Freethought & Rationalism Archive

Abacus · 06-16-2003, 09:20 AM

Imagine yourself on a space station. Not one like Mir or the ISS, but a futuristic one, similar to the rotating wheel depicted in the movie 2001: A Space Odyssey. While inside the rim of the station, you would feel like you were being pulled into the floor. When standing, you would feel your weight on your feet. You can jump, and rise up off the floor for a short time, but soon you would be pulled back down to the floor. If you were to, say, hold an egg at waist level, and then let it drop, you would observe it fall to the floor and possibly break, making a mess on the floor.

Of course we know that your experiences aren�t due to your proximity to a large mass, even though they are very similar to what we would experience here on Earth. While standing inside the rim of the station, you are being accelerated towards the center of the station. You feel this acceleration as the weight on your feet. When the egg falls to the floor, it is simply obeying Newton�s first law of motion (until it goes splat on the floor). However, it is your natural tendency to think of yourself as being stationary, and to attribute the weight felt on your feet and the motion of the egg to some mystical force known as artificial gravity. This force is a pseudoforce.

Now imagine yourself on a world with no significant atmosphere, like the Moon. You�re standing there in your pressurized spacesuit at the edge of a big, tall, vertical cliff overlooking a vast plain far below. You take a big leap into space over the edge of the cliff and go tumbling down towards the plain. Now according to what you learned in your high school physics course, a force known as gravity which somehow emanates from the moon is accelerating you, by Newton�s second law, towards the ground below you.

But you�re puzzled. You don�t feel any force at all. Just the other day, when you were riding a spaceship from the space station to the Moon, and the ship�s rocket engines were blazing away, you definitely felt an accelerating force. You also recall your time in deep space, far away from any worlds and where their gravitational influence is very small. You were outside your ship, wearing only your spacesuit. And you felt no accelerating force, just like what you�re feeling now as you accelerate towards the ground. So what gives?

Should that force that we all know as gravity be considered a pseudoforce, like the artificial gravity of a rotating space station? Should we consider the motion of the Moon in its orbit about the Earth as unaccelerated motion? Should we consider my motion, sitting in a chair in front of my computer, as accelerated motion?

Jesse · 06-16-2003, 10:00 AM

The Einstein Equivalence Principle

Demosthenes · 06-16-2003, 01:07 PM

The link that Jesse gave takes care of the first part of your post, as for the rest of the post...

Quote:

Now imagine yourself on a world with no significant atmosphere, like the Moon. You�re standing there in your pressurized spacesuit at the edge of a big, tall, vertical cliff overlooking a vast plain far below. You take a big leap into space over the edge of the cliff and go tumbling down towards the plain. Now according to what you learned in your high school physics course, a force known as gravity which somehow emanates from the moon is accelerating you, by Newton�s second law, towards the ground below you.

But you�re puzzled. You don�t feel any force at all. Just the other day, when you were riding a spaceship from the space station to the Moon, and the ship�s rocket engines were blazing away, you definitely felt an accelerating force. You also recall your time in deep space, far away from any worlds and where their gravitational influence is very small. You were outside your ship, wearing only your spacesuit. And you felt no accelerating force, just like what you�re feeling now as you accelerate towards the ground. So what gives?

The reason you can feel the force when you're in the spaceship that's accelerating is because your body has inertia and it's not rigid. As the engine fires, the ship will begin to move along with the chair that you're sitting in. You're not moving at the same exact time that the ship starts accelerating. What happens is that the chair presses on you and accelerate you along with the ship. The force exerted by the chair on you is what gives you the sense of acceleration. In futher detail, as your body start to move, the fluids in your ears' balancing and force sensing canals aren't moving at the same exact instant either, till the canals press on the fluids and accelerate them too. That's what gives you the funny feeling in your head as your brain sense the changes in the ears' apparatus

If you weren't strapped in but floating in a long corridor that's running down the axis of the ship. As the ship begin to accelerate, you'll see the corridor's walls rushing by but you're still motionless with respect to the ship. You won't feel any force at all until the end of the corridor rush up to you and make contact with you and then accelerate you along with the rest of the ship. If the ship's accelerating slowly enough, then it'll be painless, if not, then you better hope that it's still moving slowly enough so it won't plaster you against the far wall.

Quote:

Should that force that we all know as gravity be considered a pseudoforce, like the artificial gravity of a rotating space station? Should we consider the motion of the Moon in its orbit about the Earth as unaccelerated motion? Should we consider my motion, sitting in a chair in front of my computer, as accelerated motion?

Gravity can be thought of as a pseudoforce but not in the sense that you mean more of the sense that matter concentrations aren't really attracting anything. Instead they are creating space-time deformations that present geodesics which matter follow(such as your body in Moon's gravity).

