A photon is moving at the speed of light. Things moving at the speed of light do not experience distance or time (and have no mass), for them their creation and destruction are the same event.
This effect is also valid for objects with actual mass, the faster you go the slower your time moves relative to everyone else and the shorter distances become. You can't hit the speed of light but you can get fairly close.
> A photon is moving at the speed of light. Things moving at the speed of light do not experience distance or time (and have no mass), for them their creation and destruction are the same event.
How does this follow? There is still a traversal of spacetime at a limited speed between the creation and destruction. If the speed of light was infinite then yes I would agree with the proposition that no time or space experienced.
You are offering a description without the explanation.
>There is still a traversal of spacetime at a limited speed between the creation and destruction.
From your point of view, that is correct.
From the hypothetical point of view of a photon, an object moving at the speed of light, time does not pass and the distance gets squished into zero.
You can observe a partial effect by looking at cosmic rays. We can detect several decay products of cosmic rays on the ground despite these decay products being far too short lived and too slow to have actually reached the ground. However, due to their high speed, their internal clock runs "slower" compared to ours and the distance between the top of the atmosphere where they are created in a collision or decay and the ground is much shorter than they can travel at their speed.
A photon experiences the same effect times infinity; distance and time no longer have a reasonable meaning other than being 0.
I'm sorry, I still don't understand and if you can provide me with further material to research I would appreciate it. From my point of view, for there to be 0 time and 0 distance is equivalent to saying the speed of light is infinite, ie. the point of emission is equivalent to its annihilation, but that is traversed at the limited quantity of c.
It's a bit of a hard subject to digest, I admit that.
I guess one thing would be to accept that distance and experienced time aren't objective.
If you move in a train, the time you spend inside the train moving and the distance you cover from your perspective will differ from the time that is shown on the clock at the station as well as the distance between the stations. By a very tiny amount.
This process is exponential, so if you double the speed you travel at (as a number relative to four) the effect on your time and distance covered will quadruple.
When you travel at C, then this effect becomes infinite. Time passes infinitely slow to the point that the time passed becomes zero. Same for distance.
It also doesn't mean the speed of light is infinite, rather, from the perspective of the photon, ignoring the time part, the universe is exactly 0 in size. In turn that means travelling to some point in the universe, from the perspective of that photon, is instant. From the perspective of the outside observer, the photon is not traveling 0 distance, it's moving at the speed of light to a far away destination. From the photon's perspective, it's speed is not infinite, it's not moving at all, it's created and annihilated at the same point in space and time. From ours it's moving at the speed of light for a long time.
Because these are different frames of reference, it's not as easy to compare speeds experienced in one to the other, especially if one is moving at C relative to the other.
(Simplified) The entire affair is necessary because only things not having mass can move at C (and in turn, must move a C, a massless particle like a photon must always move at C). The entire rest of the universe has mass. From the photons frame of reference, everything else is moving at C. But that isn't allowed because that stuff has mass. So space itself is compressed into a 0 sized point to stop things from moving at C (from the perspective of the photon). Now, the photon however wouldn't be moving because in 0 sized space, you can't be moving at the speed of light. So in turn, time is experienced instantly and the photon is annihilated instantly so it can actually move at C (because it didn't move at all, it was destroyed instantly). In short; the photon doesn't experience time or distance because if it did it would be slower than C, it must always move exactly at C, therefore the universe arranges a situation in which the photon doesn't have to move at all, from it's own perspective.
We can parameterize any curve in 4-d spacetime with a smooth and monotonic function that maps points on the curve to real numbers. In fact, you're doing that in the text above without realizing it: the function in question is proper time.
It's fine -- commonplace, even, especially in the uncurved spacetime of Special Relativity -- to use proper time to parameterize a timelike geodesic. However, those are far from the only curves in a metric-equipped spacetime.
In particular, for a null geodesic -- a freely-falling path taken by a photon -- proper time won't do as a parametrization because proper time is zero everywhere along it. However, there's nothing particularly unusual about a photon's worldline: it's just a curve where at every point along it the tangent vector is a light-like vector.
On the other hand, along such curves we can use an affine parameter. Wald does this in his _General Relativity_ textbook this way: a geodesic is a curve whose tangent vector satisfies T^{a}\nabla_{a}T^{b} = 0 \RightArrow T^{a}\nabla_{a}T^{b} = \alpha T^{b}, where \alpha is an arbirary function on the curve. We can always reparameterize the second version into the first -- any parameter satisfying the first version is an affine parameter. We can equivalently say g_{\mu\nu}\frac{dx^\mu}{ds}\frac{dx^\nu}{ds} = 0 for all s, where g is the metric tensor and s is an affine parameter along the geodesic x(s). There's some greater depth starting at https://en.wikipedia.org/wiki/Geodesic#Affine_geodesics
Affine parameterization lets one calculate the behaviour of photons moving through curved spacetime. If we define momentum with respect to the affine parameter derivative like this: k^{\mu} = \dot{x}^{\mu} then we can take the affine parameter value at one point on the geodesic and use that value's derivative at a different point on the geodesic, giving us a momentum difference between the points that is physically the gravitational redshift or blueshift. Additionally, if \alpha = f(x) then k^{\mu}(x) encodes the photon's momentum components, and from them we can extract the relation E = pc.
It doesn't matter that the photon has no proper time because the proper time isn't really physically meaningful. We can still slice up the photon's spacetime into time-indexed 3d spacelike hypervolumes and (for a Eulerian observer at rest in this time-indexing) see that the photon is more red in the slice at time t and more blue in the slice at time t'. We can moreover, thanks to the affine parameterization, calculate how much redder it is at time t and at time t' for arbitrary observers, just like we can calculate the length contraction of a massive object or the time dilation of a clock using their respective proper times.
