Infinity Is Ruining Physics (Max Tegmark)

[david...@gmail.com]

[Note: I found this on the internet. Of course a lot of people in this newsgroup will scream that mathematics is not science, and conclude that this article is thus irrelevant. So I want to remind you guys that many serious people think it is perfectly reasonable to say that the purpose of mathematics is to provide a conceptual framework for reasoning about the real world, and from that point of view, the article is very relevant to a discussion of mathematics. And if you don't know, Max Tegmark is a well respected physicist.]


Infinity Is a Beautiful Concept — And It's Ruining Physics
Does infinity actually exist, or doesn't it?

By Max Tegmark

I was seduced by infinity at an early age. Georg Cantor’s diagonality proof that some infinities are bigger than others mesmerized me, and his infinite hierarchy of infinities blew my mind. The assumption that something truly infinite exists in nature underlies every physics course I’ve ever taught at MIT — and, indeed, all of modern physics. But it’s an untested assumption, which begs the question: Is it actually true?

A Crisis in Physics
There are in fact two separate assumptions: “infinitely big” and “infinitely small.” By infinitely big, I mean that space can have infinite volume, that time can continue forever, and that there can be infinitely many physical objects. By infinitely small, I mean the continuum — the idea that even a liter of space contains an infinite number of points, that space can be stretched out indefinitely without anything bad happening, and that there are quantities in nature that can vary continuously.

The two assumptions are closely related, because inflation, the most popular explanation of our Big Bang, can create an infinite volume by stretching continuous space indefinitely. The theory of inflation has been spectacularly successful and is a leading contender for a Nobel Prize. It explains how a subatomic speck of matter transformed into a massive Big Bang, creating a huge, flat, uniform universe, with tiny density fluctuations that eventually grew into today’s galaxies and cosmic large-scale structure — all in beautiful agreement with precision measurements from experiments such as the Planck and the BICEP2 experiments. But by predicting that space isn’t just big but truly infinite, inflation has also brought about the so-called measure problem, which I view as the greatest crisis facing modern physics.

Physics is all about predicting the future from the past, but inflation seems to sabotage this. When we try to predict the probability that something particular will happen, inflation always gives the same useless answer: infinity divided by infinity. The problem is that whatever experiment you make, inflation predicts there will be infinitely many copies of you, far away in our infinite space, obtaining each physically possible outcome; and despite years of teeth-grinding in the cosmology community, no consensus has emerged on how to extract sensible answers from these infinities. So, strictly speaking, we physicists can no longer predict anything at all!

This means that today’s best theories need a major shakeup by retiring an incorrect assumption. Which one? Here’s my prime suspect: ∞. [infinity]

Infinity Doesn’t Exist
A rubber band can’t be stretched indefinitely, because although it seems smooth and continuous, that’s merely a convenient approximation. It’s really made of atoms, and if you stretch it too far, it snaps. If we similarly retire the idea that space itself is an infinitely stretchy continuum, then a big snap of sorts stops inflation from producing an infinitely big space and the measure problem goes away. Without the infinitely small, inflation can’t make the infinitely big, so you get rid of both infinities in one fell swoop — together with many other problems plaguing modern physics, such as infinitely dense black-hole singularities and infinities popping up when we try to quantize gravity.

In the past, many venerable mathematicians were skeptical of infinity and the continuum. The legendary Carl Friedrich Gauss denied that anything infinite really exists, saying “Infinity is merely a way of speaking” and “I protest against the use of infinite magnitude as something completed, which is never permissible in mathematics.” In the past century, however, infinity has become mathematically mainstream, and most physicists and mathematicians have become so enamored with infinity that they rarely question it. Why? Basically, because infinity is an extremely convenient approximation for which we haven’t discovered convenient alternatives.

Consider, for example, the air in front of you. Keeping track of the positions and speeds of octillions of atoms would be hopelessly complicated. But if you ignore the fact that air is made of atoms and instead approximate it as a continuum — a smooth substance that has a density, pressure, and velocity at each point — you’ll find that this idealized air obeys a beautifully simple equation explaining almost everything we care about: how to build airplanes, how we hear them with sound waves, how to make weather forecasts, and so forth. Yet despite all that convenience, air of course isn’t truly continuous. I think it’s the same way for space, time, and all the other building blocks of our physical world.

