# Gravity causing distances smaller than a Plack length?

This is a thought experiment that just popped up in my head, please excuse any layman inaccuracies.

Imagine the largest, most massive galaxy in the entire universe. Let's hypothesize that it is at a great distance from earth, beyond the edge of the observable universe. Now, since all objects with mass attract each other through gravity, my own body will attract this galaxy a tiny bit.

In my mind, it seems like the distance the galaxy moves towards me because of my gravitational pull should be less then a Planck length. If so, how can this be? And if not, how small an object would it take to move the galaxy less than a Planck length?

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phinds
Gold Member
2019 Award
This is a thought experiment that just popped up in my head, please excuse any layman inaccuracies.

Imagine the largest, most massive galaxy in the entire universe. Let's hypothesize that it is at a great distance from earth, beyond the edge of the observable universe. Now, since all objects with mass attract each other through gravity, my own body will attract this galaxy a tiny bit.

In my mind, it seems like the distance the galaxy moves towards me because of my gravitational pull should be less then a Planck length. If so, how can this be? And if not, how small an object would it take to move the galaxy less than a Planck length?
First of all, objects outside the observable universe are causally disconnected from us so your assumption is wrong.

Second, there is nothing magical about a Plank length and there is nothing that says an object can't move less than a Plank length. We can probably never MEASURE anything less than a Plank length (and right now, we can't even measure things that are many orders of magnitude larger than a Plank length) but that doesn't mean it doesn't exist.

First of all, objects outside the observable universe are causally disconnected from us so your assumption is wrong.

Second, there is nothing magical about a Plank length and there is nothing that says an object can't move less than a Plank length. We can probably never MEASURE anything less than a Plank length (and right now, we can't even measure things that are many orders of magnitude larger than a Plank length) but that doesn't mean it doesn't exist.
Thanks for the reply! I'm afraid you only got me more intrigued however.

Are you saying that there is a distance limit at which gravity no longer has an effect? How far away is this limit? Does it vary depending on the mass of the objects?

phinds
Gold Member
2019 Award
Thanks for the reply! I'm afraid you only got me more intrigued however.

Are you saying that there is a distance limit at which gravity no longer has an effect? How far away is this limit? Does it vary depending on the mass of the objects?
good question. Gravity has no limit per se, and is always taken as going to infinity, but any change in gravity propagates at the universal speed limit c and thus cannot connect with us from outside the observable universe. That does NOT, however, address your original point about the gravitational attraction (as opposed to any CHANGE in that attraction) between us and something outside the observable universe.

I'm going to have to leave that one to someone who has a better grasp on this stuff than me, since I seem to have merely confused both of us on that score.

The Planck Length is a theoretical lower limit on distances which can be *measured*, not a lower limit on distances in which something can *move.* Why? Why make this distinction?

It has to do with energy. More accurately, mass-energy. And gravity. Please bear with me.

Consider an optical microscope: an optical microscope has a max magnification on the order of 2000 or so. Why is this? Why not more? Why not 10,000 or 100,000? Poor optics? If they made better lenses wouldn't they be able to see more detail?

No. The reason has to do with wavelength. Objects smaller than the shortest visible wavelength (about 400 billionths of a metre) cannot be imaged clearly for the same reason that waves in a pond pass largely unaffected around small objects like rocks and plant stems. What to do? Make the wavelength shorter? Yep. Make it smaller than the object you're trying to see/measure, but there's a hitch: for that you'll need more energy.

Blue-light photons have shorter wavelengths and correspondingly more energy than red-light photons; ultraviolet photons even more so, and so on with X-ray photons, gamma-ray photons and beyond (we don't have names for wavelengths shorter than this, but you get the picture). Whereas in red light you might be able to spot a hefty bacterium, in high-energy gamma-ray 'light' you could (in principle) 'see' atomic nuclei.

Gamma-ray photons have very short wavelengths and correspondingly high energies, but they're not even a drop in a bucket compared to the energy of wavelengths near the Planck Length. So, what makes the Planck Length so special?

Please bear with me a little longer.

