I think 'Infinity' is a purely mathematical concept; one that people can only tangentially grasp through the use of limits, i.e. "As I approach a distance of infinity.."
Despite physics being the field right after pure mathematics that uses it the most, I don't think Infinity makes any sense in the physical world. It's mostly used in the following way: The gravitational effect of the Sun approaches 0 as the distance between the point of measurement and it approaches infinity. So in theory if we travelled to roughly the centre of the Milky Way, Andromeda or anywhere else the Universe, and we measured the total gravitational effect, our Sun would theoretically contribute to that quantity. But depending on the distance its contribution would be very, very close to zero - so close we could say it is zero. It isn't from a purely theoretical perspective, but it is from a practical one. It's an assumption that is made in the process of applying the theoretical model to reality; for example, if R >> R_0 (if R is much, much larger than R_0), then F = 0 (assume that F = 0). This illustrates the only role I remember having seen Infinity take on in physics: One of being used to discover the theoretical nature and failing points of various models. That, and being added to the premise of a model in a dubious manner as something of an "afterthought" or "tweak" to make a theory spit out accurate results - like the dimensions in String Theory - but then it becomes very esoteric/abstract.
My experience and knowledge are quite limited, though, so I think input from [MENTION=825]ygolo[/MENTION] could be valuable in this discussion.
I must commend you for an informative post which indicates that you think seriously, and you have learning in math and in physics.
I don't claim to have much learning in math or in physics.
But I seek to think seriously.
The title of the thread is "Does the concept of infinity exist in physical reality?"
Do you notice that the author of the thread in his draft of the title is asking whether the concept of infinity could exist in physical reality.
The way I see it, concepts do not exist in physical reality, if they exist at all we can say that they exist in our thinking mind as we think; but that brings in the question whether concepts have existence even if there is no thinking mind like ours thinking of them, and not in physical reality but in a reality that is of the world of ideas, what we might call the realm of concepts?
So that even though we don't exist and the physical universe does not exist, there is still the existing realm of concepts.
The way I understand the mind of the thread's author, he is asking whether there is anything physical i.e. in physical reality that represents the concept of infinity.
As we take the universe to have a beginning according to the great majority of scientists, then I can say that the concept of infinity is not represented by anything in the physical universe, because the physical universe itself is not infinite, for it has a beginning and that makes it and everything in it finite.
However, I like to ask you whether the concept of infinity itself is a real, genuine, valid concept.
What do I mean by a real, genuine, valid concept, is that it must have a representative example at least possible in some realm of existence even though not physical, because the physical is already ruled out for having a beginning as to be essentially bereft of any potentiality for infinity.
So, I like to hear from you whether you might see that there is something physical that corresponds to the concept of infinity, and if at all the concept itself of infinity is a real, genuine, valid concept.
The way I see the second part of my question, my answer is there is no such real, genuine, valid concept as that of infinity: because a real, genuine, valid concept must be about at least something that can exist definitively.
Now, as the concept of infinity is about existing things that are endlessly still getting bigger and bigger and bigger and bigger..., or smaller and smaller and smaller and smaller…, or a process that is repeating itself endlessly, then such an entity cannot exist in any realm of existence because it has no definitive form, but is endlessly still in development or in change.
Amsus