Is time an illusion?

[helios]

If you tried to make a 2D plane for every possible position in a region of space, you'd have an infinitely long task ahead of you because you'd constantly have a region with 0 thickness, and it would be as if you didn't map the spot at all. Nothing 2 dimensional like this actually exists beyond the math used to explain a concept.

Such a plane would be have an arbitrary definition. The only thing special about it is that I defined where it is.
An event horizon isn't arbitrarily defined, it's the region of space where a photon could orbit a gravity well. Above the event horizon, a photon with a tangential trajectory would escape out, and below it would fall in.

it's not because there's actually a 2 dimensional object (with or without mass) existing there.

What would you say the event horizon is, if not an object? And what would you say an object is?
I would say an object is a thing with a set of properties (true statements about it), or a collection of things that share a common set of properties. Those properties separate the things that exist into belonging and not belonging to the object.

Lets go the planet analogy again (lets assume Earth). At some point, I'm too close to escape the pull of the planet. But there's a range to that. If I'm on the planet, then I obviously can't escape it. If I'm a few miles above the planet, I still wont escape it. The point of the event horizon, where there's a theoretical infinitely thin space indicating it, is to show when the end of freedom, and the start of unwitting gravitational pull into the planet. The 2D representation isn't showing anything special, it's just showing where that point in space is.

Er... Gravity has infinite range. If you're really, really far there will probably be a stronger pull from a closer object, but the Earth is still pulling you towards it at a rate of 1/distance^2.
In fact, check this out. Google lagrangian points. An object in an L3 orbit with the Sun-Earth system orbits the Sun at the opposite side of the Earth's elliptical orbit.

The gravity of normal celestical objects isn't a very good analogy for the heavily distorted spacetime of event horizons.

Lets say I want to know where my fingertips end and the vacuum of space begins (Assume I'm in space). I would have a 2D representation of an infinitely thin position. Not because there's some 2D anything there, but because the concept you want to model only requires 2 dimensions.

Your fingertips don't have a well-defined surface. They're a constellation of tiny particles with uncertain positions. Where's the surface of an atom? Answer: it doesn't have one.

[zapshe]

Such a plane would be have an arbitrary definition. The only thing special about it is that I defined where it is.
An event horizon isn't arbitrarily defined, it's the region of space where a photon could orbit a gravity well. Above the event horizon, a photon with a tangential trajectory would escape out, and below it would fall in.

A photon is massless, 0D, and emitted light goes off in all directions. Meaning no matter how small that space is of the event horizon, some light will inevitably find its way in that magic point. The whole point is the defining this space means we use a 2D representation, but there's nothing 2 dimensional about space. It's only 2D when we are trying to identify an infinitely small slice.

What would you say the event horizon is, if not an object? And what would you say an object is?

The event horizon is a concept defining a point in space in which, once crossed, light cannot escape the gravitational pull of the black hole. An object is something that can be defined in terms of space, time, and usually matter.

With your definition of an object, anything could literally be an object. My example of an abstract region of space can become an object by simply saying that this space contains 10^(Insert Number) atoms. Now suddenly I'm not trying to identify 2D planes infinitely in random space, I'm trying to do it for an "object" which I just made up.

Which goes back to my point, that this 2D "object" doesn't actually exist outside of our concepts. It's simply the fact that the pull of gravity weakens over distances. All the event horizon is is when gravity's effect isn't strong enough to suck in light. This isn't in anyway a 2D thing, the pull of gravity changes over distance. If you try to see when it changes from one infinitely specific pull-force to another, you'll get an infinitely thin representation - 1 or 2 dimensional. It's only when we try to define something that specific do we get that. And again, you can do this for literally almost anything in the universe, you can't simply say that these are all 2D objects because we defined them somehow.

Er... Gravity has infinite range. If you're really, really far there will probably be a stronger pull from a closer object, but the Earth is still pulling you towards it at a rate of 1/distance^2.

Gravity distorts spacetime as well. The different intensities don't affect the analogy I'd say. The point is that you're trying to define a point between gravity being strong enough to pull you in, and gravity not strong enough to pull you in. But gravity doesn't work like that, we're the ones investigating the concept and find a 2 dimensional answer. The effect of gravity lingers on and simply grows weaker with distance. Measuring where gravity's strength goes from one specific strength to another results in a 2D or 1D representation in order to visualize it. But try to take a range of gravity, from one non-specific strength to another, and you'll get a 3D object! The point is that as we try to define where that infinitely specific point is, the less depth we have until it's practically zero. But that's only our defining concept and not an actual property of gravity.

[helios]

A photon is massless, 0D, and emitted light goes off in all directions. Meaning no matter how small that space is of the event horizon, some light will inevitably find its way in that magic point. The whole point is the defining this space means we use a 2D representation, but there's nothing 2 dimensional about space.

How do the first and second sentences relate to the third sentence?

With your definition of an object, anything could literally be an object.

Anything that actually exists and can be distinguished from things that aren't it, yes.

