# Single photon wave packet autointerference

#### biffus22

Problem Statement
How is photon autointerference possible in a large interferometer?
Relevant Equations
The angular resolution R of an interferometer array can usually be approximated by Resolution = wavelength / maximum separation of inputs.
I've been troubled by this problem for some time now and have received several answers to it none of which I find compelling, so I am posing it again in hopes of getting something more convincing.

Here's the problem. Consider one had a large optical interferometer with two siderostats place 500 meters apart which both feed their light into a central processing unit where they interfere with one another and thus provide the resolution of a single scope of roughly 500 meters in aperture before being recorded on a CCD camera. Now we know that while the photons are travelling through space to reach the interferometer they travel as wave packets, not as particles. The wave packets thus, in a manner resembling the famous double slit experiement, pass through BOTH siderostats before interfering and then "collapsing" into particles on the CCD surface.

So far so good? The problem comes in, at least more dramatically, when we consider the case of the interferometer recording an especially dim object, perhaps a quasar 10 billion lightyears away. In such a case, the interferometer may well receive each incoming wave packet only once every few seconds. [Which is not a big problem in practice since most images have considerably longer exposire times.] This means, however, that each incoming wave packet must interfere with ITSELF in the interferometer. But that means in turn that there must be a robust enough signal reaching both of the siderostats to allow for such interference.

That, however, seems impossible to me since a photon wave packet in the optical spectrum carries with it only a very tiny momentum and energy. So how is it possible for the single wave packet to be "wide" enough, and energetic enough, to span the whole gap of the interferometer spacing and interfere with itself?? Surely there must be some maximum siderostat separation beyond which the two signals are far too weak to interfere.

That, however, does not seem to be the case, since, as we just saw with the use of radio interferometry to image the black hole event horizon in M87, it is possible to link together radio telescopes, -- which by the way receive far LESS energetic photon packets than do optical telescopes! -- around the world to produce incredibly high resolution images. How is that possible? Even just getting photons arriving at quite different times, -- relatively speaking of course, -- at different antennas in different widely spaced locations lined up accurately in time must be very difficult, and facilitating autointerference of each wave packet must be more difficult still.

So, given that we know it IS possible to create a working interferometer of virtually ANY size, how does it really work?? How can the wave packet possibly be detected well enough at two distant locations to create any interference at all??

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#### phyzguy

...Now we know that while the photons are travelling through space to reach the interferometer they travel as wave packets, not as particles. ...
Your problem is here. The picture of a photon as a localized wave packet traveling through space from the emitter to the detector is simply flawed. There are many "What is a photon" threads, and you might want to study them. The best that I can explain is to say that quantum fields do not behave as your intuition might expect.

"Single photon wave packet autointerference"

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