“Was not their mistake once more bred of the life of slavery that they had been living?—a life which was always looking upon everything, except mankind, animate and inanimate—‘nature,’ as people used to call it—as one thing, and mankind as another, it was natural to people thinking in this way, that they should try to make ‘nature’ their slave, since they thought ‘nature’ was something outside them” — William Morris

Saturday, June 25, 2011

Paging a Relativity Specialist

I'm having big trouble with an idea in Phil Dowe's otherwise quite exemplary analytical philosophy survey of contemporary theories of causation.

He uses an example—he's trying to describe things that aren't really physically “real” but “pseudo” in some sense (a distinction I dispute somewhat).

Here's the scenario: I've changed it a little for clarity. Dowe says “laser beam” and I say “laser pointer.”

He imagines a laser pointer. Then he imagines a gigantic surface. The laser pointer is very powerful. The surface is very far away.

You hit the surface with the laser pointer. Then you wiggle it back and forth. (Imagine doing this on your wall, not so hard to do.)

His claim is that the speed of the wiggling dot of laser light is faster than light.

Having read two books by Einstein and two other books on relativity theory this makes no sense to me. You just can't add to the speed of light.

Then there's the issue of the gigantic surface. It's not whether building such a thing is feasible—say you can. It's the fact that light would take so long to hit the surface and return (let's say it could, the laser is phenomenally powerful), that the experiment would in effect take hundreds of millions of years to set up for any measurable effect to occur.

Maybe this is just a failure of my imagination but I think we're in an arche-fossil like situation in which you'd have to put the surface way past the light cone to wiggle it in a way that would give (for me the illusion of) faster than light speed. Which is absurd, because such an event could never be observed (it's outside your light cone).

Scale it back a little. If you hit the moon with a laser pointer, wiggling it would still not add to the speed of light, right? So even if you had a very very accurate device that could measure the whole setup, you wouldn't see that the laser dot was faster than light. Right?

Could someone with more experience in relativity theory than me please help me out? I think Dowe's argument is very spurious.


Robin Ottens said...

Hey there Timothy. I only studied physics for 1.5 half year but I think I can answer this. The question is if a dot of light can move faster than the speed of light right?

The thing here is that the dot of light hitting the wall isn't actually one object. Rather a consecutive flow of fotons or waves hitting the surface one after the other. Perceived as one object.

When you wobble the laser. What you see isn't one object moving left to right. It's a bunch of fotons hitting the wall one after another in a stream that's moving left to right. So when you wobble fast enough and the 'dot' starts moving faster than the speed of light. It'll look like a line. And it'll actually be a row of fotons hitting the wall at the same time. ... I'm probably missing some finer details here. But I hope this answers your question correctly and clearly?

Timothy Morton said...

Thanks Robin, I appreciate that, but by "spot" Dowe does mean a sequence of photons as you specify. That isn't quite the point. The point is, can I wave a spotlight so that the patch of light travels faster than 186 000 miles per second? I don't think you can.

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Robin Ottens said...

To any observer, including the spot itself, it'd be in all positions along it's trajectory at once. So technically you are probably correct.

I believe what you'd be doing then is smearing the spot out into a line. I'm thinking in waves now, not particles.

I could totally be mistaken. This stuff goes slightly over my head as well.

Bill Benzon said...

Hmmmm . . . I don't know bollocks about physics, but let's try a slightly different situation. We're standing at point A. We're going to shine the laser pointer in some direction and then turn it off as quickly as we can. The beam will travel into the void an eventually hit our gigatamundo surface at point X1. Then we're going to rotate it, say, 60 degrees, and send another pulse out into the void precisely one-second later. It hits the surface at point X2. This surface is far enough away that X2 will be 200,000 miles away from X1.

I don't see any speed of light paradox here. Because nothing is traveling from X1 to X2 in a second. We've got one beam going from A to X1 and, a second later, another beam from A to X2. It may take a bit over a second for each beam to travel from A to the distant surface, but there's no problem with that. That's independent of where X1 and X2 are located on the surface. If X1 and X2 were only, say, a meter apart, the travel time from A to X1 and A to X2 would still be a bit over a second.

Now, instead of two pulses a second apart, let's imagine that we fire the beam continuously at the surface over the course of a second while rotating it through 60 degress. Let's further imagine that the surface is coated with a very sensitive photo emulsion that will take the imprint of the photons as the hit the surface. Will there be a continuous line from X1 to X2?

Beats the heck out of me. But, still, no photons will have gone the 200,000 mile distance between X1 and X2 in a second.

slatted light said...

Tim: I'm anything but a physics expert but actually I think Dowe's right and you're right. The main point here is: nothing can go faster than light. No-thing. For relativity theory, thingness is physical substance and/or information. Essentially what is moving faster in this case is not the laser but, as I understand it, almost something like the mathematical virtuality of its impact, though I'm not quite sure if that would be the proper term for it. If Dowe is saying the photons are moving faster than light, then no. The spot on the mooon is not a single entity. It is a succession of different spots formed by different bundles of light as they hit the moon. Each bundle travels from the laser to the moon only at the speed of light. More importantly, nothing actually travels from one point on the moon to the next. That would be 'informational' transfer and could not have the effect of breaching the speed of light. But if he's saying that the point where the laser touches the moon, the set of coordinates of impact of each discrete 'event' of impact, is moving faster than light, then he's right. The reason the laser on the moon seems to be moving 'simultaneously' is because the angular movement of the laser on earth does point toward a different place on the moon faster than light could move to that spot. To put it another way, if we cast a beam of light one light year away then wiggled it, it would seem to move at our end. But it would not move on the other end until exactly one light year. This is because the light is not a rigid 'object' and because of this, some parts of it can be moved while other parts have yet to. What's confusing here is the temptation to think we could stand, say, in a field with our laser, point it at the moon, and also have some super techno-gnarly apparatus that could let us see the arrival of the dot on the moon at the same time. That would require informational transfer, however, and would only be witnessable at the speed of light. In Dowe's thought experiment, we're really only 'seeing' the wiggle: and, yes, the wiggle moves faster than the speed of light - or, more accurately, the wiggle takes place here and along the visible beam faster than the reangling of the light could reach the other end of the beam, But the light itself doesn't move faster than light at that end. The movement is actual to us but not 'for' the laser , as it were, if the laser is considered to be a set, unitary object. It does raise the intersting question, though, of whether this isn't something of a proof of the reality of metaphysics, precisely insofar as the mathematical point that moves faster than light (so that the laser can move on our end), while no-thing in itself - because it doesn't 'move' in any tangible sense or act in any way - nevertheless not is but allows the is to take place.

There are a couple of really interesting links in relation to this that I found: this, here, on the superluminal scissors and this articel from the Times on FTL movement in shadows. Hope this helps, somewhat.