And again, you can do this for literally almost anything in the universe, you can't simply say that these are all 2D objects because we defined them somehow.

The exact position of a particular black hole's event horizon depends on a specific feature that we didn't define into existence, and that's the speed of light. That's a feature of the universe, not a value we defined arbitrarily. The speed of light is important, because it defines causality. An event horizon being where it is and not somewhere else has an effect on the universe. In the case of the cosmic event horizon, for example, defines what the observable universe is.

The point is that you're trying to define a point between gravity being strong enough to pull you in, and gravity not strong enough to pull you in.

Well, whether the Earth's gravity is strong enough to pull you in depends entirely on what other forces are acting upon you, regardless of the distance. Gravity isn't strong enough to pull you through the ground, or through the floor of an elevator that's going up.
Past a black hole's event horizon, not even infinite force would be strong enough to prevent you from falling in deeper. Like I said, not a great analogy.

[zapshe]

Anything that actually exists and can be distinguished from things that aren't it, yes.

Exactly, meaning literally anything could be made into an object, including any random volume of space that I could define somehow.

The exact position of a particular black hole's event horizon depends on a specific feature that we didn't define into existence, and that's the speed of light. That's a feature of the universe, not a value we defined arbitrarily.

Again, it doesn't really matter. The event horizon isn't something you can see or feel, it's just a point at which nothing can escape a black holes gravitational pull. Notice the word "point", 1D, or 2D if we wanted to make it more clear. At what "point" do I go from walking through a door to actually passing the door? Again, you'd have an infinitely thin 2D representation that would exist at the infinitely precise point at which the door's overhead ends. Of course you can say that atoms aren't going to be that perfectly aligned, but it's simply an analogy.

Past a black hole's event horizon, not even infinite force would be strong enough to prevent you from falling in deeper. Like I said, not a great analogy.

It doesn't undermine the analogy at all. I've compared being sucked into a black hole after passing the event horizon to being drawn into the Earth's atmosphere unwittingly after passing some point at which the gravity simply pulls you in. Perhaps other factors come into play, such as your current trajectory, speed, and other gravitational forces, but all those will do is change where the Earth's "event horizon" would be for you.

Again, 2D objects don't exist in the real world. They are things which we can use mathematically and define things. In this case, we can use them to define an infinitely specific point you'd have to cross in order to cross a black hole's event horizon. Not because anything about the black hole is 2 dimensional, but that the gravitational pull is stronger the closer you get. Then, we wanted to see where it would get strong enough for not even light to escape. Now, the concept itself can only lead one way, to a point in space. If you are any distance at all before the point, you haven't reached the event horizon. If you are any distance at all beyond it, you've crossed it.

Imagine you have a piece of paper and you put your thumbs on either side of it. Then, you keep drawing them closer and closer together until you finally reach the middle of the paper and your thumbs touch. This is literally how you find the event horizon of a black hole. How far do you need to go until light can't escape, how far out do you need to go before light can escape. Once you reach that "point", you've defined something 2 dimensional, but that was only to answer your own question, not somehow showing that there's anything 2 dimensional actually there.

Again, gravity's strength changes with distance. If you try to see where gravity's strength goes from (let's use a random number) 9.98m/s^2 to 9.9799999999999999999999m/s^2, you're getting a measurement increasingly without depth, but this doesn't mean anything about it is 2 dimensional, gravity simply gets weaker with distance and we tried to find an infinitely precise point.

EDIT: I also understand your view, that even if it's simply a concept, light actually has to pass through this point we've calculated in order to orbit or get sucked into the black hole. But as I've said, light is massless and 0D. Even though the volume of the event horizon is indistinguishable from 0 (one could argue not 0), that infinitely thin region is plenty of space for a photon of light to make it's way into. But there's nothing 2 dimensional really happening there, gravity is simply strong enough to pull light in at one point, and too weak at another point, and the distance between the two points is infinitely small. You could do this with anything else, like Earth's gravity as I've done in the paragraph above this one.

[z05DSL3A]

Again, it doesn't really matter. The event horizon isn't something you can see or feel, it's just a point at which nothing can escape a black holes gravitational pull. Notice the word "point", 1D, or 2D if we wanted to make it more clear.

Isn't the event horizon the distance from the singularity at which nothing can escape the gravity well of the singularity? In which case it is a sphere. Obviously you could look at a point on the event horizon but the point being a point would have no dimensions.

NB: I haven't been following this thread particularly, so sorry for butting in, just seemed odd.

[helios]

Exactly, meaning literally anything could be made into an object, including any random volume of space that I could define somehow.

Yep. The question is whether the thing we're calling an object would exist even if we hadn't defined it the way we did.

The event horizon isn't something you can see or feel

How is this any different from space in general?

it's just a point at which nothing can escape a black holes gravitational pull. Notice the word "point", 1D, or 2D if we wanted to make it more clear. At what "point" do I go from walking through a door to actually passing the door? Again, you'd have an infinitely thin 2D representation that would exist at the infinitely precise point at which the door's overhead ends.

