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Time Travel: Possible, or Impossible?
By Jack Hokikian, Ph.D.
Version 2.0, Updated 7/31/2013
Recently, time travel has received much attention in the media. Books and articles have been written on the subject purporting that time travel is possible and consistent with the laws of physics, and that Albert Einstein supposedly was in agreement with this assessment.  This essay examines the situation and reaches a definitive conclusion whether time travel is possible or impossible as far as physics is concerned.
Two statements of Einstein are often quoted, which presumably support the view that traveling into the past is possible. One quotation of Einstein comes from a condolence letter offering comfort to the son and sister of his longtime friend and engineer Michelangelo Besso: “In quitting this strange world he has once again preceded me by just a little. That doesn’t mean anything. For we convinced physicists the distinction between past, present, and future is only an illusion, however persistent.”  Some scientists have speculated that this remarkable statement was also a comfort to its author, who died a month later in April, 1955. 
Einstein was alluding to the fact that nearly all laws and equations of physics, including his theory of relativity, quantum theory and Newtonian mechanics are time-reversible. They make no distinction between future and past.
Does this mean that physics is telling us we live in a reversible world and that the passage of time is merely an illusion? The Second Law of Thermodynamics—the Law of Increasing Entropy—holds the answer.
The Second Law is about the irreversibility of natural processes and, consequently, the flow of time. It states that there is a physical quantity called entropy that increases in all processes irreversibly. Physicists identify entropy as a measure of the disorder or complexity of a system. 
(The First Law is about a physical quantity called energy. It states that the amount of energy in the universe is constant; energy cannot be created or destroyed but can be transformed from one form to another.) 
Thus, if we ask: What was the entropy of the universe yesterday compared with today’s and tomorrow’s? The answer is: Yesterday, entropy was less than today; tomorrow, it will be greater than today. As time flows from past to future, entropy always increases in the same direction, irreversibly.
So there is a distinction between past, present, and future; changes do occur through the passage of time and the Second Law provides a measure of these changes through the concept of entropy. Stated differently, today’s world looks different to us from yesterday’s because of all the increases in entropy due to the processes, transformations, events and happenings since then.
Without the Second Law, we can form incorrect and even absurd worldviews, and many prominent people have. This brings us to the second often-quoted statement of Einstein, a statement that supposedly gives the green light to the possibility of communicating with the past and even traveling and revisiting the past, a.k.a. time travel. Einstein’s statement comes from a reply to an essay that his longtime friend and colleague at Princeton University—the renowned mathematician and logician Kurt Gödel—had written.
In 1949, Gödel wrote an essay in which he used Einstein’s relativity theory to point out that we can send a message to the past. Gödel went a step further. Using Einstein’s general theory of relativity, he arrived at a universe whereupon we can physically travel to the past. He stated that “by making a round trip on a rocket ship in a sufficiently wide curve, it is possible in these worlds to travel into any region of the past, present, and future, and back again, exactly as it is possible in other worlds to travel to distant parts of space.”  Time travel enthusiasts have been thrilled by this declaration, especially by what Einstein wrote about his best friend’s work.
In the same book, some pages later in an article entitled “Reply to Criticisms,” Einstein commends politely his colleague’s paper with these words: “Kurt Gödel’s essay constitutes, in my opinion, an important contribution to the general theory of relativity, especially to the analysis of the concept of time.” This often-quoted statement has been used as a reaffirmation by Einstein that, according to physics, time travel is possible. But did Einstein really confirm Gödel’s findings? Not at all. Just the opposite. He immediately wrote: “The problem here involved disturbed me already at the time of the building up of the general theory of relativity, without my having succeeded in clarifying it.”
How does Einstein clarify the issue? He doesn’t do it within general theory of relativity. He goes outside relativity to thermodynamics and invokes the Second Law, the law of irreversibility of natural processes and the increase of entropy—the inseparable sister of energy. With the aid of a diagram, Einstein shows Gödel that we cannot “telegraph” back to our own past because the flow of time has an arrow and “there exists no free choice for the direction of the arrow.” He makes it clear that he wants to secure “the one-sided (asymmetrical) character of time.” These are strong and unambiguous words. Einstein explains the reason: “What is essential in this is the fact that the sending of a signal is, in the sense of thermodynamics, an irreversible process, a process which is connected with the growth of entropy (whereas, according to our present knowledge, all elementary processes are reversible).” 
