Curiosities of physics...and math

RocketMan on 27/9/2007 at 02:00

1.

Here's something that always pissed me off about the way we are taught how light behaves. So its pretty much well known that according to special relativity, the speed of light has to be a constant 2.99 x 10^8 m/s. If photons could slow down there'd be no point even calling them photons as their energies are a function of frequency alone and assume a constant speed. Plus the speed of light is a natural product of Maxwell's equations of electromagnetism. Here's the problem. According to every physics book out there that I've ever seen, light slows down when it travels through a medium. Err...ok. Now I can understand that it takes longer for light to escape while being transmitted through a medium but only if we assume this is because of absorption/reradiation. For example it takes years for a solar photon to travel from the core to vacuum of space (I think its years) because of the huge mass of hydrogen in the way. The light is constantly being absorbed by electrons and re-emitted, not to mention its trajectory isn't a straight line. This is an extreme case though. When we consider something more normal like glass, how do we deal with the speed of light? It is well documented that the total duration of the journey through the glass is greater than if it were not there but I can only make sense of this if the photons are interacting with the glass. My physics teacher has always told me (and the textbooks imply) that the photons simply slow down. They offer no mechanism for this change in speed. If in fact photons can slow down while maintaining a straight, interaction-free trajectory, then this violates the fundamentals of special relativity...

Your thoughts...

2.

In probability/statistics there are a few basic rules that many ppl are aware of in every day life. Gamblers in particular are constantly reminded that no matter how long they play a slot machine and lose, their chances of winning do not increase in the future as a result of their long history of losses. Most ppl are compelled to believe that things should even out if they keep playing and so they think that somehow the next time will offer a greater chance of a win.....however it is well established that any and all trials of set of trials conducted under identical conditions will yield the same probability of a certain outcome each and every time, INDEPENDENT of the history of previous trials.

Having advertised that I am aware of these firm rules of mathematics I'd like to now challenge them because they don't make sense to me. Now try to hold in your irritation until after I've made my case as many reading this have already decided that I am wrong (isn't that a funny little quirk of human nature?) Anyway here's my problem.

It is also a well known and rational outcome of mathematics that if you have a set of trials, lets say 100 and lets say we are flipping a coin (an ideal coin with only 2 outcomes), that the outcomes should be 50% heads and 50% tails. That is, since the probability of a single outcome is 50%, we expect that after 100 trials 50% of the trials should be heads. We also know that the probability of getting consecutive outcomes that are the same follow the rule P = p^n I don't know if those are the right letters but basically getting 2 heads in a row has a probability of 0.5 x 0.5 or 25% and every consecutive head that follows has a lower and lower probability of occuring because we expect the total sample distribution to be 50 50 and getting consecutive heads screws up the balance and biases it towards heads. Tossing 100 times and getting 100 heads is a very very rare event so it has a low probability. The probability is 0.5^100. Anyway here is where I have a conflict. The probability of a trial's outcome never changes regardless of history....however the outcome of a SET of trials diminishes as the balance deviates from a 50 50 distribution. What this tells me is that there is some sort of a tendency, expressed in mathematics, governed by physics, for outcomes to balance out. Where do we see this behaviour? I say entropy behaves a lot like this. Entropy is the tendency for all physical systems to decay into a state of chaos or maximum disorder. 100 coin tosses coming up 50 50 is the most disorderly system you can have for 100 coin tosses. If you had 100 heads and 0 tails that's like having a room where all the oxygen is on the left and all the nitrogen on the right....its well sorted, takes a hell of a lot of work to achieve, and is highly orderly, homogeneity is not. Of course the fact that probability and entropy are linked is nothing new but what it says to me is that entropy should tell us the truth as it is a physical phenomenon that we can observe. If entropy makes all things tend to disorder then I really truly think that entropy has some sort of a presence, call it what you will, but some sort of effect that makes coins change their outcome.

If I flipped 99 coins and they turned out heads, I think entropy does something, what I don't know, but something to change one of the next trials to tails such that the larger the trial size gets, the more chaotic and evenly distributed it becomes. Something's gotta make tails come up so that you don't have heads forever. If something didn't change the outcome then why is it that the probability of consecutive trials diminishes exponentially with n? It makes intuitive sense though doesn't it? I think entropy is what's responsible for keeping n small. If I'm playing roulette and I lose on black 5 times in a row, well I'm gonna bet black the next time. I know its against the logic of math but I'll trust my intuitive sense of entropy over math.

Thoughts?

