Couple of questions

[DDPP]

First, let me say I love astronomy cast. I discovered it only last week or so, and I've already listened through all of them. I'm going to have to listen to some of them again though... some of these concepts are hard to grasp.

Anyway, I have a couple of questions.

fist... Let's imagine we're a photon traveling through a vacuum. Since we are traveling at the speed of light (duh), and time slows down the faster you go, does that mean that photons "experience" no time? or I guess I should say they experience a fraction of a second as an infinity of time... or how does that work?

second... I hear photons are massless, because if they had any mass, it would have to be infinite because of the speed it's traveling at. How is it that photons can push things with light pressure?

and finally... if the universe is expanding and the further away a star is the faster it appears to be expanding, how does that affect light? shouldn't it appear to slow down because it has to travel longer? it's kind of like a treadmill. The space is "pushing" the photon out as it expands, so shouldn't it affect the APPARENT speed of light?

I have more questions, but I guess I'll save those for later :P

[astrohou]

Notation: the "$...$" term is the mathematical formula expressed in LaTeX form.

Your 1st question: yeah, you are right:clap: . Let's consider it in the following way. The speed of light is "c", which can be expressed in 4D flat space-time (Minkowskian space-time) as $dx^{2} + dy^{2} + dz^{2} = c^{2}dt^{2}$. In general theory of relativity, space-time is defined by metric. An infinite small Minkowskian space-time interval can be expressed as $ds^{2} = -c^{2}d\tau^{2} = -c^{2}dt^{2} + dx^{2} + dy^{2} + dz^{2}$, where \tau is the so called "proper time". The proper time in a certain inertial frame can be measured by a "clock" relatively stationary to this frame. So, in such circumstance you mentioned in your question, $ds^{2} = -c^{2}d\tau^{2} =0$, obviously, $\tau = 0$. The proper time of photons is zero. That is to say photons "experience" no time.
While in general, the metric is expressed as $ds^{2} = -c^{2}d\tau^{2} = g_{\mu\nu}dx^{\mu}dx^{\nu}$, where $g_{\mu\nu}$ is the metric tensor with its diagonal components (-1, 1, 1, 1) in Minkowskian space-time.

Your 2nd question: it's quite sure that photons are massless or its "stationary mass" is zero. However, momentum of photons "p", also the identifier of photons energy with $E = cp$, is not zero. We consider a photon scattering process by momentum theorem. A photon scattered by a particle maintains its magnitude of momentum but the direction of momentum. So its momentum has been changed. According to momentum theorem, there must be force acted on the photon, so did the particle. Therefore, the so called light pressure come into being.

Your 3rd question: I'm not sure. Recent opinion was convinced that the expansion of universe doesn't affect the speed of light, but the energy of photons. However, as the quantum field theory's point of view, the speed of light is determined by the property of vacuum. Vacuum is such a fantastic thing that few people could know exactly, thus, at least I can't confirm the effect of expansion to the speed of light, especially in the extreme early universe.:think: