What is infinity in simple terms
Infinity is a complex concept to understand. In ordinary life, we do not encounter anything that has no beginning and end.
It is all the more surprising that such an abstraction is encountered so often: in physics, mathematics, and, of course, in religion and philosophy, where it is very justified. After all, only the flight of imagination can be truly infinite.
What is infinity in simple words
This concept is used everywhere and constantly, but “infinity” always means something slightly different.
Infinity in mathematics
The development of mathematics began with geometry, which is an entirely applied science: measuring land for crops, designing a construction site. Where can infinity come from in geometry?
It is simply not needed. It has no practical meaning here…
And what is surprising is that as early as 300 BC in Euclid’s “Elements” there is already a mention of an infinite straight line. In the sense that a straight line can be extended infinitely. Does this mean that the first person in history to write a work on mathematics, who created “Euclidean geometry”, described infinity in it? Not exactly.
Yes, a line is infinite, but a line segment has its own size. But in practice, the infinity of a line meant only that its length is not important. When it came to real measurements, all quantities in geometry had their own size.
Infinity comes in two types:
- Potential infinity — something that can, in principle, be continued indefinitely.
- Actual infinity — a truly infinite quantity.
For example, the series of natural numbers is infinite (you can try counting yourself), to any number x you can always add +1.
Infinity is not a number!
Although we sometimes perform operations with it just like with numbers. But one cannot say that there is a number greater than infinity.
In mathematics, it is considered that:
x+ ∞ = ∞
∞ – x = ∞
x * ∞ = ∞
∞ / x = ∞
∞ + ∞ = ∞
In simple words, infinity in mathematics is not some very large number, but a special abstraction that is applied when necessary.
The infinity symbol first appeared in the 17th century. There are several versions of its origin:
- It is a snake biting its own tail, symbolizing eternity
- The notation for 1000 in Roman numerals in the form of CIƆ
- The omega letter ω (the last in the alphabet)
Infinity in physics
If mathematics consists entirely of abstractions, then physics, of course, is a science that studies reality. So what is infinity in physics?
Can force, acceleration, or mass be infinite? Probably not. What about voltage or current? Also no? But still, there is room for the infinite.
For example, the amplitude of oscillations can be conditionally infinite. If the frequency of forced oscillations equals the natural frequency of the system, resonance will occur, the amplitude will increase to infinity, and therefore the system will collapse.
In relativistic physics, it gets even more interesting. When a particle with a non-zero mass moves at the speed of light, its energy tends to infinity.
And what about time? Is time itself infinite? It is generally accepted that, at a minimum, time has a beginning, which is the Big Bang, and from this moment we count… everything. Whether there was something before the Big Bang or not is not so important; in any case, we cannot know.
But interestingly, at the initial moment of the Big Bang, the universe was in a state of singularity, when the temperature of matter was infinite, as was its density.
But in most cases, it all depends on the problem being solved. For example, when calculating orbits for artificial satellites, the Earth’s mass is considered infinite (because it is so much larger than the satellite’s mass that there is no point in accounting for this difference), but if we consider the same mass in the Earth-Moon system, it cannot be neglected.
Is the universe infinite?
Modern science answers — yes, the universe is infinite. This is surprising because at the same time there exists the “Big Bang Theory,” according to which the Universe still had a beginning (that very explosion that occurred 14 billion years ago).
At the same time, we do not see anything except light directed towards Earth. If the size of the Universe were finite, it would be logical to expect that light, having circled the finite space, would return. But this doesn’t happen.
We are indeed limited in our observations and cannot see anything beyond the so-called “particle horizon” (also called the cosmic light horizon). But this is because light from the farthest stars has not yet reached us since the moment of the Big Bang. And what is beyond the horizon? Infinity? Or are there boundaries to the universe after all?
There are several options:
- A flat universe extends to infinity
- The universe has boundaries
- It is closed upon itself
What does science say?
Critical density
Cosmologist scientists know how to calculate the finiteness of space. For this, the indicator of “cosmic microwave background radiation density” is used. And this is 0.00001 of the mass of a proton in one cubic centimeter of matter, very little. To measure this value, a special apparatus WMAP (Wilkinson Microwave Anisotropy Probe) was launched in 2001, so the information is verified.
In the existing model of our space (the Friedmann Model), three options are possible. The average density can be greater than, less than, or equal to the critical density.
- If the average density of the universe is greater than the critical density — its curvature is positive and it is closed
- If the average density is less than the critical density — its curvature is negative and it is boundless
- If both values are equal — the universe is flat* and open
To explain this in simple words — high density means a large mass of matter, which in turn will curve space-time to a closed state. Low density, on the contrary, will not allow it to close and hints at the infinity of space-time.
*”flat” here does not mean two-dimensional, like a sheet of paper; it is a mathematical abstraction describing the property of space curvature.
So, what is infinity really? It all depends on the point of view and circumstances. In one case, it’s a philosophical abstraction meaning nothing in the real world; in another, it’s a perfectly understandable quantity.
