A simple observation regarding the equivalence of acceleration and gravity

[girlwonder]

okay I'm going to prove this to you all, and I'm going to do it real simple like, real low-tech and cheap just to be a brat, a little experiment.

 

[DaveC426913]

okay I'm going to prove this to you all, and I'm going to do it real simple like, real low-tech and cheap just to be a brat, a little experiment.

Before you do the experiment, will you do us the courtesy of critiquing your set up so we can be satisfied it's valid? eg. If you decided to do this with two cars, I would (continue to) raise serious objections about how you're going to achieve "constant acceleration".

 

[gabee]

I think mechanics know a lot about mechanics. teehee. They do though, really. No physics, no car. EVERYTHING operates on physical law.

lol

What I'm getting at is that the reason why the equivalence of acceleration and gravity works, is because only the floor is accelerating towards the man, and not vice versa, clearly it doesn't work then. Obviously the man was right. What's wrong is our present understanding of gravity and spacetime.

It WOULD work if the man were to accelerate toward the floor. Imagine the man wearing a belt, to which is attached a chain that passes through a small hole in the floor. Then the same "unseen force" pulls on this chain instead. The man pushes on the floor, which accelerates the room, and in his frame of reference the forces are exactly the same as before. The point is that you WON'T have two forces--one pulling on the man and one pulling on the room in the opposite direction. Newtonian gravitational force is a function of the two masses: GMm/r^2. To simulate the gravitational pull of the Earth in the man's frame of reference, you can EITHER pull on the man OR pull on the room. Not both, or the man would feel twice as heavy!

By the way, even if two forces were pulling on the man in opposite directions (as you describe with the two cars) there would be no net acceleration in either direction and the forces on the man would be constant. Instead of complicating the matter by trying to describe lying speedometers and burning rubber and friction against the road, just think of two forces. A constant applied force has a constant acceleration...not an increasing acceleration...so the net force would be zero and he would not move. Only if you increased the forces for some reason would the forces on the man increase (they won't do it naturally over time!).

 

[country boy]

okay I'm going to prove this to you all, and I'm going to do it real simple like, real low-tech and cheap just to be a brat, a little experiment.

Please don't hurt yourself. Some demonstrations are better left as thought experiments.

It is true that gravity is not like other forces we are familiar with. When you are being accelerated in your car, you feel the force on your back. However, when you are being accelerated by gravity (in free fall) you don't feel any force. The reason for this difference is that the force of gravity, as described by Newton, is proportional to each mass that it acts on, so that in F = ma the mass cancels. This means that the acceleration does not depend on the mass. The gravitational force is being applied to all parts of your body and all those parts are accelerating at the same rate. There is no transfer of force through your body, no pushing at your back, to give you a sensation of applied force.

When you are stationary in a room in a gravitational field you are being pulled down against the floor, but you don't move down because the floor is applying an equal force up against you. You feel that force pushing you up, but you don't move up because gravity is causing you to apply an equal force down. It's easy to see that the little man in the accelerating room feels these same forces. The case of your two cars pathetically tugging against each other with their wheels spinning is analogous to the room being pulled up by a chain while your ankles are being pulled down by another chain. (Gravity is nicer than a chain because it distributes the pull instead of concentrating it at your feet.)

The special property of the gravitational force that it acts on all masses equally, i.e., that it accelerates all bodies at the same rate, is what led Einstein to the equivalence principle. There is no apparent difference between being in free fall in a gravitational field (in a falling elevator) or floating freely with no gravity (in a room in deep space). Likewise, the accelerating room in zero gravity feels the same as the stationary room in a gravitational field. It's all because the inertial mass 'm' in F = ma is the same as the gravitational mass 'm' in Newton's gravitational force.

Note, I have now cast my vote.

Incidentally, are you related to Little Stevie?

 

[girlwonder]

Okay, I've really thought about it. You're right. i get it now. It was a misunderstanding. The force would still be constant, but what fun I've had.