On 3/29/22 10:55 AM, Ed Lake wrote:
> When we view light from a distant galaxy, we do not see that galaxy
> where it is today, we see that galaxy where it WAS when it emitted
> the light. The light traveled in a STRAIGHT LINE from POINT OF
> EMISSION to me.
Actually it follows a null geodesic through spacetime. Gravitational
lensing conclusively demonstrates this -- there are many instances
of observing multiple images of a single distant quasar or galaxy, so
the light trajectories cannot possibly be "straight".
As always, you MUST specify the coordinates relative to which you
measure a speed (or velocity). Ditto for an acceleration and a duration.
Note it simply is not possible to accelerate at 1g (=9.8m/s^2) relative
to an inertial frame for a year, even in a gedanken. But rockets are
usually specified by their PROPER acceleration. If a rocket started from
rest in an inertial frame and had a proper acceleration of 1g for a year
(either in that frame or elapsed proper time), it would indeed approach
speed c relative to that frame.
When considering relativistic speeds like this, one must evaluate the
accuracy of an inertial frame over such large distances and times. In
this case, if the ship started from earth, the ICRF would remain an
accurately-inertial reference frame, as the rocket never approaches any
star. But not necessarily for 10 years....
> My question is: If I am traveling at such speeds, and if I send a
> beam of light from one side of my ship to the other side, will the
> light travel in a straight line across the room as I see it, or will
> the light travel in a curved line down toward the floor?
As usual, your words are ambiguous. You REALLY need to learn how to ask
a specific, self-consistent question. Of course to be able to do that
you would have to understand some basic physics, which you have
repeatedly refused to do.
"At such speeds" kind of implies you are no longer considering the
acceleration. If the rocket ceased accelerating after a year, and you
then do this, the light beam will traverse the ship in a straight line
(measured relative to the rocket's inertial frame).
But that implication is not necessarily what you meant, and "floor"
implies it keeps accelerating. If the rocket is still accelerating at 1g
when you to this, then the light beam will traverse the ship in a
parabola (measured relative to the rocket's locally inertial frame).
This applies at all times during the acceleration, not just after one
year; the spot position on the far wall depends on the proper
acceleration, not time or speed relative to anything. This assumes that
the laser is affixed to its wall with sufficient rigidity so it does not
rotate relative to the ship, and the far wall is similarly rigid.
Note it is not possible to accurately measure the difference between a
straight line and that parabola, unless you can measure the difference
between acceleration on and off -- in that case, if the ship is 10
meters wide then the difference would be ~5E-15 meters; even ignoring
the impossibility of measuring a laser spot position to such accuracy,
with current technology that is not possible to measure [#].
[#] Today the highest-resolution measurement of distance
is ~1E-12 meters, which just happens to be in our
Precision Laser Metrology Lab at IIT.
> I am emitting light in a direction that is at a right angle to MY
> direction of movement.
Not really. You are implicitly assuming some sort of "absolute motion",
which is invalid.
> Wouldn’t light travel across the room to a point on the wall that is
> NOT at a right angle to my direction of movement, but in a straight
> line through space from the original point of emission?
I must guess what you are trying to say. My interpretation of your words
means the answer is: No. In particular, the laser is affixed to the
ship, not somewhere in "space" (whatever you mean by that).
> If true, I could mark points on the far wall that would indicate
> where the light photons will hit when my rocket is moving at
> different speeds.
Nope. The position of the light beam at the other wall depends on the
ship's proper acceleration, not its velocity (relative to anything). And
for the difference to be measurable in a 10-meter-wide spaceship the
acceleration would need to be far too great for humans to survive.
A simple spring scale with a calibrated weight would measure such a
ship's proper acceleration vastly better than the position of a laser
spot on the opposite wall.
> [... further nonsense ignored]
Tom Roberts