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### Author Topic: How can light have no mass?  (Read 14566 times)

#### Ben

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##### How can light have no mass?
« on: 08/06/2010 09:30:04 »

Hi, how light can travel at c, have energy but no mass even though E=mc^2 ?

how does this work?

Cheers

What do you think?
« Last Edit: 08/06/2010 09:30:04 by _system »

#### graham.d

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##### How can light have no mass?
« Reply #1 on: 08/06/2010 12:04:22 »
Photons, if you think of light as particles, have zero rest mass. This is another way of saying they can't exist unless they are travelling at lightspeed (in a vacuum). The "m" in E=mc^2 is the mass at the velocity that the object has. According to Special Relativity this mass increases with velocity relative to an observer. At the speed of light this mass would go to infinity and it would take infinite energy to get it to that speed (so it can't happen). The equation is not violated because you could think of the zero rest mass being multiplied by infinity and ending up with a finite number! However it is probably more correct to say that photons are exceptions. The energy of a photon is proportional to its frequency so that

Energy = Plancks constant x Frequency

#### lightarrow

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##### How can light have no mass?
« Reply #2 on: 11/06/2010 12:09:00 »

Hi, how light can travel at c, have energy but no mass even though E=mc^2 ?

Because that equation is wrong...

A lot of times popular books write that (in)famous equation believing to know the real meaning or making the reader believe to have understood it.
The fact is that the equation E = mc2 is valid only if the body is not moving. Have you ever seen a not-moving photon? So, how can that equation be valid in this case?

The correct equation is:

E2 = (mc2)2 + (cp)2

where p is the body's momentum. In the case of a photon, E = cp (this last relation comes from classical electrodynamics, that is Maxwell's equations, that is from XIX century), so m = 0.
« Last Edit: 11/06/2010 12:10:33 by lightarrow »

#### graham.d

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##### How can light have no mass?
« Reply #3 on: 11/06/2010 17:28:31 »
Lightarrow is correct, but for many of us, in the past, it was taught that E=mc^2 was correct if you took the view that the mass increases with velocity
m*=m•[1/√(1-v²/c²)]

If you expand this for v<<c you get the more classical

E = mc² + ½mv²

It has become the convention today to have m as just the rest mass and to not consider the mass as increasing with velocity. It is a technicality which makes little difference in special relativity but is a more important distinction in General Relativity and in Electrodynamics.

In teaching many subjects, especially Physics, it can be hard to get off the ground if you are too rigorous though.

#### acsinuk

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##### How can light have no mass?
« Reply #4 on: 17/06/2010 17:02:46 »
Ben
You have to conserve energy not matter.  Light energy is electromagnetic and like electricity in a conductor it does not increase in mass with more kWs inside.
Think of electromagnetic light energy as a loop of flux current helixing forward through space. OR like lightning plasma in a vacuum.
Electromagnetic energy is magnoflux energy and can exist without matter.
CliveS

#### Pmb

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##### How can light have no mass?
« Reply #5 on: 26/06/2010 23:48:18 »
Because that equation is wrong...
The equation is not wrong. People simply need to know the correct interpretation and definitions of the terms in that equation. IF E is the total inertial energy of the particle then the m is the relativistic mass of the particle. If E is the proper energy of the particle then the m is the proper mass of the particle.

#### lightarrow

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##### How can light have no mass?
« Reply #6 on: 27/06/2010 23:19:38 »
Because that equation is wrong...
The equation is not wrong. People simply need to know the correct interpretation and definitions of the terms in that equation. IF E is the total inertial energy of the particle then the m is the relativistic mass of the particle. If E is the proper energy of the particle then the m is the proper mass of the particle.
Yes, but since the OP interpreted it in the correct way, that is:
1. E = total energy
2. m = mass (invariant mass, as most physicists intend now and as the OP intended since he stated: "how light can travel at c, have energy but no mass"),
then the formula is wrong for photons, so is wrong in general. The other one I wrote has the advantage to be always correct, so I personally prefer it.
« Last Edit: 27/06/2010 23:23:33 by lightarrow »