We Don’t Need the Infinite
Let’s face it: Despite their seductive allure, we have no direct observational evidence for either the infinitely big or the infinitely small. We speak of infinite volumes with infinitely many planets, but our observable universe contains only about 1089 objects (mostly photons). If space is a true continuum, then to describe even something as simple as the distance between two points requires an infinite amount of information, specified by a number with infinitely many decimal places. In practice, we physicists have never managed to measure anything to more than about seventeen decimal places. Yet real numbers, with their infinitely many decimals, have infested almost every nook and cranny of physics, from the strengths of electromagnetic fields to the wave functions of quantum mechanics. We describe even a single bit of quantum information (qubit) using two real numbers involving infinitely many decimals.

Not only do we lack evidence for the infinite but we don’t need the infinite to do physics. Our best computer simulations, accurately describing everything from the formation of galaxies to tomorrow’s weather to the masses of elementary particles, use only finite computer resources by treating everything as finite. So if we can do without infinity to figure out what happens next, surely nature can, too — in a way that’s more deep and elegant than the hacks we use for our computer simulations.

Our challenge as physicists is to discover this elegant way and the infinity-free equations describing it—the true laws of physics. To start this search in earnest, we need to question infinity. I’m betting that we also need to let go of it.

[David Petry]

I posted this last week, and nobody responded to it. So I'm posting it again. I really think you guys ought to think about it.

[zelos...@gmail.com]

Whats new? It is known physics is finite and uses of infinity/infinitesimals etc are to simplify the mathematics because the differens is too miniscule to matter.

[Avicenna]

On 9/26/20 12:29 PM, david...@gmail.com wrote:
> Infinity Is a Beautiful Concept — And It's Ruining Physics
> Does infinity actually exist, or doesn't it?
>
> By Max Tegmark
Infinity Is a Beautiful Concept — And It's Ruining Physics
Does infinity actually exist, or doesn't it?

By Max Tegmark

It shows Tegmark is confused about physics. A good physicist separates
science and metaphysics - metaphysics is not science.

Infinity is just a human concept and the symbol for infinity cannot be
used in any manner as any object in mathematics. Physics may use objects
like numbers, vectors, etc.. but infinity is not any object in
mathematics. The universe being infinite is not amenable to the
scientific methods. So there is not question "Does infinity actually
exist ?". Infinity never could be our physical reality and therefore
outside of the domain of physics which deals with reality.

In mathematics, we do use infinity as limit as x -> infinity - it is
logical here. It is even acceptable in physics to consider the x-axis of
a space co-ordinate to extend towards infinity, but you can't get
anything real except through fraudulent arguments.

[Tim Golden BandTech.com]

I think key here is that he is challenging the many worlds interpretation that has come into vogue. Sadly though he has done it without challenging their lack of regard for conservation. Please not that the me that misspelled every word typed here in every way that I ould mistype them is rather a lot of me and the rest of the universe to go around. That sort of infinity has breached Cantor by a long shot. Never gets discussed. Here even Tegmark the gamer lets it go by.

[David Petry]

Here's what's new:

"This means that today’s best theories need a major shakeup by retiring an incorrect assumption. Which one? Here’s my prime suspect: ∞. [infinity]"

So what Tegmark is saying is not only that (actual) infinity is not needed, but the acceptance of (actual) infinity is leading physicists down a dead end path, so change is needed.

[David Petry]

On Thursday, October 1, 2020 at 5:37:34 AM UTC-7, Avicenna wrote:
> On 9/26/20 12:29 PM, david...@gmail.com wrote:
> > Infinity Is a Beautiful Concept — And It's Ruining Physics
> > Does infinity actually exist, or doesn't it?
> >
> > By Max Tegmark

> It shows Tegmark is confused about physics. A good physicist separates
> science and metaphysics - metaphysics is not science.

In this newsgroup, there are people who will claim that Einstein was confused abouot physics. You (Avicenna) may wish to use Google to learn who Max Tegmark is.

[WM]

Am Donnerstag, 1. Oktober 2020 08:45:21 UTC+2 schrieb David Petry:

> I posted this last week, and nobody responded to it. So I'm posting it again. I really think you guys ought to think about it.

Thanks for posting this. It will become a substantial contribution to chapter V of https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf in the next edition.

