Physics geekery

[Schatten]

I'm at the tip of an even sided triangle, side length one lightyear. The opposite side to me is a wall. I'm projecting a dot with a laser pointer on one end of it, then flick my wrist to draw it over to the other end.

 

What will I observe on the wall one year later?

 

a) A line appears, because in order to travel the LY distance in the time I flicked my wrist the light dot has to be in all places at once

It takes a year for the light dot to travel the distance, since it can't move faster than lightspeed

c) Fuck you Einstein, the dot zooms over the wall with warp 9

 

I'm tending towards a), which becomes a bit amusing if you take a LY long stick instead of a laser pointer- I imagine it would look like a ginko leaf.

 

Can anybody provide a more expert explanation of what would happen?

[Komag]

Here's what I think...

 

Part of it is how we see. If you wave around a burnt ember stick from a campfire at night, you will think you see a swirly line, but it's just the effect of the light burning into your retina and not fading instantly.

 

If you are currently looking at the first dot, it must be assumed that you have been standing there holding the original position for two years, long enough for the light to get to the first point (one year) and reflect back the dot you see (another year). If you don't need to see the dot first, you could just start the laser, point, then flick.

 

When you flick your wrist to point exactly at the other dot, you will then have to wait exactly two more years. In the mean time you can just drop the laser, go home, eat a sandwich, etc. Come back in two years, then you look out there and see the first dot, then a line flash across the sky for a moment, then you see just the second dot, then it goes away (because at that point two years ago you dropped the laser).

 

If your eyes didn't retain any image residue at all, you would instead see the single dot fly across the sky just as fast as you flicked your wrist, but no line.

 

 

... but I could be wrong

[Schatten]

I think we can disregard human limitations for sake of simplicity (also the waiting times, which are rather obvious). The interesting point is how that light dot would behave.

[Komag]

Okay then, so you would see the dot fly across, not a line. Even though the dot would appear to move that light-year distance in just a fraction of a second, that super-light speed is only an illusion, as nothing is actually moving laterally. All the light is only moving straight away from you (a point), and then, from infinite other distant points (that lie along the path from the distant point A to distant point , straight back to you. So, as you said, option B is out.

 

You could think of it as having a super tennis ball serving machine that spits out balls 1000/second at the speed of light. You turn it on and turn it the full arc in one second then turn it off. The balls travel out from their point of origin, all hit the other wall almost simultaneously but not quite (there is one second difference from the first to the last), then all bounce back to you and reach you in like manner, smacking your face in 1000 different places from left to right over the course of the one second.

[sparhawk]

Your movement causes photons to be emitted along the path that you flicker your wrist, but we can assume that you only send one photon at the start and one at the end position, to simplify it. Each point travels along and hits the wall after on year, so I would say you see the starting point after one year on the wall, and you will see the end point after one year plus the time it takes to turn the light beam around. Since this takes only a split second, you should see the second photon after the first photon hitting the wall.

 

I mean, the same would happen if instead of flicking your wrist around, you simply switch it off and back on after a second. On the wall you should see the first photon hitting the wall after one year, then one second dark and then the second photon coming in.

[OrbWeaver]

A "light dot" is not a physical object, and therefore there is no limit on how fast it can "move". Assuming that the light does not spread out at all, and that you (or another observer) are present at the destination after ayear to view the result first-hand, you would see exactly what you would expect to see -- a "dot" moving rapidly from one end of the target to another over the same duration taken to move the torch from one angle to the other.

 

This is of course not actually a moving dot, but the intersection of an advancing curve of photons with the flat wall over a short interval. You can simulate this using a hose pipe and water: rapidly change the direction of the hose and watch the curve of water droplets moving forward to strike their target.

[Schatten]

So, if I left the laser pointer on, the light dot would "skip" over the wall - I thought of that, so I included the option that instead of light you'd use a stick: the end of that must travel the distance continuously.

[OrbWeaver]

A stick is a totally different matter -- because its shape is fixed, the other end of the stick must always correspond to where you are pointing the near end. A wave of advancing photons (or water droplets) has no such restriction, because it is not a rigid, physical object.

 

With a stick, the motion will indeed be restricted by the speed of light, like any other object. I think you are getting confused by thinking of the laser pointer like a stick, when it is in fact like a hosepipe (it only seems like a stick because we only ever use laser pointers over very short distances).

[Schatten]

Meaning the stick would behave how?

 

Edit:

Btw, I realize quants would behave differently than the stick. You see, I love dicking around with the absolute limit that lightspeed represents, looking for loopholes.

[OrbWeaver]

Depends on the physical properties of the stick I suppose.

 

* If it was weak, it would just break.

* If it was strong and rigid, it would be almost impossible to move it because of its huge mass and size. You would need a lot of energy to accelerate it, and no matter how hard you tried the far end would never be able to move faster than light-speed.

