# Photons -- can they have mass and travel at c?

1. Mar 21, 2015

### lavoisier

Hi everyone,
many (sigh), many years ago, when I was in high school, I recall a little discussion we had with some classmates, which I gave little thought to at the time, but thinking back to it now, could never really figure out.
It was about relativity. The story was that nothing could reach the speed of light, because the energy needed to achieve that would be infinite, and the mass of the object would then also be infinite.
And one of the guys said, what about things that *do* travel at the speed of light, like photons? Haven't they got any mass? The obvious answer (not coming from me) was that, as they were waves rather than particles, indeed they had no mass, they were only energy. And he said, but if mass and energy can turn into one another, and particles and waves are the same (we had probably just been taught the De Broglie thing), then anything that has energy has also got mass, so how can photons travel at the speed of light and still have finite mass?

I suppose such questions don't even arise in physicists' circles, but for an outsider like myself they can make matters quite puzzling.
Can you please explain where my classmate's reasoning was wrong?
Thanks!

2. Mar 21, 2015

### DaveC426913

Photons are massless particles.

3. Mar 21, 2015

### Blackberg

A photon's energy can be converted to mass, but there is no mass while the photon exists. It's one or the other :
[No mass and speed of light] or [mass and not speed of light]

Also, being a wave is not a reason for not having mass.

4. Mar 21, 2015

### rootone

Last edited: Mar 21, 2015
5. Mar 21, 2015

### Staff: Mentor

Actually, this is not true. Anything that has mass has energy, but not everything that has energy has mass. The relationship between mass and energy is $m^2 c^2 = E^2/c^2 - p^2$. For $p=0$ this simplifies to the famous $E=mc^2$, but for a photon $p=E/c$ so $m=0$

6. Mar 22, 2015

### manogyana25

But how can something that has no mass have energy??

7. Mar 22, 2015

### Staff: Mentor

Why would you think that having energy requires an object to have mass?

8. Mar 22, 2015

### lavoisier

Thank you all very much for your replies, I think the picture is a bit clearer in my mind now.
One thing that escapes me in this reasoning is, when we talk about 'rest mass', or 'momentum', I guess these concepts require telling whether something is in motion or at rest. But doesn't that require a frame of reference? Can it be determined in absolute terms?
I am at rest compared to my living room, but not compared to a car passing in the street, or the Sun, or another galaxy...
I seem to remember light can't be at rest because it's made of oscillating fields, which by definition must always move and do it at a speed that doesn't depend on their position. But how can I tell the momentum of a particle without measuring its position in space at two different points in time?
I suspect this was one of the starting points of the reflection that resulted in relativity, which (clearly) I didn't understand.

9. Mar 22, 2015

### Staff: Mentor

You cannot. The momentum of a particle is not invariant. It changes depending on the frame of reference it is measured from.

10. Mar 22, 2015

### manogyana25

So energy is present even without mass? I cannot understand. But how can an object without mass do work? Energy is the ability to do work right??

11. Mar 22, 2015

### Staff: Mentor

In the case of a single massless particle, yes. However there's a caveat here. Let's say that a photon is created within a system of objects. If you look at the system prior to the creation of a photon, and then look at the system after the creation of the photon, and also include the created photon as part of this system, then the mass of the system as a whole will remain unchanged. In other words, the system had X amount of mass prior to the create of a photon. After the creation of the photon the system, which also includes the photon, still has X mass. But if the photon leaves the system, an the system now has less mass, with this missing mass equal to the energy content of this massless particle as per Einstein's equation.

The key here is that a massless particle always travels at c in all reference frames and can never be 'at rest', so it can never have mass. But the system of which it is a part of has additional mass equivalent to the energy content of that particle.

