We like Hossenfelder because she says what she thinks; not necessarily because we agree with her. (Today’s world is so full of yes men that the word “yes” is in danger of going out of business via becoming meaningless… )

Having come to the conclusion that infinity is not real, Sabine Hossenfelder thinks that maybe singularities aren’t real either:

Okay, why infinities are not, in her view, real:

Infinity and zero are everywhere in physics. Even in seemingly innocent things like space, or space-time. The moment you write down the mathematics for space, you assume there are no gaps in it. You assume it’s a perfectly smooth continuum, made of infinitely many infinitely small points.

Mathematically, that’s a convenient assumption because it’s easy to work with. And it seems to be working just fine. That’s why most physicists do not worry all that much about it. They just use infinity as a useful mathematical tool.

But maybe using infinity and zero in physics brings in mistakes because these assumptions are not only not scientifically justified, they are not scientifically justifiable. And this may play a role in our understanding of the cosmos or quantum mechanics. This is why some physicists, like George Ellis, Tim Palmer, and Nicolas Gisin have argued that we should be formulating physics without using infinities or infinitely precise numbers.

Sabine Hossenfelder, “Is Infinity Real?” atBackRe(Action)

And singularities?:

But what happens if you fall into a black hole singularity? Well, you die before you reach the singularity because tidal forces rip you to pieces. But if your remainders reach the singularity, then that’s just the end. There’s no more space or time beyond this. There’s just nothing.

At least that’s what the mathematics says. So what does the physics say? Is the black hole singularity “real”? No one knows. Because we cannot see what happens inside of a black hole. Whatever happens there is really just pure speculation.

Most physicists believe that the singularity in black holes is not real, but that it is instead of the same type as the other singularities in physics. That is, it just signals that the theory, in this case general relativity, breaks down and to make meaningful predictions, one needs a better theory. For the black hole singularity, that better theory would be a theory for the quantum behavior of space and time, a theory of “quantum gravity” as it’s called.

Sabine Hossenfelder, “Are Singularities Real?” atBackRe(Action)

Why would a person need to believe that neither infinity nor singularity are real?

Math nerds? Can you help us figure this stuff out?

Bravo. Science should be about OBSERVATION, not speculation. It you can’t observe and measure it consistently, it’s not a subject for science. Leave speculation to sci-fi.

When you use math to explain the natural world you come across disturbing things from time to time. The more closely you examine the world, and the more you understand the things you are investigating, the more you realize there are some things that just can’t be explained rationally.

These things can be very simple or extremely complex. You don’t have to look at black holes. Take the simple number line. On casual inspection it seems to be continuous. But look more closely and as Berlinski writes “Like plush that under strong light reveals a series of alarming moth holes, the familiar number system is filled with strange gaps, places of reverberating emptiness. And the word for that is weird.”

There are many incommensurable magnitudes, the square root of 2 is an example, but others abound. The number line is dense and it appears on the surface that between any two points there are an infinite number of values between them. But this can be proven to be not true at all. Like black hole singularities, irrational numbers transform the line from a simple reliable concept into an uncertain approximation of reality. At some level our use of math to describe the real world breaks down.

That upsets some people and they don’t like having to think about it too much. Does Sabine think the square root of 2 is real? I think she’d say that it’s just pure speculation.

In this life some things we are not meant to know. Not everything is discoverable, no matter how smart you are. When you find evidence of this it may lead you to ask yourself uncomfortable questions. It’s easy to just set it aside and think about it later, you know, after the Theory of Everything and quantum gravity has been developed.

For now we see through a glass, darkly; 1 Corinthians 12.

@ Sabine

:-/

Uhm I give u PI

David Hilbert gave it for his opinion that “the infinite is nowhere to be found in reality. It neither exists in nature, nor provides a legitimate basis for rational thought.”

I suspect hossenfelder is aware that there are infinitely many digits in the decimal representation of pi. But unless someone has successfully written them out that’s not evidence for actual infinities

No, we’re maths nerds. You need a physicist to tell you about the real world.

Put me down as:

Infinity is not real in the sense that one can only try to imagine it.

Singularities? Not even sure what that means.

Andrew

Whether or not infinity is real, it is useful. 😎

Has Sabine Hossenfelder been reading my posts here on infinity?

Infinities and irrational numbers invite discussion of the Metaphysics of Mathematics:

https://thopid.blogspot.com/2018/11/the-metaphysics-of-mathematics.html

That is just touching the surface, and the well is deep.

A singularity in physics, is like dividing by zero in 5th grade math class. We are not told “that’s deep”, or “wow, we’re in another dimension!”. Rather we are told, “Don’t do that, you’ll hurt yourself.” When physics hits a singularity, at least in the previous century, we knew we had done something wrong. Now we get patted on the back and welcomed to the shrine of exotic physics theories and greeted by physicists in brown cassocks with stipends at physics institutes with names like “Perimeter” or “Advanced”.

Basically the equations have perfectly normal solutions that are being overlooked because “singularities” are all in vogue. Black holes, event horizons and singularities don’t exist because they don’t have to, and the Designer of the Universe knows at least as much as my fifth grade teacher.