4 ms·

Below the Planck distance, "closer" ceases to be a meaningful concept. Similarly, distances larger than the size of the observable universe may also be meaningl

Below the Planck distance, "closer" ceases to be a meaningful concept. Similarly, distances larger than the size of the observable universe may also be meaningless.

deleted 1y ago
[deleted]
hnuser123456 1y ago
The co-moving radius of the universe is about 3x larger than the observable universe, but I don't think there's any practical measurements larger than that. We don't know how much is beyond that because potentially a large chunk of the universe is already forever outside our past and future light cone.
kstrauser 1y ago
Why is that? I've heard this before but don't understand what it actually implies. Like, why can't 2 things meaningfully be half a Planck distance apart?
- Nevermark 1y ago
  Imagine that at some small distance, space itself is quantum, so quantized. I.e. at the bottom, space is a discrete graph with incredibly small edges. Possibly very tangled and not even layed out in obvious dimensions over short distances. We don’t know if that is the case. That is only one possibility. But it seems very clear that whatever happens at the Planck distance or lower isn’t simple smooth space as we model it for larger scales.
  - tsimionescu 1y ago
    Unfortunately for this idea, special relativity tells us that Planck length is an observer-dependent phenomenon. That is two objects that are at a distance that is more than the Planck length apart for one observer will be closer than the Planck length for another observer and vice versa. So Planck length can't be a fundamental property of space-time, unless special relativity breaks down at some point even for non-accelerated observers.
    - Nevermark 1y ago
      I would suspect since general relativity would break down that special relativity certainly would. The “relativity” aspect will almost certainly still apply in some way, and still form an emergent basis for the special relativity effects you point out. All of general relativity has to be emergent from the to-be-discovered laws of the underlying small scale structure of space. (I.e. general relativity isn’t wrong, it is just not complete. Similar relationship as with Newton’s Law of Gravity, which was also correct, but breaks down beyond the conditions it covers well, because it was not complete.) The smallest scale is also where we expect more “light” shed on the initial conditions of the universe and potentially the insides of black holes. Two other conditions where general relativity already breaks down.
      - tsimionescu 1y ago
        If special relativity breaks down, so does QFT - since QFT is based on special relativity just as much as on QM.
        Nevermark 1y ago
        “Breaks down” just means our equations don’t know what to say about a situation. It doesn’t that any particular phenomena we understand today will break down. Just we will be able to see richer behavior, that has been there all along, than our models cover today. And so be able to understand more conditions than we do today. And perhaps new capabilities to engineer things than we have today. Obviously quantum field theory, as it exists today, breaks down at the Planck distance too, since it can’t tell us what is happening at smaller distances either. This isn’t the least bit controversial or surprising. It just means that even with both theories, we can’t explain everything yet. When we do have an accurate theory of the fine structure of space and time, it will also be a theory of the fine structure of fields. Since space-time is integral to both theories. It may even be the long sought after unification. But for distances much larger than the Plank distance, the fine structure theory will still simplify into the GR and QFT we have today. Just as GR under many conditions we encounter every day, further simplifies to Newton’s Law of Gravity.
- AnimalMuppet 1y ago
  Imagine the universe is made out of graph paper, with only the points of intersection of the lines being actually "real". That is, space is actually discrete. If that is true, then you cannot meaningfully talk about things being "half a square" apart. People (some people) think that the universe really is that way, at the Planck distance. Actual experimental confirmation is somewhat lacking at this time...
  - tsimionescu 1y ago
    More importantly, this idea doesn't work in the context of space dilation. Per special relativity, the distance between objects is arbitrarily different for different observers, so any grid you draw will be wrong for me if I'm moving at a different velocity than you. This is especially bad because it doesn't just depend on the magnitude of the velocity, but also the direction - space is compressed in the direction of motion. So two observers moving at an angle to each other will have very different views of the grid.
