What does the frame of reference of a photon look like?

There are two ways of looking at it. One is to see how quantities vary as you go really fast. Then, for some things, you can say that there is a limit at c. You could conceivably get very, very close, at least in thought. However, there are other things that don't change at all. The absolute value of an interval, for instance. There's nothing you can do about that; no matter how much you step on the gas, you aren't any closer to changing the fact that it will always be the same. For those things, I don't think you can do much. Oh, and another thing that irritates some people. Any signal going less than c traverses what is called a time-like interval, which means, approximately, that it's going faster through time than it is through space. That seems funny, because it's not like our ordinary idea of "fast" is space compared to time. However, it you can get your head around it, it works better. Why is dime dilated when something moves? Well, it's "motion stick" has turned from pointing straight in the time direction so it can point a bit in the space direction. You can actually think of it as a kind of rotation, only you have to use hyperbolic instead of circular sines and cosines and all that to do the trig in the time direction. ETA: I realize I didn't explain what an interval is. It's a distance in space and a distance in time. So, say I fart, and somebody in London farts two seconds later. That's an interval. Moving things cross intervals. You leave Florida now, and you arrive in New York a couple of days later. There is distance in time and space. Under relativity, times change and distances change, but when you take them together as an interval, the absolute value doesn't change. That works for light, too. The absolute value of the interval between two events connected by c doesn't change, so c itself doesn't change. All the things in your past and future, such that there is a time-like interval between them, are said to be in your light cone. That's because it looks like a cone when you draw it: Of course, it would really be a 3-cone rather than a 2-cone, but they're hard to draw. Note that almost everything in the universe is outside your light cone. It is neither in your future nor your past. My first materials science teacher at MIT said that, since an ice cream cone is only a half cone, you should pay half price. He also pointed out that a full cone wouldn't work, because the ice cream would fall out, and you'd have to put mashed potatoes in instead. End ETA. There really isn't any such thing as the frame of reference of a photon, but if you go really fast, you can imagine the limit. The universe would collapse to a plane. Which is kind of fun to think about. Two dimensions would go away completely, but it would seem you could still do calculations on the other two. What would that look like? What would it mean? Sometimes I get the inchoate feeling that the idea of a photon traveling is the wrong way to look at it. I'm not smart enough, though, to figure out a better way.

I don't know why questions about moving at or beyond c is such a popular question on Quora. It seems so simple. You recognize the question is meaningless, yet you ask it anyway. The theory says you can't have such a frame, so obviously the theory is not going to be helpful in answering what happens when the theory is violated. That there is no frame in which a photon is at rest is a postulate. That is, we have nothing except a finite number of observations that are consistent with it. There is no theoretical basis for it. The theory springs from the postulate, so the theory cannot explain its own assumptions. Many people think of c as some kind of barrier, like the sound barrier; that as you pumped more energy into your rocket engine your speedometer would go up and up and up until it asymptotically  approaches c but can never reach it. This is an incorrect interpretation. In relativity, I can go arbitrarily far in an arbitrarily short amount of time. I could eat breakfast on earth and be at alpha centauri before I was hungry for lunch. Observers on earth would say it took a little more that 4.3 years, but since my clock only ticked off a few hours they say it is slow. For me, it turns out a.c. is much closer than earth observers say because of length contraction, so I can reach it much sooner than 4.3 years without ever exceeding c. Tit for tat. But not only can't you catch up with a photon, you can't even approach one. No matter how fast you go with respect to some reference point, your measurements of the speed of light will always come up as c.  So its not like you can almost get into the frame of a photon, you are always just as far away as it ever was. When you measure the speed of light, you are doing an experiment to determine the value of the universal constant c, and just like the charge of the electron and other universal constants, the value does not depend on the speed of your laboratory.

"It came to me that time was suspect!" - Albert Einstein - Food for thought :: Say you take a massive particle, which has three degrees of spin freedom and thus can be brought to rest in three dimensional space, and rotated in three directions, and you put it in a giant particle accelerator determined to push it to the speed of light, which has two degrees of polarization, so it can only be rotated in two directions, perpendicular to its motion. Matter particles are also matter waves, with a de Broglie wavelength. Once you gave your matter particle enough energy - momentum to have a de Broglie wavelength near the Planck scale, the energy - momentum density in spacetime would be high enough to form a black hole. However, above a certain energy scale, the Higgs boson would decouple from the gauge field, and your matter particle would lose a degree of spin freedom, going from three to two, hence would be invariant only in two directions, not the three required for rotational invariance in the rest frame of a point particle. Hence, in a sense, losing that extra spin degree of freedom would require the newly massless particle, like a photon, to go the speed of light. The constancy of the speed of light is a postulate of special relativity; reasoning about the constancy of the speed of light within the special theory of relativity yields singularities and logical contradictions, as you would expect. The ticking of clocks and length of measuring sticks is defined in terms of the speed of light. Special relativity is a relative theory, after all, where light plays the central role. For a photon, proper time is zero but also singular because proper time is also defined by the speed of light. We do not know a deeper theory that explains the constancy of the speed of light: if we did, then we could answer your question. All we can say now is that a photon can find no rest. We did, however, use the concept of spin here to learn some more about the problem and the question than can be learned purely from the theory of special relativity. Spin is a purely quantum mechanical phenomena, and hence is "outside" the special theory of relativity. In fact, spin is a natural consequence of putting special relativity and quantum mechanics together in a logically consistent way, as exemplified by the famous Dirac equation solutions. Physics, nature is a tapestry. Taking limiting cases is typically extremely useful, but you must know when it has limits. In particular, singular quantities typically signify that your theory does not contain enough knowledge to answer the question. Case in point. Let me finish with some references, since my explanation might seem somewhat esoteric. The following book will help you appreciate what I am saying in detail, far better than I could in a Quora answer. Relativity :: John Wheeler and Edwin Taylor, Spacetime Physics N David Mermin, It's About Time Quantum mechanics, symmetry, Higgs mechanism and symmetry breaking :: JJ Sakurai, Modern Quantum Mechanics Tony Zee, Quantum Field Theory in a Nutshell

What did the proton say after traveling across the universe for thirteen billion years? "Is it just me? Or did it suddenly get a lot redder in here?"