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What does it mean to say “Gravity is the weakest of the forces”?
Strongest force in nature

It is usually taught that the gravitational force is the weakest but I wanted to know if it will be always so. For example, On earth gravity is weaker than electromagnetic force or weak nuclear force, so is it that on black hole also if gravity is strongest than other forces shall be more stronger than it or it's that gravity becomes most strong suppressing others.

Because if other forces increase in same proportion than it will have serious implications.

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marked as duplicate by Qmechanic, David Z Sep 28 '12 at 22:42

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

    
    
@Qmechanic:those discussion are more in terms of comparison between forces, what I want to know is something else. For ex, if weak nuclear force is stronger than gravity on black hole than atoms can't stay atoms but the gravitational pull shall also shred them. Which one wins...if someone has idea ! –  Rorschach Sep 28 '12 at 10:12

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Your question isn't as straightforward as you might think, because if you drop an atom into a black hole it will fall freely and will not feel any force attracting it to the black hole. This sounds odd, but it's the same reason that astronauts in the International Space Station feel weightless even though they're being attracted by the Earth's gravity. A freely falling object doesn't feel any gravitational force.

However an object falling into a black hole will feel tidal forces. This happens because one side of the atom is slightly nearer the black hole than the other side, so it's attracted more strongly. The end result is that the atom is stretched in the direction towards the black hole and squeezed in the direction at right angles to it's motion. This is known somewhat colourfully as spaghettification.

So the question really is whether at some point the tidal forces get so strong that they tear the atom apart. Presumably first the electrons would be torn off then the nucleus would be torn apart.

Well the key feature of a black hole is that classically (i.e. ignoring quantum theory) the singularity at the centre of the black hole has zero size and the tidal forces at the singularity are infinite. This means that yes, at some point the tidal forces will get stronger than even the strong force and the atom will be completely torn apart. Presumably even the protons and neutrons would be torn into separate quarks.

But, and it's a big but, we almost certainly can't treat this classically because we expect quantum effects to become important that close to the singularity. Exactly what will happen no-one knows because we don't have a theory of quantum gravity that can describe this situation. If String Theory is the correct description at such small distances then presumably at around the string scale from the centre the atom would start behaving as a collection of seperate strings rather than the particles we are familiar with.

Response to comment:

Suppose you're hovering above a black hole and you let down a rope until it touches the event horizon. The rope will always be torn apart. This happens because all forces, electrostatic, strong and weak, propagate at the speed of light, and at the event horizon even the speed of light is not high enough to escape.

So if this is the experiment you're thinking off, then once your charged particle has got sufficiently close to the event horizon you would not be able to pull it back out with a particle of the opposite charge.

However this isn't to do with the fundamental strength of the gravitational force. It's because one electron has a hard time resisting the gravitational force of an entire black hole.

Response to response to comment:

If you're asking "is gravity stronger than the electromagnetic force" then you need to define what you mean. You are quite correct that at a black hole event horizon the electromagnetic force would not be enough to hold together an object that partially crossed the event horizon. In that sense gravity at the event horizon is stronger than the electromagnetic force, and indeed it's stronger than any force.

But a physicist would not conclude gravity was stronger because you're not comparing like with like. To do a fair comparison you need to take two test particles with both charge and mass, put them some set distance apart and measure first the electrostatic force between them, then the gravitational force between them. Whether you're near a black hole or not, this experiment will conclude that the gravitational force is much much weaker than the electrical force.

If you conclude that gravity is stronger than electromagnetism at an event horizon all you're really saying is that the gravitational force due to the (at least) $10^{31}$ kilograms of a black hole is stronger than the electrostatic force from the $10^{-19}$ coulombs of charge on an electron. Well, yes, that's not terribly surprising!

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thanks for nice explanation but I was thinking that if I am sitting on a black hole with charged body in my hand than will I be able to pick up oppositely charged body like we do on earth...will the gravity still be weak force compared to electrostatic force? –  Rorschach Sep 28 '12 at 10:45
    
I've updated my answer. Could you have a look and see if this makes sense. Part of the problem with answering is being sure of exactly what you're asking! –  John Rennie Sep 28 '12 at 11:07
    
what I am understanding is that here gravity overcomes other forces right at event horizon and increases even more from there on towards the center. So, gravity is no more the weakest force ? –  Rorschach Sep 28 '12 at 11:23
    
I've added some more to my answer to address your comment. –  John Rennie Sep 28 '12 at 17:25

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