Feb 10 2023

The Speed of Gravity

Published by under Astronomy
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I recently received an e-mail question from an SGU listener about the speed of gravity. They were questioning a statement they heard by Neil DeGrasse Tyson that if the sun were magically plucked from existence, the Earth would not feel the effects for 8 minutes and 20 seconds – the time it takes for light to travel from the sun to the Earth. This blew their mind, writing: “That statement doesn’t make sense to me. What DeGrasse is saying is that we don’t actually orbit the sun but a point in space where the sun was 8 minutes 20s ago.”

Actually, that’s exactly right. He did get it. We see the sun as it was 8 minutes 20 seconds ago. We also feel the sun as it was at that time – in every way. The speed of light is more than the maximal relative velocity that energy travels through the universe, it is the speed at which reality propagates throughout the universe. No effect can exceed the speed of light – not information, matter, energy, or force.

We can use the General Relativity conception of gravity, that matter curves space time and that matter and energy travel in a straight line through curved space. You have likely seen the typical graphical representation of this, with a heavy object like a planet or star distorting a grid of spacetime like a heavy ball resting on a stretched piece of fabric. This is actually just a conceptual aid, not an accurate depiction. It is missing one dimension – space is represented as a two-dimensional fabric stretching into a third dimension. You need to add a dimension to represent reality, which is three dimensions. Some experts say that three dimensional space is being curved in a fourth dimension, but others say you can work the math to describe the curvature of 3D space without invoking a 4th spacial dimension. I’m not sure what the current consensus is – I’ll have to look deeper when I have time (if anyone has a good reference, please share it in the comments).

But either way, if we use this conceptual aid to imagine how gravity bends space, and we use Neil’s example of plucking the sun out of existence, what would happen is that the curvature of space created by the gravity of the sun would go away, rippling out from the former location of the sun, at the speed of light. So the Earth would continue to move through this curved space until the ripple of reality reached it, the curve flattened out, and the Earth would then travel on a straight line through relatively uncurved space (at least no longer curved by the sun).

Weird, I know. This is because we evolved in a world without visible relativistic or quantum effects, so these effects are not intuitive to us. As far as we are able to perceive in our local environment, time is a constant and everything is pretty much happening at the same time. The delay of the speed of light is not significant.

We actually live in a time bubble traveling out from us at the speed of light. The same is true of everything in the universe, it all affects everything else only at the speed of light. This further means that we can only be affected by stuff in the universe that is no further away in light years than the age of the universe. That is the time-horizon of the universe – the visible universe. The entire universe is larger than that but some of it has expanded so far away that it is now more than 13.7 billion light years away (the approximate age of the universe). It might as well be in a different universe – nothing there can affect us.

That time horizon is expanding at the speed of light. However, the universe is expanding faster. This does not violate relativity which deals with the speed at which stuff moves through the universe, not the expansion of space-time itself. Because of Hubble’s law, the farther away something is the faster it is moving away from us, things at the other end of the visible universe can be moving away from us at faster than the speed of light. This further means that, even though our time horizon is expanding, it incorporates a progressively smaller fraction of the total universe. Eventually, in the distant future 150 billion years or so from now, our entire visible universe will consist only of those galaxies which are bound to us by mutual gravity in our local group. By then we will have merged into one large elliptical galaxy.

The universe will look very different to those future astronomers. I wonder how much they will be able to infer about the history and nature of the universe from their limited perspective. There will be nothing but a uniform cloud of stars. No other galaxies, no looking back in time beyond our own giant blob of a galaxy. It’s interesting to think about.

Also, we can be glad that we live in the time that we do. The observable universe is a big and interesting place and we can still look all the way back to the beginning. That will not always be true.

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