This article addresses the nature of limits, including how new discoveries alter our existing knowledge, how limits inherent in nature can constrain our understanding of the natural world, how these limits have changed over the years, and the implications of these limits for future civilizations.
Before enumerating the limits and/or end of science, it is appropriate to acknowledge science’s many extraordinary accomplishments. The advances in science made over the past hundred years have been nothing short of astounding:
- We’ve split the atom, traveled to the moon, decoded the human genome and saved countless lives with robotic surgery and designer drugs.
- As it stands today, science has amassed a remarkable scientific baseline that spans from a fraction of a second after the Big Bang to predictions as to the universe’s ultimate fate; and from the most elementary subatomic particle, to the largest galaxies and beyond.
Just a few of science’s baseline constituents are:
- biology: cell theory, germ theory, evolution and natural selection,
- Chemistry: kinetic theory of gases, molecular theory, the standard model of particle physics.
- physics: atomic theory, the Big Bang theory, Theory of Relativity, quantum field theory, Universal law of gravitation
- mechanics: Newton’s laws of motion,
- quantum mechanics: Heisenberg’s uncertainty principle
- relativity theory: Special relativity, General relativity
- cosmology: Kepler’s law of planetary motion, Hubble’s Law of constant expansion
Despite this success, scientists, since practically the beginning of time upon forging a new discovery, have claimed that science has essentially reached its limits, or that the end of science is near. Physicists, in particular, have long believed themselves to be on the verge of explaining almost everything.
In 1894 Albert Michelson, the first American to receive a Nobel Prize in science announced that all the fundamental laws of physics had already been discovered. In 1928 Max Born, another Nobel prize-winner, said that physics would be completed in about six months’ time. In 1988, in his bestselling “A Brief History of Time”, cosmologist Stephen Hawking wrote that “we may now be near the end of the search for the ultimate laws of nature.” Now, in the newly published “The Grand Design”, Hawking paints a picture of the universe that is “different from the picture we might have painted just a decade or two ago”. He asserts that increases in our understanding, instead of reducing the unknown, seem to unfold increasingly more new mysteries. We continue to grapple with realties beyond our understanding, from the inner workings of our minds to the intrinsic mechanics of the universe.
Given the above, one could conclude that current scientific knowledge includes most of the fundamentals of science, and all there is left to know are more details and unimportant nuances. Past discoveries have historically had a tendency to modify prior theories, rather than completely replace them. For example, Einstein’s Special Relativity may form the basis for GPS technology, but Newton’s mechanics still continues to serve as the basis for the majority of every day challenges. Moreover, for future challenges such as a “theory of everything” the plausible alternatives may be beyond experimental confirmation and would be more philosophical than science.
Despite this somewhat overly optimistic characterization, there are a number of genuine problems remaining for science to solve. The most important “mysteries of science” at this time include the following:
- What preceded the Big Bang? An increasing number of Cosmologists believe that the big bang was not the true beginning, and that there may have been antecedent events such as the spawning of a new “bubble” within a multiverse of universes.
- Is there life elsewhere? (The universe is an enormous place. Astronomers estimate that there are approximately 100 billion to 1 trillion galaxies in the Universe. That would suggest that there are between 10 sextillion and 1 septillion stars in the Universe, that have existed for nearly 14 billion years. Is it conceivable that within this time and space, we are the only planet that spawned sentient life?
- Are there other Universes, other dimensions? Multiverse theory suggests that there may be a world beyond our universe, consisting of a multitude of different universes, each with their own laws of nature. String Theory suggests the material world is comprised of tiny strings vibrating in 12 dimensions.
- What is the fundamental “Theory of Everything?” (The single formula that explains all materials and their interactions with all of the forces). While science has essentially unified most of the particles and their interactions, they have yet to incorporate the force of gravity. A unified field theory is what Einstein spent the latter part of his life searching for (unsuccessfully).
- What is the quantum theory of gravity? Both General Relativity and Quantum Mechanics incorporate gravity, and each has been proven to a high degree of accuracy. However, when you attempt to apply the equations at very high speeds, or very small distances, the formulas result in nonsense.
