# Why does light Ray bend in accelerating elevator but not..

1. Jan 29, 2016

### Snip3r

This may be a basic question but why does light ray bend in accelerating elevator but not in one with constant velocity. I know a frame of reference with constant velocity is indistinguishable from a stationary one from the inside but I feel like like somehow the light seems to know whether it's frame is stationary or accelerating. How is that possible? Thanks

2. Jan 29, 2016

### Staff: Mentor

If you look at things in an inertial frame, the light ray's path is straight; it's the accelerating elevator's path that is bent. A constant velocity elevator has a path that is straight from the standpoint of an inertial frame. (From the standpoint of the accelerating elevator, the constant velocity elevator's path is also bent, just like the light ray's.)

3. Jan 29, 2016

### A.T.

It's not stationary vs. accelerating but inertial vs. accelerating. Light doesn't know anything. We define those frames, where light rays don't bend etc. as "inertial", and the other frames as "accelerating".

4. Jan 29, 2016

### Snip3r

Are you saying that the path of the accelerating elevator itself is bent from inertial standpoint?

5. Jan 29, 2016

### Ibix

The elevator is moving in a straight line through space. However it is following a curved path through spacetime.

You can see this easily for the Newtonian limit. Assume the elevator is moving in the y direction. In some inertial frame, its y position is given by $y=y_0+ut+at^2$, where $y_0$ is its initial position, $u$ is its initial velocity and $a$ is its acceleration. The elevator is not moving in the x or z directions, so this is a straight line through space. However, remember that in relativity time is also a dimension. The elevator is moving in the t and y directions, and the relationship is a parabola, not a straight line. So this is a curve through spacetime.

The same principle holds in a full relativistic treatment, but the relationship between y and t is not so simple.

6. Jan 29, 2016

### _PJ_

The way I understand it is that:

Lighty travels in straight lines (null lines) since it travels with speed c, all pointsd ate shrunk to 0 distance (spatial) for its frame. Therefore, to preserve invariant speed, Time distance, for the light is stretched to infinity- a photon has "no notion of time passing" if you forgive the improper andthropomorphism.
This is evident from special relativity, and assumes flat spacetime.

For accelerated (which is equivalent under gravity) motion, General Relativity defines the geometry of spacetime. The null lines are still always straight, but just in non-euclidean geometry. It is spacetime warping that determines the perceived path of light.
Spacetime is warped by energy - the change in gravitational potential in an elevator for example, warps spacetime in such a way that the light's straight path is along the curved geometry.

At least, that is what I believe is the case.

7. Jan 29, 2016

### Ibix

This is not correct. Light does not have a frame. If it did, then in this frame light would (by definition) be at rest and also (by definition) be travelling at 3x108ms-1. This is paradoxical. It is meaningless to attempt to describe how time and distance would appear to a photon.

I gather that some older presentations claim this, but it is not correct by the modern definition of the difference between special and general relativity. The modern definition is that you only need general relativity when there is gravity present. Special relativity covers flat spacetime, which is what we have here. The accelerating elevator does not do anything to spacetime. Certainly it is reasonable to use a set of curved coordinates inside the elevator, but this is not the same as a curved spacetime.

This is not correct. There is no warping of spacetime going on here, as you can see easily by observing the path of the light ray from an inertial frame. It's straight. All that is happening is that an observer inside the elevator is using a curved coordinate system to describe flat space. Since the coordinates are curved, the straight path of the light appears curved.

8. Jan 29, 2016

### Staff: Mentor

It is true that light travels on null straight lines (geodesics), but null geodesics are not the only kinds of geodesics.

The geometry of spacetime is the same for both inertial and accelerated motion. Also, "accelerated" motion in the context of GR means motion under a force other than gravity; motion solely under gravity is not accelerated--objects moving solely under gravity are in free fall, weightless, with zero proper acceleration.

9. Jan 29, 2016

### Snip3r

I am not sure if I understand that. Let me clarify my assumptions. Lets say I am in an accelerating elevator (upwards) with a meter stick on two sides of them standing upright and i flash a light from the top of one to the other. I will observe the light to hit the other some where below the top. If I do the same experiment in one with constant velocity I will see it hit exactly at the top. If my assumptions are correct whats going on here? I mean lets say an observer in stationary frame watches the light ray flashed from the accelerating frame at t=0, he will see it to hit the top of his meter stick but the one in accelerating frame see it hit below his meter stick?

10. Jan 29, 2016

### Janus

Staff Emeritus
Both observers, the one in the accelerating frame and the one in the non-accelerating frame will see the light strike in the same spot( below the top of the accelerating meter stick.
Consider it this way: let's say that your elevator and the accelerating elevator are side by side and have exactly the same velocity at the moment each of you flash your light from one wall to the other from identical heights above your floors. You will see you light strike the opposite wall of your elevator at the same height above the your floor as it was fired from. You will also see the light fired in the accelerating elevator hit a point on its elevator's wall that is at the same height above your floor. This is because at the moment the light was fired its source was a rest with respect to you. After the light is fired the other elevator, due to its acceleration moves upward with respect to your own. Thus the same light hits a spot on its wall that is closer to its floor than it is to your floor. Thus from your perspective the light traveled a straight line which the accelerator changed velocity with respect to and from someone in the accelerating elevator, the light appears to take a curved path.

