Why doesn't a photon's mass increase to infinity?

[Francis Ward]

Pretty self explanatory really. If a photon has a mass (1.67 * 10^-27 kg), and it travels at the speed of light, why does it's mass not increase to infinity?

 

[Orodruin]

If a photon has a mass (1.67 * 10^-27 kg)

It doesn't.

why does it's mass not increase to infinity?

Also, mass is an invariant quantity. Relativistic mass is an obsolete concept that is no longer in active use among physicists.

 

[sweet springs]

That is worth questioned not for photon but for neutrino that have been assumed to have speed of light but recently identified to have mass. Neutrino speed and mass relation is not explained yet.

Just for fun cosmic background of 3K temperature neutrino gas has energy/c^2 in molecule average, 3*3*1.38E-23 Joule / (3E+8)^2 (m/s)^2= 1.38E-39 kg = m gamma. m is very close to zero and gamma is a large number.

 

[Nugatory]

Pretty self explanatory really. If a photon has a mass (1.67 * 10^-27 kg), and it travels at the speed of light, why does it's mass not increase to infinity?

Where did you see that $1.67\times{10}^{-27}$ kg?

Most likely you were reading something that was reporting an upper bound on the photon mass. All our theories predict that the photon has zero mass, but when it comes to performing experiments to measure the mass of the photon there's always going to be some experimental error. So if we measure the photon mass to be zero but our experiment has a possible error of $1.67\times{10}^{-27}$ kg, we report the result as an upper bound: "Whatever the photon mass is, it has to be something less than $1.67\times{10}^{-27}$ kg". That doesn't mean that anyone is expecting the actual value to be anything other than exactly zero.

If the photon mass is something very small but not exactly zero then its speed would also be something very slightly less than $c$ (and we'd regret the historical accident that led us to call $c$ "the speed of light").

To get a sense of what "not exactly zero" means here, it would be good exercise to try filling in the blanks in the sentence "$1.67\times{10}^{-27}$ kg is to a liter of water (which weighs 1 kg) as [blank] is to [blank]". The Pacific ocean would be a good start on the second blank.

 

[PeterDonis]

If a photon has a mass (1.67 * 10^-27 kg)

Are you sure you don't mean "proton"?

Where did you see that $1.67\times{10}^{-27} kg$?

Probably somewhere that was giving the mass of the proton (not photon).

Most likely you were reading something that was reporting an upper bound on the photon mass

I wouldn't think so, since the upper bound on the photon mass is much smaller; about $10^{-54}$ kg last I checked.

 

[Nugatory]

I wouldn't think so, since the upper bound on the photon mass is much smaller; about $10^{-54}$ kg last I checked.

Ah - right. I must confess that I didn't even check, just fixated on the "travels at the speed of light" bit.

 

[Orodruin]

It should also be pointed out that if the photon does have a non zero mass, then it would - ironically as it may sound - not travel at the speed of light.

 

[sweet springs]

Oh! it's like Jesus was born in 4 B.C. or length of equator is 40,075 kilometres.

 

[Francis Ward]

Reading further, documents say that photons (not protons) have a mass varying from massless to the figure I said. If Einsteins equation is to hold true (IF) then photons must have mass, or must be energyless. Or, they have mass and do not travel at the speed of light.

 

[sweet springs]

$$E^2=p^2c^2+m^2c^4$$
Is the equation. m=0 and E>0 stand.

 

[Nugatory]

Reading further, documents say that photons (not protons) have a mass varying from massless to the figure I said.

If you could provide a link to whatever you've read that says that? Either it's wrong or you've misunderstood it, but we can't tell which if we haven't seen it.

If Einsteins equation is to hold true (IF) then photons must have mass, or must be energyless.

Einstein's equation is $E^2=(mc^2)^2+(pc)^2$, which allows for particles with energy by no mass.

 

[Mister T]

Pretty self explanatory really. If a photon has a mass (1.67 * 10^-27 kg), and it travels at the speed of light, why does it's mass not increase to infinity?

Protons have a mass of $1.67 \times 10^{-27}$ kg and they never travel at the speed of light..
Photons have a mass of zero and they always travel at the speed of light.

Mass doesn't increase with speed.

There is this old-fashioned thing called relativistic mass that increases with speed, but that is not what physicists mean by mass.

 

[girts]

folks, by reading this discussion a question arises, now we say the photon has no mass and that it is the quanta of EM radiation as we can measure specific wavelengths corresponding to specific energies, now I don't doubt the part where we can measure the frequency of the photon as we have done numerous times, but reading this discussions I kind of get the feeling that we only say that the photon has no mass because it works nicely with the Einstein equation which itself works nicely with everything else, is that correct?
so do we have definitive physical experimental evidence of the photon having exactly no mass at all or did we concluded that part based from math?because we are saying that in order for the photon to travel at light speed which is defined as c it can't have any mass otherwise it would require infinite energy to accelerate it to c but what I find interesting is that the speed c is not some infinite number instead it is (I assume by physical hard evidence) measured to be a specific velocity which in itself is not infinite, so theoretically if the photon indeed has some minor minor mass couldn't it then as well travel at the speed it does?

