# Principle of Equivalence

1. Nov 11, 2008

### Offalycool

Hi all. First post so please forgive the noobness.

I have been listing to an audio book of "A briefer history of time" by that well known genital man and I have hit upon something I don't understand. My understanding of the Principle of Equivalence is that you will not be able to tell if you are in a rocket ship accelerating in space or a room that is at rest in a gravitational field on Earth. From this we are supposed to deduce there is no observable distinction between inertial motion and motion under the influence of the gravitational force.

The thing I don't understand is; I thought that inertial motion and accelerating motion are different. If the rocket ship is accelerating and the resulting effect is a gradual strengthening of force upon the spaceman, it would continue to grow stronger until the force overwhelmed the poor fellow and we would run into the "mass can't reach the speed of light" issue.

On the other hand my understanding of inertia is that it will remain constant until a force acts upon it. How can the illustration of a force which require constant acceleration show how there could be no observable difference between an inertial motion and a motion under the influence of the gravitational force?

I'm sure I have missed something obvious. Thanks in advance.

2. Nov 11, 2008

### DiamondGeezer

If the acceleration is constant, then so is the force on the spaceman. QED

3. Nov 11, 2008

### Offalycool

Physics 101 for me then. I guess I just felt a natural objection after following his train of thought on the impossibility of maintaining a constant acceleration indefinitely.

Thanks.

4. Nov 12, 2008

### Fredrik

Staff Emeritus
The equivalence principle is really only exact in the the limit where the size of the room and the time interval during which the experiments are performed goes to 0.

Constant coordinate acceleration is impossible to maintain. Constant proper acceleration (the same coordinate acceleration in every co-moving inertial frame) is possible to maintain and this would feel like a constant force.

You might also want to check out the other thread about the equivalence principle that was started recently.

5. Nov 13, 2008

### Naty1

In the limit as v approaches c and relativistic mass increases dramatically, you are right that constant acceleration isn't realistic...but what Einstein said was the forces felt in the two situations, acceleration and gravity, are equivalent...and that is a subtle difference from your quote. All this stuff is subtle. In fact I think what Einstein really said/meant is that if you felt a force equal in magnitude from gravity and from acceleration, you couldn't distinguish between them...

This is probably closest to Fredriks post
"The equivalence principle is really only exact in the the limit where the size of the room and the time interval during which the experiments are performed goes to 0."

Unruh's law is another way the two forces are not quite"identical".

And by the way, what is "noobness".

Last edited: Nov 13, 2008
6. Nov 13, 2008

### tiny-tim

Welcome to PF!

Hi Offalycool! Welcome to PF!

You're talking about two almost opposite situations …

one is the comparison between forces felt from acceleration and from gravity …

the other is where no forces are felt (this is inertial motion, of an inertial observer ), and you can't tell whether there is no gravity, or whether you are free-falling in gravity (and if so, you can't tell how strong the gravity is).

If you accept the Principle of Equivalence when forces are felt, no matter how small, then what do you expect to happen when no forces are felt?

There must be types of motion in which all force does disappear!

Surely it is only natural to say that such motion corresponds to zero acceleration in either Newtonian space or Einsteinian special relativity, and therefore to an inertial observer?

To put it another way: the Principle of Equivalence is that you will not be able to tell, from the forces on you, whether you are in a rocket ship accelerating in space or a rocket ship hovering at a fixed height in a gravitational field on Earth … and this applies however large or small those forces are … so if the forces lessen, you know that, if you were hovering at a fixed height, you certainly aren't now … your rocket ship must be reducing its "hover-power" and gradually descending … and it applies even if the forces disappear … you will then not be able to tell whether you are in a rocket ship drifting in space or a rocket ship that is free-falling in a gravitational field on Earth.
Noobosity, noobiferous apraxia, noobitudination, or having clean wellies.

hmm …how could a non-noob not know that?