I I don't see how a black hole's event horizon can be crossed

[Foretranimal]

TL;DR

Is it possible that Eienstien's equivalence principle does not apply to the perspective of someone falling through the event horizon of a black hole, because that perspective does not and cannot exist?

OK, so this has bugged me for a while about the equivalence principle and the black hole information paradox.

If black holes "evaporate" via Hawking radiation, then they cannot exist forever.

So, from my external perspective, watching the person fall in, they slow down, freeze, and redshift to "nothing," but never cross the event horizon.

Does the equivalence principle say my perspective is valid? If it does, is it possible that that person really never crossed the event horizon?

The thing I have always read is that when the in-faller crosses, they feel nothing special. But this paradox seems to assume the crossing happens. If the crossing never happens, is there an information paradox at all?

If it takes forever to cross the event horizon, and a black hole's existence is less than forever, would the black hole evaporate before that unfortunate person crosses the horizon?

It seems more like the event horizon has no "there" or "inside" the event horizon - the horizon is an asymptotic limit of what exists. There is no inside, like there is no "before" the Big Bang. If you remove the assumption, there was a crossing, is there still a paradox?

I have no expertise in this area, so there may well be something basic I am just missing.

 

[PeterDonis]

there may well be something basic I am just missing.

There is. First, read this Insights article:

https://www.physicsforums.com/insights/black-holes-really-exist/

 

[Dale]

If black holes "evaporate" via Hawking radiation, then they cannot exist forever.

So, from my external perspective, watching the person fall in, they slow down, freeze, and redshift to "nothing," but never cross the event horizon.

The standard Schwarzschild coordinates that you refer to in the second statement are on a different manifold than the Hawking spacetime for the first statement.

Does the equivalence principle say my perspective is valid? If it does, is it possible that that person really never crossed the event horizon?

The equivalence principle does not say your perspective is valid. The principle of general covariance says your “perspective” is valid, where your “perspective” is any coordinate chart you choose. If you choose to use a chart that doesn’t include the horizon then your “perspective” cannot make any claims, positive or negative, about what crosses the horizon.

If it takes forever to cross the event horizon, and a black hole's existence is less than forever,

There is, to my knowledge, no coordinate chart on any spacetime where both statements are true.

 

[PeterDonis]

If black holes "evaporate" via Hawking radiation, then they cannot exist forever.

True. But they can exist for a very, very, very, very, very long time. For example, the expected evaporation time by Hawking radiation for a 10 solar mass black hole is about $10^{70}$ years.

from my external perspective, watching the person fall in, they slow down, freeze, and redshift to "nothing," but never cross the event horizon.

Not if the hole evaporates. An evaporating hole is different from an "eternal" hole, which is where the "slow down, freeze, and redshift to nothing" description comes from.

If the hole evaporates, you see the person cross the horizon at the same time as you see the final evaporation of the hole.

Does the equivalence principle say my perspective is valid?

The equivalence principle has nothing to do with your scenario. The equivalence principle is local. What a distant observer sees when a person falls into a black hole and the hole later evaporates is not local.

is it possible that that person really never crossed the event horizon?

No.

The thing I have always read is that when the in-faller crosses, they feel nothing special.

That's true.

If it takes forever to cross the event horizon

It doesn't. The person falling in only experiences a finite amount of time by their clock before they cross the horizon.

It takes a longer and longer time for the distant observer to see the person getting closer and closer to the horizon. But that's because the light takes longer and longer to get out to the distant observer. It has nothing to do with what's happening to the person close to the horizon.

would the black hole evaporate before that unfortunate person crosses the horizon?

No.

It seems more like the event horizon has no "there" or "inside" the event horizon

This is not correct. There is a region of spacetime inside the horizon. This is true even for an evaporating black hole.

the horizon is an asymptotic limit of what exists.

Wrong.

There is no inside, like there is no "before" the Big Bang.

Wrong.

If you remove the assumption, there was a crossing

You can't, because that would be wrong. See above.

