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Science and Astronomy Questions
midtskogenDate: Monday, 08.12.2014, 07:26 | Message # 301
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Is this easy to calculate?

I'm driving (at normal speed) and the traffic light in the intersection 100m ahead turns red. If I decide to accellerate - a lot - how fast must I go to get a green light due to blueshift as I enter the intersection?

I'm not sure how complicated the question is. It's probably significant how close to the traffic light I will be going?





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WatsisnameDate: Monday, 08.12.2014, 08:40 | Message # 302
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Yes, this is pretty easy to calculate, though I'm not going to do it completely accurately (I'm ignoring length contraction as your velocity increases).

Basically you're asking two things:
(1) What speed is required to blueshift red (~650nm) photons into green (~550nm)?
This turns out to be about 16% of the speed of light.
(2) What acceleration is required to achieve this speed over a distance of 100 meters?
Since .16c doesn't involve severe relativistic effects, I'm going to pretend that Newtonian kinematics (a=dv/dt, v=dr/dt) are valid. Then the solution is that the acceleration necessary is about 12 trillion meters per second squared, or a trillion G's. This is probably not survivable to you or anyone within a large distance of you. smile



Added: I'm also obviously treating your initial speed as zero (because compared to your final speed it might as well be -- the correction is trivially small), and that the traffic light is directly in front of your path (allowing otherwise would be important to the result, but it isn't the interesting part of the problem and its physics.)







Edited by Watsisname - Monday, 08.12.2014, 09:11
 
HarbingerDawnDate: Monday, 08.12.2014, 08:57 | Message # 303
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It's important to note, however, that when you reach the light your velocity relative to it will be 0, so it will be red, so really you need to reach 0.16c in a shorter distance, like 80-90 meters, in order for the light to ever appear fully green to you.

Also, at that speed, and assuming your vehicle's total mass is 1000 kg, then your kinetic energy would be roughly equivalent to 250 megatons of TNT (ignoring relativity), or 5 times as powerful as Tsar Bomba. Everything around you for a significant distance would be destroyed. smile





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WatsisnameDate: Monday, 08.12.2014, 09:21 | Message # 304
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Quote HarbingerDawn ()
It's important to note, however, that when you reach the light your velocity relative to it will be 0, so it will be red


Actually this isn't quite true because of relativistic aberration. Think of the photons from the light as rainfall which you are driving through -- your car is plowing through them. This makes the traffic light appear bluer (though not by as much) and still ahead of you even as you are passing directly beneath it at the intersection.

Full accounting of this would yield a pretty complicated solution.





 
midtskogenDate: Monday, 08.12.2014, 18:28 | Message # 305
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Thanks. I've been wondering about this for some time, but I haven't known the correct calculations. My remark about complexity was precisely about that I wouldn't go straight at the light and I would see photons from an "old" position of the light as I go past it.

Of course, I might not see the light at all because of the fusion of the atoms in the air between me and the light.

I might get a speeding ticket, but I would despute the red light effence. smile





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WatsisnameDate: Monday, 08.12.2014, 20:46 | Message # 306
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Yeah, the complexity involved by not going straight at the light and figuring change in wavelength as you enter the intersection is pretty high. The result would involve a geometric correction to the redshift formula (accounting for the light's altitude and horizontal distance from entrance to intersection [is it zero?]), and a correction for aberration. Simplifying to the case of straight line motion to the light provides a quick answer and is also a lower bound for the necessary acceleration.

