Do Photons Gain Infinite Mass at Light Speed?

[antariksh]

Just a thought, according to Einsteins relativity mass changes with speed and tends to become infnite as it approaches 'c'. Since photons too have mass, why doesn't their mass become infinite since they travel at c?

 

[mathman]

Photons have zero "rest mass", so that the Lorentz transformation can't be used - ie. m= (0/0)*c².

 

[Gyroscope]

How is it possible for photons to have momentum if they are massless?

 

[ranger]

Read these FAQs:
http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html
http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

 

[ranger]

How is it possible for photons to have momentum if they are massless?

The momentum is related to wavelength:

p = \frac{h} {\lambda}

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html#c2

 

[robphy]

Photons have zero "rest mass", so that the Lorentz transformation can't be used - ie. m= (0/0)*c².

Rather than the phrase "rest mass", it might be more appropriate to use the term "invariant mass" or (up to factors of c) "invariant norm of the momentum 4-vector". With this term, then it is easier to see that one can apply the Lorentz Transformation to the photon's [necessarily non-timelike] 4-momentum.

One sees that its square-norm being zero is true in all inertial reference frames. In addition, its temporal component is essentially the relativistic energy (up to constants, the frequency) of the photon. Similar to the "relativistic mass" (or better, up to constants, "relativistic energy"), the relativistic energy of the photon can be boosted toward infinity. (Of course, the "factor" is different... for the photon, it is "k" (the doppler factor), which is \gamma(1+v).)

Of course, what you can't do is to boost from the frame of a timelike particle (where that particle is at rest) to one for a null (or lightlike) particle.

 

[jtbell]

Photons have zero "rest mass", so that the Lorentz transformation can't be used - ie. m= (0/0)*c².

That's not the Lorentz transformation. The Lorentz transformation equations for position and time are

x^\prime = \gamma (x - vt)[/itex]<br /> <br /> t^\prime = \gamma \left( t - \frac {vx}{c^2} \right)<br /> <br /> for position and time, and<br /> <br /> p^\prime = \gamma \left( p - \frac {vE}{c^2}\right)<br /> <br /> E^\prime = \gamma (E - vp)<br /> <br /> for momentum and energy. As far as I know, they are valid for light (photons) as well as for particles with nonzero &quot;rest mass&quot;.

 

[bernhard.rothenstein]

Just a thought, according to Einsteins relativity mass changes with speed and tends to become infnite as it approaches 'c'. Since photons too have mass, why doesn't their mass become infinite since they travel at c?

photon momentum and energy is a frequent topic on the forum. consider a tardyon (u<c) the momentum of which transforms as
p=gp'(1+V/u') (1)
E=gE'(1+Vu'/c^2) (2)
state that special relativity theory ensures a smooth transition from the properties of the tardyon to the properties of a photon and make in (1) and (2) u=u'=c in order to obtain in its case
p(c)=gp'(c)(1+V/c) (3)
E(c)=gE'(c)(1+V/c) (4)
Is there more to say?
sine ira et studio

 

[nakurusil]

photon momentum and energy is a frequent topic on the forum. consider a tardyon (u<c) the momentum of which transforms as
p=gp'(1+V/u') (1)
E=gE'(1+Vu'/c^2) (2)

Doesn't look correct. Here are the correct ones.

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/vec4.html

For the photon you can further simplify the above by using the fact that energy and momentum are related by E=c*\sqrt&lt;p,p&gt;.

 

[duordi]

We are not sure that light has zero rest mass or that it travels 100% of the speed of light.

But we do know it is very close to it. Make that very very close.

 

[yenchin]

We are not sure that light has zero rest mass or that it travels 100% of the speed of light.

But we do know it is very close to it. Make that very very close.

Light does not travel at the speed of light? Then why do you call it "the speed of light"?

 

[duordi]

Is 99.9999999999 equal to 100?

No it isn't, but can you tell? That is the point.

If a person is accelerated to 99% of the speed of light and that person measures the speed of the photon passing him he will determine the photon is traveling past him at the speed of light.

So if two photons are traveling in parallel paths what speed do they measure of each with respect to the other?

