There is an even simpler thought experiment you can do to reach this conclusion: consider what the result of measuring anything to an infinite precision could possibly look like. It would require somehow recording an infinite amount of information. How would you do that, particularly when you take into account that everything you can interact with to make an information storage device is subject to the Heisenberg uncertainty principle?
> consider what the result of measuring anything to an infinite precision could possibly look like. It would require somehow recording an infinite amount of information
This is Zeno's dichotomy paradox [1]. Finitely-defined infinitely-complex systems (e.g. fractals and anything chaos theory) are the escape.
Division? Our productorial sect believes the universe does not have such a useless operation. Multiplication by fractions is the true implementation of the NaN one!
> a much simpler escape: That space is ultimately discrete (i.e. that there's an elementary length) rather than infinitely continuous
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.
More expensive, harder to maintain and keep current, and a tangent to the core matter; Starlink satellites leak radiation and could be shielded, Starlink satellites could be {switched off | turned low} off over Quiet Zones but are not.
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.
As of 2024, Xuntian is scheduled for launch no earlier than late 2026 on a Long March 5B rocket to co-orbit with the Tiangong space station in slightly different orbital phases, which will allow for periodic docking with the station.
Leaving aside the fact that an optical telescope isn't a microwave array nor is it a Square Kilomtre Array of radio telescopes with each component larger than your example ...
Putting an instrument in orbit has all the costs of development of a ground based instrument, additional costs to space harden and test, additional costs to lift, limited ability to tune, tweak or extend when in orbit, hard constraints on size and weight, and other issues.
Xuntian allows for periodic docking, sure. How will this not be more expensive and limited than (say) walking | driving out daily or weekly to much lager instruments on the ground?
This band of electromagnetic radiation lies within the transition region between microwave and far infrared, and can be regarded as either. )
> Putting an instrument in orbit has all the costs of development of a ground based instrument, additional costs to space harden and test, additional costs to lift, limited ability to tune, tweak or extend when in orbit, hard constraints on size and weight, and other issues.
Who is to say they won't pull a Space-X, maybe even overtaking it, going fully reusable?
Which allegedly lowers the costs, giving more economically access to space and lessening the constraints on payloads, while giving all the advantages of being in space?
So .. all the cost, time, and resources of building an instrument on the ground.
With the additional cost of lifting it to orbit, the additional cost of difficulty of in orbit maitainaince, and the additional weight and dimension restraints of going to orbit, the additional costs of over designing to harden for space and limited access.
Yes, there are advantages to being in space. They vary by application.
That aside it's still cheaper to build an instrument or instrument array that's deployed on the ground.
Unconvinced. Because building the whole system, not some isolated dishes somewhere amounted to 1.3 Billion EUR, operating it up to 2030 adds another 0.7 Billion EUR. 2 Billions. Chump change for sure.
Now we can compare that with the JWST and typical cost overruns in american boondoggle style, or look at the latest shining star, EUCLID. Just 1.4 Billion EUR for the latter.
Then there was GAIA at about 740 Million EUR, with the orbiting article at 450 Million EUR alone, plus another 250 Million EUR for the data-processing org.
All of these with more or less conventional rocketry, and not co-orbiting anything for more easy maintenance and upgrading.
My gut feeling tells me we will have cheaper and more reliable access to space, with larger payload capacity, necessitating less 'origamics' for the space parts, and that chinese concept seems sound, too. Very much so, in fact.
How much that will cost I have no clue.
But again, if something like this is becoming reality, no matter by whom, some former assumptions about cost, feasibility (at all, because payload weight and dimension constraints are relaxed, needing less 'origamics') will have to be rethought.
That was my point, in general. Not limited to any special application.
Sure, when we get there again, can make regular trips, and have consequence free energy to burn that'd be great.
In the interim, and as a general rule for all private entities, it'd be nice to not pollute the commons with unnecessary discharges and sparkles and to carry through on pinky promises to maybe do something about that.
If it were not so you could encode an arbitrary amount of information into the specific length of a one dimensional object. It would be like a physical Taylor series, but since you can go arbitrarily small you can encode arbitrary coefficients. In fact, if you had a physical disc you could encode everything at every point along its circumference. Which is, like, everything squared or something.
There are a large number of continuous physical quantities, not only length (though all continuous quantities are dependent in one way or another on space or time, which are the primitive continuous quantities), and the reason why you cannot encode an arbitrary amount of information into a specific value of such a quantity is because it is impossible to make an object for which such a quantity would have a perfectly constant value. All the values of such quantities are affected by noise-like variations so you could store information only in the average value of such a quantity, computed over some time and any such average would still be affected by uncertainties that limit the amount of information that can be stored.
