# How does mass know that space is curved?

as mass moves through spacetime, it follows the geodesics of local spacetime curvature as rendered by nearby large masses such as stars, planets, etc (and all other mass to whatever degree).

how does mass know that the spacetime through which it passes is curved? ie, how is the curvature of a geodesic imparted to a particle of mass? i know the particle thinks it is just moving along a "straight" line, but from my observer perspective, it looks like a curve to me...

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As the geometry is fixed (a given curvature) the particle has no choice but to move along a geodesic line, by definition of geometry.

But I personally prefer thinking of a gravitational force in a plane space-time rather than of a curved space-time.

This question is borderline philosophy, so it's not going to have a nice, definite answer.

I think the idea is that mass doesn't know how space is curved. As far as inertia is concerned, it always moves straight ahead.

It's just as if you were driving across the country. To you, the road is straight (at least, we can imagine a perfectly straight road that doesn't curve left or right). As you travel in a straight line across this road, you are completely unaware of the curvature of the Earth beneath your wheels.

DrGreg
Gold Member
how does mass know that the spacetime through which it passes is curved? ie, how is the curvature of a geodesic imparted to a particle of mass? i know the particle thinks it is just moving along a "straight" line, but from my observer perspective, it looks like a curve to me...
Note that if you are on the Earth's surface, or hovering at a constant distance above the Earth, the reason the path of a freely falling mass looks like a curve to you is because you are accelerating upwards. That effect isn't spacetime curvature. If, instead, you were also freely falling yourself, nearby falling masses would seem to following a straight line, near you at least. Spacetime curvature is what makes distant masses appear to be changing velocity relative to you.

Think of two lines drawn on a globe, both northward from the equator. They start off parallel, at a constant distance apart, but as they approach the north pole, it is clear they are getting closer together, even though both lines are "straight" and couldn't be drawn any straighter.

Note that if you are on the Earth's surface, or hovering at a constant distance above the Earth, the reason the path of a freely falling mass looks like a curve to you is because you are accelerating upwards. That effect isn't spacetime curvature.
What I said was just an analogy. Locally straight need not imply globally straight.

DrGreg
Gold Member
Note that if you are on the Earth's surface, or hovering at a constant distance above the Earth, the reason the path of a freely falling mass looks like a curve to you is because you are accelerating upwards. That effect isn't spacetime curvature.
What I said was just an analogy. Locally straight need not imply globally straight.
Indeed. I said that just in case jnorman hasn't got the right picture for what spacetime curvature is.

It doesn't. It follows the geodesic, which means that it is taking the path of least resistance. That makes it similar to the question, "how does the ball know it is rolling downhill?"

Some actually define this as "straight," because it is the path between two points that requires the least effort getting from A to B. Others define the geodesic as "straighter than straight" for the same reason. While "straight" is an intuitive term that we all understand (or think we do), it is rather ill-defined. What we call a straight path on planet Earth actually always has a slight curve to it, but because most paths that we deal with are so small relative to the size of the Earth, we cannot and do not notice it. Engineers of large bridges or enormous buildings must take it into account, however.

A.T.
i know the particle thinks it is just moving along a "straight" line,
Why do you ask about the particle being aware of the curvature then? The particle is not only "thinking" that, it is in fact going straight ahead.
but from my observer perspective, it looks like a curve to me...
But how schould the particle know how it looks to you? And why should the particle care? Your perspective is based on the intuitive assumption of a flat space-time, and entirely your own problem, not the particle's. Last edited:
I do not like comparison with moving on a curved surface - such a moving is constrained to the surface whatever the particle velocity is. In a gravitational field particles with different velocities "choose" different trajectories.

A.T.
I do not like comparison with moving on a curved surface
You probably mean a curved surface representing 2-spatial dimensions, and no time dimension. It works better if you include the time dimension, so you really have an analogy for curved space-time, not just space:
http://www.relativitet.se/spacetime1.html
such a moving is constrained to the surface whatever the particle velocity is.
Correct, just like the particle is constrained to the 4D-space-time. The velocity of the particle in space is defined by the direction in space-time.
In a gravitational field particles with different velocities "choose" different trajectories.
Correct, just like in the analogy I linked above (second picture).

You are right, we have to include time as another "space" variable of a curved space-time, that is why analogy with moving on a curved space surface is somewhat misleading.

Also, moving in a gravitational field is accompanied with EM radiation, if the probe body is charged. It is not equivalent to moving of a neutral body, so the geometrical approach seems to me a little bit wrong.

Dale
Mentor
how does mass know ... the particle thinks
Can you formulate your question without anthropormorphizing? That may help you get to the actual physics you are interested in.

okay - let me try again. how does curved spacetime convey its curvature to a particle? if we assume for the moment that there is no "graviton" particle which imparts force to another particle altering its trajectory, there must be some other mechanism by which a particle interacts with spacetime. maybe i am asking "what exactly is curved?" - whatever it is, it is invisible, and has no apparent mechanism of interaction with mass/energy. or maybe i am asking "what is a field?" - we dont seem to know the answer to that one either (if you think you do, please explain to me how a magnet works...)

A.T.
there must be some other mechanism by which a particle interacts with spacetime.
What do you mean by "mechanism". Some simple mechanical analogy? Some use toy cars or tape on curves surfaces:
http://www.relativitet.se/spacetime1.html
Ot you could invent something like this: space-time varies in density. Particles have some extend in space-time, so the more dense regions slow one side of the particle more. Therefore the trajectory of the particle bends towards the denser region. Just like light rays bend towards the optically denser area.
maybe i am asking "what exactly is curved?" - whatever it is, it is invisible, and has no apparent mechanism of interaction with mass/energy.
Intrinsic curvature is an abstract mathematical concept. It happens to be useful to describe the behavior of stuff in a gravitational field.
or maybe i am asking "what is a field?" - we dont seem to know the answer to that one either
Sure we do, we invented it: just another mathematical abstraction.
(if you think you do, please explain to me how a magnet works...)
The magnetic field describes how magnets affect other things. If you want to know why it does so, any answer will create the next why-question. So why bother? The magnetic field describes how magnets affect other things. If you want to know why it does so, any answer will create the next why-question. So why bother? Why bother asking why the sky is blue?
Why bother asking why the sun rises every morning?
Why bother asking why children inherit charcteristics from their parents?

This "science can't answer 'why' questions" attitude seems very strange, and it's one I've noticed a lot on this board.

A.T.