Gravity vs. Acceleration

1. Jan 9, 2008

Bullwinkle

I've always wondered why gravity and acceleration are explained as two completely different concepts, yet they can be perceived to be the same exact thing under the right set of circumstances.

Example: The room you are sitting in is mounted to the rear wall of the spaceship, so that you are sitting inside the craft perpendicular to its rear wall. The spaceship now accelerates forward at a constant rate that exactly matches that G-force of gravity on Earth. If you hadn't known your room was just transplanted to the accelerating spaceship, you would still think you were sitting in the room on Earth!

Obviously the Earth is not accelerating in one direction, since "gravity" wouldn't then exist on the opposite side and we'd all fly off into space. But what if the entire universe was not only expanding, but it's nucleus was constantly accelerating in an ever-widening 3D spherical pattern. Perhaps mass simply warps the fabric of space such that the more mass, the more of this constant rate of acceleration that is exerted as "gravity." Do we know enough about the relationships between constant spherical acceleration, centripedal force, and even electromagnetism to discount such a theory?

2. Jan 10, 2008

Mentz114

You're right about the fact that gravity and acceleration cannot be distinguished in some circumstances.

If you don't have access to any books on this subject, you might like to look it up in Wiki. Newton first proposed a gravitational law, which works very well at explaining most of what goes on in the solar system. In 1915 Einstein proposed a more complex theory based on the 'curvature' of space-time. It is called General Relativity. You could look that up also.

There are also other threads in the forum discussing the 'Einstein's elevator' which is like your rocket.

3. Jan 10, 2008

jcsd

Bullwinkle your reasoning is pretty simlair to the same reasoning that motivated the general theory of relativity. In General relativity, there is no definite distinction between gravitional forces and the so-called pseudo-forces experinced by an accelarting observer. They are both the result of choosing local spacetime coordinate systems where the Christoffel symbols do not vanish.

Howver in most situations involving gravity you cannot take a global inertial frame a simple transform into a non-inertial frame to model the grvaity. One of the strokes of genius behing genral relativity was to allow instrinsically curved spacetimes (where golbally inetrial frames do not necessarily exist, unlike flat spacetime), which allowed for all gravitional situatiosn to modelled.

4. Jan 11, 2008

Bullwinkle

Thanks for the useful info guys, I will check out wiki and these other forums on Einstein's elevator. I just thought it to be quite strange how two different forces could be perceived to be the exact same (although I guess they are not really that different afterall, according to General Relativity) -- especially since I cannot think of any other examples in nature/physics where that is known to be the case (i.e., electromagnetism could never be mistaken for acceleration).

Regarding the curvature of space/time: Even in a fractalized or imperfect curvature, wouldn't there be theoretical pathways where light would ultimately travel all the way around to meet its starting point again, as long as it wasn't snatched-up by a blackhole?

5. Jan 11, 2008

jcsd

The thing about pseudo-forces and gravitational force is that the force exerted on a body is directly proportional to it's mass in both cases. This not so for other forces.

Spacetime is modelled using smooth manifolds which don't exhibit self-simlairity (except trivially for the flat case I guess) and you'd have to expand what you mean by 'imperfect'. But yes it is perfectly possible to have closed null wordline, one example would be in the photon sphere of a black hole.

6. Jan 11, 2008

CJames

It is my understanding that what your saying is actually quite close to what general relativity has to say about gravity. Essentially, if you are in free fall, you are not accelerating. The surface of the earth is accelerating toward you. If you are standing on the earth, you are being accelerated upward by the electromagnetic force (the repulsion between the electrons in your shoes and the electrons in the dirt). The warp in spacetime that is gravity causes objects which are "at rest" to decrease or increase their distances from one another with time, while objects that are accelerating toward or away from each other at just the right rate will maintain a constant distance from one another with time.

The earth is a good example of this. Every grain of sand or drop of magma that composes the earth is being accelerated away from the center of Earth by the electromagnetic force. The warp in spacetime ensures that this acceleration does not change the distance between the points that make up the earth. But it is this acceleration away from the center of the earth that causes you to "feel" gravity.

7. Jan 11, 2008

Mentz114

CJames:
No, you are not.
What EM force is that ? First I've heard of it. Do you mean 'centripetal force'.

No it isn't. I find your whole post a bit disturbing, some of it seems right but the details are not.

8. Jan 12, 2008

CJames

Like I've said before, I'm not a physicist, so I could be wrong. And maybe I wasn't explaining myself too clearly. But here's my logic.