#### acsinuk

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##### How can light have no mass?
« Reply #7 on: 28/06/2010 11:04:33 »
virtual photons are not particles, anti particles or massless beta rays. In my view they are made up of a tiny volume of magnetic flux a sort of magnoflux energy bubble.
Light is just a vibrating volume of electromagnetic loop current energy only.
CliveS

#### yor_on

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##### How can light have no mass?
« Reply #8 on: 30/06/2010 06:13:27 »
It all depends on how you interpret the word mass I think :)
We say that instead of 'invariant mass' (aka matter) a photon have a momentum.
That momentum it gathers due to its intrinsic energy and its motion, as I understands it.

Matter on the other hand is something you can hold and feel, it doesn't need to move to gather its intrinsic energy, not macroscopically at least :) There are different types of mass, we speak of relativistic mass f.ex. that type of mass is created by invariant mass and/or motion, when it's only motion without invariant mass we like to define that as momentum instead nowadays. Light can push things due to that momentum even though it misses out on all invariant proper mass.

What energy 'really' consists of is a very tough question, that I don't think anyone can answer, not as I've seen at least. But both photons and invariant mass you can 'break down' to energy, and with high enough energies you find it 'spontaneously' creating particles that we deem to be of 'invariant mass' aka matter. So the formula is correct, even though we find an enormous difference between light and, let's say an apple :)
« Last Edit: 30/06/2010 06:23:15 by yor_on »

#### Geezer

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##### How can light have no mass?
« Reply #9 on: 30/06/2010 06:44:21 »
What energy 'really' consists of is a very tough question, that I don't think anyone can answer, not as I've seen at least. But both photons and invariant mass you can 'break down' to energy, and with high enough energies you find it 'spontaneously' creating particles that we deem to be of 'invariant mass' aka matter. So the formula is correct, even though we find an enormous difference between light and, let's say an apple :)

Yoron - My understanding is very limited, but I think that is the really big question.

#### acsinuk

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##### How can light have no mass?
« Reply #10 on: 30/06/2010 09:51:13 »
Yes, it is a really big question and needs to be answered as researchers who are looking into squeezing more digital information into a fibre optic cable now know that lazer light can be quadrature amplitude modulated. This to me proves that light is a volume helix beam of magnoflux energy and has nothing to do with classical matter at all. There is an article in theiet.org 20 February 2010 magazine which will enlighten you on ths subject
CliveS

#### imatfaal

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##### How can light have no mass?
« Reply #11 on: 30/06/2010 10:49:47 »
Clive - thats a little bit of a leap.  QAM is an encoding method which utilises π/2 out-of-phase waves (quadrature waves) to encode more information than simple amplitude modulation.  I do not understand how the existence of a encoding method (which could, technically if not practically, be used with sound waves as carriers, or even more extremely use waves on a piece of string) can 'prove' an esoteric theory relating to the fundamental qualities of electromagnetic radiation.  Matthew

#### Pmb

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##### How can light have no mass?
« Reply #12 on: 30/06/2010 12:41:16 »
Yes, but since the OP interpreted it in the correct way, that is:
The OP didn't understand what the m and E are in that equation. Every time people ask this question it's always the same misunderstanding. But its always best to ask the OP what/how he thinks something is defined then merely assume we know. If a person is asking a question such as this then it's safe to say that there is something they are misinterpreting. The fact that he needs to ask this question demonstrates that he is mistaking the definition of a term in that equation.

#### acsinuk

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##### How can light have no mass?
« Reply #13 on: 01/07/2010 11:24:30 »
Imatfaal
If a single light photon is able to be not only polarized; but be quadrature modulated means that it is more than a two dimensional wave and must therefore contain a 3D volume of magnetic magnoflux energy.
CliveS

#### wolfekeeper

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##### How can light have no mass?
« Reply #14 on: 01/07/2010 14:28:11 »
I don't think anyone knows whether a photon has mass or not, off-hand I don't think it's ever been experimentally established one way or another.

