# A silly question ?

1. Mar 29, 2008

### epithet

Or maybe it isn't and apologies in advance if this isn't the appropriate forum but I was wondering if it is possible to take a photo of something travelling at the speed of light ?

If so, how...if not, why not ?

2. Mar 29, 2008

### Staff: Mentor

No, because nothing massive can travel at the speed of light. You can't take a photo of something that can't exist.

Alternatively you could say yes because light travels at the speed of light and you always take photos of light in some sense, but I don't think that is what you meant.

3. Mar 29, 2008

### belliott4488

Ha ha - I was going to say the same thing as DaleSpam - every photo you take is a picture of photons, and they all travel at the speed of light! :tongue:

But no, in practical terms, neither you nor any physical object that you might like to photograph can travel at the speed light, so the answer to your question is, "sorry, no."

On the other hand, there's nothing that says you can't take pictures of objects that move at less than the speed of light, even if they move arbitrarily close to the speed of light. It just takes more and more energy to get them to move that fast, but you can still do it. In fact, that's kind of what particle physicists do at high-energy particle accelerators when detect the by-products of high-energy collisions. In the old days they literally did this with film cameras.

4. Mar 29, 2008

### tiny-tim

Welcome to PF!

Hi epithet! Welcome to PF!

A shadow can move at the speed of light (or faster), and you can take a film of a shadow moving!

And if a large material object could go faster than light (it can't, of course), then provided it interacted with light, you should be able to see it (either directly, or indirectly by seeing it obscure the background stars beind it) … unless, of course, it's moving directly towards or away from you.

5. Mar 29, 2008

### Staff: Mentor

6. Mar 29, 2008

### epithet

Thanks for the welcome

even for a shadow I was thinking more that by the time the light reaches the shutter the object will have moved on. So would you have to set the shutter speed up to as short a time as possible and point the camera ahead of the object or is that just wishful thinking ?

7. Mar 29, 2008

### DaveC426913

You're over-thinking it. The light from the object IS where the object is. It's not like if you point your camera ahead of the object it will magically "see" faster than the light can travel.

8. Mar 29, 2008

### belliott4488

or, to put it another way, by the time the light reaches you, the object will indeed have moved somewhere, but you don't care - you're still "seeing" the light from where the object was. It's a little like looking at a star that vanished years ago, but whose light we're seeing today. You're seeing history.

That has nothing to do with how fast the object is moving, of course - it's just a matter of how long the light takes to reach you.

9. Mar 29, 2008

### epithet

I know it seem silly but please indulge me a little more.

I was kinda thinking of light travelling as sound does.

You hear a plane overhead and look up to see where the sound comes from but the plane isn't there, its way ahead so to record the sound at max volume you would point the mic where the sound comes form not where the plane is.

hmmm...so in taking a photo of a star, you're actually taking a photo of the light emanating from it travelling at c and not the star itself as it may have already gone supernova, but thats only because the light is coming straight at you and not moving sideways across the sky like a plane.

If the star were moving across the sky where would you point the camera or would you just not see it or would it look like a comet with a trail ?

I suppose that depends how far away the object is again yeah ?

10. Mar 29, 2008

### Hootenanny

Staff Emeritus
Again, I feel that you're over-thinking it, how would you take a picture of the moon?

11. Mar 29, 2008

### tiny-tim

Ah … but that's because you use one method (sound waves) for hearing, and another (light waves) for seeing.

Since they travel at different speeds, they come from different directions.

But you and the camera are both using light, travelling at the same speed, and therefore from the same direction!

12. Mar 29, 2008

### my_wan

13. Mar 29, 2008

### shalayka

If you have an object moving near the speed of light (relative to you), the photons it emits will be highly shifted in frequency due to the relativistic Doppler effect (this is analagous to the shift in sound frequency of passing cars). If the object is moving straight toward you, the photons would be extremely energetic and would probably melt you and your camera (or at least give you a nasty case of cancer). If the object is traveling perpendicular to, or away from you, then the photons would be very non-energetic, leading to a picture so weak that you probably would not see it on film (assuming you're talking about capturing photons in the visible portion of the electromagnetic spectrum).

The relativistic Doppler effect is very straightforward when the object is traveling perpendicular to you at a reasonably large distance. It's identical to the formula related to time dilation / length contraction:

$$\nu' = \nu \sqrt{1 - \frac{v^2}{c^2}$$

Here $$\nu'$$ is the frequency of light emitted when the object is moving, and $$\nu$$ is the frequency it emits when it is at rest. As the body's velocity increases to the speed of light, $$\nu'$$ decreases to $$0$$. It would become "invisible", even to devices made specifically for capturing and recording ultra-low frequency radio waves. Of course, as mentioned in previous replies, nothing massive can reach the speed of light (relative to you).

This is a fundamental part of Special Relativity, and was introduced in Einstein's first famous paper on the subject of relativity 'On the Electrodynamics of Moving Bodies'.