 

[rbj]

Photons have zero "rest mass", so that the Lorentz transformation can't be used - ie. m= (0/0)*c².

or, looking at it another way, instead of mapping rest mass to "relativistic mass" (or "inertial mass" or whatever it is you get when you divide momentum by velocity),

m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}

map it back the other way:

m_0 = m \sqrt{1 - \frac{v^2}{c^2}}

so, if the photon has a finite inertial mass

E = m c^2 = h \nu

or

m = \frac{E}{c^2} = \frac{h \nu}{c^2}

and the momentum is

p = m v = \frac{h \nu}{c^2} v

but if the velocity of the photon is c, then

p = m c = \frac{h \nu}{c}

no matter what that finite value is, the rest mass (or "invariant mass") is still zero when v = c.

m_0 = m \sqrt{1 - \frac{c^2}{c^2}} = m \sqrt{1 - 1} = 0

that's my oversimplistic spin on it.

 

[yenchin]

No it isn't, but can you tell? That is the point.

If a person is accelerated to 99% of the speed of light and that person measures the speed of the photon passing him he will determine the photon is traveling past him at the speed of light.

So if two photons are traveling in parallel paths what speed do they measure of each with respect to the other?

The speed of light is, well, the speed of light. If you think that photon travel at 0.999999999999c where c is the current value of the speed of light, we can just define the "correct" speed of light as c'=0.999999999999c.

 

[pervect]

No it isn't, but can you tell? That is the point.

If a person is accelerated to 99% of the speed of light and that person measures the speed of the photon passing him he will determine the photon is traveling past him at the
of light.

So if two photons are traveling in parallel paths what speed do they measure of each with respect to the other?

Photons don't experience time, and thus they can't measure speed. The closest thing to "experiencing time" is that photon geodesics can be parametrized in terms of an affine parameter, which however is neither like time (timelike) nor like space (spacelike), but null.

There are a number of FAQ's and threads on this

http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/headlights.html
https://www.physicsforums.com/showthread.php?t=132528

and there's a lot more I've skipped over, including one by robphy that was particularly good that I can't find.

 

[duordi]

You are correct pervect

For this reson if a photon has zero rest mass it may also be an unstable energy unit but without the time to decay for certainly it would have decayed in billions of years of travel if it contained a time component.

As to the light speed.

If a photon has a rest mass particle then it can not attain a speed of C but will only attain a velocity of C ‘ which is slightly less then the theoretical speed of light C.

In this case the measured speed of light is C ’ and the true speed of light C must be calculated or by other means to be known.

The photon must also be a stable energy unit to prevent decay.

 

[rbj]

We are not sure that light has zero rest mass or that it travels 100% of the speed of light.

But we do know it is very close to it. Make that very very close.

Light does not travel at the speed of light? Then why do you call it "the speed of light"?

the quantity we call c is the wavespeed of electromagnetic propagation in a vacuum that you get from solving Maxwell's Equations. you know:

c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}

it would be more precise to say that "We are not sure that photons have zero rest mass or that they travel at 100% of the wavespeed of light." BTW, this was something totally new to me a year ago. i still have trouble believing it. (there is the aesthetic part of me that wants the dogma that the speed of photons are c which means they must have zero rest mass.)

 

[duordi]

Interestingly C was defined by definition in 1983.
Permittivity (E)of free space is defined by C and the Maxwell equations.
Permeability (u) is measured.

Which means C can not be determine by ( or is not determined ?) by the Maxwell equations.
Unless (E) can be measured.

http://en.wikipedia.org/wiki/Speed_of_light

 

[nakurusil]

Interestingly C was defined by definition in 1983.
Permittivity (E)of free space is defined by C and the Maxwell equations.
Permeability (u) is measured.

Which means C can not be determine by ( or is not determined ?) by the Maxwell equations.
Unless (E) can be measured.

http://en.wikipedia.org/wiki/Speed_of_light

Correct, as per wiki:

"In metric units, c is exactly 299,792,458 metres per second (1,079,252,848.8 km/h). Note that this speed is a definition, not a measurement. Since the fundamental SI unit of length, the metre, has been defined since October 21, 1983 in terms of the speed of light; one metre is the distance light travels in a vacuum in 1/299,792,458 of a second."

