Questions from a 13-year-old

[DallasDad]

My son watched the first episode of Curiosity (with Stephen Hawking) tonight. He had a couple of questions about it, shouted out during the episode, then discussed afterward.

1. How do scientists know that time "stops" within a black hole?

2. What does it mean to say that time stops? How can anything happen if there is no progression from one instant to the next?

3. If the original infinitesimal black hole had time stopped, how could it have changed into the big bang? He gets that before the big bang (if one can even discuss such a concept) there was no time, but says this means nothing happened. How could there be a transition from one state to the next without a before and after?

4. When I tried to tell him about quantum fluctuation, we both got muddled by questions 1,2, and 3. How can a particle pop into existence if time has stopped?

If the answers involve statements like, "Well, back then, in the first femtoseconds of the universe, different physical laws applied," his question will be guaranteed to be, "How do scientists know that?"

We've been through all the classic experiments about relativity together, so he understands (at an elementary level) about falsifying hypotheses, and how some of the hardest-to-understand ideas in science have been tested. We also briefly discussed Hubble's work, so he understands how the idea of expansion was developed.

His math is at the algebraic level. I don't think showing him more advanced formulae would help very much. I'd like something more practical and appropriate for his developmental level. To pull an example out of my hat, something like "The same theories and formulae that explain black holes explain X. If the theories were wrong, X wouldn't work, so even if we can't understand exactly everything that went into the big bang, we can know the theories are correct because we can see X working."

My first thought for X was the relativity corrections required by the GPS system, but I think that's a bit too esoteric. Can we find an X more like a toaster, or a racecar?

[rjh01]

Not sure about black holes, however time does slow down when gravity increases. We know this because clocks run slower on Earth than in outer space. Also scientists failed to correctly calculate the orbit of Mercury until relativity was discovered.

We also know that time slows down when something is moving close to the speed of light. We know this because radioactive particles live longer than they should in an accelerator.

[shadron]

One thing that may be a block to understanding is that you may be confusing the event horizon with the black hole it contains when you say that time stops in the black hole. The event horizon is not a wall; it is only sensible by its lack of radiation outside it. As you accelerate towards the black hole, both the speed and gravity increase, and so time slows down. The black hole itself is a singularity - a point, and as you near it time slows, such that it truly stops, and you reach the speed of light, and the gravity becomes infinite, only when you've actually "arrived".

[marplots]

Here's a way to think about #3

When the big bang happens, time starts too. If you want to think of "before" time started and "after" time started, that's OK, I suppose, but it's misleading.

Sometimes people will use an analogy based on directions on the surface of the Earth. What's north of the north pole? Well, nothing; it's as north as you can get. But what's the north pole south of? Again, nothing. The question assumes there is someplace that doesn't exist on the surface of the earth. Without extending the dimensions involved, the questions don't work.

You can also ask him to imagine time stopping. That's usually pretty easy. Then ask what happens after time stops. Well, nothing happens, time has stopped. That question doesn't make any sense.

Then ask him what it would be like for someone to travel backwards from time stopping to now. It's a parallel situation with the beginning... nothing happens... then something happens -- and one of the things that happens is time.

[JJM 777]

Originally Posted by rjh01

time does slow down
(...)
We know this because clocks run slower on Earth than in outer space.

I wouldn´t accept that as a direct proof, because it is possible that the circumstances affect the clock as a device, not time itself.

A bad allegory: my wristwatch goes off correct time. That proves something about the device, not time itself.

Originally Posted by rjh01

time slows down when something is moving close to the speed of light. We know this because radioactive particles live longer than they should in an accelerator.

I wouldn´t accept this as proof either, because it is possible that the circumstances affect the lifetime of radioactive particles, not time itself.

A bad allegory: the Japanese live longer than Americans. That proves something about Japan, not about time itself.

[rjh01]

Originally Posted by JJM 777

Originally Posted by rjh01

time does slow down
(...)
We know this because clocks run slower on Earth than in outer space.

I wouldn´t accept that as a direct proof, because it is possible that the circumstances affect the clock as a device, not time itself.

A bad allegory: my wristwatch goes off correct time. That proves something about the device, not time itself.

Originally Posted by rjh01

time slows down when something is moving close to the speed of light. We know this because radioactive particles live longer than they should in an accelerator.

I wouldn´t accept this as proof either, because it is possible that the circumstances affect the lifetime of radioactive particles, not time itself.

A bad allegory: the Japanese live longer than Americans. That proves something about Japan, not about time itself.

Wrong on both counts. If your wristwatch goes off correct time the time it tells will not be predictable. However the what I have said is predictable. It has also been done many times. GPS depends on it.

[arthwollipot]

Without getting into the concept of approaching limits, I'd try this:

Time doesn't stop, so much as slow down. The closer you get to the centre of the black hole, the slower time runs. When you're really close, time runs really slow, and you probably wouldn't notice it running at all, it's that slow.