#### lightarrow

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##### How can light have no mass?
« Reply #15 on: 02/07/2010 20:04:18 »
I don't think anyone knows whether a photon has mass or not, off-hand I don't think it's ever been experimentally established one way or another.

I have proved it has no mass in my first post...

#### Pmb

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##### How can light have no mass?
« Reply #16 on: 05/07/2010 12:17:22 »
Quote from: lightarrow
I have proved it has no mass in my first post...
That is not a proof. You started with a relationship which assumes that the m that it starts with is proper mass which is zero for photons. It is not a proof at all.

To be more precise; you basically said E = mc^2 was wrong but offered no clarification or justification for such a claim. You then pulled the expression E^2 - (pc)^2 = (mc^2)^2 out of thin air without a defining those terms. It follows that m = 0 for a photon. However one can just as easily say that E = Mc^2 holds at all times and then pull (Mc^2)^2 - (pc)^2 = (mc^2)^2 out of thin air and then state that m = proper mass and M = "mass" (what you refer to as relativistic mass). There would not be any error in doing so and in fact many physicists/physicst text authors do just that. Most often when they do so they use the notation m = M and m_0 = m
« Last Edit: 05/07/2010 12:52:45 by Pmb »

#### lightarrow

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##### How can light have no mass?
« Reply #17 on: 06/07/2010 11:29:28 »
Is a photon's mass zero or not?

#### Pmb

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##### How can light have no mass?
« Reply #18 on: 06/07/2010 13:29:29 »
Is a photon's mass zero or not?
As you know, whether a photon has mass depends on what you mean by "mass." I.e. it depends on how the term "mass" is defined. The following relationships are true

Let m = proper mass and M = inertial mass (aka relativistic mass aka mass)

For particles or closed systems we have

m is the magnitude of 4-momentum
M = |p/v| = m/sqrt(1 - v^2/c^2)

Proper mass of photon = 0
Relativistic mass of photon is not zero but has the value M = p/c. E = pc for photon so p = E/c. Therefore M = (p/c)/c = E/c^2

You can find this defined and explained in many relativistic texts such as the following (the following texts use m as inertial mass and not proper mass)

Special Relativity, A. P. French, MIT Press, page 20
Quote
Let us now try to put together some of the results we have discussed. For photons we have
E = cp

and

m = E/c^2

(the first experimental, the second based on Einstein's box). Combining these, we have

m = p/c

Relativity: Special, General and Cosmological, Wolfgang, Oxford Univ., Press, (2001), page 120
Quote
According to Einstein, a photon with frequency f has energy hf /c^2, and thus (as he only came to realize several years later) a finite mass and a finite momentum hf/c.

Introducing Einstein's Relativity, Ray D'Inverno, Oxford Univ. Press, (1992), page 50
Quote
Finally, using the energy-mass relationship E = mc^2, we find that the relativistic mass of a photon is non-zero and given by m = p/c.

Combining these results with Planck's hypothesis, we obtain the following formulae for the energy E, relativistic mass m, and linear momentum p of the photons:

E = hf             m = hf/c^2            p = hf/c

Also found in Concepts of Mass In Contemporary Physics and Philosophy, Max Jammer, Princeton University Press

The same thing is found in Alan Guth's lecture notes from his course at MIT, the Early Universe.

Were you aware of the fact that some physicists define M in this way in recently published relativity texts?
« Last Edit: 06/07/2010 13:33:10 by Pmb »

#### acsinuk

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##### How can light have no mass?
« Reply #19 on: 07/07/2010 20:48:42 »
PMB
A photon has no mass; it is made from magnetic energy only. If you look up wikipedia "Eulers formlua" you will see a diagram that shows the inphase and quadrature modulation of magnoflux energy. Laser light is 3D magnetic energy and forms a helix [ magnoflux tunnel] as the photons move through a magnetized volume of space.  Any physics model of a photon or light that is not 3D is therefore highly suspect in my view
CliveS