THE LIMITS OF SCIENCE
Given the impressive scientific accomplishments to date, and the significant unexplained mysteries of science, how likely is it that we will ultimately know everything there is to know about science? Are their limits to what science can possibly tell us?
There are in fact, limits to what science can tell us. The noted author John D. Barrow addresses the problem in his best-selling book titled Impossibility — The limits of science and the science of limits. My article is based largely on ideas contained in this work.
Donald Rumsfeld, Secretary of Defense during the Bush administration popularized a type of quandary with respect to limits when he claimed: “We know what we know, and we know what we don’t know; but we can’t know what we don’t know we don’t know”. (In other words the intersection of the two sets).
The unfortunate fact is that there are definite limits in science and mathematics that restricts what we can ever know about science. In the following sections, I’ll summarize the principle factors that limit what science can tell us.
1. MAXIMUM LIMIT IN THE SPEED OF LIGHT AND RELATED DISAPPEARING HORIZON
In 1905 Albert Einstein, in one of his well-known thought experiments realized that there is constancy in the speed of light, i.e., the maximum speed at which all energy, matter, and information in the universe can travel. As a law of nature, the speed of light will always be 186,282 miles per second, irrespective of its source or propagation. (I.e., whether a flashlight is pointed in the direction of or in the opposite direction to the earth’s rotation, light travels at exactly the same speed.). As a practical consequence, any portion of the universe that is beyond this limit (3x 1027cm) is essentially invisible to us.
A closely related, cosmological limit is known as the disappearing horizon problem. It arises out of the fact the fact that, according to Hubble’s Law, the galaxies are moving away (receding) from each other at staggering rates of approximately 71 kilometers per second per Megaparsec. This expansion is in addition to the big bang’s normal expansion. This movement is believed to be the added result of a ubiquitous, invisible dark energy, or scalar field known as quintessence that acts like a repulsive gravity.
While we here on earth are presently fortunate to be able to see the universe all the way back to its origin, cosmologists of the future, due to the disappearing Horizon will only be able to see their own galaxy and, barring some for some kind of interstellar communications will have no fathom of other galaxies or the Big Bang or the universe’s origin.
Some problems are more complex than the prevailing computational technology or economic resources permits. We are confronted by a host of practical problems, too complicated for the human brain to solve unaided, which even the fastest computers that Nature allows cannot solve. These problems are said to be intractable. Many of them sound simple, but their solution can involve more space and time than the entire Universe is capable of providing. These limits are limits resulting from practicalities, costs, and time. Moreover, there might be unexpected limits that define more fundamental levels of impossibility. The further we stray from the everyday realm of human experience in our quest to understand the nature of the Universe, the more daunting are the limits we encounter.
A simple example of an intractable problem is the Towers of Hanoi mathematical puzzle. It consists of three rods, and a number of disks of different sizes which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape.
The objective of the puzzle is to move the entire stack to another rod, assuring that: only one disk may be moved at a time; each move consists of taking the upper disk from one of the rods and sliding it onto another rod, on top of the other disks that may already be present on that rod, and no disk may be placed on top of a smaller disk. The number of moves increases exponentially as the number of disks increases. Given a computer program that calculated a move every second, then for 40 discs the program would take 34,841 years (1,099,511,627,776 /60 /60 /24 /365.25), which would clearly be intractable in human life terms.
On a more scientific note, formulating a Grand Unified Theory connecting the four fundamental forces of nature was among the objectives of the Superconducting Supercollider (SSC) a 55 mile in circumference ring collider near Waxahachie, Texas, with energy of 20 TeV per proton. This energy component is almost three times the current 14 TeV of its European counterpart, the Large Hadron Collider (LHC) at CERN in Geneva. The SSC was billed by physicists as their giant microscope to observe the fundamental particles of matter, a tool that would lead to the greatest progress in physics since quantum mechanics. Experiments using the supercollider would have proved or disproved key theories in particle physics.
These objectives became economically intractable when the estimates for completion of the project rose above $11 billion, and the project was cancelled for budgetary reasons, after an expenditure of $2 billion. Scientists say the project’s cancellation was a significant setback to the field of high-energy physics.