Last edited: Jan 29, 2016
11. Jan 29, 2016

Staff Emeritus
Can we leave GR out of this? This is a B thread, and it's unnecessary. The question could have used a train car instead of an elevator - gravity is not an essential part of this problem.

For that matter, neither is light. You have an object moving at constant velocity in an inertial frame, and its path will be curved if you us an accelerating coordinate system.

12. Jan 29, 2016

### Snip3r

Wow. That was clear as crystal. Thank you.

13. Jan 30, 2016

### mviswanathan

Some clarification required: Is the accelerating elevator is similar to a stationary elevator on Earth. Does this mean that the light curving will occur in the stationary elevator on Earth?

14. Jan 30, 2016

### Staff: Mentor

Yes and yes.

15. Jan 30, 2016

### alw34

Ibix post #5 is one good illustration of straight line path in space being curved in spacetime.

Another example is how one two dimensional curve appears differently in space alone versus in both space and time:

"World line of a circular orbit about the Earth depicted in two spatial dimensions X and Y (the plane of the orbit) and a time dimension, usually put as the vertical axis. Note that the orbit about the Earth is a circle in space, but its worldline is a helix in spacetime." [Here the acceleration is due entirely to directional change not speed change.] https://en.wikipedia.org/wiki/Theor...eneral_relativity#Kinetics_of_circular_orbits

16. Jan 30, 2016

### Snip3r

Sorry to start this again but
Let's say another elevator/earth moving down at constant velocity and the moment light is flashed, all are side by side at the same level. Now the guy in the downward elevator will expect it to hit the wall at the same height from his floor as it was fired but it will hit somewhere above that isn't it? But why? His frame is inertial as well. What am I missing here? Thanks

17. Jan 30, 2016

### Janus

Staff Emeritus
In this case, the light fired from the source attached to his elevator will hit at the same height in his elevator, but he would not expect either of the lights emitted by the other two elevators to hit at the same height as his own light. The other two elevators and their light sources will have a upward motion with respect to him at the moment the flashes are emitted, and while he will see them traveling in a straight line, it will be at an upward angle with respect to his own, due to aberration. He will still see the lights from the other two elevators hit the same spots on those elevators as observers in those elevators do. The observer in the other inertial-frame elevator will see the light from the third elevator traveling at a downward angle. The the observer in the accelerating one will see it traveling at a downward angle with an additional curve.

18. Jan 30, 2016

### Snip3r

This where I have trouble understanding why the guy in downward elevator can't expect the light to hit the wall at the same height from his floor. Because when the light was fired by the upward elevator, both were at same level and the photon just fired horizontally to both elevators at that instant should hit the wall at the same height as it was fired as far as the guy in downward elevator is concerned isn't it?but the photon travels at an angle though fired horizontally with respect to downward elevator.why? Thanks

19. Jan 30, 2016

### Janus

Staff Emeritus
For now just consider two elevators. Both are inertial but have a relative vertical motion with respect to each other. Each has his own light source. According to each his light travels straight across and hits the opposite wall at the same height above his floor as it was fired from. Where each elevator's own light hits its own wall is not something that can be disagreed about as far as the observers in either elevator is concerned. If elevator A says the light strikes a given point on its wall, then the observer in elevator B must agree that it strikes that same spot on elevator A's wall. But elevator A is moving with respect to elevator B. So let's say that at the moment the light is emitted in elevator A, the source is 1 meter higher than the floor of Elevator B. That means that at that same instant, the spot on A's wall where it will strike is also 1 meter above B's floor. But in the interval that it takes the light to cross Elevator A, Elevator A, along with that spot on the wall has moved with respect to Elevator B and and the spot will no longer be 1 meter above the floor of B. Thus it leaves one height with respect to B's floor and arrives at a different height above B's floor.
This also makes sense when seen from the respect of Elevator A. Its light goes straight across, and at the moment of emission is a distance from the floor of B, but in the time it takes the light to cross Elevator A, Elevator B, along with its floor has moved and thus when the light reaches the other wall, the distance between it and the floor of B has changed.

20. Jan 30, 2016

### mviswanathan

As I understand:
1) when there is only relative velocity, say in Up/Down direction alone: With horizontal (with respect to individual elevator) light emission, the other observer will see the light being emitted at an angle to his horizontal - exactly similar to the case of a ball being thrown.
2) In case of the second elevator having acceleration, the inertial observer will notice additional curvature in the path - again same as a ball being thrown.
So, not considering the 'time' in each elevator, the effect of acceleration on the path shape of the ball and light are the same (or is it?).