# Photon

#### Voltboy

Joined Jan 10, 2007
197
I was wondering, after a chemistry class..
my teacher said that a photon has energy but doesn't have mass.. But according to Einstein's theory E=mc^2, if m= 0 then m*c^2 = 0, so a photon doesn't have energy..
also the teacher said that gamma rays travels faster than light, which sound completely ridiculous to me because gamma rays are EMR which are the same as light...

Thanks in advance #### studiot

Joined Nov 9, 2007
4,998
The correct equation to derive the energy of a photon is to use Plank's equation:

E = h$$\nu$$, where E is the energy, H is Plank's constant and $$\nu$$ is the frequency.

By substitution you will come up with a value for the energy of the photon ( note that gamma rays have higher frequency and therefore higher energy than visible light)

You can then work Einstein's equation backwards to calculate the mass of the photon at the speed of the radiation (=c).

The photon is a particle which has zero rest mass. Einstein's theory of special relativity says that the mass of any particle increases with velocity, becoming infinite at the speed of light. Thus if you try to evaluate the mass of the photon directly from E=mc$$^{2}$$ you will end up with an infinity times zero situation - difficult to evaluate.

I doubt that the lecturer said that gamma radiation moves faster than light, without further qualification of the comparative circumstances. What did he say in full?

#### Voltboy

Joined Jan 10, 2007
197
So photons mass mass isn't 0 but is undefined right??
and yes.. the teacher said "gamma rays travel faster than light speed" and wrote Alfa < c, beta almost c, gamma > c.

Thanks

#### studiot

Joined Nov 9, 2007
4,998
No I didn't say the mass of the photon is not zero.

I said the rest mass is zero.

According to Special Relativity, mass increases with speed. Every particle has a particular mass at rest (zero speed). The photon happens to have zero mass at zero speed.

What would be fun would be a particle with negative rest mass.

#### theamber

Joined Jun 13, 2008
322
Why didn't you ask your teacher??? that is why he gets paid.
Ask him and let us know what he said.
Light behaves as a wave(no mass) and as a particle(with mass). But nothing with mass could move at maximun speed of light. But it can move close to the maximun speed.
An object with mass moving to the maximun speed of light will be frozen in time.
Time cease to exist because light is the limit of time in our world.
But If something ever moves faster than the speed of light even...then something that we cannot explain in our understanding of the world will happen...
It is possible that gamma rays could move faster but that will not be seen in our world because our limit is c.

#### Voltboy

Joined Jan 10, 2007
197
According to Special Relativity, mass increases with speed. Every particle has a particular mass at rest (zero speed). The photon happens to have zero mass at zero speed.
So a photon mass, when its traveling speed will be..? infinite?

Light behaves as a wave(no mass) and as a particle(with mass). But nothing with mass could move at maximun speed of light. But it can move close to the maximun speed.
Thats something i never understood, is it wave, particle or both at same time. If its a particle i know its photon, but when its a wave what is it?

Thanks for helping guys #### studiot

Joined Nov 9, 2007
4,998
Let's start at the beginning, where hope I you understand things, and work through a little at a time. It is always best to work from what you know towards what you want to know.

Did you understand Plank's law?

This applies to any single oscillator or oscillatory system whose energy at any point can be described by a plot of a sine wave against time. This type of oscillator is called harmonic.

'A single' means one photon, one electron, one atom or whatever.
On a macroscopic scale, say a pendulum swinging, you have to multiple by the total number of atoms in the pendulum to obtain the total energy of the oscillator.

If we are agreed on this we can move on to the next stage.

#### theamber

Joined Jun 13, 2008
322
You have to make yowr own conclusions with what you understand. No one knows all the answers.
Light acts as a wave under certain experiments and observations, under others it acts as a particle. We are just playing with this stuff we don't know ANYTHING for certain. There are tons of articles about this on google.
For example it takes 8 minutes for the light of the sun to reach us but for a photon traveling at near the maximun speed of light it takes an instant. Time is relative and its more accentuated at very fast speeds. The earth gets hit by aprox. four pounds of photons from the sun everyday. I could assume that when light waves slow down a little they pick energy in the form of photons probably the photons are like a side effect they were never in the wave to begin with.

#### Mark44

Joined Nov 26, 2007
628
For example it takes 8 minutes for the light of the sun to reach us but for a photon traveling at near the maximun speed of light it takes an instant.
Photons can't get from the sun to the Earth in "an instant." Light reaches its "maximun" speed in a vacuum, which is close to what is present for much of the 93,000,000 miles between the Earth and the sun. The speed of light in a vacuum is about 186,000 miles/sec or about 300,000,000 m/sec. If you divide the distance to the sun by the speed of light, you'll get about 8 minutes, not "an instant."
Mark

#### triggernum5

Joined May 4, 2008
216
One place you can imagine photonic mass at work would be a solar sail.. A sail that could carry a ship away from the sun at an ever accelerating rate..
Now different colors of light have different masses.. Every color of light has an associated frequency which is abreviated as
in Plank's E=h
.. Blue light has a higher frequency than red light, and thus more 'E'nergy since h in E=h
is a constant..
So h is a constant, and we know
for whatever photons we're dealing with, so we can sub that Energy into E=mc^2 and solve for m.. Essentially we are using the fact that h
= mc^2..
Now mass is kind of irrelevant actually when talking photons since we can't hold or weigh them.. Where it does show up is in the momentum (p), where p = mv (velocity).. Higher frequency photons will impart more momentum on our sail..