The cost of satisfying our growing demands for knowledge are somewhat offset by increases in effectiveness and capacity in computing power. Several elements of digital technology are improving at exponential rates in accordance with Moore’s law, which considers the size, cost, density and speed of components: (principally: transistors per integrated circuit, density at minimum cost per transistor, hard disk storage cost per unit of information, and Network capacity). Moore’s law describes a driving force of technological and social change in the late 20th and early 21st centuries. This trend has continued for more than half a century. Sources in 2005 expected it to continue until at least 2015 or 2020. However, the most recent future estimates indicate that transistor counts and densities will double only every three years.
3. UNDECIDABILITY OF CERTAIN MATHEMATICAL PROBLEMS
Throughout history science and math have been closely associated, particularly with respect to the confirmation of experimental results. However in 1922 Kurt Godel, an Austrian mathematician and close friend of Albert Einstein, discovered an unexpected limit in mathematics referred to as his Incompleteness Theorem. This theorem postulates that a system can be either accurate (consistent) or complete, but not both. That is to say, within any sufficiently complex mathematical system there will be undecidable propositions.
It seems on the strength of Gödel’s theorem that the ultimate foundations of the bold symbolic constructions of mathematical physics will remain embedded forever in that deeper level of thinking characterized both by the wisdom and by the haziness of analogies and intuitions. For the speculative physicist this implies that there are limits to the precision of certainty that even in the pure thinking of theoretical physics there is a boundary… An integral part of this boundary is the scientist himself, as a thinker.
As Stephen Wolfram remarked, “If truth can outrun provability, reality can outrun knowledge”. The pattern needed to abbreviate the string of symbols might be one of those truths which cannot be proved. Thus, you can never know whether your ultimate theory is the ultimate theory or not. Some deeper version of it might always exist: it might just be part of a larger theory. One may speculate that undecidability is common in all but the most trivial physical theories. Even simply formulated problems in theoretical physics may be found to be provably insoluble.
4. HUMAN LIMITS
Another fundamental limit in science is the human mind, itself, and the inherent limits imposed solely by our humanity. The human mind was not designed with science in mind. It did not evolve for that purpose. We possess our physical and mental attributes as a result of a random process of adaptation to ancient environments whose challenges no longer confront us today.
We are evolved instead with traits favoring social interactions, acquiring safe habitats and food, pursuing creature comforts, attracting mates, avoiding hazards and predators, and fostering as many offspring as feasible. There is no logical reason why we should possess the conceptual ability to comprehend the way the Universe works. It would require a coincidence of cosmic proportions if the Universe were complicated enough to give rise to life, yet simple enough for one species to understand its deepest structure after merely a few hundred years of concerted scientific investigation. There is no reason to expect the Universe to have been constructed for our convenience.
There is a considerable gap in sophistication between our own mental capacity for conceptualization and that required for unraveling those enormous complexities in the states that Nature has created with its simple laws. Einstein is said to have been several decades ahead of the time in his discovery of General Relativity. The idea would have eventually been discovered later, perhaps in some form of hidden symmetry. It was only a result of his pure genius that the ideas came to him as early as they did. The same situation might be said for string theory, or a Theory of Everything. According to Michio Pichu, a well know science writer, the main reason we haven’t solved these problems is that no one currently alive is smart enough to solve the equations,
Of course we can and do use the power of computers to leverage our human limitations, particularly that of our mind. This is a strength that we can amplify enormously by artificial means. In the future, the increasing use of networked computers will provide us with a powerful tool to offset our individual limitations. In effect, we shall be evolving, artificially, a large-scale version of the human brain. But while there are advantages to this evolutionary development, there are pitfalls. While there are obvious powerful advantages, they are not a panacea. There remain intractable problems that require so much computational time to solve that they are for all practical purposes insoluble.
5. TECHNOLOGICAL LIMITS
Someone once said the acid test of all scientific progress is whether it allows us to build better machines. This view is provoked by the position that we occupy in the spectrum of sizes of natural things. We are far bigger than the atoms and far smaller than the stars. We must create artificial senses if we are probe the worlds of the large and small, understand environments that display extremes of temperature and density, or come to terms with overwhelming complexities. We have found that the path to understanding the deep structure of the Universe, its laws and complex states, leads us to explore conditions far removed from those which were familiar to our ancestors. The limits to what we can ultimately discover are likely to be imposed by limits of technology rather than by limited imagination.
