What do physicists think about the reach of gravity? I understand the normal belief is that it extends infinitely far, growing weaker with distance. Is this the case? Or is there a point, some sort of Planck situation, where the influence of gravity “winks out” to zero.
Does Alpha Centauri really react to my paperclip?
Gravity’s reach is thought to be infinite, though nobody has been to infinity to report back as of yet.
In Newtonian physics, gravitational field strength gets less the further away from the source, but never goes to zero.
In general relativity the of a spacetime modelling a source surrounded by a vacuum, the Riemann curvature tensor is nonvanishing (i.e. gravity has an infinite reach in general relativity too).
It is worth noting that the speed of gravity is c, so that while gravitational influence may be infinite, it is limited to the light-cone of the source.
So moving your paperclip now will impact Alpha Centauri in 4.5 years time, and we won’t see the effect for another 4.5 years.
This may be a reach. If 0.99999999 . . . = 1, then by the same principle, shouldn’t 0.00000 . . . 1 = 0?
No.
How many zeros are in front of the 1?
The first number you typed is an actual number. The second number isn’t.
That’s easily resolved by expressing it as (1 - 0.999…)
Away back in that not-quite-infinite thread about the value of 0.999… the question came up, about what 0.000…1 would mean. That came from one of the several guys who just could not wrap his head around the idea that 0.999… = 1 and who was arguing that it must always be infinitesimally less than 1. The analogous 0.000…1 was suggested, being always infinitesimally infinitesimal – but never 0.
I proposed that the notation 0.000…1 could be given a meaningful and sensible definition in a way very similar to the way 0.999… (or any other infinite decimal) is defined. And surprise, surprise! The idea works out, and you can imagine 0.000…1 (with an infinite number of 0’s in there) as having a specific value. Turns out, it’s 0. Huh.
ETA: And just to make this post have something to do with the OP, by the way: Not only is it thought that the influence of gravity extends infinitely far, but it’s also theorized to extend out in more dimensions than the usual 3. That’s one theory of why gravity is such a weak force, compared to the other forces.
If gravity is carried by quantum particles, isn’t there a minimum gravitational pull, by only one particle? (Assuming stronger pull = more particles)
Particle exchange can be viewed as transferring energy and momentum from one object to another. If all gravitons have the same energy & momentum, then you might have a point. But this scenario seems unlikely; after all, photons differ in their energy and momentum based on their frequency, and there’s no reason to suspect that gravitons behave any different.
Hmmm, hadn’t heard that before. Does that mean that gravity is potentially a stronger force, just in higher dimensions?
Hypothesized, not theorized. And that hypothesis, elegant though it may be, is unfortunately not holding up well under current experiments.
It is, however, theory that gravity is truly infinite in range.
Would a compass on the moon point towards the Earth?
Compasses react to magnetic fields, not gravitational. I’m pretty sure that on the Moon, the dominant magnetic field is either some trace of small field the Moon itself has, or the Sun’s. And even if the Earth’s area of magnetic influence did extend out that far, the direction of the field there would be mostly perpendicular to the line from the Moon to the Earth.
According to NASA, the moon spends six days each month within influence of the Earth’s magnetic field (the time around a fool moon, when the moon enters the tail of the field.) They hypothesize that it could be strong enough to cause moon dust to hover.
I wasn’t aware that NASA acknowledged the adventures of wizards.
If there was a speck of dust on one side of the universe, and another speck on the other, and the universe was otherwise empty, would they attract each other? (Edit: To a noticeable degree?)
Since 0.999…=1, then 1-0.999…=0.
Yes, but not to a noticeable degree. Even if the universe was not otherwise empty, the answer would be the same. Gravity is a property of matter and doesn’t care if there is other matter around.