#### theamber

Joined Jun 13, 2008
322
Photons can't get from the sun to the Earth in "an instant." Light reaches its "maximun" speed in a vacuum, which is close to what is present for much of the 93,000,000 miles between the Earth and the sun. The speed of light in a vacuum is about 186,000 miles/sec or about 300,000,000 m/sec. If you divide the distance to the sun by the speed of light, you'll get about 8 minutes, not "an instant."
Mark
I already said that 8 minutes earlier did you read or comprehend my las post???
That is for an stationary observer time frame. But if you where a photon riding at an incredible speed close to the maximun speed of light but never reaching it, time will slow down considerably to your (photon) time frame. So the photon time is not our time because light motion is what dictates time. So the faster anything moves the slower the time moves with respect to stationary observers or observers moving at a slower pace. Nothing can reach the maximun speed because then that will not part of our world.

#### Voltboy

Joined Jan 10, 2007
197
Did you understand Plank's law?
Yes I'm following you.
So the faster anything moves the slower the time moves with respect to stationary observers or observers moving at a slower pace. Nothing can reach the maximun speed because then that will not part of our world.
Isn't a photon in a vacuum traveling at light speed? and if it does the time won't go by right.

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#### studiot

Joined Nov 9, 2007
4,998
So we can calculate a packet of energy from Plank's law. I'll leave it as an exercise to put in real numbers ( ask for help if you need it) and call this Ep the energy of a single photon.

Now a quick summary of special relativity states that:

For a rest mass of Mo the mass will increase with velocity according to the equation

Mv =$$\ \ \ \frac{Mo}{sqrt{1-\frac{v^{2}}{c^{2}}}$$

Where v is the velocity and Mv is the mass at that velocity.
c is of course the velocity of light in the medium concerned.

Now as I said all particles have a particular rest mass, photons and also neutrinos have zero rest mass.

So for any value of velocity less than c the Mv for a photon = zero times a large (finite) number = zero.

But when v = c we the expression becomes $$\frac{0}{0}$$ an indeterminate form.

So we use E = mc$$^{2}$$ putting E = Ep, since the photon is travelling at the speed of light. Not faster, not slower.

From this we can calculate a 'mass' for the photon. This agrees with sensitive measurements made in vacuum.

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#### Mark44

Joined Nov 26, 2007
628
I already said that 8 minutes earlier did you read or comprehend my las post???
That is for an stationary observer time frame. But if you where a photon riding at an incredible speed close to the maximun speed of light but never reaching it, time will slow down considerably to your (photon) time frame. So the photon time is not our time because light motion is what dictates time. So the faster anything moves the slower the time moves with respect to stationary observers or observers moving at a slower pace. Nothing can reach the maximun speed because then that will not part of our world.
It was not at all clear to me that you were talking about different frames of reference. ("For example it takes 8 minutes for the light of the sun to reach us but for a photon traveling at near the maximun speed of light it takes an instant.") If the last part of that sentence had said "it takes an instant, from the photon's perspective." I would have understood what you were trying to say.

#### Voltboy

Joined Jan 10, 2007
197
Thanks Studiot.. I think I now understood it.

#### triggernum5

Joined May 4, 2008
216
Actually, I think studiot's mechanics are off.. That type of thinking leads to tachyons though, if you're willing to consider imaginary rest mass..
Reaching an indeterminate form doesn't mean you can pick the most convenient outcome.. The approach Einstein used was:
E = mc^2 = sqrt((p^2)(c^2) + (m0^2)(c^4))
Then, by setting the rest mass to 0 and subbing in Planck, we can get:
p = E/c = h
/c = h/lambda

#### studiot

Joined Nov 9, 2007
4,998
I would be interested to see your derivation of

E = mc^2 = sqrt((p^2)(c^2) + (m0^2)(c^4))

without using the more elementary equations I put forward and without reaching a 0/0 situation.

As I understand it, Einstein or someone squared two of the equations which flowed from special relativity subtracted them and took the square root, explicitly to avoid the 0/0 situation. He also chose the positive square root over the negative one for no apparent reason (other than it worked out better).

As I see it this costs us an extra page of algebra, but gains no new result.

It should also be remembered that Einstein was steadfastly against the quantum theory.

#### triggernum5

Joined May 4, 2008
216
True, kind of.. Einstein was against the indeterminacy of QM, but its irrelevant to photon mass/momentum..
So anyways, without alot of unneeded eqn formatting, http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html
The relativistic momentum equation was a factor, it just needs some revamping when dealing with 0 rest mass.. (To keep the mathematics honest)

#### studiot

Joined Nov 9, 2007
4,998
If you want to be honest, the derivation you linked to has a 0/0 which it sidesteps by eliminating v between the square of the relativistic momentum and square of the relativistic total energy equation.
Then it takes only the positive square root without reason, just as I said.

You haven't gained anything by this manipulation over what I proposed.

The plain fact is that you cannot derive Plank's equation from special relativity. Both give independent 'estimates' for the total energy of a harmonic oscillator.

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