# The Naked Scientists Forum

### Author Topic: How can light have energy if it has no mass?  (Read 14639 times)

#### Ian McDonald

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##### How can light have energy if it has no mass?
« on: 27/09/2011 22:30:05 »
Ian McDonald asked the Naked Scientists:

If light has no mass:

(a) How can light be subject to gravity?
(b) How can the equation E=mc2 be correct? If we let E be the energy of a photon (or a billion, gazillion photons), and m be the mass of that/those photons (i.e. zero), then E=0 x c2, or E=0. So if photons have no mass, it would seem they can have no energy either, which is patently incorrect.

What do you think?
« Last Edit: 27/09/2011 22:30:05 by _system »

#### Pmb

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##### How can light have energy if it has no mass?
« Reply #1 on: 27/09/2011 22:55:26 »
Ian McDonald asked the Naked Scientists:

If light has no mass:

(a) How can light be subject to gravity?
(b) How can the equation E=mc2 be correct? If we let E be the energy of a photon (or a billion, gazillion photons), and m be the mass of that/those photons (i.e. zero), then E=0 x c2, or E=0. So if photons have no mass, it would seem they can have no energy either, which is patently incorrect.

What do you think?
You're thinking about proper mass instead of relativistic mass. There's no reason that proper mass has to be non-zero for a general particle. However particles with zero proper mass can be non-zero.

#### Soul Surfer

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##### How can light have energy if it has no mass?
« Reply #2 on: 27/09/2011 23:45:43 »
a) light is subject to gravity it loses energy climbing out of the gravitational well of a star or a planet and is deflected by it as it passes this energy loss and deflection is very small for normal gravitational fields but has been measured many times and corresponds exactly to theory.

b)  The equation refers to the trapped energy contained in the mass of a particle and therefore only applies to particles with mass.  this energy would be released if the particle was annihilated by its antiparticle and both became pure energy as photons.  Photons definitely have energy and momentum depending on their frequency.

#### yor_on

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##### How can light have energy if it has no mass?
« Reply #3 on: 27/09/2011 23:50:03 »
Ian, you know that light has a energy :) Every time you go out in the sun you feel that energy warm you up. So no matter what equations you consider you have to admit to that. And so we turn it around, if energy can be defined by something mass less, as ethereal as light, isn't that then the original definition of energy? And looked at from that perspective matter, as it is so densely 'packed', becomes incredibly energy rich.

Tell me what matter is, and how it can exist.

#### JP

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##### How can light have energy if it has no mass?
« Reply #4 on: 28/09/2011 05:18:47 »
Ian, you know that light has a energy :) Every time you go out in the sun you feel that energy warm you up. So no matter what equations you consider you have to admit to that.

Yor_on nailed it.  There are at least two definitions of mass that make sense in special relativity, and they both agree with our concept of mass and with each other when things are moving at slow speed relative to us.

If you choose to use the one called relativistic mass, E=mc2 holds, and light has a non-zero value of m so that it can have energy.

The more common choice, and the one that's used when saying light is massless, is the invariant mass.  If you use the invariant mass, the proper equation is E2=m2c4+(pc)2, where m=0 for light, and p is momentum, which is non-zero.

#### lightarrow

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##### How can light have energy if it has no mass?
« Reply #5 on: 28/09/2011 20:09:09 »
Ian McDonald asked the Naked Scientists:

If light has no mass:

(a) How can light be subject to gravity?
Take a stone and let it fall down. Measure its acceleration. Does it depend on mass? No.
So, even a massless object can fall down accelerating...

Quote
(b) How can the equation E = mc2 be correct?
Infact it's false.
The correct one is E2 = m2c4+(pc)2, as JP wrote.
E = mc2 is valid *only* if the object is still.

#### yor_on

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##### How can light have energy if it has no mass?
« Reply #6 on: 29/09/2011 15:32:23 »
Very sweet thinking LightArrow :) I will have to remember that one. And thanks JP.

That example is very true, mass has nothing to do with gravitational acceleration, although it (the mass) will have to do with the 'energy' displaced/displayed, as whatever it is 'falling' hits something refusing to yield, as the ground.

#### freewilly

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##### Re: How can light have energy if it has no mass?
« Reply #7 on: 30/10/2015 19:29:33 »

If you choose to use the one called relativistic mass, E=mc2 holds, and light has a non-zero value of m so that it can have energy.

The more common choice, and the one that's used when saying light is massless, is the invariant mass.  If you use the invariant mass, the proper equation is E2=m2c4+(pc)2, where m=0 for light, and p is momentum, which is non-zero.

