Confusion about a laser shining perpendicular to a moving inertial frame

[gupyuson]

I found this nice book on Google
http://tinyurl.com/yh2y2zb
that does a great job explaining relativity, however, even though the conclusions make perfect sense to me so far, I'm stuck on a conceptual issue when reading over the classic thought experiments that makes me feel like I'm still missing something.

Given that the motion of an inertial frame is indiscernable from within that frame...

If I'm in an inertial frame moving "up" at .9c relative to an external observer, who shoots a laser beam towards me perpendicular to my direction of motion from their perspective, and the beam enters my proverbial space-elevator at a point exactly midway up one wall, the external observer should observe it striking a point below the midpoint of the opposite wall. I should observe the same thing, except that I observe that the laser beam was shot slightly at an angle relative to my walls. The second picture midway down this page: http://tinyurl.com/yze2b7v illustrates this concept, and it seems reasonable.

Second, if I position a laser pen exactly half way up one wall in my elevator, exactly horizontal to the floor of my elevator, and position a target exactly half way up the other wall, I should observe that the laser beam runs horizontally and hits the target, but an external observer sees that the beam moves at an angle, upwards with the elevator, to hit the target. Fine.

Here's the dilemma. If the external observer is looking at my elevator so the beam goes from their left to right, then my elevator floor should look horizontal to them, even as it rises, which means my laser pen should also appear horizontal to them as it shoots. But they would see the laser beam leave my pen at an angle. Even though my laser pen ALWAYS shoots straight as observed from its own reference frame. Does this simply mean that a laser will appear to leave a source at an angle if the source is moving relative to the observer? So a moving light source behaves differently than a relatively motionless one?

What's more, if I were to position a straw somewhere between my laser pen and the target, I would think nothing of the beam going straight through and hitting the other side, but wouldn't the observer observe the laser start out at an angle, then apparently change direction to follow the horizontal straw, then exit at an angle to hit the now higher target? Although this might not be a problem if you consider each photon entering the straw at an angle and continuing up with the straw as it rises, rather than the entire beam as a continuous line. But still, overall, how could it appear a straight line?

If my laser appears hits the wall slightly below the target from my perspective, then I can tell that I'm moving. If I turn around and move down, I would see the laser hit above the target, thus telling me I'm moving in the other direction, even if I could not tell how fast relative to anything else since the light would always take the same amount of time as measured by me to cross the elevator.

So what gives?

 

[Doc Al]

Here's the dilemma. If the external observer is looking at my elevator so the beam goes from their left to right, then my elevator floor should look horizontal to them, even as it rises, which means my laser pen should also appear horizontal to them as it shoots. But they would see the laser beam leave my pen at an angle. Even though my laser pen ALWAYS shoots straight as observed from its own reference frame. Does this simply mean that a laser will appear to leave a source at an angle if the source is moving relative to the observer? So a moving light source behaves differently than a relatively motionless one?

In your elevator frame, the pulse from the laser moves horizontally, at all times maintaining a constant distance from the floor. Of course, viewed from the external frame, the elevator and its floor are moving. So sure, the beam will be seen as moving at an angle. (But still maintaining a constant distance from the floor.) Nothing special about light here. As you walk from one side of the elevator to the other, you'll be seen as moving at an angle also.

What's more, if I were to position a straw somewhere between my laser pen and the target, I would think nothing of the beam going straight through and hitting the other side, but wouldn't the observer observe the laser start out at an angle, then apparently change direction to follow the horizontal straw, then exit at an angle to hit the now higher target? Although this might not be a problem if you consider each photon entering the straw at an angle and continuing up with the straw as it rises, rather than the entire beam as a continuous line. But still, overall, how could it appear a straight line?

Putting a straw in front of the beam won't change anything. The straw maintains its horizontal alignment with the floor. Of course, if the external frame traces the path of the light pulse as it traverses the straw, it will be at an angle with that frame's axis.

If my laser appears hits the wall slightly below the target from my perspective, then I can tell that I'm moving. If I turn around and move down, I would see the laser hit above the target, thus telling me I'm moving in the other direction, even if I could not tell how fast relative to anything else since the light would always take the same amount of time as measured by me to cross the elevator.

So what gives?

Nothing much. Viewed from your frame, your laser (and you) operate in a perfectly normal manner. Nothing you do within the elevator with your laser pointer will enable you to tell that you are moving with respect to some other frame.

 

[gupyuson]

After I posted this, I realized, of course, that the beam would always appear horizontal since it consists of many photons at different points along their paths, each taking a different path since the source is always moving up. So nix the straw.