I'm not sure what you're arguing here. The threshold of a door is wherever you define it is. There's nothing about the physics of a door that will give you an unquestionable defintion of its threshold.

Again, 2D objects don't exist in the real world.

So you keep saying, but you haven't defined what you mean by "object", so it's a non-statement.

Imagine you have a piece of paper and you put your thumbs on either side of it. Then, you keep drawing them closer and closer together until you finally reach the middle of the paper and your thumbs touch. This is literally how you find the event horizon of a black hole. How far do you need to go until light can't escape, how far out do you need to go before light can escape. Once you reach that "point", you've defined something 2 dimensional, but that was only to answer your own question, not somehow showing that there's anything 2 dimensional actually there.

So, let me get this straight. Someone asks you "where's the event horizon?"
Your first answer: It's between here and here, in a region no thicker than 1 mm.
Your second answer: It's between here and here, in a region no thicker than 1 um.
Your third answer: It's between here and here, in a region no thicker than 1 nm.
...
Your final answer: It's between here and here, in a region no thicker than 0 m, but there isn't anything two dimensional actually there.
So your answer had nothing to do with reality? Why did you bother with that pointless exercise?

[zapshe]

Yep. The question is whether the thing we're calling an object would exist even if we hadn't defined it the way we did.

Yes, this is the basis for your argument. That even if we hadn't of defined it and made into into an "object", it would still be real. However, I'm saying that's not true. To get from one point to another point in the universe, you'll end up crossing through infinitely many 2D points. But you wouldn't think to say that each one is a 2D object, right? Same with the event horizon. A black hole has gravity which gets weaker over distances, and there's nothing more to it. You wouldn't call every infinitely small measurement of space that it's gravity occupies as 2D objects, right? Now, we notice that light gets sucked when too close, or orbits the black hole at just the right distance. Again, we didn't think anything about the black hole's gravitational pull was 2 dimensional, even though the same rules apply for its gravity at points beyond and before the event horizon. Now that we have an interest in this specific point, which is no different than any other one, we have gone and made a 2D representation of this infinitely precise coordinate.

How is this any different from space in general?

Nothing. The universe is 3 dimensional and gravity works on a 3 dimensional plane. You're the one arguing that there's a 2 dimensional object there.

I'm not sure what you're arguing here. The threshold of a door is wherever you define it is. There's nothing about the physics of a door that will give you an unquestionable defintion of its threshold.

Ever see those movies where there's a random door in the middle of nowhere? And when they walk through it they end up somewhere completely different? At what point do you go from walking through the door, to ending up at your destination? There's an infinitely thin 2D plane between the end of the doorway and the beginning of the space of your destination. Again, you could argue that the atoms aren't going to be perfectly aligned like this, but again, it's an analogy.

However, I think this analogy works perfectly because it would fit your definition of an "object". In order to get to this magical other side, you have to cross a 2D plane, the point at which you've made it through the door and into the other place, similar to an event horizon. But there's not actually a 2D plane there, it's simply to answer our question of where does this end and that begin. You'll define it as a 2D plane because something actually happens at that point, it defines something. But that's no different than me simply walking about and saying, "To get from point A to point B, I have to cross this 2D point in space." Yea, it's true, but there's no reason to think that it means there's a 2D object actually there.

So you keep saying, but you haven't defined what you mean by "object", so it's a non-statement.

I mentioned my definition in an earlier post. An object is something that can be defined by space, time, and usually matter or energy. My definition doesn't include random things we made up to solve problems or answer questions.

So, let me get this straight. Someone asks you "where's the event horizon?"
Your first answer: It's between here and here, in a region no thicker than 1 mm.
Your second answer: It's between here and here, in a region no thicker than 1 um.
Your third answer: It's between here and here, in a region no thicker than 1 nm.
...
Your final answer: It's between here and here, in a region no thicker than 0 m, but there isn't anything two dimensional actually there.
So your answer had nothing to do with reality? Why did you bother with that pointless exercise?

If it's not self-explanatory then I wont get too deep into it. But, how is an event horizon represented or shown? By a 2D plane, at which, when passed through at a certain point, will mean light cannot escape the black hole. There's a distance at which the gravity is just weak enough to not suck in light, but strong enough to not let it escape. And know that the event horizon is not where the photon sphere is (where light actually orbits the black hole). But lets look at this from another angle. Lets suppose the event horizon somehow had calculable depth. Now the event horizon is a 3D object by your standards? Again, there's nothing there other than what we've defined, but to you, that's more then enough to call whatever we find an "object"?


EDIT:

Isn't the event horizon the distance from the singularity at which nothing can escape the gravity well of the singularity? In which case it is a sphere. Obviously you could look at a point on the event horizon but the point being a point would have no dimensions.

Yea, I pointed this out before too, I think the post is on Page 4. But either way, the argument stands that it's not a 2D object.

[helios]

But you wouldn't think to say that each one is a 2D object, right? Same with the event horizon. A black hole has gravity which gets weaker over distances, and there's nothing more to it. You wouldn't call every infinitely small measurement of space that it's gravity occupies as 2D objects, right?

