This is Zeno's dichotomy paradox [1]. Finitely-defined infinitely-complex systems (e.g. fractals and anything chaos theory) are the escape.
[1] https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Dichotomy_p...
Sure. The point is the gedankenexperiment proves nothing. We don't need to "[record] an infinite amount of information" to encapsulate the infinity between any pair of real numbers.
Statements were made that shielding would improve after Ver 1.0 .. it got worse. Statements were made that sats would go low power over quiet zones, they do not.
Returning to your erudite point "and stuff"
The NASA Cosmic Background Explorer (COBE) satellite orbited Earth in 1989–1996 ...
Inspired by the COBE results, a series of ground and balloon-based experiments measured cosmic microwave background anisotropies on smaller angular scales ...
The sensitivity of the new experiments improved dramatically, with a reduction in internal noise by three orders of magnitude.
Hmmm, it appears the ground based results were a dramatic improvement over the sat based data.
[0] https://www.physicsforums.com/insights/hand-wavy-discussion-...
>> Just because you can't record something...
>>> Who said anything about recording?
Depends on what you're measuring. To illustrate why that isn't a facetious response, consider the difference between 'measuring' pi, 'measuring' a meter and 'measuring' the mass of a proton. (Or, for that matter, the relative mass of three of something to one of it.)
Pick your method. It’s the ratio of a circle’s circumference to its diameter.
I think it's reasonable to say we can't truly measure pi, though.
And you can neither know nor measure a random real.
Jorge Borges' way of telling a story as analogy is beautiful and simple.
It takes the resources of the universe to simulate the universe.
The electron might be smaller. Its diameter is known to be smaller than 10^-22m, but could be much smaller than that.
Further below the Planck Length, there are strong indications that the universe isn't continuous -- it's discrete. That there's an absolute limit to precision, something really quite analogous to a pixel. This elementary length could be somewhere around 10^-93m.
There are indications discrete space is plausible. It's actively debated.
There are also strong indications space is continous, e.g. Lorentz symmetry. (This was recently the death knell for a branch of LQG.)
Hm.
Momentum space being compact does seem weird..
Of course, if rather than a discrete group for space, you just have a discrete uh, co-compact(? Unsure of term. Meaning, there is a finite radius such that the balls of that radius at each of the sites, covers the entire space [edit: “Delone set” is the term I wanted.]), uh, if you take a Fourier transform of that lattice…
Err… wait, but if the lattice is a subgroup, how does the Fourier transform relate to…
I think the Fourier transform of a Dirac comb is also a Dirac comb (with the spacings being inversely proportional) If you multiply the Dirac comb by something first… Well, if you multiply it pointwise by e^(i x p_0 /hbar) , then the Fourier transform will have whole thing shifted by p_0 , and this is periodic in (width of the spacing of the comb in momentum space)
So, if you consider all the pointwise multiples of a Dirac comb in position space (multiplying it by arbitrary functions), then I guess the image of that space under the Fourier transform, is going to in some way correspond to functions on S^1, I guess it would be functions periodic in the width of the comb in momentum space.
So, if instead of a regular comb, you jostle each of the Dirac deltas in the position space comb by a bit first (a different random amount for each)… I’m not sure quite what one would get…
The operative word being "seems". Position and momentum (and indeed real numbers in general) are mathematical models that predict observations. But the observations themselves are the results of physical interactions that transfer energy, and those can only ever be discrete because energy is quantized.
Maybe one can make the argument that position itself is quantized (thus the position of the mirrors can not be varied continuously), but we do not have experimental reasons to believe space is discrete (and quantum mechanics does not require it to be discrete). And while it is pleasing to imagine it discrete (it is more "mathematically elegant"), we do not have any significant rigorous reasons to believe it is.
Edit: Moreover, if you want to describe (in quantum mechanics) the interaction between a finite system and the open environment around it, the only way to get a mathematical description that matches real-world experiments is to have continously parameterized energy levels for the systems making up the open environment. If you assume that only discrete values are possible, you will simply get the wrong result. Most quantum optics textbooks have reasonably good discussion of this. E.g.:
Quantum Optics by Walls and Milburn
Quantum Optics by Scully and Zubairy
Methods in Theoretical Quantum Optics by Barnett and RadmoreYou're assuming spacetime behaves like the set of reals (something with cardinal ℵ1, if you accept the continuity hypothesis), an object that even if you stay confined within the bounds of pure mathematics, behaves in very, very weird ways.
It may be that spacetime at small scales maps better to a different kind of mathematical object and not even a grid-like one.
Edit: My understanding is that all bodies are the size that they are because the inner/outer pressure equalizes, and this has many equilibriums based on the makeup of the body. Black holes are the ultimate degenerate last-stand where the make up is basically raw "information" which cannot be compressed any further while allowing said information to be recovered, which seems to be a fact of our universe. And it just so happens that the amount of information is proportional to the surface area of the black hole rather than its volume, which is probably a statement about how efficiently information can be compressed in our universe. One dimension is redundant?
The surface of space doesn't require something in a higher dimension pushing it out. That such an object may appear to have internal volume from our perspective doesn't need to be any more real than the apparent depth behind a mirror.
