The question appearing in my title:
Did time have a beginning?
certainly does look like an obvious “shared question/problem” within a session concerned with time. This does not mean, however, that my task will be a simple one. Why? In his 1959 lecture Charles P. Snow stressed the language barrier between scientists and humanists. He argued that, in response to questions such as What do you mean by mass, or acceleration?, no more than 10% of the highly educated people would have felt that one was speaking their own language. I am myself convinced that this language problem between the two cultures has only gotten worse since that famous lecture. The concepts themselves are perhaps not so difficult to communicate, but the language is an almost unsurmountable barrier.
The question of our origins, of howfar back in the past we can go, has been a concern since the beginning of mankind. It has been of interest to artists (110 years ago Paul Gauguin painted his famous canvas Where are we coming from? Who are we? Where are we going?), while philosophers have long been arguing about whether time had a beginning or goes back forever. Aristotle, for one, held the latter point of view, whereas St. Augustin said that a question like What was God doing before he created the world? did not make sense since God created time with the world. Giordano Bruno took a different attitude about such matters, and had to pay the consequences. . .
Incidentally, one could ask a related (and equally shared?) question: Will time have an end? I will not talk about this question because of lack of time, but it is perhaps interesting to notice that most religions insist that there was a creation –and thus a beginning – while accepting eternity in the future. They appear to take a rather asymmetric attitude towards past and future.
In conclusion, even if we all share these problems, “we do not share the language,” as C.P. Snow himself said. In the following, I will try my best to convey what physicists think today about this issue not without stressing that, unlike in other disciplines, scientists are never 100% sure about their own conclusions: as much emphasized by the late Nobel Prize winner Richard Feynman, always living in doubt is one of the greatest strengths of science.
I will start by talking about different attitudes concerning time in “classical” physics, meaning by “classical” (again a matter of language!) “before the advent of quantum mechanics (QM).” I will then recall how classical physics appears to lead, inevitably, to the “beginning-of-time myth” and explain why I regard this as a myth rather than a solid scientific conclusion. Next, I will argue that, once QM is taken into account, our perspective must change drastically. However, the question is only well-posed if one has a consistent way to include quantum mechanics in Einstein’s general relativity, something that has defeated all attempts for many decades. To conclude, I will argue that a new theoretical development, known as String theory, can provide such a consistent framework and allow us to address that question in a serious way. While the final answer to the question is still not known, I will describe some possible new scenarios inspired by string theory and some concrete ways to test them experimentally.
Time in Classical Physics
Even in classical physics the concept of time underwent a few revolutions. For instance, in Galileo’s or Newton’s views, time, or better any time interval, is the same for all observers. In special relativity, a theory introduced by Einstein about 100 years ago, time intervals depend on the relative motion of the observer and the observed.
Let me give an example: consider the lifetime of an unstable particle (how long it lives on the average before decaying). For a given particle species, this is a fixed number for any observer who travels together with the particle. However, if we watch the particle from a different observation point, namely if we move with some velocity v with respect to the particle, we discover that the particle’s lifetime is increased by a factor = (1−v^2/c^2)−1/2 > 1, the famous “Lorentz factor” which is always larger than 1 and can be very large if the relative velocity v approaches the speed of light c. This phenomenon is seen everyday in accelerator physics, for instance at CERN, and is used to make beams of an unstable particle last long enough to be useful for doing experiments.
When one talks instead about General Relativity (GR), the extension of Special Relativity introduced by Einstein in 1915, then time intervals are even more observer-dependent. They also depend on the gravitational field, on how strong gravity is at the position of the clock. For instance, clocks tick with slower pace if you are here in Venice than if you are on top of Mont Blanc. If we synchronize two clocks on earth and one is taken for a while to a higher altitude, when it comes back to its original altitude it shows a slightly (very slightly!) later time than the clock that stayed all the time at the lower altitude.
This prediction of GR has been tested and is even of practical interest. Although the differences in time due to the gravitational field of the earth are very small, if one wants to reach the needed precision for the now widely used Global Positioning System (GPS), one needs to take this GR correction into account.
General Relativity and the Beginning-of-Time Myth
General Relativity is a very successful theory for describing gravitational phenomena in many physical situations. The deviations from Newtonian gravity predicted by GR have been tested with great precision, while some of its new implications, like the existence of black holes and of gravitational waves, have by now been confirmed either directly or indirectly.
