# Does Infinity mean 'potential' Infinity?

• tom aaron
In summary: However, recent observations suggest that the universe is expanding at an accelerating rate, meaning it is likely to continue expanding indefinitely. This means that the universe is potentially infinite in size, but we can only observe a finite part of it due to the limitations of the speed of light. In summary, the concept of infinity in relation to the universe is still being debated and explored, but current theories suggest that the universe is potentially infinite in size and has been expanding since the beginning of time.
tom aaron
Potential for infinity?

According to Inflation theory, (Big Bang type models)

The observable Universe can be measured. We put a specific size on space/time of 13.8 billion years based on expansion from some Singularity.

My question. When we speak of 'infinity' are we speaking about infinity being the size of space or is infinity the 'potential' size/age the Universe will become?

Another approach. We draw a line and say it goes on to infinity. We then put a point on the line. Is the current size of the Universe at 'that' point on the line (13.8 billion years) or is it Infinity? In future, a hundred billion years or a trillion, we can move that point along the line but it is always 'finite'.

We can say something goes on forever 'in theory' but can it only be as old/ big as whatever space/time is 'now'? We can say something 'will' expand forever (infinity) but this doesn't me it has 'already' expanded forever. Can something with a current finite size be infinite? Is Infinity always a 'potential' but not the reality at any current moment?

It isn't settled yet if the universe is infinite or finite in space at present time. (Note that we have to make strong assumptions about the universe to even meaningfully talk about a "present time" at far off parts of the universe.) If it is infinite now, then it was always infinite all the way back to the singularity, at which point all of our theories break down. Note that you can have expansion of an infinite universe. It just means everything gets farther apart. A galaxy a billion l-yr away becomes 2 billion l-yr away, and a galaxy 2 billion l-yr away becomes 4 billion, etc.

The universe appears very close to spatially flat and somewhat close to isotropic and homogenous. If the universe is spatially flat or hyperbolic and globally isotropic (and homogeneous), then it has to be infinitely large. The problem is that there is no way to fully measure that the universe is globally isotropic; there could always be edges lying just outside our detection range.

Khashishi said:
It isn't settled yet if the universe is infinite or finite in space at present time. (Note that we have to make strong assumptions about the universe to even meaningfully talk about a "present time" at far off parts of the universe.) If it is infinite now, then it was always infinite all the way back to the singularity, at which point all of our theories break down. Note that you can have expansion of an infinite universe. It just means everything gets farther apart. A galaxy a billion l-yr away becomes 2 billion l-yr away, and a galaxy 2 billion l-yr away becomes 4 billion, etc.

The universe appears very close to spatially flat and somewhat close to isotropic and homogenous. If the universe is spatially flat or hyperbolic and globally isotropic (and homogeneous), then it has to be infinitely large. The problem is that there is no way to fully measure that the universe is globally isotropic; there could always be edges lying just outside our detection range.

Thanks

One of your points makes me rephrase my question. One can have expansion 'within' an infinite Universe but if the Universe itself is infinite, is it itself expanding? Does a spatially flat Universe expand?

I know than infinity is a mathematical concept. I can get my brain around the theory. However, outside of theory within mathematics is there such a thing as Infinity? We can say a line goes on forever, but there is no actual line. There is a symbol for an infinite line...a symbol for an infinite number.

Anyways, seems that Infinity is always a potential state rather than an actual state of existence. Perhaps like added dimensions in String theory, our human brains aren't capable of getting around the concept of infinity, other than in math.

All we have are tantalizing hints and that may be all we ever have. Observation strongly suggests the universe is of finite age - around 14 billion years. A universe of finite age is spatially constrained to a size called the 'observable universe' due to the finite speed of light. It could be larger than that but, due to cosmic exansion, there is no way to ever know with any certainty. Light from sufficiently remote regions of the universe will never reach us, not even in theory. So its not like we can just wait around for a tera year for light from regions currently beyond our view to cross the gulf and reveal hitherto unseen vast expanses of the universe.