Those infinitely-many 2D planes are not a one-way street for causality. They have no physical properties that make them special.
This is like arguing that there's nothing special about pi because between any two reals there are uncountably-many irrational transcendental numbers.

Again, we didn't think anything about the black hole's gravitational pull was 2 dimensional, even though the same rules apply for its gravity at points beyond and before the event horizon. Now that we have an interest in this specific point, which is no different than any other one, we have gone and made a 2D representation of this infinitely precise coordinate.

You've lost me. Is your argument that the event horizon exists as a consequence of being predicted by general relativity, that it being two dimensional is a consequence of GR (and thus if there were no humans it would have no defined shape), or what?

However, I think this analogy works perfectly because it would fit your definition of an "object". In order to get to this magical other side, you have to cross a 2D plane, the point at which you've made it through the door and into the other place, similar to an event horizon. But there's not actually a 2D plane there, it's simply to answer our question of where does this end and that begin.

That's ridiculous. So how would you categorize that portal if not as an "object"? To me the word "object" implies three things:
* The thing existing and the thing not existing are distinguishable states of reality.
* The thing in question exists. E.g. Invisible pink unicorns are not objects.
* The thing is one. If you divide an object at best it changes and at worst it stops existing. E.g. A person changes if you trim their fingernails, changes more radically if you cut off their arm, and ceases to be if you cut them down the middle.

An object is something that can be defined by space, time, and usually matter or energy. My definition doesn't include random things we made up to solve problems or answer questions.

So far that definition of "object" is not incompatible with mine, since space, time, matter and energy are the only things that exist in the universe. So, "defined" how?
"Random things we made up to solve problems or answer questions", eh? Well, since the idea of "object" is itself a human construction, that would mean the only objects in the universe are elementary particles (if they exist). If my definition is capable of encompassing anything, yours excludes almost all things of interest.

Lets suppose the event horizon somehow had calculable depth. Now the event horizon is a 3D object by your standards? Again, there's nothing there other than what we've defined, but to you, that's more then enough to call whatever we find an "object"?

Let's imagine that at this hypothetical spherical shell event horizon, particles that enter it have a random chance of being instantly transported one light day in a random direction with all its momentum negated, after penetrating some depth into the shell. From a macroscopic point of view, half of the mass falling in continues falling in and the rest explodes instantly, and then falls back in.
Yes, I would say such an anomalous region is an object.

Now, let's suppose that around a black hole there was a spherical shell (say, between 100000 and 110000 km) that was basically indistinguishable from the space below and above it. No, I would not say that was an object, although it might be part of an object.
Or let's suppose that instead some sections of that shell behave differently, or they behave differently at different times. Then it might be an object, or it might be multiple objects, or the situation might be more complicated

[zapshe]

This is like arguing that there's nothing special about pi because between any two reals there are uncountably-many irrational transcendental numbers.

Pi is important because it's a constant for all circles, it would have nothing to do with how many irrational numbers you'd have to go through infinitely.

You've lost me. Is your argument that the event horizon exists as a consequence of being predicted by general relativity, that it being two dimensional is a consequence of GR (and thus if there were no humans it would have no defined shape), or what?

No, I'm saying that the event horizon is simply a point we've defined within the gravitational pull of a black hole. Just like any other point you could possibly define around the black hole, gravity will go from one strength to another. It's only that we care specifically about that point that we actually decided to represent it 2 dimensionally and name it the event horizon. What if we simply didn't care about where light couldn't escape a black hole's gravitational pull? What if instead, we cared more about how gravity weakened over distances and decided to make a 2D representation of that? The only reason it's an "object" is because we cared about it and decided to make a 2D representation.

Things happen all over the universe. People, planets, galaxies, they all have to pass infinitely precise 2D points in space to travel, but we don't care about that, even though it's a fact, so those aren't things we've deemed objects by your standards.

So how would you categorize that portal if not as an "object"? To me the word "object" implies three things

We can call it a portal and know that it's an object. But that would be a characterization of the door. The infinitely thin 2D representation of space after that door is not an object, simply the point at which one place ends and another begins. You have to pass through this 2D plane to reach the other side, but that's true for any movement at all. If you want to get to your car, leave the room, etc., you have to pass through infinitely many 2D planes. They aren't all objects. You only consider them objects when you have a vested interest in them. But what if we didn't care about the magic door, and instead our curiosity was about how the hell we can pass through infinitely many 2D planes when moving in 3D space! We could make 2D representations (not really get anywhere) and then those would be objects, even though we don't consider them such now.

So far that definition of "object" is not incompatible with mine, since space, time, matter and energy are the only things that exist in the universe. So, "defined" how?
"Random things we made up to solve problems or answer questions", eh? Well, since the idea of "object" is itself a human construction, that would mean the only objects in the universe are elementary particles (if they exist). If my definition is capable of encompassing anything, yours excludes almost all things of interest.