There is mounting evidence, for instance, that at the center of our galaxy (the Milky Way) there is a gigantic black hole whose mass is more than a million solar masses. There is not yet, instead, any direct evidence for gravitational waves. Several detectors are presently looking for them, but do not have, presumably, the required sensitivity. However, we can argue indirectly for their existence through the study of how binary stars change their period of rotation over many years. That fits extremely well with what we would expect on the basis of emission of gravitational waves according to GR.
To summarize, GR seems to be very well applicable to isolated systems, to waves in empty space, to the Universe as a whole. For instance, the attractive nature of gravity is responsible for the growth of small initial density fluctuations in the Universe and thus for the emergence of the large-scale structures that we observe in it, galaxies, clusters of galaxies. Ruth Durrer will be talking about this later in this conference. There is no apparent reason for mistrusting GR in yet unexplored regimes, however we have to face some less pleasant consequences of it.
That same universal property of gravity, being always attractive, is also responsible for gravitational collapse, the formation of black holes and, unfortunately, of what physicists (or mathematicians) call “singularities.” In their language, a singularity means some place in space, or some instant in time, where some physical quantities become infinitely large. In fact, Steven Hawking and Roger Penrose have shown, under very minor assumptions, that these singularities are almost unavoidable in GR: for instance, there should be a singularity behind the so-called horizon that surrounds a black hole.
More important for this talk, GR predicts the existence of a cosmological singularity lying some 13.5 billion years in our past. This is what is now generally known as the Big Bang (BB). Thanks to this powerful theorem, we have to conclude that having a beginning of time is inevitable since once you hit this infinity, it does not make any sense to extend the solution of your equations beyond that point. This general consequence of GR has led us to believe in the beginning-of-timemyth.
The Beginning of Time: a Necessity or a Myth?
Why do I talk about time having a beginning as a myth and not as a consequence of the laws of physics? The point is that the Big Bang singularity is a necessity only if one considers GR as an exact theory at all length and time scales. However, there is a simple argument showing that, once we take Quantum Mechanics into consideration, the whole question has to be reconsidered as one approaches the socalled Planck scale of distances or of time.
Planck’s scale was introduced by Max Planck at the very beginning of the last century (actually he did so in 1899). He noticed that a particular combination of the gravitational (so-called Newton) constant GN, of the Planck constant h (appearing in Heisenberg’s uncertainty principle) and the speed of light c, provides a fundamental length scale or, dividing that length by the speed of light, a certain time scale. These length and time scales are incredibly small. The Planck length, for instance, is about 10−35 (meaning zero point followed by 34 zeros and a 1) meters, while the Planck time is about 10−43 seconds.
The uncertainty principle implies that, if one would try to perform a measurement in a region which is smaller than a Planck length one would need such a large energy that a black hole will appear and hide the same region where one wanted to carry out the measurement. But when we talk about the Big Bang singularity we talk about time scales which are even smaller than the Planck time and of regions which are smaller than the Planck length. It is therefore very dangerous to neglect quantum effects in these regimes. I hope to have given you an idea of why QMcan change our point of view, particularly as we approach the Big Bang singularity. Unfortunately, taking quantum effects into account within Einstein’s General Relativity turned out to be a very difficult – if not impossible – task. This leads us, if you wish, to a modern version of Einstein’s dilemma.
Einstein, who, incidentally, contributed a lot to the development of QM (after all he received his Nobel prize for the quantum theory of the photoelectric effect and not for General Relativity!), soon realized that there was a clash between QM and GR. Once faced with this dilemma he decided in favor of his own “baby,” GR. His famous sentence God doesn’t play dice! has often been quoted as meaning that Einstein did not like the lack of determinism implied by QM, a theory that provides only probabilities for certain things to happen rather than others, something like playing dice games. But do we really have to make a choice between GR and QM? Well, perhaps not, perhaps we can have the cake and eat it. Indeed, about 40-years-ago, physicists came up with a new revolutionary theory that appears to avoid Einstein’s dilemma.
At the same time, this theory unifies our descriptions of the infinitely large, to which classical physics applies, and of the infinitely small, to which quantum physics applies. It is called String theory and I will try to tell you in as simple terms as I can what it is. I will try to explain that, although the basic assumptions underlying this theory are extremely simple, their consequences are very far reaching and, to a large extent, still widely unexplored.
String Theory:What’s That?
What are the basic postulates of string theory? In conventional relativistic quantum theory, known as quantum field theory, particles are considered to be point-like. There is, of course, quantum mechanical uncertainty, but the important thing is that a point has a finite number of degrees of freedom: its position, its velocity and possibly a few others. In string theory, instead, all elementary particles, when looked at with sufficient resolution, are actually one-dimensional objects, strings, (called “stringhe,” instead of “corde,” in a very bad Italian translation). Some of them are like a violin string with two ends: they are called open strings. But there are also strings which have no ends: they are like small loops: and are called closed strings.