 

[Ibix]

You can model a photon having mass. It doesn't travel at c in that case. This changes nothing about relativity, which simply requires that there be a finite invariant speed, not that anything must travel at it.

There are measurable consequences to a photon having mass, though, one being that the electric field inside an isolated charged spherical shell would be non-zero. It's zero if and only if the photon mass is zero, and increases as you increase your assumed photon mass. Given the precision of the measurements like this that we can make we know that any mass the photon has is below 10^-54kg, taking Peter's word for the value.

And the thing about something having such a tiny mass is that it would take almost no energy to accelerate it to 0.999999...9c relative to any observer attempting to stop it - which is why we would always see them traveling at a speed that is currently experimentally indistinguishable from c.

 

[PeterDonis]

I kind of get the feeling that we only say that the photon has no mass because it works nicely with the Einstein equation which itself works nicely with everything else, is that correct?

No. See below.

do we have definitive physical experimental evidence of the photon having exactly no mass at all or did we concluded that part based from math?

You can never prove experimentally that the photon mass is exactly zero; all experiments have some finite error. But you can experimentally set an upper bound on the photon mass; as I posted earlier, the latest experimental upper bound is about $10^{-54}$ kg. So we certainly aren't concluding anything "just from math" in this case.

https://en.wikipedia.org/wiki/Photon#Experimental_checks_on_photon_mass

 

[Mister T]

but reading this discussions I kind of get the feeling that we only say that the photon has no mass because it works nicely with the Einstein equation which itself works nicely with everything else, is that correct?

Depends on what you mean by "works nicely". If you mean that those equations describe the very same behavior that we observe nature exhibiting, then yes, that is the only reason.

 

[girts]

ok I get what you are all saying.
Ibix mentioned here and I also see it written in the wiki article that if photon had a mass with value above that lowest current detectable threshold then there would exist an E field inside a hollow but closed conductor like in a metal sphere, now can someone explain why would that be and by what mechanism?I assume this is out of the scope of this thread but the article also mentions that photons do develop non-zero "effective rest mass" within superconductors, now I wonder what does it really mean, I assume it shouldn't mean that the photon suddenly changes its fundamental properties but instead acts like it had done so?
well maybe someone here has some good link to a place where this would be explained well, thanks in advance.

 

[Dr Whom]

Proton's have this mass and do not travel at the speed of light. Nor do neutrinos.
Photons have energies that is exactly consistent with a massless object traveling at the speed of light.
They need to travel at this speed for very many reasons. At the speed of light they experience zero time from their point of origin to the time they are absorbed, which can be billions of years for us slow matter objects. In this way they preserve precisely the information encoded within them at the moment of their creation. Consequently, we see the stars exactly as they were the moment the photons left them. Without this basic property we would have a great deal more difficulty in understanding the universe.

 

[PeterDonis]

At the speed of light they experience zero time from their point of origin to the time they are absorbed

This is not correct. The correct statement is that the concept of "experienced time" does not apply to photons. It only applies to objects that move on timelike worldlines.

In this way they preserve precisely the information encoded within them at the moment of their creation.

Your implied logic here is also not correct. The fact that a photon's worldline is null (has zero "length" according to the metric of spacetime) does not mean the photon cannot change during its travel.

 

[nitsuj]

Can we not measure the exact energy of a photon? Maybe more specifically the momentum it "imparts" on whatever body. Wouldn't there also be an understanding of the potential cause(s) of the error beyond "the photons mass is non-zero"?

Said different; "experimental error" not a "physics error".

 

[Orodruin]

Can we not measure the exact energy of a photon?

No. You can never measure anything exactly. Measurements are always subject to measurement errors leading to uncertainties.

 

[sweet springs]

Smart astrophysics people could show idea of photon mass estimation making use of GR, e.g. BH light bending or extension of wave length via inflating universe.

 

[Ibix]

Ibix mentioned here and I also see it written in the wiki article that if photon had a mass with value above that lowest current detectable threshold then there would exist an E field inside a hollow but closed conductor like in a metal sphere, now can someone explain why would that be and by what mechanism?

Bearing in mind that my knowledge of quantum field theory is somewhat limited, the following is my understanding. Photons are excitations of the (quantised) electromagnetic field. That means that if they have mass it's because the electromagnetic field has a non-zero mass density associated with it. And that would make a difference to the behaviour of all electromagnetic phenomena, not just the speed of light.

