Griffiths Afterword and Superluminal Shadows

[yosofun]

Hi, I'm trying to understand Griffiths' (Introduction to Quantum Mechanics) argument that shadows can't transmit information. In his Afterword, he mentions that there are many things that travel faster than light, to quote,

"If a bug flies across the beam of a movie projector, the speed of its shadow is proportional to the distance to the screen; in principle, that distance can be as large as you like, and hence the shadow can move at arbitrarily high velocity. However, the shadow does not carry any energy; nor can it transmit a message from one point to another on the screen. A person at point X cannot cause anything to happen at point Y by manipulating the shadow."

I don't see why a shadow can't transmit a message. (Isn't making a shape with your hands and putting it up to the light and projecting the resulting shadow onto the wall a sort of information travel via shadows?)

 

[tdunc]

Havent read the book.

You can have a dynamic Fourier transform over a time.. The shadow is only a part of the light "beam" or wave as a whole, it is a hole or several (shape) in the light beam, a deformation in the wavefront. Shadows are not real things, the light beam that contains the shadow is a real thing...

To modify the shadow you change the orientation of the source light or the obstruction, the change will be transmited at the speed of light from that point until it reaches the surface on which the shadow is observed. You do not ever manipulate the shadow, the shadow is a "property" for lack of better word, of the light beam.

As far as a huge distance is concerned or what griffiths was eluding to, similar to the good old flashlight across the moons surface paradox, this is kinda up for interpretation of how you want to say it. I believe there are spatial regions that light is not being sent, in other words the light or any shadow in the light is not continuous across the region of space, there are gaps. In actuality nothing abnormal is happening, no superluminal anything. The faster you move the flashlight, the larger the gaps. You have to think individual photons being emitted, rather than waves to get it. You know what a strobe light is? Its something to that effect, where gaps are represented by dark instances. And youll figure that the light skips or 'jumps' the distance of these gaps in between a point A to point B on the moons surface. The error is when you think this travel, the light source on the surface, is continuous and thus superluminal. The area of the surface that it "skips" are represented by areas in which no photons were sent.

Sigh ok I know what I am talking about but its hard to explain it ;)

Ah I know what I want to say, the gaps become larger the greater the distance from the source and surface. The paths of the photons to be linear, such that the distance between photons that were emited at the same time grows.

 

[vanesch]

I don't see why a shadow can't transmit a message. (Isn't making a shape with your hands and putting it up to the light and projecting the resulting shadow onto the wall a sort of information travel via shadows?)

Ah, that's because you didn't get the gist of what Griffiths was saying, and I agree that it is confusingly stated. There IS of course transmission of information FROM THE BUG TO THE SHADOW ; and this travels of course at the speed of light: when the bug decides to move, the screen will only see this some time later (distance bug-screen/c).
But what Griffiths meant, was: there's no information transmission that you can "piggy back" on the shadow FROM ONE POINT OF THE SCREEN TO ANOTHER.

A simpler example: imagine a light bulb putting light to the left and to the right, on two screens, each a lightyear away (one left, the other right of the bulb). Now, at t1, one puts a cap over the lightbulb. 1 year later, ON BOTH SCREENS, the shadow appears simultaneously. Nevertheless they are 2 lightyears away from each other. So you can say that the shadow "moved INSTANTANEOUSLY" over a distance of 2 lightyears, but that is of course not transmitting any information from one screen to the other.

It is a rather silly idea, after all...