Recent content by loop quantum gravity

I would guess we would see something similar to the universe where sliders landed that they go somehow backwards in time. (I believe it was in their second season, one of their best episodes). I mean in Feynman digrams anti-particles seem to proceed backwards in time w.r.t the regular particles.

So here I have an interesting classical DG research question. I also think that in the general case it doesn't converge to a finite geometric shape. But how to prove it?

I would guess since it's a classical mechanics principle, it adheres to the three rules of Newton. But Q and R theories don't adhere to this third law.

So I was thinking about repeating an evolute of an evolute ad infinitum, it doesn't necessarily converge to some finite geometric shape, does it? Suppose we have a curve ##\gamma: [a,b]\to \mathbb{R}^n##, and let ##\dot{\gamma}(t)## be the tangent to the curve, and ##n(t)## its normal to the...

yes there exists an M such that... Anyways I thought it to be an interesting logical-calculus exercise to understand every subtelty. I guess I can ask an AI for further assistance. Thanks though!!

How about other variations of the quantifiers and perhaps also changing sometimes the logical connective from implication to conjunction? Usually the definition in books for bounded functions is as such: $$\forall M>0 \forall x (|f(x)|<M)$$ I can see indeed what you mean that it may be a bounded...

The definition of a continuous function at a point ##x_0## is: $$\forall \epsilon >0 \exists \delta >0 \forall x(|x-x_0|<\delta \rightarrow |f(x)-f(x_0)|<\epsilon)$$ What would happen if we change it to another defintion as: ##\exists \epsilon >0 \forall \delta>0 \forall x(|x-x_0|<\delta...

No need to get upset, I think that also in theory there are hypothetical tachyons; which I am not sure how they can ever be detected (just like Dirac magnetic monopole which was up until now never been observed). Just because up until now we haven't observed FTL speeds doesn't mean they don't...

I didn't understand what is that "hot slush". I also don't understand what is "normal" day for any object in chaotic dynamical systems; isn't it an oxymoron to have a "normal" day in the solar system or any other star system?

a decade or so allegdly physicists found a neutrino with a speed faster than the speed of light. After a few weeks they found a mistake in the experiment. At the time they did the experiment they glossed over this detail. I don't understand, there cannot be an experiment that detect speeds...

Flukes tend to accumulate in recent years, I wonder if there's more than statistical errors here involved here. I mean as an amateur basketball player I once scored from an entire whole court; but it's not something that will repeat itself ever so often if you get my drift. So if we want our...

All my preprints before chatGPT were read carefully by others, they weren't papers per se in journals. I didn't think to myself that LLM can produce references that don't even exist. It's really upseting to hear that it does such a thing. But it also means we can't accept everything it writes...

As the saying goes:"the Moon is not there, if nobody is looking..." :oldbiggrin:

fixed that, thanks!

How to prove the following claim? that: $$m=\lfloor \log_2 n \rfloor= \lfloor \lg n \rfloor$$ from $$n=2m+k−1$$ ? Obviously we have $$m=log_2(n−k+1)$$ . ##k## is the number of leaves. My question has arisen from the solution here: https://walkccc.me/CLRS/Chap06/6.1/ of 6.1-2. Thanks in...