Why Does Mass Pull on Other Stuff?

[Paige_Turner]

Why doesn't it repel things... or just pass through and leave distance unchanged?

 

[PeroK]

Particles in curved spacetime move according to the principle of maximal proper time, which produces the observed trajectories.

 

[PeterDonis]

Why doesn't it repel things... or just pass through and leave distance unchanged?

Mass doesn't "bend space". It bends spacetime. More precisely, stress-energy bends spacetime; that includde mass (more precisely, energy density), but it also includes other things, like pressure. The particular way stress-energy bends spacetime depends on the particular properties of the stress-energy; for example, "dark energy" (which has positive energy density but negative pressure) pushes things apart instead of pulling them together (that's why it causes the expansion of the universe to accelerate).

 

[Paige_Turner]

> Particles in curved spacetime move according to the principle of maximal proper time

Do you mean, "minimal proper time?"

 

[PeroK]

Do you mean, "minimal proper time?"

No, it's maximal proper time.

 

[Grasshopper]

Do you mean, "minimal proper time?"

No, it's maximal proper time.

Does this make any sense?

In your own rest frame, you don't move through space, but you always move through time. That is an instance of "maximal proper time," right? And then presumably the more an object moves through space, the less through time, but their proper time is always going to be greater than zero — and in fact their proper time will always be the largest it can be — because all objects are at rest in their own rest frame (and therefore in their own frame are moving through spacetime entirely through the time dimension).

 

[Paige_Turner]

That's absolutely fascinating; it's just the kind of stuff i come here to find out, and yes it makes sense. ty.

...But isn't it inconsistent with he principle of least action? Light takes the path of the sum of histories, but that adds up and cancels out to the path that takes the least time, right? A geodesic is the shortest possible path on the 4D manifold, etc?

 

[PeterDonis]

Does this make any sense?

Yes.

In your own rest frame, you don't move through space, but you always move through time. That is an instance of "maximal proper time," right?

Only if you are in free fall. Don't confuse proper time with coordinate time. In fact, I would advise forgetting about coordinates and frames altogether when thinking about this. The rest of your post is simply compounding that error.

 

[PeterDonis]

isn't it inconsistent with he principle of least action?

No, because the action for an object moving through spacetime is the object's rest mass times minus the proper time. So maximizing the proper time is the same as minimizing the action.

 

[PeterDonis]

Light takes the path of the sum of histories, but that adds up and cancels out to the path that takes the least time, right?

Light moves on null geodesics, which do not maximize proper time; proper time is a meaningless concept for null curves.

The "least time" principle for light propagation is a special case of the principle of least action, yes; but it's not the same thing that we're talking about when we talk about a timelike geodesic maximizing proper time.

A geodesic is the shortest possible path on the 4D manifold, etc?

Not a timelike geodesic on a Lorentzian manifold, no. A timelike geodesic is the longest possible path between two points.

Actually, in a curved spacetime, this is only true locally; there might be paths with longer proper time that are not "nearby" to a given geodesic. For example, consider a circular free-fall orbit about a planet like the Earth. This is a geodesic, so if we pick two events that are exactly one orbit apart, the orbital path through spacetime will locally be the longest possible path that connects those two points; but only locally. There will be another geodesic path that is longer--namely, the purely radial path, which would be realized by a ball thrown upwards from the first event (i.e., just as the orbiting object passes) with just the right velocity to fall back down and reach the second event (i.e., it falls down past the orbiting object just as it has completed exactly one orbit). But this radial geodesic path is not "locally" accessible from the circuliar orbit path (roughly, because the orbit path winds once around the Earth, but the radial path does not).

 

[Paige_Turner]

> the object's rest mass times minus the proper time.

WOH.Action is one of the things I'm currently trying to understand.
So maximizing the proper time is the same as minimizing the action.
That was key info, thx.

I wish I knew how many more of those understanding nuggets I have to collect before I'll understand what the eff is going on--how nature works.

Would that minus sign happen to be the same as the minus sign in the interval metric equation? Is it negative for the same reason that in the interval, the elapsed time is subtracted from the sum of the squared space distances?

 

[PeterDonis]

Would that minus sign happen to be the same as the minus sign in the interval metric equation?

No. Heuristically, the minus sign comes from the fact that the Lagrangian is kinetic energy minus potential energy, and rest mass is part of potential energy in relativity.

 

[Paige_Turner]

No. Heuristically, the minus sign comes from the fact that the Lagrangian is kinetic energy minus potential energy, and rest mass is part of potential energy in relativity.

Yaaack! That was the key.

With your info plus reading about Langrangians and action for the past hour, I've learned as much today as in any college class. That makes me both delighted and excited because it links all the stuff I noticed about cyclic trading of energy between dimensions, like in pendulums, and the nature of potential energy and gravity. It's an important (to me) path I've been looking for. Thank you.

Since I can never seem to understand something without understanding a whole lot of other stuff, i have more more questions about action and the Planck constant, but I'll ask them in another thread.

 

[PeterDonis]

i have more more questions about action and the Planck constant, but I'll ask them in another thread.

Note that if the question involves Planck's constant, it probably belongs in the quantum physics forum.

 

[Paige_Turner]

> it probably belongs in the quantum physics forum.

No way. I'm staying away from that quantum stuff. It's scary.

 

[PeterDonis]

I'm staying away from that quantum stuff. It's scary.

You can't stay away from quantum stuff if you ask questions involving Planck's constant.