What are the 'infinities' that physicists keep finding in their theories?

Answer 1

Often physicists use models in which the calculations can be made only by summing the first few terms of a series. Each of the terms can be calculated, in principle, given time and a lot of effort. But in practice only the first few terms are used.

In performing such approximate calculations various divergences, or infinities arise, which would cancel out if it would be possible to calculate all terms. These infinities are therefore mathematical artefacts that arise due to the approximations.

Several tricks are used to work around the infinities and find the correct answer. For an example, see my reference.

Answer 2

Here is an example of how you can get infinity.

The force of gravity on an object is expressed by the equation

(GMm)/r^2 = F where F is the force of grgavity, G is the gravitational constant, M is the mass of one object, m is the mass of the other object, and r is the distance between the two.

Now, the bigger the distance, r, between the two objects is, the weaker the force of gravity becomes. Does the force of gravity ever get to 0? The answer is, no, not mathematically.

You see, any time you have a fraction when the top stays the same and the bottom changes, the larger the number on the bottem, the smaller the whole fraction becomes. Example. 1/2=0.5, 1/4=0.25, 1/8=0.125, 1/100 = 0.001

In fact there isn't a number big enough to put in the bottom (the denominator, as it's called) that will make the whole thing = 0

Back to the original equation, you can't find a number to plug into r that will make the force of gravity = 0. But you can say, the larger r becomes, the closer the force of gravity gets to 0. In other words, as r approaches infinity, F approaches 0.

There are cases in the physical world where "discontinuities" exist. In other words, the mathematical equation may tell you one thing is supposed to happen, and in reality, something totally different happens.

Answer 3

You are asking for a definition of a concept that can not (by definition) be defined.

Confused? How about this?

There are an infinite number of infinities..

Answer 4

I believe the two infinities are of the big and the small.