One of the most constant lengths that have ever characterized an artificial object has been the length of the international prototype meter kept in France and used to define the meter until 1960. To minimize the length variations, that meter bar was made of platinum-iridium alloy and it was measured at a temperature as constant as possible.
Despite the precautions, which included gentle removing of the dust and handling with soft grippers, the length of that meter bar fluctuated continuously. Even if it was attempted to keep a constant temperature, very small fluctuations in temperature still caused thermal expansions and contractions. Every time the bar was touched, a few metal atoms were removed from it, but other atoms from the environment remained stuck to its surface, changing the length.
All these continuous variations have nothing to do with the possibility of the space being discrete, but they limit the amount of information that can be stored in any such value.
For now there exists absolutely no evidence about the space or time being discrete and not continuous. There have been attempts to make theories based on the discreteness of the space and/or time, but until now they have not provided any useful result.
No, this is a wrong argument. We can specify arbitrarily low temperatures by hypothesis, obviating the objection. If you want to get pedantic you could note that measuring something that is, say, 10^-30m is unphysical - not even laser interferometry gets that small, or anywhere close. However, given that the argument uses a counter-factual, you'd have to extrapolate all the ways that would affect apparatuses.
Instead, my way is simpler by generating an absurd result that if you could build and measure a thing to arbitrary precision you can encode infinite information into it. This is enough for me to reject the counter-factual without going through the messiness of thinking through hypothetical realistic experiments.
The one interesting place to consider is at the Schwarzchild radius of a black hole, where presumably information accumulates to an absurd degree, monotonically over time. I don't really know enough about it to comment intelligently, so I won't except to note its existence.
Another simple escape: space is a mental category. It's not a feature of reality, it's a requirement for representing the world to a conscious subject.
The Schrödinger wave-function is expressed in a unit which is the square root of an inverse cubic meter. This fact alone makes clear that the wave-function is an abstraction, forever hidden from our view. Nobody will ever measure directly the square root of an inverse cubic meter.
Freeman Dyson, Why is Maxwell’s Theory so hard to understand?
Sorry, my mistake, I was distracted when I wrote that reply. Yes, I did write that, but it's not actually essential to the point I was trying to make, which was: what could the result of measuring anything to an infinite precision possibly look like?
> what could the result of measuring anything to an infinite precision possibly look like?
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.)
By repeatedly throwing a needle on a striped pattern: [1]. Obviously, you will need an infinite number of throws for an infinitely precise measurement of pi.
That would affect only a few borderline trials and would average out with subsequent throws. It would be much more worrisome that the length of a needle or the width of a stripe is not infinitely precise, that would consistently affect all the trials.
Considering that we don't know the value of pi (not that we could write it out nor read it), I'm not sure your definition of "measure" is the same as mine or most people's.
Hmm, I should say "the numerical value of pi in base 10" (or really any rational base), even if we were to weaken that with the qualifier "a to arbitrary degree of precision".
We know pi in the sense of "a unique real number satisfying many useful properties".
Isn't "3.14" pi to an arbitrary degree of precision? Or am I misreading that.
> We know pi in the sense of "a unique real number satisfying many useful properties".
We know it a lot better than that. We have efficient programs that output the numerical value of pi for as many digits as you want.
There's a bunch of real numbers we can identify that are far harder to make use of or approximate, and don't have easy exact description of their value.
You can calculate or 'measure' an arbitrary approximation of that ratio by various methods, but calculating all of it takes infinite time, which I don't have and thus can't do it.
I think the Pythagoreans had the same silly crisis about square root of two that you have about the real-valued measurements. And the solution, I believe, would be the same: there simply are two physical things with lengths that relate to each other exactly as sqrt(2) to 1.
So, how would result of measuring e.g. length of something to an infinite precision look like? It would look like two particles that are kept at rest relative to each other; the distance between them is the measured distance. Whether this distance has to be commeasurable with the Planck scale or not is an interesting question but it really can go either way.
And how do you measure the length of a burning rod (that's moving past by you at a considerate speed) in the face of relativity of simultaneity? I guess it's impossible, and so the very concept of length must be meaningless.
To actually try to answer your question: I don't know. But that's just me; and ain't there some interesting experimental setups with super-cooled crystals? In any case, inability to imagine something is hardly a convincing proof of anything.
In some cases it is. Do you think perpetual motion machines are impossible, or is that just a matter of our inability to come up with a sufficiently clever design?
