8 ms·

How would a passing gravitational wave look or feel? (2017)

90 points by ynoxinul 1y ago

dboreham 1y ago
Obviously as "a disturbance in the force".
sockboy 1y ago
It's fascinating to think about how such tiny ripples in spacetime could be detected and what it might feel like if we could perceive them directly. The scale and subtlety are just mind-blowing.
maaaaattttt 1y ago
On a somewhat related note I'm wondering what the expansion of the universe means for our bodies and matter in general? I think, like the accepted answer suggests, the forces on the atomic level make it so that larger structures get back to a certain equilibrium even if constantly streched equaly in all directions. But I have a hard time imagining what the universe expanding really means on a human/solar system scale. I know of the inflatable balloon analogy, but to me, matter is not on the ballon, rather it is the rubber the ballon is made of. I have never seen this really explained in details to the general public which I belong to. Maybe that's a sign I'm completely misunderstanding the subject though.
- freedomben 1y ago
  Personally I like the raisins in a baking muffin analogy better as it's 3 dimensional
  - randallsquared 1y ago
    The inflatable balloon analogy has the advantage that, two-dimensionally, there's no "edge" beyond which you could travel.
- itgoon 1y ago
  https://www.youtube.com/watch?v=gEyXTQ9do-c https://www.youtube.com/watch?v=gEyXTQ9do-c https://en.wikipedia.org/wiki/Big_Rip https://en.wikipedia.org/wiki/Big_Rip
- 3cats-in-a-coat 1y ago
  The whole "expanding Universe" model is repeatedly dealt blows in the past few years, so I'd accept it as a plausible, but not sufficiently demonstrated hypothesis and not waste time bothering about the impact on our bodies. But if you will, think about it like that. All life adapts to its environment. All life. All the time. Everywhere. And the expansion is not that fast that a single generation of anything from a one day fly to a centenarian turtle, or a millennia old tree has to bother about it. It's invisible at our timescale. I've always thought why animals were so huge at the beginning. Not just dinosaurs, but insects the size of a large dog. Maybe it's the oxygen rich environment. Maybe it's evolutionary processes shrinking size in time to optimize energy needs and improve survival. Maybe gravity somehow changed in time, or it was the expansion of the Universe or a myriad of sci-fi reasons we can come up with. But life adapted and moved on. So that's what expansion means for us. One of millions of variables we constantly adapt to. If it's slow enough, no problem. But if it's hitting us fast like the accelerating climate change or technological progress, that... we may have problems with. That's when you see unrest, violence, crime. Wars. Famine. Suffering. The Universe is not our problem. We... are our own problem.
  - TeMPOraL 1y ago
    Almost agreed, but I feel compelled to correct one thing, because it's a common and annoying misconception "nature lovers" harbor: > One of millions of variables we constantly adapt to. If it's slow enough, no problem. But if it's hitting us fast(...), that... we may have problems with. That's when you see unrest, violence, crime. Wars. Famine. Suffering. No. Famine, starvation, disease, suffering, mass deaths - and even wars - are exactly the process through which life adapts to slow changes. That's what it means for ecosystems to thrive, for nature to be in balance - that balance is held dynamically, by constant cycles of excessive slaughter followed by mass starvation. We brought a lot of new problems on the table, both for ourselves and all other life, the latter of which can't even keep pace. But senseless suffering and comically painful death - that one came from nature, and we're actually successfully reducing it.
- mr_mitm 1y ago
  Expansion happens only in the Lemaitre-Friedmann-Robertson-Walker walker metric, which is a solution to the Einstein equations in a homogeneous universe. That's a fine approximation to our universe at the largest scales, but not on the scale of a solar system. Spacetime locally around the earth looks much more like a Schwarzschild solution. So we're not experiencing expansion. If you are asking hypothetically, if a human body were floating in the intergalactic medium, then yes, the accepted answer you quoted would apply.
  - oersted 1y ago
    A translation would be appreciated, OP was asking for an explanation for the general public. Even highly technical people will struggle to understand this if you use such insider jargon without clarification. Surely expansion is happening at every scale but locally other factors dominate right? To what degree? Is it mainly gravity? Electromagnetic attraction between atoms and/or molecules? The naive mental model that I have is of two balls tied with a rubber band, each on a treadmill going in opposite directions. Since the rubber band attraction dominates, they slip on the surface of the treadmill and their distance is barely affected even if the surface underneath “expands” outwards quite quickly. Is this a reasonable analogy or is it too simplistic? Of course the rubber band force is proportional to the distance, while the attraction forces we are talking about are inversely proportional. And I have no idea if the expansion of the universe can be reasonably modeled as an outwards “drag force” on matter. How “sticky” is matter with respect to space?