Please could someone explain why the second equation is right? The second equation involves momentum which is the objects mass x velocity and you said the mass is 0. Therefore you are saying E2 is still 0 and so is E ∴ contradicting everything you just said. E=mc2 and E2=m2c4 + (pc)2 don't work when equating energy of light.

Don't use E=mc2 and E2=m2c4 + (pc)2 when finding energy of light, use E=hf and f=hc / λ, where h is plancks constant, f is frequency of the photon and lamda is the wavelength of the photon to work energy out from its wavelength, NOT MASS.
« Last Edit: 30/10/2015 19:46:01 by freewilly »

#### evan_au

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##### Re: How can light have energy if it has no mass?
« Reply #8 on: 30/10/2015 23:39:03 »
Quote from: freewilly
The second equation involves momentum which is the objects mass x velocity and you said the mass is 0.
The photon carries momentum - this is the mechanism behind the solar sail, with its deployment recently tested in space by the Planetary Society. http://sail.planetary.org/

The momentum of a photon is p=h/λ.

« Last Edit: 30/10/2015 23:40:47 by evan_au »

#### lightarrow

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##### Re: How can light have energy if it has no mass?
« Reply #9 on: 31/10/2015 08:10:22 »
Please could someone explain why the second equation is right? The second equation involves momentum which is the objects mass x velocity and you said the mass is 0. Therefore you are saying E2 is still 0 and so is E ∴ contradicting everything you just said. E=mc2 and E2=m2c4 + (pc)2 don't work when equating energy of light. Don't use E=mc2 and E2=m2c4 + (pc)2 when finding energy of light, use E=hf and f=hc / λ, where h is plancks constant, f is frequency of the photon and lamda is the wavelength of the photon to work energy out from its wavelength, NOT MASS.
Momentum, in general IS NOT m*v! It's m*v ONLY for particles of non zero mass AND at low speeds.

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lightarrow

#### Thebox

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##### Re: How can light have energy if it has no mass?
« Reply #10 on: 31/10/2015 08:38:20 »
Ian McDonald asked the Naked Scientists:

If light has no mass:

(a) How can light be subject to gravity?
(b) How can the equation E=mc2 be correct? If we let E be the energy of a photon (or a billion, gazillion photons), and m be the mass of that/those photons (i.e. zero), then E=0 x c2, or E=0. So if photons have no mass, it would seem they can have no energy either, which is patently incorrect.

What do you think?

Hello, it is a simple explanation really,   light propagating (travelling) through space is under no opposing force from space itself, light is Physically able to flow freely without obstruction through space, light is neither of concrete existence or a virtual existence , it is of a physical presence.  A physical presence that remains electrical neutral until is obstructed by an object or a medium that is of a concrete existence. Light propagating through space has no net charge, and only when light makes surface contact with something of a concrete existence does a charge occur.   I like to call light a ''convertual'' energy, it remains dormant until activated.

But I am not a scientist, but I am sure most scientists could not disagree with this.

#### Thebox

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##### Re: How can light have energy if it has no mass?
« Reply #11 on: 31/10/2015 08:44:56 »
Quote from: freewilly
The second equation involves momentum which is the objects mass x velocity and you said the mass is 0.
The photon carries momentum - this is the mechanism behind the solar sail, with its deployment recently tested in space by the Planetary Society. http://sail.planetary.org/

The momentum of a photon is p=h/λ.

What do you mean by a Photon carries ''momentum''?

Do you mean when a Photon hits something it applies a force?

#### lightarrow

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##### Re: How can light have energy if it has no mass?
« Reply #12 on: 31/10/2015 18:30:45 »
Quote from: freewilly
The second equation involves momentum which is the objects mass x velocity and you said the mass is 0.
The photon carries momentum - this is the mechanism behind the solar sail, with its deployment recently tested in space by the Planetary Society. http://sail.planetary.org/ The momentum of a photon is p=h/λ. See: http://en.wikipedia.org/wiki/Radiation_pressure#Radiation_pressure_by_reflection_.28using_particle_model:_photons.29
What do you mean by a Photon carries ''momentum''? Do you mean when a Photon hits something it applies a force?
Yes and there is no need to consider photons, that is a quantum description: a classical description of the electromagnetic field (Maxwell equations, Lorentz force) is enough: when light hits an object, it makes a force on it, this is for ex. the principle of solar sails, as evan_au wrote:
https://en.wikipedia.org/wiki/Solar_sail

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lightarrow

#### The Naked Scientists Forum

##### Re: How can light have energy if it has no mass?
« Reply #12 on: 31/10/2015 18:30:45 »