#### lightarrow

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##### How can light have no mass?
« Reply #20 on: 07/07/2010 21:16:26 »
Is a photon's mass zero or not?
As you know, whether a photon has mass depends on what you mean by "mass." I.e. it depends on how the term "mass" is defined. The following relationships are true

Let m = proper mass and M = inertial mass (aka relativistic mass aka mass)

For particles or closed systems we have

m is the magnitude of 4-momentum
M = |p/v| = m/sqrt(1 - v^2/c^2)

Proper mass of photon = 0
Relativistic mass of photon is not zero but has the value M = p/c. E = pc for photon so p = E/c. Therefore M = (p/c)/c = E/c^2

[cut]

Were you aware of the fact that some physicists define M in this way in recently published relativity texts?
Then, why the Particle Data Group says that photon's mass is zero? :

#### Geezer

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##### How can light have no mass?
« Reply #21 on: 08/07/2010 02:48:31 »
There does seem to be something slightly paradoxical going on here.

As I understand it, it takes an infinite amount of energy to accelerate any mass to the speed of light.

But photons are accelerated to the speed of light, apparently without consuming an infinite amount of energy, so how can they have mass?

#### Pmb

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##### How can light have no mass?
« Reply #22 on: 10/07/2010 06:15:33 »
PMB
A photon has no mass;..
You failed to get my point, which is when people refer to a photon as having zero mass they mean that the proper mass of a photon is zero. Not that it's inertial mass (aka relativistic mass) is zero. I never said that the proper mass of a photon wasn't zero. That'd be silly.
« Last Edit: 10/07/2010 06:26:02 by Pmb »

#### Pmb

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##### How can light have no mass?
« Reply #23 on: 10/07/2010 06:24:32 »
Then, why the Particle Data Group says that photon's mass is zero?
Because you're supposed to know  that by mass they mean proper mass, not inertial mass. If you also look at the site you might see that the lifetime of a free neutron you'll see that it says 15 minutes. You're also supposed to know that they mean proper lifetime. We all know that the life time of a particle increases with speed. But that isn't evident in the lifetime that they give of 15 minutes.

Those things are read and used by professional physicists and whoever reads them knows what those terms mean. I know that it refers to proper mass (aka rest mass). Nobody has to tell me that. But that's particle physics. If you expect to go to other branches of physics and expect the term to mean what you think it does then you'll be sorely mistake. E.g. Misner, Thorne and Wheeler's text "Gravitation" uses mass in one key derivation where it means "inertial mass" (what you'd call relativistic mass) but merely says "mass." Other texts are the same.

Show me where you think I made a mistake. And please don't tell me that one definition is "right" and the other is "wrong" because that's not a valid arguement when the relativity literature uses the same term both ways. Mostly as a matter of taste. Some people get tired or writing "rest" and others get tired of writing "inertial" in front of the term "mass". That's the only real difference.

Quote
Hi, how light can travel at c, have energy but no mass even though E=mc^2 ?

how does this work?
And it is this question that I'm responding to. As such I was basically explaining what the "m" in that expression stands for and my answer is that it refers to the inertial mass of a body, not its proper mass. The proper mass of a photon is zero while the inertial mass is not. There are other kinds of mass too,i,e, passive gravitational mass, active gravitational mass.
« Last Edit: 10/07/2010 08:17:33 by Pmb »

#### Pmb

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##### How can light have no mass?
« Reply #24 on: 10/07/2010 06:28:00 »
There does seem to be something slightly paradoxical going on here.

As I understand it, it takes an infinite amount of energy to accelerate any mass to the speed of light.

But photons are accelerated to the speed of light, apparently without consuming an infinite amount of energy, so how can they have mass?
You're thinking of Euler's definition of mass, not Newton's. Newton defined inertial mass as that which determines momentum, not that which determines acceleration. And thats how its used in modern physics.

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##### How can light have no mass?
« Reply #24 on: 10/07/2010 06:28:00 »