Doc Al said:
Realizing that this is just an amusing thought experiment (lots of luck "viewing" a passing photon), from your inertial reference frame the electron is moving at some speed v while the photon moves at speed c. From your frame, the photon gains distance on the electron at the rate "c - v". From the electron's frame, the photon moves at speed c.
Well then, is there any problem?
Doc Al said:
So? While you're at it, why not take a pretend snapshot, in which case photon and electron will both be at rest.

What's the point?
I don't know if you really don't understand my question or I am describing something wrong. Why must take a rest frame between photon or electron? Maybe I'll make it clearer: First,
"Say I had recorded a racing show between photon and electron, I can see that photon and electron is moving with their velocities respectively, I see photon is moving away from electron with a velocity", and then,
"I watch the show again and but this time I let the show plays slower, now I see the photon is still moving away from electron but this time it is moving away slower then before (the photon and electron is moving slower as I watch the slowed show this time)"
Actually, there is a big difference which I set-up onto relativity I know, which is I let the time become variable, which mean that if I can slow down the time clock to see if there is something act different. So I came up with another speculation thought:
"For another case, if I watch that slowed movie play, the electron will move slower but the photon won't (red-shifted), and thus photon will move away from electron faster" which is oppose the result above.
Doc Al said:
Huh? If you have a question, try to rephrase it.
Sorry, there is some mistake:
AlienUFO said:
...but for photon it maybe just red-shifted instead of slowing down.
Yes, I make the sentence confusing. You see, the "photon is slowing down" I mean here is the consicounce of "slowed movie show". "Photon is red-shifted instead of slowing down" is the way I think that when we apply varieties of time speed, photon will not "slows it speed" but red or blue shifted (but is not same as blue-shifted by gravity).
I am sorry for that because I am not honest with my question... well one thing I didn't mention here is my thought on "expending universe". With idea above, maybe we can say "the universe is slowing down instead of expending". I think that weither the Universe is expanding or slowing down, both are explaining red-shift effect, but make no difference. (And that's why I kept the question unclear)
I just wanted to ask, if this is posible? My another porpose is to learn more about relativity.