Is Our Universe Infinite?


Mathematical lines are, well, mathematical constructs. So they can represent things that make no “common sense” in the real world unless you realize the construct. For enample, the mathematical equation y=x represents a straight line running forever at a 45 degree angle thru the x,y axis, where x represents the horizontal axis numbers and y represents the vertical axis numbers. Yet, consider the equation y=x square - 3*x divided by x-3. Looks more complicated. Yet it also represents the same straight line, except it has a “hole” at x=3, since the denominator is zero at x=3, so the equation is undefined there. You COULD call that a non infinite line in the sense that it has a hole in it. Mathematical equations can be constructed that they can do lots of wonderful things, that are quite useful in science in engineering, but viewed in the physical plane, can make your head spin if you’re not used to the abstractions used.



But I see you are somewhat versed in abstract math.


The fact that something can make your head spin does not make it non-real. Take for example the use of the smart phone to make purchases and transfer money or to buy and sell stock options. The technology involved here might make your head spin, but still the smart phone is a real tangible object that you can hold in your hand.


Yes, and you can use it without understanding how it works. But you also have to respect the overall audience in the threads.

The thread question of is the universe infinite can be answered in many, many conflicting ways, depending how you view things. In one respect, since we are finite, we can’t experience infinite. Yet if you abstract it, sure, infinity becomes more managable. And some people start to understand where you’re coming from.

Then it’s possible to introduce the concept of orders of infinity. Aleph 2, Aleph 3, etc depending on whether you’re in an additive, multiplicative, exponential etc universe representation.

All those concepts were introduced. All are valid. It is less clear that they’re useful.


Science proceeds not so much with the infamous scientific method or even Popper’s falsification approach, it proceeds according to set of principles, I can identify three: (1) philosophical (2) abstraction, and (3) mathematical formulation.

The philosophical principal with which science proceeds is derived from Logical Positivism. In summary, science:
(a) rejects the idea that reality has some purpose,
(b) rejects attempts to explain natural phenomena by an essence or a secret cause of things,
© rejects as meaningless any explanation not verifiable through the senses,
(d) advocates the study of constant relationships without delving into the underlying causes.

Regarding a finite universe. The big bang theory is the only explanation that fits philosophical principal © the theory begins with an indefinitely minute object called the singularity that existed in an unknown background and from which all matter, energy, space, and time emerged, and was at one point in time the size of a pumpkin, and expanded to the present finite size whatever that might be. There is no way the universe can expand to an infinite size.

All other explanations for the present cosmological observations are speculations designed to avoid the obvious creation event that the BB implies. Bubble universe, string theory, the big crunch, and a pumpkin size universe in something else are pure speculation, unless of course the something else is the Mind of God.

For Catholics that might not subscribe to a finite universe, God is infinite and if the universe is also infinite, you are playing with pantheism, still a heresy.



Moreover, if the universe is expanding, which physicists tell us it is, then tomorrow it will be of greater extent than it is today, which means it cannot possibly be infinite today if it can be bigger tomorrow.


I believe that the universal space is defined by rational numbers, hence is discrete in which the inherent spacing between points is the Planck constant. I also believe that sometime in the future, in addition to discrete space replacing continuous space as the foundation of reality, algorithms will replace equations to describe the observations, and that information will replace energy as the basic impetus for the dynamics of reality.

The only way most equations are currently being solved is with computers, meaning algorithms. Algorithms have the advantage of being capable of including contingencies, that most equations currently face when applied to the real world. For example, equations don’t deal with surfaces that always show up in the semiconductor world.

Last I heard the only way to solve a 3-body problem is with a computer. And a Physics Professor started one of my Solid State courses with, "the Shroedinger wave equation can model the structure for all the elements up to and including hydrogen. Peace!



Dark energy is speculative but is needed to explain the accelerating expansion of the universe. Has anyone seen dark energy?
Dark matter is needed to explain the strength of gravitational forces between galaxies. Has anyone verified dark matter through the senses?


You don’t explain how this can be reconciled with Lorentz invariance.


In the case of semiconductors, I thought that the potential along the atomic chain was a cosine function and the Schrodinger equation could be used away from the Brillouin zone boundary, whereas close to the Brillouin zone you would obtain standing Bloch waves?


This seems to be willfully trying to miss Hawking’s point. The coordinate system Hawking is referring to is the “four direction” system; or a 2 dimensional plain. There’s no “up” in that system, so trying to posit up when you’re dealing with what amounts to a two dimensional plane is illogical, and violates the geometry of that system.

Being pedantic doesn’t actually win an argument.


You got it. The pumpkin size refers to the size of the observable universe if you were there to look out at it at that time.

I think that people imagine that if you were at the ‘edge’ of the pumpkin sized universe, you could peer out and see what was ‘outside’. But wherever you are in my observable universe, you are at the exact centre of your observable universe. So you could be ‘outside’ the pumpkin as far as I was concerned, but you would always be at the centre of yours.

The term Big Bang implies a single point at the centre of the universe from which everything exploded. Whereas the expansion (not explosion) happened everywhere. There is, was and never will be a centre.


Not to imply the the universe is or is not infinite, but a line’s properties don’t necessarily have an isomorphic relationship with the universe. “The finger that points at the moon is not the moon” comes to mind here. Bujt that may be too abstract for general conversation. You will find that a math based description of the universe may have limited applicability;not ever property of a line is also a property 9f the universe.


How do you explain the effectiveness of mathematics in describing and modelling motions and dynamical physical forces? Do you think it would be possible to understand fluid flow, radio waves, superconductivity, electricity and magnetism, etc., without mathematics?


I think there may be a gap between my intended message and the received message. Math is quite effective over a broad range of real world problems. But there are also limits to the relationships that can be established between a math based model of something physical and how that physical thing actually behaves. The isomorphism between the two while useful isn’t necessarily applicable across an infinite range. Coming up with the concerto of an object of infinite length doesn’t mean there is necessarily an infinite distance.


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