Suppose there is a person who owns a device which can stop and resume time. When the person stops the time, will he be able to see the things around him? I imagine not, because stopping time will stop the movement of photons itself, thus depriving the person of his ability to see. Or, is it such that particles with no rest mass like photons continue to move?
Time to Load Up on Sunscreen
The unfortunate truth is that there is no way to make time stop stories work from a physics perspective. There isn't even a good way to make them work by pretending that everyone else slowed down considerably / the protagonist sped up considerably. It all creates significant physics-related challenges. (this doesn't mean they can't be good stories though!)
Note: This post concerns only vision during a time-stop event. Motion (including breathing) in such a scenario has its own crazy ramifications, but since the question was just about vision that's what I'm narrowing this post to.
To start things off, let's assume that whatever needs to occur within the body of the person able to perceive time "normally" (the "protagonist") just works. Any chemical/electrical/etc. process that occur within the bounds of any cells of the protagonist "just work". That will simplify things considerably and remove a lot of unnecessary discussion.
Within the bounds of that premise, let's look at how to make vision work.
As you suggest, vision requires the continuing motion of photons. Let's further assume that the stopping of time does not affect photons and consider the consequences. OK, but where do those photons come from?
Where Photons Come From
Case 1 of 4 – inside a building, lightbulbs still working
If the protagonist is inside a building and lightbulbs work the existence of photons would suggest that the electrical grid still works. That would mean that, depending on the area, wind, water, gas, coal, solar (etc) power generation still works. Since most of those methods rely on turbines turning, it would seem that time stopped in a very particular way indeed! Even solar power requires chemical reactions to occur.
Case 2 of 4 – inside a building, lightbulbs not working
If the protagonist is inside a building and lightbulbs do not appear to continue functioning, it would suggest that the electrical grid stopped functioning as expected. That would seem the most consistent with time stopping.
Case 3 of 4 – outside, more than 7 minutes of light available
If the protagonist is outside and has more than 7 minutes of available light (the time it takes for the light from the sun to reach the earth) it would suggest that nuclear reactions can still take place. That starts to get a bit awkward, because then we need to start discussing what nuclear reactions do work and which don't – such as allowing fusion but disallowing fission. And you're going to want to disallow fission because otherwise when you re-start time you're going to see nuclear meltdowns occurring all over the world (presuming you stop time for a while).
So this is maybe possible, but you do have to allow fusion to function as usual while disallowing fission.
Case 3 of 4 – outside, less than 7 minutes of light available
If the protagonist is outside and has less than 7 minutes of available light, the suggestion is that time stopping is universal. Interestingly though, if the protagonist stopped time for 5 minutes and re-started it the world would receive 2 more minutes of light before being plunged into darkness for 5 minutes. That would be one way to let the world know that someone with time stopping powers (which oddly does not affect photons) exists!
On What Photon Interactions Look Like
Case 1 of 3
Let's say we take the path that says "photons continue to reflect off of matter, except for the protagonist" because it seems the cleanest. I'm afraid that in such a situation the protagonist will be robbed of the ability to see colors. And what they would see would be insane. Oh, and it would probably kill them. The reason being that the creation of colors is a function of particular wavelengths being absorbed and others being reflected. If no light is absorbed it must be reflected, which would mean everything would reflect as though it were a mirror.
Let that sink in for a second: everything behaves like a mirror. People are 3D mirrors. Buildings are 3D mirrors. Each blade of grass is a 3D mirror. The only thing the protagonist sees then is what is reflected in those mirrors. Note: Because these perfect reflectors are not mirror-smooth they will not generally reflect actual images (though clear glass would become a mirror itself). Due to micro scattering of light, most surfaces would shine white.
If they are on the dark side of earth all they would see are reflections of the stars everywhere, reflected very oddly and generally in a non-distinct way (due to micro scattering). Visually distinguishing up from down could be very difficultand the entire scene would be incredibly confusing.
If they are on the bright side of earth things get a lot worse. As we have already established that the protagonist interacts with light normally, that means they are the only absorber of light within visible distance in a world full of mirrors. The amount of reflected light that hits them would be enormous and quite likely fatal after a relatively short period of time. Even a limited, non-fatal jaunt would likely result in some form of light-blindness (duration and permanence dependent on exposure).
