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Let us assume that an object is travelling at speed of light and a flash light is kept pointed in the opposite direction to the velocity of object. Then can we see the beam of light coming out from the flash light if we stand still behind the object?

And will we be able to see anything behind us or will it be dark as we are travelling at the speed of light and it will not be able to to reach to our eye? And is my assumption correct that a man standing beside the object will see the object infinitely long?

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3 Answers 3

Ok let us assume that an object is travelling is travelling at speed of light

No, let's not do that because it violates known physics. You can't use physics to describe scenarios which violate physics.

If the object is traveling at some large fraction of the speed of light, the light from the flashlight will be Doppler-shifted: http://en.wikipedia.org/wiki/Relativistic_Doppler_effect

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We can't accelerate a flashlight to the speed of light to see what happens, but luckily for us the universe has kindly done the experiment for us. In fact it's done it in two different ways.

Firstly, you probably know that because the universe is expanding, the further away we look the faster galaxies are moving away from us, and if you go far enough away the galaxies will be moving at the speed of light relative to us. The light that reaches us from those galaxies is affected by their motion in the same way as your hypothetical torch. What happens is that the light is red shifted and loses energy. We can't actually see what happens at Z = $\infty$ because the CMB gets in the way, but we can easily calculate that the wavelength of the light we see goes to infinity and the energy of it goes to zero.

Secondly, if you drop your torch into a black hole you get exactly the same effect as accelerating it up to the speed of light. Again we can't actually see the torch reach the speed of lighht because we'd have to watch for an infinite time, but again we can easily calculate that the light will red shift to infinite wavelength and it's energy will fall to zero.

Your last question should really be asked in a separate question, but for the record as a fast moving torch passes us we see it rotated but not changed in length. NB this is what we see in the sense that if we took a photograph that's what would be on the film. If you're asking what is the length of the torch in our frame, rather than what we see, then the torch would shrink to zero length as it approaches the speed of light.

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I have posted my answer 54 secods after yours, but I think broadly peaking our answers converge. –  JKL Feb 24 '13 at 11:40
    
I couldn't get the last para why would we see it rotated if it moves with speed of light then it will travel a large distance in short time and light reflected from it's surface will reach almost at same time from every distance and it will look as if it is elongated what' wrong in this assumption please clear my doubt –  Akash Feb 24 '13 at 17:29
    
@Akash: see physics.stackexchange.com/questions/47224/… –  John Rennie Feb 24 '13 at 18:43
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Do you mean the flash light is somewhat fixed at the back of the moving object flashing backwards as the object is moving forward at the speed of light?

If this is the case, then will discuss the question according to known laws of physics, i.e. special relativity. In the most general case where an observer observes a light source moving away from him/her, will be able to deduce the speed of the light source by using this relativistic result

$$v=c\frac{z^2+2z}{z^2+2z+2} \tag{1}$$ where

$$z=\frac{f-f_0}{f_0} $$

is the doppler shift the observer measures. The Doppler shift in turn is given by the equation (also relativistic)

$$f-f_0=f_0\left[\sqrt{\frac{c+v}{c-v}}-1\right] \, . \tag{2}$$ In the case you are talking about the source is travelling at sped of light v=c , so that from equation (2) it follows that the light is “infinitely red-shifted”, i.e z=∞ and then equation (1) shows that it is consistent with v=c . The source does not appear to travel at speed higher than the speed of light, as one would intuitively expect based on notions of Newtonian mechanics. So, yes the object will be observed but its light will be infinitely red shifted.

As for the question “will we be able to see anything behind us”, as long as there are objects to reflect the light and be able to came back to us within our life-time, yes we will be able to see them.

Finally, the person standing at some point beside the line of motion of the object, if this is how you mean it, will see it infinitely contracted not “infinitely long” as the object goes by the person.

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