2015-06-09 20:38:22 8 Comments

I read that a photon is said to have zero mass at zero velocity.

Does this mean that they only exist in a state of probability until observed && interacting with some system? And then when observed they collapse into a particle that has velocity and said mass?

Or is it possible to have a photon behaving as a particle without mass?

This feels intuitively like the "wrong question", but could someone please explain to me how a photon, if it is energy, has no mass?

Are there any naturally occurring examples of photons without mass?

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## 1 comments

## @Ian 2015-06-09 20:47:37

I think there is some confusion here. Photons are always massless. They also always move at the speed of light. Therefore every example of a photon in nature has zero mass.

Perhaps you are thinking about a photon moving through a medium other than a vacuum. In this case, we can view the photon plus the interactions with the medium as a quasiparticle with a nonzero mass and a speed slightly less than the speed of light. But then we are no longer considering a true photon, so there is no contradiction with the first paragraph.

Edit: To answer your comment, in special relativity the energy of a particle is

$$E\equiv\gamma mc^2$$

where

$$\gamma \equiv \frac{1}{\sqrt{1-v^2/c^2}}$$

When we plug $v=c$ and $m=0$ into the formula for the energy, we find that $\gamma$ goes to $\infty$. Therefore, this expression for $E$ is an indeterminate form, so it should seem reasonable that any particle with zero mass moving at the speed of light can have a finite energy.

Perhaps a more useful formula for the energy in this situation is

$$E^2=p^2c^2+m^2c^4$$

where

$$p\equiv\gamma m v$$

is the definition of momentum in special relativity. You can derive this formula using the definitions of energy and momentum in special relativity. From this formula, you can see that the energy of a massless particle is finite and proportional to its momentum.

Perhaps some of your confusion results from trying to use the nonrelativistic formulas for energy and momentum to understand the behavior of highly relativistic light.

## @ruben_KAI 2015-06-09 20:52:05

How can something with energy have no mass?

## @David Hammen 2015-06-09 20:56:26

@RubenBaden - By moving at the speed of light. Massless particles always move at the speed of light. And they have non-zero energy. And non-zero momentum. Welcome to the weird world of relativity.

## @ruben_KAI 2015-06-09 21:00:25

so it takes an infinite amount of energy to move something with mass infinity close to the speed of light, but once something is at the speed of light it has no mass? are there other particles that move at the speed of light without any mass?

## @Ian 2015-06-09 21:11:37

Look at the definition of energy provided above. That should convince you that only massless particles can move at the speed of light with finite energy.

## @ruben_KAI 2015-06-09 21:29:06

I've never been able to be convinced by a definition alone.

## @Ian 2015-06-09 21:30:43

If you want to get philosophical, what do you mean by energy then? If you want to talk about energy you necessarily have to refer its definition.

## @userLTK 2015-06-10 04:43:04

You might want to look up the Higgs Boson - though that's getting a little more advanced. All particles move at the speed of light and have only energy mass, no rest mass, unless they interact with the Higgs field, at which point they have mass and don't travel at the speed of light. The idea that something can have no mass and only energy seems counter-intuitive, but that's what the the science tells us.