You can always make 2D or 1D constructions in order to realize things. The event horizon can be visualized as a 2D/1D or even a sphere as mentioned earlier. That doesn't matter, those constructions we've made aren't objects, they aren't real. There are no 2D planes in a 3D universe. Such a thing would have infinitely small depth to the point where it couldn't exist.

Let's imagine that at this hypothetical spherical shell event horizon, particles that enter it have a random chance of being instantly transported one light day in a random direction with all its momentum negated, after penetrating some depth into the shell. From a macroscopic point of view, half of the mass falling in continues falling in and the rest explodes instantly, and then falls back in.
Yes, I would say such an anomalous region is an object.

It would be a weird region of space to say the least, but not an object. No one would say, "We've found a 3D object around a black hole.." Instead, people would say, "There's a 3 dimensional region around the black hole.." It's a region of space around the black hole, not an object. An even if it was, I believe the original argument starting all of this was that I said an object cannot exist in a 3D world as 2D, which obviously I meant something my definition. A black hole's event horizon can be represented by 1D or 2D, but that simply doesn't change the fact that nothing can exist in this universe that's not 3D.

For example, lets take a look at the event horizon. Our 2D representation would be a plane, that once passed through center, you can't escape a black hole's gravity even at the speed of light. Now, lets look at this 2D plane from up top, we can't see it, there's no depth. Let's start shifting our view down to look at it straight on. Wow! It suddenly starts coming into view! Well, lets try this. I try to walk through the 2D plane, and it obstructs my way. But if I try to move my hand through it from the top, where it has no depth, would my hand pass through!?

Clearly, a 2D object can never exist in a 3D universe. Just because we can represent certain things with 2D representations, doesn't mean anything about it is 2 dimensional.

Now, let's suppose that around a black hole there was a spherical shell (say, between 100000 and 110000 km) that was basically indistinguishable from the space below and above it. No, I would not say that was an object, although it might be part of an object.
Or let's suppose that instead some sections of that shell behave differently, or they behave differently at different times. Then it might be an object, or it might be multiple objects, or the situation might be more complicated

How do you figure? A spherical shell is already a better representation of an event horizon then any 2D plane would be. The shell would show you ALL the possible points you could pass through in order to have passed the event horizon. A 2D plane would only represent one point, which would normally be the very center of that plane. Why would one be an object and the other not by your standards?

[helios]

I have a reply typed up that I've saved for later, because first I think it's really, really important to get this out of the way, otherwise we just won't be able to communicate.

Our 2D representation would be a plane, that once passed through center [...] A 2D plane would only represent one point, which would normally be the very center of that plane.

1. Planes don't have centers.
2. A plane is an infinite set of points, even when finite (an infinite plane and a finite plane contain the same number of points).
3. Who ever said an event horizon is a plane? That would be absolutely ludicrous.


---------------------------------

Pi is important because it's a constant for all circles, it would have nothing to do with how many irrational numbers you'd have to go through infinitely.

The event horizon is important because it's the edge of causality, it would have nothing to do with how many flat planes you'd have to go through infinitely.
I fail to see your point.

I'm saying that the event horizon is simply a point we've defined within the gravitational pull of a black hole.

Event horizons aren't defined, though. "Event horizon" as a term, yes, but event horizons are consequences of gravity, not of definition.

The infinitely thin 2D representation of space after that door is not an object, simply the point at which one place ends and another begins. You have to pass through this 2D plane to reach the other side, but that's true for any movement at all.

You have to at least agree that that portal (not the whole doorway, just the threshold itself) being there and it not being there are not indistinguishable, though. Suppose the doorway is free-standing and you stand outside the frame. If it's just a normal doorway you can hug the frame and touch your hands to each other. If the portal is there you can't do that.

No one would say, "We've found a 3D object around a black hole.."

Physicists would never consider things not made of matter as objects. At the most they might call non-matter particles objects. Suffice it to say we're not discussing physics here, although it resembles it superficially.

A spherical shell is already a better representation of an event horizon then any 2D plane would be. The shell would show you ALL the possible points you could pass through in order to have passed the event horizon.

Surely "ALL the possible points you could pass through in order to have passed the event horizon" would consist of the entire universe outside the event horizon.
Honestly, I don't know what you meant here. An event horizon is an oblate spheroid. At worst we'd have to say it's a turbulent isosurface (e.g. when two black holes merge). It absolutely can't be a region with non-zero volume.

For example, lets take a look at the event horizon. Our 2D representation would be a plane, that once passed through center, you can't escape a black hole's gravity even at the speed of light. Now, lets look at this 2D plane from up top, we can't see it, there's no depth. Let's start shifting our view down to look at it straight on. Wow! It suddenly starts coming into view! Well, lets try this. I try to walk through the 2D plane, and it obstructs my way. But if I try to move my hand through it from the top, where it has no depth, would my hand pass through!?

I don't what would happen if you found a solid (i.e. you can't pass through its side) 2D rectangle just floating in space. Since I'm not claiming such things exist, I don't think I need to answer that question.

