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Old 05-11-2012, 12:44 AM #1
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Smile Laser pointer travelling faster than the speed of light?

Since laser beams are to travel infinitely across the universe until the light is absorbed by matter, let's just say that I take a laser pointer, turn it on, point it at the night sky and flail it across in my wrist hitting saturn from the earth which is about 1.2 billion kilometres away (close enough for the laser beam to reach saturn as it's not lightyears away). Do you think that the laser dot or the beam moving across saturn moves faster than the speed of light? For instance another matter reachable within less than a light year, if saturn is too close for the laser to travel faster than the speed of light or maybe a machine that can move faster than my wrist might be contributing factors for making a laser pointer dot travel faster than the speed of light. The farther away the matter from earth is, the more sensitive the speed of the laser beam with the movement of your wrist is when it hits the matter. Think of it as this, you point your laser pointer at something that's 5 feet and the dot doesn't move as much. Now point it at something that's 500 metres away with the same steadiness as a target at 5 feet, the dot from the laser will move all over the place. Same concept as pointing it at planets and other matter in space. What do you guys think. I hope my explanation isn't too complicated.


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Old 05-11-2012, 12:46 AM #2
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Default Re: Laser pointer travelling faster than the speed of light?

And let's just say that the laser has 0.0 MRAD
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Old 05-11-2012, 01:28 AM #3
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Default Re: Laser pointer travelling faster than the speed of light?

I'm not entirely sure what you're asking but I think I have a feeling of what you're trying to say...

Light is a constant.

Imagine you were in a car and there was a radar sign in front of you, now imagine that instead of detecting the speed of the car, the radar sign was detecting the speed of the light coming out of the car. That radar sign will measure at an astounding 1079252848.8 km/h.

Now.. when the car starts moving @ say 100 km/h, you'd think the speed of the light coming out of the car would increase by 100 km/h, after all you'd think that the moving car would give the light "an extra push".

But surprisingly, that is NOT what happens. All our radar equipment and speed testing equipment in the world will only and always measure light travelling at 1079252848.8 km/h, whether the car is moving or not.

But how could this be? How could all measurements of light speed always come out the same? If you were running at a wall, it's coming at you faster than if you're standing still, with respect to that wall. But that's not true with light.

The speed of light is the same for everybody.

So here's how Einstein made sense of this extraordinary puzzle. Knowing that speed is just the measure of space in which something travels over time, Einstein proposed a truly stunning idea: that space and time could work together, constantly adjusting by the right amount so that no matter how fast you might be moving, when you measure the speed of light, it ALWAYS comes out to be... 1079252848.8 km/h.

To respect that absolute quality about light, time had to cease to be absolute, space had to cease to be absolute. And those two had to become relative, in such a way that they slosh between each other.

If space and time being flexible sounds unfamiliar, it's because we don't move fast enough in our daily lives to see this in action. But if you were in the car moving at near the speed of light, the effects would no longer be hidden.

For example, if you were on a street corner as I was went by close to the speed of light, you'd see space adjusting so that my car, it would appear just inches long, and you'd also hear my watch tinking off time VERY slowly. But from my perspective inside the cab, my watch would be ticking normally and space inside the car would appear as it normally does. Now when I look outside the car, I'd see space wildly adjusting.. all to keep the speed of light constant.

So with Einstein, time and space are no longer rigid and absolute. Instead, they meld together with motion, forming a single entity, that came to be called, "space-time". Einstein made reason conquer sense.

This notion of space and time being a unity, to me, is one of the greatest insights that has ever occurred in science. It's so counter-intuitive to everything we've ever experienced as human beings.

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Old 05-11-2012, 03:42 AM #4
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Default Re: Laser pointer travelling faster than the speed of light?

Good explanation Ryan, but I think he was asking about the "tracking" motion of the light on the object it is being pointed at.

I've thought about this before too. And while yes, the dot may "seem" to be moving faster than light, that doesn't mean anything. There is nothing "moving" at that speed. The light travelling through space is still moving at the constant c and only the direction is changing.

Because nothing is actually moving faster than light, yes, it would be allowed to track a laser dot "apparently" faster than the speed of light.

I'm pretty sure, anyway.
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Old 05-11-2012, 03:49 AM #5
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Default Re: Laser pointer travelling faster than the speed of light?

Isn't this comparing angular velocity vs linear
velocity?
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Old 05-11-2012, 03:55 AM #6
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Default Re: Laser pointer travelling faster than the speed of light?

^ That's exactly it.
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Old 05-11-2012, 03:55 AM #7
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Default Re: Laser pointer travelling faster than the speed of light?

That's exactly what I was trying to explain . Ryan's explanation is quite interesting as well
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Old 05-11-2012, 04:14 AM #8
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Default Re: Laser pointer travelling faster than the speed of light?

Well first of all, the light isn't instantly hitting Saturn, not even close. Though light is fast, and for most purposes can be considered instant, it still takes around 50 minutes to take light from earth to hit Jupiter.

I'm not quite sure I follow your explanation, but I think what you're saying is how come the dot doesn't count as going faster than the speed of light? And like what was said earlier, you are confusing angular velocity and linear velocity.

Also, I used to think when I was young, that you did the same exact thing, except with a massive metal pipe, and got some machinery to shake it, the tip of the pipe would move faster than the speed of light. But of course the speed at which any metal compresses is obviously far less than the speed of light.
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Old 05-11-2012, 05:45 AM #9
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Default Re: Laser pointer travelling faster than the speed of light?

