Based on the fact that if an aircraft with bright headlights installed on the forward edge of its wings (and are therefore pointing forward) is traveling at less than the speed of light, then the pilot and passengers will therefore be able to view that the flight path area forward of the aircraft is being illuminated by those headlights, would either of the following four scenarios be true or false? If false, why?

(1) If the same aircraft is traveling at exactly the speed of light then although the pilot and passengers can look out the windows and see that the headlights are both indeed illuminated, would they view that the illumination does not extend any farther forward of the aircraft than the headlights’ light bulbs?

(2) If the same aircraft is traveling at the speed of light plus 1/1000 of one mile per hour, would the pilot and passengers then not be able to view (or perceive) any illumination whatsoever emanating from the headlights or their light bulbs?

(3) If the same aircraft is traveling at ten times the speed of light would the illumination from the headlights then be viewed (or perceived) by the pilot and passengers to be illuminating the space to the rear of the aircraft?

(4) If the same aircraft has its headlights installed on the rear edge of its wings instead of its forward edge and its light is therefore projecting toward the rear of this aircraft, and this aircraft is traveling forward at twice the speed of light, then is the light projected by these headlights toward the area to the rear of the aircraft also traveling at twice the speed of light?

No, the pilots and passengers would observe the beam of light extending in front of the aircraft at the speed of light.

We don’t have any good mathematical models about what happens if one could actually go faster than the speed of light. What we do know is that special relativity tells us that it is impossible for an object with mass to accelerate faster than the speed of light relative to some other object.

See #2.

See #3. But also keep in mind that if the aircraft were traveling slower than the speed of light and had rear-facing headlights, the beam of light would still go backwards at exactly the speed of light.
So here are the lessons we take away from this:

A. We can make predictions about what happens when you get close to the speed of light using math, and we can test those predictions by measuring stuff in the universe that is traveling very fast. So far, the math has proven to be a very accurate predictor, so we are reasonably confident that it describes some aspect of how the universe works. But we don’t have any way to make predictions about what could happen at faster-than-light speeds, and indeed our model (which we are very confident in) says that it’s impossible to get there, anyway.

B. All velocities are relative. When you say “traveling close to the speed of light” you have to say what that speed is relative to. If my airplane is going 0.9c relative to the surface of the earth, and I have another plane right beside it going 0.8c, then from the perspective of the other plane, the first place is only going 0.1c.

C. There are no privileged observers. There is no special place where we can stand and point to something and say “that’s going X speed.” That’s why we call this stuff relativity.

D. The speed of light (that is, actual electromagnetic radiation) is constant. Every observer will always see photons traveling at exactly c, regardless of the relative velocities of whatever is generating those photons. That means a guy on the ground seeing a plane going 0.9c, and a guy on an adjacent plane seeing it go 0.1c, would both observe the plane’s headlights sending out photons at exactly c. How does that work? Time dilation! Length contraction! The two observers would measure the same speed of light, but the plane would look very different to each of them, and the people in each reference frame experience time (and therefore their measurement of velocity) differently.

My info is that (1) the speed of light can be slowed when light is passing thru a translucent
material but photons cannot exceed the constant “speed of light.” Also have read that light
speed is constant only within the universe, that the speed of expansion is 5 to 55 times the
speed of light. (2) there is no way to actually go to “warp speed”. You may recall the latest
Startrek movie showed Captain Kirk traveling from earth orbit to a distant nebula in about
10 minutes.

If they are travelling at the speed of light in a vacuum they are photons som other massless particle and probably not sentient.
If they are travelling at the speed of light in air, they are instantly turned into a plasma from colliding with the air.
If they are magically travelling at the speed of light in air without disintegrating I’d assume they build up a “shockwave” of light like an object travelling at Mach 1 would for sound.
(2) (3) (4) don’t make sense in a universe where you can’t increase the speed of any object to or beyond the speed of light in a vacuum.

Of course, in this universe it is impossible for an airplane to travel at c, but there are things that do, like photons, obviously. So what would a photon experience, if you strapped some (imaginary, massless) headlights to it and made it sentient? Well, for the photon, dilation of time and space is infinite. No matter how far it goes from the perspective of an outside observer, the photon itself will experience traveling no distance at all. Furthermore, it will not experience any time in which to to ponder this strange situation.

This is called Cherenkov radiation. It doesn’t happen with airplanes, of course, but it’s not uncommon when dealing with subatomic particles (though usually the medium in question is water, not air).

Chronos beat me to it, but I’ll just add that this is why you sometimes see a blue glow in pictures of nuclear reactors or storage pools for nuclear waste. Here are some good examples.