Event horizons are not planes. You can't "come in from the top" of an event horizon. An oblate spheroid has a surface facing towards you no matter from which direction you look at it. Now, as to whether an event horizon is solid in the sense I used in the previous paragraph, I suppose you could say that they're solid in one direction but not in the other.

Our 2D representation would be a plane, that once passed through center [...] A 2D plane would only represent one point, which would normally be the very center of that plane.

1. Planes don't have centers.
2. A plane is an infinite set of points, even when finite (an infinite plane and a finite plane contain the same number of points).
3. Who ever said an event horizon is a plane? That would be absolutely ludicrous.

[zapshe]

1. Planes don't have centers.
2. A plane is an infinite set of points, even when finite (an infinite plane and a finite plane contain the same number of points).
3. Who ever said an event horizon is a plane? That would be absolutely ludicrous.

Not what I meant. Picture a 2D plane. Every point on that plane doesn't have the event horizon, only the "center point" - which will be a collection of infinitely many points I suppose. Which is why it can be represented as 1D as well. Only when the event horizon is represented by a sphere (whether or not perfect) will you have an event horizon at every possible point.

A 2D plane can't curve the way a sphere would, but the sphere would be infinitely thin. It would be weird and impossible an object, but we could always draw it.

The event horizon is important because it's the edge of causality, it would have nothing to do with how many flat planes you'd have to go through infinitely.
I fail to see your point.

Pi isn't an object, it's a number..

Event horizons aren't defined, though. "Event horizon" as a term, yes, but event horizons are consequences of gravity, not of definition.

Yes, this is the argument I'm trying to shoot down. You're saying that it exists whether or not we define it - Which is true. But, that can be said for ANYTHING. The infinitely many 2D planes I have to walk through to go anywhere exist - but we haven't defined them. Are they objects or not? Do we have to define them for them to be objects? Or does the fact that they exist without us make them objects? Either way, it would lead to either infinitely many objects or a definition for objects that doesn't make sense (it's only an object if we define it).

You have to at least agree that that portal (not the whole doorway, just the threshold itself) being there and it not being there are not indistinguishable, though.

Yes, it's fine to define where that threshold is, but saying it's an object makes us question our standards. Is it only an object when the thing in question peeks our interest? Yes, there's a portal that past this 2D plane you'll end up passing through, but there's also a coordinate of space right next to me that I'd have to pass a 2D plane in order to pass through. Why is one an object and the other not?

Suffice it to say we're not discussing physics here, although it resembles it superficially.

What are we discussing then..? Philosophy? Terminology?

Surely "ALL the possible points you could pass through in order to have passed the event horizon" would consist of the entire universe outside the event horizon.

No idea where you got that, perhaps you misunderstood. If you wanted to know where the event horizon was for every possible direction you could approach the black hole, you'd have a sphere. Maybe not a perfect sphere, doesn't really affect the argument. A 2D plane would only show you where the event horizon is for the one particular direction you happen to want to see the event horizon on.

An oblate spheroid has a surface facing towards you no matter from which direction you look at it.

Exactly what I meant by a sphere would be a better representation than a 2D plane which would only consist of one point of the event horizon.

Event horizons are not planes.

Yes, they aren't planes, they aren't 2D. Only the way we represent them can be 2D. Proving my point, there's nothing really 2D about it, it's just how we represent it.

Since I'm not claiming such things exist, I don't think I need to answer that question.

Well, we got into this because I said 2D objects can't exist in this universe and you said you weren't convinced of that. We were talking about physics and solid objects and then we got into another definition of objects which I don't think relates to the original argument.

But even so, defining an object the way you do makes it possible for literally anything to be an object.

[helios]

Oops. I just realized I screwed up my previous post. I forgot to not post that bit of text before the dashes.

Pi isn't an object, it's a number..

It's both.
https://en.wikipedia.org/wiki/Mathematical_object
I think whether all real numbers are objects is a debate in the philosophy of mathematics (I'm sure constructivists would say "no"), but simple constants such as 0, 1, pi, e, etc. are definitely objects, as their definition is between axiomatic and fairly simple.
Obviously not all mathematical objects are numbers.

The infinitely many 2D planes I have to walk through to go anywhere exist - but we haven't defined them. Are they objects or not?

saying it's an object makes us question our standards. Is it only an object when the thing in question peeks our interest?

Do those planes have any distinguishing properties between each other, besides their position along your path?
An event horizon is distinguishable from normal space because its a one-way street. A portal is distinguishable because it changes the topology of the surrounding space (for example, a square around the door frame would have 8 corners of 90° degrees each). Whether anyone thinks this is interesting or not, the portal and the event horizon are fundamentally different from normal space.

What are we discussing then..? Philosophy?

Obviously. The title of this thread is "is time an illusion?" That's as metaphysical as it gets.

Not what I meant. Picture a 2D plane. Every point on that plane doesn't have the event horizon, only the "center point" - which will be a collection of infinitely many points I suppose. Which is why it can be represented as 1D as well. Only when the event horizon is represented by a sphere (whether or not perfect) will you have an event horizon at every possible point.