    - Kranar 1y ago
      No expansion does not happen at every scale. Expansion is a phenomenon that applies only when you average out unbounded systems at very large scales. By unbounded I mean systems whose kinetic energy is greater in magnitude than its potential energy. Even galaxies themselves don't expand over time. One question would be what do you hope to gain from a potential analogy. If you want a very down to Earth, practical and somewhat physical understanding, then the simplest and best explanation is that there are systems of objects in our universe, at very very large scales, that have a group velocity that is greater than the escape velocity needed to attract it to any other system of objects, and those systems are observed to be accelerating away from each other. No analogy is needed for this, it's just a fact presented plain and simply. There is no theory that predicts a cause for this, but the best theory of gravity, general relativity, is a very flexible and open-ended framework that allows one to plug all kinds of different and imagined scenarios into it and see the results, even if those scenarios have no actual physical interpretation. Some people did play around with imagined results like an expanding universe, a contracting universe, an infinitely large universe, a closed but unbounded universe etc etc... General relativity doesn't predict any of these universes but it does let you explore these possibilities. When Edwin Hubble observed that galaxies are moving away from each other then this observation was made to fit into the existing theory of general relativity. In order to take the raw observation and fit it with general relativity which interprets gravity as a purely geometric phenomenon, it did so by reframing this behavior not exactly as an intrinsic motion belonging to these large scale systems but rather as if these systems are stationary but there is more and more space filling up the universe in-between these large scale objects which gives them their apparent motion. This is a means of reconciling the geometric view of gravity, ie. space-time, with the actual observed data. The specific technical details of how this reconciliation is performed is as OP mentioned, the FLRW metric which is here but as you said is too technical for most people to appreciate: https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtr... You might then ask, what does this solution predict happens to atoms, or our solar system? Perhaps it predicts a very small and imperceptible expansion because other forces dominate, but nevertheless it must predict something, right? This is a tempting position, but it's not quite right. The key reason is that the FLRW metric, which explains Hubble's observation as the literal stretching of space, literally don't make sense and can't be solved for systems like planets, solar systems, or even galaxies because it can only be used if certain requirements/preconditions are fulfilled. These requirements are present only on the absolute largest scales where the universe looks fairly even/balanced, there is no center of mass, there is no region of the universe that is more special than any other region. In our solar system the sun is a pretty special center of mass and the solar system is not evenly balanced, same thing goes for our galaxy, and hence none of the models currently studied to describe Hubble's observations work for both the extremely large scale universe as well as for other scales.
- spauldo 1y ago
  Matter isn't pinned to the space it's in (source: try walking around). As space expands, the other forces which are orders of magnitude stronger than the expansion of space slide matter along so that distances don't change. You can only detect the expansion of space by measuring the distance between things that are so spread apart that the other forces between them are essentially zero.
  - CGMthrowaway 1y ago
    That's an interesting point. The expansion of space still impacts matter on an atomic level though. The space between atom core and electrons influences its bonding abilities and other properties Analogy, take two attracted magnets, or two opposing electrodes, and expand the space between them. Things change
    - spauldo 1y ago
      The magnet analogy works here, so let's give it a try. Put one magnet on a table and then put one under the table so that it's held up by the magnet above it. Then observe what happens. This will take a while, so maybe go get a 2^128 cups of coffee. The space between the magnets is expanding, just like space everywhere. Assuming the table and magnets are immune to deterioration over time, you can come back after several billion years and the distance between the magnets will have stayed the same. Space expanded, sure, but the stuff occupying the space didn't. The forces that hold an atom together are significantly stronger than what's holding the two magnets in the example above.