We've had a number of previous threads on this general topic, and the confusion you have is a common one. But it's still a confusion that you need to unlearn.

 

[Nugatory]

Does the equivalence principle say my perspective is valid?

The equivalence principle says that sitting in a box at rest on the surface of a gravitating body (for example, in a closed room on the surface of the rest) is indistinguishable from sitting in a box that is being accelerated in empty space - Google for "Einstein's elevator" for more.

And of course this is completely different and has nothing to do with has nothing to do with watching something falling into a black hole.
The "it takes forever to reach the event horizon" thing is a misleading description of what's going on. If we start a stopwatch at zero and drop it into a black hole, it will fall through the event horizon and it will read some finite value when it does - so clearly the horizon is crossed in finite time. However, the light from that crossing event will never reach us on the outside, so if we choose to define when something happens as "when light from it reaches our eyes, minus the time it took for light to get from there to our eyes" we will conclude that it never happened.

 

[Foretranimal]

There is. First, read this Insights article:

https://www.physicsforums.com/insights/black-holes-really-exist/

Thanks!
This is going to take some time, and likely re-reads, but it is spot on the question.

 

[DaveC426913]

This, in a nutshell, is usually the key that unlocks the solution to the apparent paradox, IMO:

It takes a longer and longer time for the distant observer to see the person getting closer and closer to the horizon. But that's because the light takes longer and longer to get out to the distant observer. It has nothing to do with what's happening to the person close to the horizon.

 

[Foretranimal]

There is. First, read this Insights article:

https://www.physicsforums.com/insights/black-holes-really-exist/

This one is difficult to get:

"But it turns out that there is an additional wrinkle here: there is more than one possible “infinity” in an asymptotically flat spacetime. There are five; they are called future and past timelike infinity, future and past null infinity, and spacelike infinity. Why is this? Because spacetime includes time as well as space, so there are three kinds of curves, timelike, null, and spacelike, and the first two kinds have two different directions, future, and past. (Technically speaking, the light cone at every event in spacetime has two interior regions–future and past–which are disconnected, but only one exterior region–the spacelike region.) Each of these, if extended indefinitely, ends up at a different “infinity”."

Is this related to the idea that inside the event horizon, time becomes spacelike and space becomes timelike? I have read that, but don't understand.

Source: https://www.physicsforums.com/insights/black-holes-really-exist/

 

[Foretranimal]

The "it takes forever to reach the event horizon" thing is a misleading description of what's going on. If we start a stopwatch at zero and drop it into a black hole, it will fall through the event horizon and it will read some finite value when it does

OK, but if we drop that stopwatch and don't jump in with it, doesn't that stopwatch experience a different now from the dropper's now, as it approaches the horizon? To me, it seems like that now, when the stopwatch has that finite value, isn't my now.

 

[Foretranimal]

True. But they can exist for a very, very, very, very, very long time. For example, the expected evaporation time by Hawking radiation for a 10 solar mass black hole is about years.

Even a very, very, very, very, very long time is less than infinite time. I think even a very, very, very, very, very, very, very, very, very, very long time is still less, yes?

If the hole evaporates, you see the person cross the horizon at the same time as you see the final evaporation of the hole.

For supermassive black holes, it is even mind-bendingly longer - like the last thing that can happen that has any causal relevance to anything.

Given that we are in the realm of exponential exponents, which might also be exponents. I want to know why this matters - even if it is in a simplified way.

 

[Foretranimal]

Google for "Einstein's elevator" for more.

I think I get Einstein's happiest thought: freefall in a gravitational well is indistinguishable from rest - not only are they indistinguishable, they are the same thing.

Is that right?

 

[Foretranimal]

The standard Schwarzschild coordinates that you refer to in the second statement are on a different manifold than the Hawking spacetime for the first statement.

Thank you for the response. I don't understand what a manifold is in your context. With internal combustion engines, manifolds generally serve to either merge or split air or water flows. I have read about manifolds with respect to theoretical physics - and I have no idea what that means... :)

 

[Foretranimal]

The equivalence principle does not say your perspective is valid. The principle of general covariance says your “perspective” is valid, where your “perspective” is any coordinate chart you choose. If you choose to use a chart that doesn’t include the horizon then your “perspective” cannot make any claims, positive or negative, about what crosses the horizon.