For example, let's say you have a box with a light source and a battery, all of which weighs exactly 10 kilograms, out in space. Then you turn on the light and emit a single photon. The system, which is the box + light source + photon still has 10 kilograms of mass. If that photon then escapes the box, perhaps by exiting through a small window, the box + light source now has slightly less than 10 kg of mass, with the missing mass carried away in the energy content of the photon.

You could say that in order to see the mass of the photon you need to specify a system of which it is a part of and then look at the mass of the system as a whole.

Sure, and work is a force applied over a distance. So you have an EM wave, made up of photons, exerting a force on charged particles, performing work on them.

12. Mar 22, 2015

### Staff: Mentor

Look at the equation I posted. Something with no mass can have energy as long as its momentum is equal to E/c.

13. Mar 22, 2015

### Staff: Mentor

Yes. Energy and momentum are both relative quantities, meaning that you have to specify the reference frame and different frames will disagree.

On the other hand, mass is invariant. All frames agree on the mass of a particle, and it isn't necessary to specify the frame.

14. Mar 22, 2015

### ZapperZ

Staff Emeritus
Many of the questions posted here have been covered by our FAQ. The new members should spend some time going over the FAQ entries.

Zz.

Last edited by a moderator: May 7, 2017
15. Mar 22, 2015

### lavoisier

Thanks again.
Apologies for not looking up the question beforehand.
Just a thought: it's probable that all the knowledge in the world is already written down somewhere and can be looked up on Google without bothering anyone.
If some people ask questions on forums and others take the time to reply, perhaps it's because they want to do it, not because it's strictly necessary.

16. Mar 22, 2015

### davenn

Yes, its good to have people interaction. But that isn't what is being frowned upon

@lavoisier Now please don't take this personally .... its just a general observation that is common on all forums these days ....
The problem is, that a large portion of people these days don't know how to ( or are to lazy to) do even the most basic research themselves
They just want all the answers handed to them without doing any work themselves

Here at The Physics Forums, we try and encourage people to think for themselves and do some personal study and IF they read explanations for their
queries they don't understand fully or partly THEN come and pose a well thought out question on what it was in class or on Wiki etc that they specifically didn't understand.

Those people will find others much more willing to help those that at least have an attempt at helping themselves

I enjoy helping out. its one of the 2 main reasons I'm on this forum. The other is for my own learning
as I read through other answers .... I have learnt so much
But even I, when I see something I don't fully understand, at least give Google a blast before
posing any question on here myself

cheers
Dave

Last edited: Mar 22, 2015
17. Mar 22, 2015

### rootone

Also a lot of misleading and fundamentally wrong information can be obtained by Googling.
PF is a good place to learn what are in fact the accepted scientific paradigms at present, even though some of them are arguable.
Though it might seem a bit frosty at first, you gotta admit it's better than facebook if you want to have an intelligent discussion.

Edit:
Oh, I should mention something on topic while posting - yes there can particles with zero rest mass, such as photons, and they always travel at the speed of 'c' in a vacuum if Einstien got it right..

Last edited: Mar 22, 2015
18. Mar 23, 2015

### Toleedo

This is maybe a bit off topic but, I thought I read somewhere that there is a theory that a photon comes into existence through the superposition of de broglie waves? Does anyone know about this?

19. Mar 23, 2015

### lavoisier

I have to say I was always impressed by the scientific quality and depth of the answers I got on this forum (other forums are nowhere near as good, TBH), and being a scientist myself I understand that 'people skills' are not always prominent in the 'technical' person. That's fine. We're exchanging information here, not gossiping about our ex-best-friend's divorce while sipping tea (that's why I am not on facebook).
Frosty? Not really, or at least not always .

I got the message, and I'll try to stick to the rules to the best of my abilities.
Anything not to see again those boldface fonts and mid-sentence capitals... <shudder>

20. Mar 23, 2015

### Staff: Mentor

Hi Toleedo, welcome to PF!

Do you have a more specific reference? I don't recognize anything obvious from the description. It might be best to start a new thread on the topic once you found that thing you read.