Well, the laser dot is an image not a real thing. So the dot can travel at faster than the speed of light.

For the metal pipe, it is real so it can only reach the speed of light. Of course to reach the speed of light you would need to apply infinite force for a finite amount of time or a finite force applied for infinite time on the pipe which is... impossible

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Old 05-11-2012, 07:00 AM #10
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Default Re: Laser pointer travelling faster than the speed of light?

What the OP is asking is to find the radius between the emission point and the proposed arc path where the arc length exceeds the distance light travels in the time it takes to angularly displace the emission point's position by an arbitrary degree.

For example: you rotate your wrist 180 degrees with the laser pointer on in one second. Now, how far out would the arc of the laser's path have to be such that the arc length exceeds 300,000 meters.

I'm no mathematician or astrophysicist so I can't do the math for you, only explain the theory.
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Old 05-11-2012, 09:18 AM #11
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Default Re: Laser pointer travelling faster than the speed of light?

Quote:
Originally Posted by Sigurthr View Post
What the OP is asking is to find the radius between the emission point and the proposed arc path where the arc length exceeds the distance light travels in the time it takes to angularly displace the emission point's position by an arbitrary degree.

For example: you rotate your wrist 180 degrees with the laser pointer on in one second. Now, how far out would the arc of the laser's path have to be such that the arc length exceeds 300,000 meters.

I'm no mathematician or astrophysicist so I can't do the math for you, only explain the theory.
Ah I see.

I'm going to try and sit down, grab a pencil&paper and develop an equation...

First, we have to make some assumptions that the line of sight is always going to be clear (not blocked by stardust, comets, meteors or planets). Second, we assume the wrist motion will be along 1 axis to make calculations simpler.

We start off by measuring, using a protractor or similar tool, the maximum comfortable angle you can snap your wrist from resting position (you'll have to try to snap your wrist as straight as possible along one axis, to ensure there's no curvature in the path for accurate calculations). We'll call this angle "A".

Then we calculate how fast it takes for you to snap your wrist the same amount of degrees from position t0 resting point to position t1 endpoint. Let's call it "t" to represent time.

We then figure out how long it takes light to travel "t" time. The "shape" the laser beam forms by going through the motion, t0 to t1, is a 2-dimensional cone. Trig won't work. Like Sigurthur said, there's going to be an "arc" across angle A. There's another way to calculate "x", where x is the "arc length" across angle A:



So with the above equation, you can now just add in the variables and find out "x" arc length.

Therefore, if "x" is < than "l", then your angular velocity is lower than the linear velocity of light, meaning the laser beam is faster than you can point, the dot is "on target" along your laser aperture's line of sight at all times.

If "x" is > than "l", then your angular velocity is higher than the linear velocity of the laser, meaning while in motion, you are pointing infront of the laser beam aka the laser is lagging behind it's destined path aka you moved your wrist faster than the speed of light aka I think this is impossible (have I gone wrong with this conclusion?).

Someone might want to check my math though

But here's my 2 cents anyway

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Old 05-11-2012, 10:24 AM #12
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Default Re: Laser pointer travelling faster than the speed of light?

Circumference = 2*r*pi.
Angle = 180 degrees = 1/2 circle
Arc length of 1/2 circle = r*pi
Assume you take 1 second to flick the laser 180 degrees
t=1s
c=3x10^8m/s
r=c*t/pi = 3*10^8*1/3.14159 = 9.55*10^7m = 9.55*10^4km = 95500km = 59340mi
Anyone see problems with my math?

Earth - Moon distance is 384400km
So if you point your laser at the moon, chances are your dot is moving on it faster than the speed of light?

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Old 05-11-2012, 10:32 AM #13
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Default Re: Laser pointer travelling faster than the speed of light?

Sounds about right but when X > L you would not see the beam lagging, only an observer at distance L would see the beam lagging. Thus I don't think your wrist speed has to be higher than linear C. If X = L that makes sense, your wrist must have an angular velocity equal to C. If you greatly increase L relative to X (or A) the photons would not have reached L by time your hand has moved from t0 to t1.

Example: L = 1 light year, X = 15 deg, X = 1.57 light years.

In this example it will take 1 year for photons emitted at A t0 to reach X t0. This doesn't solve the OP's question, which is at what exact point of L in relation to A, does the phenomena occur, but it does prove that your wrist's angular velocity is dependant on the ratio of L to A and there are cases where impossible wrist speeds are not necessary.

Edit: too late for me to check your math, Apocalypse, but if it's right then very cool. Now figure out for every degree of wrist motion how much longer r needs to be to maintain the effect.
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Old 05-11-2012, 03:09 PM #14
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Default Re: Laser pointer travelling faster than the speed of light?

Yes, this effect is observed coming from certain astronomical phenomena, like the ejection jets getting squirted out of (just before it would be lost forever at the Event Horizon) powerful black holes in galactic centers, where the accretion disk is squirting out the X-ray and plasma jets out of the "poles". Nothing is actually moving faster than light, but due to the angle of view, or the jet sweeping across and lighting up other interstellar matter, "Superluminal Motion" is perceived.

Superluminal motion - Wikipedia, the free encyclopedia

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Old 05-12-2012, 10:04 AM #15
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Default Re: Laser pointer travelling faster than the speed of light?

It's quite amazing how if you know the name of something, all the information you could ever want is just a few seconds away, but if you don't know what it is called and don't have access to a learning institution you are SOL.
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Old 05-12-2012, 05:21 PM #16
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Default Re: Laser pointer travelling faster than the speed of light?

^ I agree.
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