Valid is the wrong word. Let me amend that to say both perspectives are real and exist.

We have a 20-foot barn, with doors fore and aft. I have a stationary watch standard on the roof with a switch where she can instantaneously open or close the magical barn doors at the same time. We also have a stupid fast ladder-bearer with a 25-foot ladder carrier, who I am granting the ability to arbitrarily accelerate and travel at any allowed/possible speed (less than c). My super-fast-laderman is named Ernest, and the switchmaster is named Jenefer.

If Ernest stops being lazy, he can accelerate as close as he needs to with my ladder, and if he travels fast enough, distance dilation will shrink his ladder to less than the 20 feet between doors (Jenefer's perspective), and that shrinkage shrinks the length of the ladder, allowing it to pass through this impossibly long barn.

From Ernest's perspective, the nearest door opens 1st, and as he is running through the barn, he sees the exit open while the entrance is still open.

Jenefer sees a compressed ladder, and the doors open/close at the same time. Ernest sees all the ladder's length, but sees the door open and close at different times.

My understanding of this is that they do not share the same now, because Jill has so much movement in space, she has less movement in time, with respect to Ernest.

because there isn't a universal now. The only law is causality: this caused that. When this or that happened is a matter of the reference frame.

This is how I try to visualize it. I am open to better understanding.

The point I'm trying to underscore is that my understanding is that there are no universal "now" with respect to reference frames.

 

[PeterDonis]

Is this related to the idea that inside the event horizon, time becomes spacelike and space becomes timelike?

No. The five infinities I mentioned in the article aren't important for what we're discussing here. They're a more technical point that comes into play when you want to make rigorous definitions of terms like "black hole" and "event horizon". But I don't think we need that level of rigor here.

I have read that, but don't understand.

The "time becomes spacelike and space becomes timelike" is a pop science description of a feature of a particular coordinate chart, Schwarzschild coordinates. It has nothing to do with the actual physics.

 

[PeterDonis]

Even a very, very, very, very, very long time is less than infinite time.

That's true, and that's why I said that an evaporating black hole, which only lasts for a very, very, very, very, very long time, is different from an idealized "eternal" black hole that lasts for an infinite time.

I want to know why this matters

You stated it yourself, in what I quoted at the top of this post.

 

[PeterDonis]

a different now

"Now" is not a physical thing in relativity. It's a convention. Trying to think in terms of "now" will only get you very confused, particularly in a scenario like this.

 

[PeterDonis]

My understanding of this is that they do not charge the same now

If you mean that relativity of simultaneity is involved in the "barn and ladder" scenario, yes, that's true.

But relativity of simultaneity is not involved in what we're discussing in this thread.

 

[Foretranimal]

If you mean that relativity of simultaneity is involved in the "barn and ladder" scenario, yes, that's true.

But relativity of simultaneity is not involved in what we're discussing in this thread.

OK, and I don't doubt you. But I'm not trying to be right, I'm trying to get a better understanding of this.

It may be wrong, but the parallel I am seeing is that the now of viewing the infalling person is not the same now of the external observer.

 

[Dale]

Valid is the wrong word. Let me amend that to say both perspectives are real and exist.

Valid is a fine word. If you want to go beyond valid then a more clear description is that the principle of general covariance says that all “perspectives” agree on the laws of physics and the result of applying them to any given experiment.

my understanding is that there are no universal "now" with respect to reference frames.

I agree. There is no universal “now”. Causality is universal.

I don't understand what a manifold is in your context

A manifold is the mathematical representation of the geometry of spacetime. It has distances and times and angles and speeds, but coordinates are optional

The point I was making regarding manifolds is that there is not even theoretically any spacetime where both the conflicting claims you mention hold. It is not a real conflict because they are two different t spacetimes. In particular, in a spacetime with an evaporating black hole things don’t take forever to fall in.