- daxfohl 1y ago
  The only reason I've heard that isn't super handwavy is that measuring it would require a wavelength with enough energy to create a black hole. IDK if that's true or not, and IDK if that also means the distance doesn't exist or if it's just not measurable. I've also heard that there's nothing special about planck length other than it being universal constant that we and any conceivable aliens would agree on as a standard of measure. So, idk.
- griffzhowl 1y ago
  It's just that it's physically impossible to measure such small scales. To probe a smaller scale you have to put more energy into a volume (roughly, because you have to force particles closer together), and at some point you have to put so much energy into such a small volume that it becomes a black hole, then any more energy you put in will just make the black hole bigger. So there seems to be a fundamental limit to how short a scale we can probe, and therefore we can't give a physical meaning to smaller scales. Nima Arkani-Hamed talks about htis in a few lectures online. This is just according to our current theories, and you don't need any speculative ideas about granularity of space. Mathematically, there's no problem in considering arbitrarily small length scales, because current theories are based on continuous space and time dimensions, but since we can't give physical meaning to small length scales, that's a clue that a more fundamental theory will somehow not be based on continuous space and time
  - daxfohl 1y ago
    Here's a summary of my layman's understanding, which could be wrong. To my understanding there's nothing special about it except once you get to quantum field theory, and specifically spin-2 particles, which are the ones that hypothetically carry gravity (i.e. gravitons). (They're hypothetically gravitons because mathematically they result in conservation of the "stress-energy tensor", which is the same thing that Einstein's field equations give. And this isn't coincidence; it's because both are second-order field theories preserving Lorentz transforms aka special relativity). But notably if you only get through non-relativistic quantum mechanics, there's nothing special that happens at Planck length. Planck length becomes special in QFT because at Planck length, the feedback (my force on you affects your force on me affects my force on you etc) of the quantum field mathematically explodes in something called "UV divergence". Notably, this also happens for other force carriers, not just gravitons, but a mathematical trick called Renormalization fixes that. Renormalization is based on shady techniques like assuming the sum of all whole numbers is -1/12. (IIUC this is a fairly straightforward pure mathematical result from complex analysis, required to ensure consistency of Fourier transforms for infinite sequences, known as analytic continuation / Riemann zeta function. Of course it makes no sense that nature should behave that way, but one day some physicists thought "let's try this weird math" and it matched experiments). However that technique only works for lower-spin fields (E&M, weak, strong) because the feedback is linear, hence sum(1+2+3+...). But in spin-2 fields the feedback is (quadratic? exponential?), and the same trick still gives an infinite result. Ultimately one could say this is the only thing standing in the way of a complete theory of quantum gravity. If we could get the math for gravitons not to blow up at tiny scales, we'd be done (experimental verification notwithstanding). String theory is one attempt: "Let's say there are no point particles, only strings, and this problem goes away". Other approaches exist too. But ultimately right now, there's no way to say for sure whether sub-Planck exists, doesn't exist, exists in some ways but not in others, or whether all of physics is wrong and we have to start over. A quick addendum: Planck energy is approximately the chemical energy in a tank of gas. Planck mass is about that of an amoeba (so an antimatter bomb made out of an amoeba would explode like a tank of gas (Hiroshima was 0.6 grams of mass), a photon with that energy would have a Planck-length wavelength, and an amoeba-mass black hole is Planck-length). Given there's nothing overly special about Planck energy or mass, my money is on there being nothing special about Planck length either. Hopefully at least some of the above is correct.