A side note: When Einstein wrote this in 1949, i.e., all particle interactions are time-reversible (or time-symmetric), scientists did not know that the rare and unstable particles called K-mesons occasionally—in 0.2 percent of cases—decay in a manner that violates time symmetry. This fact was discovered in 1963. Physicists James Cronin and Val L. Fitch received the Nobel Prize for this discovery in 1980. 
The sending of a signal is not the only process that is irreversible. All processes—physical, chemical, biological, geological, cosmological, you name it—are irreversible. The Second Law is based on this unshakable fact. It tells us undoubtedly that we live in an irreversible universe. 
As it turns out, Aristotle had examined the characteristics of time analytically. He had concluded that time has both durational, which we measure through clocks, and an arrow-like character.  When the Second Law of Thermodynamics was formulated by Rudolf Clausius in the nineteenth century, stating that entropy increases inexorably in all processes and that “the entropy of the universe strives to attain a maximum value,”  Sir Arthur Eddington declared that entropy increase gives us the direction of “time’s arrow.” 
Interestingly, Gödel himself did not believe that time travel made sense at all. This is what he wrote in the essay about travel to the past. “This state of affairs seems to imply an absurdity. For it enables one e.g., to travel into the near past of those places where he has himself lived. There he would find a person who would be himself at some earlier period of his life. Now he could do something to this person which, by his memory, he knows has not happened to him. This and similar contradictions, . . . .” 
If Gödel believed what he was proposing, he would not have used such words as “absurdity” and “contradictions” for traveling back in time. In essence, Gödel was telling his close friend that something is seriously wrong here and that he should look into the matter. And Einstein did that and reminded him of the Law of Increasing Entropy, which does not permit us to send a signal back to the past even at the speed of light, let alone travel back with a spaceship and visit the world at some earlier period.
The sending of a spaceship requires great consumption of energy. And the more energy we use, the more entropy we generate, which makes time’s arrow move into the future, thus falling farther behind from our goal to visit the past. No human ingenuity or technology is going to outsmart the Second Law. The Second Law is in absolute control of all natural processes. Because of its power and generality, Sir Arthur Eddington declared, “if your theory is found to be against the Second Law of Thermodynamics, I can give you no hope; there is nothing to do but to collapse in deepest humiliation.”  He has been correct ever since.
If we could travel back in time and find ourselves at some earlier period of our life here on Earth, as Gödel describes, we would also find all the oil that we have burned since then. We would then pump the oil, put it in the spaceship, bring it back and consume it again. (While we are at it, we could also bring the younger version of ourselves back and live together.) In physics, this state of affairs is impossible as it violates the unshakable Second Law.
Actually, the universe of the past does not exist to go back to it. The universe is constantly undergoing transformations of energy/matter from one form to another irreversibly. For instance, when we burn the gasoline in our cars, it gets transformed to other forms of energy/matter irreversibly. In the process, the entropy of our world increases irreversibly. In fact, Clausius chose the word entropy because in Greek, it means "transformation." 
The Laws of Thermodynamics are different from all other laws of the universe; all the forces of Nature in their interactions and all natural processes obey the Laws of Energy and Entropy, also called principles or super laws. That’s why the Laws of Thermodynamics are often capitalized . They act as the Supreme Governor of all events and processes occurring in our universe.
Incidentally, the Laws of Thermodynamics are independent whether our universe is expanding, pulsating, rotating or a static place (Gödel’s universe was rotating). When the Laws of Thermodynamics were discovered, scientists did not know that the universe was dynamic. When the evidence came in that our universe is expanding, what changed was our view of how the universe began and how it is evolving. Through observation, cosmologists are continually refining their theories on the origin and thermodynamic evolution of our universe. The Laws of Thermodynamics, however, remain intact.
In his book, Physics of the Impossible: A Scientific Exploration into the World of Phasers, Force Fields, Teleportation, and Time Travel, Dr. Michio Kaku writes: "[Stephen] Hawking also raised a challenge to the world of physics. There ought to be a law, he proclaimed, making time travel impossible. He proposed a 'Chronology Protection Conjecture' to ban time travel from the laws of physics in order to 'make history safe for historians.' [New Paragraph] The embarrassing thing, however, was that no matter how hard physicists tried, they could not find a law to prevent time travel. Apparently time travel seems to be consistent with the known laws of physics. Unable to find any physical law that makes time travel impossible, Hawking recently changed his mind. He made headlines in the London papers when he said, 'Time travel may be possible, but it is not practical.'" 