How does this not break the foundations of quantum theory? For example the Heisenberg uncertainty principle itself implies that the conjugate of a discrete variable must have a continuous spectrum. Thus if there are no continuous variables, there can be no discrete ones either. Either this or we need to throw out one of the variables and call it non-physical/observable -- and yet it very much seems like both position and momentum are things.
The Pontryagin dual of a discrete (locally compact abelian) group is a compact group, and the Pontryagin dual of a compact abelian group is a discrete (locally compact abelian) group…
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…
> it very much seems like both position and momentum are things.
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.
Energy levels in simple finite systems are indeed quantized, but this does not mean we can not make the energy quanta be continuously parameterized. For instance, if your system is two mirrors facing each other and you are using the quantum description of the light trapped between these mirrors, you can pick any real value for the energy separation between levels of this system simply by continuously varying the distance between the mirrors.
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 Radmore
> this does not mean we can not make the energy quanta be continuously parameterized
Sure, but can you measure those continuously-parameterized energies? I don't see how.
Continuously parameterized energies are no different from continuously parameterized space. They are part of the mathematical model we use to make accurate predictions, but we have no direct access to either, and (AFAICT) we cannot possibly have access to them because that would violate the no-cloning theorem.
I am not sure I follow. Here is my attempt to respond to what you raised but feel free to redirect me if I misunderstood.
The following is a (simplified, abstracted) way to measure an arbitrary energy value.
1. Set the system up so that the carrier of the energy is a photon (e.g. let the two-level system decay[1] or use some form of transduction or whatever).
2. Send that photon to pass by two semi-transparent mirrors at a certain (continuously parameterized) distance between each other.
3. If the photon passes through both mirrors (as detected by a photon detector at the other side), it means its energy is equal to some known constant divided by the distance between the mirrors. If it does not pass it means it has a different energy.
4. Repeat the experiment many times as you slowly vary the distance between mirrors.
I guess in point 4 there is an issue that you need to repeat the experiment with a new realization of your photon each time. Does that have bearing on the initial point being discussed?
You are probably seeing this at this point, but just for completeness: this technique is no different from tuning a musical instrument with a tuning fork.
I papered over some details about whether we want to detect transmission or reflection and exactly what type of transparency the mirrors need to be, etc.
[1] Funnily, the usual way in which someone would prove that decay can happen at all does rely on the existence of a continuous spectrum of energies. This is the same topic I raised above when citing Quantum Optics textbooks.
> this technique is no different from tuning a musical instrument with a tuning fork.
Yes, I get that. But there are two problems. First, you cannot tune an instrument precisely. Precise tuning of a real musical instrument isn't even a meaningful concept because any wave with finite temporal extent has non-zero bandwidth. It's the same with energy. The exact same uncertainty relationship between frequency and time produces the Heisenberg uncertainty relation between energy and time, so it is not possible to produce an isolated photon at a known time with a known energy. The best you can do is produce a lot of photons so you don't have to wait forever for one of them to arrive at your detector. So the problem with the setup you describe is that in step 2 the concept of "that photon" is not well defined.
Second...
> I guess in point 4 there is an issue that you need to repeat the experiment with a new realization of your photon each time.
Yes, that too. But you need to do more than that: in order to get a meaningful result you'd need to produce photons with the same energy, i.e. you'd need to use a laser or some other kind of tuned cavity. But it is not meaningful to identify individual photons emitted from a laser because they are identical bosons.
> It would require somehow recording an infinite amount of information
You'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.
The article made the wrong statement. The thought experiment isn't that you can't measure length with infinite precision. It's that you can't measure length with precision better than the Planck length. No infinities are involved here.
Integers have perfect precision, but finite storage. For example, pi is infinite information and digits in float, but finite when represented as a single symbol
The Planck Length is a practical limit to the precision you can possibly attain in space.
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.
The attainable precision is limited to much lower values by much simpler causes.
The theory that the Planck length has any significance is just a speculation.
Nobody knows how interactions would behave at distances so small and there are no known methods that could compress anything into volumes so small. There is no basis to believe that extrapolating the behavior from normal distances and sizes to the scale of the Planck length is valid.
There are pure speculations that are interesting, but in my opinion any speculation about the Planck length is not interesting, because nobody has been able to formulate any prediction based on such a speculation that can be verified in any way.
Most speculations about the Planck length are made by people who obviously know very little about the meaning of the so-called fundamental constants or of about the significance of the useful natural units for physical quantities, to which the Planck length does not belong.
The Planck length is just one way to express the intensity of the gravitational interaction, i.e. an alternative to Newton's constant of gravitation. Its numeric value does not say anything about any other physical phenomena.
