A confusing statement

Objects with mass curve space-time.

That sounds absurd, but hear me out...

If you've read these articles (which you definitely should if you're interested in General Relativity) "the day that proved Einstein a genius" and "black holes - everything that you need to know", then you'll know that there's substantial evidence that's been produced over the past century that proves gravity is not simply a force, but what do I mean by curvature of space-time?

It's better described with imagery as opposed to vocabulary, but, simply put, it's similar to how a bowling ball placed on a trampoline will cause the fabric to bend around the bowling ball; and the heavier the bowling ball, the more the fabric bends.

Additionally, if you were to place a lighter object on the same trampoline close enough, it would accelerate towards the bowling ball.

This acceleration is a result of the curvature, and in the case of massive celestial objects like planets and stars, it's what we call "acceleration due to gravity".... So it's technically not a force, despite being referred to as such by the general population.

This concept is derived from General Relativity, a "theory" (although it's about as certain as anything is going to get) introduced by none-other than Albert Einstein himself, and it's since been proven time and time again.

It's also important to note that this curvature also decreases exponentially with the distance from the objects centre of mass, meaning that the further away from the centre of mass of an object you are, the weaker the curvature of the space-time due to that object that you reside in.

But it's not a linear relationship - doubling the distance between two objects won't just halve the "force" of gravity felt by the two objects, rather it will quarter it.

I refer to this equation a lot in my articles, purely because it's one of the most fundamental equations when it comes to understanding gravity - Isaac Newton's law of gravitation, which states that:

"Every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers."

Naturally, both clauses are fundamental to understanding how objects interact with each other gravitationally in the universe, but it's the latter that we're particularly interested in when clarifying what I mentioned earlier about "the curvature decreas[ing] exponentially with distance"

Isaac Newton's law illustrates this by stating that the "force" of gravity felt between two objects is "inversely proportional to the square of the distance between them"

What this means is that, if you halve the distance between the centres of the two objects, then you multiply the "force" of gravity between them by 4, not 2.

I suppose the main takeaway from this is that distance has more of an effect on the gravity that objects feel to other objects than mass does. If you double the mass, you double the "force" of gravity felt between objects, but if you halve the distance, you quadruple the "force" of gravity.

Obviously this article is about how gravity is really an effect of curving space-time, so I know that seeing the word "force" here isn't all that reassuring as I've just told you that it's not a force.

Isaac Newton invented his law of gravity way before Einstein even existed, so at the time of writing it, he would've assumed gravity was a force like everyone else.

So, to summarise, space-time curves exponentially, rather than linearly.

Hopefully, this is a pretty straight-forward concept to understand if you think back to the bowling ball example.

Imagine a bowling ball on a trampoline - you can picture in your head how the fabric of the trampoline would curve dramatically right beside the bowling ball, and level out rapidly as you move away from the marble, as opposed to it sloping and levelling out gradually. Therefore, we can see that curvature due to mass is exponential, as opposed to linear.

Obviously we're talking about a physical piece of fabric here, as opposed to the fabric of space-time, which naturally has it's differences, but I think it's a pretty neat way to visualise it if you're struggling.

It's important to remember that this curvature is not 3 dimensional, otherwise we would physically be able to observe space bending with mass, which is not the case.

The whole concept of Einstein's curvature of space-time involves living in a 4 dimensional world, where time is the 4th dimension. While this is only theoretical at this point, history testifies that you've got a hard job proving otherwise.

Make no mistake, I'm not a qualified physicist or astronomer - I simply dedicate a lot of my time researching and learning as much as I possibly can about our universe, but my understanding is that Einstein's equations are robustly sound, and no-one as of yet has been able to prove them to be anything otherwise.

This 4 dimensional world is what's known as a Manifold, and if you take a look at the book that I've recommended in the products section of my website, titled "Space-time and Geometry" by Sean Carroll, then you'll see the word "Manifold' appearing quite often.

It's my absolute favourite book for learning about everything space-time related, and highly recommend it to anyone interested in astronomy or physics in general. You can pick it up here to support the website at no extra cost!

We can take this even further by looking at some of the theories that are currently under-works today.

Like this....

Take the Earth and it's motion around the Sun.

We can't see the Earth falling toward the Sun on a slope of space as proposed by this concept of curvature, because we can only witness the universe in 3 dimensions - up, down, left, right, forward, back.

However, in some higher dimension, the Earth is perhaps very gradually falling toward the Sun, in a straight path.... But we observe this as the Earth going around the Sun in its orbit. That sounds awfully confusing, but let's look at an example from none other than Stephen Hawking, in his book "A brief History of Time".

He uses this analogy to help explain the observation of the Earth orbiting around the Sun:

Imagine a jet going in a straight line from A to B. Its movement doesn't deviate from being straight, but as it flies over mountains, it's shadow that is casts on the Earth appears to be moving up and down over the mountains. Now, this shadow is not moving linearly, despite the Jet moving in a straight line in the 3D world that we observe.

It's just hypothetical, so don't worry if you find it terribly confusing as it quite simply is just that, confusing, but interesting none the less!

This isn't the only wild theory out there, but I'm not going to go into every detail here - maybe I'll write a post that goes through the most supported theories? Let me know if that's something you'd be interested in and I'll happily do that.

But, hopefully, you've now got the gist of gravity being the consequence of an object curving space-time, and not a force that you'll often hear it being described as.

As I said earlier though, some of my other posts go into a bit more detail of the effects that it can have, including that on time, but also discuss the most important revelations that proved gravity cannot be a force - so check them out if you've got the time and are interested in that kind of field of astronomy/physics.

Thanks for reading!