Regards, WM

[horand....@gmail.com]

Well, what Tegmark is saying is that infinity is not needed *in physics*, but so are a lot of other things, such as abstract art, twelve-tone music, the Etruscan language, etc. That, however, is no argument that these things should not be studied for their own ends. (If it is, then it is a very pernicious form of censorship.) And note well that Tegmark does *not* say that Cantor was wrong. Cantor's set theory does work fine for most things, and when it does not, one can always use something else instead.

Nobody has denied that there may be other axiom systems that may even be beneficial to the development of new ideas (non-Euclidian geometry comes to mind), but a coherent mathematical theory of ultrafinitism has not been found, and it is not clear that it can.

[Sergio]

hes called Mad Max

[Sergio]

On 10/3/2020 10:47 AM, horand....@gmail.com wrote:
> On Thursday, 1 October 2020 16:29:52 UTC-3, David Petry wrote:

<snip>

>
> Nobody has denied that there may be other axiom systems that may even be beneficial to the development of new ideas (non-Euclidian geometry comes to mind), but a coherent mathematical theory of ultrafinitism has not been found, and it is not clear that it can.
>

ultrafinitism is a useless dead end, a novelty to a few, flawed
reasoning to most.

[mitchr...@gmail.com]

string knows point particles are quantized
at the infinitely small instead of a quantity that
is Planck...

Mitchell Raemsch

[horand....@gmail.com]

On Saturday, 3 October 2020 12:59:52 UTC-3, Sergio wrote:

Well, Yessenin-Volpin and Ed Nelson were serious mathematician, however misguided they may have been. I personally doubt very much that ZFC can be proven to be inconsistent, and all the alternatives to ZFC have to give up something. But the fact that people are working on falsifying ZFC does not disqualify them from serious discourse and is, in fact welcome, so long as they do it honestly.

[zelos...@gmail.com]

Demonstrating more what a worthless piece of shit that "book" is

[Ross A. Finlayson]

A "Mathematical Universe Hypothesis" (for physics) isn't necessarily digital.

When I here people say "physics is finite" I know they're wrong, or,
at best working on a platform not the "true foundation".

Singularity theory and what about asymptotes or for a spiral space-filling curve which
is also a singularity, makes for mathematical effects about the infinite.

Normalization or "physics' usual way of making mathematics tractable beyond
finitude" or, "re-de-normalization".

A Mathematical Universe Hypothesis is a reasonable idea, for the ubiquitous success
of mathematics in physics and then furthermore for foundations as reason, the
mathematical universe is infinite (and, singular). Tegmark's direction after
his coining the term isn't the only way to go in its conception.

Quantization after the ultraviolet catastrophe and blackbody radiation, makes for
effects in the discrete but that's all above continuum mechanics.

Tegmark's "Mathematical Universe Hypothesis" is good reading but then
"I compute digitally" is just a (not necessarily impractical and often practical)
incompleteness. It's similar with Wolfram, another genius.

Superstrings are as about 50 orders of magnitude smaller than us, but
even that is just an allusion to a yet-granular overlay atop a smooth continuum.

The Planckian is a regime about geometrical effects in the small.

These days Ramsey theory and quasi-invariant measure theory about
the running constants of fundamental (and, unified) physics is where
results in the infinite that belie (besides completing) those in the finite
see mathematical development as what will later automatically equip
the mathematical physics with tools for the infinite.

(The "super", and "total".)

Something like my old "Factorial/Exponential Identity, Infinity" is
really quite baffling, though it's built from space concerns and these
days such a notion is framed in (infinite) Ramsey theory.


Mathematics _owes_ physics mathematics of (real) infinity.

[Dan Christensen]

Tegmark writes: "We physicists can no longer predict anything at all!"

Does make him a crank, a publicity hound or both? Hmmm....


Dan

[Ross A. Finlayson]

No, everybody knows that QM and GR disagree to about 120 orders of magnitude.

(Penrose in his latest book pretty clearly writes some reasoning for this.)

You can prove that in DC proof with any one-line stipulation
you care to start and end with.

Not having a theory of real infinity does pretty much make sure
it's not "foundations", of physics.

Maybe it would help if you read a few hundred more pages of
his book. But, maybe it's easier for you just to ask people who
don't know whether he's a crank that he is, and having posed it
up then courtesy "material implication" that "[insert any name here]
is a crank is a crank is a crank".

