Distance travelled by an electromagnetic wave

[flyerpower]

Suppose a spaceship is at 1 light year distance by Earth and it sends a message back home through an electromagnetic wave, we choose a frequency so that the wave will be a radio wave which requires little energy to produce.
How do i know if the wave will reach the Earth? and what characteristics will it have (besides frequency, wavelength and energy which i suppose are invariable)?
In other words i want to know in what manner is a radio wave detectable and what variables the distance that a radio wave can travel depends on so as it is still detectable after it reaches the destination, OR can a radio wave travel forever and yet the message can be decoded?

 

[JeffKoch]

You haven't mentioned anything about ridiculous spaceship speeds, so the wave will arrive at Earth looking just like it did when you sent it, except much weaker. The receipient can signal you back, so after 2 years you'll know if they received your message. Detecting and decoding and message contained in the wave is a complicated problem, and with the information you have given the only answer is "it depends". Basically it comes down to signal-to-noise ratio, which depends on how many wave photons the message contains and on the background noise statistics.

 

[flyerpower]

so the wave will arrive at Earth looking just like it did when you sent it, except much weaker.

This is my question actually, what is the physical meaning of that weakness? by what physical concept is it described?

 

[JeffKoch]

Weakness in terms of photons per unit time per unit area back on Earth. This number scales as 1/distance**2, which is why the sun at a distance of 1 light year would appear as just a bright star in the night sky, not quite as bright as Jupiter appears from Earth. Put it 33 light years away and it becomes barely visible to the eye, put it much farther away than that and the only way to detect it would be to use a telescope and add photons over a long period of time with an electronic detector or photographic film. Put it much farther away than that, and the signal fades into the background noise that is associated with the maximum time you can sum over, using the largest telescope you have, i.e. it's gone and you'd never know it's there.

 

[flyerpower]

Ok, so it is described in terms of photons/unit time/area, that would be something called irradiance, right?

And one more question about light, i can't make the intuition of what the frequency and weavelength of an EM wave mean. Well i know they represent variations in electric and magnetic fields but can they be described in terms of photons (light as a particle)? like the wavelength would be the distance between two separate "photons wave" and the frequency would be the the number of "photons wave" per unit time (it might be stupid what i say above but I'm just trying to make some intuition of what those phyisical measurements mean compared to everyday phenomenons that we see).

 

[JeffKoch]

Ok, so it is described in terms of photons/unit time/area, that would be something called irradiance, right?

And one more question about light, i can't make the intuition of what the frequency and weavelength of an EM wave mean. Well i know they represent variations in electric and magnetic fields but can they be described in terms of photons (light as a particle)? like the wavelength would be the distance between two separate "photons wave" and the frequency would be the the number of "photons wave" per unit time (it might be stupid what i say above but I'm just trying to make some intuition of what those phyisical measurements mean compared to everyday phenomenons that we see).

You have to talk about photons with very weak signal levels because the signal that hits the Earth (photons/time/area, which is watts/area if you prefer) cannot be arbitrarily small and remain continuous, i.e. it's quantized in terms of the number of "hits" per unit area per unit time. So you are counting numbers, and you introduce counting statistics. This is not a remote abstract limit, with weak signals that people try in real life to measure, you often need to consider photon counting statistics to evalute signal-to-noise and data quality. This is why the Hubble Deep Field images had to be integrated over a ridiculously long time, like two weeks, in order to generate anything useful - it's not because the detector isn't sensitive enough, it's because of photon counting statistics.

Light can be thought of as both a particle and a wave depending on circumstances and what qualities of light you are looking at, which is another way of saying we don't really have a clue how to think about it, but in the wave view it has a wavelength and frequency associated with a transverse traveling wave composed of time-varying electric and magnetic fields.

 

[flyerpower]

Ok, thank you, it's not yet fully clear for me, but I'm starting to get some intuition, i'll do more research :). Thanks again.