Common Misconceptions within Physics and Astronomy

[Goemon]

What does acceleration even mean at the event horizon?

The same thing it means anywhere else... and in this case, if you want to remain stationary at Schwarzschild radius r = 2m, you'll need to generate infinite thrust. Which is probably hard on your fillings.

[Diadem]

You can't be at r=2m. That's my point. It's ill-defined.

[doogly]

There's nothing wrong with r=2m.

I think you are looking at the metric as if it were significant; it is not. Pure coordinate artifact. Get thee to the curvature.

[gmalivuk]

What does acceleration even mean at the event horizon?

It means proper acceleration, as measured by the person at (or near) the event horizon.

However, what I wasn't considering was gravitational time dilation. Is that what makes it possible for proper acceleration due to gravity to be arbitrarily low near the horizon, despite approaching infinity as measured by a distant observer?

Edit: I'm inclined to think no, given the same discussion when it happened before. The conclusion there, which seemed sensible to me at the time, was that hovering motionless with respect to a (static) black hole gets harder as you get closer, and the required force approaches infinity as you approach the event horizon.

[Diadem]

There's nothing wrong with r=2m.

I think you are looking at the metric as if it were significant; it is not. Pure coordinate artifact. Get thee to the curvature.

Of course it's a pure coordinate artifact. But that's the point. Your metric blows up at r=2m. So terms like 'acceleration' become meaningless. Sure you could look at the situation using a different set of coordinates. And acceleration would make perfect sense in the new coordinates. But what does that mean, compared to acceleration as measured in the old coordinate system? Nothing, it's meaningless. You can't compare quantities measured in different coordinates system.

What does acceleration even mean at the event horizon?

It means proper acceleration, as measured by the person at (or near) the event horizon.

However, what I wasn't considering was gravitational time dilation. Is that what makes it possible for proper acceleration due to gravity to be arbitrarily low near the horizon, despite approaching infinity as measured by a distant observer?

Well the acceleration as seen by a far away observer will in fact go to zero. Objects that fall into a black hole slow down and 'never' reach the horizon because at that point they will appear frozen in time (except that they'll also be redshifted into invisibility. But that's not relevant here). So an outside observer will see both velocity and acceleration of an object falling into a black hole approach zero.

[doogly]

What old coordinates are you talking about?

You are at the event horizon. You have coordinates in which you are presently at rest. But, you stop being at rest. You experience acceleration in this system. That's what we're talking about.

[Diadem]

What old coordinates are you talking about?

You are at the event horizon. You have coordinates in which you are presently at rest. But, you stop being at rest. You experience acceleration in this system. That's what we're talking about.

Ok. Back before leaving for the black hole, you were sitting at earth, and measured the acceleration in free fall there. You measured it at 9.81 units of r per unit of t^2. Now you sit at the event horizon of your black hole. Your old (t, r ,θ, φ) coordinates became singular, so you abandoned them in favour of (v, u, θ', φ'). You again measure your acceleration. You measure it as, I don't know, 5 units of u per unit of v^2.

Which is bigger?

I don't know. Do you?

[gmalivuk]

So an outside observer will see both velocity and acceleration of an object falling into a black hole approach zero.

I'm hovering just outside a black hole. From here, I couldn't really care less what some jerk sitting safely at infinity thinks he sees. The accelerations and forces I care about are the ones I observe from here.

Ok. Back before leaving for the black hole, you were sitting at earth, and measured the acceleration in free fall there. You measured it at 9.81 units of r per unit of t^2. Now you sit at the event horizon of your black hole. Your old (t, r ,θ, φ) coordinates became singular, so you abandoned them in favour of (v, u, θ', φ'). You again measure your acceleration. You measure it as, I don't know, 5 units of u per unit of v^2.

Which is bigger?

I don't know. Do you?

We're changing coordinates, not metrics. I brought my stopwatch and my scale and my measuring tape with me from Earth. Are they afraid of black holes? Have they magically stopped working because they know that if you choose your coordinate system poorly, crazy stuff happens at the event horizon?

