What is the length of a meter at an event horizon?

[captcass]

Here is one I am sure you folk can help me with.

The length of a meter must adjust with the rate of time to maintain c.

I take this to mean that if we cut the rate of time by .5, we have to double the length of the meter.

If the rate of time appears to approach 0 at the event horizon of a black hole, shouldn't a meter seem to approach infinity in length?

If so, why do we perceive a compression of space instead instead of an expansion of space? Do Lorentz contractions explain it?

Thanks

[Strange]

You are trying to apply concepts from special relativity to a black hole. That is doomed to failure!

The coordinate speed of light (the speed of light as measured by a distant observer) at the event horizon is zero.

Also, the "rate of time" does not approach zero. Coordinate time (the "rate of time" the distant observer sees) goes to infinity: clocks go slower so a second gets longer and eventually becomes infinite at the event horizon. (This might just be a confusion in the use of words; "rate of time" is ambiguous at best.)

 

Edited February 27, 2018 by Strange

[captcass]

Thanks. That helps a lot. So if the second is longer, then the meter is shorter and so we compression?

[Strange]

Not necessarily, because the (coordinate) speed of light is not constant. 

More here: http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html

I don't think there is an unambiguous or unique way of comparing lengths. It will be different of the ruler is in free fall or hovering at the event horizon. It might even depend on which coordinate system you use.

 

[captcass]

There is a direct correlation in SR, right? The Lorentz contractions show us slower clocks and shorter meters that maintain c?

[Strange]

3 minutes ago, captcass said:

There is a direct correlation in SR, right? The Lorentz contractions show us slower clocks and shorter meters that maintain c?

Yes. 

[captcass]

Great. Thanks, Strange, that was driving me nuts at the event horizon.

25 minutes ago, Strange said:

It will be different of the ruler is in free fall or hovering at the event horizon

Wouldn't all objects be in free fall unless under propulsion?

At the black hole, when the clock rate slows, velocity would appear to go to 0 and the object would then appear to just hover?

[Strange]

23 minutes ago, captcass said:

Wouldn't all objects be in free fall unless under propulsion?

Yes.

Quote

At the black hole, when the clock rate slows, velocity would appear to go to 0 and the object would then appear to just hover?

Not quite. It would get slower and slower and then disappear. You would never see it stuck there (despite all the popular science articles) because it would fall through the event horizon in finite time and so there would be a finite number of photons available to be seen. 

[captcass]

20 minutes ago, Strange said:

because it would fall through the event horizon in finite time

Thank you. This is what I thought.

You have really helped me here.

[MigL]

If you were falling through the event horizon with a 1 m long stick, you would measure it to be exactly 1 m.

[captcass]

1 hour ago, MigL said:

If you were falling through the event horizon with a 1 m long stick, you would measure it to be exactly 1 m.

Exactly. And a second would be a second and light would be traveling at c. Einstein said at one point he thought you could drive a car through it.

I am now wondering what an observer at the event horizon would see in our direction, as we see compression there. Would they also see us as at the event horizon of a black hole, in compressed space, or as being at the edge of the galaxy, in expanding space, as we perceive it?

If expanding, would that present the same as what we see at ~13.9 Gly

OMG! I just noticed I went from a -10 to a -9. See, I told you folks, there is a god!

[captcass]