[sphenisc]

Originally Posted by arthwollipot

Without getting into the concept of approaching limits, I'd try this:

Time doesn't stop, so much as slow down. The closer you get to the centre of the black hole, the slower time runs. When you're really close, time runs really slow, and you probably wouldn't notice it running at all, it's that slow.

If you approach a black hole time will run normally for you throughout your journey. It's only for a distant observer that your time can be said to be slowing downing - relative to their local clock.

[arthwollipot]

Originally Posted by sphenisc

If you approach a black hole time will run normally for you throughout your journey. It's only for a distant observer that your time can be said to be slowing downing - relative to their local clock.

This is true. But for a 13-year old I'd probably gloss over it unless I got an indication that the kid was genuinely interested. And then I'd go for the 'but wait, it gets better!' gambit.

[W.D.Clinger]

Originally Posted by DallasDad

1. How do scientists know that time "stops" within a black hole?

As several people here have already noted, that sounds like a popularization, which may also be conflating two different things:

• The singularity (at the "center" of a black hole) isn't part of the spacetime universe: Its defining characteristic is that the spacetime universe doesn't include the singularity, and the mathematical notion of spacetime can't be extended to include the singularity. Since the singularity isn't part of spacetime, the usual notions of time don't make sense at the singularity.
• As seen by distant observers, clocks slow down as they approach the event horizon of a black hole, and are never seen to enter the event horizon. That, however, is an observer-dependent (relativistic) effect. If the observer himself were approaching the event horizon, his wristwatch would continue to operate normally, and he'd see himself passing through the event horizon at a normal rate of speed.

Originally Posted by DallasDad

2. What does it mean to say that time stops? How can anything happen if there is no progression from one instant to the next?

We don't know what happens at a singularity. We don't even know what the word "happen" might mean at a singularity.

Originally Posted by DallasDad

3. If the original infinitesimal black hole had time stopped, how could it have changed into the big bang? He gets that before the big bang (if one can even discuss such a concept) there was no time, but says this means nothing happened. How could there be a transition from one state to the next without a before and after?

We don't know. Maybe he'll be the first to figure it out someday.

Originally Posted by DallasDad

4. When I tried to tell him about quantum fluctuation, we both got muddled by questions 1,2, and 3. How can a particle pop into existence if time has stopped?

Except for the singularity, time continues inside the event horizon of a black hole. That means there's no conceptual problem with Hawking radiation.

Originally Posted by DallasDad

If the answers involve statements like, "Well, back then, in the first femtoseconds of the universe, different physical laws applied," his question will be guaranteed to be, "How do scientists know that?"

We're just guessing that different physical laws applied. What we know for sure is that the physical laws we think we understand can't apply at the singularity. (The singularity is defined by the fact that the spacetime manifold can't be extended to include the singularity without breaking the laws of general relativity.)

Originally Posted by DallasDad

something like "The same theories and formulae that explain black holes explain X. If the theories were wrong, X wouldn't work, so even if we can't understand exactly everything that went into the big bang, we can know the theories are correct because we can see X working."

My first thought for X was the relativity corrections required by the GPS system, but I think that's a bit too esoteric. Can we find an X more like a toaster, or a racecar?

Some of the usual values for X are:

• precession of Mercury
• gravitational lensing
• Shapiro delay
• gravitational redshift and the Pound-Rebka experiment
• expansion of the universe (inferred from the Hubble Law)
• cosmic microwave background radiation
• relative abundance of hydrogen and helium (predicted by Big Bang nucleosynthesis)

General relativity's prediction of a nearly isotropic microwave background radiation, which was first observed twenty years later (by accident), was one of the more spectacular values for X.

By the way, I'd emphasize that while general relativity is the best theory we've got for explaining the above values of X, we might someday have an even better theory. Although general relativity can't explain what goes on at singularities, we hope to develop more comprehensive theories that will.

[Cayvmann]

Originally Posted by arthwollipot

Without getting into the concept of approaching limits, I'd try this:

Time doesn't stop, so much as slow down. The closer you get to the centre of the black hole, the slower time runs. When you're really close, time runs really slow, and you probably wouldn't notice it running at all, it's that slow.

I usually describe something slowing by using the concept of time. How do you describe slow time, without time? Seems self referential to me. Maybe there's an absolute time, that this time is slower than?

[sphenisc]

Originally Posted by Cayvmann

I usually describe something slowing by using the concept of time. How do you describe slow time, without time? Seems self referential to me. Maybe there's an absolute time, that this time is slower than?

Okay Arti, you've got the kid interested...go for it!!