Here's a link about Neil Turok's "Physics Needs a Revolution"
and I don't necessarily imagine you get it at all.

https://groups.google.com/g/sci.logic/c/ffUUIucwB58/m/4tRxSgPoBgAJ

https://www.math.columbia.edu/~woit/wordpress/?p=8361

Woit quotes Turok:

"I mean, partly people become very pessimistic and say, oh my god,
I’ve devoted 50 years of my life to studying this incredibly technical
and difficult theory and now I find it’s blown up in my face, it’s not
giving any predictions at all…and so some people talk about the
multiverse where the universe would be wild and chaotic on large scales
and almost anything you could imagine would actually exist somewhere
in the universe. I mean, this is literally a scenario which became very
popular among a category of physicists, that there is a multiverse out
there. Yet the evidence is exactly the opposite. That, as we look around
us, things could not be simpler. There’s no evidence for chaos on large
scales in the universe. It’s totally the opposite. It’s pristine, elegance,
minimalism is all we see. So, I think this is a very, very exciting time
to be doing theory. The challenge is enormous. The clues are enormous.
We’re waiting and we’re preparing and we’re encouraging people to take
radical leaps. "


The "predictions or extrapolations don't carry out" bit isn't "crank",
and for physicists it's "fact".

[Dan Christensen]

On Monday, October 5, 2020 at 5:11:50 PM UTC-4, Ross A. Finlayson wrote:
> On Monday, October 5, 2020 at 6:37:01 AM UTC-7, Dan Christensen wrote:
> > Tegmark writes: "We physicists can no longer predict anything at all!"
> >
> > Does make him a crank, a publicity hound or both? Hmmm....
> >
> >
> > Dan
>
> No, everybody knows that QM and GR disagree to about 120 orders of magnitude.
>
> (Penrose in his latest book pretty clearly writes some reasoning for this.)
>
> You can prove that in DC proof with any one-line stipulation
> you care to start and end with.
>
> Not having a theory of real infinity does pretty much make sure
> it's not "foundations", of physics.
>

Even proofs of the basic algebraic identities you learned in high school get unwieldy fast if you don't have an infinite supply of numbers to play with. So, even if the universe turns out to be incredibly huge but finite in some sense, you are STILL going to need those algebraic identities based on infinite sets of numbers for ordinary, earth-bound science and engineering. You need to be able to prove that addition is commutative, associative, cancelable, etc. to solve algebraic systems by both numerical and analytical means. Think of infinity as the grease to keep the wheels of mathematics spinning.


Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

[Ross A. Finlayson]

I'd read that as better and something that's agreeable and
mostly goes without saying.

This is only talk about _expanding_ and _improving_ the understanding
of foundations, there's no retro-ignorance in this.

In fact "grease for wheels" is an apt metaphor, basically
what analysis results in the smooth.

For example, consider metaphor of superstrings as
"graphite for atomic lock".

One way to confirm this is that there must be no smallest
distance in smooth space-time, because if there are right
angles, that makes a square, and its diagonal would be
an irrational number, contradiction QED.

[Dan Christensen]

Irrational numbers would still be essential in algebra and calculus used in science and engineering.

[Ross A. Finlayson]

Doubtless.

Numerical methods are algorithms for approximating real terms
with only finite and bounded numerical resources.

Symbolic calculation quite most usually reduces the systems
to one simple plan, that then the plan is executed in numerical
methods, what for symbolic calculators to solve and arrive at
symbolic and their corresponding nearly/almost solutions in
acknowledgment for the conscience of their error terms.

The story goes that the first guy who proved (root two was irrational),
and, held to his conscience that it is so, was thrown from the boat
by Pythagoreans, where today we only refer to Pythagoras and the guy
from the boat. The Greek's "apeiron" in their time was anathematic to
reason, today it still is and and we have many much more complete
systems of definition where it's so washed away.

https://en.wikipedia.org/wiki/Hippasus

Following courtesy Wikipedia:

"Hippasus is sometimes credited with the discovery
of the existence of irrational numbers, following which
he was drowned at sea. Pythagoreans preached that
all numbers could be expressed as the ratio of integers,
and the discovery of irrational numbers is said to have
shocked them. However, the evidence linking the discovery
to Hippasus is confused. "