The numeric smallness of Planck's length is just an expression of how weak the gravitational interaction is in comparison with the other interactions. It does not have any other significance.
Im my murky conception of reality, the existence of Planck limits indicates that reality is discrete, and that therefore quantum uncertainty must exist.
For example, I pound the picnic table. Presumably this is somehow transmitted thru the entirety of the Earth, or at least thru a tiny portion of it. But is there a cutoff ? Where is the cutoff ? Where is the effect simply too small to "register" in any conception of reality ?
I am not sure what the thought experiment is here — it is more like two facts, one about the Planck scale (and things break there) and the other about a black hole (its information is proportional to its surface).
However, there are deeper things around. Seth Lloyd suggested that we use information density to derive general relativity from quantum theory:
https://arxiv.org/abs/1206.6559
Not only are these not thought experiments by most definitions, this is also not really an article by most definitions. It's as if the author had a few interesting yet unrelated thoughts, scribbled them down and covered up for the lack of depth with fancy illustrations and transitions.
They're not unrelated thoughts. The author is describing current mysteries in physics related to the edges of what we could theoretically measure.
The article actually seems clear and straightforward to me. I'd only add that I wish there were links at the end regarding what scientists are proposing right now for resolving those mysteries.
The (what very much feels like an) assertion that "If a collision concentrates enough energy in a small enough region, the particles form a black hole" seems very much rabbit out of a hat.
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.
Besides the silly, but inevitable HN complaints about the format of the webpage presentation, (great presentation btw)
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.
> 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.
thats interesting, but im curious what the basis for that thought comes from?
Did quanta get bought by Forbes or something? I seem to recall they had a lot more informative articles than whatever this was. Further, there is no indication on how the first two postulates/statements force one to conclude the latter. Also? The whole format of the thing screams "LOOK AT ME". This is a very weird... thing (I hesitate to call it "article") coming from a site that previously had some interesting content (in the actual sense of the word, not the current colloquial sense)
Is the problem the author can't let go of not understanding? That they need everything to be, for lack of a better term, quantifiable? That there must always be no boundary to our ability to measure? Do they demand an answer to why there is a limit to what we can see at the end of the universe (beginning/surface)?
Is this something AI shat out for clicks? Did they fire actual writers at quanta? Did they smoke a bunch of DMT? Are you ok, quantamagazine? Do you need us to call for help? I'm a bit annoyed that I had to read that, thinking there would be some point, that the top thread was exaggerating, but they weren't.
One of my favorites is a different interpretation of the events happening inside a black hole being inscribed in its surface: that there is no inside and the events happen at the surface, which seems totally normal because spacetime is so extremely stretched there things don't realize they look like a 2D surface from outside observers.
The observational limits described here remind me very much (albeit that I read it 40 years ago) of Blood Music by Greg Bear. The ending (as I remember it) has nano-scale intelligences observing the universe so closely that the fabric of spacetime starts buckling under the strain.
I still don't understand why a black holes needs an inside at all. If they are equivalent to their surface then why not dispense with having an interior and just be a surface?
Why isn't the surface smaller then? Probably something inside is pushing out? It's full? Also on the way to a black hole bodies clearly have insides. Do they somehow evaporate the moment a black hole forms?
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?
"Pressure" as a concept doesn't apply to black holes. They are the size they are because of their mass. The bigger the mass, the larger area where their gravity is so great light can't escape. Scientists model black holes as only have a mass and a spin on the inside because that's all the external universe cares about. Information being inscribed on the exterior is an artifact of tike dilating as an object approaches a black hole, iirc.
> Why isn't the surface smaller then? Probably something inside is pushing out?
Hoberman spheres expand and contract via forces that act only along the structures that make up the surface, and this is a simple classical object. I don't see why a more exotic physical object like a black hole couldn't only have properties defined by its surface.
> Why isn't the surface smaller then? Probably something inside is pushing out?
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.
Agreed. Couldn’t black holes warp spacetime to the extent that there is no such place as “inside”? Time dilation is infinite at the event horizon, after all.
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.
The time dilation at the event horizon is infinite for an external observer. It appears that the person falling into the black hole slows down and never passes the event horizon. They redshift until you can't see them anymore.
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!
> For the unfortunate person falling into the black hole, there is nothing special about the event horizon.
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.
> 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.
This isn't true. As long as the two observers can't communicate with each other, they absolutely can have different results. To put it in simpler terms, the requirement of physics is that an experiment has a unique result according to some rule, but different experiments can have different results even if they break our intuitions.
