Is the light from the Sun the same as the light from a bulb?

What we experience as light are photons impinging on our retina. First we must understand the distribution of photons, and see if they are the same.

You are right to say that the spectrum of light from the sun is different that that from a light bulb. The solar spectrum compared to an incandescent bulb (the ones with a filament) looks like this:

We see both the sun and the bulb pretty much emit photons all over the UV/Visible/InfraRed spectrum. But, do so at different intensities. That means there are a different number of photons of different colours impinging into your eye. So the total light, or the spectrum of photons, is not the same. But, what about the photons themselves?

So are these photons the same - the short answer - no.

The long answer is that photons have other features you can detect, for instance, the polarisation (the direction in which the electric and magnetic fields oscillate). Further, the photon has a "length" of the wave packet but this cannot be measured directly.

For the example you give, the photons from the sun and the bulb would have a broad range of polarisations and "lengths".

But, let's consider if we could make them all photons the same, i.e. can we make them indistinguishable? As photons are bosons, you can put them into the same state and if you did this - you'd get a laser. The photons here have the same wavelength and polarisation but would have a slight spread of energies. We can take this idea further and consider a bose-einstein condensate of photons, only then would all the photons be doing the same thing.

So, to summarise, when you have lots of photons, you can make assumptions where the light come from because of the spectrum, but if you were given one photon which could plausibly be produced from the sun or the blub, it would be impossible to tell if it came from a filament or the sun.

Edit: correction for incandescent light bulb

She's right that there's a difference, and you are right that it's all just electromagnetic waves!

The key to this is that there is no such thing as "white light" when you really get down to it. Each light emits a range of wavelengths of light. If they have a sufficiently even distribution of wavelengths, we tend to call that light "white," but we can only use that term informally.

Both the sun and the light bulb emit so-called "Blackbody radiation." This is the particular spectrum of light that's associated with the random thermal emissions of a hot object. Cool objects tend to emit more of their energy in the longer wavelengths like reds and IRs, while hotter objects emit more energy in the shorter wavelengths like blues and UV.

(Note, there are other possible emission spectra, but those are associated with different materials doing the emissions and, for the purposes of this discussion, they aren't too important. We can just claim the emissions are all blackbody)

If you notice, as you get hotter, a larger portion of the energy is emitted in the blue, violet, and ultraviolet. That's how you get a sunburn from the sun. It's harder to get a sunburn from an artificial light, not because it's artificial, but because those lights are almost always cooler than the sun. They don't have as much UV content. Instead, they have more red and yellow, which incidentally is why pictures taken indoors look very yellow. If you use a strobe, however, all those yellow hues go away because a strobe light is very warm, with lots of blues.

You can get a sunburn from artificial light, of course. Tanning beds are the obvious example, but there are other interesting ones. When you're a jeweler working in platinum, for instance, you need to wear UV protective gear (like glasses or even sunscreen). Platinum's melting point is so hot that it actually emits quite a lot of UV light and can give you a sunburn!

Other than these spectra, there is nothing different between light from an artificial source and light from the sun. Photons are photons.

The sun puts out about 8% of its energy in UV (which does the damage), about 44% in visible, and the rest in IR. A standard incandescent puts out effectively no UV, 10% visible and the rest in IR. Halogen lamps can be operated at higher temperatures with a reasonable lifetime, and produce some UV, with perhaps 15% visible.

The difference is expressed in terms of the temperature of the emitting surface. The sun is effectively at about 5500 degrees K, while a normal incandescent will run about 2700 K, and a halogen about 3000 K.

On the one hand, in principle it's "simple" to produce a lamp with light essentially equivalent to sunlight - just run it at 5500 K. Problem is, no known substance will take that heat without melting.

On the other hand, there are a large number of M class stars with a surface temperature of about 3000 K (not ours, of course - ours is a G class). Tourists to a planet in orbit around an M class would not need sunblock, for the same reason you don't need sunblock under incandescent lighting,

So, no, incandescent lighting is not unnatural or artificial in the sense your friend thinks. The same cannot be said for most white LED bulbs, which have a spike in the blue portion of the spectrum, and this does not occur in nature.

Either light from a bulb, or light from the Sun, will illuminate my path well enough that I can avoid stepping on the cat. In that sense, they're the same.

The light from the Sun has a color blip, right where early atomic physics suggested the element with two protons in its nucleus would radiate. That element, called Helium (from Helios, Greek word for the Sun) really does exist.discovery of Helium

There isn't any of it (nor evidence of it) in light from a typical light bulb. So, in that sense, light from the Sun and from a light bulb are NOT the same.

Here are already several good answers, but one thing hasn't been addressed, which might be what your friend refers to. The Sun and an incandescent bulb both emit (close-to) Planck spectra (as shown in Tomi's and Cort Ammon's answers). In contrast, fluoerescent bulbs, or tubes, emit spectra that have multiple spectral lines. Depending on which gas is used in the tube, or what material the tube is coated with, various spectra can be achieved.

The color perceived by humans depend on the ratio between the intensity at three wavelength intervals in the blue, green, and red range, respectively. This is because we only have three different color-sensitive photoreceptor cells, called "cones" (in contrast, dogs only have two types of cones and thus lack one "color dimension", while butterflies have five, and mantis shrimps have 16!).

This means that different spectra can be percieved by humans as the same color. An example of a typical fluorescent lamp is shown below. On top of the spectrum, I've drawn the three spectral ranges that humans are sensitive to. The lamp spectrum is seen to have some larger peaks in the blue, green, and red range, and humans would interpret this roughly as "white". But the same color could be made — "artificially" as your friend might call it — with some other lines, e.g. with the line labeled "5" replaced by two smaller lines to either side and with slightly different peak ratios. Or, with a Planck spectrum of roughly 6000 K.

^{Spectrum of a typical fluorescent lamp (black), and sensitivity curves of the three different human cones (blue, green, and red). Source: Wikipedia + my own hand-drawing.}

Your friend sounds like an interesting person to have an argument with but I suspect that the lovely graphs from the other replies are not really going to help you. One comment was about UV tanning lamps. This is the way to go with your friend, bring other examples into the discussion so you can illuminate (!) exactly where her artificial/natural ideas come from. I am thinking light from a candle, light from a fire/flame, lightening, electrical sparks, moonlight, reflections from mirrors, stars in the night sky, etc. You should then be able to find out where her (fuzzy or fixed) boundaries are and tweak the discussion accordingly.

If you look at it photon-by-photon, you could not tell the difference between sunlight and laserlight or candlelight. An analogy: if you only looked at one molecule in ice, you could never be sure it was not steam. some molecules in steam are moving very slowly, and some molecules in ice could be moving, for at least a short time, very quickly.

It is only the statistical distribution of the speeds of the molecules that makes a difference between ice and steam. (And either one can burn you.)

Similarly, there is a vast and very practical difference between the statistical distribution of the photons in sunlight and the photons from candlelight.