Clizby Wampuscat
Well-Known Member
Why is an infinite regress not possible?
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Infinite Regress
- Thread starter Clizby Wampuscat
- Start date
Huh? What is infinite regress.
Twilight Hue
Twilight, not bright nor dark, good nor bad.
Chains break maybe? And you can't clone a clone forever!
Heyo
Veteran Member
It isn't impossible. Infinite regress is absurd, i.e. we have difficulty to imagine it. There is no infinity in reality, so we lack an example. The only discipline that deals with infinities is Maths and you'd probably call infinity absurd when you imagine that adding up the infinite number of natural numbers, you get -1/12.
Brian2
Veteran Member
Because time as we know it has not been there since eternity.
How would you know?
Heyo
Veteran Member
Well, there is a possibility that space is infinite but we don't know that yet. Let's just say we have no experience of something infinity.
I think it is impossible to experience an infinity (in its fullness) whether it exists or not, mainly because I can't see how an infinity could be measured.
We Never Know
No Slack
So if we measure anything as far as we can with our limited knowledge, is it right to say its infinite?
We Never Know
No Slack
Heyo
Veteran Member
That's easy. Take an infinite length. Put a yardstick to it, end over end and count. You just have to do it infinite times.
The argument is that if there was an infinite past, it would take infinite time to reach the present. So we'd never reach now. Yet we've arrived here at the present. So the past must not have been infinitely long.
Other people could probably do a better job phrasing it but that's how I understand the argument.
It would neither be correct to say it is infinite, nor to say it is not infinite without knowing.
In my opinion.
We Never Know
No Slack
Exactly. So if we don't know, who can claim either way.
You don't get that. In physics, we might. Mathematicians don't make such claims (not without serious preamble and carefully noting the conditions under which divergent series can be made to converge to particular sums with additional assumptions that may or may not satisfy uniqueness and why we might want to tolerate this for e.g., approximations). Euler and other early contributors to the calculus didn't have the notion of sets (let alone infinite sets) to work with nor did they have a notion of limits (but rather a non-rigorous, wooly concept of infinitesimals).
However, since the development of QED and the divergences caused via self-interactions in systems described by this earliest of quantum field theories and the foundational QFT for the rest of the standard model, adding together infinitely many terms from a divergent series became a tool and a problem.
The tool is that it allows for the extraction of physical values from the theory that can be compared to the results of experiments, as the physical theories involved nonsensical integrals and summations that always returned infinite values. By carefully regularizing and renormalizing the terms corresponding to the different contributions to e.g., the mass or energy or some similar physical value in QED (or QFT more generally), one use this kind of summation and rearrangement of divergent series to yield finite results.
The problem is the very reason, in mathematics, one doesn't claim that divergent series actually equal any number at all, let alone -1/12. One can change how one groups the terms, or rearranges the terms, or combines divergent (or even convergent) series, and in each case one can get any value one wants.
In physics, uniqueness comes from experiment. We imagine that there exists a uniquely define bare parameter (e.g., the bare mass of the electron) and then there are contributions coming from e.g., the self-energy, the coupling to the (quantized) EM field, virtual photons, etc. The theoretical sum equals infinity, but we can postulate that the electron actually has a finite bare mass and "wrap up" the infinite divergences into this value in a consistent way up to arbitrary scales.
Of course, if we measured something different, we could obtain that value (or any other) too.
Things are worse mathematically, because you aren't constrained by physically measured values. Hence, for example, there is no reason to use one particular way to handle divergent series and obtain one particular finite result when any other could be obtained by grouping/rearranging terms differently (or similar tricks).
In undergraduate mathematics, showing that we obtain ludicrous results by being careless with infinite summations is part of teaching caution about what happens when one uses the "rules" one has for manipulating convergent sequences and series on divergent ones.
Secret Chief
Stiff Member
syo
Well-Known Member
This. ?
Clizby Wampuscat
Well-Known Member
I agree. I hust get a lot of people telling me it is impossible. I have never seen a proof that eliminates the possibility. Most arguments are just incredulity.
Clizby Wampuscat
Well-Known Member
Why is time required for an infinite regress?