A Really Long stick, c, Space, Poking a Friend, Relativity and Stuff

So during my Physics 11 class I thought up of a very interesting thought experiment of sorts and I have been planning on writing about it for about half a year now? No, less than that. Anyways I haven't gotten around to it yet but I will do that eventually and it will be put on this blog. This was inspired during my Psychology class, of which I tend to call by many different things such as Philosophy class. This is because at times it becomes just that. A lot of the time it becomes just that. This individual class that inspired this turned into one of these about half way.

We watched a documentary about how things are produced, and the negative side of it. All the waste, pollution, exploitation of people and land. It was fairly eye opening even though I had seen it before. We were told to write a one page long response to the documentary and then a small blurb about our perception of time. I did what I could to grind a one page reply out of my mind and then went to the time topic. It has been posted on this blog, I beleive titled 'My Perception Of Time' or something like that. During this class we got into the topic of philosophy and physics. I have a habit of pulling them into one topic and shifting from one and the other. I'm sure this will be apparent in my posts if I get to either topic. This went to the speed of light, the speed of light in a vacuum (c; 3.00x10^8m/s) and one of my friends in the conversation presented me with a thought experiment that blew my mind at first.

Say you are in space. You have a pole. This pole is 1 lightyear long. You are at one end of it. Your friend is at the other end of it. Keep in mind this is just a thought experiment, so many people look at this and go, "Pfft, you can not have a pole that long," and I would like to -Slap Them With A Blowfish- (This reminds me, check my Posterous; bugworlds.posterous.com for a post I will put up soon after this. The slap with a blowfish will be understood if you do) with the fact that it is a thought experiment. Einstein based much of his work off thought experiments and are very well known now, so don't blow this off for it's impossibility. It is meant for you to think. Back on topic; now you have this 1ly long pole and you have pushed it. I will poke your friend immediately, right?
The answer to this is maybe. Keep reading.
And to add a more interesting concept into this, assuming your friend is poked right away, did you just cause something to move faster than the speed of light?

At first I couldn't find a problem with this model. It seemed sound, but with some more thinking I had one of those realization moments I love, it was during math class, "Wait a second! When you translate a graph that is ten units wide, four units left you are only moving it four units left. Not ten units left. The individual points move, you don't consider it as a whole." I can't beleive I didn't realize this at first but I understood that his model was wrong. After some more looking into this and thinking I found more errors but this is the first one.

What is the distance between your friend and their end of the pole? Lets say it is 1m, and you have just pushed the pole 1m forward. The pole has only moved 1m. Every individual point has moved 1m forward. Not 1ly. Duh? Yes, duh indeed. This kills one idea of it, but doesn't the energy move the entire distance? It does.

Another thing to consider is if the pole has moved the 1m instantly, the light is still moving at c. That means the pole will be received instantly and a year later the image of you poking your friend will be received... Assuming they're looking the correct direction for the duration of your image pushing the pole. Since this is a thought experiment though, that does not matter. Back to the pole and it's moment, just keep the light traveling off you to your friend in mind.

The energy that you have added to the system (The system being closed and consisting of the pole. You are not part of it because you are just adding energy to it but not doing anything more so you can be viewed as adding a force to the system. Your friend is the receiving end of the system, so they might be part of it? It doesn't matter, just technicalities.) transfer the entire distance of the pole, the entire 1ly length, instantly. This is true only if the pole is perfectly ridged and does not warp. Misfortunately it is impossible to have perfect rigidbility and even if it was it might not apply still.

Even at small scale nothing moves instantly. It moves at the speed of a wave, a longitudinal wave I beleive due to the pole being a solid. It may appear to be instant, but that's just because you cannot notice the slight time delay because it is so slow. It is negligible. This wave, it will be at the speed sound will travel through the pole. For a better explanation on this I advise you check the links at the bottom. I am assuming the atoms in this have the same resistance as air at zero degrees celsius. Sound, at zero degrees celsius moves at about 332m/s. As air heats up or cools down the density of it changes and so does the speed. To avoid complications I"m assuming this pole has the same resitance that air has. Lets crunch some numbers, this following list is in no particular order.

1ly is aprox. 9.46x10^15m long.
c is aprox. 3.00x10^8m/s.
There are 315,366,000s in a year.
The speed of sound at 0C is aprox. 332m/s
At this speed, sound will travel 1,047,015,120,000 meters in one year. That's 1 trillion, forty-seven billion, fifteen million, one-hundred-twenty thousand meters.
At this speed, it will take aprox. 2.85x10^13 seconds for sound to travel the length of the pole
That can also be looked at as 4.75x10^11 minutes,
Or 7,914,993,307 hours,
Or 329791387.8 days,
Or aprox. 903,538 years.
To put this into perspective, we are in the year 2010. That's aprox. 450 times the length of our calendar (assuming our calendar has started at the time that has been given the title year zero). The world is aprox. 4.5 billion years old; or 4,500,000,000 years; so in 4.5 billion years light could travel this pole 4,980,421 times, that's 4,980,421ly. These numbers are starting to lose their point.

The number we need is the aprox. 903,538 years. Since it would take this long for sound to travel the length of the pole, and we are assuming the pole has the same resitance as air at 0C, then it will also take that long for the energy to go through all of the pole.

Because the pole is not impossibly rigid and the energy will travel through it as a wave the poke is not going to hit your friend right away. It will take the above time to do so. The image of you pushing the pole is still traveling at c.

If you poked your friend who is at the other end of a one light year long pole: One year after you push the pole your friend would see you pushing it. 903,537 years after that your friend would be poked.

Keep this in mind next time you poke someone with something. They don't get poked right away, there is a slight delay that doesn't matter at real world scales.

Credit must be given to http://www.physicsforum.com/showthread.php?t=386687 and http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#4 for helping me out with this.

- Bugworlds ; I know my blog must be interesting to me atleast if I need a calculator beside me to write what I'm writing.