A 2D plane would only show you where the event horizon is for the one particular direction you happen to want to see the event horizon on.

Hm...
A plane needs two parameters to be defined: a normal and a point which contained by the plane. The point it contains, if I understand you correctly, is something on the event horizon.
As for the normal, it would seem you want it to be a vector pointing away from you, but towards where? The center of the black hole?
Still not sure what information you can derive by intersecting such a plane with the event horizon.

Exactly what I meant by a sphere would be a better representation than a 2D plane which would only consist of one point of the event horizon.

What you said was "a spherical shell is already a better representation..."
A spherical shell and a sphere are not the same thing. A sphere is a surface with no volume. A shell is a volume, like a hollowed out coconut.

A sphere: "all the points P such that distance(P, center) = r".
A closed ball: "all the points P such that distance(P, center) <= r".
An open ball: "all the points P such that distance(P, center) < r".
A shell: "all the points P such that r1 <= distance(P, center) <= r2".

Yes, they aren't planes, they aren't 2D. Only the way we represent them can be 2D. Proving my point, there's nothing really 2D about it, it's just how we represent it.

Flat planes are not the only 2D shapes. I said it previously. A sphere is 2D. It's a surface. It can't be embedded in a 2D space, but it is 2D itself. Maybe you think that "two dimensional" means "it can be embedded in 2D space", but it doesn't mean that.

[zapshe]

It's both.
https://en.wikipedia.org/wiki/Mathematical_object

Now we're jumping from one definition to another. They are homophones, they don't mean the same thing. By your definition up until this point, its not an object.

Do those planes have any distinguishing properties between each other, besides their position along your path?

You mean, do they have a distinguishing property besides their distinguishing property? Event horizon is what separates the side where light can escape and light cannot escape. The "event horizon" for the portal is where one position in spacetime ends and a new begins (objectively). The planes along my path is where point A ends and point B begins.

Whether anyone thinks this is interesting or not, the portal and the event horizon are fundamentally different from normal space.

Yes, different. But does that make one object worthy and the other not? Why aren't event horizons the thing we overlook and space be the fascinating thing we makeup objects on? Again, by your definition, anything can be an object. Just because the event horizon marks something not as common as space or something that's more researched, doesn't mean it's more of an object than anything else.

Obviously. The title of this thread is "is time an illusion?" That's as metaphysical as it gets.

Which is why I brought logic and reasoning in and said "of course not". We weren't discussing "philosophy" apparently until we discussed 2D objects and event horizons.

A plane needs two parameters to be defined: a normal and a point which contained by the plane. The point it contains, if I understand you correctly, is something on the event horizon.
As for the normal, it would seem you want it to be a vector pointing away from you, but towards where? The center of the black hole?
Still not sure what information you can derive by intersecting such a plane with the event horizon.

Not really what I was getting at. The 2D plane would be a flat sheet. In the center is where the event horizon would be for anything approaching the 2D plane to make a 90 degree angle (so heading directly towards it).

What you said was "a spherical shell is already a better representation..."
A spherical shell and a sphere are not the same thing. A sphere is a surface with no volume. A shell is a volume, like a hollowed out coconut.

I don't think I have to elaborate, there's only one possible way to have a sphere showing the event horizon. It'll obviously have no volume, it's infinitely thin. It's like a bubble, only outlining the event horizon.

Flat planes are not the only 2D shapes. I said it previously. A sphere is 2D. It's a surface. It can't be embedded in a 2D space, but it is 2D itself. Maybe you think that "two dimensional" means "it can be embedded in 2D space", but it doesn't mean that.

This highly depends if we're talking about mathematically or physically. Mathematically, sure! We can have a curving 2D object. It'll be 3D yet still have no volume. However, such a figure is impossible in a 2D or 3D universe. You can't curve something like that in a 2D universe, you need 3 dimensions. And in 3 dimensions, you can't have a side be infinitely thin like that.

[helios]

Now we're jumping from one definition to another. They are homophones, they don't mean the same thing. By your definition up until this point, its not an object by your definition the we've been using.

Isn't it?

I would say an object is a thing with a set of properties (true statements about it), or a collection of things that share a common set of properties. Those properties separate the things that exist into belonging and not belonging to the object.

You could argue that numbers don't "exist" in the same sense as matter, but I was arguing by analogy. Pi is an object in mathematics in the same way that an event horizon is an object in the universe. That between two real numbers there are infinitely many numbers that share some of the properties of pi (being transcendental) has no bearing on pi's specialness, and that between two points in space there are infinitely many planes has no bearing on an event horizon's specialness.

You mean, do they have a distinguishing property besides their distinguishing property? Event horizon is what separates the side where light can escape and light cannot escape. The "event horizon" for the portal is where one position in spacetime ends and a new begins (objectively).

But an event horizon and the portal have the same properties as just arbitrary planes, but they have some that are unique (at least in their vicinity).