[Diadem]

So an outside observer will see both velocity and acceleration of an object falling into a black hole approach zero.

I'm hovering just outside a black hole. From here, I couldn't really care less what some jerk sitting safely at infinity thinks he sees.

But you did, in the post I was responding to. You said "despite approaching infinity as measured by a distant observer?". I was just pointing out they go to 0, not infinity.

]We're changing coordinates, not metrics. I brought my stopwatch and my scale and my measuring tape with me from Earth. Are they afraid of black holes? Have they magically stopped working because they know that if you choose your coordinate system poorly, crazy stuff happens at the event horizon?

I see what you mean. Yeah, you can measure them locally. But we were talking about acceleration as compared to that on earth. Well, what does such a comparison mean? Me and my brother are sitting on a railway station. We both measure the speed of a passing train as 50 kph. Then I board a train, my brother remains behind. We then both measure the speed of the train I'm in. My brother measures it as 60 kph. I measure it as 0 kph. My brother concludes my train is faster than the previous one, I conclude it's slower. Which one of us is in the right?

[Goemon]

My brother concludes my train is faster than the previous one, I conclude it's slower. Which one of us is in the right?

Your brother. (What do you measure your brother's speed to be?)

But that's not really relevant, since there's no such thing as "proper velocity", but there IS such a thing as "proper acceleration". If you're experiencing 25000g acceleration, it doesn't matter how many of MY meters per MY seconds^2 your velocity is changing. You're going to get pancaked, and I can easily compute how many microseconds you will experience before your scalp intersects your toenails. Acceleration is NOT relative: either you're doin' it or you ain't. And if you're trying to "hover" just outside an event horizon, you're doin' it with a vengeance.

For the record, the magnitude of the acceleration of an object "hovering" at radius r above a black hole as measured by a distant observer is

(m/r^2)(1-2m/r)

the PROPER acceleration, which everyone agrees upon and which equals how many g's the subject is experiencing, is

(m/r^2) / sqrt(1-2m/r)

2m = Schwarzschild radius. So yes, the acceleration as measured in "schwarzschild meters per schwarzschild second^2" goes to zero, but the proper acceleration becomes infinite.

[Diadem]

I think you just made the point I've been trying to make, though I'm a bit confused now, and also way too tired to be doing physics. Will return to this tomorrow.

Note though that acceleration is not the same as measured by different observers, even inertial ones in SR. Acceleration is not relative, but that doesn't mean it always has the same magnitude.

Proper acceleration is just acceleration as felt by the thing itself. It's the same for everyone, but all distant observers have to do a transform to calculate it, they can't measure it directly.

[doogly]

Proper is pretty proper. It's good shit. If you have to do a little work to get it, welcome to observational physics, it seems like you usually have even more to do ; )

[gmalivuk]

Proper acceleration is just acceleration as felt by the thing itself. It's the same for everyone, but all distant observers have to do a transform to calculate it, they can't measure it directly.

Yep, and it's been proper acceleration that everyone else was talking about this whole time.

But you did, in the post I was responding to. You said "despite approaching infinity as measured by a distant observer?". I was just pointing out they go to 0, not infinity.

Right, I initially had it flipped around. Hence the edit where I corrected myself and answered my own question in the negative.

[Quizatzhaderac]

As for my strange definition of "moving" I'll use "has non zero momentum".

This is still frame-dependent.

In addition, it does not account for spin, which is non-zero in every frame.

I never said it wasn't frame dependent.

It does account for spin. Objects with spin have angular momentum, and under my situational definition are moving.

Anyway back to the original subject, after reading the OP's list I have some comments:

Thought the laws of Gravity applied everywhere
They do, we just don't understand them is certain extreme circumstances.

Thought gravity is not the weakest for of nature
typo: force, not for

Thought ice is always water, not carbon dioxide, methane, and ammonia
Really more of a matter of definition then understanding. Solid volatiles became know as ices by analogue to (water) ice. It would make as much sense to say that ice can be made from SiO2 because the Latin word for glass derived from ice by analogue.

