Main Question or Discussion Point
What Uncertainty Principle actually is? I searched on the internet and got an amazing answer that the energy could form out of thin air. Who could explain more specifically to me, who is in year 11.
I realize that most people on this forum probably find this video to be a good example of HUP in action, but I'm wondering if someone could explain why the laser light spreads out as the slit gets narrower and narrower. HUP tells us what will happen, but it doesn't really explain why it happens.Hi Brucezhou, and welcome to Physics Forums!
I've posted this little demonstration of the Uncertainty Principle a couple of times before, but I'm happy to post it again :
It turns out that all the states in the quantum mechanical state space in which the position is well localized to a small area have a large spread in momentum. Now you can always ask a deeper level of why, why do the states have this property? I think you will always run into a dead end where it can't be explained to you at a deeper level. It might be instructive to watch this video:Why does the light spread out as the slit gets narrower?
A good way to think of this, in my opinion, is to recognize the importance of wave mechanics in telling particles what to do. We used to think waves and particles were two totally separate things, and light was a big debate because it has both properties. With de Broglie, even moreso than Heisenberg, we found that it was a perfectly natural aspect of all particles to behave according to wave mechanics.Why does the light spread out as the slit gets narrower?
Ken G, I like this explanation, but I wonder if you could clarify what is happening at the source of the laser beam, and at the slit. Hopefully my question will make sense. I assume that at the source, photons are constantly being emitted in large numbers, and from a relatively broad area compared to the wavelength, and that these photons spread out in a familiar wave fashion. Outside of the narrow beam of light that we see, the light is undergoing destructive interference, and inside the beam, the light undergoes constructive interference. Therefore we see a narrow beam of light. Is this basically correct?A good way to think of this, in my opinion, is to recognize the importance of wave mechanics in telling particles what to do. We used to think waves and particles were two totally separate things, and light was a big debate because it has both properties. With de Broglie, even moreso than Heisenberg, we found that it was a perfectly natural aspect of all particles to behave according to wave mechanics.
Now, the big thing that wave mechanics is all about is the phenomenon of interference. That which can happen is that which experiences constructive interference in the appropriate wave, what doesn't happen is what experiences destructive interference. This simple observation completely explains the initial narrowing of the beam as the slit narrows, and the eventual widening.
A beam of light goes where its wave function experiences constructive interference, which is in the direction of the beam, and it doesn't go where the beam itself is setting up destructive interference, which is in the sideways directions. To set up that destructive interference, the beam only needs a cross section of many wavelengths, so as long as it is many wavelengths wide already, cutting down on the cross section of the source (by narrowing the slit) only makes the beam narrower-- since the constructive interference is cut down, with no impact on the region of destructive interference.
However, if the slit is narrowed further, until it is only a few wavelengths wide, now it is not just the region of constructive interference that is affected, but the destructive interference is also being made less effective. The beam starts to "leak out" into regions it couldn't get to before. By the time the slit is narrower than a single wavelength, the destructive interference has been almost completely disrupted, and the beam can go almost anywhere. Details of the surviving destructive interference can cause "fringes", or intensity modulations, but basically you've lost the destructive interference that was responsible for collimating the beam by making the slit so narrow.
So the seemingly counterintuitive behavior of the light going more places when the paths it can take to get there are reduced, makes perfect sense when you recognize that paths convey not only the constructive interference that permits behavior, but also the destructive interference that limits behavior.
Yes, completely correct.I assume that at the source, photons are constantly being emitted in large numbers, and from a relatively broad area compared to the wavelength, and that these photons spread out in a familiar wave fashion. Outside of the narrow beam of light that we see, the light is undergoing destructive interference, and inside the beam, the light undergoes constructive interference. Therefore we see a narrow beam of light. Is this basically correct?
The latter. But remember, it's not the photons that interfere, it is the amplitudes. There are wave amplitudes before there are photons-- you only calculate the photon flux after you know the wave amplitudes. So all the interference happens first, which then determines how many photons will go where. Huygens' principle says you can treat the slit like a source of wave amplitudes, the strength and coherence of which is determined by the laser, but once you have that, you can forget about the laser and just use the slit as the source of everything beyond the slit.But what happens at the slit? If the slit is less than one wavelength in width are the photons effectively forced to pass through the slit one photon at a time, thus destructive interference disappears because there are no other photons with which to interfere, or are multiple photons emerging, but all with the exact same wave description, such that they can no longer interfere constructively or destructively?
For a perfect laser, all the photons already have the same wave description, in the sense that they all have the same wave function, but not in the sense that the wave function is simple. It is the wave function of a beam. You could further break up the beam into a superposition of spherical waves, and that's when you'd see the spherical waves are destructively interfering outside the beam. But keep in mind, it makes no difference if there is just one photon coming out at a time-- they all have the same wave function anyway (in the laser idealization). So don't think about the similarity of the waves between different photons, think about the superposition of spherical waves that are interfering. If the slit is just a single point, then the wave that gets through is just a single spherical wave, the superposition has been completely culled out and with it all destructive interference and all channeling into a beam.As the slit narrows to the point where it is only 2 or 3 wavelengths wide do the resultant photons emerging from the slit take on ever increasingly similar wave descriptions such that interference disappears as the wave descriptions become more and more similar?
The superposition of interfering components within the wave function of every photon has been culled down by the slit.In essence my question is, how is the light emerging from the slit different from the light emerging from the laser source?