# Two interpretations of a gravitational event horizon

• B

## Main Question or Discussion Point

I would like to know which of the following interpretations of what happens when a local observer with a non-zero mass (i.e. not a photon) crosses the event horizon of a black hole:

1. Not only does the falling observer not *notice* anything strange (because his/her clocks run proportionally slower) - nothing strange *actually* happens (locally). The observer continues to exist, and move, towards the singularity after crossing the event horizon. All physical laws continue to hold true inside the horizon, events continue to cause other events, proper time continues to make sense.

2. Laws of nature, and therefore time, slow down (relative to remote observers in flat spacetime) as the falling observer approaches the event horizon. At the horizon, events can no longer cause other events, time freezes - not just for remote observers, but locally too, so the phrase "inside the black hole" has no physical meaning: nothing massive can actually ever cross the event horizon and continue to exist, as gravity makes any causal relationships impossible at the horizon and beyond it, so "proper time" no longer makes sense.

I believe #1 is the mainstream interpretation, but I wonder if there is an experiment that can falsify #2.

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PeterDonis
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I believe #1 is the mainstream interpretation
It's not just the mainstream "interpretation", it's the only consistent interpretation, at least if you ignore quantum effects (see below).

I wonder if there is an experiment that can falsify #2.
You don't need an experiment; requiring consistency is enough. Saying that "the laws of physics stop" doesn't make sense.

However, you left out a possibility:

3: Quantum effects change things enough so that the classical model of a black hole with an event horizon is no longer a valid approximation at the classical level. There are various speculations along these lines (for example, "firewall" models).

You don't need an experiment; requiring consistency is enough. Saying that "the laws of physics stop" doesn't make sense.
If, instead of saying, "the laws of physics slow down to a halt", I said "the gravity becomes so strong that local causality breaks down", would it make it any more consistent?

We already have to assume that the singularity is non-physical; #2 makes the singularity a much less interesting/special abstract extrapolation (if the topology of spacetime is allowed to have gaps/holes).

pervect
Staff Emeritus
My \$.02 is that if you can think of an experiment to falsify #2, it's not well defined enough to study. If you can't think of an experiment to test #2, it's not really a scientific formulation.

I don't believe there is an experiment to test #2, because I don't think it is a well defined enough proposal to have one. But if you can sharpen it up so that there is an experimental test of it, I'd have to change my mind.

pervect
Staff Emeritus
I also had another thought on the topic. One of the issues that isn't well defined for me is what sort of "time" is allegedly stopping at the event horizon. We've already argued that proper time does not stop at the event horizon, a clock that passes through the event horizon doesn't notice anything. So what, exactly, is stopping?

Rather than give my negative thoughts on the topic, I'll present the question as one that is worth thinking about. So the plan to show that my doubts about the idea are wrong and that it is well formulated would involve first finding what sort of time it is that allegedly stops at the horizon, then finding an experimental setup that measures it.

2. Laws of nature, and therefore time, slow down (relative to remote observers in flat spacetime) as the falling observer approaches the event horizon. At the horizon, events can no longer cause other events, time freezes - not just for remote observers, but locally too, so the phrase "inside the black hole" has no physical meaning: nothing massive can actually ever cross the event horizon and continue to exist, as gravity makes any causal relationships impossible at the horizon and beyond it, so "proper time" no longer makes sense.
This all hinges on the qualification that you have imposed in brackets. A particle can cross the event horizon, and its proper time is defined everywhere outside the "singularity". Understanding this is IMO beyond a B level answer, but for completeness here is a reference that explains the gory details. You might get something from looking at just the words and graphs if nothing else, look for the text around equations 7.29 to 7.55.

Dale
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I wonder if there is an experiment that can falsify #2.
Sure. Just try and cross an event horizon and see what happens.

Nugatory
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If, instead of saying, "the laws of physics slow down to a halt", I said "the gravity becomes so strong that local causality breaks down", would it make it any more consistent?
Are we talking about the event horizon or about the singularity at $r=0$? No matter how we define the "strength" of gravity at a point (strength of tidal forces at that point? Value of curvature invariants?), it need not be especially great at the horizon. In fact (and counterintuitively) the more massive the black hole, the less it is.
We already have to assume that the singularity is non-physical; #2 makes the singularity a much less interesting/special abstract extrapolation (if the topology of spacetime is allowed to have gaps/holes).
The spacetime is allowed to have gaps/holes, but the event horizon of a black hole isn't one of them. The singularity at the event horizon is a coordinate singularity, meaning that the problem is in the coordinates we use to label points rather than anything odd in the spacetime itself. (For a more intuitive example of a coordinate singularity, ask yourself what the longitude of the North Pole is. It doesn't exist, but that doesn't mean there's anything wrong with the surface of the earth there, it means that latitude and longitude are a poor way of navigating when you're near either pole).

PeterDonis
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If, instead of saying, "the laws of physics slow down to a halt", I said "the gravity becomes so strong that local causality breaks down", would it make it any more consistent?
Not unless you have a mathematically consistent model of local causality breaking down. In the context of classical GR, that would mean there would be no valid spacetime metric or manifold, which is not consistent.

Basically, you seem to be trying to formulate a precise theory in ordinary language. That doesn't work; ordinary language is too vague. Physicists use math to formulate theories for a reason.

PeterDonis
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The spacetime is allowed to have gaps/holes
Is it? The singularity at $r = 0$ is not a "gap" or "hole"; it's not part of the manifold at all. The manifold structure is continuous everywhere; AFAIK that is a requirement for any valid spacetime in GR.

Nugatory
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Is it? The singularity at $r = 0$ is not a "gap" or "hole"; it's not part of the manifold at all. The manifold structure is continuous everywhere; AFAIK that is a requirement for any valid spacetime in GR.
I was interpreting "gaps and holes" as layman-talk for "something that's not part of the manifold". You're right about the continuity requirement for a manifold, of course.