* If it was flexible, it would behave more like the light-beam/hosepipe. The local movement would travel down the stick as a wave, eventually losing its energy but possibly resulting in motion at the other end (after a very long time -- waves in a physical medium travel much slower than lightspeed AFAIK). I suspect there would be a distance after which any motion wave would have lost all its energy, and you couldn't influence the stick beyond this point. EDIT: I notice that this option is inconsistent with my earlier statement that the stick must always be rigid, however in reality I suspect this is nearer to the actual behaviour since nothing is totally rigid.

 

(All purely speculation, I'm not a physicist).

[Schatten]

Ach, that pesky mass increase! Always spoiling my plans...

 

Wait, I'll use my Dura-Stick™

 

It's mass-less, unbent- and breakable and comes in three colour flavours.

 

Hmm, but then, the lightspeed barrier doesn't apply to objects without mass, right?

[OrbWeaver]

It's mass-less, unbent- and breakable and comes in three colour flavours. Hmm, but then, the lightspeed barrier doesn't apply to objects without mass, right?

 

Precisely. The existence of such an object is physically impossible, and by stepping outside the rules of physics you render the problem meaningless in terms of ordinary physical principles.

[sparhawk]

There is at least one particle which has a zero restmass. Not sure about the others. I regularly fall asleep when I try to keep track of all the particles, their masses and their names.

[Schatten]

Wiki has a nice map:

http://upload.wikimedia.org/wikipedia/en/4...ticle_chart.jpg

(1.4 MB)

 

Tachions even have an imaginary mass, how cool is that.

[sparhawk]

Ha! Thanks! That's a usefull chart.

[demagogue]

Ah, yes, I'd found that chart.

 

 

 

On the laser dot "experiment", it reminds me of the important difference between the time-like and space-like areas of a space-time graph, because that's what it's really turning on. Since I'm trying to figure this out too, I'll try to write it out to see if I can explain it accurately to myself, novice as I am, but may be helpful to someone else, too.

 

If you looked at a spacetime graph (like this, forget the twisting; that just shows you how acceleration affects things, but the laser light doesn't accelerate):

 

 

the top and bottom areas of the X are labeled "time-like", the side areas are labeled "space-like", horizontal-axis is space, vertical is time, mixing together as spacetime, and the dots are arbitrary events that "happen" in spacetime relative to the observer, at the center of the X. the "X" itself (labeled "light-like") is the boundaries of the speed of light speedlimit for information going to/from the observer. So the top time-like area means every dot-event that you can potentially reach within the SoL speedlimit time frame (i.e., pre-event, a future potential connection), the worldline the center follows being the actual connections. The bottom time-like area means signals from past events that can reach you and tell you what "happened" within the SoL speedlimit time frame. The space-like areas on the sides of the X are just out of touch with the observer for the moment; there's a minimum, mandatory waiting time the observer has to wait for them to get into the bottom-time-like area to find out that something even "happened" ... Until then, it hasn't really happened for the observer yet (sort of weird limbo; has it happened yet or not??). (BTW, in the time-like area, there is no minimum waiting time for the mover to connect with the happening, one of the main physical differences in the two; it could make a connection as quickly approaching zero secs as you or the signal approach the SoL; of course the stationary wall always waits a year.) Regarding that space-like limbo: you would have to travel faster than SoL (impossible) to reach a dot in the space-like region in a shorter time than the mandatory SoL-limit waiting period (which is good, because then you'd arrive at the dot "after" the event happens before it happens! The whole logic just breaks down).

 

So the way you'd describe your laser experiment, by the theory/ graph: individual photons of the laser have their own worldpaths where the part of the wall they will hit (the dot we care about) stays inside the top-time-like part of the X the whole trip. But connection with the other photons and their hits (horizontal to that dot), as you can see from the animation, are falling outside the lessening dot-coverage of the top part of the X as time goes forward and the time the center-photon would have left to go the distance to make that connection decreases, up until the moment of the center's own hit at the wall.

 

When they all hit the wall (now assume the center of the X is where one photon hits the wall), it's all "happening" somewhere on the graph of the hit's pov around that moment (i.e., the dots horizontal to the center of the X). But most of the other hits are in the spacelike region as you can see (a relative few, nearby dots may have already hit in the past and are already in the bottom region, they've already signaled their nearby hit before our hit even occurs). But because most are in the spacelike region, all those photons can consecutively/ individually "communicate" with the whole lightyear-long wall in under a light year just fine. There's nothing troubling that it'd require moving faster than the speed of light to cross that wall in the same time it takes all to hits to occur across the wall. That's the very definition of them being in the spacelike region, and the graph lets you visualize it.