Another thing is that once you start accelerating, you pass through the intersection just a few microseconds later. So even ignoring G forces, fusion with air and subsequent destruction of you, your vehicle, and all else around, it'd still be pretty hard to see that the light became green. I'd suggest recording with a high-speed camera to use in your defense. tongue





 
BalakeDate: Tuesday, 30.12.2014, 15:32 | Message # 307
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So I know it's accepted that information cannot be transmitted at a speed greater than light.
I was thinking about this and wondered:

If there was a one light-year long pole, and I was at one end, and someone else at the other, couldn't I push/move the pole and use that to send information almost instantly to the person at the end of the pole (therefore breaking the cosmic speed limit)?
 
apenpaapDate: Tuesday, 30.12.2014, 15:49 | Message # 308
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It would take at least a year (probably much longer, if it happened at all) for the other end of the pole to follow your movements on Earth. The pole isn't truly a single object, but composed of quadrillions of molecules that are bound by their mutual attraction. When you move your end of the pole, it takes a little while for the molecules near your hands to pull their neighbours along by that attraction. This happens so fast it seems instantaneous on any reasonably-sized object, making the object stay in a single shape, but on a lightyear-long pole, it would take a long time for the entire pole to follow the movement of one end. It would probably look like a wave travelling over the pole.




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FireintheholeDate: Tuesday, 30.12.2014, 15:50 | Message # 309
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Quote Balake ()
So I know it's accepted that information cannot be transmitted at a speed greater than light.
I was thinking about this and wondered:

If there was a one light-year long pole, and I was at one end, and someone else at the other, couldn't I push/move the pole and use that to send information almost instantly to the person at the end of the pole (therefore breaking the cosmic speed limit)?

The speed of the pole would be the same as the speed of the sound in that matter. So if it was made of iron, it would move in 5130 m/s.





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midtskogenDate: Tuesday, 30.12.2014, 16:21 | Message # 310
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I don't think the wave would travel far. Let's assume a pole 10 cm thick. Then its mass would be like a fairly big asteroid. In order to move it, you need a lot of force, and all that force would have to be applied to an area a few cm² big. The pole would just deform or melt before there's sufficient energy to cause detectable movement of the entire pole.

Solids aren't that solid at a great scale. If the Moon suddenly fell down and smashed into Earth, people on the other side of the Earth would probably not notice a thing for the first ten minutes [apart from overseas internet sites, tv transmissions etc going offline].





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Edited by midtskogen - Tuesday, 30.12.2014, 16:26
 
BalakeDate: Tuesday, 30.12.2014, 17:21 | Message # 311
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Thanks for your answers, apenpaap, midtskogen and Fireinthehole.

Quote Fireinthehole ()
The speed of the pole would be the same as the speed of the sound in that matter.

Wow, extending on that - Is it theoretically possible to create an object so dense that its speed of sound exceeds the speed of light?


Edited by Balake - Tuesday, 30.12.2014, 17:22
 
midtskogenDate: Tuesday, 30.12.2014, 17:40 | Message # 312
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Quote Balake ()
Is it theoretically possible to create an object so dense that its speed of sound exceeds the speed of light

No.

If you try to google the speed of sound in neutron stars you might get some interesting answers.





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HarbingerDawnDate: Tuesday, 30.12.2014, 17:46 | Message # 313
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Quote Balake ()
Is it theoretically possible to create an object so dense that its speed of sound exceeds the speed of light?

No, because sound is movement of matter, and matter cannot reach the speed of light, so no medium could ever have a sonic speed > c.





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FastFourierTransformDate: Tuesday, 30.12.2014, 19:01 | Message # 314
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Quote midtskogen ()
If you try to google the speed of sound in neutron stars you might get some interesting answers.


Very interesting issue.

Quote Balake ()
If there was a one light-year long pole, and I was at one end, and someone else at the other, couldn't I push/move the pole and use that to send information almost instantly to the person at the end of the pole (therefore breaking the cosmic speed limit)?

The exact same question is answered in Veritasium:
 
WatsisnameDate: Tuesday, 30.12.2014, 21:32 | Message # 315
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Sound is transmitted by pressure forces, or the back and forth motion of particles, and since particle velocities can never exceed c, the speed of sound can never exceed c. So no material can ever have a speed of sound faster than the speed of light in vacuum.

This is also one of the reasons why gravitational collapse must lead to a black hole, and not some solid body with a stable radius smaller than the Schwarzschild radius. Speed of sound cannot exceed c, so a body crushed within its Schwarzschild radius cannot be supported by pressure forces. Collapse must continue.





 
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