could a strong gravitational wave speed up the speed of photons traveling inside it?
General relativity. The stronger the gravity the slower a clock with the photon is perceived to run from an exterior point of view, say the earth, when the photon passes close to the sun, a black hole, Jupiter, or a distant galaxy that is in the observers line of sight.
Hey I just be a retireded coal miner trying to learn this stuff. Is my view even close?
To be clear, I do not know from what point of reference a speed change is observed in your query. A photon is traveling at c.
Indeed. A photon always travels at c, but measuring distance in GR is a tricky business. For a given measurement method, a photon can easily cover the distance you measure in less than the proper time that you expect.
Is not the gravitational lensing a perceived slow down of light?
Like I said, depends on your definition of (non-infinitesimal) distance. It's probably more accurate to say that gravitational lensing increases the proper distance that a light ray would have to travel through.
How is that determined? Is not distance bound to time in GR?
In a nutshell, if you use local clocks and rulers, the speed of light is always exactly 'c'.
When people talk about gravitational lensing being light "slowing down", they are not using local clocks and rulers. Since clocks can be said to tick at different rates in GR (think of gravitational time dilation, as in the Harvard clock tower experiment), it matters which clocks you use - the constancy of 'c' by local clocks and rulers implies the non-constancy of 'c' using remote clocks and rulers.
The fact that one can reasonably use different clocks and rulers to describe the same physical situation has the potential to cause a lot of confusion, unfortunately, but I don't see any way it can be avoided.
This may be "too much information", but what is really meant by "clocks ticking at different rates" is that the ratio of coordinate time to proper time depends on the position of the clock. This is rather similar to the way that the distance a degree of longitude on the Earth corresponds to different distances, depending on exactly where you are. Near the equator, a degree of longitude is 60 nautical miles, but at higher latitudes it is a shorter distance, approaching zero if you're near the poles. The situation with clocks is similar - to compare distant clocks, one must introduce a coordinate system, and what is meant by "gravitational time dilation" is the ratio of the time the clock keeps (i.e. the proper time of the clock) to the coordinate time imposed by the coordinate system.
This may be "too much information"......
Not at all so far. In fact I am done in this thread you have coordinated my view quite nicely. Thanks much.
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