Dr. Hawking did not need to change his mind; the Second Law of Thermodynamics, the law of irreversibility of natural processes, makes time's arrow irreversible, i.e., makes time asymmetrical and time travel—revisiting the past—impossible.
Our perspective on the world is very different if we view it as a reversible system subject to our control rather than an irreversible system governed by the Laws of Thermodynamics. Many of our gross errors in judgment have come about because we have neglected the Laws of Thermodynamics, especially the Law of Increasing Entropy.
Jack Hokikian's email: firstname.lastname@example.org
 See for example, Palle Yourgrau, A World Without Time: The Forgotten Legacy of Gödel and Einstein (New York: Basic Books, 2005); Jim Holt, “Time Bandits: What were Einstein and Gödel talking about?” The New Yorker, 28 February, 2005; Jeffrey Hildner, “TIME SPACE MATTER: Seeing through the grand illusion,” The Christian Science Journal, July 2005, p. 44; Ronald L. Mallett with Bruce Henderson, Time Traveler: A Scientist’s Personal Mission to Make Time Travel a Reality (New York: Thunder’s Mouth Press, 2006)
 Pierre Speziali, ed., Albert Einstein Michele Besso: Correspondance 1903-1955 (Paris: Hermann, 1972), pp. 537-39.
 Peter V. Coveney and Roger Highfield, The Arrow of Time: A Voyage Through Science to Solve Time’s Greatest Mystery (New York: Fawcett Columbine, 1991, copyright 1990, p. 30.
 Jack Hokikian, The Science of Disorder: Understanding the Complexity, Uncertainty, and Pollution in Our World (Los Angeles: Los Feliz Publishing, 2002), pp. 17-42.
 Ibid., pp. 1-15.
 Kurt Gödel, “A Remark About the Relationship Between Relativity Theory and Idealistic Philosophy, in Paul Arthur Schilpp, ed., Albert Einstein: Philosopher-Scientist, 3d. ed. (La Salle, Ill.: Open Court, 1970), p. 560.
 Albert Einstein, “Reply to Criticisms,” in Ibid., pp. 687-88.
 Hokikian, The Science of Disorder, pp. 37-8; Martin J. Rees, Before the Beginning: Our Universe and Others (Reading, Mass.: Addison-Wesley, 1997) p. 211. See also p. 156.
 Hokikian, The Science of Disorder, pp. 25-6.
 Ibid., p. 34; A. Cornelius Benjamin, “Ideas of Time in the History of Philosophy,” in J. T. Fraser, ed., The Voices of Time: A Cooperative Survey of Man’s Views of Time as Expressed by the Sciences and by the Humanities (New York: George Braziller, 1966), pp. 3-30.
 Hokikian, The Science of Disorder, p. 29; Rudolf Clausius, “On Different Forms of the Fundamental Equations of the Mechanical Theory of Heat and Their Convenience for Application,” in Joseph Kestin, ed., The Second Law of Thermodynamics (Stroudsburg, Penn.: Dowden, Hutchinson & Ross, 1976), p. 193.
 Hokikian, The Science of Disorder, p. 38; Coveney and Highfield, The Arrow of Time, p. 24.
 Kurt Gödel, “A Remark About the Relationship Between Relativity Theory and Idealistic Philosophy, in Schilpp, ed., Albert Einstein: Philosopher-Scientist, pp. 560-61.
 Hokikian, The Science of Disorder, p. 30.
 Ibid., pp. 28-9; Rudolf Clausius, “On Different Forms of the Fundamental Equations of the Mechanical Theory of Heat and Their Convenience for Application,” in Kestin, The Second Law of Thermodynamics, pp. 186-87.
 Hokikian, The Science of Disorder, p. 147; Henry Margenau, The Nature of Physical Reality: A Philosophy of Modern Physics (Woodbridge, Conn.: Ox Bow Press, 1977 Reprint), p. 212.
 Michio Kaku, Physics of the Impossible: A Scientific Exploration into the World of Phasers, Force Fields, Teleportation, and Time Travel (New York: Doubleday, 2008), pp. 221-22.