  - maaaaattttt 1y ago
    That's what I understood from the explanation on stackexchange. But given what you said, if we take the plank length as the shortest length unit, and we consider two theoretical "objects" placed at one plank length away from each other. Does the universe expanding for these two objects mean: 1. the plank length is becomming bigger, 2. more plank lengths are added in between the two objects, 3. Something else and I'm completely off
    - 1y ago
- biorach 1y ago
  https://m.youtube.com/watch?v=5U1-OmAICpU https://m.youtube.com/watch?v=5U1-OmAICpU "Brooklyn is not expanding"
- kmm 1y ago
  Without taking into account dark energy or a cosmological constant (so on scales smaller than a few hundreds of millions of lightyears), in the usual cosmological model you can see the expansion of the universe simply as a remnant of the initial kick all matter got from the Big Bang. There is no active pushing anymore, it's just matter moving apart, constantly slowing down due to the mutual gravitational attraction. So for our bodies, planets, solar systems, even galaxies and clusters, because these are bound (either electromagnetically or gravitationally), the influence of the expansion of the universe on them is not just negligible, it's non-existent. It's a little different when wo do include dark energy and other mechanisms more complicated than a simple matter or light content. For your intuition, you can think of this as a constant omnipresent negative pressure. We have no idea how it works on scales smaller than those of the observable universe, but if we imagine it works the same on every scale, then it's an extremely tiny force constantly pulling your body apart.
- ahazred8ta 1y ago
  As near as we can tell, space is expanding by about 10 meters per year per astronomical unit. It's 7% per billion years. In practice, it would show up as a very small fudge factor in the tenth decimal place of the gravitational constant.
3cats-in-a-coat 1y ago
Gravitational waves move at the speed of light, doubtful you can "look" at it. If it's that strong it'll just seem like a shake. Like an earthquake. Except it's the universe that's quaking.
- NitpickLawyer 1y ago
  > Gravitational waves move at the speed of light Do we know if there are mediums (sp? media?) where gravitational waves move slower than the speed of light? Like light does in glass?
  - 3cats-in-a-coat 1y ago
    That's an interesting question and it's quite possible the medium matters about gravitational transmission speed. I.e. the question is how is gravity transmitted. We'd need to know a lot more about the structure of subatomic matter & interactions to answer this one. As it stands, we have no theory of gravity at all at the quantum level. I'm firmly of the opinion there's no "spooky action at a distance". All waves propagate gradually (if rapidly) through a medium, even if we decide to call that medium "vacuum" and define it as empty. Or more modernly, a "field". Waves don't propagate in nothing by definition.
- vishnugupta 1y ago
  If everything is quacking then would anyone “feel” it?
  - deleted 1y ago
    [deleted]
  - 3cats-in-a-coat 1y ago
    That's a very good question. If light speed was infinite. If sound speed was infinite. Or even if water waves were infinite, we'd never feel or see anything waving. We feel a wave by seeing the differential effect of it propagating. Which requires speed with a detectable progression. Compression, decompression. Excitation, de-excitation. So when everything is quaking, we detect it by neighboring regions not being in sync as to the direction, amplitude, phase etc. of where they're quaking at any given moment. Just like with normal earthquakes. The ground is shaking. If everything atop shook in perfect sync, you'd miss the earthquake. But otherwise, you feel it, you're destabilized. Not in sync with the ground. For gravitational waves, it's much harder for us to feel it without special, very sensitive equipment. Normally. But if it was strong enough, we would.
antiquark 1y ago
So (in theory) you could hear the chirp of merging black holes, if they were close enough. In fact, everyone on the planet would hear the same chirp. Someone should comb the historical records (or even, mythologies) for a birdless chirp heard by many people.
- yetihehe 1y ago
  I don't think life on earth would survive aftermath if such chirp was close enough to be heard.
OhNoNotAgain_99 1y ago
[dead]
deleted 1y ago
[deleted]
jeanlucas 1y ago
This would be an awesome xkcd video, they're killing it on YouTube
- spauldo 1y ago
  Probably better as a MinutePhysics video. It's not a real xkcd What-If if the Earth doesn't get destroyed. I'm really hoping Randall makes some new material soon - I enjoy the videos but I've read all the What-Ifs on his site and own both the books.
resonantsignal 1y ago
[dead]
bawana 1y ago
Interestingly, from a statistical mechanical viewpoint , entropy decreases as space expands.
deleted 1y ago
[deleted]
deleted 1y ago
[deleted]

