# How is acceleration equivalent to rest in a gravitational field

1. Apr 1, 2013

### Seminole Boy

Let me phrase the entire question: How is acceleration equivalent to rest in a gravitational field (without tidal effects)?

It's not that I am incapable understand the implications of this--it comes from a quote by DaleSpam and it seems to be rich--I just cannot break down the language he is using.

Feel free to weigh in, particularly the author of the quote.

2. Apr 1, 2013

### WannabeNewton

Let's say you are in a very small elevator (enough to fit you and your local experimental setup) so that tidal forces are negligible and say there are no windows or any other way for you to see outside. First imagine that you along with the elevator are at rest in a gravitational field $g$ and you are holding an apple. You drop the apple and see that it accelerates to the floor of the elevator with downward acceleration $g$. Now imagine that you along with the elevator are in free space accelerating upward at a rate $g$ and you again drop the apple. You will again see it accelerate downwards to the floor of the elevator at a rate $g$. There is no way you, inside the elevator so described, could perform local experiments to distinguish between the two situations - they are equivalent.

3. Apr 1, 2013

### tensor33

It's the equivalence principle. Basically it means that if you are accelerating in a space ship there is no way to tell whether you are accelerating or just sitting on the surface of a planet.
Edit: Disregard this. I see WannabeNewton beat me to it.

4. Apr 2, 2013

### Staff: Mentor

Suppose you have two identical laboratories. They are each filled with the same wide variety of experimental equipment. One laboratory is in a uniform gravitational field (i.e. no tidal effects) of 1 g and is at rest wrt the gravitating body. The other is on a rocket far away from any gravitational sources, but is accelerating at 1 g wrt an inertial frame.

The way that acceleration is "equivalent" to gravity is that any experiment carried out in those two laboratories will have the same result. For example, in the accelerating lab we know that light going from the ceiling to the floor will be blueshifted and light going from the floor to the ceiling will be redshifted. Therefore, since the gravity lab is equivalent, we know that the same thing will happen there.

The reason for mentioning tidal effects is that if they are present then you can devise experiments which will not give identical results in the two labs.

5. Apr 2, 2013

### Seminole Boy

WannabeNewton:

How--or why--are you using the word upward? How can there be upward or downward movement in boundless space?

6. Apr 2, 2013

### WannabeNewton

If I am understanding your question correctly, that is exactly the point. If I am in the elevator subject to the above mentioned conditions and I drop my apple and I see it accelerate down to the floor of the elevator as described above, there is no way I can tell if I am in an elevator that is accelerating outwards at some uniform rate $g$ or if I am in an elevator that is at rest in a uniform gravitational field $g$. Both situations would give me the same experimental result for the local experiment I conduct inside the elevator so there is no way I could tell.

7. Apr 2, 2013

### Seminole Boy

Yes, you did understand my question correctly. You're good, Mr. (Wannabe) Newton, very good.

8. Apr 3, 2013

### Brute Force

According to GR - acceleration do not bend the light, but gravity does. Just turn on your laser and measure deflection on the wall.

9. Apr 3, 2013

### Passionflower

Because the effect is similar.
However it is obviously not the same.

Also a uniform gravitational field does not exist.

10. Apr 3, 2013

### Mentz114

You'll get the same result in both the labs. See posts above.

11. Apr 3, 2013

### Staff: Mentor

Acceleration does bend the light.

12. Apr 3, 2013

### Passionflower

What do you mean by acceleration does bend the light?

Light in flat spacetime is never bent, it may look bent from the perspective of an accelerating observer but that is not the same as saying that light bends.

13. Apr 3, 2013

### Staff: Mentor

In the accelerating frame the path of light is bent. It is a geodesic in spacetime, but not in space using the foliation defined by the accelerating frame.