Case 2 of 3
Let's say that you don't want to only see unintelligible stars or suffer immediate blindness and burn to death. Your other option in that case is to have materials absorb and reflect photons as occurs in normal time. This works much better for your character when they are in the "time stop" state.
What works less well is what happens to everyone and everything else. Let's say that you stop time for 5 minutes – a reasonably short amount of time. Over the course of those 5 minutes people, buildings, plants (everything) is going to continue to absorb energy, but won't be processing it in any way as chemical reactions have stopped (if they haven't, people would be walking and talking as normal). Once you turn time back "on" however, those people and objects are all going to receive 5 minutes worth of energy in a fraction of a second.
To put this in perspective, let's say that they receive the full dose of energy in 1 second. Five minutes have 300 seconds. Receiving all of that energy in 1 second would be like putting your skin under a 300× magnifying glass in the sun for 1 second. For an idea of what that feels like, a typical decent-quality hand-held magnifying glass could have a magnification power of 10×… and less if it's a cheap one. This is 30 times more power than that.
Without really going into some calculations I'm not sure what would happen exactly, but I think it's reasonable to expect that a living cell that had 5 minutes worth of good solar energy released in it instantly would die. Even without secondary effects on the next layer of cells (which would undoubtedly occur), the result is that everyone on the sunny side of the earth would simultaneously shed a layer of skin from any exposed parts - yuck! More importantly though, their eyes would also be exposed to that same effect and could be seriously impaired by it. I hope they were blinking when time stopped!
Undoubtedly a number of things would also instantly catch on fire. Piles of cooking flour that may be in the sun, gasoline, hay chaff, etc. Also no fun.
Case 3 of 3
Courtesy of MichaelS in the comments.
In this scenario there is no interaction at all between photons and matter – the photons just pass right through. This is an interesting one because it avoids killing the protagonist or injuring large swaths of people/animals/structures, so maybe it's the way to go?
It depends on what you really need to see. If you really just need to see the sun and other stars this will work great, because there is nothing for the light to bounce off or to absorb it - so all you would see are the light emitters.
The first major downside is that you would only see things that emit light, and by "see them" I mean "see light coming from its location". Visually it would be like being in space, but with the sensation of gravity and the reality of bumping into things you can't see. The sun and stars would also be brighter, but I'm sure you don't want to stare into the sun anyway. The heat from the sun would be worse than standing at the equator at the height of summer and there is no such thing as shade, so I wouldn't recommend existing in such a state for more than a few hours at most or you'll risk succumbing to heat exhaustion.
The most consistent way to "stop time" would be to presume the world is actually a simulation of some kind, and what you have done is to halt the time coordinate in that simulation.
You are now permitted to interact with it using some different simulation layer at a particular point in time. How that simulation layer gives you interaction with the particular point in time is then the question.
If the system was carefully designed for a human-like creature within the simulation to experience it, then they could do a quick sampling of the macro-state and build a high-resolution static model of the universe. Have the "time stop" individual interact with that static model (using whatever rules the simulation chooses for this special case), and have changes propagate in an implemention-defined way when time "restarts" (including, for example, your position).
Such actions would cause arbitrary anomalies. And as physics of the frozen world does not apply while the world is time stopped, nor does it apply to transitions, there isn't much problem.
For a practical example, imagine if a snapshot of the universe's state is taken. The "hole" where you left is filled in with some kind of interpolation. The "hole" where you are is a mixture of cleared and pushed aside.
Physics runs for 10 ns, but with an extra pressure component pushing your matter out of the way of areas of dense matter in the snapshot.
Then the physics is reset with your new position.
Definition of what "you" are varies, naturally. Stuff you shed and absorb is defined through some kind of algorithm or decision process.
In this case, solid objects might to be almost completely impenetrable by the stuff you can manipulate. Air might be a bit thick, and water like molasses. Light mostly works.
But this is because the time stop isn't really time stop, but rather a directed attempt to provide what we "instinctively" would call a time stop experience based off our large-scale illusions of how the world works.
The question here is somewhat ambiguous.
Were you to stop time, you of course won't be able to see anything at all because you wouldn't see the photons.