Below the Planck distance, "closer" ceases to be a meaningful concept. Similarly, distances larger than the size of the observable universe may also be meaningless.

deleted 1y ago

[deleted]

hnuser123456 1y ago

The co-moving radius of the universe is about 3x larger than the observable universe, but I don't think there's any practical measurements larger than that. We don't know how much is beyond that because potentially a large chunk of the universe is already forever outside our past and future light cone.

kstrauser 1y ago

Why is that? I've heard this before but don't understand what it actually implies. Like, why can't 2 things meaningfully be half a Planck distance apart?

Nevermark 1y ago
Imagine that at some small distance, space itself is quantum, so quantized. I.e. at the bottom, space is a discrete graph with incredibly small edges. Possibly very tangled and not even layed out in obvious dimensions over short distances. We don’t know if that is the case. That is only one possibility. But it seems very clear that whatever happens at the Planck distance or lower isn’t simple smooth space as we model it for larger scales.
- tsimionescu 1y ago
  Unfortunately for this idea, special relativity tells us that Planck length is an observer-dependent phenomenon. That is two objects that are at a distance that is more than the Planck length apart for one observer will be closer than the Planck length for another observer and vice versa. So Planck length can't be a fundamental property of space-time, unless special relativity breaks down at some point even for non-accelerated observers.
  - Nevermark 1y ago
    I would suspect since general relativity would break down that special relativity certainly would. The “relativity” aspect will almost certainly still apply in some way, and still form an emergent basis for the special relativity effects you point out. All of general relativity has to be emergent from the to-be-discovered laws of the underlying small scale structure of space. (I.e. general relativity isn’t wrong, it is just not complete. Similar relationship as with Newton’s Law of Gravity, which was also correct, but breaks down beyond the conditions it covers well, because it was not complete.) The smallest scale is also where we expect more “light” shed on the initial conditions of the universe and potentially the insides of black holes. Two other conditions where general relativity already breaks down.
    - tsimionescu 1y ago
      If special relativity breaks down, so does QFT - since QFT is based on special relativity just as much as on QM.
      - Nevermark 1y ago
        “Breaks down” just means our equations don’t know what to say about a situation. It doesn’t that any particular phenomena we understand today will break down. Just we will be able to see richer behavior, that has been there all along, than our models cover today. And so be able to understand more conditions than we do today. And perhaps new capabilities to engineer things than we have today. Obviously quantum field theory, as it exists today, breaks down at the Planck distance too, since it can’t tell us what is happening at smaller distances either. This isn’t the least bit controversial or surprising. It just means that even with both theories, we can’t explain everything yet. When we do have an accurate theory of the fine structure of space and time, it will also be a theory of the fine structure of fields. Since space-time is integral to both theories. It may even be the long sought after unification. But for distances much larger than the Plank distance, the fine structure theory will still simplify into the GR and QFT we have today. Just as GR under many conditions we encounter every day, further simplifies to Newton’s Law of Gravity.
AnimalMuppet 1y ago
Imagine the universe is made out of graph paper, with only the points of intersection of the lines being actually "real". That is, space is actually discrete. If that is true, then you cannot meaningfully talk about things being "half a square" apart. People (some people) think that the universe really is that way, at the Planck distance. Actual experimental confirmation is somewhat lacking at this time...
- tsimionescu 1y ago
  More importantly, this idea doesn't work in the context of space dilation. Per special relativity, the distance between objects is arbitrarily different for different observers, so any grid you draw will be wrong for me if I'm moving at a different velocity than you. This is especially bad because it doesn't just depend on the magnitude of the velocity, but also the direction - space is compressed in the direction of motion. So two observers moving at an angle to each other will have very different views of the grid.
daxfohl 1y ago
The only reason I've heard that isn't super handwavy is that measuring it would require a wavelength with enough energy to create a black hole. IDK if that's true or not, and IDK if that also means the distance doesn't exist or if it's just not measurable. I've also heard that there's nothing special about planck length other than it being universal constant that we and any conceivable aliens would agree on as a standard of measure. So, idk.
griffzhowl 1y ago
It's just that it's physically impossible to measure such small scales. To probe a smaller scale you have to put more energy into a volume (roughly, because you have to force particles closer together), and at some point you have to put so much energy into such a small volume that it becomes a black hole, then any more energy you put in will just make the black hole bigger. So there seems to be a fundamental limit to how short a scale we can probe, and therefore we can't give a physical meaning to smaller scales. Nima Arkani-Hamed talks about htis in a few lectures online. This is just according to our current theories, and you don't need any speculative ideas about granularity of space. Mathematically, there's no problem in considering arbitrarily small length scales, because current theories are based on continuous space and time dimensions, but since we can't give physical meaning to small length scales, that's a clue that a more fundamental theory will somehow not be based on continuous space and time
- daxfohl 1y ago
  Here's a summary of my layman's understanding, which could be wrong. To my understanding there's nothing special about it except once you get to quantum field theory, and specifically spin-2 particles, which are the ones that hypothetically carry gravity (i.e. gravitons). (They're hypothetically gravitons because mathematically they result in conservation of the "stress-energy tensor", which is the same thing that Einstein's field equations give. And this isn't coincidence; it's because both are second-order field theories preserving Lorentz transforms aka special relativity). But notably if you only get through non-relativistic quantum mechanics, there's nothing special that happens at Planck length. Planck length becomes special in QFT because at Planck length, the feedback (my force on you affects your force on me affects my force on you etc) of the quantum field mathematically explodes in something called "UV divergence". Notably, this also happens for other force carriers, not just gravitons, but a mathematical trick called Renormalization fixes that. Renormalization is based on shady techniques like assuming the sum of all whole numbers is -1/12. (IIUC this is a fairly straightforward pure mathematical result from complex analysis, required to ensure consistency of Fourier transforms for infinite sequences, known as analytic continuation / Riemann zeta function. Of course it makes no sense that nature should behave that way, but one day some physicists thought "let's try this weird math" and it matched experiments). However that technique only works for lower-spin fields (E&M, weak, strong) because the feedback is linear, hence sum(1+2+3+...). But in spin-2 fields the feedback is (quadratic? exponential?), and the same trick still gives an infinite result. Ultimately one could say this is the only thing standing in the way of a complete theory of quantum gravity. If we could get the math for gravitons not to blow up at tiny scales, we'd be done (experimental verification notwithstanding). String theory is one attempt: "Let's say there are no point particles, only strings, and this problem goes away". Other approaches exist too. But ultimately right now, there's no way to say for sure whether sub-Planck exists, doesn't exist, exists in some ways but not in others, or whether all of physics is wrong and we have to start over. A quick addendum: Planck energy is approximately the chemical energy in a tank of gas. Planck mass is about that of an amoeba (so an antimatter bomb made out of an amoeba would explode like a tank of gas (Hiroshima was 0.6 grams of mass), a photon with that energy would have a Planck-length wavelength, and an amoeba-mass black hole is Planck-length). Given there's nothing overly special about Planck energy or mass, my money is on there being nothing special about Planck length either. Hopefully at least some of the above is correct.