Scots Taffer on 27/9/2007 at 02:10

Monkeysee doesn't post anymore. Sorry. :(

TBE on 27/9/2007 at 02:40

(http://en.wikipedia.org/wiki/Entropy_%28order_and_disorder%29) Entropy is a bitch. I think it's the universe's way of being lazy. Things do not like to stay organized unless it's the perfect setup for them. (Like the noble gas neon.)

My office right now is plagued by entropy. I better clean it, as I have a visitor tomorrow. Some French-Spanish-quasi-American dude passing through wants to have dinner ;) Why is it that things fall to shit when there's no organization? This is life :(

Fafhrd on 27/9/2007 at 05:29

I don't understand what your problem is with 1. Speed of light is a constant IN A VACUUM. The light DOES interact with glass, it transfers energy into the glass in the form of heat, slows down, and we see refraction of the light. How much energy is transferred and how much refraction occurs depends on the shape and clarity of the glass.

2 is just nonsense.

aguywhoplaysthief on 27/9/2007 at 05:57

Quote Posted by Scots Taffer

Monkeysee doesn't post anymore. Sorry. :(

What ever happened to him? He was my favorite poster.

D'Juhn Keep on 27/9/2007 at 09:42

He got laid

ercles on 27/9/2007 at 09:48

:nono: Its a crying shame

addink on 27/9/2007 at 10:44

1. What Fafhrd said
Also (http://en.wikipedia.org/wiki/Photon#Photons_in_matter) this and the concept that light traveling through matter is not a fixed set of photons, but rather energy in the form of photons being absorbed and then emitted by the matter's particles over and over again.
Any photon travels at lightspeed all the time.

2. What Fafhrd said

Quote Posted by RocketMan

If I flipped 99 coins and they turned out heads, I think entropy does something, what I don't know, but something to change one of the next trials to tails such that the larger the trial size gets, the more chaotic and evenly distributed it becomes.

You're basically inversing the meaning of chance. The distribution of chances are defined by the average outcome of a large number of experiments.

Due to the incidental* nature of the experiment(s), the chance exists that a deviation from the expected outcome occurs. But the larger the number of the experiments you do, the smaller the chance is that your outcome will deviate far from the expected. However it does not rule out the possibility of an extreme outcome. After 99 consecutive heads (the chance of which is 0.5^99) the chance to get a hundredth is still 0.5.

* If you flip your perfect coin once, you're guaranteed to deviate from the expected outcome 0.5/0.5 heads/tails.

Chade on 27/9/2007 at 11:13

RocketMan, if you get 99 heads, and no tails, and then you flip more coins, you will still have (on average) 99 more heads then tails. There is no tendency to even out the number of heads or tails you get. But as the number of tosses gets larger, the difference of 99 more heads then tails starts to look less and less important ...

In other words, NoHeads - NoTails will not tend to change in any particular direction (although it will change). But NoHeads/NoTails will tend to go to 1 as you do more experiments.

RocketMan on 27/9/2007 at 14:08

Quote Posted by Chade

In other words, NoHeads - NoTails will not tend to change in any particular direction (although it will change). But NoHeads/NoTails will tend to go to 1 as you do more experiments.

But you are contradicting yourself. I did say i felt there's a tendency for change because we observe it...not the tendency itself but the fact that rarely do we ever get 99 heads and 1 tail. We don't bother to speculate about getting 51 and 49, that's normal nor would we have a problem with 60-40 even but every time we get a decently distrubuted outcome, I think it was because something was doing its job the whole time (entropy) and keeping true the low probability of a messed up outcome like 99-1

I think it may be important to draw the distinction between a mathematical construct in isolation and the behaviour of the universe in terms of physics. I think the law that all outcomes have the same probability has to be viewed in the context that we are discussing an ISOLATED trial. Viewed globally though the context changes and suddenly large numbers of trials have a collective behaviour of maintaining a nice even distribution via some mechanism, despite each trial being distinct from any other and therefore having the same outcome. To me its a bit of a paradox to throw both phenomenon together. I'm thinking of the global cases here and decomposing the behaviour of a single trial from that.

Fafhrd don't just say 2 is nonsense unless you plan to justify that like everybody else is doing. I don't care if you think its nonsense if you don't say why.

Addink: I didn't even think to check wiki, lol. That explanation does seem to confirm though that if you track any individual photon it only does travel at the speed of light as long as its not currently being scattered, absorbed or interfered with, which is what photons do in a medium. So I guess that answers that. Thanks.