 

[Foretranimal]

But relativity of simultaneity is not involved in what we're discussing in this thread.

It may well be that I have faulty reasoning, and I have no idea. I'm trying to figure out why.

Why do I think there is a relationship between simultaneity and the crossing of the event horizon? Back to the ladder experiment: Ernest and Jenefer experienced the exact same event. Jill sees length dilation, and Ernest disagrees about the order of events. Both perspectives are real.

 

[Foretranimal]

A manifold is the mathematical representation of the geometry of spacetime. It has distances and times and angles and speeds, but coordinates are optional

Is that related to how, within a past/future spacetime diagram, you can take any perspective in the light cone and, with a geometric transformation - skew the diagram - and get the equivalent spacetime diagram with respect to any other perspective?

My mathematical background only went up to basic calculus, and I know there is much more. I'm trying to build on that.

 

[Dale]

Is that related to how, within a past/future spacetime diagram, you can take any perspective in the light cone and, with a geometric transformation - skew the diagram - and get the equivalent spacetime diagram with respect to any other perspective?

My mathematical background only went up to basic calculus, and I know there is much more. I'm trying to build on that.

Yes. Coordinates are optionally added to a manifold, but only in a manner in which all coordinates can be used to write the laws of physics and predict the outcome of experiments.

 

[PeterDonis]

It may be wrong, but the parallel I am seeing is that the now of viewing the infalling person is not the same now of the external observer.

There is no such thing as "the" now of any observer.

Why do I think there is a relationship between simultaneity and the crossing of the event horizon? Back to the ladder experiment

I.e., for a wrong reason. The barn and ladder scenario has nothing to do with the scenario we're discussing here. You should not even be trying to draw any analogies between them.

 

[Foretranimal]

The point I was making regarding manifolds is that there is not even theoretically any spacetime where both the conflicting claims you mention hold. It is not a real conflict because they are two different t spacetimes. In particular, in a spacetime with an evaporating black hole things don’t take forever to fall in.

Heh...
I may have made conflicting claims. But honestly, I did not mean to make a claim. My understanding of spacetime and blackholes are is limited. That's why I felt compelled to find some way to ask about these concepts in a place where I might get answers from people who know.

 

[PeterDonis]

I'll comment separately on misconceptions about the "barn and ladder" scenario, but really it's off topic for this thread and discussion of it should be in a separate thread.

Ernest and Jenefer experienced the exact same event.

There are multiple events in the scenario. An "event" is a particular point in spacetime. For example, "the front door of the barn opens" is an event. So is "the front end of the ladder passes the front doorway of the barn". But the whole scenario is not an "event"; it's multiple events with particular spacetime relationships.

Jill sees length dilation, and Ernest disagrees about the order of events. Both perspectives are real.

What you are calling a "perspective" is properly called a choice of coordinates. And the key thing to understand about choices of coordinates is that they aren't real things. They're human conventions to make it easier for us to do calculations. They're not part of the actual physics.

The actual physics of the scenario is the things that both observers agree on, i.e., the things that are independent of any "perspective" (choice of coordinates):

The front door of the barn opens before the front end of the ladder enters the front doorway of the barn.

The rear door of the barn opens before the front end of the ladder exits the rear doorway of the barn.

The front door of the barn closes after the rear end of the ladder enters the front doorway of the barn.

The rear door of the barn closes after the rear end of the ladder exits the rear doorway of the barn.

The time ordering of the four events according to different coordinate charts can be different because some of the events are spacelike separated. But nobody actually experiences events happening in a different order. It's just that their abstract calculation of the "times" of events that are separated from each other give different answers. But there is no physics corresponding to that. It's just an abstract calculation.

 

[PeterDonis]

It may well be that I have faulty reasoning, and I have no idea. I'm trying to figure out why.

Because you're starting from premises that have nothing to do with the black hole scenario.