90 points by ynoxinul 1y ago

Obviously as "a disturbance in the force".

It's fascinating to think about how such tiny ripples in spacetime could be detected and what it might feel like if we could perceive them directly. The scale and subtlety are just mind-blowing.

maaaaattttt 1y ago

On a somewhat related note I'm wondering what the expansion of the universe means for our bodies and matter in general? I think, like the accepted answer suggests, the forces on the atomic level make it so that larger structures get back to a certain equilibrium even if constantly streched equaly in all directions. But I have a hard time imagining what the universe expanding really means on a human/solar system scale. I know of the inflatable balloon analogy, but to me, matter is not on the ballon, rather it is the rubber the ballon is made of. I have never seen this really explained in details to the general public which I belong to. Maybe that's a sign I'm completely misunderstanding the subject though.

freedomben 1y ago
Personally I like the raisins in a baking muffin analogy better as it's 3 dimensional
- randallsquared 1y ago
  The inflatable balloon analogy has the advantage that, two-dimensionally, there's no "edge" beyond which you could travel.
itgoon 1y ago
https://www.youtube.com/watch?v=gEyXTQ9do-c https://www.youtube.com/watch?v=gEyXTQ9do-c https://en.wikipedia.org/wiki/Big_Rip https://en.wikipedia.org/wiki/Big_Rip
3cats-in-a-coat 1y ago
The whole "expanding Universe" model is repeatedly dealt blows in the past few years, so I'd accept it as a plausible, but not sufficiently demonstrated hypothesis and not waste time bothering about the impact on our bodies. But if you will, think about it like that. All life adapts to its environment. All life. All the time. Everywhere. And the expansion is not that fast that a single generation of anything from a one day fly to a centenarian turtle, or a millennia old tree has to bother about it. It's invisible at our timescale. I've always thought why animals were so huge at the beginning. Not just dinosaurs, but insects the size of a large dog. Maybe it's the oxygen rich environment. Maybe it's evolutionary processes shrinking size in time to optimize energy needs and improve survival. Maybe gravity somehow changed in time, or it was the expansion of the Universe or a myriad of sci-fi reasons we can come up with. But life adapted and moved on. So that's what expansion means for us. One of millions of variables we constantly adapt to. If it's slow enough, no problem. But if it's hitting us fast like the accelerating climate change or technological progress, that... we may have problems with. That's when you see unrest, violence, crime. Wars. Famine. Suffering. The Universe is not our problem. We... are our own problem.
- TeMPOraL 1y ago
  Almost agreed, but I feel compelled to correct one thing, because it's a common and annoying misconception "nature lovers" harbor: > One of millions of variables we constantly adapt to. If it's slow enough, no problem. But if it's hitting us fast(...), that... we may have problems with. That's when you see unrest, violence, crime. Wars. Famine. Suffering. No. Famine, starvation, disease, suffering, mass deaths - and even wars - are exactly the process through which life adapts to slow changes. That's what it means for ecosystems to thrive, for nature to be in balance - that balance is held dynamically, by constant cycles of excessive slaughter followed by mass starvation. We brought a lot of new problems on the table, both for ourselves and all other life, the latter of which can't even keep pace. But senseless suffering and comically painful death - that one came from nature, and we're actually successfully reducing it.
mr_mitm 1y ago
Expansion happens only in the Lemaitre-Friedmann-Robertson-Walker walker metric, which is a solution to the Einstein equations in a homogeneous universe. That's a fine approximation to our universe at the largest scales, but not on the scale of a solar system. Spacetime locally around the earth looks much more like a Schwarzschild solution. So we're not experiencing expansion. If you are asking hypothetically, if a human body were floating in the intergalactic medium, then yes, the accepted answer you quoted would apply.
- oersted 1y ago
  A translation would be appreciated, OP was asking for an explanation for the general public. Even highly technical people will struggle to understand this if you use such insider jargon without clarification. Surely expansion is happening at every scale but locally other factors dominate right? To what degree? Is it mainly gravity? Electromagnetic attraction between atoms and/or molecules? The naive mental model that I have is of two balls tied with a rubber band, each on a treadmill going in opposite directions. Since the rubber band attraction dominates, they slip on the surface of the treadmill and their distance is barely affected even if the surface underneath “expands” outwards quite quickly. Is this a reasonable analogy or is it too simplistic? Of course the rubber band force is proportional to the distance, while the attraction forces we are talking about are inversely proportional. And I have no idea if the expansion of the universe can be reasonably modeled as an outwards “drag force” on matter. How “sticky” is matter with respect to space?
  - Kranar 1y ago
