# Does light have a mass?

Discussion in 'Physics & Math' started by GRO, Apr 6, 2002.

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1. ### ElmoRegistered Senior Member

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The penny is poised.....

This is getting very interesting. I'd love to contribute further but for now I'll just follow and absorb.

Tom, when you said:

Did you mean when he said
etc.?

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3. ### ElmoRegistered Senior Member

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When Kaluza visualised the universe with an extra spatial dimension, he came up with a new set of equations for general relativity. There were the old ones too but the new ones happened to be Maxwells equations for EM radiation. This suggested that EM is also something to do with ripples in spacetime. Any thoughts?

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5. ### Joeblow93132Guest

Elmo,

"Tom, when you said:

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If what c'est moi indicated is correct, then mass is ALWAYS constant, regardless of speed. This idea could be a MAJOR upset to the world of subatomic physics
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Did you mean when he said
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The question then is: how are such particles accelerated? In some way, energy has to be put into them; and in practice this is done electronically, ..........
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etc.?"

Yes, that is what I meant.

For many years it has been believed by the physics community that an objects mass increases as it goes faster. Under this theory, an object could never reach light speed because if it did, it's mass would be infinite. Also the particle could not be pushed to light speed because the energy required to move the massive particle to light speed would have to be infinite as well.

The proof for this "relativistic mass" theory was based on experiments done in particle accelerators. It was observed in these particle accelerators that the accelaration of a particle would decrease as it's velocity increased. Scientists believed that the decreased acceleration was the result of the increasing mass of the particle.

As c'est moi pointed out in his post, the decrease in acceleration of the particle was not due to the increase in the mass of the particle, but was due to the decreasing difference between the speed of the particle and the speed of the force pushing the particle.

Here is the mathematical explanation.

Old theory:

Relative Mass=Rest Mass/sqrt(1-(velocity of particle/c)^2)

Acceleration=Force/Relative Mass

As you can see from the equation, scientist believed that the only way for the acceleration to decrease, as the force stayed constant, was for the mass to increase.

New theory:

Relative Force=Rest Force x sqrt((1-(velocity of particle/velocity of force)^2)

Acceleration=Relative force/Constant Mass

In this example the velocity of force is c because the force is produced by electric and magnetic fields that travel at light speed. As you can tell from the formulas, as the particle goes faster, the relative force decreases. The smaller relative force in turn creates a smaller acceleration while the mass remains constant.

Under this new theory, mass is at all times constant(with the exception of energy/mass conversion)

Tom

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7. ### nanokRegistered Senior Member

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finnally, I agree with what someone says in this post, I really think this is the kind of question that is too deep to be answered by experiments or observations. If we argue about this we could go on forever.... and thats why there is more than one theory on how the universe works. So I suggest that anyone who diagrees with the standard model switch to other theories and stop complaining about how the "most popular theory" is wrong.

8. ### James RJust this guy, you know?Staff Member

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Let's see if we can clear up some misconceptions here.

First off - distinguish rest mass from relativistic mass. The <b>rest mass</b> m of any particle is the mass you measure it to have when it is not moving. The <b>relativistic mass</b> m<sub>r</sub> is an idea which is useful in some contexts, where it can be convenient to define:

m<sub>r</sub> = m / sqrt(1-(v/c)<sup>2</sup>)

As you can see, the quantity m<sub>r</sub> gets bigger as v gets closer to c (the speed of light). When v=0, m<sub>r</sub> = m, the rest mass.

The relativistic mass can be a useful concept in some circumstances, but most physicists do not use it often. Why? Because it is a <b>frame dependent</b> quantity. What does that mean? It means that m<sub>r</sub> changes depending on the state of motion of the person measuring it. That's because the v in the definition changes.

For example, consider two cars A and B, with the same rest mass, travelling at different speeds in the same direction. A person standing still on road will agree that they have the same rest mass at all times, but will say they have different relativistic masses. Now consider the point of view of a person in car A. She will say that car A has a relativistic mass equal to the rest mass, and will say that car B has a lower relativistic mass than the person on the road says it has. In other words, the state of motion of the person (standing still on the road or travelling in car A) causes the relativistic mass of car B to change. That means the concept of relativistic mass is not one which all observers agree on. Hence, physicists prefer to use the rest mass, which everybody always agrees does not change.