As you approach the event horizon, your frame of reference slows asymptotically to match that of the black hole while the universe around you fast-forwards toward heat death. I’d expect the hawking radiation coming out at you to blue shift the closer you got until it was so bright as to be indistinguishable from a white hole. You’d never cross the event horizon; you’d be disintegrated and blasted outward into the distant future as part of that hawking radiation.
For the unfortunate person falling into the black hole, there is nothing special about the event horizon. The spacetime they experience is rotated (with respect to the external observer) in such a way that their "future" points toward the black hole.
In a very real sense, for external observers there isn't really an interior of the black hole. That "inside" spacetime is warped so much that it exists more in "the future" than the present.
Professor Brian Cox also says that from a string theory perspective there isn't really an inside of a black hole, it's just missing spacetime. I tried to find a reference for this but I couldn't find one. Perhaps in his book about black holes.
I'm no physicist so happy to be corrected on any of the above!
This is from a simplified model using black holes with infinite lifetime, which is non-physical. Almost all textbook Penrose diagrams use this invalid assumption and shouldn't be relied upon..
Fundamentally, external observers and infalling observers can't disagree on "what happens", just the timing of events. If external observers never see someone falling in, then they didn't fall in.
* generally considered a large scale fraud,
* perpetrated by (UK's Professor Brian) cox
Most that I know would say that it was disapointingly too big and too general to make specific predictions tied to this specific universe we occupy, although it had early promise.
Brian Cox didn't even make the wikipedia page so its difficult to claim he had any major role in perpertaring it as a large scale fraud.
I am, of course, joking but she posts this sort of easy and empty clickbait.
I don’t think that not being able to communicate your results makes it not scientific.
Falling "through" a hologram on the surface would be physically indistinguishable to the person falling from falling into a volume.
Space-time is not Euclidean geometry under GR.
We don’t know this. It has been as far as we’ve measured. But there are compelling reasons to at least consider discrete spacetime.
The former is the boundary, the latter is the interior + boundary. One of the great arbitrary naming conventions of math.
The sum of an infinite series can be finite [1].
[1] https://www.mathcentre.ac.uk/resources/uploaded/mc-ty-conver...
Everything is infinite if we think this way.
The whole thing seems like some over excited marketing person enshittifying the literal idea of static pages of informative just to make something "new".
I'm sorry you have issues but I'm glad the world doesn't cater to a single individual's issue.
I can't swim because of a whole in my ear drum from when the Nun at the free clinic my poor mother took me to popped that bad boy with a enthusiastic squeeze from an ear syringe and my tinnitus rings like a son-of-a-bitch when I wear ear plugs but I don't demand they fill in every swimming pool with concrete. I just walk by on those hot summer days wistfully jealous of the guy doing a cannonball and the lady doing the hand stand thing where your feet are in dry air but your head is 2 feet below the water level.
The analogy is ridiculous, yes. As it is ridiculous to build such a website that disabled people cannot possibly read. You don't have to make it perfect for them, just don't make it impossible.
(Saying this as someone who's read Kant twice and agrees with most of what he claimed. Outside his taste in music.)
I assume you mean the Critique of Pure Reason? Kant's Oeuvre is quite vast, though it wouldn't be unreasonable to have read the 3 critiques twice.
>What would Kant add to this discussion that the physicists in the article haven't considered?
Kant himself, I'm not sure, but its his model of the cosmos that we employ today, and spatio-temporality is a development out of his critical philosophy, especially his aesthetics. If you want to break space and time out of spatiotemporality it helps if you are familiar with the metaphysical undergirding of contemporary physics, since we have not treated them as separate since Einstein, even though Kant originally kept them as completely separate intuitions and did not seek to unify them but only to try and see what happens when they are set in relation. That is to say that spatiotemporality is, if we are being good Kantians, an entirely negative, transcendental view of space and time since it does not appear at the level of the senses but rather as an abstraction from them. But if we treat the second-level abstraction as real then we are bound to make errors about the empirical world, as returning to the critical project would, I believe, greatly help in re-evaluating our empirical methods.
Is this actually experimentally confirmed?
That supposes in particular that general relativity is still a valid theory at these minuscule scales, something that I believe has never been experimentally verified.
If general relativity's equations do not work at the planck scale, we know strictly nothing about black hole formation.
For those who aren’t in the know physics is in a crisis where huge portions of theoretical physics are turning out to be complete nonsense.
The fundamental challenges these experiments (and others) surface is a deep challenge to the traditional narratives of Materialism or 'Physicalism' as our understanding of what existence is. In essence science and human knowledge has lept forward technologigcally over the past 400 and esp the past 100 years because we started assuming the world was physical in nature, material and metaphysically, ie that it reduced to fundamentally physical things we could quantify and measure.
Yet, the older I get the more inclined I am to believe in some form of Idealism.. Not only in Idealism but I'm leaning towards the belief that some kind of fundamental universal Consciousness is the only fundamental property or baseline to the universe or to existence.
Time and Space is not fundamental. Locality isnt true.