# Massless photon infinite speed?

1. Aug 20, 2009

### Saaam

massless photon...infinite speed???

ok heres the deal,

a photon is massless
its mass is 0
and f=ma
then why is the speed of light not infinite

2. Aug 20, 2009

### Pengwuino

Re: massless photon...infinite speed???

Well, for one, what are you trying to connect with massless particles and F=ma?

3. Aug 20, 2009

### Saaam

Re: massless photon...infinite speed???

well if m=0,
and if F=any value apart from 0 then acceleration must be infinite?
right?
and if F=0 then acceleration would also be 0?
therefore the speed of light must be either 0 or infinite
but this is not the case
and this is why i am confused...

4. Aug 20, 2009

### Staff: Mentor

Re: massless photon...infinite speed???

Two questions:
(1) What makes you think that F=ma applies relativistically? (It doesn't.)
(2) How are you exerting a force on the photon?

5. Aug 20, 2009

### Staff: Mentor

Re: massless photon...infinite speed???

Another, IMO more general, way to formulate f=ma is f=dp/dt. A photon does not have mass, but it does have momentum.

6. Aug 20, 2009

### Tac-Tics

Re: massless photon...infinite speed???

F=ma isn't how the world works. It's a good approximation in certain cases. It has been superseded by more modern theories.

7. Aug 20, 2009

### vin300

Re: massless photon...infinite speed???

I got what you must be thinking. A system does work to release a photon and since the mass is zero, it can accelerate the photon to infinite speed but 0*oo is not zero, it's indeterminate
{oo is infinity}
And BTW, the photon when released has mass

8. Aug 20, 2009

### Staff: Mentor

Re: massless photon...infinite speed???

9. Aug 20, 2009

### vinirn

Re: massless photon...infinite speed???

The photon is massless, but it has the so-called relativistic mass, the m in the equation

$$E=mc^{2}$$​

The photon must have relativistic mass because E=hf. It's this mass that form the moment p of the photon

10. Aug 20, 2009

### tickle_monste

Re: massless photon...infinite speed???

Um, that m in the equation is the rest mass (please correct me if I'm wrong), which the photon doesn't have. You get the relativistic mass by considering the more fuller equation: E^2=(pc)^2 + (mc^2)^2=p^2c^2 + m^2c^4. The rest mass of the photon is just 0, it only has relativistic mass, so we set m=0, and we get E^2=p^2c^2 + 0 = p^2c^2.

E=[(p^2)(c^2)]^(1/2)=pc. Now, you could try to set pc = E = mc^2 to figure out what the 'mass' of the photon would be, but that's nonsensical for the following reason: to get this equation, we had to assume originally that m=0, and in our final result, pc=/=0 in general.

0 =/= pc = E = mc^2 = (0)c^2 = 0. Thus you would get the nonsensical result: 0=/=0. It's better to just say the photon has momentum.

E = hf = pc.
p = hf/c.
f = c/Lambda.
p = h/Lambda = planck's constant/wavelength.

I believe relativistic mass enters the picture when you make the equation p = mv.
m=p/v. v=c. p=h/Lambda.
m=h/(lambda)c.

11. Aug 20, 2009

### Staff: Mentor

Re: massless photon...infinite speed???

Can you provide a citation to a physics textbook or a research journal article that actually uses this "relativistic mass of the photon"?

12. Aug 20, 2009

### DrGreg

Re: massless photon...infinite speed???

In relativity, there are (at least) two different concepts of mass. To put it simply
• "rest mass" which excludes kinetic energy
• "relativistic mass" which includes kinetic energy
There are two schools of thought.

The vast majority of professional physicists call rest mass "mass" and don't talk about relativistic mass at all. They say photons are massless.

Some others call relativistic mass "mass" and rest mass "rest mass". They say photons do have mass, but no rest mass.

Hardly anyone routinely uses the phrase "relativistic mass"; it arises only in discussions like this comparing both definitions.

This is a great cause of confusion and it's a pity there isn't universal agreement over the terminology.

Unfortunately usage is not quite so black-and-white as some people think. Relativistic mass is used in the undergraduate-level text book Relativity: Special, General and Cosmological (2nd ed 2006) written by the professional physicist Wolfgang Rindler after whom Rindler coordinates are named. Sorry.

By the way, I personally support the standard convention that most other physicists use, but we can't just pretend the other convention doesn't exist. Both views are technically valid, but use mutually incompatible terminology.

13. Aug 20, 2009

### vinirn

Re: massless photon...infinite speed???

Sorry, I should have written $$E=m_{rel}c^2$$,
where
$$m_{rel}= \frac{m}{\sqrt{1-v^2/c^2}}$$
I could be wrong, but this may be converted to $$E^{2}=(pc)^{2}+(mc^{2})^{2}$$

14. Aug 20, 2009

### Saaam

Re: massless photon...infinite speed???

this is my point
if no force is exerted how can it possibly move?

15. Aug 21, 2009

### vin300

Re: massless photon...infinite speed???

Do you think something that emits light never loses energy?
Better don't talk about the 'force' on the photon because you don't know how long it acts.

Last edited: Aug 21, 2009
16. Aug 21, 2009

### Staff: Mentor

Re: massless photon...infinite speed???

Since you skipped my earlier questions, here's another: Do you think a force is required for something to be moving?

Note that photons do not exist at any speed other than c. When created, they are already moving at full speed. It's not like they are sitting around at rest, then accelerated.

17. Aug 21, 2009

### vin300

Re: massless photon...infinite speed???

A force is required to throw out some mass of the body as a photon

18. Aug 21, 2009

### Staff: Mentor

Re: massless photon...infinite speed???

It's certainly true that a body emitting a photon will experience an impulse (change in momentum) equal and opposite to the momentum of the photon. But that's not quite the same thing as exerting a force on a photon to accelerate it.

19. Aug 21, 2009

### vin300

Re: massless photon...infinite speed???

Why don't both mean the same?

20. Aug 21, 2009

### sas3

Re: massless photon...infinite speed???

Think how confusing it is from the photons point of view, it pops into existence and because it must travel at the speed of light it doesn’t experience any time and then it transfers its energy and pops out of existence in a different place. Another thing that intrigues me (and please correct me if I am wrong) is that a photon has no upper limit on the amount of relativistic mass it can carry. So conceivably the energy of the entire universe could have been contained in a single photon.

Last edited: Aug 22, 2009