Now the crunch: <b>photons have zero rest mass</b>. If you stop a photon, it disappears. Notice that if you plug in m=0 into the equation for relativistic mass above, you get m<sub>r</sub> = 0 too, regardless of speed. But you'll also notice that something is wrong with that equation when v=c (as is the case for light). In that case, we find that m<sub>r</sub> = 0/0, which is an undefined quantity. That tells us that for light, we simply cannot use the same equation as for objects travelling at less than the speed of light. What then?

Well, instead of looking as mass, let's look at energy - at an equation which works both for light AND matter particles. It is the full version of Einstein's often-misused equation:

E<sup>2</sup> = (mc<sup>2</sup>)<sup>2</sup> + (pc)<sup>2</sup>

This says that the total energy of any particle (including a photon), depends on two things - the particle's rest mass m, and it's momentum p. Notice that E is also a frame-dependent quantity, since it depends on the momentum.

Let's look at a photon, which has m=0. Then, from the above equation we find E=pc. In other words, the total energy of a photon depends only on its momentum, because it has no rest mass. Quantum mechanics tells us that the momentum of a photon of wavelength L is p=h/L, so E=hc/L. The longer the wavelength, the less energy the photon has.

Notice that although a photon has zero rest mass, it still has both momentum and energy. However, both those quantities are still frame-dependent. If an observer moves in the same direction as a photon, the observer sees a longer wavelength for the photon and a lower energy. The momentum also decreases. However, one of the main results of relativity is that ALL observers always measure the same SPEED for the photon, regardless of the observers' states of motion. In other words, the speed of light is a frame-independent quantity. The only way that can be true is if our ideas of space and time are modified. The equations of relativity tell us exactly (numerically) in what ways space and time change in different frames of reference. What's more, they match up with all experimental results, with no exceptions.

9. ### Adam§Þ@ç€ MØnk€¥Registered Senior Member

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JamesR, thanks for that. Very well written and informative.

10. ### James RJust this guy, you know?Staff Member

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Let us now turn to c'est moi's post regarding accelerating electrons. The electrons are accelerated by absorbing photons.
There are two, equivalent ways of looking at the problem, which involve two different frames of reference.

For a start, let's look at the problem from the electron's point of view. The electron sees photons "catching up" from behind. All of the photons it sees travel at the speed of light, c (no matter how fast the electron is going according to the Lab). However, the energy and momentum carried by each photon decreases over time as the electron speeds up relative to the Lab (see previous post). When the electron was travelling at the speed of light relative to the Lab, the photons it saw would have zero energy and zero momentum, and hence would be unable to speed it up any more. That is why there is a light speed limit from this point of view. So, in a sense, c'est moi's explanation is correct.

Now let's consider the point of view of the Lab. The physicists in the Lab say that the energy of the photons they are pumping into their apparatus is constant. They agree with the electron that the photons will always "catch up" to the electron. So why doesn't the electron just keep getting faster and faster, eventually exceeding the speed of light? Let's look at the energy equation for the electron again:

E<sup>2</sup> = (mc<sup>2</sup>)<sup>2</sup> + (pc)<sup>2</sup>

As more energy is transferred from the photons to the electron, m (the rest mass) doesn't change. c is also constant, so the only way E can increase is for p to increase, which is what happens.

If you have studied Newtonian physics, you will know that the momentum of an electron or other particle is p=mv, where m is the mass and v is the velocity. So, you might expect that if we keep putting more energy in, p keeps getting bigger, which implies that v keeps getting bigger without limit. But that is not the case. In fact, the equation p=mv is wrong, as was shown by Einstein. The correct equation is:

p = mv/sqrt(1-(v/c)<sup>2</sup>)

where m, importantly, is the REST mass.

There are two equivalent ways to look at this equation. The easiest way is to say that as p increases, v does not increase without limit. If you double p (by putting more energy in), you do NOT double v. In fact, you can make p as big as you like and v NEVER gets bigger than c (the speed of light). Try it: plug in p=1345267. Pick an m (e.g. m=27). Solve for v. No matter what values you use for p and m, v will always be less than the speed of light (Note: c=299792458 m/s).

But there is also a second way to look at this equation. We can re-write the equation as:

p = m<sub>r</sub>v

Here, m<sub>r</sub> is the RELATIVISTIC mass, as defined in the previous post. Now, notice that increasing p increases BOTH m<sub>r</sub> and v. So, you could say that putting more energy into the electron does two things - it speeds it up and it increases the relativistic mass. If you do the calculations, you will see that the closer the electron gets to the speed of light, the more the value of the momentum depends on the relativistic mass and the less it depends on v. In other words, one way to look at the situation is to say that as you continue pushing the electron to go faster, more and more of the push goes towards increasing the relativistic mass and less and less goes towards increases the speed, as the speed approaches the speed of light.