Unlike points, they have infinitely many degrees of freedom. This is the basic assumption of string theory: every truly elementary particle in nature is actually a string and gets its characteristic properties from the way the string vibrates. It’s like a violin, but where different musical notes correspond to different particles, yet all originating from the same basic object. This is why string theory has a magic unifying power. Other than that, there is no new assumption, one is still using Special Relativity and Quantum Mechanics as one does in the more conventional theories.
To summarize, Strings, Relativity and Quantum Mechanics, when put together, are the three ingredients of a magic cocktail. Why magic? Because of an amazing series of quantum “miracles” that emerge, automatically. . . once you shake the cocktail well enough. I will limit myself to the miracle directly relevant to our topic today, but there is a list of about a dozen such miracles.
Let us go back again by 100 years when QM solved the problem of atomic stability. Take a system like a hydrogen atom which consists of a nucleus, a single proton for hydrogen, and an electron going around it. From the point of view of classical physics this system is quite unstable because the electron going around the proton radiates out energy in the form of electromagnetic waves. You see this phenomenon all the time in particle accelerators: the electrons going around the circular accelerator ring radiate a lot of energy (this is why CERN’s electricity bill is very high: we have to give back this energy to the electrons so that they do not slow down). The same is what happens, classically, to our electron going around a proton: eventually the electron should fall into the proton (like a satellite crashing into the earth’s atmosphere) and form a very small object having the size of the proton itself (about 1 Fermi = 10−15 meters).
When, instead, one looks at the same hydrogen atom from the point of view of QM the electron, through the uncertainty principle, finds its optimal orbit, which is not sharply defined, but corresponds to an average distance from the proton of about 10−10 meters i.e. a hundred thousand times bigger. This is what gives the observed size and stability of atoms. What happens with strings? The physics is very similar to that of the atom: classical strings may have zero size, may shrink to a point, and this is how they would reach their minimal possible mass/energy. But quantum mechanics, because of the uncertainty principle, forces strings to have a minimal, or rather I should say optimal, size. One can compute what this optimal size of the strings is in terms of the Planck constant, the speed of light and another quantity, the so-called string tension. Like violin strings, also ours have a tension: out of it one can form a length, called the string length, in analogy with how Planck constructed his length.
At the end of the day one finds that today the string length is about 10 times bigger than the Planck length (this ratio may have changed over time), hence about 10−34 meters, which is still not a lot; however, it is sufficient to modify physics as one approaches the Plank length (or time), i.e. near the Big Bang, because it is somewhat larger than the Planck length.
String-Inspired Cosmologies: a Longer History of Time?
This finally takes us to string-inspired cosmology and, perhaps, to a longer history of time. The basic question is “Does the existence of this new fundamental length eliminate the singularities of GR?”. This question still occupies the minds of the few thousand string theorists working all over the world. It is a very hard question, but all indications, so far, are in favor of an affirmative answer. For instance: the finite size of strings should imply an upper limit to the density of the Universe because, having a non contractible size, strings cannot be packed beyond a certain limit. String theory is also known to provide a maximal value for temperature. Both features are in striking contrast with what happens at the Big Bang in classical GR where both density and temperature grow without any limit.
The next question is then: if the conventional Big Bang singularity is indeed avoided by string theory, what is going to replace it in string cosmology? This is an even harder question, but I emphasize that at least within string theory, it’s a wellposed question. People are working on it and, while the final answer is not known yet, we can discuss a couple of possibilities.
The first one is that time, as we perceive it today, is an emergent concept, it will emerge out of what we may call a “stringy epoch” during which neither the concept of a classical distance nor that of a classical time interval make any sense. In this alternative there would be nothing before such a stringy phase. This point of view will be the closest one, in spirit if not in detail, to Steven Hawking’s proposal, in which time, as we approach the Big Bang, becomes “Euclidean,” meaning that it would become like another direction in space.
The second alternative, which I personally prefer since it is richer in consequences, is that the Big Bang, rather than representing the beginning of time, is the result of a previous evolution, also a classical one with a well-defined concept of time. In this pre-bang evolution density and temperature grew from some infinitesimally small value up to some maximal, finite value determined by the string length.
This pre-bang epoch would be a kind of “mirror image” of what has happened after the Big Bang. Peculiar symmetries of string theory, known as dualities, allow for such a mirror phase. Effects due to the finite string size would take over after the pre-bang phase and force the Universe to bounce after going through a high-density, high-temperature string phase. You can say in one word, that the Big Bang becomes a Big Bounce. This scenario offers new ways to solve the problems of standard cosmology through the possibility that our Universe, having such a long pre-history, is much older than in conventional cosmology.
