Thinking about Eternity
What is eternity, and why do people care? Eternity is infinite time. Thinking about eternity means thinking about infinity too. Take this excursion through thinking about strange things with me.
Consider how often you hear forms of eternal and infinite in daily conversation. “My car is infinitely better than yours.” “You are infinitely worse off since you changed jobs.” “If I had eternity, I wouldn’t date you again.”
Sometimes other words substitute for eternity such as never and forever. (My father often intoned with a touch of sarcasm, “Never is a long time.”)
What does infinity really mean, and what does it mean to be eternal? Begin with infinity because it’s not such a loaded term. Religions do not offer infinite life, after all.
Infinity means something larger than anything else. It has odd and sometimes counter-intuitive properties. For example, when you add one to infinity, you get the same infinity. In algebra, you might write x + 1 = x, where this equation is true only if x is infinity.
Most of you know that the symbol for infinity is ∞, and I’ll use this symbol for the remainder of this paragraph. Therefore, ∞ + 1 = ∞ is the equation of the previous paragraph. If this works once, it will work any number of times: ∞ + n = ∞, where n is any number. What if n is ∞? That works too: ∞ + ∞ = ∞. If you stack up two infinities, then you still have something infinite. (I will not, however, go into transfinite arithmetic, which is beyond the scope of this article on thinking.) If this makes sense, then you realize that 2 x ∞ = ∞. It follows that n x ∞ = ∞ for any ordinary number n.
I hope you made it through the previous paragraph with its numerous equations. These simple properties of infinity are important for what comes next. Adding a number to infinity or multiplying infinity by a number leaves the infinity unchanged.
Imagine a line of infinite length, if you can. If you insert a bit more line or remove some pieces from it, it remains infinite. That makes sense. What does not make so much sense is that one bit of the line can be at an infinite distance from another bit. Put two markers on your imaginary infinite line. Then, insert an infinite line between them. The infinity remains the same because adding two infinities gives you the same infinity. If you understand this, then you are on the way to grasping infinity and eternity.
Apply this concept to our universe. Is it infinite? We know it began as a minuscule point of unimaginable energy concentration somewhat over 13 billion years ago. At that moment, the entire universe was, in theory anyway — no one was there to see it — smaller than an atom. Then, it grew. Because it did not grow at infinite speed, it must be finite because it has had only a finite amount of time to grow. Our universe is finite. We can think of it as being somewhat less than 28 billion light-years across (two times the age converted to light-years).
Not long ago, many scientists argued that the universe was eternal, that it always had been and always would be. They could see no way for it to have begun or for it to end. This idea conformed to essentially no religious concept of the universe. Creation stories abound in even very old religions, far older even than Judaism, and creation presumes a beginning and thus a finite existence.
Because of the peculiar properties of infinity, might those scientists have had second thoughts about an eternal and infinite universe? The one sort of demands the other even though you can imagine a finite eternal universe if you try hard enough. If the universe is eternal, then it’s had time to spread out to infinity. And, it still would be spreading. Any amount of matter in a given volume of space implies that there is matter in every volume, even if just a few atoms. Anything other than zero multiplied by infinity results in infinity. That fact would make the mass of the universe infinite.
An infinite mass would require infinite energy, both kinetic and relativistic as in E=mc2. Proposing an infinitely massive universe requires a digression into philosophy and metaphysics. How can there be an infinite amount of anything? Science could never answer such a question. Oops, I said the bad word: never. I’ll just content myself with a vanishingly small probability that science could come up with infinity as the answer to any answerable question. While nature may not abhor a vacuum, it surely abhors infinity.
Religion certainly had the edge on a universe of finite existence, of a non-eternal universe, that is, non-eternal to date. Yet, so many religions offer eternal life. Do these two concepts conflict? Before digressing into this area, consider what an eternal universe, as posited by some scientists in the past, would mean. It would mean that an infinite number of stars have existed and, probably (if you accept the conflation of eternal and of infinite universes) do now. With an infinity of stars, even if the likelihood is extremely low, as in one in a trillion, there are or have been an infinity of solar systems that match ours. Indeed, despite an unimaginably lower probability, there is an infinity of Earths upon which someone like me is typing my exact words right now. There would be an infinity of Earths upon which the dinosaurs were not wiped out, and mammals did not take over the planet.
