Imagine observers A & B are in uniform motion in freespace and seperated by 1 lightsecond which is

d = 299,792,458 m

 

But if we transmit a clock signal with a funtamental frequency of 300MHz for exactly 1 second:

f = 300,000,000 Hz

λ = 1.0m exactly

another words, in 1 second we transmit 300,000,000 lightwaves so the speed of light tells us the wave front traveled a distance of:

d = 299,792,458 m

but the sum of the wavelengths add up to

d = 300,000,000 m

 

So either light is blueshifted at v=0 or 415,084 bits of information was destroyed. So what's wrong with this picture?

But if we transmit a clock signal with a funtamental frequency of 300MHz for exactly 1 second:

f = 300,000,000 Hz

λ = 1.0m exactly

 

 

The wavelength is not 1 metre. It is c / 300 MHz = 0.999308193 metres.

Because we made a choice about the length of the meter and second (both at one point tied to details of the earth) some time ago, and have tried to preserve the choice in our non-artifact-based standards.

The wavelength is not 1 metre. It is c / 300 MHz = 0.999308193 metres.

Got it, thanks.

 

All the online wavelength calculators were showing 9 significant figures but I didn't notice that they had rounded off c = 300,000,000 m/s which was what threw me off.

So either light is blueshifted at v=0 or 415,084 bits of information was destroyed. So what's wrong with this picture?

 

Transmission of information is completely different story.

In the simplest technology, you can interpret lack of photons is bit 0, and presence of photons is 1.

Then turn on/off LED, incandescent light, or other source of light, over and over again, as fast as you need.

You can have clock ticking 1 GHz or 1 THz, and in each clock cycle, emitting photons for each 1 bit set, and not emitting photons for 0 bit.

Energy, frequency or wavelength of these photons will have nothing to do with amount of data transmitted this way.

 

Read also about AM, amplitude modulation,

https://en.wikipedia.org/wiki/Amplitude_modulation

and FM, frequency modulation.

https://en.wikipedia.org/wiki/Frequency_modulation