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Alex,
surface of water and space are completely different media, so you can not compare them to such extent.
The main differences are:
1) water surface is 2D medium, space is 3D (but this is not so important)
2) water surface is lossy media - that means that energy of waves is dissipated to heat (because water molecules are moving against each other as wave propagates).
Much better analogy may be a surface wave on solids. Very good example is application of effect called SAW filter: Surface Acoustic Wave Filter, widely used in communication industry.
Here, the losses due to heat dissipation are almost null, as the quartz (used as a substrate) is almost ideally elastic (means you can apply a pressure on it and it will deform, but when the pressure is removed it will bounce back to the original shape).
SAW filter would not work as it does if wavelength would be changing as the wave travels across its surface
Now, I am not sure if your observation (waves on water are changing wavelength) is correct, but it may be.. I will check this at some stage :-)
The space behaves much more like quartz (in terms of losses and wavelength). It behaves like it is ideally elastic (Maxwell, energy preservation etc). Where would that energy loss go? If photons are loosing energy, it must go somewhere..
And NOTHING like this was EVER observed.
So, no Alex, photons do not get tired... And the space-time expands since the BB, and it will go on expanding... until... (?)
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