[CPT ArkAngel (OP)]

Photons can be represented entirely as an electromagnetic field vectors in space and time with a unique frequency. This frequency is a measure of its energy. E=hν (h being Planck constant). The frequency is space time dependent (Doppler effect). Hence the photon energy is dependent and uniquely dependent on space time.

(one interesting point is that space time can be define relatively to a photon energy field)

If you travel in a parallel direction  to the photon direction, and accelerate until you reach the speed of light relative to your initial position, the photon energy you measure will increase until it is infinite  (when you travel at C, theoretically speaking because we all know it is an unattainable speed) according to the frequency shift relative to your change in velocity. As your velocity increase, your time measurement decrease until it stop when you reach C. So, if your time measurement decrease, you measure a higher photon frequency.

On the contrary, if you accelerate in the opposite direction to the photon direction, the photon energy you will measure will decrease until it reaches zero at the moment you travel at the speed of light relative to your initial position.

My question is: is there an accelerated trajectory where you will always measure the same photon energy? Because if there is one or more, it means the photon needs a coupling particle or photon traveling in another direction in order to keep the information of space time... Maybe there is not because of the variation in the elecromagnetic field of the photon relatively to all possible accelerated trajectory...?

[graham.d]

I think you may have got confused. If you travel in the direction of a stream of photons so that (for example) you detect them by looking back into the stream, then the doppler effect will have reduced their frequency (you must use the proper time of the clocks on your spacecraft). The energy would be lower. The reverse is true if you are fying towards the stream where their frequency, and therefore energy, would be higher.

Of course you can't travel at lightspeed (as you realise) and the photons will always be travelling at lightspeed relative to you whatever your velocity so, as you also note, it is only their wavelength that changes.

I'm not sure what you are getting at with "accelerated" trajectory. Two points to note are that: 1. you cannot measure light "from the side" only when you actually detect it and 2: Any constant (unaccelerated) trajectory through the beam gives a constant frerquency. Any acceleration will (I think) cause the frequency to change.

[CPT ArkAngel (OP)]

 Yes Graham, you are totally right, i should have used a beam of light instead of a single photon... I was too tired to have a clear mind.

I have another question since my last one was irrelevant.

If one day, i choose to leave my girlfriend who is standing in a beam of light (crying  [])and I run away in the same direction as the light beam until i reach the speed of light, the light frequency i will measure will decrease but time dilatation should increase it when i reach a near light speed???  Is there a more general equation of the Doppler effect taking account of relativity?