"Pappus merely says that the knowledge of irrational numbers
originated in the Pythagorean school, and that the member who
first divulged the secret perished by drowning. Iamblichus gives
a series of inconsistent reports. In one story he explains how a
Pythagorean was merely expelled for divulging the nature of the
irrational; but he then cites the legend of the Pythagorean who
drowned at sea for making known the construction of the regular
dodecahedron in the sphere. In another account he tells how it
was Hippasus who drowned at sea for betraying the construction
of the dodecahedron and taking credit for this construction himself;
but in another story this same punishment is meted out to the
Pythagorean who divulged knowledge of the irrational. Iamblichus
clearly states that the drowning at sea was a punishment from the gods
for impious behaviour. "

"Some scholars in the early 20th century credited Hippasus
with the discovery of the irrationality of √2. Plato in his Theaetetus,
describes how Theodorus of Cyrene (c. 400 BC) proved the irrationality
of √3, √5, etc. up to √17, which implies that an earlier mathematician
had already proved the irrationality of √2. Aristotle referred to the method
for a proof of the irrationality of √2, and a full proof along these same
lines is set out in the proposition interpolated at the end of Euclid's Book X,
which suggests that the proof was certainly ancient. The method is a proof
by contradiction, or reductio ad absurdum, which shows that, if the diagonal
of a square is assumed to be commensurable with the side, then the same
number must be both odd and even."


Finite numbers are each of course either odd or even and not both.

[Sergio]

you sound like Bot.

[Sergio]

On 10/5/2020 2:40 AM, Ross A. Finlayson wrote:
> On Saturday, October 3, 2020 at 8:59:52 AM UTC-7, Sergio wrote:
>> On 10/3/2020 10:47 AM, horand....@gmail.com wrote:
>>> On Thursday, 1 October 2020 16:29:52 UTC-3, David Petry wrote:
>> <snip>
>>>
>>> Nobody has denied that there may be other axiom systems that may even be beneficial to the development of new ideas (non-Euclidian geometry comes to mind), but a coherent mathematical theory of ultrafinitism has not been found, and it is not clear that it can.
>>>
>> ultrafinitism is a useless dead end, a novelty to a few, flawed
>> reasoning to most.
>
> A "Mathematical Universe Hypothesis" (for physics) isn't necessarily digital.

context ?

>
> When I here people say "physics is finite" I know they're wrong, or,
> at best working on a platform not the "true foundation".

generalizations are usually wrong.

you switched from digital to finite.......

>
> Singularity theory and what about asymptotes or for a spiral space-filling curve which
> is also a singularity, makes for mathematical effects about the infinite.

you a Bot.

[Ross A. Finlayson]

"New phone who dis?"

No, bot sound like me.

[Blake Fury]

Sergio wrote:

>>> Download my DC Proof 2.0 freeware at http://www.dcproof.com Visit my
>>> Math Blog at http://www.dcproof.wordpress.com
>>
>> Doubtless. Numerical methods are algorithms for approximating real
>> terms with only finite and bounded numerical resources.
>
> you sound like Bot.

What are you talking about, you dirty capitalist. Used to be 60 in the UK.
Now the retirement pension age is 66 , going to 67. Already 68 in many
shithole capitalist neo-liberal countries in europe. Some moneymakers
moneychangers sat down and realised the billions they can make - SCUM !!!
Open your eyes.

[Peter]

Blake Fury wrote:
> Sergio wrote:
>
>>>> Download my DC Proof 2.0 freeware at http://www.dcproof.com Visit my
>>>> Math Blog at http://www.dcproof.wordpress.com
>>>
>>> Doubtless. Numerical methods are algorithms for approximating real
>>> terms with only finite and bounded numerical resources.
>>
>> you sound like Bot.
>
> What are you talking about, you dirty capitalist. Used to be 60 in the UK.

For women. 65 for the for men. The vile scum feminists never
complained. The want equality when it suits then.

> Now the retirement pension age is 66 , going to 67. Already 68 in many
> shithole capitalist neo-liberal countries in europe. Some moneymakers
> moneychangers sat down and realised the billions they can make - SCUM !!!
> Open your eyes.
>

--
When, once, reference was made to a statesman almost universally
recognized as one of the villains of this century, in order to
induce him to a negative judgment, he replied: "My situation is
so different from his, that it is not for me to pass judgment".
Ernst Specker on Paul Bernays

[Peter]

Either that or two cranks arguing with one another.

[Ross A. Finlayson]

That's funny, we weren't arguing.

If you don't know I sound like a _huge_ bot and a _massive_ crank.

"If you don't know / you don't know."