You may wonder why is c defined and not measured to be 299,792,458 metres per second .
The reason is that any physical measurement has certain error attached to it, so that a number had to be chosen. To recap:

1. c is chosen
2. \epsilon_0 is defined based on c
3.\mu_0 is derived based on the values chosen at 1 and 2

So, all of the above guarantees that c is exactly 299,792,458

 

[MeJennifer]

You may wonder why is c defined and not measured to be 299,792,458 metres per second .
The reason is that any physical measurement has certain error attached to it, so that a number had to be chosen. To recap:

1. c is chosen
2. \epsilon_0 is defined based on c
3.\mu_0 is derived based on the values chosen at 1 and 2

So, all of the above guarantees that c is exactly 299,792,458

Actually the reason c is a constant has to do with how the meter is defined.

 

[jtbell]

It's worth noting that the definitions of SI (MKS) units are made for practical reasons. They are intended to permit the most precise measurements possible, with the current state of technology.

Before 1983, the second was defined in terms of the period of a certain atomic transition, and the meter was defined in terms of the wavelength of another atomic transition. Those definitions were made because they could be reproduced in laboratories with the highest degree of precision possible at the time.

At some point, measurements of the speed of light became intrinsically more precise than the precision of the definition of the meter. Since there was (and still is) no experimental indication that the speed of light is not constant, defining the meter in terms of a constant, defined value of the speed of light maximizes the precision of measurements overall.

If at some point the speed of light is shown not to be constant, then the definition of the meter will surely be changed to reflect this.

 

[ZapperZ]

If at some point the speed of light is shown not to be constant, then the definition of the meter will surely be changed to reflect this.

Actually, that need not necessarily be the case.

A second is defined using the frequency of Cs atoms right now. However, we know that the period of time is frame dependent (i.e. Cs atom in another frame would not have the same frequency). Yet, we still use this as our standard definition of a second.

So based on this, I think we can still use c to define a meter, even if we find (a very big if) situations where it isn't a constant. We just have to clearly define under what conditions this definition is to be used, just like most of our other constants.

Zz.

 

[duordi]

Interesting thoughts

Because the terms are defined from one another it is impossible to determine if indeed light photons have slightly slower velocity then a theoretical maximum mass speed of light C.

It would be interesting to use the plank constant values to determine the minimum size of a mass particle and accelerate the mass until it had a photon equivalent relativistic mass.
The percentage of the speed of light the photon would achieve could then be calculated.

Different wavelengths would mean different relativistic mass quantities and different velocities however small these velocities differences may be.
It would be interesting to calculate the difference in velocity to determine if the velocity difference is measurable.

The effect would cause different wavelengths from a distant star to reach us with time delays.
Does anyone know if a pulsar has been checked to see if the lower and higher wave lengths are received without a time delay when viewed at the greatest distance possible?

If one photon had one smallest mass particle it would cause a quantum condition because photons could only have a whole number of smallest mass particles.

 

[nakurusil]

Actually the reason c is a constant has to do with how the meter is defined.

c is constant by definition in relativity. In addition, there is ample experimental confirmation, so I don't think that c being a constant has much if anything to do with the meter is defined.
Actually, it is exactly the other way around, the definition of the meter is dependent on c:

http://en.wikipedia.org/wiki/Meter

and on the definition of the second.

 

[MeJennifer]

I do not think so.

That is fine, and you seem to be hard to convince , so I won't bother.

For others, the meter is defined in terms of the speed of light. One meter is the distance traveled by light in a vacuum in 1/299,792,458 of a second. So obviously c must be 299,792,458.

 

[nakurusil]

That is fine, and you seem to be hard to convince , so I won't bother.

For others, the meter is defined in terms of the speed of light. One meter is the distance traveled by light in a vacuum in 1/299,792,458 of a second. So obviously c must be 299,792,458.

Check my post.

 

[rbj]

Actually the reason c is a constant has to do with how the meter is defined.

I don't think so.

That is fine, and you seem to be hard to convince , so I won't bother.