So, if you measure the position of a particle falling towards a blackhole, you will see it disappear at the event horizon, and perhaps be radiated out later as Hawking radiation from that same event horizon. If you measure the position of the same particle while you yourself are passing through the event horizon, you will it will record no special interaction and see the particle moving completely normally. Since you can't perform both experiments at once, and you can't relay any data from one to the other, there is no contradiction.
This is just another case of a duality in physics, similar to how some experiments measure electrons as point-like particles completely localized to a certain place, and others measure them as waves spread out over a very large area.
If that were true, then black holes would appear as extremely bright balls of red-shifted radiation, as all particles whose trajectory ever moved towards the center of the black hole would still be visible. This is obviously not true, black holes appear as completely black objects that might have an extremely bright ring or halo of matter orbiting.
Sure, timing of the events, but infinity kind of breaks it - if external observers don't see someone falling in, then they didn't fall in yet, and if external observers see that falling in takes an infinite time (as in this case), then that is on some sense just a difference in the timing of events - however, from the observer perspective where that thing takes a finite time, they will also get to observe what happens afterwards.
Black holes don’t live forever. In principle, an external observer could watch you until the black hole evaporates. As mentioned above, if they never saw you fall in, then you never fell in. GR allows for disagreement on durations of events but not the events themselves.
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.
Laughing at someone who says “hey an idea that isn’t falsifiable isn’t a good theory and certainly not something that any other ideas or theories should be constructed upon is I think more serious than not.
There's a theological doctrine called https://en.wikipedia.org/wiki/Eschatological_verification that claims that statements like "there's God" or "there's afterlife" are perfectly fine verifiable scientific statements, except that their verification come after death or Second Coming.
Your comment reminds me of it.
A surface implies an interior, otherwise it's a just a point. A surface is a boundary, by definition there is another side, something that is being partitioned.
I like to picture poking your finger into a loosely knit jumper so that the weave bunches up densely around the outside of a large hole. If you think of an ant walking around on the threads, it would realise that there's an area of increased density. It would also notice that there's a boundary it can't get past, but if you asked it what the topology of the threads are on the "other side" of the boundary it wouldn't be able to give you an answer.
In my mind that is what a black hole is, a spherical hole in the fabric of spacetime with matter bunched up around it in a very thin shell. That's why their area is proportional to their mass instead of their volume, because there is no volume.
The area of the Sun and the Earth and every other self-gravitating body in hydrostatic equilibrium is also proportional to the body's mass. Volumes are weird though: unlike area, relativistic volume can depend on the body's (and the spacetime's) history and composition rather than just the body's mass. In general the spatial volumes inside massive bodies in curved spacetime are larger than in Euclidean-Newtonian space.
The volume deviation is carried in the Ricci tensor
The highest-scoring answer at https://physics.stackexchange.com/posts/36411/revisions is a fairly reasonable attempt to calculate the volume deviation for nonspinning ~spherically symmetric bodies with the masses of the Earth (~ 10^2 km^3) and the Sun (~ 10^12 km^3), compared to the Euclidean-Newtonian volumes. Qualitatively, dropping these symmetries and the uniformity of the matter will tend to make the volume deviation larger.
> there is no volume
The volume deviation becomes enormous for compact (relativistic) objects, and for black holes one has to exercise care in even defining a volume, since naive choices of coordinates will show a divergence. Typically the choice of a 3-space inside the horizon has a time-dependency, and most choices of 3-space will tend to grow towards the future.
Christodoulou & Rovelli's (C&R) approach: https://arxiv.org/abs/1411.2854 ("it is large" for the largest volume bounded by a BH's area should win some sort of award for understatement). https://arxiv.org/abs/0801.1734 (reference [5] of the 2014 C&R paper) takes a slightly different path to the same conclusion.
YC Ong (several other references, and a number of related later papers) has a nice article at https://plus.maths.org/content/dont-judge-black-hole-its-are... The prize quote: "To give an idea of how large the interior of a black hole could become, this formula estimates that the volume for Sagittarius A, the supermassive black hole at the centre of our Milky Way Galaxy, can fit a million solar systems, despite its Schwarzschild radius being only about 10 times the Earth-Moon distance. (Sagittarius A is actually a rotating black hole, so its geometry is not really well-described by the Schwarzschild solution, but this subtlety does not change the result by much.)" And: " These examples show that, in addition to the surprising property that the largest spherically symmetric volume of a black hole grows with time, in general, the idea that volume of a black hole grows with the size of its surface area is wrong. In other words, by comparing two black holes from the outside, we cannot, in general, infer that the "smaller" black hole contains a lesser amount of volume. "
The area of a Schwarzschild horizon is straightforward to define, and unique for constant mass. (Procedurally you could count the number of unique tangent planes at r_{schwarzschild}, but there are other ways of arriving at the area).
