I remember reading a comment somewhere on the web that made it "click" for me:
"Gravity is so weak that force of a tiny fridge magnet is able to counter gravity pull of the whole planet".
"Gravity is so weak that force of a tiny fridge magnet is able to counter gravity pull of the whole planet".
I think it works better to think of it in terms of the minimum force you can get. Imagine two test masses a fixed distance apart. The minimum non-zero electromagnetic force you can get between those two test masses is the force you get if each test mass has a charge equal to that of an electron.
I'm not sure what the lowest mass particle is that you could reasonably hold near a test point, but since you can reasonably confine an electron to a small region the gravitational force between two electrons is an upper bound on the minimum gravitational force, and that is a ridiculous number of orders of magnitude lower than the minimum electromagnetic force.
There's a similar demo for showing the strength of atmospheric pressure. You can boil a little water in a soda can, and quickly invert it into a little bowl of water. The water vapor inside quickly condenses causing a startling implosion of the can. It gives an intuitive feel for what 1 atm actually is.
You think of astronauts going to where they have to counteract that pressure, and what would happen on failure, and you think "holy shit." Then you think of James Cameron going to where the pressure is 1000 times as great, and what would happen on failure, and you think "holy fucking shit!!"
Indeed, see Byford Dolphin diving bell accident (very NSFW/NSFL):
The pull would be 1 g 6400 km away from it. At 1 m it would be over 10^13 g.
Spoiler: "AAAAAAAAAAAAAAAAAAA!!!!!!"
Say "earth" is a sphere with radius 1 meter and you're 1 meter away. And that puny magnet defeats its gravitational pull in the same way it defeats earth. How heavy would our sphere have to be in order to have the same pull as earth if it has a radius of 1 meter and our magnet is 1 meter away?
If you remember Newton's law of gravitation the force an object will feel looks like: F=Gm/r^2. G is small, 10^-11 Nm^2/kg^2, m is the mass of earth 10^24 kg, r is normally 10^6 m (the radius of the earth). Plug in these numbers you get 10 m/s^2. The real answer is closer to 9.8, but we're looking for the order of magnitude here. We're still remarkably close for how much rounding we did.
How lets say that we're now 1 meter away. How heavy would the mass have to be to still pull with 10m/s^2, which we know our magnet can defeat. (10^6)^2 ~> 10^12 so we have to be 10^24/10^12 ~> 10^12 kg.
So to defeat a tiny magnet 1 meter away you need 10^12kg. Lets pretend our mass is a cube whose volume is 1m^3. That's 10^12kg/m^3. The center of the sun has a density of 10^5kg/m^3. This is 10^7 times denser! We're lucky that our sphere is far too light by many orders of magnitude to collapse into a black hole (maybe not so lucky because it's going to explode immediately!) but it's even denser than a white dwarf. This is on the order of the mass of Mt. Everest (this is a very rough and unprincipled comparison and when you unpack it can mean many different things, but it's something easy to visualize).
So you can see. Gravity is indeed insanely weak. A magnet can defeat Mt. Everest.
The point is that you should use something human-scale to show off the strength of gravity.
So if you want a fridge-sized block that can hold things with gravity like a normal fridge holds a magnet, how heavy does it have to be? As heavy as an entire mountain.
I don't think this is the thing that the theoreticians are looking for (no Nobel Prize for me), but it is a unique feature of gravity that gravity has only one polarity. And I don't remember how this goes with the strong and weak forces.
Perhaps if you replace "weak" with "diffuse"?
If your magnet was as weak as a fridge magnet and as large as the earth it would be way way way overpowered to hold the moon in orbit.
So no, diffuse is wrong. Completely wrong. Weak is the correct word.
If I stand accused of using the colloquial meaning of "weak" instead of the physics meaning, then OK.
But a locomotive is strong. The pull of celestial bodies is stronger. The force of a locomotive is concentrated. The force of gravity is diffuse.
So using that word as a way to distinguish them is incorrect.
But that's just not the way the force of gravity is thought about by humans, because the gravitational effect is so small as to be undetectable between human-scaled bodies. So we attribute gravity to more massive things, and consider it only en masse, never divisibly.
