I Is anything in the physical world infinite?

[Hornbein]

There is no neccessity to believe that the approximations of calculus hold in the domain of the extremely small. Physics is based on the "close enough for jazz" principle. If this is ever found to be wrong it will be celebrated as a fertile source of PhD topics.

I used to think that "infinity" was naught but a useful shorthand until observations combined with theoretical considerations showed that the Universe itself might very well be infinite. I wouldn't give up on a proof. Maybe someone will come up with a way of showing that if the Universe is not flat then a contradiction results.

Real numbers aren't at all real. They are useful and traditional shorthand for successive approximations. On the other hand, imaginary numbers are fundamental and not at all imaginary. In physics one learns to place no weight on names. In physics names evolve randomly and often have a meaning unrelated to or even opposite their original purpose. This is an endless source of confusion to outsiders. You just have to get used to it.

When explaining such things to outsiders I often begin with telling them they have to clear their mind of any meaning of things like "particle" and start with a blank slate. Their original conception is an obstacle that will block all learning.

 

[Dale]

There is no neccessity to believe that the approximations of calculus hold in the domain of the extremely small.

There is also no necessity to disbelieve. And since the calculus models do work and non-calculus models don’t, the belief has merit.

 

[PeroK]

Within our technological limits we detect the CMBR in all directions as far as we can see.

The detected CMBR is a finite number of photons per second. It can't be otherwise is the point.

 

[Klystron]

I want to 'like' the last post but cannot find an emoji for "Duh".

 

[PeroK]

Here's an example of the difference between maths and physics.

If we imagine one event at time $\frac 1 2$ second. Then another event at time $\frac 3 4$ second. A third event at time $\frac 7 8$ second etc. Then, mathematically we have an infinite sequence of events within $1$ second.

But, you cannot do this physically. You might argue that there is no limit to how quickly the events can happen one after the other. Whatever limit anyone specifies you might be able to do better. But, you cannot go on indefinitely making the increment smaller and smaller. If you try to generate an infinite number of events in finite time, you must hit a limit somewhere.

One example might be how fast a computer can count. It's impossible to put an absolute limit on it, but any given computer must have a limit.

 

[Klystron]

Concur. Another non-electromagnetic physical example to answer the OP occurred to me while falling asleep: the fractal length of the coast of England*.

This measurement proceeds merrily using smaller then tinier 'fractal angles' to increase the measured length but eventually encounters some practical limit. Dale's first post succinctly addresses this contretemps, but this thread has been instructive.

*Tradition uses England or Madagascar in geometry textbooks. Any island makes an example.

 

[anorlunda]

If you try to generate an infinite number of events in finite time, you must hit a limit somewhere.

Is that true if the events are not at the same place in space? I'm thinking spacetime rather than time.

If there are an infinite number of stars, isn't there collectively an infinite number of scattering events within those stars at each second of time? (Dodging the question of how to define a second in that context.)

So I'm thinking that you must hit a limit only if you constrain the events to be contained at the same place.

 

[PeroK]

If there are an infinite number of stars, isn't there collectively an infinite number of scattering events within those stars at each second of time? (Dodging the question of how to define a second in that context.)

That's a big if. Let's assume it's true. Describe your experiment. How do you organise such as experiment. It's not enough, IMO, to wave your hands at the infinite cosmos and say it's happening!

 

[DaveC426913]

Is that true if the events are not at the same place in space? I'm thinking spacetime rather than time.

If there are an infinite number of stars, isn't there collectively an infinite number of scattering events within those stars at each second of time? (Dodging the question of how to define a second in that context.)

Simpler. If we accept the overarching premise that the universe is infinite in extent, then infinite phenomena in space (or in space time) are as trivial to find as snowflakes underfoot in winter.

 

[PeroK]

Here's a thought. If we assume that classical mechanics were correct, then a particle in motion would represent an uncountably infinite sequence of events every second - simply by virtue of being at every point $x(t)$.

That implies that nature is generating an infinite amount of information (re that particle) and it's only our experimental constraints that pick out a finite sample.

However, if QM is correct, then it is meaningless to talk about that classical trajectory and the only information that nature generates is the finite information that we obtain from our experiments.

And, if we apply QM principles to an infinite universe, then it may be equally meaningless to talk about those events as happening unless we obtain information about them by experiment.

In a way, the underlying principles of QM put a finite limit on what we can say about even an infinite universe.

 

[anorlunda]

That's a big if. Let's assume it's true. Describe your experiment. How do you organise such as experiment. It's not enough, IMO, to wave your hands at the infinite cosmos and say it's happening!

I said before that the speculation that the universe is infinite can never be confirmed.
But neither could a limit on the number of events per second in a single spot be used to give evidence about the extent of the universe.

 

[PeroK]

I said before that the speculation that the universe is infinite can never be confirmed.
But neither could a limit on the number of events per second in a single spot be used to give evidence about the extent of the universe.

The question is what experiment do you have in mind to detect and count the infinite number of events?

 

[pinball1970]

Here's an example of the difference between maths and physics.

