Re: Is relativistic length contraction/time dilation an elusion?

Hello Steven,

The "paradoxes" of relativity are often confusing. It always seems like different observers see different things occurring. It always makes me want to ask "Well, that's what they see, but what actually happened?" For example, there is the famous paradox of the ladder passing through the barn. One observer sees that the ladder is shorter than the barn; the other observer sees that the doors shut at different times. "Which really happened?" you ask.

The answer is that, in relativity, you can't talk about things happening at particular times, unless you make choose a particular reference frame. Whatever you saw happening, referenced to your own ruler and your own clock, indeed is what "really happened". The paradoxes only arise if you expect other people's clocks and rulers to agree with yours: you cannot really two things as being simultaneous. You cannot really say that someone was at a certain place at a certain time. You can't ask "what is going on RIGHT NOW, OVER THERE", and expect someone in a different frame to have the same answer.

So, to get to your question "Is relativistic length contraction/time dilation an illusion?" - the answer is NO. When a spaceship falls into a black hole, and I'm sitting at home watching it fall in, it appears to fall forever. This is a correct description of what is happening, according to the clocks and measuring devices in my frame of reference (all of which are perfectly accurate and sensible).

Imagine that a spaceship began falling towards a black hole on April 7, 2001. And imagine us sitting around today, with my mega-ultra-long-wavelength radio telescope, having the following chat:

• Ben: (twiddles knobs on telescope) Yep! - I can still see the spaceship today. It's really redshifted, but still there.
• (enter Steven) Steven: Well, we see the spaceship - but isn't that an illusion? Where is the spaceship really?
• Ben: Where is the spaceship - when?? You mean to ask, "where is the spaceship right now?
• Steven Yes, where is it now, in 2002? I would think that it actually hit the hole on April 8, 2001, and now is past the horizon and gone.
• Ben: Unfortunately, the word "now" does not mean anything, except in our own reference frame. Nor do the dates 2001 and 2002, which are after all measured on clocks in our own frame. So, I can truthfully answer that on the Earth date April 7, 2002, the spaceship is still outside of the horizon. That's what's really happening, it is not an illusion. These dates do not mean anything to the people on the spaceship, but they are still an accurate way of recording events. Maybe the clocks on the spaceship indicated "April(S) 8(S) 2001(S)" when crossing the event horizon, but so what? Different clocks always say different things.
• Steven: Thanks, that clears things up. I think I'll go read the first few chapters of Misner, Thorne, and Wheeler's "General Relativity" textbook again, of course doing all of the homework problems.

I hope that clears things up a little.

OK, you asked another question about Bose-Einstein condensates in black holes. I presume you're referring to the recent paper about "gravastars" Actually, this theory is an alternative idea for what happens inside of the event horizon - they're saying that perhaps instead of forming a singularity, the mass all forms a cold spherical shell. This requires that quantum spacetime (what we normally think of as a vacuum is actually a complicated quantum-mechanical froth) undergoes some sort of phase transition when subjected to super-strong gravitational fields. It's like how, if you push too hard on a propeller underwater, the sudden change in pressure causes the water to change from liquid to gas ("cavitation") and you get bubbles behind your propeller. I think that this paper proposes that strong gravitational forces cause the quantum vacuum to change from one phase to another, and the resulting "bubble" then holds up a shell of matter. It's an interesting theory, but for the most part it changes the physics inside of the event horizon. Outside of the horizon, I think that everything (including gravity, redshifts, time dilations) is exactly the same. Perhaps the cold "gravastar" shell extends a little way (meters? millimeters? femtometers?) beyond the nominal event horizon - in this case, perhaps we would see the spaceship crash into the gravastar in only a few seconds, or weeks, or years, rather than an infinitely long time. But that doesn't really change your question "where is the spaceship right now" - time is still distorted as described above. It's just that the spaceship's path gets interrupted before it stretches out to infinity.

I'd also point out that gravastars are NOT Bose-Einstein condensates. That's just an analogy which the authors made, but for some reason the press really latched onto it and perhaps overemphasized it.

I hope this helps a bit. I think that the gravastar theory is very exciting - it's very important that people think about how "empty space" itself responds to strong gravitational fields; after all, these were the conditions at the Big Bang, and perhaps this also addresses the "accelerating universe" mystery.

-Ben