To the extent that the gravitational force of the earth has measurable effects on more things than the electromagnetic force of the refrigerator magnet, it is more...spread out. More distributed. More diffused.
It follows the same inverse square law as everything else, but it does a lot more of it, over human-scaled distances.
And this is how high school physics teachers can be counterintuitively correct, but I think the takeaway is more about how hopeless humans are at conceptualizing very large numbers than about physics.
Also the magnetic force in a physical object does not follow inverse square, it's more like inverse of the 5th root (because there are no magnetic monopoles the two fields cancel out very quickly at distance).
So if anything the magnetic force is more diffuse than gravity since it fades out so quickly.
So if anything the magnetic force is less diffuse than gravity since it's concentrated right near the object.
The fact that both of those sentences are correct tells you quite definitively that diffuse is very very much an incorrect word.
Gravitational force is both much weaker and (for that of large bodies) diffused over a much greater area than electromagnetic force (of very small bodies). These are the circumstances of the example comparison.
"More diffuse" vs. "more greatly diffused" appears to be our disconnect here. Something which is "more diffuse" is expected to be less measurable at a single point, all other variables controlled. This is true of gravity but not for the reasons implied.
Nevertheless, if the total gravitational force of the relevant object from the example (earth) was concentrated into the same area as the total EM force of the magnet, we would have a black hole in our kitchen. Fortunately, that gravitational force is diffused over much a larger area.
Things which are more diffuse are necessarily diffused over a larger area. Not all things which are diffused over a larger area are necessarily more diffuse.
I see the hangup, and I appreciate your objection.
Edit: and thank you for the EM force inverse power law correction. I was using distant memories of the math for EM radiation, which is obviously different. But if those numbers are right, it supports the argument that gravitational force is less concentrated...and therefore more diffuse, does it not?
No, that is simply not true. Not at all. You keep saying this, and it keeps being not true.
I don't really know how else to say it to you. You have a mistake in your intuition.
> Nevertheless, if the total gravitational force of the relevant object from the example (earth) was concentrated into the same area as the total EM force of the magnet, we would have a black hole in our kitchen.
No! That is not true. If you turned the earth into a black hole, and placed that black hole in the center of where the earth used to be, you would notice NOTHING whatsoever in your kitchen. NOTHING. You could not tell the difference.
> Things which are more diffuse are necessarily diffused over a larger area.
And gravity is NOT diffused over a larger area than electric charge.
If you had enough electric charge to pull on you (assuming you were of opposite charge, at the same ratio as your mass vs earth mass) placed in the center of the earth it would act IDENTICALLY to gravity. And that charge would be very small, much much smaller than gravity, because gravity is WEAKER than the electric force. NOT because it is more diffuse.
> Edit: and thank you for the EM force inverse power law correction. I was using distant memories of the math for EM radiation, which is obviously different.
Not EM force. Magnets with two poles. EM force is the regular inverse square.
> But if those numbers are right, it supports the argument that gravitational force is less concentrated...and therefore more diffuse, does it not?
No it does not. It just means you have two opposite magnets that cancel each other out at a distance. If it were electric charge, which is a monopole, it would not happen.
I wrote: > Gravitational force is both much weaker and (for that of large bodies) diffused over a much greater area than electromagnetic force (of very small bodies).
I mean:
- *the* gravitational force is much weaker than
*the* electromagnetic force
- large bodies (earth sized) have more *gross*
gravitational force than refrigerator magnets
have *gross* EM force.
- the gravitational force of an earth sized body
extends, in the realm of practicality, much
farther than the EM force of a refrigerator
magnet. In fact both extend into infinity, but
that's only interesting in the theoretical sense.
Yes, the third one is incorrect.
> If so, you're right and my intuition and everything else is wrong.
The reason you think this way is because magnets fall off by the power of 5 (approximately, it's not a specific number, but depends on the geometry of the magnet), because of the two poles.
If on the other hand you played around with charged objects (which are monopoles like gravity) your intuition would work better for this. But unlike magnets highly charged objects are not commonly found around the house.
