Imagine a photon reaching the Hubble Space Telescope today had originally been emitted from a star in the early universe 13 billion years ago. Einstein’s Special Relativity tells us, traveling at the speed of light, that from the photon’s frame of reference, no time will have passed for the photon between the moment it was emitted from the star and the instant it was recorded by the Hubble telescope. In addition, at the speed of light, the length contraction (or Lorentz contraction) is said to shrink the distance between these two objects (the ancient star and the Hubble telescope) to zero. But herein lies the apparent paradox in two parts:

1. In the early universe 13 billion years ago when the star first emitted the photon, there was no Hubble Telescope for the photon to instantaneously collide with from its frame of reference. In other words, how can the photon instantly collide with something which won't be invented for 13 billion years?
2. Given the complete length contraction of all points in space to zero at the speed of light, how can a single photon ever be absorbed at any one particular point when, if all distance between points in the universe is zero from the photon’s frame of reference, the photon will hit each and every point throughout the universe simultaneously, not just one?

How to explain this apparent paradox in laymen’s terms.

• For starters, length contraction doesn't shrink the universe to a point, it shrinks it into a pancake. See picture in here (article isn't bad either). askamathematician.com/2011/01/… Try to imagine what happens if you have a space ship that has a switch so it can travel at the speed of light, and look at that from different perspectives. – userLTK Mar 21 '16 at 21:13

And that is why you don't do the calculations in a frame that is moving at lightspeed.

If you have two observers that are moving relative to each other you can use the Lorentz transformation to change between their frames of reference. But if one of the observers is a photon the lorentz transformation becomes singular, because $\gamma$ is infinite. Simply, you can't take a photon's point of view.

You would be much better off not thinking of a photon as a classical massless particle, but as a quantum mechanical particle. In the QM setting, you can take two points in spacetime and say that there is a certain amplitude (a value that relates to probability) for the photon to be at those two points. There is no need to think of it as ever being at intermediate points. I suggest you look up Feymann's book on "QED" for a readable account of this.

• This physics video suggests you can take a photon's point of view: youtube.com/watch?v=BoUc4-q4Ibc. – Treeves3 Mar 22 '16 at 20:12
• @Treeves3 right, and this singular point of view doesn't let you calculate anything, so it's not useful. – Ruslan Feb 19 '17 at 7:44

1) In the early universe 13 billion years ago when the star first emitted the photon, there was no Hubble Telescope for the photon to instantaneously collide with from its frame of reference. In other words, how can the photon instantly collide with something which won't be invented for 13 billion years?

This isn't relevant. Regardless of any "clock" running locally on the photon, it is still travelling for a long time (in our frame of reference) to reach its target (our telescope).

In fact if this paradox were so, it would be impossible to see anything. If say a distant probe transmits a radio signal to us, travelling for an hour or more at the speed of light, our radio receiver would have to be switched on ready to receive long before the message reached it. Again, not true.

So, there simply isn't a paradox.

1) In the early universe 13 billion years ago when the star first emitted the photon, there was no Hubble Telescope

No thats not the case. Theoretically, in photons perspective there will be no present, past and future just like there will be no space across the journey. All the events what we call present, past and future in our inertial reference frame perspective exist altogether in reality. So Hubbles telescope is already there. :)

• What do you mean by a "photon's perspective"? As James mentioned, a photon does not have an inertial reference frame. And in fact, a photon can't be strictly localized in any finite region of space, as discussed here. – PM 2Ring Apr 30 '20 at 10:12
• @PM you're not going to prevent thought experiments with semantics! Further, all that needs to change for the question to be entirely rational is to decouple "you" from a physical entity with mass to a consciousness that exists in one or more photons. All that's relevant here is awareness. So, if a photon were to be able to "witness" things, what would it experience relative to the things it was traveling past at the speed of light? Thats what I meant with the term “perspective”. Although better term could have been ‘lights perspective’ instead of using ‘photons perspective’. – Sazzad Hissain Khan Apr 30 '20 at 10:35
• I'm not trying to prevent thought experiments. The foundation of relativity is that Einstein realised that if it were possible for an inertial frame to have a speed of c relative to another frame then it would be possible to observe a "frozen" electromagnetic wave, i.e., one that isn't oscillating, but such a thing had never been observed (and still hasn't). Thus a rest frame for a photon is unphysical. – PM 2Ring Apr 30 '20 at 11:06
• Bringing consciousness and awareness into it isn't helpful. Current physics has no way of dealing with consciousness or awareness. There isn't even a decent physical definition of them. But aside from that, it's not clear how a lightspeed entity could think. See physics.stackexchange.com/q/54162/123208 & in particular this comment. – PM 2Ring Apr 30 '20 at 11:11
• @PM You forgot to see the next adjacent comment of what you referred. physics.stackexchange.com/questions/54162/… Anyway thanks for your point – Sazzad Hissain Khan Apr 30 '20 at 11:55

I am not sure the attempts to explain away the paradox here actually do work - not least because QED relies on a similar/related paradox - namely that the photon takes every available path to travel from emitter to HST. I think it's more accurate to say that our physics does not yet provide complete answers to this question but that all the evidence we have gathered shows that it provides accurate answers to it.

• There's only a paradox if you insist that a photon should have a rest frame. – PM 2Ring Apr 30 '20 at 11:20