If you are driving at the speed of light in a car and turn on your headlights, would anything happen? I thought that the light would come out but pool up in the headlights themselves. Any truth to that?

• I think this is better suited for Physics SE Sep 29 '17 at 19:39
• Since you've already violated special and general relativity to begin with, and those have worked pretty solidly for the last century, what happens next would seem to be entirely up to you... See the denominator in the special relativity velocity addition formula; in our universe, as your velocity approaches the speed of light, the marginal utility of your efforts decrease. Compare my answer to Science-based FTL drive which shows the math.
– user
Sep 29 '17 at 19:40
– CaM
Sep 29 '17 at 19:50
• I also suspect that this would be a duplicate of If I am travelling on a car at around 60 km/h, and I shine a light, does that mean that the light is travelling faster than the speed of light? over on Physics. That question isn't exactly the same, but I very strongly suspect that the answer will be the same.
– user
Sep 29 '17 at 19:50
• I'd like to point out that the operative "then turn on your headlights" will never come to pass, due to the relativistic time dilation involved. Sep 30 '17 at 1:52

Assuming a relativistic physics system...

This can't happen.

No, wait, hear me out.

I understand that the point of this site is "Well what if this did happen", but this is a fundamental exception. What you are asking is either physically not possible or assumes a completely different system of physics, which means that inherently we cannot answer it realistically.

The speed of light is a fundamental limit. Everyone knows that this means that nothing can go faster than it. However there is another limitation that few people think about because of a common misnomer about what the speed of light actually is:

The speed of light in a vacuum is not 299,792 km/s.

That number represents the the speed of a massless particle in a vacuum. This means that this speed is not an inherent property of photons specifically, but rather an inherent property of any particle with m = 0. This is a very important distinction with two very important implications:

• Photons have a mass of zero
• Any particle with a mass greater than zero cannot reach this speed

As of now, we have only really discovered one particle with a mass of zero (photons) but that doesn't guarantee they are the only ones. But this certainly guarantees that the particles that comprise your vehicle are not capable of reaching the speed of light.

So the answer to your question is that it can't happen. At least not in a relativistic physics system anyway. I wish I could give you a hypothetical answer to your question, but it just is impossible within the realm of known physics.

Oustide of the realm of known physics, yes your guess that photons might just 'pool up' on the headlights seems a good bet.

• Strip the Higgs boson from a particle and it is therefore massless. At least, it would not have the properties of having mass. Is that the same thing around here? Sep 29 '17 at 23:33
• @JustinThyme that goes beyond my understanding of physics. I've read more about relativity than I have about particle/quantum physics. Sep 29 '17 at 23:45
• See my extended answer. Sep 30 '17 at 0:53

Several issues ... it is unlikely to get your car accelerated to light speed for a variety of reasons, but let's say you're going really, really fast.

But the short-short is that light always goes at the same speed in a given medium. What will happen is that the light will be blue-shifted (w.r.t someone in front of you); that is, instead of a visible light beam your headlights will emit at higher frequency, xray or gamma ray depending on your velocity.

There are ... easier ways to mount an x-ray laser on your car. Which is in itself a laudable goal.

• +1 Love the blue shift! I swear that I mounted the headlights on my ship for in-atmosphere use and at atmospheric speeds. How was I to know what would happen when I tried to illuminate the hull number on your patrol ship as you pulled up ahead of me at light speed? Sep 29 '17 at 20:38
• @HenryTaylor If they match (your absurd) velocity when you shine the light it arrives as light, only if you happen to clip their planet (going only tens of km/s) while swiveling to the ship it blue shifts to gamma rays and kills people. Think of it as blue shifting since it comes from the front of something moving fast but red shifts as it arrives at the back of something going fast.
– user25818
Sep 29 '17 at 20:59

c (as in e=mc^2) is not the speed of light. It is not the speed of anything. it is the speed limit of the universe. it is a constant. Constants have no speed. But it does have the units of distance/time, which makes it look like speed to the uninitiated.

It is like saying the gravitational constant has, or is, gravity.

However, sometimes light does travel as fast as this speed limit, but no faster. Apparently, physics has a much better method of enforcing speed limits than us humans, on our highways.

Since the theory is that nothing with mass, (or to be more precise, exhibits the properties associated with mass, since we really didn't know what mass was until Professor Higgs came along) can travel faster than this speed limit, then the maximum speed of anything that was on something going the speed of c would be the speed it is going at (the speed of c). In that sense, then in your thought experiment, the light would just pile up in the headlight. However, a massless particle (a tachion?) which it seems can not travel slower than c, if ejected from such a vehicle, would be able to travel faster than the 'car'. Since a tachion is hypothesized to be a 'photon on the other side', would it be called 'light' on the other side?

But if c is independent of the relativistic framework, and is constant no matter how fast the object is going that it is measured on, then obviously something in the physics equations breaks down at this speed limit. That is why it is the speed limit. You end up with situations where you are dividing by zero. Or you are dealing with infinity. Or you are dealing with cases that two numbers are the same number, akin to the fact that, for instance, 10=9.99999999...

But more deeply into the thought experiment, the problem is not necessarily 'if you shine headlights in a car going the speed of c, but closer to the point, can you even create light when you are going that speed? What would exist that could emit it? A photon emitting another photon? The photons would both be traveling at the same speed. In which case they would probably just be the same photon.