[thedoc (OP)]

TroyCheers asked the Naked Scientists:
   
My mate proposes that if you are in a car travelling at the speed of light with the headlights on that you could not see the light from the headlights.  I say as they are both travelling at the same speed that the headlights would still be visible as they are in front of the driver.

Who is correct and what is the equation that shows this?

What do you think?

[Bill S]

As I understand it, if you were in a car, travelling at the speed of light, which is, of course, is impossible, you would still measure the light as moving away from you at "c".  The next question is: what would an outside observer, stationary relative to you see? 

[David Cooper]

No light would be produced at all because time would be slowed to a halt for a car moving at the speed of light.

[JP]

As I understand it, if you were in a car, travelling at the speed of light, [/b]which is, of course, is impossible[/b], you would still measure the light as moving away from you at "c".  The next question is: what would an outside observer, stationary relative to you see? 

It's not just being pedantic when you say that an observer can't move at the speed of light.  That's an integral result of relativity.  If an observer could move at the speed of light than one of the postulates of the theory would fail: that all observers measure the same speed "c" for light in a vacuum. 

So the answer to the question really should be, "you can't move at the speed of light, so the question is about something unmeasurable and it can't be answered." 

[Bill S]

One of the things that causes us hitchhikers problems is when someone with the scientific status of J Richard Gott says things like:

“If an astronaut’s rocket were to travel by us at faster than the speed of light, a light beam he sent forward could never catch up with the front of his rocket.  The light beam could never catch up because the front of the rocket would be moving faster and have a head start.  Any athlete should know that catching another runner who is running faster and has a head start is impossible.  The astronaut’s observations would be most peculiar: he would take out a flashlight and shine it towards the front of his rocket, but he would never see the beam of light arrive.  That’s not what an observer at rest would see: rather than perceiving he was at rest, this astronaut would know he was moving, and that’s not allowed by the first postulate.” 

Surely this argument should be applied the other way round:  the astronaut cannot perform any test that will establish that he is moving, therefore he must measure the speed of light as 300,000 kps, irrespective of his state of motion; or am I misunderstanding Gott, here?
 

[Bill S]

No light would be produced at all because time would be slowed to a halt for a car moving at the speed of light.

This brings us back to the question as to whether or not photons experience time.  I guess that is unlikely to be answered while it is possible to find experts who hold opposite views.  Another problem for hitchhikers. 

[evan_au]

To rephrase the question to something we agree is theoretically possible:

My mate proposes that if you are in a car traveling at 1m/s less than the speed of light with the headlights on that you could not see the light from the headlights.  I say as they are both traveling at the same speed that the headlights would still be visible as they are in front of the driver.

The driver would observe that light from the headlights traveled away from him at the speed of light, bounced off any nearby obstacles, and traveled back to the driver's eyes at the speed of light.

So headlights would still be useful in a super-fast spaceship, but the driver would need super-fast reaction time....

[alancalverd]

Car travelling at (near) light speed relative to what?

[JP]

No light would be produced at all because time would be slowed to a halt for a car moving at the speed of light.

This brings us back to the question as to whether or not photons experience time.  I guess that is unlikely to be answered while it is possible to find experts who hold opposite views.  Another problem for hitchhikers. 

I doubt experts in relativity really hold opposing views on this as it's impossible to talk about the reference frame of a photon in the language of relativity--or physics, for that matter.

[Bill S]

I doubt experts in relativity really hold opposing views on this as it's impossible to talk about the reference frame of a photon in the language of relativity--or physics, for that matter.

The trouble is that most of my information comes from pop sci books.  I'm still waiting for your book, JP.

[lightarrow]

TroyCheers asked the Naked Scientists:   
My mate proposes that if you are in a car travelling at the speed of light with the headlights on that you could not see the light from the headlights.

First, and this has already written to you, it's impossible to travel *exactly* at the speed of light, and it's not a mere technical or formal difficulty; between 299,792,457.999 m/s (for example) and 299,792,458 m/s (which is exactly light speed) there is the same difference as from 1 and infinity. Infact you need a *finite* amount of energy to reach the first speed while you would need an infinite amount of energy to reach the second (and the entire universe's energy is finite...). You would understand this studying relativity.

Second, to travel very very close to light speed, you should do it in the void, or any tiny particle, any air molecule, any atom in the space that you would hit would became an enourmosly energetic bullet that could istantaneously disintegrate you and your spaceship.
But if you are in the void you can't see light from your headlights anyway, because there isn't any particle/molecule to scatter that light back to your eyes...

Third, if you travelled at very very close to light speed and you would illuminate some obstacle in front of you, as evan_au suggested, you would see that reflected light, yes, but with a little problem: it would have incredibly high frequency *AND* incredibly high intensity (according to relativity law of frequency and amplitude transformation between two frames of reference, in this case the light source would approach you at almost light speed).
And so you would die of your very act of switching on the headlights...