If we imagine one event at time $\frac 1 2$ second. Then another event at time $\frac 3 4$ second. A third event at time $\frac 7 8$ second etc. Then, mathematically we have an infinite sequence of events within $1$ second.

But, you cannot do this physically. You might argue that there is no limit to how quickly the events can happen one after the other. Whatever limit anyone specifies you might be able to do better. But, you cannot go on indefinitely making the increment smaller and smaller. If you try to generate an infinite number of events in finite time, you must hit a limit somewhere.

One example might be how fast a computer can count. It's impossible to put an absolute limit on it, but any given computer must have a limit.

I have not read every post. Does your point apply the the Planck length also?

Is Planck length/2 a meaningless statement in terms of existence rather than measurement?

It is there we could just never measure it?

 

[jbriggs444]

Is Planck length/2 a meaningless statement in terms of existence rather than measurement?

It is there we could just never measure it?

What does it mean for a thing to be "there" if you cannot measure it?

I'll leave to one side the question of whether it is theoretically possible to measure with precision better than the Planck length.

To me the answer is that Planck length / 2 is there in the model. But the model may have features beyond what the reality requires.

 

[pinball1970]

What does it mean for a thing to be "there" if you cannot measure it?

There are things in the universe that we cannot measure that are there like very distant galaxies? Or strings? Dark matter?

What I am asking is, is it not possible for something to exist, to be “there” unless we can measure it?

To me the answer is that Planck length / 2 is there in the model. But the model may have features beyond what the reality requires.

Ok. So mathematically logical (0.8 x 10-35) but not relating to reality?

I looked at Planck length on wiki...

Gravity and QM??

Black holes?

Obviously completely out of my depth on that so I will take your word for it. EDIT: There a lot of Planck length threads on PF I will look at

 

[haushofer]

If you define "infinite" as "going on forever", yes: the discussions on PF about the ontology of quantum mechanics.

 

[jbriggs444]

There are things in the universe that we cannot measure that are there like very distant galaxies? Or strings? Dark matter?

We suspect there are. It makes our theories simpler to assume that there are. But the true state of affairs is "we do not know".

 

[Melbourne Guy]

The number of partitions something continuous can be divided into, such the space between two points or part of the electromagnetic spectrum, is infinite.

Perhaps I'm misunderstanding the concept, but with the electromagnetic spectrum, can it really be partitioned into an infinite number? Is it not constrained by the shortest wavelength?

 

[jbriggs444]

Perhaps I'm misunderstanding the concept, but with the electromagnetic spectrum, can it really be partitioned into an infinite number? Is it not constrained by the shortest wavelength?

Yes, though I think what you are getting at is that we cannot measure the difference between two possibly different wavelengths to infinite precision. So, for all we know, there might only be finitely many possible wavelengths.

 

[PeroK]

Perhaps I'm misunderstanding the concept, but with the electromagnetic spectrum, can it really be partitioned into an infinite number? Is it not constrained by the shortest wavelength?

Within the classical theory of EM there is no such thing as the shortest possible wavelength. Or the longest.

 

[DaveC426913]

Within the classical theory of EM there is no such thing as the shortest possible wavelength. Or the longest.

True about the theory, but still a red herring when it comes to physicality.

I have already pointed out practical limits on upper and lower bounds.

 

[PeroK]

True about the theory, but still a red herring when it comes to physicality.

I have already pointed out practical limits on upper and lower bounds.

There's a difference between

A) An EM wave theoretically having any non-zero finite wavelength.

B) an EM wave having a wavelength of zero or "infinity".

The first is what the classical theory says.

 

[DaveC426913]

There's a difference between

A) An EM wave theoretically having any non-zero finite wavelength.

B) an EM wave having a wavelength of zero or "infinity".

The first is what the classical theory says.

I know, and I'm not disagreeing that it's valid; I'm simply pointing out it's a red herring in a discussion about physical phenomena.

IOW, yes the theory of EMR says there's is no upper or lower limit - but the physical limits of universe supercede that, and put a real constraint on what can, and therefore does, exist.

 

[Drakkith]

Perhaps I'm misunderstanding the concept, but with the electromagnetic spectrum, can it really be partitioned into an infinite number? Is it not constrained by the shortest wavelength?

The number of different frequencies between 100 MHz and 101 MHz is infinite for example. The shortest or longest possible wavelength is different and not what I was referring to.

 

[Good Elf]

I assume we are not speaking of infinitely large things or infinity small things. Both are shorthand for limits to what our human mind can comprehend & actually does not relate to a true mathematical infinity. We need to understand that math is all about modeling & math also introduces infinities, it is only a first approximation to the way the world actually works. A match between our experiments & our theories is necessary. Humans have adopted a deconstructionist POV which is very unacceptable at the extremes. Quantum Theory instructs us quantum entanglement has no spatial/temporal limits. Many individuals cannot accept this experimentally provable aspect of our existence. The human mind is not prepared by evolution to grasp the scale of everything all at once, it's instantaneous reality & of our connection to the entire Universe instantly.

