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If you travel on car with nearly the speed of light and turn on the car headlights: will it shine in gamma light instead of visible light?

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    $\begingroup$ "...with nearly the speed of light" - with respect to what/whom? "will it shine in gamma light instead of visible light" - according to whom? $\endgroup$
    – fishinear
    Jan 24 at 13:03
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    $\begingroup$ Are you in the car? or are you standing by the side of the road, watching the car flash past you? $\endgroup$ Jan 24 at 14:22
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    $\begingroup$ George, you know I was wondering, like if you were traveling through outer space, I mean like you're going real fast, like the speed of light, you know... hoooohhhhh... and all of a sudden you started screaming... aaaahhhhh aaaaahhhhh... Do you think your brain would blow up? $\endgroup$ Jan 24 at 23:52

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It is a relativistic effect so it depends on the relative velocity with respect to the light source.

Imagine that your car is moving close to the speed of light relative to some road (let us forget about the physics of your car and the road for this question). If you are inside the car, for you the lights are in the visible spectrum. For somebody still with respect to the road, let us call this person P, there is what is called a Doppler shift. P will not measure the electromagnetic radiation with the same frequency as you.

The Doppler shift depends on the relative velocity (direction included). If the car is moving towards P at relativistic speeds, then P may detect gamma radiation (frequency goes up, blueshift). If the car is moving away from P, the shift is in the other direction and P may detect low frequency radio waves instead (frequency goes down, redshift).

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    $\begingroup$ Of course, you probably wouldn't see the light from your car, since it needs to reflect from a surface to return to your eyes - that might be tricky with the frequencies involved :D $\endgroup$
    – Luaan
    Jan 25 at 7:48
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    $\begingroup$ Just a dumb thought of mine- what if OP attaches a reflector in front of his car's headlight? What frequency would he find? $\endgroup$ Jan 25 at 7:58
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    $\begingroup$ @AbdurRakib visible too. as long as the source is in the same frame of reference as the driver, the driver will see the frequency of the source (in that frame). $\endgroup$
    – Mauricio
    Jan 25 at 8:30
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    $\begingroup$ @AbdurRakib However, if the road has cateyes on it. Those would be illuminated by the car's headlights, the reflected light would be double blue shifted... $\endgroup$
    – Aron
    Jan 25 at 9:17
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    $\begingroup$ @AbdurRakib when the light hits the mirror in the street, the mirror is in a different frame compared to the car. It sees the frequency to be blueshifted as the car is moving towards it. When it reflects and strikes back your car, your car is again in a different frame and the light from the mirror is coming towards it so it gets blueshifted again. $\endgroup$
    – Mauricio
    Jan 25 at 10:57
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Only to someone outside the car; if they are in your path they will firstly be irradiated to death, and anything left will be vaporized in the ensuing collision.

Of course, if they are behind the car, they will see all the lights red-shifted, and they will survive!

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    $\begingroup$ So, people it front of car will see the huge gamma radiation and behind the car only a radio waves? $\endgroup$
    – Robotex
    Jan 24 at 15:12
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    $\begingroup$ Of course, a car with a Lorentz gamma factor of a million cannot travel through an atmosphere. And if it's on an Earth-sized planet without an atmosohere, it's also going to have difficulties with the extreme centripetal force required to maintain its circular motion as it circumnavigates the planet 7 times per second. ;) $\endgroup$
    – PM 2Ring
    Jan 24 at 15:22
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    $\begingroup$ @PM2Ring if you can get something up to a significant fraction of the speed of light, keeping it in a circular orbit should be child's play by comparison. Good luck surviving the necessary forces though. $\endgroup$ Jan 24 at 23:40
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    $\begingroup$ "Of course, if they are behind the car, they will see all the lights red-shifted, and they will survive!" No, the car will constantly collide with air molecules at relativistic velocities, causing a shower of radiation in all directions. $\endgroup$ Jan 25 at 1:05
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    $\begingroup$ It is a nice change to see some "realism" and "practicality" applied to these discussions ;) We have come a long way since Mr Tompkins! $\endgroup$
    – m4r35n357
    Jan 25 at 10:43
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The key point to bear in mind if you are perplexed by questions like this is that all motion is relative, and all the effects of SR apply symmetrically between two inertial reference frames.

When you sit in your car and turn on the headlights, they produce visible light. To a particle passing the Earth at 0.99999999999c the light from your headlamps appears to be gamma rays. If you were able to drive your car at 0.999999999999c past the Earth then when you turned on your headlights they would produce visible light, but that visible light in your frame would appear to be gamma radiation to people on Earth. The key point is that your headlamps don't change, and nor does their output, but how that appears to others does change as a result of the Doppler effect.

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  • $\begingroup$ "all motion is relative" - even motion with speed of light? If two objects moving with speed of light but without acceleration, will they see no movement and no relativistic effects? $\endgroup$
    – Robotex
    Jan 24 at 15:25
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    $\begingroup$ Firstly, no object can move at the speed of light. Otherwise, all inertial motion is entirely relative. My point is that you are NOW as you read this moving at nearly the speed of light relative to passing muons- do you feel any different as a result? Does the world around you look any different? No, of course not. However, you would observe relativistic affects applying to the muons who are moving relative to you. $\endgroup$ Jan 24 at 16:34
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"Gamma light" is confusing. Light is the visible part of the EM spectrum, kind of glossing over variations in who can see what. Gamma radiation means different things to different people -- according to this

Astrophysicists define gamma radiation as any radiation with an energy above 100 keV. Physicists define gamma radiation as high-energy photons released by nuclear decay.

If you use the latter definition, no. If it's not coming from nuclear decay, it's not gamma radiation. Page 8 of this document has an intensity spectrum graph -- it looks like very little energy is emitted by a tungsten filament in halogen in wavelengths shorter than 250 nanometers -- gamma rays are around ten picometers, so you'd have to blueshift them quite a bit. According to this online blueshift calculator, it'll happen at 299,792,457 m/s, the speed of light being 299,792,458 m/s.

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  • $\begingroup$ I'm calling "light" for all the EM spectre $\endgroup$
    – Robotex
    Feb 10 at 14:28
  • $\begingroup$ @Robotex go ahead and redefine terms all you want, but it's going to be a barrier to communication $\endgroup$ Feb 18 at 19:28
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It really is very simple. The wavelength of "light" from the headlamps as seen by a stationary observer will shorten due to the Lorentz contraction effect. The formula for this contraction is relative length = l * √(1 - v²/c²) where l equals the original length (or wavelength), v is the velocity of the source, and c is the velocity of light. If we express velocity as a proportion of c, then here are a few results. For v = 0.1c, l = 0.995 For v = 0.5c, l = 0.866 For v = 0.9c, l = 0.436 For v = 0.99c, l = 0.141 For v = 0.999c, l = 0.0447 On the electromagnetic spectrum, taking the wavelength of visible light as 550nm (nanometres), at v = 0.999c, this would reduce to 25nm, which would put it in the long x-ray area. Only when v was up around 0.99999999999c would the "light" be short enough to be classed as gamma rays.

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You’re missing the key point:

It will depend on what materials the headlights are made out of ! Its filament metals, LEDs, etc. ? What are they made out of ? What wavelengths do they transmit when their atoms/molecules are stimulated electronically ?

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