However, if your story has this level of real-life physics, then you'll have problems trying to describe how you halt time.
If this person truly stopped time, and somehow not stopped time for themselves, then you are right, they would not be able to see. What you see in movies and stories where "time stops", is more of a pausing of all momentum. So things with mass stop moving, but things like photons (massless) continue to work. However, even there, you have inconsistencies, since photons are generated by things like electrons (which have mass) oscillating between energy levels in the atom. Of course, that does not necessarily mean they are moving, but rather gaining and losing energy, which is hard/impossible to picture happening without movement.
Still, I think the inconsistencies at that level would be the sort of thing you can hand-wave away. I think a story that explained that rather than "stopping time" that what the device did was "pause momentum" would be more accurate, to the point of being far more interesting on that score.
I will propose a simple model. Let's say your protagonist is able to create a spherical "bubble" around him, and cause time to flow differently inside and outside of the bubble.
This difference in the "flowing" of time means that all physical processes develop at a different pace. To create the stop effect, the rate at which physical processes work inside the sphere would have to be much faster than the outside rate (infinitely faster if we are talking about true timestop - we will get there).
Let’s keep things very simple. Suppose everything inside the sphere is, let's say, three billion times faster than everything outside, meaning that our protagonist could live an entire lifetime of ~ 95 years while one second passes outside. This means that the energy per unit of (inside) time that will reach any energy collection-detection system (e.g. the human eye) inside the sphere, originating from an object outside the sphere will be three billion times smaller than what would be detected ordinarily. Thus, our protagonist would be pretty much in the dark.
Still, in principle, special equipment could enable him to "see" the outside world - by collecting and amplifying this weak radiation, much like what we do when we explore the universe with telescopes and sensitive energy detectors.
There are, of course, many open questions, whose answers will probably depend on the exact nature of the interface between those two "worlds" and how the light would behave there. For example, do incoming radiation suffer a frequency shift? How is incoming light affected by optical phenomena in the interface (refraction, reflection, diffraction)? Notice that the speed of light in vacuum would have to be different in each world!
In addition, what I described is an extreme slowdown, or apparent timestop if you like, but not true timestop. Each step closer to true timestop takes you a step closer to total darkness - if the world outside does not move at all, this means that the physical processes inside the bubble happen infinitely faster than in the outside, so that millennia would pass without a single electron-volt of energy crossing the boundary...
The question, as posted, makes little sense. As it is written, it seems like you want to know the answer in a hard SciFi setting, i.e., you want to have everything to be real as in our physical world with the little addendum of allowing to freeze time for the whole universe except one little bubble around your own person.
I know that you did not ask whether it is possible, but how one detail (photons) would work if it were possible. This is a rather technical question which could only be answered if we knew how this stuff actually works.
Unfortunately, there is no consensus about what time actually is. See https://en.wikipedia.org/wiki/Philosophy_of_space_and_time for a rather interesting list of possible interpretations. Note that physics doesn't help there at all, so far. It knows a lot about how (space)time behaves, but nothing much more. For example, they don't even know for sure whether spacetime is quantized, what it is "really" made out of, and so on.
For example, neither physics nor philosophy can tell us whether it would be more correct to describe time as in "past - now - future" or only "before - later"; i.e. whether the present moment is something that actually exists, physically (and is different from all moments past and future). It is a pretty interesting idea ( https://en.wikipedia.org/wiki/Eternalism_(philosophy_of_time) ) to say assume there is no "now", and all moments in time (sic) are the same, existing at the same time (sic) etc.. Note that the word "time" is used in different levels in the previous sentence, and the second one actually makes no sense at all.
If you tell us which kind of time you'd like to use in your particular story, people may come up with ideas about whether/how seeing is possible. In a hard science setting: no chance, just pick your favourite handwavium visual effect and run with it. Or invent some witty way to get around the issue. For example, if you were to ask how to stop local time, that would be easy and paradox free (check out "Marooned in Realtime" for a wonderful book about that).
If the stopping of time required photons to stop moving I would think everything would be literally frozen, as in 0 degrees kelvin and then it would cease to exist because if things aren't moving then no forces are working and if force is zero and time is zero and speed is zero and acceleration is zero then mass is zero and energy is zero. Then universe implodes. Maybe?