PDA

View Full Version : Racing dots



GrapesOfWrath
2001-Dec-09, 10:45 AM
There are many demonstrations of things that can go faster than light. If you have a long wave not quite parallel to shore, the place where that wave meets shore could move faster than light--but the particles of water themselves do not. Just our concept of where the wave meets the shore does.

One other common example is shining a (very focused) laser on the moon for a while, and then turning and shining it on your wall. It would seem the spot produced by the laser would jump 240000 miles in about a second--faster than the speed of light. Still, no actual particles go that fast--just our concept of the "spot."

However, if you do the trigonometry, something else seems to happen. Assume the moon is 1.3 seconds away, and you train the light on it, then turn it towards a wall 3 meter (10 nanoseconds) away, smoothly turning one quarter turn in one second. A piece of paper extends along the wall all the way to the moon, also 3 meters away from the dot on the moon.

The dot on the moon doesn't start "moving" for 1.3 seconds, of course, but another dot appears on the paper in 80 microseconds, about 24 km above the surface of the earth. That second dot splits into two dots, one racing to the moon, and the other dropping to your room. Of course, it takes the whole rest of your turning (1 second minus 80 msec) to get to your room. The other dot races up the paper to the moon at slightly less than light speed, and eventually meets up with the dot arriving from the moon, sometime after 1.3 seconds, but not much.

At no time, did any of the three dots exceed the speed of light. When the dot appeared in your room, though, it was still on the moon! Time travel!
_________________
rocks

<font size=-1>[Fixed formatting and spelling]</font>

<font size=-1>[ This Message was edited by: GrapesOfWrath on 2001-12-09 05:51 ]</font>

Simon
2001-Dec-09, 06:51 PM
...Interesting. It only seems that way of course because the dot isn't an actual object, just a point where a stream of photons are hitting and being reflected, and those photons already emitted keep going after the source of them is turned away.

But it still makes some neat turns on perceptions. Like you said, the dot being in two places at once. Or the beam of light; how fast would it be moving as it swept through space if you measured it from, say, a lightyear out?

GrapesOfWrath
2001-Dec-09, 09:23 PM
On 2001-12-09 13:51, Simon wrote:
But it still makes some neat turns on perceptions. Like you said, the dot being in two places at once. Or the beam of light; how fast would it be moving as it swept through space if you measured it from, say, a lightyear out?

Let's see, if you had a piece of paper a lightyear out, in a large circle, and spun around in one second just after turning the light on, the dot would appear on the paper--one year later--and spin completely around the paper in one second. Two pi lightyears in one second.

I would like to get ahold of that laser.

2002-May-01, 02:01 PM
<a name="20020501.5:56"> page 20020501.5:56 aka Push to 1 from 10
On 2001-12-09 16:23, GrapesOfWrath wrote: To: 2-5-01

anyway
a parrallel discussion about
Light
Particles
WAVE
and me as a DeFective

John Kierein
2002-May-01, 04:51 PM
The moon's shadow travels at the speed of light, but when the earth enters the moon's shadow, it feels it instantaneously.

This is applicable to the speed of gravity. Van Flandern says that gravity is faster than c, but I think he's thinking of this phenomena. See the book "Pushing Gravity".

Martian Jim
2002-May-03, 08:05 AM
you sure the laser is hitting the moon and not just bouncing off the ozone layer or something? cos i dont think you would see the reflection of the laser on the moon (unless it was a very big lazer)

you could see it if it was the death star lazer through

_________________
the guy that has come from mars, for no reason (no reason, or you think for no reason......)

<font size=-1>[ This Message was edited by: Martian Jim on 2002-05-03 05:48 ]</font>

GrapesOfWrath
2002-May-03, 12:10 PM
Moon, definitely moon.

Hey, this is my gedanken. Like I said, I'd like to get ahold of a laser like that.