[DallasDad]

Thanks, everyone. You've provided many excellent ideas for me to explore with him. I wish there were something more mundane to use for a lesson, but if he can ask the questions he's asking, he should be able to follow some of the examples.

I suspect he's asking more about epistemology^[1] than GR, although of course the two are intertwined via the scientific method.

^[1] By epistemology, I mean the three "great questions" of knowledge: 1) What do we know? 2) How do we know? and 3) How do we know we know? He's on stage 2 in most areas of philosophical reasoning, but is still skeptical of formal proofs unless he can translate them into something concrete. In an attempt to capture his cupidity and expand his reasoning capabilities, I've introduced him to simple cyphers recently. He loves having figured something out as much as he dislikes the skull sweat required (much as I, a writer, hate writing but love having written). Perhaps if I introduce some of the GR experiments as puzzles, he'll be more willing to dig into them. One of the hardest things for him (as with most of us, actually) is wanting the understanding without doing the work.

[bjornart]

Originally Posted by DallasDad

Thanks, everyone. You've provided many excellent ideas for me to explore with him. I wish there were something more mundane to use for a lesson, but if he can ask the questions he's asking, he should be able to follow some of the examples.

I suspect he's asking more about epistemology^[1] than GR, although of course the two are intertwined via the scientific method.

^[1] By epistemology, I mean the three "great questions" of knowledge: 1) What do we know? 2) How do we know? and 3) How do we know we know? He's on stage 2 in most areas of philosophical reasoning, but is still skeptical of formal proofs unless he can translate them into something concrete. In an attempt to capture his cupidity and expand his reasoning capabilities, I've introduced him to simple cyphers recently. He loves having figured something out as much as he dislikes the skull sweat required (much as I, a writer, hate writing but love having written). Perhaps if I introduce some of the GR experiments as puzzles, he'll be more willing to dig into them. One of the hardest things for him (as with most of us, actually) is wanting the understanding without doing the work.

What we know when it comes to black holes and the big bang is that the universe can be described by maths, the maths we currently have has proven to fit the universe we observe, but there are some odd results relating to time and gravity and the universe's origin. Some of those odd results have given predictions that have turned out to be correct, such as some relating to black wholes, others we presume are true because we have no good alternatives and they fit what we observe today.

[epepke]

Basic question: have you explained Special Relativity for him? That might be better than starting with gee whiz science shows. Special Relativity can easily be explained qualitatively to any reasonably bright 13-year-old. If he can handle the Pythagorean theorem, then it can be explained quantitatively as well.

I'm suggesting this because a thorough grokkage of the fact that times and distances differ depending on the observer is, I think, necessary even to start with things like black holes and the big bang. I recommend not just giving him a book but doing it as a father/son thing. If you need a book to work from, I recommend Martin Gardner's Relativity Simply Explained.

It's also important to understand the concept of a singularity. I start with an old joke. There is a house, and all sides have a southern exposure. A bear walks by. What color is the bear? The answer, of course, is "white," because the only place on Earth that could be is at the North Pole. So what is North of the North pole? There is no answer. All directions are South. The mathematics of North/South/East/West break down at the North Pole; it is a singularity.

[W.D.Clinger]

Originally Posted by epepke

It's also important to understand the concept of a singularity. I start with an old joke. There is a house, and all sides have a southern exposure. A bear walks by. What color is the bear? The answer, of course, is "white," because the only place on Earth that could be is at the North Pole. So what is North of the North pole? There is no answer. All directions are South. The mathematics of North/South/East/West break down at the North Pole; it is a singularity.

That's a nice example.

At the risk of going into too much detail, that's an example of a coordinate singularity, which can be fixed (locally!) by adopting a different coordinate system (which will then have its own coordinate singularity somewhere else). With black holes, what appears to distant observers as a stoppage of time at the event horizon is also a coordinate singularity; observers travelling into the black hole experience no slowing of time within their own local coordinate system.

The Big Bang singularity and the singularities that reside within black holes are essential singularities: They cannot be made to disappear by choosing a different coordinate system.

[arthwollipot]

Originally Posted by Cayvmann

I usually describe something slowing by using the concept of time. How do you describe slow time, without time? Seems self referential to me. Maybe there's an absolute time, that this time is slower than?

You're right, but in explaining it to a non-technical person, you have to gloss over it. Most people will understand what you mean when you say 'time slows down' and if they question that phrase, then you can go into further detail about precisely what that means.

[TrapperJ]

Originally Posted by DallasDad

before the big bang (if one can even discuss such a concept) there was no time, but says this means nothing happened. How could there be a transition from one state to the next without a before and after?

Since time as we know it began at the big bang, it's hard to visualize it. Several top theoretical physicists are postulating what may have happened before the big bang. The link below goes through a few of them in laymans terms so hopefully that will help you explain/understand it.

zidbits.com/2011/10/what-happened-before-the-big-bang/