If your sweater "weave" represents a set of orbits around the black hole and your ant free-fall along those rather than walk, you are getting close to a solution of the geodesic equations for a black hole. A free-falling ant will stick quite firmly to geodesic motion around a black hole. However, there are definitely plunging orbits that will take the orbiting-ant inside the horizon, and there is an innermost stable circular orbit (ISCO) that isn't solid like the yarn: a small perturbation of an orbiting-ant there will knock it into or away from the BH. But an un-knocked ant can circle forever.
The ISCO (3r_{schwarzschild} for a Schwarzschild black hole) is quite a lot of ant-lengths above the horizon of a BH (2r_{schwarzschild}). Spinning black holes have a narrower gap between the ISCO and the point of no return.
The point of no return for a spinning hole is just that: the ant can't backtrack, but will continue moving "forward" from there, and for a massive enough black hole it could do so for an hour or more before it feels the discomfort that precedes spaghettification. The "no drama" conjecture holds that the freely-falling ant won't even notice crossing the point of no return, although astrophysically it is likely to have noticed things falling inwards on different trajectores even above the point of no return (at ISCO around an astrophysical black hole the ant has a good chance of being knocked by something on an intersecting trajectory).
> fabric of spacetime
Misleading terminology. It's not a substance. Spacetime is nothing more than a collection of possible trajectories, and none of them needs to be realized. (Our universe has an enormous number of unrealized trajectories compared to ones on which real bodies move).
> bunched up in a very thin shell
The "thin shell" is just a set of points of no return, and for an astrophysical black hole where exactly each point is can be rather fuzzy since it depends on the outside universe which is filled with moving ants (and galaxies).
The interior contains a singularity, which may as well be the entirety of the interior. Maybe it has a "degenerate interior", which is very different than a region of space.
I'm not a topological expert, but I'm pretty sure you can have a surface without an interior. A unit sphere would be a good example of a surface without an interior.
But physicists already made spacetime redundant by dividing it back to space and time. This was started by Dirac who restated general relativity with Hamilton formalism. The slicing of spacetime was completed in the sixties with ADM formulation. Also we know spacetime does not exist in practice because when we say "universe is expanding" we mean "space is expanding." It makes no sense to say spacetime is expanding.
Your comment is divorced from the coordinate freedom of general relativity.
In any spacetime you care to do an ADM split on, there are an infinite number of real-valued smooth scalar fields whose gradient is everywhere non-zero and timelike available to serve as the coordinate time.
In the standard cosmology the at-rest isotropic and homogeneous distribution of matter provides an obvious coordinate time function, but physics still has to work for other inertial and accelerated observers, so there is nothing preventing anyone from using a non-comoving observer's proper time in the ADM split.
Nits:
* Hamiltonian formulation of general relativity
* ADM formalism
The expansion is in the metric, and most visible (and most amenable to interpretation as an expansion of space) when using comoving coordinates. However, we are allowed to work in any system of coordinates, and when we do a general coordinate transform, we lose the interpretation of the metric expansion as an expansion in space.
("We see in both [Milne & de Sitter] cosmologies that the interpretation of redshift as an expansion of space is dependent upon the coordinates one chooses to calculate z." -- https://academic.oup.com/mnras/article/422/2/1418/1036317 final sentence in §3.4 de Sitter space).
The standard cosmology's FLRW spacetime (and also de Sitter space, where the vacuum constant positive scalar curvature makes for an easier-to-understand expansion history) is time-orientable. There are more points in spacetime in the future direction from an arbitrary point anywhere in the entire spacetime, than in that point's past.
However, the real distribution of matter is in our universe lumpy, as is easily demonstrated right here on Earth. Standing on the ground you can tell that locally there is neither isotropy nor homogenity (you can see quite far up into the sky, but not so far into the ground). Moreover, there are differences in isotropic pressure, convection, heat conduction, and shear stresses between the air and ground, none of which are features of the perfect fluids in the FLRW model. So locally the FLRW metric is not suitable, and since the Earth is very much not vacuum de Sitter is even less suitable. Consequently it should not offend anyone to read that Manhattan isn't undergoing cosmological expansion. Most things within ten kiloparsecs of here are gravitationally collapsing. It requires coordinate contortions to interpret interplanetary or interstellar space in the Milky way as expanding, and switching to different systems of coordinates will blow up that interpretation.