    No expansion does not happen at every scale. Expansion is a phenomenon that applies only when you average out unbounded systems at very large scales. By unbounded I mean systems whose kinetic energy is greater in magnitude than its potential energy. Even galaxies themselves don't expand over time. One question would be what do you hope to gain from a potential analogy. If you want a very down to Earth, practical and somewhat physical understanding, then the simplest and best explanation is that there are systems of objects in our universe, at very very large scales, that have a group velocity that is greater than the escape velocity needed to attract it to any other system of objects, and those systems are observed to be accelerating away from each other. No analogy is needed for this, it's just a fact presented plain and simply. There is no theory that predicts a cause for this, but the best theory of gravity, general relativity, is a very flexible and open-ended framework that allows one to plug all kinds of different and imagined scenarios into it and see the results, even if those scenarios have no actual physical interpretation. Some people did play around with imagined results like an expanding universe, a contracting universe, an infinitely large universe, a closed but unbounded universe etc etc... General relativity doesn't predict any of these universes but it does let you explore these possibilities. When Edwin Hubble observed that galaxies are moving away from each other then this observation was made to fit into the existing theory of general relativity. In order to take the raw observation and fit it with general relativity which interprets gravity as a purely geometric phenomenon, it did so by reframing this behavior not exactly as an intrinsic motion belonging to these large scale systems but rather as if these systems are stationary but there is more and more space filling up the universe in-between these large scale objects which gives them their apparent motion. This is a means of reconciling the geometric view of gravity, ie. space-time, with the actual observed data. The specific technical details of how this reconciliation is performed is as OP mentioned, the FLRW metric which is here but as you said is too technical for most people to appreciate: https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtr... You might then ask, what does this solution predict happens to atoms, or our solar system? Perhaps it predicts a very small and imperceptible expansion because other forces dominate, but nevertheless it must predict something, right? This is a tempting position, but it's not quite right. The key reason is that the FLRW metric, which explains Hubble's observation as the literal stretching of space, literally don't make sense and can't be solved for systems like planets, solar systems, or even galaxies because it can only be used if certain requirements/preconditions are fulfilled. These requirements are present only on the absolute largest scales where the universe looks fairly even/balanced, there is no center of mass, there is no region of the universe that is more special than any other region. In our solar system the sun is a pretty special center of mass and the solar system is not evenly balanced, same thing goes for our galaxy, and hence none of the models currently studied to describe Hubble's observations work for both the extremely large scale universe as well as for other scales.
spauldo 1y ago
Matter isn't pinned to the space it's in (source: try walking around). As space expands, the other forces which are orders of magnitude stronger than the expansion of space slide matter along so that distances don't change. You can only detect the expansion of space by measuring the distance between things that are so spread apart that the other forces between them are essentially zero.
- CGMthrowaway 1y ago
  That's an interesting point. The expansion of space still impacts matter on an atomic level though. The space between atom core and electrons influences its bonding abilities and other properties Analogy, take two attracted magnets, or two opposing electrodes, and expand the space between them. Things change
  - spauldo 1y ago
    The magnet analogy works here, so let's give it a try. Put one magnet on a table and then put one under the table so that it's held up by the magnet above it. Then observe what happens. This will take a while, so maybe go get a 2^128 cups of coffee. The space between the magnets is expanding, just like space everywhere. Assuming the table and magnets are immune to deterioration over time, you can come back after several billion years and the distance between the magnets will have stayed the same. Space expanded, sure, but the stuff occupying the space didn't. The forces that hold an atom together are significantly stronger than what's holding the two magnets in the example above.
- maaaaattttt 1y ago
  That's what I understood from the explanation on stackexchange. But given what you said, if we take the plank length as the shortest length unit, and we consider two theoretical "objects" placed at one plank length away from each other. Does the universe expanding for these two objects mean: 1. the plank length is becomming bigger, 2. more plank lengths are added in between the two objects, 3. Something else and I'm completely off
  - 1y ago
biorach 1y ago
https://m.youtube.com/watch?v=5U1-OmAICpU https://m.youtube.com/watch?v=5U1-OmAICpU "Brooklyn is not expanding"
kmm 1y ago
Without taking into account dark energy or a cosmological constant (so on scales smaller than a few hundreds of millions of lightyears), in the usual cosmological model you can see the expansion of the universe simply as a remnant of the initial kick all matter got from the Big Bang. There is no active pushing anymore, it's just matter moving apart, constantly slowing down due to the mutual gravitational attraction. So for our bodies, planets, solar systems, even galaxies and clusters, because these are bound (either electromagnetically or gravitationally), the influence of the expansion of the universe on them is not just negligible, it's non-existent. It's a little different when wo do include dark energy and other mechanisms more complicated than a simple matter or light content. For your intuition, you can think of this as a constant omnipresent negative pressure. We have no idea how it works on scales smaller than those of the observable universe, but if we imagine it works the same on every scale, then it's an extremely tiny force constantly pulling your body apart.
ahazred8ta 1y ago
As near as we can tell, space is expanding by about 10 meters per year per astronomical unit. It's 7% per billion years. In practice, it would show up as a very small fudge factor in the tenth decimal place of the gravitational constant.