Gravity isn't really a force, it's a warp in spacetime that causes geodesics to, for example, move away from one another when they are on the same side a spatial axis passing through the center of a planet over time or, move toward each other when they are on opposite sides of a spatial axis passing through the center of a planet over time. Objects following these geodesics aren't really accelerating. Anything deviating from a geodesic, on the other hand, IS accelerating. Geodesics in warped space are either going to converge or diverge. If worldlines of objects are maintaining a constant distance from one another over time in a gravitational field, at least one of those wordlines is not following a geodesic. Therefore, at least of of those worldlines is accelerating.

In the case of any point at the surface of the earth, by the equivalence principle, you would be accelerating away from the center of the earth at 1G. What is causing you to accelerate away from the center of the earth? Gravity, a phantom force, is pushing you against the surface of the earth. Why don't you fall through it? The electromagnetic force. (Is that the right terminology? Maybe I'm not being precise.) Specifically, the electrons in the atoms of your feet are repelling the electrons of the surface of the earth (and the electrons of your feet are repelling the electrons of higher parts of your feet, and so on up to your legs, hips, torso, head) so that you don't fall through the Earth's crust to the center of the earth.

It's really the same thing in most equivalence principle thought experiments. If you are in a spaceship accelerating at 1G, you FEEL the force of "gravity" because of the electromagnetic force repelling your shoes from the floor of the spacecraft.

So gravity itself is simply the result of geodesics in warped spacetime. But the force you actually FEEL, the one that distinguishes your frame of reference from that zero G frame of reference of an object in free fall, is the electromagnetic force.

Please tell me I'm right?

Or, if I'm wrong, I suppose that's not so bad either. I get to learn something new, which is never a bad thing.

9. Jan 12, 2008

A.T.

According to GR you are. Only free falling objects are not accelerated.
It is the force that prevents you from walking through a wall (like a ghost, not like the Incredible Hulk)

10. Jan 12, 2008

CaptainQuasar

On this topic - within Einstein's Elevator, wouldn't the pseudo-force of acceleration appear as something like a scalar field, whereas an extremely sensitive instrument could detect that true gravity is a gradient?

11. Jan 12, 2008

A.T.

You sound right to me in regards to GR. But I'm not a physicist either

Last edited: Jan 12, 2008
12. Jan 12, 2008

CJames

Captain Quasar

There are clear differences between a "true" gravitational field and the force felt by an accelerating object. For one, if you had an artificial gravity system provided by the centrifugal force, you would feel a force pulling you to the side if you climbed a ladder.

A true gravitational field creates a warp in space and time which is clearly measurable from any reference frame. The point made by the equivalence principle is that the force felt by an accelerating object is the same as the force felt by an accelerating object. That is, if a beam of light were in an accelerating spaceship, it would be seen to curve, just like a beam of light in a gravitational field. The difference is that a beam of light within the "graviational field" of an accelerating spaceship would "bend" by the same amount at any point within the spaceship, while a beam of light in a "true" gravitational field would "bend" by different amounts depending on distance from the source of gravity. This is why mass is said to actually warp space and time, while the "force" created by an accelerating spaceship or a rotating carousel does not.

13. Jan 12, 2008

A.T.

The equivalence principle considers an idealized homogeneous gravitational field (gradient = 0) within the elevator.

14. Jan 12, 2008

CJames

Thanks AT, for reducing my temporary paranoia that I had no idea what was talking about. ;)

15. Jan 12, 2008

Poop-Loops

I'm sorry, why would an electromagnetic force accelerate you? If I shine a flashlight at you, you won't fall backwards. So how much light would it take to actually accelerate someone against Earth's gravity?

16. Jan 12, 2008

CJames

Not light. Specifically it's the electric repulsion between the electrons of your feet and the electrons of the dirt (or whatever your standing on). Like repels like, opposites attract. Like I said, maybe my terminology is imprecise. But I'm talking about the same force that keeps all "solid" matter from passing through all other "solid" matter. The same force that keeps your hand from passing through a wall. Technically I guess this subject doesn't necessarily even belong in the relativity section, but it's directly related to the subject matter of this thread. Gravity creates a phantom force that pulls you toward the center of the planet by warping space and altering your geodesic. The electromagnetic field creates a real force that keeps you at rest and prevents you from falling through the floor.

17. Jan 12, 2008

CJames

Also, although this is distinct from what I was talking about, light does technically carry momentum, and it does transmit a force. A powerful enough laser would in fact make you "fall backwards". But again, this is very different from the repulsion between electrons that I was talking about.

18. Jan 12, 2008

A.T.

In case you want to try this out: Hold a mirror in front of you. This will double the momentum you receive, and prevent the powerful laser beam from going trough you.

19. Jan 13, 2008

Bullwinkle

I suppose solar sails could provide the evidence needed here as well.

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