What Uncertainty Principle actually is?

[Brucezhou]

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.

 

[jfizzix]

In quantum mechanics, not everything about an object is something we can measure in a single instant. Sometimes measuring one property of an object like its position interferes with our ability to measure its other properties like its momentum.

There are two principle ideas as to where this comes from:

Version 1:
Measuring the position of an object requires you hit it with small wavelength high energy particles (of light), but because it's been hit with particles, you can't know what its momentum was as well as you could otherwise. On the other hand, you could measure the momentum by bombarding it with large wavelength low energy particles of light, but you can't know exactly where the particle was at a level any smaller than the wavelength of the light you use to look at it.

Version 2 (Modern version):
Our inability to measure every property of an object in a single instant is a fundamental part of the quantum nature of these systems. The wavefunction of a particle that's well-defined in position contains a lot of different wave components, each with its own wavelength. This means it does not have a well-defined wavelength. On the other hand, a wavefunction with a well-defined wavelength does not have a sharply defined position, as a single wave extends over all space.

 

[DennisN]

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 :

https://www.youtube.com/watch?v=KT7xJ0tjB4A

 

[msumm21]

Just wanted to continue with the version2 (modern) description above, because if you understand that well I think you will be intrigued. In quantum mechanics particles don't really have the properties of a specific position and momentum, ... in general. I.e. it's MORE than just us being uncertain of it's position/momentum, it actually doesn't have a specific position/momentum. One way some people imagine it for position is that a particle is kinda spread out or smeared out over space. Similarly for momentum, when an electron is not interacting with it's surroundings in certain ways it's speed is kinda spread out over a range of speeds. When something (e.g. a measuring device) interacts with a particle in a way that determines information about it's position, then it typically CHANGES the state of the system so that the "position" is indeed collapsed down to that particular area (so now you can have less "uncertainty" about it's position, you know it's located in that small region). However, that same change of state also includes a change the "speed properties" of the particle such that it's speed is spread out over a larger range. So, the more precisely you know the particles position, the more it's momentum is spread out over a large range (again, not just your uncertainty of it's momentum, but it's "momentum properties" themselves).

 

[haael]

Uncertainty happens, when you try to describe quantum objects using classical physics. In my view it's a logical flaw. It happens for two related reasons:
1. Treating a discrete quantity as if it was continuous.
2. Treating a quantity that is associated with some macroscopic object, or collection, or ensemble, as if it was associated with a microscopic object.

Basically, microscopic object don't have "position", "momentum" or "energy" in the sense of classical physics. There are related phenomena with the same names that are associated with microscopic objects, but they mean something different. When you try approaching the quantum realm with concepts from classical physics, you get uncertainty.

 

[Fiziqs]

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 :

https://www.youtube.com/watch?v=KT7xJ0tjB4A

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.

Why does the light spread out as the slit gets narrower?

 

[msumm21]

Why does the light spread out as the slit gets narrower?

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:

 

[jfizzix]

If you think about the light as waves, you need a lot of different frequency components to have a sharp pulse. On the other hand, you need to have a very long pulse if it is to be well defined in frequency.

If a beam of light contains only a single frequency, then it can be described as a single sine wave extending out forever in space. If you add sine waves of different frequencies together, at some points the waves will add constructively, and at other points, they will add destructively. To have a pulse, you need to add a range of frequencies together.

 

[Ken G]

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 more so 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.

 

[Fiziqs]

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.

How do you measure the momentum of a particle?

 

[Fiziqs]

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 more so 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.

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?

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? Or is there some other reason that the photons exiting the slit are different from the photons being emitted at the source?

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?

In essence my question is, how is the light emerging from the slit different from the light emerging from the laser source?

Thanks

 

[Ken G]

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?

Yes, completely correct.

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?

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.

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?

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.

In essence my question is, how is the light emerging from the slit different from the light emerging from the laser source?

The superposition of interfering components within the wave function of every photon has been culled down by the slit.

 

[Khashishi]

You could model the universe as comprising of information (Work with me here). You can describe the state of the universe by providing enough information to distinguish it from any other state. For example, in a classical picture, to specify the state of a ball, you give the position and momentum of the ball.

In classical mechanics, there's essentially infinite information needed to specify the state of the ball because you need to specify the position and momentum to exact precision, and any small deviation will result in a different state. In quantum mechanics, there is a limit on how much information that goes into specifying the state. If you try to describe a state with position and momentum that are very close to another state, you end up describing the same state. Basically, quantum mechanics imposes some kind of finely spaced grid on the universe's dynamics, except this grid is not imposed on either position or momentum, but rather on the combination of position*momentum. The Heisenberg uncertainty principle is a result of this microscopic quantization of this combination of position and momentum, called phase space.

If you imagine we were in some simulation, where our position is constrained to points on a grid, then our "uncertainty" in position would be given by the grid spacing. Quantum physics is different because it is the combination of position*momentum. Getting speculative here, but perhaps it is because space and time are actually emergent quantities and the underlying grid of the universe exists in some kind of phase space.