Unaccelerated motion is called constant velocity in physics. Velocity has two quantities, speed and direction. Acceleration occurs when velocity's speed or direction or even both is changing(because acceleration is simply a change in velocity like velocity is a change in position). Although the moon's speed is constant, it's direction is constantly changing as it goes around in its orbit. So it has a constant acceleration. As for you, it depends on which frame of reference you're using. If you take your frame of reference to be your house or even the entire neighborhood, then you aren't accelerating and your velocity is zero since you're sitting in your chair. If your frame of reference is the sun, then you're accelerating because you're in a orbit around the sun along with the rest of earth.

Jesse · 06-16-2003, 01:27 PM

Quote:

Originally posted by Demosthenes
The link that Jesse gave takes care of the first part of your post, as for the rest of the post...

The equivalence principle takes care of both parts of his post--it states that being at rest in a gravitational field is equivalent to accelerating in deep space, and that moving at a constant velocity in deep space is equivalent to falling in a gravitational field (uniform acceleration), which was the second part of his post. From the link above:

Quote:

Another way of saying the Principle of Equivalence is the following:

* The Physics performed in Laboratory falling freely under the influence of a uniform gravitation field is indistinguishable from the physics performed in an inertial frame (where Newton's Laws of motion are valid).

In other words, if the cable in the elevator is cut, and the experimentor is in free fall, she will not feel her own wieght. It would be as though there is no force of gravity acting at all. Objects int he elevator with her will free fall too, and the relative motion of everybody will appear to be equivalent to being in free space, with no gravity.

Here's another page which explains how most of general relativity can be derived as a consequence of the equivalence principle:

http://www.physics.nyu.edu/courses/V85.0020/node48.html

Quote:

The General Theory of Relativity is a complicated mathematical theory. However, we can get some idea of the consequences of the postulates by adopting the following procedure:

Look at some events in an accelerating reference frame. Use the Special Theory of Relativity to view these events from an inertial frame relative to which the other frame is accelerating. From within the accelerating frame, attribute the effects to a gravitational field. Conclude that the same results would occur in a true gravitational field.

To see how the method works, let's look at some examples.

* Bending of light in a gravitational field: Consider first an accelerating rocket in outer space. We have already seen that if you release a ball in this rocket it accelerates to the bottom of the rocket as viewed in the rocket frame. Imagine that you throw a ball horizontally in the rocket frame. From the reference frame outside the rocket (inertial frame) the ball moves on a straight line since no forces act on it. From inside the rocket frame, the ball will move on a curved arc, just as in a gravitational field. Now instead of throwing a ball, flash a laser beam on and off in the horizontal direction. From outside the rocket frame, the light will propagate horizontally at the speed of light since the speed of light is the same in all inertial frames. However from inside the rocket frame, just as for the ball, the light will follow a curved arc (the curve is much smaller for light since its horizontal velocity is enormous compared to that of the ball). The observer inside the rocket attributes this curvature to a gravitational field. Thus we can expect that light will bend in a true gravitational field and that the speed of light is not constant in a true gravitational field.

* Gravitational red shift: Now imagine a rotating reference frame (disk) in outer space. There are identical clocks at the center of the disk and on the circumference of the disk. From an inertial frame outside the disk, the clock on the circumference is moving at a speed v relative to the inertial frame, while the clock at the center is stationary relative to the inertial frame. From the Special Theory, it then follows that the clock on the circumference runs slower than the clock at the middle. In the rotating frame, the observer attributes this difference in clock rates to a gravitational field which is stronger the further you are from the center of the disk. Thus we can conclude that in a true gravitational field that clocks run slower closer to the mass producing the field. This known as the gravitational red shift.

Since clocks run at different rates at different points in a gravitational field, it is impossible to synchronize clocks in a gravitational field. The gravitational red shift can also be used to ``explain'' the twin paradox. When the space twin turns around, she must accelerate. In her frame there appears to be a strong gravitational field and she is much closer to the center of the field than the Earth twin. Therefore, when this field is on, the Earth twin's clock is moving much faster than hers and this ``explains'' why the Earth twin is older. This does not really explain anything. It just gives a consistent picture of the result, but that is all. There is no true gravitational field in the twin paradox. The fact that the space twin is younger is related to the structure of space-time.

* Non-Euclidean geometry in a gravitational field: Back on the disk, let's measure the ratio of the circumference of the disk to its diameter. To do so we lay meter sticks around the circumference and along the diameter. Viewed from outside the disk in an inertial frame, the meter sticks along the circumference are shorter than their rest length, while those along the diameter are equal to their rest length (since the velocity is in the tangential direction, only length in the tangential direction is modified). Thus it will take more meter sticks than ``normal'' to go around the circumference and the ratio of the circumference to the diameter will be greater than . Inside the rotating frame, the observer attributes the fact that geometry is non-Euclidean (in Euclidean geometry the ratio of circumference to diameter equals ) to the presence of a gravitational field. Thus, we conclude that in a true gravitational field, space, or, more generally, space-time, is non-Euclidean.

It should also be apparent that, since the length of meter sticks changes in the rotating frame, it is impossible to have uniform meter sticks in a gravitational field.

Demosthenes · 06-16-2003, 01:47 PM

oops should have said the first two parts

Abacus · 06-16-2003, 03:28 PM

I know about the Equivalence Principle. In fact, it's what I had in mind when I wrote my post.