OTOH, we do "see" reflections on the moon from lasers on the Earth. But our seeing is done with instruments. Us pitiful humans have always tended to need a little help seeing, especially after forty.

2002-May-03, 05:01 PM
Yeah? I did try to make a little scents
out of the Lunar Range data from
http://almagest.as.utexas.edu/~rlr/mlrs.html
but gave up on that. Made no centss to me whatever
NOW about Gravities "SPEED" I think Gravity
"WAVES" travel at whatever speed they feel like
{kind of like cars on a freeway}
Slow, Fast, and in different sizes & shapes
so theres a broad spectrum of the on many
paramaters. THEY are not one Size, one Shape, or one speed. So they are not easily detected. BUT IT IS POSSIBLE !!!!.

John Kierein
2002-May-03, 09:59 PM
I think gravity travels at c just like the moon's shadow. But if you step into the shadow you feel it instanteously.

GrapesOfWrath
2002-May-03, 10:50 PM
I understand that your contention is that gravity is a result of mass shadows, but what do you mean by the shadow travels at c, in terms of mainstream physics.

Do you mean that when an object moves into position, the light that has already passed it is not obstructed, and the shadow won't appear until the last particles have arrived, which will be at a rate c over the distance to the shadow?

John Kierein
2002-May-04, 03:30 AM
Yep. The shadow is just a "hole" in a field of light. So it travels at c. Another way to look at it (no pun in 10, dead)is to consider the edge of the shadow. It is light. As the body moves the edge of the shadow moves at c.

GrapesOfWrath
2002-May-08, 03:47 PM
Just to fill in the details of the original post, per request, and to check my work, I'll walk through the algebra.

The "paper" is 3 meters away, and 400,000,000 meters (http://www.planetscapes.com/solar/eng/moon.htm) long, and we'll use a speed of light (http://www.xs4all.nl/~jcdverha/scijokes/11_4.html#6) of 300,000,000 meters per second.

I turn one quarter turn in one second, but the photons creating the spot on the moon don't start their motion until 4 x 10^8 m / 3 x 10^8 m/s = 4/3 second later. I said it would be 1.3 seconds.

I am assuming that there is a 3 meter "wall" on the moon also, but that's nearly inconsequential. Still, for time t from 0 to 1 second, the "dot" appears on the paper at time T = t + 3 meters / sine(t x pi/2) / c

In that formula, t represents the time taken to turn the beam, and t times pi/2 is the angle which has been turned. 3 meters divided by the cosine of the complement of the angle (the cosine of the angle) is the distance that the photons will have to travel. Divide that distance by c the speed of light to get the time when they hit the paper.

When do the photons first hit the paper? We want to minimize T = t + 3 meters/c / sine(t x pi/2). The derivative of T with respect to t is 1 + 3/c x (-pi/2) cosine(t x pi/2) / sine^2(t x pi/2)

Setting that equal to zero, to find a minimum, and substituting (1 - cosine^2) for sine^2, and solving the quadratic, we get
t = 2/pi x arccos((sqrt(4 + (3pi/2c)^2)-3pi/2c)/2), or about 80 msec.

Did you guys get that too?

roidspop
2002-May-08, 06:01 PM
That's what I got, after muddling around for a long time. I didn't do anything as elegant as using derivatives, minmax and the quadratic equation...I just set up a loooong spreadsheet and found the point where d went to 3. It surprised me. I had expected to see the first 'touch' materializing much higher. Allowing for travel time back down to the observer, the differences become quite substantial. As to the spreadsheet, I haven't used one for trig before and was irked at first to see that it wanted the angles in radians, and then relieved that all I had to do was use "radians(90*t)". Thanks for the diversion!

<font size=-1>[ This Message was edited by: roidspop on 2002-05-08 14:03 ]</font>

GrapesOfWrath
2002-May-08, 08:52 PM
Oops, I just noticed that I misinterpreted something. At time 80 msec., the photons are leaving the laser, but they don't appear on the paper for another 80 msec (by coincidence,sorta).

