Gravity and acceleration are equivalent?

[Kayra]

Can anyone tell me if this is still considered to be true?

 

Several aspects of this concept are bothering me. Specifically, some of the consequences of the "Man in the box" thought experiment that Einstein proposed.

[InfiniteNow]

For an observer within a particular frame of reference, the effects of gravity and acceleration cannot be discerned from one another.

 

 

http://en.wikipedia.org/wiki/General_relativity#Treatment_of_gravitation

One of the defining features of general relativity is the idea that gravitational 'force' is replaced by geometry. In general relativity, phenomena that in classical mechanics are ascribed to the action of the force of gravity (such as free-fall, orbital motion, and spacecraft trajectories) are taken in general relativity to represent inertial motion in a curved spacetime. So what people standing on the surface of the Earth perceive as the 'force of gravity' is a result of their undergoing a continuous physical acceleration caused by the mechanical resistance of the surface on which they are standing.

[Kayra]

You see, that is the part that bothers me.

 

Gravity occurs in a gradient, but the acceleration effect on the man in the box is not.

Or?

 

A super sensitive measure of gravity on the top and bottom of the box should be able to reveal if you are under the effect of gravity, or acceleration.

 

PS: THANK YOU for leaving the math out of this :angel: I work better with visuals.

[InfiniteNow]

A super sensitive measure of gravity on the top and bottom of the box

should

be able to reveal if you are under the effect of gravity, or acceleration.

why?

[Kayra]

why?

 

Because acceleration from gravity occurs on a gradient. If it didn't, the universe would collapse in on itself as all gravity everywhere whould be felt everywhere else.

 

 

Acceleration from a rocket engine would be consistant throughout the box.

 

Or?

[InfiniteNow]

Not sure what you mean by gradient, or how this is different from acceleration. Frankly, I'm no good at the math of it all either, and we may be venturing into a realm that requires math to describe it. Anyway, maybe if you could help clear up for me what you meant by gradient and why this does not happen with acceleration, we might get somewhere...

 

 

:angel:

[Kayra]

OK, lets try this.

 

We put 2 men in identical boxes.

One we launch into interstellar space (no local gravity fields of consequence) and strap a rocket engine to his box capable of accelerating him at 1g

One we leave on the surface of the earth.

 

According to Einstein, using any instruments at their command, these men should not be able to determine the difference between gravity and acceleration, regardless of the equipment they use to measure acceleration.

 

Lets say we built those boxes with the dimensions 10m x 10m x 1,000m and placed shelves at 1 meter intervals alone one wall.

 

The man in space under the effects of acceleration would find no measurable difference in that acceleration, regardless of which shelf he placed his instruments on.

 

The man on earth however would measure a reduction in acceleration the higher he placed his instruments.

[InfiniteNow]

The man in space under the effects of acceleration would find no measurable difference in that acceleration, regardless of which shelf he placed his instruments on.

 

The man on earth however would measure a reduction in acceleration the higher he placed his instruments.

I don't think such a difference in measurements on the ship versus on Earth would be found. Do you have evidence to support that the measurements would vary in this way?

[Kayra]

I don't think such a difference in measurements on the ship versus on Earth would be found.

 

So which would you find in both boxes, an acceleration gradient, or no gradient?

 

 

Do you have evidence to support that the measurements would vary in this way?

 

Just common sense I fear.

Gravity does occur in a gradient, that much is beyond dispute really. The higher up we go, the weaker the effect of it.(less acceleration). But as hard as I try, I cannot visualize acceleration from a rocket engine occuring as a gradient.

[Pyrotex]

Not sure what you mean by gradient,...

A gradient is "the rate of change" of something along a given path.

Acceleration is "the rate of change" of velocity.

One is general, the other specific.

You are walking down a gently sloping park, leading to a level soccer field.

The gradient here will be the rate of change of your local topographic altitude.

 

The sloping park will have a small gradient, say 1 inch drop per 10 feet horizontal. Gradients are relative to some direction!!! So if you went in the opposite direction, the gradient would be 1 inch rise per 10 feet horizontal. The gradient in some direction would be zero. Generally, what we want is to find the maximum slope; walk down the slope so you descend at the maximum rate; pick the steepest path down the slope -- this is generally refered to as "the gradient" of the slope.

 

The soccer field is level and therefore has no slope. Gradient = zero.

 

There is a gradient in your gravitational field.

There is a gradient in the chocolate sprinkles per square inch on your vanilla ice cream.

You can have a gradient in the thickness of your hair on your scalp.

There is a gradient in the density of traffic on I-10 West at rush hour.

[Pyrotex]

OK, lets try this.

We put 2 men in identical boxes...

In both boxes, we give each man a pair of perfect plumb bobs on perfect 10 meter wires, and a laser interferometer for measuring distance.

 

Each man hangs the plumb bobs from his ceiling as far apart as possible.

Each man then uses the laser interferometer to measure how parallel the wires are.

 

One man discovers the wires are perfectly parallel.

 

The other man discovers the wires are parallel only to about a few hundred times the thickness of a hydrogen atom. In other words, if the wires were geometrically extended, they would eventually MEET 4,000 miles away!!!

 

The first man is in space, in a rocket accellerating at 1 G.

 

The second man is on the surface of a 1 G planet, with radius 4,000 miles.

[Kayra]

In both boxes, we give each man a pair of perfect plumb bobs on perfect 10 meter wires, and a laser interferometer for measuring distance.

 

Each man hangs the plumb bobs from his ceiling as far apart as possible.

Each man then uses the laser interferometer to measure how parallel the wires are.

 

One man discovers the wires are perfectly parallel.

 

The other man discovers the wires are parallel only to about a few hundred times the thickness of a hydrogen atom. In other words, if the wires were geometrically extended, they would eventually MEET 4,000 miles away!!!

 

The first man is in space, in a rocket accellerating at 1 G.

 

The second man is on the surface of a 1 G planet, with radius 4,000 miles.

 

That makes complete sense. You created a perfect visual.

That makes 2 ways that they are different then.

 

I am glad to hear this, as it made absolutely no sense in my mind.

[InfiniteNow]

A gradient is...

Thanks... serious brain fart I suppose. Time for another cup of joe...

 

:angel:

[InfiniteNow]

Also, sorry Kayra. I really wasn't sure about the answer to your question, but wanted to explore it with you.

 

 

Thanks Pyro for jumping in. :angel:

[Kayra]

Also, sorry Kayra. I really wasn't sure about the answer to your question, but wanted to explore it with you. QUOTE]

 

No worries :angel: You forced me to properly define the question.

 

 

I think this actually helped me to understand something else. Gravity is acceleration caused by the curvature of space. It is this curvature that causes the gradient. That is why the box in space has no measurable gradient, because space is realtively flat there.

 

Both are still acceleration, one through curved space, and one through flat space.

[Pyrotex]

...Thanks Pyro for jumping in. :angel:

"Jumping in" is my middle name! You're welcome! :eek2:

[TheFaithfulStone]

The first man is in space, in a rocket accellerating at 1 G.

 

The second man is on the surface of a 1 G planet, with radius 4,000 miles.

 

Wait, isn't that a function of the shape of the attractor, and not gravity itself?

 

If I were to take a huge cylinder with the mass of the earth and stand on end of it, then my plumb-bobs would show as being absolutely equal.

 

And there is that whole "curved space" thing.

 

TFS