What does When the Universe was one minute old mean?

[bapowell]

It is confusing, as we have two frames of reference. Note that they say: "taking an infinite time to reach it" - is that from our "at rest" point of view?

Yes, "to the distant observer" it "takes an infinite time to reach it". This means that, on the distant observer's watch, it takes an infinite amount of time for the free falling observer to cross the horizon.

The free falling observer is oblivious to this fact, and just goes right on falling into the black hole. Even though he can't say exactly when he crossed it, he does indeed cross it, and after a finite amount of time.

 

[John Bleau]

I'm wondering if the event horizon itself is observer-dependent. Say now that the observer is on Earth, which is revolving around the sun. When Earth is moving in the direction of the black hole, I doubt that makes the observer suddenly see the traveler cross the event horizon. I imagine this is the case regardless of the observer's velocity (as long, anyway. as we're not catching up to the traveler) - to us it takes an "infinite amount of time" for him to reach the event horizon.

Are we on the same page on this?

 

[John Bleau]

I'm wondering if the event horizon itself is observer-dependent. Say now that the observer is on Earth, which is revolving around the sun. When Earth is moving in the direction of the black hole, I doubt that makes the observer suddenly see the traveler cross the event horizon. I imagine this is the case regardless of the observer's velocity (as long, anyway, as we're not catching up to the traveler) - to us (observers) it takes an "infinite amount of time" for the traveler to reach the event horizon.

Are we on the same page on this?

 

[bapowell]

The event horizon of a black hole is observer independent. It is a property of the asymptotic structure of the spacetime, not on the worldline of any particular observer.

Also, it's not just a matter of relative motion. Are you suggesting that as long as the outside observer is moving then he no longer sees the free falling-into-the-black hole observer's time dilating? I probably started that by saying "to an observer at rest" in an earlier post. Since we are talking about gravitational time dilation here, what's relevant is the curvature of spacetime in the neighborhood of each observer. The intense gravity of the black hole is redshifting the free falling observer's time relative to the outside observer, regardless of the outside observer's state of motion.

 

[John Bleau]

Apart from your first sentence, we're on the same page.

Let's now take your last sentence. It will serve well to illustrate just why I'm confused.

The intense gravity of the black hole is redshifting the free falling observer's time relative to the outside observer, regardless of the outside observer's state of motion.

Let us now take a second traveler B, following the first traveler A toward the event horizon. Let us also say that traveler A's velocity is such that he remains in front of B (ie, between B and the event horizon, or heading toward the EH at greater velocity). From B's perspective, A takes forever to cross the event horizon, yet is between it and B. How can this be so while at the same time B, from his own perspective, crosses the event horizon in finite time?

 

[bapowell]

Good question, John. I'm not immediately sure what the answer is. I would suggest that once B reaches the event horizon, his clock is equally redshifted relative to A's clock. Perhaps they both fall in at the same time according to B, while A thinks that A falls in first. There's no paradox here, since simultaneity is observer dependent.

 

[John Bleau]

Thanks bapowell,

I consider the question still open, though it has strayed somewhat from the original post (though it's still related in a manner I was hoping to clarify). My own conception of the event horizon is similar to the speed of light in SR - we can accelerate as much as we please, the speed of light remains unattainable. Likewise for "approaching" the EH. But possibly this is a topic for another thread after which we could return to this one. Or maybe it's already been broached - I don't know, I'm new here.

Anyway, thanks, I learned quite a bit.

At any rate, I have to get back to work. I'll pop by tomorrow or next week.

 

[DevilsAvocado]

There's another much more sophisticated version of this.

Okay, that explains it.

 

[DevilsAvocado]

... My own conception of the event horizon is similar to the speed of light in SR - we can accelerate as much as we please, the speed of light remains unattainable. Likewise for "approaching" the EH.

I think the answer to your EH question is here:

http://en.wikipedia.org/wiki/Event_horizon#Interacting_with_an_event_horizon"
...
For the case of the horizon around a black hole, observers stationary with respect to a distant object will all agree on where the horizon is. While this seems to allow an observer lowered towards the hole on a rope to contact the horizon, in practice this cannot be done. If the observer is lowered very slowly, then, in the observer's frame of reference, the horizon appears to be very far away, and ever more rope needs to be paid out to reach the horizon. If the observer is quickly lowered by another observer, then indeed the first observer, and some of the rope can touch and even cross the (second observer's) event horizon. If the rope is pulled taut to fish the first observer back out, then the forces along the rope increase without bound as they approach the event horizon, and at some point the rope must break. Furthermore, the break must occur not at the event horizon, but at a point where the second observer can observe it.

Attempting to stick a rigid rod through the hole's horizon cannot be done: if the rod is lowered extremely slowly, then it is always too short to touch the event horizon, as the coordinate frames near the tip of the rod are extremely compressed. From the point of view of an observer at the end of the rod, the event horizon remains hopelessly out of reach. If the rod is lowered quickly, then the same problems as with the rope are encountered: the rod must break and the broken-off pieces inevitably fall in.

These peculiarities only occur because of the supposition that the observers be stationary with respect to some other distant observer. Observers who fall into the hole are moving with respect to the distant observer, and so perceive the horizon as being in a different location, seeming to recede in front of them so that they never contact it. Increasing tidal forces (and eventual impact with the hole's gravitational singularity) are the only locally noticeable effects. While this seems to allow an in-falling observer to relay information from objects outside their perceived horizon but inside the distant observer's perceived horizon, in practice the horizon recedes by an amount small enough that by the time the in-falling observer receives any signal from farther into the hole, they've already crossed what the distant observer perceived to be the horizon, and this reception event (and any retransmission) can't be seen by the distant observer.

Edit: http://en.wikipedia.org/wiki/Apparent_horizon" is observer-dependent.

 

[John Bleau]

Thanks for your reply, DA.

This suggests to me that if our universe is emerging from a white hole or falling into a black hole, then there is no reaching the singularity. It would mean that, in fact, we have been emerging from the Big Bang indefinitely.

I suspect that "when the Universe was one minute old" is a projection of our local geometry to the singularity. On the rubber sheet model, this would be akin to our extending a straight line and not having it curve along the rubber sheet.