A "swiss cheese" universe with collapsing vacuoles in an expanding cosmology reflects that it's only when we go from ~kpc length scales to ~Gpc length scales that the distribution of matter behaves enough like perfect fluids to allow for an exact solution to the Friedmann equations. The collapsing vacuoles are usually modelled like Lemaître-Tolman-Bondi with a thin shell boundary; this results in a vacuole that time-orientable and has fewer spacetime points in the future direction. "Hole" time functions and "cheese" time functions must be different (hole clocks tick slower as they fall towards the centre).
This is just another proof that spacetime as a real entity does not exist. If there are infinitely many spacetimes, spacetime cannot be the fabric of the universe but it can only be fodder for academic careers. There is one universe but an infinite number of spacetimes. So which spacetime is the true one? None of them. You pick and choose one and write a paper on your chosen spacetime and collect your academic points. Another physicist chooses another popular spacetime and she writes a paper on that spacetime. The whole thing is a joke.
Of course one picks a simplified spacetime and investigate how that works, extracting ways to relate the simple model to actually-observed astrophysical phenomena. Just like how quantum physicists 70 years ago were working with simple models of the weak interaction, comparing their models to tracks in cloud chambers, ticks of geiger counters, or ratios of radioactive elements found in spectral lines.
It turns out that one can knit together simplified models and build up a good description of a real complex system, but this has been known since at least the dawn of thermodynamics, if not since the time of Newton.
Indeed, Nasa and its counterparts have been working for decades with an approximation of the solar system: new bodies inside Neptune's orbit keep being found practically every year. It's not remotely likely that we know all the bodies of the solar system even out to Neptune (much less beyond), let alone their orbital parameters and how those evolve over mere millions of years <https://en.wikipedia.org/wiki/Stability_of_the_Solar_System>. Does that mean publishing the results of studies of long-running models of our solar system "can only be fodder for academic careers"? Even if it spots anomalies that lead to the actual discovery of very dim bodies?
> collect your academic points
The academic points mostly come from being cited by an author poking holes in your paper. Go investigate google scholar.
This is called the academic dialogue. And yes, a variety of scores are kept (e.g. the loathsome h-index).
But I guess you don't care, because you are happy writing obviously ignorant nonsense on hacker news for engagement and upvotes, right?
> There is one universe but an infinite number of spacetimes
There is possibly one unique spacetime that fully describes the universe, but guess what, we simply do not have enough computer power on the planet to validate such a model.
Here's the recent state of the art in computational cosmological simulation, n-body with n in the hundreds of billions:
There are more than a hundred billion stars in this galaxy; there are more than a hundred billion galaxies in our sky. And there are more than a hundred billion particles in a star. And there are lots of motes of dust and blobs of gas between stars. So we're quite a few orders of magnitude too small in n in our n-body simulating to be able to pick out our own universe, exactly described, from a large set of simulations.
We also obviously don't have an infinite number of observations, since neutrinos and gravitational waves are hard to detect at all (and we only see a small part of the frequency space of both), we've only just started having really good views in the near infrared (JWST), our views in X-Rays and gamma rays are fuzzy because of technological limits, and so on and so forth. We are just at the start of https://en.wikipedia.org/wiki/Multi-messenger_astronomy four centuries after Galileo used a telescope to find the four biggest moons of Jupiter. (Incidentally, three moons of Jupiter were just discovered two years ago, because hey telescopes are not all-powerful and all-seeing. Guess how they figured out where to point the Victor M. Blanco Telescope?).
> The whole thing is a joke
Honestly, it's amazing that you aren't embarrassed by how obvious your ignorant contrarianism is.
Write back if you're actually interested in expanding your knowledge rather than mocking people you don't know whose work you know very very very very little about.
Good stuff for a sci-fi novel. Black holes become the spinning hard drive platters of the universe. To preserve the Earth from existential destruction, we must fling it into a black hole.
This takeaway is a variation on an old theory. Perhaps we are already inside a black hole, and the expansion of spacetime is the rate of the black hole's growth in another universe.
I remember as a kid asking how many possible speeds there are between 60 mph and 0 mph. Infinite right? So how does the car get from 60 to stopped when mom hits the brakes?
Fortunately or not, largest artificial accelerators are still not powerful enough to produce artificial black hole.
Sometimes from deep Universe, appear particles with much more energy than achieved at labs, and some theories say, their energy enough to create BH, but have not confirmation with decades observations, may be because scientific method need tens or better hundreds appearances in one place to confirm, but have less than half dozen.
Any black hole should exhibit such weirdness around the event horizon and singularities though. If we had a reconciliation between GR and QM that resolved these issues for gigantic black holes, then arguably we'd also understand small black holes.