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tom aaron said:
One can have expansion 'within' an infinite Universe but if the Universe itself is infinite, is it itself expanding? Does a spatially flat Universe expand?
Yes, it does. Infinite isn't just a large number. 3 x 1 billion = 3 billion, however 3 x infinite = infinite. So if the universe is infinite and the distances between the Galaxies grow by factor 3 it is still infinite. You can't distinguish a larger infinite universe from a smaller one. You can do that if you look at a finite part of the infinite universe, like the observable universe.
tom aaron said:
Anyways, seems that Infinity is always a potential state rather than an actual state of existence. Perhaps like added dimensions in String theory, our human brains aren't capable of getting around the concept of infinity, other than in math.
No, the universe is either finite or infinite. To my impression most cosmologists think of an infinite universe. In this case it was infinite from the very beginning with the observable universe as a tiny part of it at all times. However the universe must not necessarily be infinite. That question depends on it's topology. Theoretically and even if spatially flat the universe could be e.g. a torus ( like a donut) and would be spatially finite then in finite time.

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A spatially flat universe can be expanding.
Simply, we don't know if anything in the universe is truly infinite because all of our experiments are finite. But just because we can't measure infinite doesn't mean that it doesn't exist. Some people have some philosophical issues with infinity, but some people have philosophical issues with motion or with quantum mechanics, so I don't think pure philosophy can be relied on to tell us what we want to know about the universe. Science works by inductive reasoning. We haven't found an edge (or repeat zone) of the universe yet, so we assume one doesn't exist. It's not mathematically rigorous, but that's all we have.

Khashishi said:
A spatially flat universe can be expanding.
Simply, we don't know if anything in the universe is truly infinite because all of our experiments are finite. But just because we can't measure infinite doesn't mean that it doesn't exist. Some people have some philosophical issues with infinity, but some people have philosophical issues with motion or with quantum mechanics, so I don't think pure philosophy can be relied on to tell us what we want to know about the universe. Science works by inductive reasoning. We haven't found an edge (or repeat zone) of the universe yet, so we assume one doesn't exist. It's not mathematically rigorous, but that's all we have.

Thanks.

True. However, my issues with infinity are not philosophical. I would say that infinity itself is usually a philosophical 'filler' for what we don't know. It's a mathematical construct to rationalize our very limited ability to isolate and measure variables of existence. Is the observable Universe all that there is? Perhaps it is finite but a quintillion times larger. Not infinite. A sextillion is not a large number mathematically...easy to add a few powers of 10...then some more. Anything less than infinity is small on an infinite scale but overwhelming on a human perceptional scale.

Anyways, there seems to be some point at which physics is less about observation and more about mathematics. Some assumption (philosophical assumption) that the Universe conforms to the math. Of course, math may be all we have to study it those levels beyond observation. Infinities fit math models and we assume they might apply to explaining matter and energy.

No. It's mean very very large value.
Always there is a potential greater than which we are considering.
Potential is a function of space. Since space is never ending then potential is also never ending.
Therefore we're talking about an infinite potential.

## 1. What is the definition of 'potential' Infinity?

'Potential' Infinity refers to the idea that something has the potential to be infinite, but it is not currently infinite. It is a concept used in mathematics and physics to describe quantities that are unbounded or have no limit.

## 2. How is 'potential' Infinity different from 'actual' Infinity?

'Actual' Infinity refers to something that is currently infinite and has no limits, while 'potential' Infinity refers to something that has the potential to become infinite, but is not currently infinite.

## 3. Can something be both 'potential' Infinity and 'actual' Infinity?

No, something cannot be both 'potential' Infinity and 'actual' Infinity at the same time. It is either one or the other, depending on its current state.

## 4. What are some examples of 'potential' Infinity?

Examples of 'potential' Infinity include a line that extends to infinity, but is not currently infinite, and a function with an asymptote that approaches infinity but never reaches it.

## 5. How is the concept of 'potential' Infinity used in science?

The concept of 'potential' Infinity is used in various fields of science, such as physics, mathematics, and computer science. It helps scientists understand and describe quantities that have no limit or are unbounded, and it is used in many theories and equations to make accurate predictions and calculations.

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