3cats-in-a-coat 1y ago

Gravitational waves move at the speed of light, doubtful you can "look" at it. If it's that strong it'll just seem like a shake. Like an earthquake. Except it's the universe that's quaking.

NitpickLawyer 1y ago
> Gravitational waves move at the speed of light Do we know if there are mediums (sp? media?) where gravitational waves move slower than the speed of light? Like light does in glass?
- 3cats-in-a-coat 1y ago
  That's an interesting question and it's quite possible the medium matters about gravitational transmission speed. I.e. the question is how is gravity transmitted. We'd need to know a lot more about the structure of subatomic matter & interactions to answer this one. As it stands, we have no theory of gravity at all at the quantum level. I'm firmly of the opinion there's no "spooky action at a distance". All waves propagate gradually (if rapidly) through a medium, even if we decide to call that medium "vacuum" and define it as empty. Or more modernly, a "field". Waves don't propagate in nothing by definition.
vishnugupta 1y ago
If everything is quacking then would anyone “feel” it?
- deleted 1y ago
  [deleted]
- 3cats-in-a-coat 1y ago
  That's a very good question. If light speed was infinite. If sound speed was infinite. Or even if water waves were infinite, we'd never feel or see anything waving. We feel a wave by seeing the differential effect of it propagating. Which requires speed with a detectable progression. Compression, decompression. Excitation, de-excitation. So when everything is quaking, we detect it by neighboring regions not being in sync as to the direction, amplitude, phase etc. of where they're quaking at any given moment. Just like with normal earthquakes. The ground is shaking. If everything atop shook in perfect sync, you'd miss the earthquake. But otherwise, you feel it, you're destabilized. Not in sync with the ground. For gravitational waves, it's much harder for us to feel it without special, very sensitive equipment. Normally. But if it was strong enough, we would.

antiquark 1y ago

So (in theory) you could hear the chirp of merging black holes, if they were close enough. In fact, everyone on the planet would hear the same chirp. Someone should comb the historical records (or even, mythologies) for a birdless chirp heard by many people.

yetihehe 1y ago
I don't think life on earth would survive aftermath if such chirp was close enough to be heard.

OhNoNotAgain_99 1y ago

[dead]

deleted 1y ago

[deleted]

jeanlucas 1y ago

This would be an awesome xkcd video, they're killing it on YouTube

spauldo 1y ago
Probably better as a MinutePhysics video. It's not a real xkcd What-If if the Earth doesn't get destroyed. I'm really hoping Randall makes some new material soon - I enjoy the videos but I've read all the What-Ifs on his site and own both the books.

resonantsignal 1y ago

[dead]

bawana 1y ago

Interestingly, from a statistical mechanical viewpoint , entropy decreases as space expands.

deleted 1y ago

[deleted]

deleted 1y ago

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