But what are these problems of Big Bang cosmology that we would like to solve? One of them can be described as follows. Consider how big the Universe (better: that part of the Universe that we can observe today) was very early on, say a few Planck times after the Big Bang. The answer, in standard hot Big Bang cosmology is that its size was a fraction of a millimeter. One millimeter is very small compared to its present size; yet it is huge if compared with the distance traveled by light during its short “life” after its birth (about 10−43 seconds), namely 10−35 meters. That means that the baby Universe was 30 orders of magnitude larger than the distance traveled by light. The baby Universe was very big for its young age!
This puts us in front of a very big puzzle: since the distance traveled by light is the maximal distance over which you can have communication among different parts of the system, it’s very hard to understand how the Universe could become homogeneous enough in such a short time (this homogeneity is reflected in the uniformity of the observed temperature of the cosmic microwave background: 2.7 degrees above absolute zero irrespective of the direction in the sky). It is like if you turn on a heater in a corner of this room: it takes a while before you feel the increase of temperature at the other end of the room, because this room is quite large. The only way to account for present data is to “fine tune” the initial state of the Universe very very precisely.
This is what physicists do not like. They have thought a lot about this problem and concluded that, if one insists that the Universe had a beginning at the Big Bang, there is only one way out: the primordial Universe had to be much smaller than in conventional theories. This gave rise to a very successful paradigm, called “inflationary cosmology,” in which we insert in very early cosmology a phase of accelerated expansion of the Universe (inflation) making the baby Universe much smaller than the 1 millimeter mentioned before. However, if we accept that there was a pre-bang epoch, the Universe right after the bounce was already very old and had a lot of time to thermalize. The interesting thing is that these new cosmologies not only have some philosophical interest, they have observable consequences too, so that one can test experimentally what happens near the Big Bang, or even earlier if there was something before.
It sounds very bizarre that you may be able to probe today how the Universe was at – or before – the Big Bang, but this is not so. It is related to a phenomenon called “freeze-out” of certain structures when the Universe is expanding very fast (relative to the size of the structure itself). These large-scale structures “defrost” today carrying with them information about the Universe as it was when they froze out immediately after or even before the Big Bang. It is similar to a prehistoric animal caught in the ice millions of years ago, and revealing itself to us now, after defrosting.
There are several good examples of what we may call pre-bangian relics, relics from before the Big Bang: one is a stochastic background of gravitational waves, very much like the already mentioned electromagnetic background that fills up our Universe at a temperature of 2.7 degrees above absolute zero. Gravitational waves, unfortunately, are much harder to detect but, as I mentioned, there are plans to do so. Other predictions of these unconventional cosmologies concern the galactic and intergalactic magnetic fields whose origin is otherwise mysterious, as well as some peculiar structures in cosmic microwave background anisotropies. For further suggested reading on string cosmolog see [1, 2, 3].
Let me conclude: the belief that time had a beginning is indeed a myth based on extrapolating GR beyond its limits of applicability. If one takes the beginning-oftime point of view, then the inflationary paradigm is the only possible solution to the puzzle of hot Big Bang cosmology. But string theory, thanks to its magic properties, should be able to remove the Big Bang singularity of GR and to allow for the possibility of a pre-bang phase, offering a new solution to those cosmological puzzles.
The new symmetries implied by string theory suggest a mirror structure for the pre-bang phase: a cold and almost empty Universe which, through a process similar to gravitational collapse, leads to a high temperature-density phase which replaces the singular Big Bang event of standard cosmology.Most important, these pre-bang or big bounce cosmologies make (better, will make, since we are still working on this difficult problem) distinct predictions on today’s (or near-future) cosmological observables and can thus be discriminated from more conventional scenarios. So, the question of whether time had a beginning may turn out to have an experimental answer one day. . .
I would like to thank the organizers of this conference, and in particular Professor Ernesto Carafoli, for having provided a unique opportunity for exchanging ideas across so many different cultural areas in such a splendid environment.
1. G. Veneziano: The Myth of the Beginning of Time Sc. Am. 290, 5 (2004)
2. M. Gasperini: L’universo prima del Big Bang (Franco Muzzio Editore, Roma 2002)
3. M. Gasperini and G. Veneziano: Beyond the Big Bang, ed. by Rudy Vaas (Springer, Berlin, Heidelberg, in press 2009)