Posts Tagged ‘special relativity’

How long is a very fast piece of string?

June 20, 2012 3 comments

In his work on special relativity, Einstein outlined the relation between time and distance, and in doing so, changed physics as we know it. In recent posts I’ve outlined a way to rebuild that effect using a discrete network-based approach. However, those posts have avoided addressing a one of the most astounding experimental consequences of that theory: Lorentz contraction.

Lorentz contraction, simply put, describes the fact that when an object is travelling fast, it appears to squash up along its direction of motion. This gives rise to the well-known barn paradox, in which a ladder too long for a barn will seemingly fit inside that barn so long as it’s moving quickly enough. (I don’t recommend trying this at home.)

With the kind of discrete system that I described, objects have fixed length, regardless of how fast they’re going. So how can I possibly claim that the essence of special relativity has been captured?

The answer is simple: There is no actual, physical Lorentz contraction.

Am I denying that Lorentz contraction is an observed phenomenon?  No. Do I contest the fact that it can be experimentally demonstrated to exist? Absolutely not. It happens, without a doubt, but what I’m proposing is that, in reality, Lorentz contraction has everything to do with time, and nothing at all to do with length.

Far from being a wild and implausible conjecture, this idea is actually a necessary consequence of other things we know about nature. For starters, that physical particles are observed to be point-like. At the scales that experiments have been able to probe, particles don’t behave as if they have width. And if particles don’t have width, at least of a kind that we recognize, how can they possibly be compressing? The answer is, they can’t.

So where does the Lorentz contraction we observe in experiment come from? It comes from synchronization. Or, to state the case more exactly, from the relationship between objects where their relative velocity is mediated by messages being passed between those objects.

Consider a fleet of starships readying to take part in a display of fancy close-formation flying. They all start at rest somewhere near the moon, each at a carefully judged distance from each other. Then, the lead pilot of the formation begins to accelerate and the others pull away with him to keep the formation in step. Because the formation is tricky to maintain near the speed of light, the ships use lasers to assess their relative distances. They measure how long it takes for each laser ping to return from a neighbor and use that to adjust their velocity.

Should we expect the fixed formation of starships to exhibit Lorentz-contraction just like every other fast moving object? Of course we should, whether the ships are inches apart, or separated by distances wider than the solar-system. Should it make a difference if the starships are tiny, and piloted by intelligent bacteria? Or even of zero length? Not at all.

So, in other words, the size of the starships themselves is irrelevant. It’s the testing of the distances between them using lasers that makes the difference. And this, of course, is what particles do. They exchange force-carrying particles to determine how far away they want to be from each other.

What does change, depending on how fast you’re going relative to someone else, is the wavelength of light that you see coming from other people. Things moving toward you look bluer. Things moving away turn red. And the good news is that wavelength isn’t the same thing as length.

To illustrate this, try to build yourself a mental cartoon of a particle emitting a photon. The particle looks like a bowling ball. The photon looks like a length of rucked carpet being spat out the side of it. The length of the carpet sample determines the wavelength of the light. Now take your cartoon, wind it back to the start, and run it forward very slowly. At first, the carpet will be just sticking out of the bowling ball. A few frames onward you can see how rucked and wiggled it is. A few frames after that and the carpet is all the way out and flying on its way, maybe with a tiny Aladdin on it.

We can play this little sequence out because the carpet sample has physical extent. This means that carpet-emission isn’t a single event–it’s a sequence. And this will be true for any model that we build for photon emission that gives wavelength physical meaning.

This leaves with realization that one of the following two statements must be true:

  • Photon emission is instantaneous. Therefore particle wavelength doesn’t involve physical length. Therefore we need an extra mechanism to explain why wavelength should be affected by Lorentz contraction.
  • Photon emission requires time. Therefore particle wavelength is real. Therefore it’s possible (perhaps preferable) to model it as a pair of events: a start and an end.

By treating the emission of a photon, or any other messenger particle, as a pair of events, our problems with Lorentz contraction evaporate. The timing of the start-of-photon and end-of-photon events is determined by how fast the emitting particle is travelling. Similarly, the perceived wavelength of a photon by a receiving particle is determined by the subjectively experienced delay between the start-of-photon and end-of-photon events. And, voila, temporal effects substitute for spatial ones.

This puts constraints on our choice of simulation model, of course. If we’re going to model photons with start and end events, that’s going to have implications on the kinds of wave implementation we can reasonably use. Fortunately though, the implementation I outlined for my posts on the double-slit experiment will work just fine.

I won’t lie to you and say that everything about this approach is solved. How the timing of photon events of this sort translates into energy is something I still don’t have an answer for. And it’s debatable how useful this way of treating relativity will ever turn out to be. However, I think what this model demonstrates is that when it comes to physics as weird as relativity, it’s worth looking for workable implementations that don’t rely on the mathematical tools we usually use. Their requirements can shed light on assumptions in the theory that we’re often not even aware that we’re making.