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.
> 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.
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.
> 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
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.)
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.
> 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.
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?
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!
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'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.
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 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?
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 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.
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.
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.
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.
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.
[1] https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Dichotomy_p...
There's a much simpler escape: That space is ultimately discrete (i.e. that there's an elementary length) rather than infinitely continuous.
> 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.
If space is discretized, we should see "upscaling artifacts" in the CMB, but we don't.
Is there? Planck length isn't a pixel.[0]
[0] https://www.physicsforums.com/insights/hand-wavy-discussion-...
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.
> 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.:
Just because you can't record something doesn't mean it doesn't exist.
Who said anything about recording? What would the subjective experience of measuring something with infinite precision possibly be like?
> would require somehow recording an infinite amount of information...
>> Just because you can't record something...
>>> Who said anything about recording?
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.)
How do you measure pi?
> How do you measure pi?
Pick your method. It’s the ratio of a circle’s circumference to its diameter.
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.
> there are strong indications that the universe isn't continuous -- it's discrete
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.)
It would simply be written down on an infinitely long strip of paper.
You could use a Turing machine tape for the job. I'm told they're stored in the parentheses mines beneath MIT, somewhere near the point masses.
Möbius strip for double surface area....I can practically see the cheese TV comercial
I have similar reasons for not believing that the world that we experience is a computer simulation.
> 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.
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.
Black holes also have a charge!
> 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.
Since when is the surface of the universe that of a hypersphere?
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!
Because if you free-fall into a black hole you can go past the event horizon.
Can we? Is there a way to test this assumption? If not, then it's not science, right?
If you free fall into a black hole you are testing it.
I don’t think that not being able to communicate your results makes it not scientific.
I think the test involves communicating your results. It's the same thing with the afterlife
> if you free-fall into a black hole you can go past the event horizon
Falling "through" a hologram on the surface would be physically indistinguishable to the person falling from falling into a volume.
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.
> surface implies an interior, otherwise it's a just a point
Space-time is not Euclidean geometry under GR.
But it is continuous, at least until you hit or pass through the singularity.
> it is continuous
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.
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.
? It by definition has a radius of 1.
unit sphere != unit ball
The former is the boundary, the latter is the interior + boundary. One of the great arbitrary naming conventions of math.
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 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?
> how does the car get from 60 to stopped when mom hits the brakes?
The sum of an infinite series can be finite [1].
[1] https://www.mathcentre.ac.uk/resources/uploaded/mc-ty-conver...
Not infinite if we take into the account that we have a physical car. Speed many but not infinite steps.
Everything is infinite if we think this way.
Zeno’s paradox.
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.
It's really bad even for me on my phone. The text content fades away before I can scroll it completely into view. No reader mode available.
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".
How could it be made more accessible to you?
They could be regular web pages without the silly scroll animations, just like in the good old days.
Just make it a web page, not a powerpoint presentation.
reader mode supported. sometimes they are sometimes no.
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.
You're a moron if you believe these two things compare even remotely
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.
What would Kant add to this discussion that the physicists in the article haven't considered?
(Saying this as someone who's read Kant twice and agrees with most of what he claimed. Outside his taste in music.)
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.
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.