# Accelaration is equal to gravity

1. Mar 7, 2005

### paulhunn

I was on my way to school this morning and i suddenly thought of somthing about relativity that has been bugging me ever since. Would i be right in saying that one of Einsteins theorys or relativity (cant remember which) says that accelaration is equal to gravity and that the force felt from each is indistingushable. So in the vacuum of space if you accelarate at a certain rate a force is felt pulling you in the direction opposite the accelaration that is equal to the earths gravitational constant g (9.81 ms^-2). So if you accelarated at double this rate then the force acting in the opposite direction of the accelaration would be about 20ms^-2. If you accelarated at this rate towards the earth then the force acting due to gravity would be 10^ms-2 and the force due to accelaration would be 20ms^-2 in the opposite direction. The resultant force acting on the object would be 10ms^-2 in the direction opposite the earths gravatational pull and newtons laws of motion state that an overall force acting on an object causes accelaration in the direction of the force so it would cause accelaration in the direction opposite the earth. I know i must have missed somthing and it is probably staring me right in the face but any help would be greatly appreciated.

Paul

2. Mar 7, 2005

### Timbuqtu

Yes they have something to do with each other, the theory is called: general relativity

Actually your reasoning is fine. Imagine your sitting in an elevator which is moving the way you described and you measure your own location with respect to the elevator. Then you would accelerate (w.r.t. the elevator) towards the ceiling of the elevator with an acceleration of 10 ms^-2 (assuming the floor is pointing towards the earth), that is 10 ms^-2 in the direction opposite to the earth.

3. Mar 7, 2005

### cepheid

Staff Emeritus

Can somebody explain to me what this "force due to acceleration" is? It seems to be fishy. (so does the fact that all the numbers in your example were accelerations, but you called them forces). I thought that acceleration was caused by a force, and not the other way around. Furthermore, both of the forces you guys used in your examples seem to be what, if I'm not mistaken, are termed "pseudoforces" -- the force "pushing" you to the ceiling of the elevator, and the force pushing you back (in a direction away from the earth...or backward relative to your spacecraft). In reality, as measured from some inertial frame, aren't the forces acting on the spacecraft itself just the force due to gravity, and the thrust of the rocket (both of which face toward earth in this example)???

I'm working with experience in the classical framework here, haven't studied GR, so bear with me.

4. Mar 7, 2005

### dextercioby

Have you been presented with the relationship cause-effect in the case of Newton's second law for constant mass bodies

$$m\vec{a} =\sum_{k} \vec{F}_{k}$$ ?

Daniel.

5. Mar 7, 2005

### Crosson

Quoting from the ultimate book, Gravitation by MTW:

"All of the laws of science have this deep and subtle character, in which they both define concepts and make statements about these concepts".

That is really the best way to interperet Newton's equation, which takes on richer and richer character the harder you look at it.

6. Mar 8, 2005

### cepheid

Staff Emeritus
That's a great quote, but I guess I just don't have that sort of insight in this case. I admit that the 2nd law as stated here doesn't imply anything about a cause-effect relationship. It could be interpreted as stating that if there is a net external force on a body...it will be observed to accelerate with an acceleration in the direction of the force, and with magnitude F/m.

On the other hand, it can also be interpreted as stating that if an object is observed to undergo accelerated motion, there must be a net external force acting on it in that direction, with magnitude ma.

But where my caution lights go on is when we use this second interpretation, combined with a so called "observation" or perception of accelerated motion of a body, to conclude that there is a force acting on that body in the direction of the acceleration, even when no such force is readily identifiable =(. Here's a little made up example: So I'm in a bus, and the driver slams on the gas...but I don't believe we're actually moving. All I know is that some sort of mysterious force seems to throw me backward. Naively, I tell myself, "well, my motion is not consistent with that described in Newton's first law (I'm accelerating rearward), so there must be a net rearward force acting on me."

Then somebody more knowledgeable in physics corrects me, noting that I was not in an inertial frame, so I shouldn't have expected Newton's first law to hold (from my point of view). From his point of view, the bus accelerated around me, whereas I did not, because of my inertia. There are no forces acting on me (except friction on the floor...which eventually does sweep me along with the bus...just not very well).

If I remember right, this was the interpretation advocated by my first year text, which stated vehemently that there was no such thing as a "force of acceleration" which pushed one back in one's seat when his car accelerated. I was fine with this, for a time.

Leave it to my physics prof (when we took Lagrangian mechanics) to cloud the issue considerably, by speaking of "centrifugal forces" among other things. He held that these are real forces, that they "exist", because after all one can feel them. Well, without resorting to some definitions of "force", isn't that more of a philosophical question anyway?