Thought there are only 3 dimensions
Again, definition. When a lay person says that there are three dimensions they mean spatial dimensions. It's more accurate to say physicists use four dimensions as they describe space-time, not space.

The astrophysics section seems to be a mislabeled miscellaneous category

Thought glass is a solid
I've seen other lists of misconceptions saying the opposite. I've also personally had a chemistry phD tell me glass being liquid is an urban legend, that the unevenness of old windows was a result of original manufacture, and that one could find old windows thicker at the top.

Thought weak force is the weakest force/Thought the electromagnetic force is the strongest
I've read that color > EM > weak > gravity. However since (as I understand it) color and weak don't have a k/d² propagation I don't really understand how they're comparable and hence well ordered. I'd bet people who don't "know" weak > gravity generally don't know what it means to be the weakest force.

Thought water drains differently in the southern hemisphere
Good one, although I did have to look them up. If/when you add explanations be sure to mention that the effect is there, it's just trivial compared to other sources of momentum at play. I guess people in Rand-Mcnally don't really wear hats on their feet either.

Thought there is only one type of water (i.e. no D2O )
Another good one. If/when you add explanations be sure to mention that it has significant chemical differences, otherwise it may seem that D2O isn't really a different chemicall.

Thought time and space are infinite (or universe is infinite)/Thought the universe is too big to measure/Thought there could only be one universe
This is begging the question. The "observable" universe is finite, as in the rest of the universe inferred from observed effects. It makes sense for scientists to only talk about what's observable/testable, but that doesn't mean the other statements are wrong, so much as using unscientific definitions.

[mfb]

Objects with spin have angular momentum

No. Spin is not angular momentum, and it can be shown that is behaves in a different way.

And even if it would be: All (known) charged elementary particles have a nonzero spin. Therefore, all charges would move, according to your definition.

I've also personally had a chemistry phD tell me glass being liquid is an urban legend, that the unevenness of old windows was a result of original manufacture, and that one could find old windows thicker at the top.

That is right.

I've read that color > EM > weak > gravity. However since (as I understand it) color and weak don't have a k/d² propagation I don't really understand how they're comparable and hence well ordered.

In quantum field theory, the strength of the strong, the electromagnetic and the weak interaction can be given via dimensionless parameters. It is easy to compare them, and it is related to the strength at small distances.
For gravity, it is a bit tricky, as there is no natural unit of its charge (mass) like with the other forces. You can use the planck mass, but then gravity is strong by definition and the charges of all known particles are extremely low. Therefore, the strength of gravity is usually considered as the force between two protons, which you can compare with other forces.

[Dopefish]

No. Spin is not angular momentum, and it can be shown that is behaves in a different way.

Isn't it? I'm fairly sure I've be taught that spin is just intrinsic angular momentum. It's not the same as orbital angular momentum where something is physically spinning, but I was under the impression that it's still angular momentum.

If you wanted to talk about total angular momentum, you'd need to combine both the orbital stuff and the intrinsic spin stuff, which wouldn't make sense if they were different things entirely.

[doogly]

They are similar enough that you have to grab some Clebsch Gordon headaches to muss with them.
But usually when you hear the word spin you think about a point moving around some circley shaped thing with some other point in an origin, and there is nothing like this for intrinsic spin. If when you hear "angular momentum" you think about Clebsch Gordon rather than a moving thing, then congratulations, you have finished your dose of kool aid for the day.

[Aiwendil]

In quantum field theory, the strength of the strong, the electromagnetic and the weak interaction can be given via dimensionless parameters. It is easy to compare them, and it is related to the strength at small distances.

It's perhaps worth adding that if you define the strengths of the forces in terms of these dimensionless parameters, the weak force is actually stronger than electromagnetism. But it's effectively weaker because it's carried by massive bosons (the W and Z) whereas electromagnetism is carried by the massless photon.

[Whitebluur]

So much good stuff. Thank you all