If you’re in a vacuum, like space, how can you even measure velocity? On Earth we measure velocity versus stationary objects, but in space everything is moving. The Earth is spinning, while rotating around the sun. The sun is part of the Milky Way galaxy which is also spinning and moving.

In space there is no velocity, I propose.

Sure, you can say you’re moving away from Earth at 200,000 miles per hour, but so what? If you compared that to another celestial body traveling at 199,998 miles per hour then you are only moving at 2 miles per hour.

In space, there is no such thing as velocity. It’s all relative. I think that’s the basic concept of relativity, no? It boggles my mind. How can you even say you’re traveling at the speed of light? Relative to what?

The speed of light itself is relative to anything and everything. No matter your reference frame, light in a vacuum will always be moving at the same speed relative to you. This is the heart of Special Relativity, and can be used to derive length contraction, time dilation, and all the other “weird” effects of SR (which actually aren’t weird at all, once you understand them).

You are, however, correct that any velocity other than the Speed of Light itself can be reduced to zero by looking at it in the correct reference frame. In this sense, there’s no such thing as “almost the speed of light”: No matter how fast you go, you’re always just as far away from the speed of light.

Velocity is always relative. Being in space has nothing to do with it. On earth, I can be on a train moving 60mph relative to the ground, but 120mph relative to train going in the opposite direction, or 66,000mph relative to the sun.

This idea of relative velocity is not new, since it’s easily observable and common sense. Galileo and Newton knew about it.

That’s the whole trick about relativity. The theory grows out of the idea that the speed that light travels is always constant, no matter where you’re measuring it from. It’s the only velocity that isn’t relative; as you get closer and closer to the speed of light, the difference in velocity observed by people in different reference frames approaches zero.

Velocity is your change in position relative to some object divided by time. If we start with the premise that every observer will measure the speed of light to be the same regardless of their reference frames, then how do we reconcile that with the common-sense notions of relative velocity that we have from Newton? The only other variable is time. If our observers in different reference frames experience time differently, then their measurements of velocity will also be different. We’ve done experiments which prove that things traveling different velocities relative to one another experience time differently. The result of that time dilation is that every observer will always measure the speed of a photon to be exactly c.

So, how can you make a space ship travel at the speed of light, when the speed of light is just relative? If I’m on The Enterprise and traveling at 0.5 c away from Earth my outside lights will still be emitting light at c relative to me. If Chekhov increases our speed to 0.75 c away from Earth the outside lights will still be shining at c.

Now let’s say we speed up to the speed of light relative to the Earth. The outside lights will still be shining at c relative to me. The Enterprise however, is only moving at the speed of light relative to the Earth. What if we are now in another galaxy and our speed matches that of another solar system. Suddenly, we’re not moving at all: we’re stationary.

I can’t wrap my head around this. I can accelerate away from Earth at the speed of light and then suddenly not be moving at all compared to my surroundings.

In the universe that we know about, your ship can’t go as fast as the speed of light. So it’s meaningless to ask what would happen in that case. But let’s say your Enterprise can go almost the speed of light, say 0.999c. That’s possible.

Now let’s say you’re hurtling at 0.999c towards a solar system which is traveling towards you at, say 0.5c relative to your position. Wouldn’t they observe you going about 1.5c, faster than the speed of light? And wouldn’t you observe them going the same speed?

No, because you measure velocity by looking at a clock. And the clocks on your bridge and on the planet run at different speeds because you’re in different reference frames. We can actually calculate the velocity that each observer would measure in this situation, using a formula called the Lorentz Transformation. In each case, every observer would measure a velocity less than c.

Yeah, it’s pretty nutty. The big problem with modern physics is a lot if it can only be described and not directly looked at or imagined.

I think a good way to think about it is, “if we know the speed of light has to always be the same, what do we have to mess with for the universe to still make sense?” And the answer is time.

Just as an aside, this is why most amateur attempts to play with time and space fail. To get answers that make sense scientists have to define everything with precision mathematically. After Einstein they learned that every measurement must be made inside a reference frame, the “the relationship between a moving observer and the phenomenon or phenomena under observation.” The relationship requires two entities. An empty universe or a universe with a single particle creates problems, but that’s not our universe. We can always find an observer and an observed to define the scope of our measurements. In real physics, it’s immensely more complicated than this, and not so anthropomorphic: one entity can be a field or a coordinate system. The bottom line is that everything has a definition so questions like yours can always be answered.

FWIW, Star Trek’s space ships are not the best example to use. The writers knew it would be impossible (unlike a half-human half-Vulcan science officer) to move at the speed of light or faster.

Star Trek’s “faster-than-light” space ships warp the immediate surrounding space. The ships don’t move in “warp drive.”