 

[girts]

well I assume @Ibix that no one has ever seen a photon and unlike a proton or an electron it even can't be seen as it's just a name given to what we observe as being discrete events of energy striking say a metal plate and knocking out electrons with corresponding energy levels so we kind of decided that there must be something particle like hitting on the other side.
I guess its kind of mind boggling and interesting that we can detect these quanta of the EM field yet their so mysterious, it kind of seems like we know certain properties of a person and their character without ever knowing or even being able to see the person.@nitsuj, I think we can measure the energy from even a single photon IIRC, but what has that to do with it's mass (even if there is some) ?

 

[Mister T]

Can we not measure the exact energy of a photon?

No, we cannot. There is always some uncertainty associated with the measurement.

 

[Mentz114]

well I assume @Ibix that no one has ever seen a photon and unlike a proton or an electron it even can't be seen as it's just a name given to what we observe as being discrete events of energy striking say a metal plate and knocking out electrons with corresponding energy levels so we kind of decided that there must be something particle like hitting on the other side.
I guess its kind of mind boggling and interesting that we can detect these quanta of the EM field yet their so mysterious, it kind of seems like we know certain properties of a person and their character without ever knowing or even being able to see the person.@nitsuj, I think we can measure the energy from even a single photon IIRC, but what has that to do with it's mass (even if there is some) ?

Photons are very interesting and show wave properties. Have a look at this tutorial article
http://iopscience.iop.org/article/10.1088/0143-0807/37/2/024001

[Edit]
I just noticed this is the relativity forum so this post may be inappropriate here.

 

[Ibix]

no one has ever seen a photon and unlike a proton or an electron it even can't be seen as it's just a name given to what we observe as being discrete events of energy striking say a metal plate and knocking out electrons with corresponding energy levels so we kind of decided that there must be something particle like hitting on the other side.

Of course, what you mean by seeing a proton is that your eyes absorb these "discrete events of energy" as they arrive in a way you interpret as consistent with them having been deflected by some particle. All observation has an element of interpretation to it, and protons and electrons are no more real than photons.

 

[Dr Whom]

This is not correct. The correct statement is that the concept of "experienced time" does not apply to photons. It only applies to objects that move on timelike worldlines.
By moving only on spacelike worldlines at the speed of light no time passes. Basic SR.Your implied logic here is also not correct. The fact that a photon's worldline is null (has zero "length" according to the metric of spacetime) does not mean the photon cannot change during its travel.

In what way do you believe photons change during their travel? If they did then the information they contain would be compromised making all observational data unreliable. .

 

[ZapperZ]

In what way do you believe photons change during their travel?

It's position. And this is not a "belief" either.

Zz.

 

[Dr Whom]

So besides their position they do not change or undergo any entropic increase or equivalently experience time. Which is precisely what I stated in the first place. Elementary SR.

 

[Orodruin]

So besides their position they do not change or undergo any entropic increase or equivalently experience time. Which is precisely what I stated in the first place. Elementary SR.

Photons do not exist in elementary SR. You need QFT for that. Furthermore it is generally not relevant to talk about what is “experienced by” a classical massless particle, since it has no rest frame.

Also, photons do not have a well defined position operator.

 

[PeterDonis]

In what way do you believe photons change during their travel?

In a curved spacetime, their frequency/wavelength changes as they travel.

 

[Ibix]

By moving only on spacelike worldlines at the speed of light no time passes. Basic SR.

Please quote correctly. This was something you wrote, not something Peter wrote. It's also incorrect - light travels on null worldlines, not spacelike ones, and proper time is not defined along them. Coordinate time is, though. So a correct statement would be that proper time is not a concept that applies to light.

In what way do you believe photons change during their travel?

Redshift is the obvious one.

If they did then the information they contain would be compromised making all observational data unreliable. .

It seems like you are saying that only things traveling on null worldlines can carry information. If you are claiming that, could you explain how a CRT monitor works? If you are not claiming that, could you say what you do mean?

 

[nitsuj]

@nitsuj, I think we can measure the energy from even a single photon IIRC, but what has that to do with it's mass (even if there is some) ?

thinking that radios, eyes and other thing don't get more massive from absorbing more photons. That their energy is "free" of mass; is massless.

if the incoming photons' momentum net to zero on the body does that add to the mass of the body

 

[nitsuj]

No. You can never measure anything exactly. Measurements are always subject to measurement errors leading to uncertainties.

What about, are the errors and uncertainties known; their causes? I'd consider the uncertainty principle to be a known unknown and kind of irrelevant with respect to experimental errors. Surely for the equipment and other parts of the experiment the source of the errors are known, mitigated and corrected for as reasonable.