You need to start fresh, from premises that apply to the black hole scenario. Your background might not be enough to even know what those are. But that means you shouldn't even be trying to formulate questions about what you think happens, because you don't know enough yet to be able to predict what should happen. You should be asking what the correct premises are to start reasoning from.

 

[Foretranimal]

You should not even be trying to draw any analogies between them.

I respectfully disagree: There is intrinsic value in looking at a flawed analogy for the purpose of figuring out why the analogy is flawed, provided you are open to corrected understanding.

 

[PeroK]

Heh...
I may have made conflicting claims. But honestly, I did not mean to make a claim. My understanding of spacetime and blackholes are is limited. That's why I felt compelled to find some way to ask about these concepts in a place where I might get answers from people who know.

When I was learning relativity I realised that all this about "perspectives" and "observers disagreeing" was unnecessary and leading the student (me) in the wrong direction. I realised that in physics there are coordinate systems, events and measurements, and I focused on that.

If you focus on events and coordinates, something like the barn and pole paradox just isn't a paradox at all.

My advice is: there is no such thing as a "perspective" in physics. You can analyse a physical scenario using any coordinate system; and, an observer can make a local observation, by measuring something locally. Note that an observer cannot make a direct measurement anywhere other than where they are. They can, however, infer that an event took place at a different place and time, based on their local measurements.

Note that in relativity it's possible to have events that cannot be observed by all observers. These events happen, in the sense that they are in the global model. And any observer can give them coordinates in an appropriate coordinate system. But, some observers can never make a local measurement that is a direct observation of that event.

In other words, it's nice if light from an event eventually reaches you. But, if it can't ever reach you, that does not mean that the event does not take place.

 

[Foretranimal]

Because you're starting from premises that have nothing to dowith the black hole scenario.

Awesome - thank you. Please tell me how my premises are flawed, so I might learn.

Your background might not be enough to even know what those are

OK, I believe you. What are my specific background limitations you are referring to?

I'm asking so I might know where I can improve them.

But that means you shouldn't even be trying to formulate questions about what you think happens.

I should not ask questions I don't already have a specific background to ponder and ask?

Why? Are you saying I should just stop thinking about this because I am not an expert?

Is there an inherent wrongness in asking questions that push the limit of your understanding?

Should I stop asking curious questions?

I'm asking so I might know where I can improve.

because you don't know enough yet to be able to predict what should happen.

No, I am not predicting anything, I don't have the background to make predictions - that is exactly why I am asking. I'm not asserting anything; I am asking.

You should be asking what the correct premises are to start reasoning from

OK, if it wasn't clear: I am asking for exactly that. Thanks in advance if you would like to offer guidance.

 

[Foretranimal]

When I was learning relativity I realised that all this about "perspectives" and "observers disagreeing" was unnecessary and leading the student (me) in the wrong direction. I realised that in physics there are coordinate systems, events and measurements, and I focused on that.

When I say disagree, I am only referring to observations made in different referance frames. I do not see a paradox in the differeing perspective of simultaniously, and non-simultaniously in there is no universal now.

As I understand it, the only differation of simultaniously/non-simultaniously is causality, becasue there is no now.

My advice is: there is no such thing as a "perspective" in physics. You can analyse a physical scenario using any coordinate system; and, an observer can make a local observation, by measuring something locally. Note that an observer cannot make a direct measurement anywhere other than where they are. They can, however, infer that an event took place at a different place and time, based on their local measurements.

I respectfully dissagree: while it may be apocriphal, The story of Eienstien's childhood facination was trying to picture what a light wave looked like if you traveled alongside at it's speed. Would you see a standing wave?

We know now the question is an impossility - but understanding what a faulty idea is faulty, can be a path to learning.

Note that in relativity it's possible to have events that cannot be observed by all observers. These events happen, in the sense that they are in the global model. And any observer can give them coordinates in an appropriate coordinate system. But, some observers can never make a local measurement that is a direct observation of that event.

Honestly, that seems intuitve to me, too. But there is no way to demonstrate any existance outside your personal light cone experience. How can we know for sure there is anyting real there?

Is that unobsevable place there for you and me when we can never affect it?