# What would happen if photons had a mass equal to 1/100 of a hydrogen atom? [closed]

As we know, light has no mass. Well light having mass is the primary problem with fast(er) than light travel. Thinking about this classic, yet sad problem made me wonder, what would happen the the world if light photons suddenly had equal mass of 1/100 of Hydrogen atoms?

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## closed as too broad by JDługosz, fi12, Aify, March Ho, Scott DowneyMar 8 at 10:06

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I'm sure somehow everything as we know it would cease to exist. – bowlturner Mar 7 at 19:18
Would they still travel at light speed? – Rob Watts Mar 7 at 19:34
@RobWatts You suggest "light not travelling at the speed of light"? – Hohmannfan Mar 7 at 19:39
This sounds like a question for xkcd's: what-if – DJ McMayhem Mar 7 at 23:06
@sdrawkcabdear: The idea of using the relativistic mass equivalent as per $E=mc^2$ as actual mass has been dead for decades. When a physicist today says "mass", they mean by definition the invariant mass (which is not a rest mass for a photon because photons do not rest. They always move at the speed of light, as everything with zero invariant mass does), see this answer at physics.SE. – ACuriousMind Mar 8 at 1:36

### Note that introducing a mass for the photons would have fundamental implications on the electromagnetic force and thus large consequences on many parts of the physics as we know it.

But that has been treated by other answers or in the comments below.

But if, out of curiosity, we handwave that away, we can see that there would be a lot of implications of this that you have to take care of otherwise, as @bowlturner suggested, the result is massive destruction. For example:

# Doomsday 1

According to someone on Reddit's calculations as a rough estimate, $10^{17}$ photons hit a square centimeter in full sunlight each second. That converts to $10^{21}$ photons per square meter.

Now consider your heavy photons. Using the non-relativistic calculation for kinetic energy (note that the relativistic calculation would be even greater), we get $K=0.5mv^2=0.5mc^2\approx 7.5\times 10^{-13}~\rm J$ per photon.

That means each square meter will be receiving about $7.5\times 10^8~\rm J$ per second. Compare that to the $6.3\times 10^{13}~\rm J$ of the nuclear bomb that was dropped on Hiroshima. We're getting that much energy per $10^5$ square meters of area, or the area of circle with a 178 meter radius. The initial fireball produced by the nuclear bomb was 370 meters in diameter. So the energy delivered is comparable to that of being near ground zero of a nuclear explosion.

Keep in mind, that's the energy delivered per second by your heavy photons.

In other words, the Earth is going to be obliterated. Absolutely and completely.

# Doomsday 2

Another issue with the first scenario is that it violates conservation of mass and energy - a lot of it suddenly comes out of nowhere. Let's try slowing them down enough that their kinetic energy is equal to the energy they had beforehand.

Using a photon somewhere in the visible spectrum, $0.5mv^2=K=E\approx 2~\rm{eV}=3.2\times 10^{-19}J$. Solving for velocity with the heavier mass, we get $v=138~\mathrm{km/s}\;.$ That doesn't sound so bad.

...until you notice that that's less than escape velocity from the sun's surface (617km/s). Also, from the Earth you only need to go 42km/s to escape the Sun's gravity well, so going 138km/s isn't going to be enough to get a photon from the Sun to the Earth.

So photons can't reach the Earth, the Earth goes dark and freezes, and everybody dies. Whoops.

# Doomsday 3

Okay, so what happens if instead of reducing their speed we reduce how many there are? Using my previous estimate numbers, $3.2\times 10^{-19}~\rm J$ per photon compared to $7.5\times 10^{-13}~\rm J$ per heavy photon means a reduction to about one one-millionth of current levels.

Of course, that's way higher than the bond dissociation energy of any known type of bond. So rather than being absorbed and providing heat, these photons are going to be blowing chemicals bond apart. So the photons are still deadly.

# Doomsday 4

In each of the above scenarios, I've intentionally ignored quantum mechanics. What happens if we take quantum mechanics into account?

Well, photons are electromagnetic waves, so that means the electromagnetic force is affected. That affects how electrons are bound to an atom, and how atoms would bind together to form compounds.

So if you aren't going to handwave away quantum mechanics, all molecules are going to just kinda fall apart.

Note that in each of these scenarios I'm only focusing on a single aspect of why things would go horribly wrong. There are going to be additional things causing havoc that I haven't mentioned, such as in the first scenario the ramifications of conservation of mass and energy no longer being true.