Last edited: Mar 29, 2008
14. Mar 29, 2008

### JesseM

I'm not so sure that objects traveling very close to the speed of light would be particularly hard to see--as I said in post #38 in this thread, I don't think the relativistic Doppler formula is meant to apply to reflected light:

15. Mar 29, 2008

### shalayka

I'm very sure that the relativistic Doppler effect would apply. I'm not sure what you mean by "reflected light". The object emits a photon, it travels through space, it hits the photoreceptor. I'm not sure where reflection comes into play... Even then, my understanding of mirrors is that they generally transmit photons of the same frequency that impinge upon them.

If this effect did not apply in actuality, then we would not have been able to deduce the rotation curve of a galaxy, or subsequently invent the concept of dark matter.

Last edited: Mar 29, 2008
16. Mar 29, 2008

### epithet

I'd lengthen the exposure time to allow more light to filter into the shutter I suppose. I don't see where your going with this and sorry but all that tech talk just sails right over my head.

17. Mar 29, 2008

### JesseM

If light hits the object and reflects off it, this isn't really the same as being emitted by the object, is it? It's more like an elastic collision.

Maybe elastic collisions would be the best way to think about this. If we had a train of equally-spaced rubber balls aimed at a large moving wall, and each ball collides elastically with the wall, instantaneously coming back in the opposite direction at the same speed (which we can assume is c since the balls represent photons), will the relativistic Doppler shift formula give the correct answer to the change in spacing between the outgoing train and the ingoing train? I don't think so--for example, if the ingoing train of rubber balls were moving in the +x direction at speed c with a spacing of 10 light-seconds between each successive member of the train (representing the wavelength of a light wave), and the wall is moving in the -x direction at 0.6c, then the time between successive balls hitting the wall will be 6.25 seconds. So if ball #1 hits the wall at t=0 s and position x=10 l.s., with ball #2 at position x=0 l.s. at this moment, then ball #2 will hit the wall at t=6.25 s and position x=6.25 l.s., at which moment ball #1 (moving at c in the -x direction ever since hitting the wall) will be at postion x = 10 - 6.25 = 3.75 l.s. So, the distance between outgoing balls will be 6.25 - 3.75 = 2.5 l.s., or 1/4 the distance between ingoing balls.

In contrast, the relativistic Doppler equation would predict that the wavelength of waves from a source approaching at 0.6c would shrink by a factor of 1/2 relative to the wavelength in the source's frame. Note that in the above I wasn't even considering how things looked in the wall's frame, I was just comparing the wavelength of the ingoing train in my frame to the wavelength of the outgoing train in my frame...because of time dilation, if we see 6.25 s between successive balls hitting the wall, in the wall's frame this is only 0.8*6.25 = 5 seconds between successive hits, so if the wall also sees them moving at c then it must see the wavelength as 5 l.s., which means the wavelength of the reflected train in our frame (2.5 l.s.) is indeed 1/2 of the wavelength of the reflected train in the wall's frame as predicted by the Doppler formula. The point is that although the Doppler formula is still correct for reflection, it isn't telling us what we're interested in here, which is the difference between the wavelength of incoming waves in our frame and the wavelength of the reflected waves in our frame.

However, now that I think of it, in the limit as the wall's frame approaches c, the wavelength of the reflected light does approach zero, i.e. infinite blueshift. If we imagine the same situation as above except with the wall moving in the -x direction at 1c rather than 0.6c, then if ball#1 is hitting the wall at position x=10 l.s. at time t=0, and ball#2 is at position x=0 l.s. at that moment, then ball #2 will hit the wall at x=5 l.s. at time t=5 l.s., and ball #1 will be at exactly the same position at that time.

Still, if we applied the same analysis to a reflecting object neither moving straight towards us or straight away from us, I think the shift in wavelength between the ingoing light and the outgoing light could be by some finite factor, so that in this case we would be able to see the object all right even in the limit as its speed approached c in our frame.

Last edited: Mar 29, 2008
18. Mar 30, 2008

### Hootenanny

Staff Emeritus
My point was simply that the moon is moving across the sky and one can easily take pictures of the moon without making any adjustments, as one could do for stars.

19. Mar 31, 2008

### Ich

You just square the formula, this will make things always worse, never better.

20. Mar 31, 2008

### belliott4488

I don't know if this is epithet's concern, but there is a problem with taking pictures of the moon, and especially the stars, which is that they move during the interval that your shutter is open. For the moon this is not typically a problem, since the shutter need not be open for very long, but with stars it causes the "streaks" that you see in many photographs of the night sky.

In any case, to photograph something moving near the speed of light, you'd have to have an extremely fast shutter speed, or you'd end up with a smeared image.

Otherwise, say if you imagined you had a camera that could form an image from the light that strikes its focal plane at one discrete instant, then I don't see why you'd have any trouble photographing something moving at the speed of light, or even faster, like a shadow that JesseM suggested. You'd simply capture an image formed from the light that came at one instant in time from the "something" (I won't call it an object, since shadow aren't objects). In other words, with this infinitely fast shutter speed, you'd "freeze" any object, no matter how fast, and thus you couldn't tell in the resulting photograph how fast it was moving.