Say I have 100 particles in a vacuum that are spread out such that their movement caused by a time variant electromagnetic field does not have an effect on each other. That is the particles can not exchange any energy among themselves. The varying electromagnetic field must be experienced in quanta (a photon particle). Does this mean that it will take at least 100 photons worth of light to excite all the particles?
Let us be clear of what type of particles we are talking about. At the atomic and elementary particle level the quantum nature of light is important. At the macroscopic level it is meaningless to talk about photons because the macroscopic wave is composed out of zillions of photons.
Let us take a hydrogen gas in a vacuum tube. It is neutral and not interacting other than with the random scatters of the gas molecules.
A single photon can interact with the spill over electric field of an atom , lose part of its energy, and continue to hit another atom or even more as long as it can find one and there is enough energy left to the end photon. Now the probability of this happening has to be computed given the boundary conditions of the density of the gas, the volume etc etc.
The answer for single photons impinging on 100 neutral atoms/molecules is that fewer than 100 might do the job.
Yes, it must happen at once.
From the point of view of the EM field, you have created one large entity - so it can only react as an entity.
You confuse the issue by assuming that the energy required to get to the next energy level for this object is 100 times that of one particle. The arrangement could be anything, and indeed, larger objects usually have smaller energy steps to get to the next level. So when the object is excited, the individual particles don't notice anything, in much the same way as a passenger on an jet does not feel the effects of the air hitting the craft at 1000km/hr.
A single photon is absorbed by a single 'thing' at once. Whether that thing is made of 100 particles, or a trillion does not make a difference. An atom absorbs a photon, changing its energy level, not an electron. Or you can have a molecule absorb a single photon.
When you say the particles cannot interact, yes it will take at least 100 photons to excite all the particles. You could have one particle absorb a photon, then radiate a lower energy photon that is absorbed by another particle but you have ruled that out by saying no interaction.