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Assuming advanced alien technology to create and control wormholes, how big would a wormhole be that would allow a radio signal to pass through? Is there a way to know the size of the mouth as compared to the throat? Also, would such a wormhole mouth put out energy? I've read that wormhole mouths look like black holes when viewed from outside, so would it produce Hawking Radiation?

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    $\begingroup$ You should probably specify which frequency you are using etc. If I remember well there is a relation between the holes in a mesh used for a Faraday cage and the wavelenght to be blocked by it, but i don't have time to pull up all i need for a proper answer. What Im thinking is that you could use the same relationship when it comes to a wormhole: a bit bigger than the size that would block it and it would pass. The rest is just theories you can do what you prefer with $\endgroup$ – Erik vanDoren Mar 29 '16 at 23:28
  • $\begingroup$ Probably somewhere in the AM or FM range. $\endgroup$ – B. Evett Mar 29 '16 at 23:57
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    $\begingroup$ I'm voting to close this question as off-topic because this is way too broad and feels very non-researched - you've also got several questions nested into your question body. $\endgroup$ – Aify Mar 30 '16 at 4:47
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    $\begingroup$ I'm voting to close this question as off-topic because it is better suited for Physics SE, not worldbuilding. $\endgroup$ – Youstay Igo Mar 30 '16 at 5:34
  • $\begingroup$ I dont think it should be closed but Physics would for sure give a better answer probably including even all the science and a lot of wormholey theories behind it $\endgroup$ – Erik vanDoren Mar 30 '16 at 12:05
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How big would it have to be? Not very big. Radio waves are electromagnetic radiation, just like visible light. Assuming a focused signal, you'd need an opening about the size of a laser pointer. Maybe a bit bigger to ensure the message gets through.

The rest of your questions.... Well, it's up to you. We have no observational evidence that wormholes actually exist, so you could make them have whatever properties you want.

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  • $\begingroup$ How did you do the size estimate, given the large wavelengths and potentially large amplitudes of radio waves? $\endgroup$ – HDE 226868 Mar 29 '16 at 23:09
  • $\begingroup$ You are quite right to question me, thanks. I had only really thought about wavelength and ignored amplitude. Basically saying "The more energy they add, the closer the waves become to visible light, so we can use that as a general estimate." It doesn't help that there doesn't seem to be information about the general amplitudes used in common applications (ie WiFi is ~2 GHz frequency, but what amplitude? Nobody says). So yeah, this probably isn't right. $\endgroup$ – John Robinson Mar 30 '16 at 0:02
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The wormhole, or any hole for that matter, must be comparable in size to the wavelength of the radiation in order for it to pass through unobstructed. Consider for instance a faraday cage: https://en.wikipedia.org/wiki/Faraday_cage

If you look at the images, the faraday cages depicted are transparent. This is because the distance between the wires of the cage is larger than the wavelength of visible light and so visible light is not blocked. However, longer wavelengths like radio and some regions of microwaves are blocked, which is the desired result.

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