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Also the second one is debatable - the acceleration of one magnet to another is higher that the acceleration of an object falling on earth.
Even a lightly charged object can accelerate another object at greater than what the earth can manage.
The reason I use acceleration to measure gross force is because gravity (and charge) depend on the product of the two objects and distance - the only single number you can assign a single object is acceleration and even that depends on distance.
When I say gross force, I mean the sum total of all relevant force exerted by the object. So the gross gravitational force of the earth is strong enough to hold the moon in orbit, but clearly the magnet has no such ...strength.
Now obviously (I shouldn't use that word!) in the case of massive bodies like earths and moons, there's a more complex interaction going on than a one-sided force. But there's a total magnitude of force that just doesn't exist in the magnet.
A lit match burns paper more readily than the sun, but clearly the sun distributes a larger amount of gross energy over a wider area than does a match.
> Even a lightly charged object can accelerate another object at greater than what the earth can manage
Ack. Considering acceleration without mass is no way to properly reason about force! Surely I remember that much, at least.
Regardless, I will desist and defer. Though I do wish I felt that I now understood something more clearly than I did before. :(
There is no such concept. Really. I promise you, there is no such concept! The amount of force it exerts simply depends on who is close to it, rather than any property of the Earth. Like, if the moon was not there would you say the total of all relevant force is lower? But nothing changed on the Earth. So this concept does not apply to the Earth, rather it applies to the specific situation.
I do get what you are trying to say, but it's just not correct. The force depends on the specific setup of where the bodies are, not an intrinsic property of Gravity, or the Earth.
> So the gross gravitational force of the earth is strong enough to hold the moon in orbit, but clearly the magnet has no such ...strength.
Only because it is small, it would not take much charge to hold the moon. I did the math for you - it would take about 3 tons worth of electrons to hold the moon. That's it - about 1 car worth. (If you could somehow keep all those electrons in one place, which you can't.) Walk outside and look at a car - if it was replaced with equivalent mass of electrons it would be enough to hold the moon (if the moon had some extra protons on it). I mean you can push a car, that's how little mass it is, yet it's enough to hold something as heavy as the moon.
Another way to look at it is if you took 1 electron away from every grain of sand sized piece of the earth - just one single electron, the resulting charge would be enough to hold the moon. (And give one extra electron to every grain of sand sized piece of the moon.) Charging a grain of sand with one extra electron is nothing, it's a minuscule amount, it's too low to even measure.
> Ack. Considering acceleration without mass is no way to properly reason about force!
The nice thing about gravity is that it's invariant to mass since the force goes up right along with the mass. If you scale the charge of the object together with the mass then the acceleration of a charged object will also be invariant to mass.
i.e. if you made the magnet bigger (heavier) it would also be more magnetic, so the acceleration would stay the same (more or less).
> Regardless, I will desist and defer.
It's OK, I don't mind the conversation.
> Though I do wish I felt that I now understood something more clearly than I did before. :(
Remember that we started with you saying gravity is diffuse and electromagnetism is concentrated. All I did is try to show you that that is not a good way to look at it.
I readily concede that "diffuse" has ambiguous meaning and therefore a poor choice, however.
Beyond that, I don't think what I'm saying is any more complicated or controversial than the example of the match and the sun.
My attempts to clarify have revealed further gaps in my precision of phrasing, but your explanations haven't identified any specific points of confusion for me. I'm sure that says more about my comprehension than about your explanations.
We're now in open battle with HN's anti-dialogue margin creep -- and we know who wins that battle, every time -- so I'll take my distant memories of undergrad mechanics and E&M, mark the page dirty, invalidate the cache, etc.
Thanks again for your efforts, they're not as wasted as they appear.
If I hold a tiny magnet 5 feet above the piece of metal, and the earth is 5 feet below the piece of metal. in which direction will the piece of metal move. In other words while I don't think my examples are any great ones, I don't think the example you're quoting really makes much sense either.
On Preview: I see there's an explanation for why being far away from the magnet makes the magnet have less effect than being far away from a gravitational object https://news.ycombinator.com/item?id=10727977