More bizarrely, there would be Earths that are a year ahead of us in time and that, could we see them and know that their state a year ago matched ours, would allow us to see the future. The paradoxes pile up as you contemplate more and more. It all begins to sound much like science fiction.
Once you understand that the laws of thermodynamics are based on stochastic reasoning (all about the probabilities associated with enormous numbers), then you know that an eternal universe has had places on planets (even on Earth clones) where a vacuum suddenly appears for no reason, just the random movement of molecules. While this happens all of the time on a nano scale of maybe dozens of molecules in unnoticeably tiny patches of air, it has never happened in, say, a whole room. The chances are so small that it would take an amount of time that is incredibly long compared to the age of the universe for this to happen. But, eternity is just such an amount of time.
Furthermore, this event could have happened infinitely many times. Some of these occurrences could literally have been an eternity ago, but not at the beginning of the eternal universe you’re imagining now because it had no beginning.
You see, infinity and eternity create paradoxes, problems that seem to have no solution, no way to reconcile with the reality we observe around us. Those scientists who were so certain that the universe must be eternal didn’t stop to consider these problems or else chose not to trace the thread of logic to its ultimate conclusions. In an eternal universe, you might be “reborn” as an exact match, including all memories, into a world where disease has been conquered — except that you wouldn’t be you in a world without disease because that’s not the world that shaped who you are. Still, even if the chances are one in a googol (that’s 10100), a random coming together of atoms and molecules could create exactly you as you are today. Eternity is strange.
The song says that all good things must end. Actually, as far as we can tell, all things must end. The Earth will be blasted by our sun’s explosion in around four billion years. Long before that, the sun’s steady increase in temperature will fry the planet. It may be balmy on Mars by then, especially if we figure out how to terraform it, rather than colder than anywhere on Earth as it often is today. Some scientists believe that even the protons that make up the nuclei of the atoms that constitute all visible matter will eventually decay.
The universe began with an implausibly immense explosion that threw all the matter created outward a near light speed. The gravitational and other forces were so intense that they distorted space-time in what cosmologists call “inflation” when space itself expanded faster than the speed of light. Depending upon that initial speed and the amount of mass (and its cohort, energy — remember Einstein), gravity should either pull all of that matter back again, just as tossing a ball up in the air has it falling back, or allow it to expand outward at ever decreasing speeds, which is what happens to a rocket once it reaches escape velocity and the rocket engines shut off, or just coast to an ever-diminishing speed that only reaches zero at eternity.
However, the latest measurements tell us that distant galaxies are not slowing in their mad dash away from us (and everything else) but are accelerating. Scientists call this effect “dark energy,” but this is just a catch term meaning that they don’t know why the universe is flying apart faster and faster. The universe is thinning out. Galaxies are growing old and only being renewed (as in forming new stars at a higher rate) due to collisions with one another. As things thin out, the number of galactic collisions will decline. Eventually, stars will stop forming. Every star ultimately uses up its hydrogen fuel and dies. It may die quietly or may go nova in a spectacular explosion.
Someday, unless the measurements are way off, the last star in the universe will die. The galaxy will be dark, populated by extremely thin gas and black holes. Then, the black holes too will evaporate if Stephen Hawking is right. If protons do decay, then even the gas will disappear. Charge neutrality requires that any electrons will meet positrons and disappear in a flash of photons and neutrinos. This will leave only photons, neutrinos, and dark matter (whatever that is) spread out so thinly that they encounter one another only every few centuries.
Yet, no matter how far forward you project the future, it’s always finite, never eternal, because you cannot fully envision eternity or infinity. Our universe has a finite age. No matter how many millions or billions or trillions of years you add to that age, it’s still finite. The Second Law of Thermodynamics tells us that the universe, like a giant wind-up machine or battery-powered device, is running down — and there’s no one to wind it up again or to replace the batteries.
Either way, we are limited. Only by reaching beyond our four-dimensional spacetime (or 11-dimensional if you’re into string theory) can we hope to stop this universe from dying. It’s a good thing that we have millions of years to figure it out.
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