One of the things I really like about physics is the artistic beauty of the way the math works. Now I am no theoretical physicist I have always been more towards the experimental side but sometimes when the 2 collide it really makes me see probably what people who love great art see. I can’t really explain the feeling that I can get from it like someone who love art probably can’t either (difference is they try with as many words as possible while physics try using as few symbols as possible although we prove we can use so few symbols with hundreds of symbols J ). But it is I guess the one thing I can relate to when people go on about how great modern art is.
Take for example a femtosecond lasers. Most laser people see are monochromatic i.e. they emitted light of a single wavelength (for the purposes of this post anyway). However when you pulse a laser on and off at high speeds you see something amazing they are white (talking laser in the visible spectrum here there are ultraviolet laser with the same broadband spectrum but the eye can’t see them. But the same principle applies) . Now you can only do this with certain types of lasers and you can’t do it with a laser pointer no matter how hard you try. To pulse at this speed you use various techniques that I wouldn’t get into now but they are pretty cool. By the way an femtosecond is 1*10^-15 or 0.000000000000001 seconds. I.E very short.
So why would it be white I hear you ask well. That comes down to theoretical physics quantum to be precise and Heisenberg’s Uncertainty Principle.
Werner Heisenberg was a German physicist who headed up the Nazis nuclear program. There is much debate over whether he a.)Mis calculated the critical mass needed for a bomb. b.) deliberately slowed down the program to stop the Nazis getting the bomb or c.) Didn’t really care for the bomb and directed the research towards Nuclear power. What ever the reason thankfully Hitler didn’t have a bomb. Heisenbergs as it is known by some. Can be explained by this thought experiment.
If you want to see an electron a photon has to hit off it and then enter your eye. However when it hits it changes the electron. Like a cue ball hitting a snooker ball changes a ball. Thus you cannot be certain of where the ball is. As you are seeing it at the point of impact not where it has been moved to. This can be represented as so.
Where delta (the triangle) is the difference in x (position) and delta p (momentum) is the difference in p. And this is equal to planks constant/2. As this is equal to a constant if one value goes down to keep the equation balanced the other has to go up. For example x+y=10. Lets say x is equal to 4 and y=6. If we make x =3 then for everything to balance y has to go up to 7. So basically the more you know x (position) the less you know about p (momentum).
As the joke goes Heisenburg gets pulled over driving by a cop. The cop says do you know how fast you are going. He replies no but I know where I am.
Anyway this leads on to relativity and this equation derived from the Time Dependent Schrödinger equation. (Schrödinger of the cat fame)
Basically in this one. E is energy and t is time. Thus the more you know about the t the less you know about the E. Now when you are pulsing a laser at attoseconds you know very precisely how long the pulse is so that means you don’t know the value of the energy very well.
E=hv is an equation from Max Plank where h is planks constant and u is the frequency. Frequency and wavelength are related by c=fv. Ok so if you are uncertain about the energy you are uncertain about the frequency and thus uncertain about the wavelength. As you are uncertain of the wavelength. Then it could be any number of wavelengths you simply cannot say as you cannot see a single wavelength you see many.
You see white light. Beautiful