 

But because other hits/dots are still outside the graph's time-like region (in this post-hit situation, now the bottom part of the X) after the half-second it took to flick the laser, they cannot all communicate with each other in that same time-frame.* A hit-area could get the signal from a relative few, nearby other hits/dots that get into the bottom-time-like region over the next half-second, but far from all. Over a year's time, all of the dot-signals will eventually enter the bottom-time-like area as it covers more dots as time passes (you see in the animation), so an observer at that wall will see them "trickle" in. The far right end of the wall will actually see most of the light streak go in time-reverse because of this, as the right-most photons hit first, but the left-most photons reflecting off the wall come a year later. I mean, all of this is intuitive, but the graph just lets you see how the experiment actually plays out in the theory, and why it's just fine.

 

.................

 

By the way, fascinating implication: Some events/dots in the space-like parts can never get into the time-like territory for us to see it, no matter how long you wait; they are so far apart after faster-than-light inflation of the universe (so the theory goes), and the universe is still expanding at lightspeed, so that light can never have the time to cross it all. So there might be two alien civilizations that can never even be able to know about each others' existence, because they are forever in the space-like areas viz. each other; a signal from one can never reach the other. But like Schatten's experiment, both might still get Schatten's laser signals because the planets are both in the two signals' respective time-like areas. And say the decoded signal teaches English, earth culture, plays Simpson's episodes, etc (assuming they are both smart enough to decode it). Both civilizations (in the permanent space-like area viz. each other) might learn our culture and language, and start speaking English. Even though they can absolutely never even know about each others' even existence, it's physically impossible, much less communicate!, they might speak the same language and be able to understand each other, and share a lot of information (mutually taken from us)! An astounding idea, IMO, and all thanks to Schatten's handy experiment.

 

 

---------------

 

* Big footnote, this doesn't count quantum effects, where a kind of signal actually could (or seems to) travel across the entire length of the lightyear long wall instantaneously. There is actually an experiment which is set up very similarly to this laser/wall set-up that shows just how weird QT is with this light-year-long signaling. But that's for another post!

Edited June 14, 2007 by demagogue

[demagogue]

I read this editorial in the newspaper today and it reminded me of this thread.

 

http://www.nytimes.com/2007/06/20/opinion/...l?th&emc=th

[demagogue]

Here's another supposed strange implication of special relativity, that black holes can't exist.

 

http://sciencenow.sciencemag.org/cgi/content/full/2007/621/1

 

(I was going to paste this into to my last post, so I wouldn't be double-posting... but I don't know how to delete this post now. sorry.)

 

Anyway, the argument is first that because of SR, time slows (to an outside observer) for something falling in as it gets closer to the black hole's event horizon, until time basically stops right at the horizon. The light just stays hovering on the horizon; and later light from inside can't get out.

 

Second, black holes also give off Hawking radiation over time. Quantum pairings (spontaneous creation of particle + antiparticle) will happen right at the horizon, where one side falls in and the other doesn't. But because of conservation, the escaping particle has to get its antiparticle back, and because quantum info doesn't have to obey SR it can get it back. (I think that's the idea?). So it's radiated back from surface of the horizon, and the black hole loses that little mass, which adds up over (a long) time.

 

And now these guys are saying that, for an outside observer, if time is stopped at the horizon, basically the whole future-history of the horizon perpetually happens all at once (?). So the black hole would radiate away before it can even be formed, like trying to fill a bottomless glass. So black holes can't exist.

 

But something seems fishy about this argument. Seems like somebody would have thought of that before and figured out why it doesn't work. Interesting food for thought, though.

Edited June 25, 2007 by demagogue

[sparhawk]

The problem exists IMO only for some observer that falls into the black hole. For an outside observer, obviously the time doesn't slow down, so the black hole can exist for a very long time, where the outside observer would never experience it, while a particle that was captured would see all eternity flashing by in an instant. Theoretically in zero time. But then, a zero time would violate special relativity because it means that cause and effect will also appear in zero time.

[Schatten]

The problem does not apply to massless particles, does it? For all we know matter could transmute at the event horizon and loose it's mass- so you'd have a bubble of higgs bosons or something, which exists on the verge of time.

 

If they'd only find that damned thing, I guess a lot would become clearer.

[sparhawk]

How do you propose that massive particles loose their mass and transform into massless?

[Schatten]

Well, it's wild speculation on my side, of course. I could imagine the event horizon to act like a wall in a particle accelerator, only the barrier would be timespace. So while (subatomic) particles with mass get stopped there, massless particles could advance further.

[sparhawk]

Maybe that's a good idea. If massive particles would be stopped there (which might make sense), it would also get rid of the inifinity problem, because such particles would never reach the center. It might also exaplain why black holes are so massive. The inside of a black hole wouldn't even exist then. Or it might be simply another universe.

[Schatten]

Reading up a bit on black holes, I doubt my theory would hold on for long.

There's a lot of really difficult physics going on, and appearently no model which can explain it satisfactory. At least my attempt would manage without that pesky, quantum theory defying, singularity.

[sparhawk]

Yup! That's what I meant. I only wonder what other problems it would have though.