As we discover new aspects of the world we add to our long list of models. This is because we have evolved to thrive at certain scale. Our interaction with the world would be quite different if we were the size of a flea, bacteria or the size of a land locked Blue Whale for example. That is all about evolution & fitness for purpose. But actually these models are only (of themselves) purely intuitive & conceptual & do not specifically relate to the physical world on/at all scales. Scale is of utmost importance & it is why we find it difficult to understand our place in our world but I respectfully remind everyone there are no models that have stood forever. The price of Truth is always the properly constructed observation/experiment not our wishing to be something we are not.

 

[Rev. Cheeseman]

Summary:: Is anything in the physical universe unlimited or just in math?

Is anything in the physical universe unlimited or infinite or does Infinity only exist to make some math work? Is Infinity a real thing outside of math?

Well, infinite basically means no limit. Empty space or void that is totally devoid of everything has no limit. So, there you go. But empty space that is totally devoid of everything is just hypothetical. If empty space is nothing more than the totality of electrons, then this is another example of infinite in the real world.

 

[Good Elf]

@wonderingchicken:

To see a World in a Grain of Sand
And a Heaven in a Wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour...

The meaning of any word has no absolute applicability. There needs to be agreement—an applicable lexicon. Words require a full context. One way to think of infinity in Math is to divide 1 by zero... that is an infinity but can any human mind fully grasp what it means? The result of this division is a number bigger than any human mind can comprehend or ever write down—it size may be approached—but adding a single digit makes it 10 times bigger than before... without any limits, a number raised literally to infinity in tenfold steps, yet it is so easy to write this as a 'simple' fraction... to comprehend it is quite another thing entirely.

Saying something has no limit is also 'highly qualifiable'. You said "infinite basically means no limit". If I said you could run away with 'no limit'... would you get to infinity? It is conceivable that the further away you escape to, the closer you will be to where you first left because our Universe may be unbounded yet finite like a bug caught on the inside of an inflated balloon, it can walk forever but never reach infinity, actually it can't even get out to a distance greater than the size of the balloon. The surface of the Earth is like this—unbounded yet finite (only curved in the opposite direction). Like bugs... we live in 'Plato's Cave' with bodies formed in & by that environment. There are limits to what is directly seen.

Being totally devoid of anything is not infinity—it is a zero. "If empty space is nothing more than the totality of electrons, then this is another example of infinite in the real world". We are in fundamental disagreement about the use of the word 'electrons' being equated to 'empty space' & 'infinite'. Space being empty of everything... what is the difference between infinity & zero? You must tell me... first!

 

[Rev. Cheeseman]

@wonderingchicken:

To see a World in a Grain of Sand
And a Heaven in a Wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour...

The meaning of any word has no absolute applicability. There needs to be agreement—an applicable lexicon. Words require a full context. One way to think of infinity in Math is to divide 1 by zero... that is an infinity but can any human mind fully grasp what it means? The result of this division is a number bigger than any human mind can comprehend or ever write down—it size may be approached—but adding a single digit makes it 10 times bigger than before... without any limits, a number raised literally to infinity in tenfold steps, yet it is so easy to write this as a 'simple' fraction... to comprehend it is quite another thing entirely.

Saying something has no limit is also 'highly qualifiable'. You said "infinite basically means no limit". If I said you could run away with 'no limit'... would you get to infinity? It is conceivable that the further away you escape to, the closer you will be to where you first left because our Universe may be unbounded yet finite like a bug caught on the inside of an inflated balloon, it can walk forever but never reach infinity, actually it can't even get out to a distance greater than the size of the balloon. The surface of the Earth is like this—unbounded yet finite (only curved in the opposite direction). Like bugs... we live in 'Plato's Cave' with bodies formed in & by that environment. There are limits to what is directly seen.

Being totally devoid of anything is not infinity—it is a zero. "If empty space is nothing more than the totality of electrons, then this is another example of infinite in the real world". We are in fundamental disagreement about the use of the word 'electrons' being equated to 'empty space' & 'infinite'. Space being empty of everything... what is the difference between infinity & zero? You must tell me... first!

Both zero and infinity are the same if you're a critical thinker. Both possessed no limits at all. What you're trying to tell me is incessant or nonstop moving such as like an ant walking incessantly on a ball. People confused unbounded part of the "finite but unbounded universe" hypothesis with incessant motion on something.

 

[PeroK]

One way to think of infinity in Math is to divide 1 by zero... that is an infinity but can any human mind fully grasp what it means? The result of this division is a number bigger than any human mind can comprehend or ever write down—it size may be approached—but adding a single digit makes it 10 times bigger than before... without any limits, a number raised literally to infinity in tenfold steps, yet it is so easy to write this as a 'simple' fraction... to comprehend it is quite another thing entirely.

Although it may sound poetical to say that no one understands mathematics, it's not the case. The mathematics of infinite sets is well understood by any competent mathematics student.

 

[DrClaude]

Time to close this thread. Thanks to all that have participated.