Physical infinities, what are the limitations?

[iDimension]

From a mathematical point of view there can and is many different infinities that exist. I'm curious what happens when we try to use a physical infinity in cosmology. I'm not going to lie I don't even think my brain is capable of comprehending this but can two physical infinities exist simultaneously?

How can two objects which occupy the same volume both be infinite at the same time? If they can't both be infinite at the same time then how can it be that two, three, four or 10⁵⁰⁰ universes can exist, all of them being infinite and all of them existing at the same time?

If one object is infinite in volume then it stands to reason that there is not more volume left over for another another to coexist.

If it is somehow possible for another infinite universe to coexist, then where is it located? In some sort of external meta-space or something?

 

[voko]

First of all, we do not yet know whether our universe is finite or infinite.

Second, any sort of "multiple universe" business is not a well established mainstream physical theory.

Therefore, it is premature to discuss how multiple infinite universes can co-exist (and this is also against the rules of this forum).

But infinite objects, in general, can co-exist. Take two straight lines. They are infinite, yet you can have as many as you want.

 

[Bandersnatch]

How can two objects which occupy the same volume both be infinite at the same time? If they can't both be infinite at the same time then how can it be that two, three, four or 10⁵⁰⁰ universes can exist, all of them being infinite and all of them existing at the same time?

They can be removed from each other in higher dimensions. Just like you can have infinitely many infinitely long lines on a 2d plane, or infinitely many 2d planes in 3d space.

 

[iDimension]

They can be removed from each other in higher dimensions. Just like you can have infinitely many infinitely long lines on a 2d plane, or infinitely many 2d planes in 3d space.

But how can infinitely many 3d objects coexist?

Btw physical 1d and 2d objects don't actually exist.

 

[Drakkith]

But how can infinitely many 3d objects coexist?

Why shouldn't they be able to? There is an infinite amount of room for them to exist in (if our universe is infinite in size).

 

[A.T.]

I love the title of this thread. Infinities, where does it end?

 

[iDimension]

Why shouldn't they be able to? There is an infinite amount of room for them to exist in (if our universe is infinite in size).

Because if an object is infinite then by it's very definition that object must be everything that can exist otherwise that object is not infinite. What you are suggesting is that there can exist infinitely many finite objects which is allowed but not more than 1 singular object whos size is infinite.

Consider flipping a single coin an infinite number of times. There can only be 1 set... the infinite set. You can't have the set $A={h,h,h,h\cdots\infty}$ and $B={t,t,t,t\cdots\infty}$ because each set itself is infinite.

So you would need more than 1 coin if you wanted to create 2 sets. The same goes for an infinite object, the infinite object takes up infinite volume leaving no volume for another object.

 

[A.T.]

Because if an object is infinite then by it's very definition that object must be everything that can exist

That is the definition of "everything", not of "infinite".

 

[The_Duck]

Because if an object is infinite then by it's very definition that object must be everything that can exist otherwise that object is not infinite.

Counterexample: there are infinitely many odd numbers, yet there are also numbers that are not odd.

The same goes for an infinite object, the infinite object takes up infinite volume leaving no volume for another object.

Counterexample: consider an infinitely long rod of radius 1 meter. There's plenty of space around the rod for other objects.

 

[Alexandre]

Sixty Symbols recently posted a video about infinities.

 

[Drakkith]

Because if an object is infinite

Who said any object was infinite? An infinite number of objects is not the same as an infinitely sized object.

 

[mathman]

It is very important to distinguish infinity as a term in mathematics from any physical concept of infinity.

 

[ChrisVer]

For flipping the coins, why do I have the feeling the set is pretty much finite?
It's either h or t...
so your Whole set is $W= \left\{ h,t \right\}$
Now either you drop t, or h for infinite times, they will still exist in W, which is obviously finite and has (set) order $2 \ll ∞$.

 

[iDimension]

Who said any object was infinite? An infinite number of objects is not the same as an infinitely sized object.

Nobody has said anything is infinite but I said if our universe is infinite.

 

[Drakkith]

Nobody has said anything is infinite but I said if our universe is infinite.

You asked about an object of infinite size, but your original question was about the universe being infinite, not an object. Note that the universe isn't a singular, physical object. Empty space exists within the universe, so a universe of infinite size has an infinite amount of space for objects to exist within.

 

[Khashishi]

Your questions are too vague and not what physics is about. Physics and science is about making measurements and models that explain the measurements in a simple way. Sometimes models use infinity, and it's just a number to make the model work better. I blame popular science writers for getting people to focus on this meaningless stuff.

 

[iDimension]

Your questions are too vague and not what physics is about. Physics and science is about making measurements and models that explain the measurements in a simple way. Sometimes models use infinity, and it's just a number to make the model work better. I blame popular science writers for getting people to focus on this meaningless stuff.

So you're saying that everything and anything that exists is finite? Which can't possibly be true. The only possibly way I can see finite being true is that it s physically impossible to travel behond this finite object but then one must ask how?

I just find it impossible to believe or comprehend how something can be all that exists and be finite. Help me understand

 

[ChrisVer]

The last was a word-play?
If "all that exists" is finite, then that something ,which is "all that exists", is finite.
Take for example all the water on earth, it's all the water there is on earth, but both its vollume and Earth's vollume is finite.

Now about infinity, I don't really like it... I think infinity in physics means some very large value of a quantity... The bad infinities appearing not as limits, are problematic for the theories. However that's a theory (mathematical) concern and it's not actually measured in experiments.