At the speed of light, increasing p does not increase v at all. Instead, all of the increase in p goes towards increasing the relativistic mass.

11. ### thedIT GopherRegistered Senior Member

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To add a bit of info to James excellent post.

The theory of Special Relativity, described by James, only applies to frames [1] moving with constant velocity, so called Inertial Frames. It does not apply to frames that accelerate.

To describe systems that are accelerating you have to invoke General Relativity. As I said earlier, Einstein stated that there is no difference between acceleration and gravity. Hence General Relativity describes the behaviour of objects in gravitational fields or accelerating frames. The above equations become invalid except in very local circumstances where there is still an inertial frame of reference.

Does this mean that you can break light speed or accelerate mass beyond light speed. It is embodied in both theories that light speed is the maximum velocity anything can reach and nothing with rest mass can achieve light speed. But a key word is 'local' and 'inertial frame of reference'. About 30+ years ago Astronomers studying the jets from active galaxies found that some jets had velocities that where faster than light. The key issue here is that the jets and us, the observor, are not in the same intertial frames of reference. So yes, you can exceed light speed providing the frames are non-inertial. The only problem is, we don't know how to manipulate this fact to our advantage. Essentially you need to be about 7 or 8 billion light years away and accelerated by a million solar mass black hole to appear to exceed light speed.

I would also ask people to ponder this.

It is my belief that if something is allowed in the Universe it happens. That is, we would observe it. Let's assume for a moment that our current understanding of how things work are totally wrong and an artefact of incorrect mathematical models. In other words, light has rest mass, light speed is an artificial limit imposed only by Relativity. If both my statements are true then we would expect to routinely see objects obeying them, there would be lots of evidence that objects with rest mass exceeded light speed and light had rest mass. To date, nothing of this nature has been seen. So, it is assumed that Relativity is the best description of how things work.

Something else to ponder on. One of the founders of Inflation, Anders Albrecht, teamed up with an up and coming theoretician, Maguejio. They where unhappy with aspects of modern Cosmology. They have suggested that light speed is variable in time, it was much faster in the early Universe. Can't remember the details but some one studying distant quasars found a fature in a spectrum that was interpreted as light speed being faster at that time.

As I say, the Universe is lot stranger than we can possibly imagine. Some of these ideas are very, very strange but no one told the Universe it had to obey our concepts of normality.

12. ### thedIT GopherRegistered Senior Member

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Drat

Meant to add a bit on frames.

A frame of reference is a description of how you view the world, how you are moving with respect to something else.

The general idea is that you can arbitrily assign coordinates x,y,z and t to your position and assume that you are the zero point of that coordinate system, call us observor O. An inertial frame of reference is one of an object moving with constant velocity V away from you in the x direction, say. From the other objects point of view, observor O', it has coordinates x', y', z', t' and you are moving with velocity V' away from it.

Special Relativity is nothing more than the description of how things moving with constant velocity <i>relative</i> to each other describe events they can mutually observe. In order to do this you have to set up <i>transform equations</i> that allow both observors, O and O', to agree upon the same events. If you think about it they will see events differently based on the details of how they are moving relative to each other. This transform equation was found by Lorentz and Fitzgerald to be,

x = x' sqrt (1 - (v/c)^2 ) + sqrt (1 - (v/c)^2 ) v t'
y = y'
z = z'
t = t' sqrt (1 - (v/c)^2) + sqrt (1 - (v/c)^2 ) v x'

If both observors see something moving at light speed so v=c, they both agree that it is moving at c. In other words, light speed is invariant. It is not changed by a transform equation. That is more normally explained as light speed is the ultimate speed but only for inertial frames of reference.

Frames of reference give everyone a headache and they cause many, many arguments. One way of thinking about this is as follows,

How fast are moving?

Your probably sitting in a chair, stationary, aren't you. But the chair is sitting on the surface of the Earth rotating at some velocity. In your frame of reference (FOR) you are stationary, from another FOR you are rotating. But the Earth moves around the Sun. From the FOR of the Sun being stationary you are moving at considerable velocity. But the Sun goes round the Galaxy. You get the idea. From the FOR of a stationary observor 10 billion light years away, we are travelling at a considerable fraction of light speed.

So do we see all the funky things like mass increases, lengths contract, time sows down. No, because to us there is nothing wrong, we are stationary. It is the preception of the remote observor that sees these affects.

Good isn't it.