For others, the meter is defined in terms of the speed of light. One meter is the distance traveled by light in a vacuum in 1/299,792,458 of a second. So obviously c must be 299,792,458.

he must have deleted that post, because i was about to tell him to check it out at the NIST site if he doesn't believe it.

some of the other stuff he said (like \mu_0 being derived) is not correct either.

 

[nakurusil]

I don't think so.
he must have deleted that post, because i was about to tell him to check it out at the NIST site if he doesn't believe it.

some of the other stuff he said (like \mu_0 being derived) is not correct either.

http://en.wikipedia.org/wiki/Speed_of_light

http://en.wikipedia.org/wiki/Meter

https://www.physicsforums.com/showpost.php?p=1239526&postcount=24

 

[rbj]

Check my post.

what's there to check? you said two things that are demonstratively incorrect. check the NIST site to see how these get defined so that c = 299792458 m/s. and how \mu_0 is defined, not derived.

 

[nakurusil]

what's there to check? you said two things that are demonstratively incorrect. check the NIST site to see how these get defined so that c = 299792458 m/s. and how \mu_0 is defined, not derived.

Look at "Overview" here:

http://en.wikipedia.org/wiki/Speed_of_light

mu_0 value is chosen such that 1/\sqrt(\epsilon_0mu_0)=299,...

 

[nakurusil]

what's there to check? you said two things that are demonstratively incorrect. check the NIST site to see how these get defined so that c = 299792458 m/s. and how \mu_0 is defined, not derived.

Look at "Overview" here:

http://en.wikipedia.org/wiki/Speed_of_light

\mu_0 value is chosen such that 1/\sqrt(\epsilon_0 \mu_0)=299,...

 

[rbj]

c is constant by definition in relativity. In addition, there is ample experimental confirmation, so I don't think that c being a constant has much if anything to do with the meter is defined.
Actually, it is exactly the other way around, the definition of the meter is dependent on c:

http://en.wikipedia.org/wiki/Meter

and on the definition of the second.

a postulate is not a definition. a definition is something that is not a "truth" that is proposed. a postulate (such as the invariancy of c in SR) is something akin to a physical law.

we could define a meter to be the distance that sound in air at STP travels in 1/331.5 second and that would fix the speed of sound in air at STP to be 331.5 m/s. does that mean that the speed of sound is defined to be constant in the same way that c is believed to be constant?

c = 299792458 m/s because the meter was defined to make it so. now, if these VSL guys are correct (i don't think they are) then the distance between the two little scratch marks on the prototype meter will have changed, in terms of the present definition, if the speed of light actually did change sufficiently.

but i agree, that to speak of a changing speed of light, especially when the base units are defined as they are, is meaningless. the only numbers about the that we measure are ultimately dimensionless numbers. if \alpha changes, that is meaningful, but there is no meaning in saying that c, G, \hbar changes in and of themselves. if the number of Planck lengths in the Bohr radius changes, that is meaningful and, assuming the old prototype meter stick is a "good" meter stick (and it doesn't lose or gain atoms), then the number of Planck lengths between those little scratch marks will have changed.

but the fact that c=299792458 is a matter of how they defined the meter and SR could not have predicted or determined that.

 

[rbj]

Look at "Overview" here:

http://en.wikipedia.org/wiki/Speed_of_light

\mu_0 value is chosen such that 1/\sqrt(\epsilon_0 \mu_0)=299,...

baloney. you need to read up on some of this.

\mu_0 = 4 \pi \cdot 10^{-7} in whatever units because of how they defined the Ampere. check it out yourself.

 

[nakurusil]

baloney. you need to read up on some of this.

\mu_0 = 4 \pi \cdot 10^{-7} in whatever units because of how they defined the Ampere. check it out yourself.