Pi Man
2002-Oct-23, 07:25 PM
Here (http://www.badastronomy.com/phpBB/viewtopic.php?topic=614&forum=1&21) is a related topic. If the stick was infinitely rigid, then it would work, but we know of no such material(unless nutronium-the stuff of which neutron stars are made of- would fit the bill)

A notch in a pair of scissors could go faster than light if the scissors were long enough. As the notch(the point at which the two blades meet) gets farther away, it accelerates, so it could potentially go extremely, extremely fast even if the actual molecules of the scissors did not go faster than light.

I have heard it argued that matter goes faster than light where black hole accretion occurs. It is argued that the jets that come out of the "poles" of the accretion disk accelerate to a speed greater than c.

A wheel of an infinitely rigid material could go above speed c, but relativistic effects in that case would be *REALLY WIERD*. The circumference of the circle would end up being imagionary, and it's area would be complex! The edge would somehow curl into another dimention in order to be imagionary!

overrated
2002-Oct-24, 12:10 AM
Let's say, hypothetically speaking, that we had a pair of scissors 1 AU long. And in the "notch" where the blades intersect, there is a post. The post sticks down into the notch. Then we close the scissors. If we do it fast enough, can we accelerate the point where the blades intersect--and thus the post--faster than c?

Get NASA on this, stat!

xriso
2002-Oct-24, 05:58 AM
It's okay for mathematical points and quantities to move faster than light speed. For example, the phase velocity of the components of quantum wavefunctions usually travel faster than light speed. This isn't any big deal though, because it's the velocity of the wave packet that really matters. Hmm.. matters.. I just made an unintentional pun.

By the way, I really liked that earth-moon paper strip idea. If it weren't pointed out to me I probably would have said that the dot moves towards Earth.

(Something else like that): If you had a bunch of targets placed at one-lightsecond intervals, you could shine your laser at the back one, then after a second, switch to the next closest one, then after another second, the next ... You could be "simultaneously" shining your laser dot on as many things as you liked. /phpBB/images/smiles/icon_smile.gif

Alternately, put reflectors up instead of targets, again one lightsecond apart, but switch to the closer one every two seconds. Then you would be blasted by many laser beams all at once.

Fruh-Batz
2002-Oct-24, 11:07 AM
On 2002-10-23 15:25, Pi Man wrote:
Here (http://www.badastronomy.com/phpBB/viewtopic.php?topic=614&forum=1&21) is a related topic. If the stick was infinitely rigid, then it would work, but we know of no such material(unless nutronium-the stuff of which neutron stars are made of- would fit the bill)

A notch in a pair of scissors could go faster than light if the scissors were long enough. As the notch(the point at which the two blades meet) gets farther away, it accelerates, so it could potentially go extremely, extremely fast even if the actual molecules of the scissors did not go faster than light.


Your "infinitely rigid" argument also applies to your second example. You could only get the notch moving faster than c if the scissors were infinitely rigid. The EM effect causing the scissors at one point to go together travels at c. Another way to look at it is that this would also make it possible for you to send information faster than light by pushing the scissors together at the end and have someone watch the other end. (LEGAL NOTICE: If the author (hereafter referred to as "I") should by virtue of his Limited Knowledge of Physics Have Messed It Up, You may regard this Nitpick as Null And Void.) /phpBB/images/smiles/icon_biggrin.gif
[edited for spelling error: it hurts my eyes]

<font size=-1>[ This Message was edited by: Fruh-Batz on 2002-10-24 07:47 ]</font>

Argos
2002-Oct-24, 12:13 PM
On 2002-10-23 20:10, overrated wrote:
Let's say, hypothetically speaking, that we had a pair of scissors 1 AU long. And in the "notch" where the blades intersect, there is a post. The post sticks down into the notch. Then we close the scissors. If we do it fast enough, can we accelerate the point where the blades intersect--and thus the post--faster than c?