So as you can see by my rambling, I'm terribly confused. Do these "pseuoforces" such as the "force of acceleration", and "centrifugal force" actually exist? That is one way of summarizing what I'm asking, but it's not a very good summary, because again...it seems more philosophical than anything. What I want to know is whether they should be regarded as forces, and if so...why do so many physics teachers cringe when people mention those particular examples? What I want to know is what is the *consistent and correct* way of intepreting the physical situation?

Thanks.

P.S. I still don't think our pilot in the rocket ship has any forces acting on him other than Earth's gravity, and the thrust of the rocket...both pointing towards the planet.

Last edited: Mar 8, 2005
7. Mar 8, 2005

### cepheid

Staff Emeritus

1. This is one of the great conspiracies of physics

OR

2. My line of reasoning is so idiotic that it doesn't deserve a response.

I hope it's neither 1 nor 2, because I just made them both up as some nonsense to type here in order to bump the thread.

8. Mar 11, 2005

### cepheid

Staff Emeritus
I've exhausted my creativity as far as finding excuses to bring this up again...so I'll simply:

*bump*

9. Mar 11, 2005

### Staff: Mentor

That depends on what "actually exist" means. Different people may use different definitions, which would lead to different answers to your question.

10. Mar 11, 2005

### James R

Inertial forces, such as centrifugal forces, exist, but only for observers in non-inertial reference frames.

Thus, if you are in a car going around a bend in the road, the force which pushes you to the outside of the bend (the centrifugal force) is very real for you, sitting in the non-inertial car. But for somebody standing on the road side, no force pushes you across your seat towards the outside of the bend. The inertial roadside observer says that your body tried to go in a straight line as the car was accelerated under you. The force was not on you, but on the car, and it was a centripetal force, not a centrifugal one.

11. Mar 12, 2005

### cincirob

This may or may not help. As a mechanical engineer I was taught that gravity is an acceleration. We draw free body diagrams of masses with little arrows to represent forces. For a mass in the vicinity of Earth, we apply a force at the centroid of the mass equal to mg. The idea being that the mass is being accelerated with the rate g (g=32.2 ft/s/s at the Earth's surface). From Newton, F=mg would give you the force that would produce the same acceleration.

Now for a mass sitting on the earth I view it as the mass being accelerated toward the Earth EVEN THOUGH IT ISN'T MOVING. This lack of motion seems to bother a lot of folks. In this reasoning the lack of motion is explained by the fact that the Earth applies a force of the same size in the opposite direction. Looking at it this way the mass is being accelerated at g downward and is being accelerated upward at a where a=F/m. a=-g

I think this squares with Einstein's (and Newton's) concerns over Newton's depiction of gravity causing forces on masses. The concern centers on the fact that every mass, whether it's a feather or a bowling ball, gets the same acceleration. If it's forces, then you have to explain how the Earth knows it needs to apply one force to one mass and a different force to another so that acceleration is always g. Since Newton considered empty space just that, empty, he couldn't concieve of space having any effect on masses. Einstein's general relativity combines space and time into spacetime and spacetime has properties. One of those properites is that masses distort spacetime and the result is a field which accelerates all masses.

12. Mar 12, 2005

### Davorak

Yes as Timbuqtu, said they are indistinguishable and it is a postulate of GR.

The key word is “felt.” There is no real force in the opposite direction of acceleration. The only real force would be that in the direction of acceleration.

The observed effects when under such acceleration are indistinguishable that is the statement that you are remembering. That means if you were in a closed box in space accelerating at g then you would not be able to tell if you were on a planet experiencing gravity or in space accelerating.

A key difference in the two situations is that the box accelerating through space requires a constant input of work, while standing on a planet does not does not require a constant input of work.

See above there is no force in the opposite direction of gravity. As you pointed out the acceleration can not be pointing away from earth otherwise you would start moving away from the earth which would be nonsensical.

Now you have defined the acceleration of the box the person is in and not the force which is applied to it. That means when it is accelerating with 20m/s^2 toward the earth 10m/s^2 comes from earths gravity and 10m/s^2 must be coming from an outside force. This means the box and the passenger are experiencing 20m/s^2 acceleration toward the earth.

Now let me address some objections that some people might raise. Someone might raise the objection that from the box from the person observes acceleration away from earth of 10m/s^2. The passenger does observe this, however this frame of reference is not a valid from to determine the force with said observation. This is because the box system to start accelerating went through Jerk(derivative for acceleration). This breaks the symmetry of the person accelerating in a box and a person observing the same thing with out an accelerating box.
Analog:
Time dilation: Frame A’ moves with a relative velocity of ½ c compared to frame A. Now there is an identical objects B’ in A’ and B in A. Which object B or B’ experiences less time then the other? It is impossible to tell which one is experiencing time dilation. In order to know what effect time dilation will have on B and B’, i.e. which one will move slower through time then the other you need to know which object experienced acceleration.

For the my question to be valid object B and B’ need to start out in the same reference from and then have B or B’ accelerate to ½ c.

