Photons are completely immutable, while they travel they don't change at all, if a photon was a "smergsboard" it would remain "smergsboard" during the whole trip.

One of the most interesting ways I saw explaining this, is imagine 'spacetime' as a cartesian space.

You have 4 axis, X, Y, Z and time.

EVERYTHING has speed of 'c', so you use trigonometry and rotations to figure the values, light, that have a speed of 'c' in the 3 space axis, then obviously have speed of '0' in time axis.

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Now, one interesting application of that knowledge is how they figured the speed of neutrinos... As I just wrote, if something is travelling at speed of light, it is 'frozen', never changing...

But 10 years or so ago people figured that neutrinos change mid-flight, there are 3 (or more... people are unsure yet) 'flavors' of neutrinos, and during tests people noticed that even if you make a machine that generates only one specific flavor, what reaches on the other side is not necessarily that flavor, meaning they changed mid-flight...

But if they change, then they have some speed in 'time', this means then that the speed in space must be smaller than light.

Right now there are couple experiments where people are trying to use the changes in neutrinos to calculate their speed in 'time', and then by elimination figure their speed in space. I find it quite interesting, how people can use math to figure physics when our instruments aren't precise enough.

    (Δs)2 = 0

        It is wrong to then equate this to some sort of proper time Δτ, find that

    Δτ = 0

    for a photon, and thus conclude that photons always "experience" zero proper time. No. Remember that Δτ is defined as the 
    time difference between two events as measured by an observer (i.e., an inertial frame) that actually travels between the events. Photons 
    have no reference frames! So the definition of Δτ doesn't apply to null paths.

But as I was alluding to with my 'tomayto, tomahto' remark, this is a question of semantics, and we're not really arguing about physics, but labels.

If you plug c into the Lorentz transformation you get an infinity, which doesn't tell you anything particularly useful.

There's no physical way to accelerate to light speed, so it's meaningless to make assertions about how the "experience" of travelling at light speed would be different to the (presumably simpler) experience of travelling at < c.

The problem is that relativity is a classical theory, and it says nothing about the underlying physical processes of photon creation/destruction and propagation.

Maybe one day a Theory of Quantum Gravity will fix that problem and provide a detailed low-level picture of what actually happens when things move through spacetime. But we're not going to get there for a while.

In the meantime, we'll carry on using concepts like "position" and "time" without really understanding the mechanisms that generate them.

And if that sounds obvious, it really isn't. It's astounding that the universe knows where everything is and where it's going. Not only does it somehow keep track of all those changing spacetime relationships within a self-consistent system, but it also generates the counterintuitive geometry described by relativity.

How does it do that? No one knows.

It's just a colloquial description of the fact that the time interval between two events along a null geodesic is zero.

Yet it is fascinating that (1) any system of thought (including science itself) must rely on axioms; (2) by Godël's incompleteness theorem, no system of thought can prove its own axioms; and (3) thus it would seem that faith is inescapably required to believe in anything at all.

When evaluating world views, perhaps the best metric is to evaluate which of them requires the least faith.

For my part, when considering the known universe's mere existence, atheism seems to require a lot more faith than theism.

To each their own - but I don't see "There are some things we cannot describe in our system of knowledge" as a particularly strong proof for the existence of God.

Perhaps some of us have been imbued with an unhealthy and naive lust for certainty, in part by an education system that put an emphasis on right and wrong answers rather than on the quest for better questions?

To me, the latter is an encouragement to rationally evaluate existing belief systems against each other, since it reduces all of them to a level playing field. From there, one can apply a simple twofold truth test to each system: correspondence to reality and internal consistency.

There is a world of difference between thinking something caused our universe to exist and perhaps giving it the name "god", and believing in a specific god or specific claims about any god.

2. God is not part of this universe.

3. God, having been the cause of this universe, can be described as all powerful - at least in the same way Big Bang was powerful.

4. God is outside of time.

The above requires no faith at all - to me it's obvious God described in points 1-4 is true.

Now the following requires a degree of faith:

5. God is one, indivisible, at least in the same way a quantum (by definition) is indivisible.

6. God, rather than having zero consciousness, is completely conscious, having equal or more consciousness than all the consciousness in this universe.

If God is all powerful by definition of having caused the universe then I find it harder to believe the specific claim that God in fact, is not conscious, even less than a starfish. And when we are talking about God, it's more likely to be all or nothing, so my specific claim is that God is completely conscious, and being outside of time, all-knowing.

Photons are similar. You see the peak of the wave moving around, but the wave itself is everywhere and eternal... until other forces get involved anyway.

But at the moment when you drop a pebble into a pond, there are definitely parts of the surface which are moving and parts which are not, and the influence of the energy you introduced with the pebble can clearly be seen to spread outward over time.

Granted this doesn't map directly onto electromagnetic waves because the mechanisms involved in wave propagation are different.

We commonly think of time in the linear time line sense.

It's more accurate to think of it as a big mesh of points of interaction.

Think more Cartesian space than left->right