# Gravitational Field Paradox Explanation?

1. Nov 4, 2012

### Theheretic

Gravitational Field Paradox Explanation??

Hi everyone. If electric and gravitational field has an infinite nature-meaning that the effect one charged particle has on another charged particle always remains even though it diminishes over distances but can never reach absolute 0-then how is this possible without being some sort of paradox?

It seems to me similar to a layman's version of quantum entanglement concept.
What I mean is, if you think of a gravitational effect an object has on another object via 'gravitational field'. For instance let's say the earth exerts a certain gravitational field on a person floating in space a few thousand miles above the earth. Then let's say you move that person billions of light years away to the very edge of the known universe. The earth is said to be still exerting a gravitational field on that person just a very miniscule and mostly negligible amount. Yet to my understanding it is STILL an amount and can never be 0.

So my main question is this: Since the earth is always exerting this gravitational field onto this person instantaneously, then isn't this a "faster than light" sort of transmission? For instance let's say that right now the earth is exerting this gravitational field on this person/object who is 15 billion light years away. And right this instant the earth was blown up to smithereens and completely annihilated. An equation would show presumably that the earth no longer exerts any field on this person 15 billion light years away instantaneously. The field of exertion presumably does not travel at light speed so I don't think it is right to say that it will now take 15 billion light years for the gravitational effect to wear off.
I know this may be getting into the general area of the higgs-boson but if we wanted to simplify away from that then we can use the electromagnetic field or etc.

So how is it that the "field" that is exerting the gravitational or electromagnetic pull on the person from 15 billion light years away, "INSTANTLY" knows that the earth no longer exists and thus no longer exerts that pull?

Just to phrase this question into a slightly simpler thought experiment in case anyone is confused about my question (since I'm a completely un-educated noob in this regard so I realize some of the things I may be saying or describing are asinine).

But let's take a hypothetical vacuum that is as wide as our universe but has no other matter in it that is able to exert any sort of electromagnetic or gravitational influence. i.e. not a single atom of matter exists OTHER than 2 objects that are separated by 15 billion light years. Since these objects are the ONLY 2 things in existence, if my fundamental understanding of these things serves, then the 2 objects will begin floating towards each other albeit at perhaps an exponentially and microscopically slow rate. But they will be exerting a gravitational pull on each other even from 15 billion light years away since as I understand it, gravitational "field" has no limit and can never be 0.
So let's just say they're slowly creeping towards each other from 15 billion light years away and one of those objects suddenly disappears or is somehow annihilated (for the sake of this conversation let's pretend it's able to break law of conservation of matter and be annihilated). Then how does object #2 that is 15 billion light years away instantly stop pulling towards the gravitational field of object #1? This would require a superluminal instantaneous "communication" of the gravitational field from 15 billion light years away. Whether it's a higgs boson or whatever is responsible for gravity how can it immediately inform the 2nd object that is 15 billion light years away to stop being exerted by the force of the 1st object???

2. Nov 4, 2012

### Theheretic

Re: Gravitational Field Paradox Explanation??

I seemed to have answered my own question through subsequent research.

http://en.wikipedia.org/wiki/Speed_of_gravity

Gravitational "waves" travel at the speed of light and thus are not "instantaneous".

How about electric charge fields? When a particle has a positive charge and attracts or repels another particle of a negative charge? What constitutes this? Electromagnetic fields which also travel at light speed?

3. Nov 4, 2012

### AJ Bentley

Re: Gravitational Field Paradox Explanation??

Since light is nothing more than wobbling electro-magnetic fields you can probably figure this one out yourself.

4. Nov 4, 2012

### Bill_K

Re: Gravitational Field Paradox Explanation??

Not the same issue. Both electromagnetic and gravitational waves travel at a finite speed c. But the Coulomb field for a charge, and the Newtonian field for a mass, don't have anything to do with waves.

These fields do appear to be instantaneous, and in some formulations they are indeed treated this way. But the reason they can get away with it without violating relativity is because of the conservation laws. A charge cannot just suddenly appear, nor can a mass. Thanks to charge conservation, the charge has "always" been there (or somewhere!), and thus the Coulomb field surrounding it has always been there too. Likewise for gravity, the source of the gravitational field is energy (technically, the stress-energy tensor), and energy is locally conserved - it cannot suddenly appear or vanish.

This is exactly what can NOT happen.

Last edited: Nov 4, 2012
5. Nov 4, 2012

### AJ Bentley

Re: Gravitational Field Paradox Explanation??

That's a bit misleading. It's more that the field (there's actually only one, shared by all particles) has existed since the beginning of the universe.
What we are talking about here is changes in that field caused by the movement of charges. Those changes propagate at c.

Since charge cannot spontaneously appear out of nothing, the field cannot change discontinuously. If such a thing were to happen somehow, the field might propagate at some other speed - maybe infinite - who knows? Maybe that has something to do with non-locality.

6. Nov 4, 2012

### Bill_K

Re: Gravitational Field Paradox Explanation??

Not a bit! Some quantizations of electromagnetism involve an instantaneous Coulomb interaction in the literal sense.
Some do and some don't. Radiation does. But both electromagnetism and gravity allow "nonradiative motions". For example the lowest order of gravitational radiation involves the third time derivative of the source's quadrupole moment. If the source moves in such a way that it has no quadrupole moment, it won't radiate. Even if it has a quadrupole moment, it won't radiate if the third derivative vanishes. The Newtonian field certainly changes, but no radiation is produced.
Hypothesizing something happens that cannot happen in the first place naturally leads to paradoxes.

7. Nov 4, 2012

### AJ Bentley

Re: Gravitational Field Paradox Explanation??

When I'm trying to explain something in layman's terms, I like to keep it simple.
There are always sophisticated argument at the fringes of exploration that can be invoked as 'exceptions' to established rules.
I consider it misleading to bring them up unless the OP has the tools to fully understand the subtlety.

8. Nov 4, 2012

### sshai45

Re: Gravitational Field Paradox Explanation??

So does this mean, basically, that demanding relativity holds essentially forces the conservation laws to hold, and also that if there were such a thing as a perpetual motion machine, we could also go back and kill our grandfathers before our parents were born?

9. Nov 4, 2012

### Bill_K

Re: Gravitational Field Paradox Explanation??

That's a good idea. Also keep it correct.

10. Nov 4, 2012

### sshai45

Re: Gravitational Field Paradox Explanation??

However, I thought the thing was that instantaneous "force" was OK, but instantaneous "transfer of information" was not. The latter is limited by c.

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