In this fashion it is not valid to analyze the observed force inside the box headed to earth as a real force.

Yes.
My prof said something similar during analytical mechanics but said they were a convenient way of making a correct Lagrange equation nothing more.
This is incorrect. The symmetry breaking between the two frames is caused by acceleration/jerk/(next order JerkJerk<-I know it is not this but I can not think of the really name at the moment and I am to lazy to look it up.)/(etc.)
I was going to do a box pushing on a box example but this post is too long already.

I hope this clears things up.

13. Mar 15, 2005

### James R

Davorak:

I'd appreciate it if you could point out for me exactly what you think is incorrect about my post. A vague mention of jerk is not enough to justify your assertion that I'm wrong.

14. Mar 16, 2005

### Davorak

I did not mean to be vague. Here is a more in depth explanation of my logic.

Ok at the bottom I have some reference which you can read or not at you leisure. I am not an expert on GR however I do know a few axioms and I believe I have applied them correctly.

Let me now define what I mean by pseudo forces. Take Cepheid’s bus example, we will deal more with this later, when the bus driver slams on the gas Cepheid feels a backward force. Now if it is not possible to tell the bus is accelerating with out observing the outside world then the force is real. On the other hand if the Cepheid can tell by some measure that the bus is accelerating then the backward force is a pseudo-force, since Cepheid will be able to tell that he was reaming still rather then accelerating with the bus.

The GR axioms I applied:

1. The equivalence principle: It is impossible to tell the difference between a uniform gravitational field and an accelerating reference frame.
2. Time runs slower in an accelerating reference frame and or uniform gravitational frame.
3. The stronger the gravitational field or the faster an accelerating reference frame is the slower time will flow.
The above axioms applied to Cepheid’s bus example:

Let’s say there are two clocks one attached firmly to the bus and one attached firmly to Cepheid. These clocks are nearly perfect time keeping devises and work on almost infinitely small ticks.
The bus driver slams on the gas causing the Cepheid to feel a backwards force. While accelerating Cepheid looks down at his clock and the buses clock and notices that the buses clock is running slower then his.(If he was accelerating perfectly with the bus Cepheid would feel no backward “force”)
Cepheid was accelerating slower then the bus and hence why the buses clock ran slower. When he see this Cepheid knows that he is not being pulled backward but rather that the bus is accelerating forward.
If Cepheid was to actually experience a backward force he would notice his clock moving slower then the buses.

This is the analog of the example I gave last time in SR.

Thus the non-initial frame forces are not indeed real forces since there is a way to distinguish between the two.

This logic may or may not apply to your direct example of a rotating frame. Since the acceleration would be perpendicular to the motion. I not 100.0000% the above example would still hold, however I have an even simpler way of knowing that the observation made in the rotating frame and the stationary frame are not equivalent.

The rotating from can be observed to be a rotating from without observing the surrounding world through the Coriolis effect.

Observing the Coriolis effect informs the passengers that they are in a rotating frame hence informing them that they are in a non-initial reference frame. This allows them to know that they are not being pulled outward but rather reaming still while the car is turning.

Even if I am misinformed about GR in my first example the Coriolis effect still holds true and hence why the centrifugal force is a pseudo-force and not a real force.

The link below has a little move of kids playing on the merry go round.
http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/crls.rxml

“The Coriolis and centrifugal forces are referred to a fictitious forces; they appear as two extra terms if Newton's laws of motion are written in terms of coordinates measured with respect to a rotating set of axes.”
“The existence of these fictitious forces apparently provides a means of detecting a non-inertial frame. In other words, accelerated motion appears have an absolute existence, whereas linear motion is always relative (to another object).”
http://physics.pdx.edu/~egertonr/ph311-12/relativ.htm

“A non-accelerating reference frame in the presence of a uniform gravitational field is indistinguishable from a reference frame undergoing uniform acceleration.”
“Clocks run slower in a gravitational field.”
http://www.physics.nyu.edu/courses/V85.0020/node18.html

Typing “force” so many times makes me want to watch a Star Wars movie.

15. Mar 17, 2005

### James R

Davorak,

Thanks for the explanation. It seems to be clear and correct to me. I still don't quite see how what I said was wrong, but I agree with your explanation. I think we both effectively said the same thing in two different ways.

16. Jun 13, 2005

### Gravitor

So is gravitation just a pseudo-force?

One of the thought experiments used to illustrate that there is no way of distinguishing between constant accelerated motion and a gravitational field in general relativity is the experiment with an elevator in intergalactic vacuum being accelerated by a constant force.

Does it mean that everything inside the elevator that is not attached collides with the floor after a number of seconds? If for instance a human standing on the elevator's floor drops a ball (in the absence of a gravitational field), does the elevator's floor accelerates upward to meet it? Does the same happen if the human jumps off the floor?