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This is completely wrong. You can't just calculate the impact of massive photons without acknowledging that a massive mediating boson would introduce an exponentially decaying factor into Coulomb's law, and effectively making the electromagnetic force more akin to the weak force, which is completely invisible at the classical level (with the low mass in the question, it might be a bit more visible, but none of these scenarios actually reflect what would happen). Without long-range (i.e. massless) electromagetism, the world as we know it, even atoms, would not exist. – ACuriousMind Mar 8 at 1:12
@ACuriousMind That's why I have my note - I know there are a lot of other reasons why this is going to be a disaster, but I'm not going to be able to cover them all. Also, it's just as easy to say that somehow the electromagnetic force is unaffected as it is to say that photons suddenly have that much mass. – Rob Watts Mar 8 at 2:25
I have downvoted because the question is tagged "science-based" and this answer is flat-out wrong scientifically. You've manipulated equations with no respect to the underlying physical phenomena. – ApproachingDarknessFish Mar 8 at 3:23
Photons are inherently quantum mechanical. At the classical level, there are no photons, just the electromagnetic field, and the classical effect of massive photons would be a short-range electromagnetic force. You're applying a purely classical thinking to something that doesn't even exist at the classical level. That's not science-based, it's scientifically inconsistent. – ACuriousMind Mar 8 at 10:24
He's not talking about fixing everything, he's talking about understanding the raw basics of what a massive carrier boson implies. This isn't nth order stuff, it is the very first thing that needs to be considered. – dmckee Mar 8 at 21:18

Very not good.

In quantum field theory, interactions are mediated by force carriers. The range of these force carriers depends on their mass. Photons are the force carriers for electromagnetism. Being massless is why EM has an infinite range.

Mass would change that.

All of electromagnetism would be range limited, and to fairly microscopic distances. The earth's magnetic field would vanish, and magnets would stop working, because they can no longer affect things at a distance.

The only things that could produce light would make light with wavelengths in the gamma spectrum of energies. Normal light wouldn't happen.

Photons wouldn't travel at c - in fact, it doesn't solve the speed limit problem.

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This is the correct answer. Modifying the mass of the photon has far more fundamental impacts on the way electromagnetism and in particular propagation of light work than the silly doomsday scenarios in the currently top-voted answer. – ACuriousMind Mar 8 at 1:09
Also, most chemical bonds depend an interactions between electrons. For that matter IIRC the electric charge has something to do with hadrons and electrons forming atoms. Essentially all matter would be plasma. – Ville Niemi Mar 8 at 9:50

What's the difference between electromagnetism and the "weak" force? Mass! Massive bosons would mean that the electic force would have a short range. This would mess up the existance of atoms.

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I need no stinkin' atoms! – Hohmannfan Mar 7 at 23:47
This. $\hbar c \approx 200\,\mathrm{MeV\,fm}$, and the presumed mass is about $10\,\mathrm{MeV}$ meaning that atoms would be confined to radii of 40 or 50 times the size of the nucleus which would totally change their character. And there would be no long range radiation at all. Again: a few tens of femtometers at most. – dmckee Mar 8 at 1:33
No radiation means no radiative cooling of gasses, so clouds would not collapse, as is the case for dark matter in the real universe. – JDługosz Mar 8 at 2:29

Not good.

The Sun emits approximately $4.2 \cdot 10^{44}$ photons/s, and with your stated mass, that would be $7 \cdot 10^{15}$ kg/s. That means it would have radiated away all its mass in just $3.3$ billion years, slightly disappointing for us living $4.5$ billion years after it was formed.

So, for something a bit more destructive, a mass moving at the speed of light (per definition) exerts an infinite force on things it hits. In short, everybody dies, and absolutely every part of the universe is torn apart. Solar cells may be slightly more efficient though.

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The sun would not put out so many. It would put out a number based on the energy produced. – JDługosz Mar 7 at 23:43
@JDługosz Yeah, but that is not great for us either. What the consequences are depends on the exact interpretation of the question. – Hohmannfan Mar 7 at 23:46

Then the coulomb force would be $$F_E=\frac{Qq}{4πε_0r^2}e^{-\frac{mγr}{ħ}}(1+{\frac{mγr}{ħ}})$$ with $F_E$ being the electric force, $Q$, and $q$ being the electric charges, being the $ħ$ being the reduced Planck constant, $ε_0$ being the permittivity of free space, $r$ being the distance between the charges, $mγ$ being the mass of photons.

This means that the force between two electric charges would decrease with distance exponentially instead of simply with the square of the distance. This also means that it would be possible to figure out that photons would have a mass of 1/100 the mass of a hydrogen atom based on how the force between two electric charges would decrease with distance.

If light had a mass of 1/100 the mass of a hydrogen, then it would be possible to travel faster than photons as photons would travel at less than $c$, but it would not be possible to travel faster than $c$ as while $c$ is referred to as the speed of light it really does not depend on there being light, but instead depends on the Lorentz factor. So if you want a universe where it's possible to travel faster than photons, then having massive photons would allow this, but if you want a universe where there is no cosmic speed limit, you would need to make more changes than simply having massive photons.

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Nothing would change from our perspective because all the information about what would have happened had the change not occurred would still be present in the universe due to unitary time evolution. So, even though the universe looks like having become completely different with short range electromagnetic interactions, atoms suddenly decaying as a result, etc. etc., you can transform to a different basis in Hilbert space by applying the inverse time evolution operator to the time before the change happened and then the time evolution operator using the wrong Hamiltonian that doesn't include the change of the mass of the photon.

If you write down the quantum state of the universe in terms of this new basis, then the universe looks the same as what it would have been, had the photon stayed massless. In particular we would still exist, observing the same universe that from our perspective hasn't changed at all.

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