of statistical thermodynamics, realized that after the molecules of a gas in a closed, isolated container have reached a state of thermal equilibrium — that is, are moving in complete disorder with maximum entropy — there will always be little pockets forming here and there where entropy is momentarily decreasing. These would be balanced by other regions where entropy is increasing; the overall entropy remains relatively stable, with only minor up-and-down fluctuations.
Boltzmann transferred this pattern from a container of gas to the universe at large. If the Brownian motion created these situations in a glass jar of nitrogen or carbon dioxide on a table in Boltzmann’s office in the University of Vienna, then the universe as a whole with its many galaxies might exhibit the same behavior, simply on a larger scale:
Boltzmann imagined a cosmos of vast size, perhaps infinite in space and time, the overall entropy of which is at a maximum but which contains pockets where for the moment entropy is decreasing. (A “pocket” could include billions of galaxies and the “moment” could be billions of years.) Perhaps our flyspeck portion of the infinite sea of space-time is one in which such a fluctuation has occurred. At some time in the past, perhaps at the time of the “big bang,” entropy happened to decrease; now it is increasing. In the eternal and infinite flux a bit of order happened to put in its appearance; now that order is disappearing again, and so our arrow of time runs in the familiar direction of increasing entropy. Are there other regions of space-time, Boltzmann asked, in which the arrow of entropy points the other way? If so, would it be correct to say that time in such a region was moving backward, or should one simply say that entropy was decreasing as the region continued to move forward in time?
One way to formulate Boltzmann’s question is to compare these two phrases:
Increasing entropy in time
Increasing entropy is time
Does disorder increase over time — in time, within time? Or is time the increase in disorder?
Is it valid to transfer, as Boltzmann does, the pattern from gas confined in a container to the entire universe? There may be some differences between the two cases. In the situation of gas in a sealed glass jar, the observer, in this case the physicist in the laboratory, is in a situation which, if not that of omniscient God, is at least similar: the observer hovers above the jar, and even if the pockets of disequilibrium are not visible, is able to view the entire “universe” of the experiment at once, and able to watch the the experiment from inception to completion.
When the concept is transferred to the entire physical universe, or to one like it in a thought experiment, the situation of the observer is more problematic. The word ‘entire’ entails that the observer be in the universe. The observer is not in an omniscient role and able to view the universe from the outside. If one were to be in a universe, then how would one know if some pockets of this universe had a time which ran in a different direction than other pockets of this universe?
There might be some empirical problems, as Martin Garnder points out: if the observer is in a pocket of the universe in which time is running forward, and attempted to observe a pocket of the universe in which time were running backwards, he would not be able to see such a pocket, even if it were present, because it would be inhaling light rather than exhaling it. A separate problem would arise when the observer asked whether he was resident in a pocket of the universe in which time ran forward, or whether he resided in a region in which time ran backward. Here one might invoke the Leibnizian principle of the identity of indiscernibles: time running forward and time running backward would be empirically the same for the observer.
The notion of a pocket of the universe absorbing rather than emitting light, because time was running backwards in that pocket, has caused some, like Raphael Bousso and Netta Engelhardt, to ask whether a “black hole” has a local time which runs backward.
The difficulties in determining about a pocket of space, whether its time runs forward or backward, tempts one to posit a sort of meta-time, which would act as a framework around the entire universe, and would allow the observer to determine whether times in different pockets of space were running in the same direction or in different directions.
When one describes a universe in which some regions have time running forward and other regions have time running backward, it is tempting to add a phrase to this description: “at the same time” or “simultaneously.”
One might say: “In this universe, the time in region A is running forward, and at the same time, the time in region B is running backward.” But in saying this, one has introduced the notion of meta-time.
But the idea of meta-time is problematic. It can lead to an infinite regress of meta-meta-time and meta-meta-meta-time, etc.
It is worth noting that Boltzmann came to this problem from the discipline of physics, or chemistry, or physical chemistry. One of his books is titled Gastheorie. The behavior and properties of gasses are treated statistically. A jar of nitrogen or CO2 contains billions and trillions of molecules, randomly vibrating and traveling to and fro. It is not possible to detail the exact movements of each individual molecule, and such information would yield little insight into the physics of gasses. But a statistical view of the movements of all the molecules helpfully characterizes the behavior and properties of the gas in question.
When Boltzmann then begins to ponder entropy decreasing and time running backwards in his glass jar of gas, Martin Gardner explains that “No basic laws would be violated, only statistical laws.”
Given that our general, even universal, experience is one of time moving forward, then how might one justify the hegemony of forward-moving time in human experience, and the absence of backward moving time? The emphasis here is on ‘experience,’ given that the hypothetically possible cases of backward moving time are not part of direct experience; those cases are invisible: the gas in the jar, or the galaxy which absorbs light rather than emitting it.
What explains the ubiquity of forward-moving time, given the possibility of backward-moving time? The answer again relates to statistics, as Gardner writes:
It was here, in the laws of probability, that most 19th-century physicists found an ultimate basis for time’s arrow. Probability explains such irreversible processes as the mixing of coffee and cream, the breaking of a window by a stone and all the other familiar one-way-only events in which large numbers of molecules are involved. It explains the second law of thermodynamics, which says that heat always moves from hotter to cooler regions, increasing the entropy (a measure of a certain kind of disorder) of the system. It explains why shuffling randomizes a deck of ordered cards.
Young students are often given this example: a solid object, e.g., a rock, could suddenly disappear in a cloud of dust and vapor, if the Brownian motion of all its molecules randomly happened to behave in precisely the right way. But the probability of this happening is so close to zero that it is treated as zero. It is a statistical explanation.
Similarly so with the directionality of time, as Gardner writes:
Physicists and philosophers argued that statistical laws provide the most fundamental way to define the direction of time.
So Boltzmann’s view of time is ultimately a statistical one, and the questions which his view raises are to be understood in that way.
The questions which Boltzmann’s work, directly or indirectly, raises are still open, and still the focus of research and debate.