Yes, I know that. How do you explain the "Overview" then? It indicates that \epsilon_0, \mu_0 are arranged, chosen, fitted, however yo want to call them such that 1/\sqrt\epsilon_0\mu_0=299,... . And that is the value attributted to c

 

[nakurusil]

a postulate is not a definition. a definition is something that is not a "truth" that is proposed. a postulate (such as the invariancy of c in SR) is something akin to a physical law.

we could define a meter to be the distance that sound in air at STP travels in 1/331.5 second and that would fix the speed of sound in air at STP to be 331.5 m/s. does that mean that the speed of sound is defined to be constant in the same way that c is believed to be constant?

c = 299792458 m/s because the meter was defined to make it so. now, if these VSL guys are correct (i don't think they are) then the distance between the two little scratch marks on the prototype meter will have changed, in terms of the present definition, if the speed of light actually did change sufficiently.

but i agree, that to speak of a changing speed of light, especially when the base units are defined as they are, is meaningless. the only numbers about the that we measure are ultimately dimensionless numbers. if \alpha changes, that is meaningful, but there is no meaning in saying that c, G, \hbar changes in and of themselves. if the number of Planck lengths in the Bohr radius changes, that is meaningful and, assuming the old prototype meter stick is a "good" meter stick (and it doesn't lose or gain atoms), then the number of Planck lengths between those little scratch marks will have changed.

but the fact that c=299792458 is a matter of how they defined the meter and SR could not have predicted or determined that.

You missed the point , entirely. I reacted to MeJennifer's statement that said textually c is a constant because...

 

[rbj]

Yes, I know that.

no, you're saying something else.

\mu_0 has had a defined value long before c did. \mu_0 gets its defined value from how they defined the SI unit of current (the Ampere) which, along with the SI unit of time, defines the SI unit charge. don't know if it was Faraday or Boyle or Coulomb or who it was that first measured the inverse-square nature of the electrostatic force, but i imagine that they may have had a crude measured value for \epsilon_0. presumably with Maxwell, they got to relate \epsilon_0 and \mu_0 to c which was measured independently (i presume by the likes of Michaelson) and offered both experimental confirmation of the unified E&M theory of Maxwell, but also offered a better value for \epsilon_0 since they can relate it to the defined \mu_0 and a more accurately measured c. but c was still measured, in terms of the existing meter and second. until they redefined it in 1960 and 1983. they defined the meter in terms of c as they did so that the length of the new definition agreed, as well as they could determine at the time, with the length of the old definition. it's possible now that the distance between those two little scratch marks in the prototype meter bar is measured (using the present definition of the meter) to be something slightly different than a meter (present definition). i would chalk that one up to experimental error or advancement of metrology since 1983 rather than to a change in the speed of light since 1983.

but \mu_0 did not magically come out to be \mu_0 = 4 \pi \cdot 10^{-7} because of how they defined c (or the meter, however you wish to put it).

some of this might be semantic, but you are objectively mistaken to say that \mu_0 = 4 \pi \cdot 10^{-7} because of how they defined c. that's just incorrect.

 

[rbj]

You missed the point , entirely. I reacted to MeJennifer's statement that said textually c is a constant because...

lessee...

MeJennifer said:

Actually the reason c is a constant has to do with how the meter is defined.

you said:

\mu_0 value is chosen such that 1/\sqrt(\epsilon_0 \mu_0)=299,...

i'm placing my bets with MeJennifer.

 

[rbj]

Interestingly C was defined by definition in 1983.
Permittivity (E)of free space is defined by C and the Maxwell equations.
Permeability (u) is measured.

oh, i missed this! this is where the evil misconception started. most certainly the Permeability of Free Space \mu_0 is not measured, but defined as a consequence of the definition of the unit of electrical current, the Ampere.

 

[ZapperZ]

Can't someone get ahold of the latest CODATA and figure out how these values were obtained?

Zz.

 

[rbj]

Can't someone get ahold of the latest CODATA and figure out how these values were obtained?

what do you mean, Z? the stuff at NIST: http://www.physics.nist.gov/cuu/ reflects the CODATA values but c, \epsilon_0, \mu_0, Z_0 are not CODATA measured values. they are defined in SI. I'm sure you know that, Z. but I'm not sure what you're asking for here.

 

[rbj]

If at some point the speed of light is shown not to be constant, then the definition of the meter will surely be changed to reflect this.

