B Help Understanding the Uncertainty Principle

[Chris Frisella]

To check my understanding, imagine this scenario:
You have a very small surface rigged as a light detector (the contact surface is let's say a single atom). You then fire off single photons towards it. As soon as you get a read on the detector, you know very precisely where the light is/was, and you could also know the energy of the photon very precisely because the atom would only accept a certain energy level. One might also imagine that the path the light took was a straight line between the emitter and receiver, but I suppose it wouldn't necessary have to be, therefore an uncertainty in momentum. So would the uncertainty principle in this case come down to just the direction the photon comes from?

 

[Nugatory]

You have a very small surface rigged as a light detector (the contact surface is let's say a single atom).

And how are you going to get a precise time signal from this single atom in the contact surface? For that matter, how did you localize it in space in the first place?

In effect, you've assumed the existence of a device that does not obey the uncertainty principle, and then concluded that if you have such a device you can violate the uncertainty principle. The logic is sound but the conclusion is no better than the starting assumption.

 

[Chris Frisella]

And how are you going to get a precise time signal from this single atom in the contact surface? For that matter, how did you localize it in space in the first place?

Good question. I'm a little rusty in my nanotechnology, but I do recall seeing an imagine of an etching made by removing single atoms. I just googled a bit and it sounds like scanning tunneling microscopes could be the answer. So, imagine a needle-like instrument that's held in place in your lab. At the very tip of this needle you have a single atom. Focused on this atom you have a scanning tunneling microscope. Perhaps you could then observe a specific alteration in the atom caused by an interaction with the emitted photon. Then you would know it was there and its energy level.

"Simulations of different types of scanning probe microscopy with atomic-scale sensors..."
www.sciencedaily.com https://www.sciencedaily.com/releases/2014/11/141127082305.htm

I get where you're coming from, but it sort of seems like all of this is plausible...
But anyway, my question was more to do with keeping the uncertainty principle intact. Looking back to my original post, would the uncertainty come from just the direction the photon strikes the atom?

 

[FraserAC]

Scanning tunnelling microscopy works via the principle of quantum tunnelling. It does not work like a conventional microscope, (an object under study is bombarded with photons and then passed through a magnifying lens, allowing the user to see an image).

STM's have a needle, like you mention here! The end of the needle can generate a current when within a close proximity to an atom on the surface of the object under scrutiny, due to quantum tunnelling, which is in itself, an inherently quantum mechanical phenomenon and as such is effected by the uncertainty principle.

These currents vary based on the proximity of the surface (If the stm is running at constant height mode) and you can build up an image of the surface by doing this. You do get atomic resolution by doing this, since the quantum tunnelling interaction is between atoms.

 

[Chris Frisella]

Scanning tunnelling microscopy works via the principle of quantum tunnelling. It does not work like a conventional microscope, (an object under study is bombarded with photons and then passed through a magnifying lens, allowing the user to see an image).

STM's have a needle, like you mention here! The end of the needle can generate a current when within a close proximity to an atom on the surface of the object under scrutiny, due to quantum tunnelling, which is in itself, an inherently quantum mechanical phenomenon and as such is effected by the uncertainty principle.

These currents vary based on the proximity of the surface (If the stm is running at constant height mode) and you can build up an image of the surface by doing this. You do get atomic resolution by doing this, since the quantum tunnelling interaction is between atoms.

Ok. So if you used this setup to image an atom as it absorbed a photon, it seems like you could know with high certainty the location and momentum of that photon at the moment of interaction.

 

[Nugatory]

Using this technology, how would you know if and when a photon had been absorbed?

You also have to be a bit careful about interpreting these images as literal pictures of the atoms underneath the needle tip. We're measuring the current through the needle as it moves from one point to another and illuminating the pixels according to the intensity of that current when the needle is at various points. Thus, those solid-looking shapes are actually vaguely defined regions in which there is a high probability of finding an electron.

 

[Jilang]

The problem is with the statement " the atom would only accept a certain energy level". How precise does it have to be? If it needed to be spot on to a zillion decimal places, nothing would ever happen!

 

[bhobba]

Ok. So if you used this setup to image an atom as it absorbed a photon, it seems like you could know with high certainty the location and momentum of that photon at the moment of interaction.

It much more complicated than that - unfortunately:
http://www.physics.usu.edu/torre/3700_Spring_2015/What_is_a_photon.pdf

The real answer to the whole thing is that states in a quantum atom like hydrogen are not stationary (ie they really change in time) due to interaction with the quantum EM vacuum that permeates all space. It leads to something called the Fermi Golden Rule that is the real explanation:
http://staff.ustc.edu.cn/~yuanzs/teaching/Fermi-Golden-Rule-No-II.pdf

The derivation of this fundamental rule really requires Quantum Field Theory and is one of the first indications of a sickness in ordinary QM. To make matters worse QFT has its own sickness re-normalization is required to correct. Here is a simple introduction I wrote from the modern Wilsonian viewpoint:
https://www.physicsforums.com/insights/renormalisation-made-easy/

Basically for QFT to make sense you really need a cutoff - there is a sickness in QFT because it considers infinite energies and momentum's. Long before that it is strongly suspected other theories, maybe string theory, takes over so including them can't be trused. To get around it you cut them off.

Thanks
Bill

 

[Chris Frisella]

Nugatory, I get you. Thanks for the answers. bhobba, good stuff-thank you.