> the universe arranges a situation in which the photon doesn't have to move at all, from it's own perspective
No, you've chosen to use concepts from Special Relativity in a limit in which you get yourself into trouble. The photon has a non-zero-length worldline, and you can slice it arbitrarily; you're not restricted to the one unique slicing in which you are least able to talk about its evolution.
Let's see if we can expand your understanding a little, if you like. I'll also try to make some sense in case someone else sees this in the future.
The tl;dr (cf final paragraph below) is that even though it is hard to make sense of a photon-with-wristwatch (does it ever tick?), General Relativity is a theory in which we can calculate the behaviours of an object travelling at the speed of light interacting with other things travelling at the same speed or slower. Moreover, in General Relativity light can redshift and blueshift due to local gravitational influences and by travelling cosmological distances through the metric expansion of space. We may need to know how much redder it is at some point in spacetime compared to some other point in spacetime, and to some extent that question depends on the photon and its history. We can make sense of the history part as follows:
First think four-dimensionally. Rather thinking of the propagation of than an object with some spatial extent from point A in space to point B in space at a later time, let's start with a pointlike object, literally of dimension zero.
Let's promote this 0-d object in 3-d space to a 1-d object in 4-d spacetime. That promoted object is a worldline. Points A and B are now simply two different points on the worldline.
Now we need a distance function along the worldline. As we're interested in the distance between A and B we want to choose any arbitrary function that gives a monotonic value along the worldline, for example starting with 0 at A and ending at some larger number at B, with every point in between having a value between 0 and the value at B.
If our worldline is everywhere timelike then we can simply extract the proper time at each point on the worldline from the line element of the spacetime's metric.
However, for a photon, the worldline is everywhere lightlike, and the proper time is undefined at every point, so we can't use it.
Attempting to reason about this, by for example setting the proper time to the same value (e.g. zero) everywhere on the worldline, leads to incorrect conclusions in your explanation a couple postings back.
Instead, we can choose an arbitrary function. The requirement, again, is that the value at A is less than the value of B and every point inbetween along the worldline. We can without difficulty do better than using a function that returns an undefined or identical value at A, B and points inbetween.
Ideally we can choose a function that gives a number at every point on the worldline, even extending beyond A or B, and which we can relate to the the curvature of the spacetime in which we find our worldline. If the interesting part of our worldline is always on a single null geodesic, then there is a good choice of function: the affine parameter. It satisfies the geodesic equation, and gives the right tangent vector for anywhere along the geodesic.
Decomposing back into our 0-d particle, this means that at any point in anyone's time, one can use the affine paramater on the 0-d particle's trajectory to figure out how its vectors parallel evolve between two points on that trajectory. Indeed, an observer from her or his perspective can predict where the particle will go, and where it has come from.
An object with spatial extent goes from a worldline to a worldtube, but the principle is the same: each point on the worldtube can be distinguished using an appropriate function. For a photon, we still use the affine parameter, because photons travel on null geodesics. They just freely-fall through curved spacetime until they have some direct interaction; that's all being on a null geodesic means.
In a spacetime with timelike worldtubes and lightlike worldtubes we have a network of intersections in spacetime, and we are interested in the behaviours at those intersections. Anyone can apply an arbitrary system of coordinates -- or distances along each intersecting worldtube -- and calculate physical quantities at the intersection points in spacetime. Because these intersections are in spacetime there is no "I got to that point in space first and just missed it"; time really doesn't matter -- the point is that at the same point in spacetime, two worldtubes interact.
General Relativity (in our 4-d universe) almost always lets us build a small region of locally flat spacetime around such an intersection, such that we can then use the Special Relativity background for calculations. The Standard Model, Quantum Electrodynamics, and other relativistic theories describing light all work in this flat-spacetime Special Relativity bubble, even if the wider spacetime is curved.
Alternatively, we know how to foliate spacetime along well-chosen timelike axes, which also slices all worldtubes into objects of spatial extent moving from one spatial slice of spacetime to the next. This is a 3+1 formalism on General Relativity, but it's important that it's still General Relativity with worldtubes on curved spacetime (which has a metric for which we can find lightlike and timelike geodesics). But even in such approaches we don't have the behaviour photons making no sense against the chosen timelike axis. Indeed, we can look at the lapse function which generates a proper time increment even for photons: \delta\tau = \alpha(t,x)\delta t.
In physical cosmology, we can slice up our universe along a time axis called the scale factor, and then we find a lapse function (and shift vector) for everything in the spacetime. A free-streaming photon's worldtube has properties (e.g. wave-vector) that are well defined at each scale factor.
Whether a cosmic microwave background photon can ask itself whether it feels tired (redder) as we take the scale factor closer to our present day, or otherwise check a "scale factor wristwatch" or look out the window to see where the horizon is, is really a problem for metaphysics. We can calculate it in General Relativity, and work out that it is redder today than it was at the surface of last scattering. Moreover, we can calculate counterfactuals: a CMB or quasar photon that freely streams to us along a path that never takes it near a galaxy (other than ours) versus a CMB or quasar photon that takes a trajectory that brings it near a massive galaxy or cluster will have different redness on arrival here. Compare the redness to a clock-on-spaceship: along the first trajectory nowhere near massive objects, we get one reading of the clock on arrival, but along the trajectory which passes near the massive galaxy or cluster we will have a different (earlier) reading. The second clock ticked slower because it went near a massive object. The second photon is redder because it went near a massive object.
