If a photon travelled a billion light years to come to Earth, how do those billion years pass from the photon’s perspective?
In: Physics
A photon _does not have_ a perspective.
Answers to questions like this rely on the introduction of a “co-moving inertial reference frame”, which is a mathematical transformation to a frame of reference where the observer is stationary. It’s a core principle of relativity that we can predict the result of observations made from any inertial reference frame using measurements made in any other inertial reference frame. That’s how we can make statements about observations from another observer’s “perspective”: by mathematically transforming our measurements into the co-moving inertial reference frame of the other observer.
But the other core principal of relativity is that the speed of light is constant in _all_ inertial reference frames. That means there is _no_ frame of reference where light is stationary, and _no_ principal we can use to make predictions about observations “from the photon’s perspective”.
Short answer: No
Long answer: A photon’s frame of reference (i.e what would a hypothetical observer riding along with a photon experience) is not ordinary. The notion of space and time as we know it, does not exist. The closest way of imagining it is to say time stops i.e beginning is the middle is the end and there’s no difference along the path. The reason why this frame of reference is not ordinary is because it’s not an inertial frame of reference and the act of measurement itself is not possible.
No, photons do not experience time at all. The closer you go to light speed the “slower” time moves at light speed time stops.
From a photons perspective all things are instantaneous. The photons leaves the star 2 billion light years away and hits your eye at the same instant. The star and your eye are also infinity close together from the perspective of the photon.
TL;RD relativity is a hell of a drug
That time passes instantly for the photon. The moment it is emitted, and the moment it is absorbed, are a single moment when considered from the photon’s reference frame. In effect, photons don’t experience time at all.
The spacetime interval between the photon leaving its origin to arriving at earth is s^2 = ct^2 – x^2, which is equal to zero since x=ct (the photon travels at the speed of light). For any ordinary object traveling at a speed less than the speed of light, the proper time experienced by that object between any two events happening on its own trajectory (world line) is equal to the spacetime interval between the events. It is unclear whether this idea can be extended to photons, but if we assume it can, it means the proper time between the two events is zero. That is, from the photon’s perspective, it leaves and arrives at the exact same time.
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