Einstein's famous equation E=mc^2 comes into play here. Basically what this equation says is that matter and energy are *equivalent*; that is, there is no fundamental difference between them. None whatsoever. *We humans* see matter and energy as distinct, as very different sorts of things, but Physics, however, makes no such distinction. To Physics, mass and energy are one and the same thing: mass has an equivalent energy; energy has an equivalent mass, and who cares what it 'looks like'. Now, where there's mass-energy, there's also gravity (more accurately, spacetime curvature). So what does this have to do with measurement limits?

Everything.

As you increase the energy, you increase the equivalent mass whilst at the same time reducing the wavelength. Essentially what you are doing is packing more and more mass-energy into a smaller and smaller space. At some point you're going to hit a brick wall. What happens when you pack enough mass-energy into a small enough space? Gravitational collapse?

Oh, but what is the wavelength at this point? You guessed it: the Planck Length.

Energies that produce wavelengths smaller than the Planck Length result in black holes and there is nothing we can do about it (not that we have the capability to do so at the moment but, if we did, this is what would happen). It is why measurements smaller than a Planck Length are not possible, not even in principle. Besides, as everyone knows, black holes make terrible rulers: trying drawing a straight line with one, hopefully before it evaporates (Hawking radiation, but that's a tale for a different day).

Are you saying that there is a distance limit at which gravity no longer has an effect? How far away is this limit? Does it vary depending on the mass of the objects?
As far as we know, gravity has infinite range (there are other fundamental forces in nature which do not). While gravity has infinite range, gravitational *disturbances* propagate at finite speed, namely, the speed of light. One consequence of this is the word 'Observable' in 'Observable Universe.' Why not just 'Universe'? Why qualify it?

The reason is this: the Universe is expanding. The deeper into space you look, the faster spacetime (and everything in it) is receding there. At some distance - at the limit of the Observable Universe - it is receding at the speed of light. Beyond this point, it is receding faster than the speed of .... wait a minute! Nothing travels faster than the speed of light, so how can this be?

Good question.

While it is true that nothing can travel faster than the speed of light *within spacetime,* spacetime *itself* has no such limitations. It can expand as fast as it likes - and it does. Thing is, we'll never see what happens there. For this we would need a 'signal' which travels faster than the speed of light. On the flip-side, whatever we do here will never be felt there for the same reason. *Disturbances* in the curvature of spacetime propagate *within* spacetime and so are subject to the universal speed limit. Your breathing in and out disturbs the local curvature of spacetime a tiny bit, and these ripples in spacetime travel outward at the speed of light. In about 2.2 million years the ripples will arrive at the near edge of the Andromeda galaxy. The effect will be very minute, as you might imagine, but it will arrive nonetheless. Just good luck measuring it. For that you'll need a black hole. :)

Edit -
http://en.wikipedia.org/wiki/Observable_universe
and
http://en.wikipedia.org/wiki/Metric_expansion_of_space

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phinds
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2019 Award
The reason is this: the Universe is expanding. The farther you look, the faster spacetime (and objects there) is receding. At some distance - the limit of the *observable* universe - it is receding at the speed of light. Beyond this point, it is receding faster than the speed of
Overall an excellent explanation. Thanks.

The above, however, is incorrect. Things well inside the observable universe are receding at c and things at the edge of the OU are receding at about 3c.

The above, however, is incorrect. Things well inside the observable universe are receding at c and things at the edge of the OU are receding at about 3c.
You are correct. When you throw in co-moving distances and all that, yes, but I didn't want to complicate things overmuch. My bad.

Assuming the Planck length is what we think it is the only implication of your thought experiment is that we would be unable to measure any movement of that galaxy until it had moved one plank length.

This may not be the proper place for this inquiry and if so please move it or show me how to do so. While I understand that (and how) it has caused great consternation for Quantum Loop Gravity and even some forms of String Theory, when considering the data from ESA HERE it still makes my head hurt to contemplate sizes "orders of magnitude smaller than Planck Length".

Is there any news on this front? I have yet to see much.