Now I have real work to do.

13. ### Adam§Þ@ç€ MØnk€¥Registered Senior Member

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Thanks also to Thed. This is all very good stuff.

If you people who have studied this stuff extensively have the time and inclination, I would like to see a thread full of explanations of all this from start to finish, beginning with the basic ideas and rules. Crackpot theories and insults could be left to other threads, maybe legitimate questions in that one thread now and then. I know it would be a bother to write in old work in huge batches and such, but it would be interesting.

PS: As a poor full time student, I don't have the money to go buying heaps of books about this stuff, although I did recently pick up for only a few dollars a second-hand copy of Fundamentals Of Waves, Optics, And Modern Physics, 2nd Ed, by Hugh D Young.

14. ### c'est moiall is energy and entropyRegistered Senior Member

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it's not over yet

thanks to thed and james r for the effort!

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James, I am pleased that you took the time to say your thought on my quote

In your first part you say the same thing as me. Agree.
Then you change your FOR which is meaningless because as you all keep on repeating, the speed of light is constant in all FOR.
what I discussed doesn't necessarily contradict this, but it might contradict that an object with rest mass cannot reach this speedlimit. The only way the latter was 'prooved' was through particle acceleraters.

"Now let's consider the point of view of the Lab. The physicists in the Lab say that the energy of the photons they are pumping into their apparatus is constant. They agree with the electron that the photons will always "catch up" to the electron. So why doesn't the electron just keep getting faster and faster, eventually exceeding the speed of light? Let's look at the energy equation for the electron again: "

look, there you give an explanation which is mathematically completely correct, nothing to say, but it does in no way disproof my interpretation which I feel is simpeler and is just common logic

"If you do the calculations, you will see that the closer the electron gets to the speed of light, the more the value of the momentum depends on the relativistic mass and the less it depends on v."

or very simply that your electromagnetic energy as a limit itself and can never be expected to push any particle fast enough to break relativity

"In other words, light has rest mass, light speed is an artificial limit imposed only by Relativity."

no, imposed by the way we have to put in energy

"If both my statements are true then we would expect to routinely see objects obeying them, there would be lots of evidence that objects with rest mass exceeded light speed and light had rest mass."

no, for the same reason it doesn't work in particle acceleraters

15. ### Joeblow93132Guest

James,

I believe that c'est moi is right.

Let me explain the so-called increasing mass phenomena using classical physics.

First, imagine that you have an electron at rest in a particle accelerator. Now the accelerator generates a photon of electric field which is heading towards the electron at the speed of light. The photon has a relativistic and/or real mass of m.

The formula for the kinetic energy of the photon would be:

E=mv^2/2 or E=mc^2/2

The photon impacts the electron, and photon stops because the electron is at rest. Because the photons velocity is decreased from c to 0, all of the photons energy is transfered to the electron.

As a result the electron begins to move at a speed of v2.

v2=sqrt(mass of photon x mass of electron x c^2)

The next photon that hits the electron will not transfer its entire energy, because the electron is now moving. In this case the energy that is transfered is:

E=(mc^2/2)-(mv2^2/2) or E=m(c^2-v2^2)/2

As you can see the energy transfer is less than the energy transfered by the original photon. The electrons final speed would be (assuming no energy is lost):

V3=sqrt(mass of photon x mass of electron*(c^2-v2^2))

As you can see from this formula, the energy provided by the photons to the electron decreases after each photon impact. It gives the false impression that the mass of the electron is increasing. Also notice how similiar this formula is to the "relative mass" formula.

From this formula I get the impression that the electron will never be able to reach light speed.

Please feel free to correct me if I'm wrong.

Tom

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16. ### (Q)Encephaloid MartiniValued Senior Member

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James R

I was going to say something similar. Thanks for saving me the effort. And what an effort.

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joeblow

The photon has a relativistic and/or real mass of m.

The photon impacts the electron, and photon stops because the electron is at rest. Because the photons velocity is decreased from c to 0, all of the photons energy is transfered to the electron.

Spot the flaw. If photons had 'rest mass', they would be considered a particle with mass. What happens when you smash massive particles together in an accelerator?

As a result the electron begins to move at a speed of v2.

No. One particle does not transfer its energy to the other particle where the other particle simply begins to move. They are smashed into pieces. An analogy of smashing particles would be like determining the structure of a television by looking at the pieces after it has been dropped from the Empire State Building.

Do you now see another explanation as to why photons have no mass?