JT, how would we ever know if the speed of light is changing? what would be the standard against which we measure the speed of light? when we measure anything, ultimately what we have are dimensionless quantities that we conceptually attach dimensionful units to. but since these dimensionless quantities are ratios of like-dimensioned physical quantities, if this ratio changes, how would one know which of the like-dimensioned physical quantities to attribute this change to?

 

[nakurusil]

lessee...

MeJennifer said:




you said:



i'm placing my bets with MeJennifer.

You are still missing the point. I give up, not worth it.

 

[rbj]

You are still missing the point. I give up, not worth it.

what duordi said and you confirmed and reiterated is factually incorrect (about the permeability \mu_0).

what MeJennifer said is factually correct.

whatever your point is, i guess i did miss it.

 

[nakurusil]

what MeJennifer said is factually correct.

whatever your point is, i guess i did miss it.

Actually the reason c is a constant has to do with how the meter is defined.

NOT. Or maybe you think it is correct?

 

[MeJennifer]

Here is the http://www.physics.nist.gov/cuu/Units/meter.html"

The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second.

Furthemore from the same page:

Note that the effect of this definition is to fix the speed of light in vacuum at exactly 299 792 458 m·s-1.

 

[nakurusil]

Here is the http://www.physics.nist.gov/cuu/Units/meter.html"
Furthemore from the same page:

Yes, the sentence means that it makes c equal to the specific value of 299,... Do you understand the difference between that and making c a constant?
c is a constant for profound physical reasons, not because of the definition of the meter. You don't simply make c a constant

 

[rbj]

Here is the http://www.physics.nist.gov/cuu/Units/meter.html"

while we're at it, here it is for the Ampere:

The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 \times 10^{-7} Newton per meter of length.

The expression "MKS unit of force" which occurs in the original text has been replaced here by "Newton," the name adopted for this unit by the 9th CGPM (1948). Note that the effect of this definition is to fix the magnetic constant (permeability of vacuum) at exactly \mu_0 = 4 \pi \times 10^{-7} H \cdot m^{-1}.

 

[MeJennifer]

Yes, the sentence means that it makes c equal to the specific value of 299,... Do you understand the difference between that and making c a constant?
c is a constant for profound physical reasons, not because of the definition of the meter. You don't simply make c a constant

It seems that you rather deny the reality of certain things than admit you are wrong.

 

[rbj]

Yes, the sentence means that it makes c equal to the specific value of 299,... Do you understand the difference between that and making c a constant?
c is a constant for physical reasons, not because of the definition of the meter. You don't simply make c a constant

if it changed, how would we meaningfully measure it? you might want to read some stuff from Michael Duff http://www.arxiv.org/abs/hep-th/0208093 or http://xxx.lanl.gov/abs/physics/0110060 or just check out the Physical constants or Planck units articles at Wikipedia.

here's a good quote from John Barrow:

[An] important lesson we learn from the way that pure numbers like \alpha define the world is what it really means for worlds to be different. The pure number we call the fine structure constant and denote by \alpha is a combination of the electron charge, e, the speed of light, c, and Planck's constant, h. At first we might be tempted to think that a world in which the speed of light was slower would be a different world. But this would be a mistake. If c, h, and e were all changed so that the values they have in metric (or any other) units were different when we looked them up in our tables of physical constants, but the value of \alpha remained the same, this new world would be observationally indistinguishable from our world. The only thing that counts in the definition of worlds are the values of the dimensionless constants of Nature. If all masses were doubled in value [including the Planck mass m_P ] you cannot tell because all the pure numbers defined by the ratios of any pair of masses are unchanged.

you see, whether it is c, h, G, or e, it's not really meaningful to consider the changing of any of these dimensionful physical constants. it's only the dimensionless physical "constants" that mean anything (have "operational distiguishability") if they changed.

still, MeJennifer had it right and, doggedly you have been holding on to your guns, you did not.

 

[nakurusil]

if it changed, how would we meaningfully measure it?

Who's talking about changing? What exactly do you understand in the post that you just quoted?

you see, whether it is c, h, G, or e, it's not really meaningful to consider the changing of any of these dimensionful physical constants. it's only the dimensionless physical "constants" that mean anything (have "operational distiguishability") if they changed.

Where am I talking about changing? Where did you see that in ANY of my posts?