PAllen
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Is it? The singularity at $r = 0$ is not a "gap" or "hole"; it's not part of the manifold at all. The manifold structure is continuous everywhere; AFAIK that is a requirement for any valid spacetime in GR.
technically, you can remove the horizon and leave a valid manifold - you just have to leave an open set. Then it is continuous everywhere. Of course, it can also be analytically continued. But mathematical manifolds are built all the time by 'removing a point' or 'removing a submanifold'. It is only for physical reasons that these are untenable solutions in GR.

PeterDonis
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@PAllen, all of the points you raise are valid, but I think they are beyond the scope of a "B" level thread.

Basically, you seem to be trying to formulate a precise theory in ordinary language. That doesn't work; ordinary language is too vague. Physicists use math to formulate theories for a reason.
I do not have enough education, spare time, and possibly IQ, to build a new modern theory, but other people on this forum could spot an obvious mistake and help me direct my curiosity somewhere else.

I do not frequent this forum so I don't know how annoying repeated fallacies are for the old-timers :) but I still feel the need to explain why I had both interpretations in mind.

Mainstream interpretation #1 (that massive objects just keep moving towards the singularity) has a number of paradoxes. The first one is the singularity - yes, I understand the North Pole argument and that it may simply be a coordinate issue, but I believe there are also some open questions on what happens with matter at that point? The second one is the black hole information paradox. If massive objects never cross the event horizon in the first pace, both paradoxes are resolved nicely - the singularity becomes just an abstract mathematical extrapolation into essentially a rupture in spacetime topology, and information is never lost.

Interpretation #2 is influenced by the apparent similarity between a massive object trying to reach the speed of light and one approaching a gravitational event horizon. In both cases, all distant observers will agree that they will never see either event happen. The question I am asking myself is: what if that consensus is not an illusion, but the objective reality? (It may be a meta-physical question, since "reality" is hard to define).

...If matter never crossed the event horizon, why or how could that possibly work? This indeed requires a new theory. I cannot build one, but if I could - where would I start?

I'd probably start from understanding time. In reaching the speed of light and reaching the event horizon time dilation is very prominent. I think of time as a relative rate of physical causes and effects. A massive object moving away from a photon causes the light to travel extra distance, delaying the "cause" (photon emitted) - "effect" (photon absorbed) relationship. The notion of time as a rate of cause-effect relationships can be applied to all physical laws, including physical existence and motion itself: an object existing in point X with momentum M "causes" itself (or a copy) to occupy point X+dX with the mass, energy, and momentum M preserved (carried over). If "cause-effect" has maximum "local reach" (defined by the constant speed of c) then a massive object cannot attain the speed of light simply because it cannot "cause" itself to appear outside its local cause-effect cone.

Would it be right to apply the same cause-effect interpretation to what happens near a gravitational event horizon? Can there be any consistent math that would allow gravity to slow "cause-effect" relationships down and "compress" the future cone so it ends at the horizon and never extends past it? The falling "Achilles turtle" observer would still not notice anything strange as their clock would slow down proportionally; all distant observers would still see the same picture. The only (falsifiable?) prediction this interpretation seems to make is that it claims that no massive object has ever crossed a gravitational event horizon in the history of Universe, never will, and no information has ever been "lost" in black holes (that wasn't there in the first place).

(All of this applies to massive objects only. I am not sure how to extend interpretation #2 to photons and neutrinos. Perhaps they do reach the event horizon and perhaps they orbit it indefinitely - if so, then all external energy and information exists on black hole surfaces, nothing is inside their volumes. Alternatively, they move in and reach the singularity).

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PAllen
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Textbookspirit is a better goal than netspirit

Nugatory
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In both cases, all distant observers will agree that they will never see either event happen. The question I am asking myself is: what if that consensus is not an illusion, but the objective reality?
"Will never see either event happen" is an imprecise way of saying "light from either event will never reach the eyes", and whether that happens or not is an objective reality - either light reaches the eye or it doesn't. Everyone who understands relativity understands that this is an objective fact and not an not an illusion, so your question is based on a mistaken understanding of what the consensus is.

In a curved spacetime it is harder to reason about which eyes will be reached by light emitted by which events, so it's a good idea to try to figure all of this stuff out in flat spacetime first. Taylor and Wheeler's "Spacetime Physics" would be a good start. Once you understand the flat spacetime case (and especially the crucial distinction between proper time and coordinate time) you'll be able to take on the curved spacetime case including the black hole event horizon. When you do, start with a Kruskal diagram (Google is your friend here) to avoid being misled by the coordinate singularity at the event horizon when you use Schwarzschild coordinates.

Dale
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This indeed requires a new theory. I cannot build one, but if I could - where would I start?
You should start by learning the current theories. We can help you there.

PeterDonis
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I do not have enough education, spare time, and possibly IQ, to build a new modern theory
Then you don't have the wherewithal to speculate about what a new theory might look like either.

Interpretation #2 is influenced by the apparent similarity between a massive object trying to reach the speed of light and one approaching a gravitational event horizon.
This apparent similarity is only apparent. When you actually look at the math, you realize that there is no valid analogy between these two cases. But to do that, you have to know the math, which means you have to know what the theory actually says, not pop science descriptions in ordinary language.

This indeed requires a new theory. I cannot build one, but if I could - where would I start?
You would start by taking the time to learn our best current theories before trying to build your own. Right now, by your own admission, you do not have the background to start, or even to speculate about where you would start, if you were going to build a new theory. The right thing to do in that case is to not speculate.

PeterDonis
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You should start by learning the current theories. We can help you there.
We can help, but I don't think this thread provides a starting point for that.