It's only possible in a "gedanken experiment". It would be true if the blades were made of an absolutely rigid material. Relativity imposes a limit on the rigidity of the blades.

This has been discussed here (http://www.badastronomy.com/phpBB/viewtopic.php?topic=614&forum=1)before.

GrapesOfWrath
2002-Nov-11, 08:56 PM
On 2002-10-24 07:07, Fruh-Batz wrote:
Your "infinitely rigid" argument also applies to your second example. You could only get the notch moving faster than c if the scissors were infinitely rigid.
Not necessarily. Depends upon how the scissors are constructed.

Just imagine a pair of closed scissors that are finely machined so that the point at which the blades rotate is very close to the line where they meet. When you open them, the "notch" travels from the far end of the scissors to the close end.

A better way of looking at the problem, so we don't get bogged down in whether the material is rigid enough, is to use a pair of blades that are rotating already. At some time, they are perfectly parallel, and in the next instance the "notch" travels from the ends to the axis. Nothing physical moves from end to axis, but the conceptual object does.

Fruh-Batz
2002-Nov-11, 10:08 PM
OK, ok. Right. I was thinking of somebody pressing together the handles and the scissors moving in response to it. When they are already in motion, that's something else. It seems that you cannot move any information faster than light from A to B. In the case of the entangled particle pair you can infer something about another system, but you cannot use that information. Is this right so far?

JS Princeton
2002-Nov-11, 10:37 PM
On 2002-05-01 12:51, John Kierein wrote:
The moon's shadow travels at the speed of light, but when the earth enters the moon's shadow, it feels it instantaneously.


The first part is true, but the second part doesn't follow. The Earth won't "feel" the moon's shadow until the 1.3 seconds have passed. The photons that have already gotten past the moon's limb will continue on their merry way to Earth for the next 1.3 seconds. This is similar to the idea that if the Sun were to instantaneously disappear we wouldn't know about if for 8 minutes.

However, shadows easily travel faster than the speed of light. Say you have an extended light source that starts at a source of 10 meters and ends up projected across a screen that's a lightyear across. Now use a well shielded blocker (that won't be upset by the brilliance of the source radiation necessary for the signal to show up on the screen) and move across the source at a leisurely pace of 1 m/sec. The projected image will have the shadow travelling across the screen at one tenth of a lightyear per second.

Note that you could not do this experiment with any sort of physical object, like a rod, that stretched to the screen. If you tried to move your end of the object at 1 m/sec you'd have to overcome tremendous torque that would end up rupturing any system with an arbitrarily large binding-energy at the point where the tangential velocity equalled the speed of light.

GrapesOfWrath
2002-Nov-12, 12:05 AM
On 2002-11-11 17:37, JS Princeton wrote:
However, shadows easily travel faster than the speed of light.
Why use a shadow? Otherwise, it's pretty much the same setup as I talked about earlier (http://www.badastronomy.com/phpBB/viewtopic.php?topic=279&forum=1&21&start=2).

JS Princeton
2002-Nov-12, 09:07 PM
Any non-physical object will do, you're right, Grapes. The only reason I used the shadow is because it was germane to John K.'s example.

Chip
2002-Nov-12, 09:46 PM
On 2001-12-09 05:45, GrapesOfWrath wrote:
There are many demonstrations of things that can go faster than light. If you have a long wave not quite parallel to shore, the place where that wave meets shore could move faster than light--but the particles of water themselves do not. Just our concept of where the wave meets the shore does...
Physicist Philip Gibbs offers some interesting viewpoints on these things here (http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html). I like the bit about the moon spinning around my head at four times the speed of light! Explained on his website. /phpBB/images/smiles/icon_wink.gif This FAQ page is from his Physics (http://math.ucr.edu/home/baez/physics/index.html) website.

<font size=-1>[ This Message was edited by: Chip on 2002-11-12 16:49 ]</font>