Thought Experiment from my daughter regarding black holes

[Mark Scalabrin]

My daughter is 12 and we like to discuss black holes. Here is our thought experiment:

Gravity bends space and time lengthening both from the observers perspective.

• Does time slow down the farther you get from objects with density? Is there a place way way out, out of the range of the Big Bang flotsam that time moves very slowly?

• Light is also impacted by gravity. Through telescopes it can be seen bending as it goes past dense objects. But gravity is not really bending light, it is bending space and light is just following the groove laid out for it.

The question she (we) have is regarding black holes. Black holes are really really dense and bend space and lengthen time to what to us would seem like infinite lengths. The photon follows this intense groove laid of for it but since it takes so long to get to the bottom, we never see it again. Space and time are lengthened to near infinity. But someday it would come out the other side right? It goes the long way and the clock slows so for all intense and purposes to us it is forever but not really.

If that is true, then all objects that fall in are following the groove laid out for them and eventually would reach the bottom or the U-turn point in space where it would start coming back out. Sure they would mashed together into sub-atom particles like quarks and gluons at that point.

Just like the light that was observed by the telescope the matter is following the same groove and will eventually reach rock bottom and start coming the other way.

So someday would more mass be moving back up than flowing down, creating a bolus that drags everything with it by changing the center of gravity. In other words a tipping point would occur when more mass is heading up than is heading down. Eventually everything would emerge, almost at once.

Are we on the correct track in our thinking? Is that not what happened during the big bang?

 

[Orodruin]

both from the observers perspective.

What observer?

Gravity bends space and time lengthening both from the observers perspective.

More accurate would be to say that spacetime is curved. "Bend" is not really a word used in this context.

Does time slow down the farther you get from objects with density?

The density of the gravitating object is not what is relevant. What is relevant is the gravitational potential. Also, gravitational time dilation is an effect that makes the time of a stationary observer near a black hole run slower than that of a stationary observer far away from it, not the other way around.

out of the range of the Big Bang flotsam

There is no such thing. Big Bang was not an explosion in the usual sense of the word. The Big Bang occurred everywhere.

Light is also impacted by gravity. Through telescopes it can be seen bending as it goes past dense objects. But gravity is not really bending light, it is bending space and light is just following the groove laid out for it.

Pretty accurate.

But someday it would come out the other side right?

No. Also, there is no such thing as a "bottom". Space and time are very intertwined in a black hole and you really cannot talk about them separately. You need to talk about the geometry of spacetime. This is notoriously difficult to imagine, in particular without having the proper underlying background in mathematics.

 

[PeterDonis]

Gravity bends space and time lengthening both from the observers perspective.

This is not correct. Your own space and time that you experience does not change at all. What changes is how you appear to other observers at different positions in the gravity well. And the only thing gravity changes about how you appear to other observers is the rate of your clock; your apparent length isn't changed.

Does time slow down the farther you get from objects with density?

No, it speeds up; more precisely, given what I said above, from the viewpoint of a given observer, call him O, time appears to run slower closer to the gravitating object than O, and time appears to run faster further away from the gravitating object than O.

Is there a place way way out, out of the range of the Big Bang flotsam that time moves very slowly?

I don't know what you mean by "out of range of the Big Bang flotsam". But a key point to keep in mind is that what I said above about how gravity affects time is only valid under static conditions: basically that you are only considering a single gravitating object and a region of spacetime around it that is not affected by anything else in the universe. On the scale of the universe as a whole, "gravity" in the sense we usually think of it is simply not a useful concept, nor is any concept of gravity affecting time. So it doesn't make sense to think of how "time flows" billions of light years away from us, as compared to here on Earth.

gravity is not really bending light, it is bending space and light is just following the groove laid out for it.

You can think of it this way if you are considering only the effect of a single gravitating object on light rays passing it. But on the scale of the universe as a whole, this intuitive model no longer works.

Black holes are really really dense

Not in the ordinary sense. Black holes are not like ordinary objects; they are not made of matter. In fact they are vacuum inside. If they are made of anything, it is spacetime curvature. The mass of a black hole is not contained in matter inside it; it is a property of the spacetime geometry itself.

and bend space and lengthen time to what to us would seem like infinite lengths.

No, they don't. Pop science descriptions are misleading in this respect; the fact that time appears to "stop" in the limit as the horizon of a black hole is reached is an optical illusion. If you were to actually fall into the hole, you would find your time to be flowing normally and you would have no trouble falling through the horizon in a finite amount of your time.

But someday it would come out the other side right?

No. Anything that falls into a black hole will never come out again.

Are we on the correct track in our thinking?

No. See above.

Is that not what happened during the big bang?

No. The Big Bang is nothing like a black hole.

If you want to get a good layman's understanding of black holes, I suggest Kip Thorne's Black Holes and Time Warps. There is a lot more in this book than just the physics of black holes; Thorne also discusses the history of black holes, how they were discovered and how our understanding of them has developed. The book was published in 1993, but everything in it is still valid today; the main advance we have made is that LIGO, the gravitational wave observatory, which was described as a future project in the book, is now actually working and detecting gravitational waves. Thorne's book does not require any advanced mathematics and, while it will take some time to work through it, much of it should be within the grasp of a bright 12 year old.

 

[Mark Scalabrin]

Thank you both for your responses. I will look up Kip Thorne's book to further my dialog with my daughter.

 

[Dale]

Space and time are lengthened to near infinity. But someday it would come out the other side right?

No. in a very short amount of proper time it gets arbitrarily close to the singularity where it gets ripped apart. There is no coming out the other side.

Is there a place way way out, out of the range of the Big Bang flotsam

There is no such place. The Big Bang doesn’t have a range. It happened everywhere in the universe.