How does the speed of light always appear constant?

[cmurray]

Two things -- 1:

So if the speed of light is a constant and never changes, no matter what reference frame you're in - then what happens if a person is moving forward at 90% the speed of light and shines a light in the direction of motion?

Perhaps I have it all mixed up, but to that person light appear to be going 186,000 mi/s forward. What then would a stationary observer to the side see?

A person in a car going 50mph throws a ball forward at 10 mph - the person in the car sees it as moving 10mph forward, a person outside sees it at 60mph. But if light can't appear to be going faster than c, does that just mean the distance appears to be much shorter or what? I'm pretty shaky on the explanation of Lorentz transformations, and who knows I may have just confused myself to the point I'm not making sense...

2:

Is the reason that a stationary observer views time differently than a fast moving observer because the fast moving observer is creating a pseudo gravitational force which bends light? Or am I again muddling different theories together?

 

[Steely Dan]

Two things -- 1:

So if the speed of light is a constant and never changes, no matter what reference frame you're in - then what happens if a person is moving forward at 90% the speed of light and shines a light in the direction of motion?

They'll see the light moving away from them at the speed of light.

Perhaps I have it all mixed up, but to that person light appear to be going 186,000 mi/s forward. What then would a stationary observer to the side see?

They would also see the light move away at the speed of light. Special relativity means that light always travels at the speed of light relative to any observer. It doesn't matter what reference frame you're in, so long as you're not in the reference frame of the light wave itself; you'll always see light, at least light in a vacuum, moving at the speed of light c.

A person in a car going 50mph throws a ball forward at 10 mph - the person in the car sees it as moving 10mph forward, a person outside sees it at 60mph. But if light can't appear to be going faster than c, does that just mean the distance appears to be much shorter or what? I'm pretty shaky on the explanation of Lorentz transformations, and who knows I may have just confused myself to the point I'm not making sense...

The person outside sees it moving at approximately 60 MPH. In actuality it's not exactly 60 MPH but a simple addition of velocities is sufficient for speeds as low as these. It is incorrect to assume this is true at speeds on the order of c, though. You cannot just add velocities then.

2:

Is the reason that a stationary observer views time differently than a fast moving observer because the fast moving observer is creating a pseudo gravitational force which bends light? Or am I again muddling different theories together?

Yes, you are muddling. Special relativity says nothing much about the gravitational force, that's all in general relativity. I wouldn't say that there's a "reason" that this occurs, it's one of those things that just "is." One way to describe is to say that because of the Lorentz contraction, someone traveling faster measures a "meter" to be shorter than what someone who is stationary measures it to be, so they cover that meter in a different amount of time. But that's really just circular, one could also say that the reason one measures a meter differently is because time is affected by how fast you're going.

 

[jtbell]

I suggest you work out a few examples with the relativistic velocity addition formula, including some in which one of the velocities being "added" is the speed of light.

 

[DaveC426913]

So if the speed of light is a constant and never changes, no matter what reference frame you're in - then what happens if a person is moving forward at 90% the speed of light and shines a light in the direction of motion?

The highly-abridged answer that you're looking for is that two people moving with respect to reach other at 90% of the speed of light each experience time differently. It is this time dilation of their reference frame that allows them both to observe the beam of light traveling at c. Read the links above for a more comprehensive explanation.