Why aren't event horizons the thing we overlook and space be the fascinating thing we makeup objects on?

Simple quantity. An event horizon has no volume, so any space with volume will be infinitely less special than an event horizon. Same as pi. Pi is special because all circles have the same ratio between their diameter and their circumpherence. It would be much less special if it could somehow be any of uncountably many values.

Not really what I was getting at. The 2D plane would be a flat sheet. In the center is where the event horizon would be for anything approaching the 2D plane to make a 90 degree angle (so heading directly towards it).

Nope, it makes no sense to me. I'm going to drop it, because I don't expect I'll be able to get it.

I don't think I have to elaborate, there's only one possible way to have a sphere showing the event horizon.

"Showing"?

Mathematically, sure! We can have a curving 2D object. It'll be 3D yet still have no volume. However, such a figure is impossible in a 2D or 3D universe. You can't curve something like that in a 2D universe, you need 3 dimensions. And in 3 dimensions, you can't have a side be infinitely thin like that.

You're doing it again. You're confusing dimensionality and embedding.
Even in mathematics you can't embed a sphere in two dimensions. A sphere is a two dimensional set of three dimensional points.
Consider these constructions:

2D object in 2D space (rectangle):

set<tuple<real, real>> s;
for (real x = 0; x <= 1) // this loop is non-computable. It runs for uncountably many iterations.
    for (real y = 0; y <= 1)
        s.add({x, y});

1D object in 2D space (circumpherence):

//radius r
set<tuple<real, real>> s;
for (real x = 0; x < 2*pi)
    s.add({cos(x)*r, sin(x)*r});

2D object in 3D space (sphere):

//radius r
set<tuple<real, real>> s;
for (real x = 0; x < 2*pi)
    for (real y = -pi/2; y <= pi/2)
        s.add({cos(y)*cos(x)*r, sin(y)*r, cos(y)*sin(x)*r});

3D object in 3D space (cube):

set<tuple<real, real>> s;
for (real x = 0; x <= 1)
    for (real y = 0; y <= 1)
        for (real z = 0; z <= 1)
            s.add({x, y, z});

[zapshe]

I swear. Anytime I forget to copy my text I lose it. I copied 90% of my posts and didn't lose them, then I forget this time and it disappears on me.

You could argue that numbers don't "exist" in the same sense as matter, but I was arguing by analogy. Pi is an object in mathematics in the same way that an event horizon is an object in the universe.

Good comparison, and I would argue that numbers don't really exist the way we think of them. Numbers are simply how we express what's happening in the world and universe. If you say "there are 5 black holes", sure, you'd be correct (assuming there are 5). And if you said, "event horizons are 2 dimensional", again you'd be right (since event horizons by definition are a an infinitely precise point in space). But the universe isn't keeping track of how many black holes there are or where the event horizon is, that's us doing that. The universe runs on whatever it runs on. Mathematics/Physics/Chemistry are what we've discovered about the mechanics that the universe runs on and what we use to make more discoveries.

Similarly, a 2D plane or sphere used to show the event horizon doesn't really exist. It's simply how we can label the event horizon so that we know where it is. The coordinate itself for the event horizon exists within 3 dimensional space. There are infinitely many coordinates, and you exist in an infinite amount of them right now. So trying to define where the event horizon is, which is where gravity weakens by a VERY SMALL and PRECISE amount, leads to a very precise coordinate. And if you want to say that after this coordinate (a coordinate would be 1D) light cannot escape, and before it light can escape, you can make a 2D plane to represent that. There obviously isn't anything 2 dimensional about any of it, but we use these 2D objects to represent them.

Nope, it makes no sense to me. I'm going to drop it, because I don't expect I'll be able to get it.

Sarcasm > 9000

"Showing"?

Unless there actually are 2D objects and spheres around a black hole to represent their event horizons, yes they are tools we use for showing the event horizon on paper - so we can visual it.

Simple quantity. An event horizon has no volume, so any space with volume will be infinitely less special than an event horizon.

Exactly my point! There's nothing stable about what makes an object by your definition. Anything can be an object with your definition, but we only make things that we are personally interested in objects. There's a lot to be desired by your definition. At this point, I may as well take the word "spirit" and say, anything that can move can be a spirit. The Earth is a spirit, but not Jupiter - I don't like Jupiter. There aren't strict enough bounds in your definition of an "object" for you to use it as if it actually defines something in particular..

[helios]

*Shrug* I give up. I don't think either of us is getting anywhere.

[zapshe]

I suppose. May we rest in peace.

[367kGNh0]

When did this drift away from the topic of "Is time an illusion"? A lot of posts ago?

[George P]

Actually it is still on topic. Mostly up-to-date on the musings of physicists who are on the cutting edge of understanding what time and space are. Too bad you are unable or unwilling to notice it.

I might have a quibble or two since the current understanding of reality is inexorably shifting away from String Theory as the Theory of Everything. But that is just me. I've had much fun watching the back and forth of the battling theories.

[helios]

How come your most common contribution to any thread (that I've noticed at least) is to insult people?