Already, our most successful theories of Nature’s forces make precise predictions about the workings of the Universe under conditions that, at present, we cannot remotely approach by direct experiment. Indeed, in order to discover whether our version of Nature’s laws is the correct one it looks as if it is necessary to investigate what happens when matter is subjected to
temperatures more than 1015 (1,000,000,000,000,000) times as great as those achievable in our most powerful terrestrial experiments. It is unlikely that direct experiments of that sort will ever be possible.
Unfortunately, our technological powers are confronted by a variety of limits. Some are financial and practical. Democracies are not usually willing to devote large fractions of their GNP to activities that offer no immediate return, when society is confronted with serious environmental or medical problems that require scientific solutions. These limits will recede only if entirely new ways are found to generate energy. But there are yet deeper limits to experimental inquiry. We have speculated about the steps that civilizations might take as they ascend to master the realms of the large and the small. Ultimately, these advances will have to come to terms with the limits that Nature imposes on how fast we can transmit information, how small we can ensure accurate timekeeping, how much energy must be expended to gain information, how close to criticality are the complex systems that we see, and how sensitive is our technology to errors and the chaotic amplification of uncertainties.
The development of technology, and the ability to test the theories that we have about the behavior of matter under extreme conditions, require us to manipulate matter, energy, and information over scales that are increasingly divorced from those of our everyday experience. I, the decisive features of the laws of Nature appear to be manifested in these extreme environments. By delving into them we are not merely seeking completeness for its own sake: the behavior of matter at ultra-high temperatures is the crux of its most basic character. One of the ways in which we could sidestep these limits on our ability to create high energies is by using astronomical observations.
6. COSMOLOGICAL LIMITS
No branch of science extrapolates so far into the unknown as cosmology, and no line of human inquiry is more at risk from limits of all sorts. As a result, there are limits to what we can know about the Universe. Those limits cut across all of Cosmology’s major unsolved problems.
In the past decade there has been huge progress in our knowledge of the astronomical universe. Technological ingenuity has provided us with light detectors of unprecedented sensitivity. Space agencies have launched astronomical satellites able to look at the Universe across the whole electromagnetic spectrum. The highlight of this program–the launch of the Hubble Space Telescope has enabled us to look at planets, stars, and galaxies with astonishing resolution. Light moves with a finite speed, and so when we ‘see’ a distant galaxy now, we see it as it was when the light left it, not as it is today. The Universe provides us with the simplest form of time machine, one that allows us to see the distant past just by looking.
Despite the success of Einstein’s theory of gravity in describing the visible universe, we know that there are fundamental limits in our cosmological search. The finiteness of the speed of light segments the Universe into parts which are within and beyond causal contact with each other. We can gather information about the Universe only from the region within the horizon prescribed by the speed of light. This prevents us from ever answering penetrating questions about the Universe’s origin or its global structure. We cannot tell whether or not it is infinite, whether it had an origin or whether it always existed (or whether it is open or closed). We can only observe the structure of the visible part of the Universe. It is likely that we are situated in a particular expanding bubble, unable to investigate the possibility that other Universes of enormous complexity blossom eternally beyond our horizon.
Future satellite missions might provide decisive tests of the inflationary bubble hypothesis, but we will forever be unable to observe anything about them since they are beyond our horizon.
Although the inflationary universe provides explanations for several of the properties of the observable universe, it nevertheless prevents us from acquiring information about events that preceded it, and consequently, the origin of even our visible part of the Universe is indeterminable. While the theories of relativity and quantum mechanics combine to provide us with an account of the universe that we see, (without regard to how it began) the penalty for this fortuitous gift is the surrendering of information about if, or how the Universe began and about all its properties beyond our horizon. As Barrow put it: “The Universe is not only bigger than we can know, it is bigger than we can ever know.”
Although science and cosmology will continue to explore the mysteries and increase our knowledge for some time to come (perhaps millions or billions of years) a time will approach when science will be incapable of further exploration, the well will run dry, and science, as such will sadly come to an end.