I guess my question is, does the Equivalence Principle imply that gravity is really not a force?

Jesse · 06-16-2003, 04:12 PM

Quote:

Originally posted by Abacus
I know about the Equivalence Principle. In fact, it's what I had in mind when I wrote my post.

I guess my question is, does the Equivalence Principle imply that gravity is really not a force?

Sort of. But what makes it more complicated is that the other "forces" may work the same way as gravity, which might mean that we should just redefine our notion of a force. The Kaluza-Klein theory tried to unify electromagnetism with gravity in terms of curvature in a fourth spatial dimension, which was assumed to be "curled up" so we don't notice it, and this idea has been incorporated into string theory, which tries to unify the strong and weak force with the other forces in the same way. String theory originally involved 9 spatial dimensions, 6 of them curled up, but then string theory was extended into a theory of "branes" which involved a total of 10 spatial dimensions.

Shadowy Man · 06-16-2003, 08:29 PM

Quote:

Originally posted by Abacus

I guess my question is, does the Equivalence Principle imply that gravity is really not a force?

No.

And in fact, the Equivalence Principle isn't technically correct, because gravity is divergent!

Jesse · 06-16-2003, 08:41 PM

Quote:

Originally posted by Shadowy Man
No.

And in fact, the Equivalence Principle isn't technically correct, because gravity is divergent!

What do you mean by divergent? Are you talking about tidal forces? I think the equivalence principle works if you assume the volume where you're doing experiments is negligibly small compared to the gravitational field you're in.

Shadowy Man · 06-17-2003, 06:06 AM

Quote:

Originally posted by Jesse
What do you mean by divergent? Are you talking about tidal forces? I think the equivalence principle works if you assume the volume where you're doing experiments is negligibly small compared to the gravitational field you're in.

Divergent as in if you take the divergence (Del dot F) of the force field you get a non-zero value.

But yes, over small enough volumes a gravitational field can appear uniform.

That's why I said technically. It may not be noticeable in most cases, but it is still not perfectly equivalent.

06-16-2003, 09:20 AM	#1
Abacus Veteran Member Join Date: Mar 2002 Location: South Dakota Posts: 2,214	Is gravity a pseudoforce? Imagine yourself on a space station. Not one like Mir or the ISS, but a futuristic one, similar to the rotating wheel depicted in the movie 2001: A Space Odyssey. While inside the rim of the station, you would feel like you were being pulled into the floor. When standing, you would feel your weight on your feet. You can jump, and rise up off the floor for a short time, but soon you would be pulled back down to the floor. If you were to, say, hold an egg at waist level, and then let it drop, you would observe it fall to the floor and possibly break, making a mess on the floor. Of course we know that your experiences aren�t due to your proximity to a large mass, even though they are very similar to what we would experience here on Earth. While standing inside the rim of the station, you are being accelerated towards the center of the station. You feel this acceleration as the weight on your feet. When the egg falls to the floor, it is simply obeying Newton�s first law of motion (until it goes splat on the floor). However, it is your natural tendency to think of yourself as being stationary, and to attribute the weight felt on your feet and the motion of the egg to some mystical force known as artificial gravity. This force is a pseudoforce. Now imagine yourself on a world with no significant atmosphere, like the Moon. You�re standing there in your pressurized spacesuit at the edge of a big, tall, vertical cliff overlooking a vast plain far below. You take a big leap into space over the edge of the cliff and go tumbling down towards the plain. Now according to what you learned in your high school physics course, a force known as gravity which somehow emanates from the moon is accelerating you, by Newton�s second law, towards the ground below you. But you�re puzzled. You don�t feel any force at all. Just the other day, when you were riding a spaceship from the space station to the Moon, and the ship�s rocket engines were blazing away, you definitely felt an accelerating force. You also recall your time in deep space, far away from any worlds and where their gravitational influence is very small. You were outside your ship, wearing only your spacesuit. And you felt no accelerating force, just like what you�re feeling now as you accelerate towards the ground. So what gives? Should that force that we all know as gravity be considered a pseudoforce, like the artificial gravity of a rotating space station? Should we consider the motion of the Moon in its orbit about the Earth as unaccelerated motion? Should we consider my motion, sitting in a chair in front of my computer, as accelerated motion?

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06-16-2003, 10:00 AM	#2
Jesse Moderator - Science Discussions Join Date: Feb 2001 Location: Providence, RI, USA Posts: 9,908	The Einstein Equivalence Principle

06-16-2003, 01:47 PM	#5
Demosthenes Veteran Member Join Date: Oct 2000 Location: a speck of dirt Posts: 2,510	oops should have said the first two parts

06-16-2003, 03:28 PM	#6
Abacus Veteran Member Join Date: Mar 2002 Location: South Dakota Posts: 2,214	I know about the Equivalence Principle. In fact, it's what I had in mind when I wrote my post. I guess my question is, does the Equivalence Principle imply that gravity is really not a force?

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