I’ve said this so many times now. Contemporary physics would greatly benefit from reading Kant. The extent of his influence on contemporary physics, especially with regard to space and time, is so great and the knowledge of his work so little in the scientific community of today. Almost all the great physicists of the 20th century were familiar with Kantian philosophy and were heavily informed by it.
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.
To be clear, you're suggesting that physisticsts reject general relativity's unification of spacetime because Kant, who obviously had no knowledge of GR nor the empiricism that supports it, did not unify them? Kant's Prize essay also pre-dates e.g. Gödel. That doesn't mean every modern mathemetician must first consider a Kantian slant to their work before rejecting it for well-established and obvious reasons. (Nor that Gödel disproves Kant.)
Deducing that Kant would want us to reject modern science because it's not based on our senses ignores entirely his work as a mathemetician. Kant was, in his own time, a modernist. Not a proto flat earther.
> To be clear, you're suggesting that physisticsts reject general relativity's unification of spacetime because Kant, who obviously had no knowledge of GR nor the empiricism that supports it, did not unify them?
I am suggesting that if someone wants to escape from the current paradigm of physics it may help to understand how it came about instead of wasting a lot of time speculating about what space and time “actually” mean.
And in any case, there is nothing in math that prevents someone from being a flat-earther. If nothing else, set theory and qauntam mechanics has done nothing but flatten our empirical world. Kant was Modern but his work was not, one can read his Opus Postumum as an attempt to reconcile his physics with an intuition that would be capable of bringing about the “feeling of life” that arrives from the experience of natural beauty—which, while very odd, clearly follows from the 3rd critique and the critical project more broadly, unless you throw out the concept of Freedom entirely and all the moral philosophy that follows from it and stay, as some have, in the analytic. But that’s clearly not what Einstein did, Einstein is a Schopenhaurian, he based GR heavily in the Aesthetic, but an Aesthetic devoid of this possible “third” intuition, that of feeling of form, since spatiotemporality annihilates all other possibilities of dimensionality besides space and time. Now what I’m saying is, its not possible for contemporary physicists to critically interrogate their theories without having a solid intellectual grounding in how they came about. Doesn’t mean that someone couldn’t simply come up with something new and brilliant spontaneously, but not by questioning spatiotemporality itself but by developing an entirely new framework that disregards it.
But that’s much more difficult than starting with the basics, right?
Reality is continuous and always changing. Space-time is just our human way of focusing on aspects of reality to understand it. Space-time is about human perception, not the reality we are trying to understand.
Please stop trying to present information in this style of webpage, I am begging you. Besides being an abysmal way to present scientific information, every time someone posts one of these it happens to be a topic I am extraordinarily interested in, but due to disabilities I have, I cannot read it even if I wasn't tremendously annoyed by it.
If you're a reader of Quanta, there's nothing new on this page. It seems like a repackaging of some simple concepts in a pretty web format to attract a less sophisticated audience.
I agree, this is abysmal ux. Doesn't even remotely work on my phone. All those stupid animations literally removing information from my screen before I've had a chance to read it. Drastically reducing the "reading surface" of the actual information attempting to be conveyed. Animations are cool and useful but they too could just be placed on a static page.
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 forget which publication, might have been the new yorker, won a pulitzer prize for a long-form article written in this style. Visually it worked very well (because it was telling a story, not trying to convey information) and the scrolling graphic transitions were gentle enough that I could manage it + reader mode. Since then, it seems like other magazines have followed suit.
I was disappointed to see reader mode wasn't available, and tried to find some other plugin to just show me the text. The couple plugins I tried could not parse it, nor could the text-only browser I downloaded called ViolonCello. (It only renders header and footer text.) It's very frustrating.
I liked the presentation and it worked great on my phone.
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 would be more like a library forcing everyone to swim through a pool in order to read a particular book. And if you complain you have a disability, someone says that the world shouldn't cater to an individual.
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.
The analogy is to stop making documentary films because one cannot see or hear.
Should businesses and academia strive to make information accessible? Yes. Should every piece of information be put into accessible formats, damn the art? I don't think so.
Good lord that was awful to read. Text popped into existence half-off the screen, disappeared just as it was entering the screen, etc. I'm operating on a 15" MacBook with a reasonable-sized window, and yet I had to scroll carefully back and forth to catch the text. And no reader mode with just the text.
"Please don't complain about tangential annoyances—e.g. article or website formats, name collisions, or back-button breakage. They're too common to be interesting."
Appreciated! And it's not that your point was wrong, of course; just the opposite—there are so many articles giving rise to such complaints that we have to try to filter the repetition.