17. ### Joeblow93132Guest

Q,

"No. One particle does not transfer its energy to the other particle where the other particle simply begins to move. They are smashed into pieces. An analogy of smashing particles would be like determining the structure of a television by looking at the pieces after it has been dropped from the Empire State Building. "

If I dropped a rubber ball from the Empire State Building, would it break into a thousand pieces??? I don't think so. Does that mean that rubber balls don't have mass???

You are oversimplifying particle interactions. A particle may break up into many pieces when impacted by another particle but this isn't always the case. Factors such as the mass and speed of the projectile particle, the stability, mass, and elasticity of the target are some of the many things that influence whether the target particle will simply move, or be shattered into other particles.

Even though the speed of photons are large, their mass is very small, probably about one thousand times smaller than that of an electron. This is why the photon would only transfer it's momentum to the electron, instead of ripping it apart. Though, maybe a photon with sufficient energy might be able to break an electron into pieces.

Tom

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18. ### (Q)Encephaloid MartiniValued Senior Member

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joeblow

If I dropped a rubber ball from the Empire State Building, would it break into a thousand pieces??? I don't think so. Does that mean that rubber balls don't have mass???

It was an analogy of what happens to particles when they are accelerated towards one another. You obviously missed the point of the analogy.

I presume you are inferring that particles 'bounce' off each other like rubber balls.

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Even though the speed of photons are large, their mass is very small, probably about one thousand times smaller than an electron.

Like a quark? What size exactly? Why haven't physicists determined the size of a photons mass yet other particles smaller than that have? You're logic is beginning to fall apart here.

This is why the photon would only transfer it's momentum to the electron, instead of ripping it apart.

Wrong conclusion. Now your reaching. So what happens to the remaining mass of the photon once its transferred its momentum to the electron? Is it added to the mass of the electron? Does it disappear? Where does it go?

Note: Please keep the concept of conservation of energy and momentum relevant in your answer. Remember, you cannot create or destroy matter.

19. ### Joeblow93132Guest

""If I dropped a rubber ball from the Empire State Building, would it break into a thousand pieces??? I don't think so. Does that mean that rubber balls don't have mass???"

It was an analogy of what happens to particles when they are accelerated towards one another. You obviously missed the point of the analogy."

You missed the point of my analogy. What is a rubber ball than a lot of subatomic particles? Why don't orbiting electrons of the molecules of the rubber ball break into pieces when they impact the orbiting electrons of the material in the earth. When the rubber ball hits the ground, don't the particles of the ball hit the particles of the ground??

"I presume you are inferring that particles 'bounce' off each other like rubber balls."

Yes, especially in cases where the particles have like-charged electric fields.

"Like a quark? What size exactly? Why haven't physicists determined the size of a photons mass yet other particles smaller than that have? You're logic is beginning to fall apart here."

You should know that scientist are attempting to avoid the fact that photons do have mass. It goes against their theories.

I doubt that there are any particles that have a mass smaller than that of a photon. A photon might be a quant of mass.

""This is why the photon would only transfer it's momentum to the electron, instead of ripping it apart."

Wrong conclusion. Now your reaching. So what happens to the remaining mass of the photon once its transferred its momentum to the electron? Is it added to the mass of the electron? Does it disappear? Where does it go?"

The momentum of the photon is transfered, not it's mass. The photon retains it's mass.

Note: The total momentum is conserved in the photon/electron interaction. No conservation laws are broken.

Tom

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20. ### Adam§Þ@ç€ MØnk€¥Registered Senior Member

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I can. But I'm special.

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21. ### Joeblow93132Guest

Special......Like the Special Olympics???????

Tom

22. ### (Q)Encephaloid MartiniValued Senior Member

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joeblow

You should know that scientist are attempting to avoid the fact that photons do have mass. It goes against their theories.

That completely makes no sense at all. If I could turn the physics world upside down by finding evidence of photon mass, don't you think I would shout it out to the world, receive a Nobel prize and get my name in the history books? Now you're being ridiculous.

I doubt that there are any particles that have a mass smaller than that of a photon. A photon might be a quant of mass.

How can a particle have a smaller mass than another particle with no mass?

The momentum of the photon is transfered, not it's mass. The photon retains it's mass.

Aha ! Now you've painted yourself into a corner. Where is the remaining photons mass? Why can't it ever be accounted for? Where does it go?

This is the serious flaw in your theory.

23. ### IggDawgRegistered Senior Member

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Photons have mass through the Higgs mechanism. Same way protons and neutrons do. Mass don't work without the Higgs field. Protons and photons both get their mass in the same way.