How can gravity be so weak (10^29 times weaker than the weak force) at the subatomic level, but at the same time be the dominant interaction at the macroscopic scale?


How can gravity be so weak (10^29 times weaker than the weak force) at the subatomic level, but at the same time be the dominant interaction at the macroscopic scale?

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Because ALL MATTER is subject to gravity, not just electromagnetic things. You can use a small magnet to pick up a piece of metal. That small magnet is pulling against the ENTIRE gravitational force of the earth and winning. If everything were electromagnetic, magnets would the dominant interactive force.

That’s one of the open questions in science. Why is gravity so much weaker than the other forces?

Regardless–the strong and weak nuclear forces have very small ranges, and the electromagnetic force links distant systems in its own way just as effectively as gravity does.

Because everything that has mass exhibits a gravitational field and the gravitational field is purely additive.

Contrast that with the electromagnetic force. Not everything has an electromagnetic charge and for the things that do, there are roughly and equal amount of positively charged things as negatively charged things, so they cancel out. At macroscopic scales, things are neutral.

If the four fundanental forces, gravity and electricity are the ones with the most range. The weak and strong forces decrease in effectiveness rapidly as you get further away.

So on our scale the only real competitor is electrical forces which is far stronger than gravity.

The small amount of charge you can build up on a balloon is capable of holding it to a ceiling, resisting the pull from the entire mass of the earth.

But your question is why didn’t it win overall?

And that is a consequence of what it attracts. A positive charge attracts a negative charge. So now these two charges sit next to each other. Seen from any distance away the overall charge is now zero (+1-1=0). This means it no longer effectively attracts any more charge.

Gravity on the other hand is mass, attracting more mass. So seen from any distance away you see… More mass (1+1=2). So this attracts… Even more mass.

Gravity attracts mass, and reinforces itself. Electricity attracts opposite charges, and undermines itself.

So on small scales, and short periods of time electricity easily wins. But longer times, and larger scales gravity wins.

Gravity gets weaker with the square of the distance. If you’re twice as far away, gravitational attraction is 4 times weaker.

The electric force usually also gets weaker with the square of the distance. So if gravity and electric attraction/repulsion compete head on, the electric field will always win, because it started out ahead.

However, when two opposite charges are sitting right by each other, their electric fields overlap to form a dipole field. This overlapped fields still extends infinitely far away, but it falls away with the cube of the distance – when you double the distance, the attractive or repulsive force is 8 times weaker. This means that at some distance, even though gravity started out weaker, the dipole field will cross it and become even weaker than that. So if you have a body with no net charge, there is no way it can be stronger than gravity if you look at a large enough scale.

Magnetic fields only come in dipole fields, so the same fact holds for them.

There are some situations where the magnetic dipole is so strong, it managers to stay ahead of gravity for a pretty long distance. Neutron stars have magnetic fields so powerful they extend well into the surrounding region of space. However, if you get to interstellar distances, that will die away and only gravity will be left.

There are other factors that make the EM forces even weaker. The actual charge distribution in many atoms is closer to a shell of negative charge around a positive charge, and in that case the only attractive force possible is from an induced dipole (the van der Waals force) – an _extremely_ weak force which (IIRC) falls away with the sixth power (doubling the distance decreases the force by a factor of _64_). Also, even if you have many dipoles, they can sit next to each other and align head-to-tail, which makes the overall field even weaker than a dipole field. In practice even getting a long range dipole attraction is very rare.