But it still remains that the outside observer observes the photons leaving the laser pen at an angle above horizontal to reach the point on the other side. Doesn't this mean that a laser pen attached to a centrifuge pointing exactly vertical (with the centrifuge rotating in the horizontal plane) should be expected to produce a wider circle on the ceiling above as the speed of rotation increases? At each moment, the laser pen is moving relative to the stationary observer. If it were to continue in a straight line at any time, it's beam should be moving at an angle just as when it's in the elevator so that the photons would always appear to strike a point directly across from the source as seen by an observer in it's frame. So it should appear to be shooting at an angle all the time it's spinning. Unless the perpendicular acceleration cancels that in some way.

 

[yuiop]

Does this simply mean that a laser will appear to leave a source at an angle if the source is moving relative to the observer? So a moving light source behaves differently than a relatively motionless one?

Yes.

What's more, if I were to position a straw somewhere between my laser pen and the target, I would think nothing of the beam going straight through and hitting the other side, but wouldn't the observer observe the laser start out at an angle, then apparently change direction to follow the horizontal straw, then exit at an angle to hit the now higher target? Although this might not be a problem if you consider each photon entering the straw at an angle and continuing up with the straw as it rises, rather than the entire beam as a continuous line. But still, overall, how could it appear a straight line?

The photon does not keep changing directions. If the laser gun was transparent, then an external observer would observe an individual photon moving diagonally upwards inside the gun and continue diagonally upwards as it leaves the gun and as it passes through the "horizontal" straw and as it leaves the straw.

To the observer inside the elevator the individual photon would always appear to moving exactly horizontal.

If my laser appears hits the wall slightly below the target from my perspective, then I can tell that I'm moving. If I turn around and move down, I would see the laser hit above the target, thus telling me I'm moving in the other direction, even if I could not tell how fast relative to anything else since the light would always take the same amount of time as measured by me to cross the elevator.

So what gives?

If you are moving with the elevator and the laser is attached to one wall of the elevator in a horizontal position then the laser will always hit its target whether you are moving up or dow, but there may be a point when you change direction (and feel acceleration) that you notice a deflection in the beam away from the target.

But it still remains that the outside observer observes the photons leaving the laser pen at an angle above horizontal to reach the point on the other side. Doesn't this mean that a laser pen attached to a centrifuge pointing exactly vertical (with the centrifuge rotating in the horizontal plane) should be expected to produce a wider circle on the ceiling above as the speed of rotation increases? At each moment, the laser pen is moving relative to the stationary observer. If it were to continue in a straight line at any time, it's beam should be moving at an angle just as when it's in the elevator so that the photons would always appear to strike a point directly across from the source as seen by an observer in it's frame. So it should appear to be shooting at an angle all the time it's spinning. Unless the perpendicular acceleration cancels that in some way.

Now this is a interesting thought experiment! Your suggestion that the laser traces a wider circle on the ceiling seems reasonable to me. An observer in the rotating frame will not expect the laser to hit a point directly above the source because he feels acceleration and experiences an apparent "gravitational force" acting outwards.

 

[Doc Al]

But it still remains that the outside observer observes the photons leaving the laser pen at an angle above horizontal to reach the point on the other side. Doesn't this mean that a laser pen attached to a centrifuge pointing exactly vertical (with the centrifuge rotating in the horizontal plane) should be expected to produce a wider circle on the ceiling above as the speed of rotation increases? At each moment, the laser pen is moving relative to the stationary observer. If it were to continue in a straight line at any time, it's beam should be moving at an angle just as when it's in the elevator so that the photons would always appear to strike a point directly across from the source as seen by an observer in it's frame. So it should appear to be shooting at an angle all the time it's spinning. Unless the perpendicular acceleration cancels that in some way.

I agree with kev above that this is an interesting scenario. I agree with you that the beam will trace out a wider circle as the centrifuge spins faster.

 

[pervect]

One thing I should point out. If you have a horizontal bar in our vertically moving elevator, and a stationary horizontal bar, all observers will agree that when they pass each other, both ends of both bars are in the same place at the same time.

(It doesn't matter which notion of simultaneity you use, either - the one in the elevator or the one on the ground).

What's going on is a bit more subtle. The easiest way to describe it - the direction of time in one coordinate system has a component that's space-like in the other. Thus the path of the light beam depends on the direction of time (more formally, the timelike basis vector) as well on the orientation of the bar.

 

[gupyuson]

Thank you all for the replies, and for helping me feel that I'm on the right track. I just recently read about the concept of rotating the space-time coordinate system to geometrically account for relative motion, which sounds like what you mean, pervect, by the space-like component of time. I liked that! I just need to wrap my head around it a bit more to put all the pieces together.