Why photons can't go any slower than the speed of light?

[KatamariDamacy]

Why photons can't go any slower than the speed of light, in vacuum? Or if they could, then why they don't?

 

[Nugatory]

Photons are light, so of course the speed they move at is the speed of light.

But if you're asking why light moves at one particular speed ($2.998\times{10}^8$ m/sec, the number we usually call $c$) and never faster or slower... Light is electromagnetic waves traveling through space, and the speed at which these wave move can be calculated from the laws of electricity and magnetism; this calculation was first done by James Maxwell in 1861.

 

[KatamariDamacy]

Photons are light, so of course the speed they move at is the speed of light.

But if you're asking why light moves at one particular speed ($2.998\times{10}^8$ m/sec, the number we usually call $c$) and never faster or slower... Light is electromagnetic waves traveling through space, and the speed at which these wave move can be calculated from the laws of electricity and magnetism; this calculation was first done by James Maxwell in 1861.

Yes, but none of that explains "why". Also, doesn't it speed of propagation for all the other kinds of waves depends on their wavelength or amplitude?

 

[Nugatory]

Yes, but none of that explains "why".

Nobody can answer a "why?" question. You ask "Why is A true?", I answer "Because B", and then you can reasonably ask "But why B?" and the only thing that will end the cycle is mutual fatigue .

In this case, we don't know why the laws of electricity and magnetism are what they are. We know what these laws are, because we've observed electricity and magnetism in experiments and found that they always obey Maxwell's equations.

Also, doesn't it speed of propagation for all the other kinds of waves depends on their wavelength or amplitude?

For some waves, but by no means all, the speed of propagation is dependent on the amplitude. Water waves are an example where the speed depends on the amplitude, sound waves in a rigid material are an example where it does not. In all cases, if you know the underlying equations you can solve them to find the speed-amplitude relationship; the solution to Maxwell's equations are waves whose speed does nor depend on the amplitude.

For all waves, the speed is related to the frequency and wavelength by the relationship "speed equals wavelength times frequency". That holds true for light as well; the higher frequency waves have shorter wavelengths.

 

[vanhees71]

Nugatory gave the only possible answer "why" electromagnetic waves (I avoid the notion of photons here, because you are always mislead if you answer questions about photons on this level of the discussion; only that much: you cannot even define a proper position of a photon; so it simply doesn't make sense to think about them as massless point particles in any way) propagate with a speed independent of the motion of the source: It's so, because that description fits all observations so far. The Maxwell theory of electromagnetic phenomena, among them of course also optics, which is a high-precision science, is among the best tested theories ever, and there is no contradiction whatsoever.

From this Lorentz, Poincare, FitzGerald and finally Einstein in 1905 came to the conclusion that Newtonian spacetime is not in accordance with all observations of physical phenomena, and one must use Minkowski space and special relativity and modify mechanics to be in accordance with all observed phenomena (including electromagnetism).

Then Einstein, by pures thought, came to the conclusion that also special relativity is not enough, because it leads to contradictions when one considers gravity. As is well known, after 10 years of big struggle, it lead him (and at the same time also Hilbert) to the development of the general theory of relativity in 1915, which later proved also to be in accordance with all observations in nature so far (although it's much more difficult to falsify it compared to Maxwell electrodynamics, because gravity is by about 40 orders of magnitude smaller than the electromagnetic interactions).

So if you ask a physicist "why questions" the cycle of arguments come finally and pretty quickly to an end. The final justification for the validity of a theory is its agreement with observations, and you can answer "why questions" only by making use of the best present theory available. Physics, as all natural science, is after all an empirical science, describing what we can objectively observe in nature. It doesn't give "final reasons" for why nature behaves as observed!

If you want to go beyond that level of understanding about nature, you leave the save grounds of the natural sciences and enter something we call philosophy (metaphysics) or esoterics. Don't ask about the boundary between these two. In my opinion there's none ;-)). For sure it's off-topic in this forum!

 

[KatamariDamacy]

Nobody can answer a "why?" question. You ask "Why is A true?", I answer "Because B", and then you can reasonably ask "But why B?" and the only thing that will end the cycle is mutual fatigue .

In this case, we don't know why the laws of electricity and magnetism are what they are. We what these laws are, because we've observed electricity and magnetism in experiments and found that they always obey Maxwell's equations.

Yes, for the most basic concepts there is no answer to "why". My favorite such pickle is - why is there something rather than nothing? However, combined or derived concepts can have "why" explanation, which is really only just a relation with other concepts. So although we don't know why gravity exist or why it has those proportions that it does, we still can explain planetary orbits, explain the speed of falling objects, terminal velocity, or escape velocity. Similarly I think there is reasonable hope this particular question can too have such explanation. In other words, even though the origin remains a mystery, it should still be relative to something.

For all waves, the speed is related to the frequency and wavelength by the relationship "speed equals wavelength times frequency". That holds true for light as well; the higher frequency waves have shorter wavelengths.

In Wikipedia there is phase velocity, pulse wave velocity, group velocity, and front velocity. Are we talking about what they call "group velocity"?

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

 

[PAllen]

In a vaccuum, phase velocity = group velocity, always, for EM radiation.

 

[Nugatory]

So although we don't know why gravity exist or why it has those proportions that it does, we still can explain planetary orbits, explain the speed of falling objects, terminal velocity, or escape velocity. Similarly I think there is reasonable hope this particular question can too have such explanation.

Yes, Newton's three laws and the the gravitational force law ($F=Gm_1m_2/r^2$) accurately describe planetary orbits, the speed of falling objects, terminal velocity, escape velocity, all of that stuff. Likewise, Maxwell's laws of electricity and magnetism accurately describe electromagnetic phenomena including the speed of light.

I don't understand how you're happy cutting off one chain of "Why?" questions with the answer "Because that's what we find when we apply Newton's equations" but not happy cutting off the other chain of questions with "Because that's what we find when we apply Maxwell's equations".

 

[bcrowell]

"Why" questions can have answers, but to decide what would be a satisfying answer, you have to decide what you consider to be fundamental and what you consider to be derived. The modern attitude is that the c in SR is not defined as the speed of light, it's just a conversion factor between time and space. What's fundamental is not Einstein's 1905 postulates (which single out light as if it had some special role) but the Lorentz transformation, which describes the properties of spacetime.

If you accept these foundations, then there is a reason light travels exactly at c, which is that massless particles always travel at c. For suppose that a massless particle had |v|<c in the frame of some observer. Then some other observer could be at rest relative to the particle. In such a frame, the particle's momentum p is zero by symmetry, since there is no preferred direction for it. Then E^2=p^2+m^2 (in units with c=1) is zero as well, so the particle's entire energy-momentum vector is zero. But a four-vector that vanishes in one frame also vanishes in every other frame. That means we're talking about a particle that can't undergo scattering, emission, or absorption, and is therefore undetectable by any experiment. This is physically unacceptable because we don't consider phenomena (e.g., invisible fairies) to be of physical interest if they are undetectable even in principle.

This is cut and pasted from section 4.3.1 of my SR book http://www.lightandmatter.com/sr/ , which gives the background info in more detail.

 

[KatamariDamacy]

I'm don't understand how you're happy cutting off one chain of "Why?" questions with the answer "Because that's what we find when we apply Newton's equations" but not happy cutting off the other chain of questions with "Because that's what we find when we apply Maxwell's equations".

That equations can predict observations is a matter of veracity. Explanations have to be deduced from relations in those equations, it's the other face of physics - interpretation. Maxwell's equations, like any other, carry some meaning and reasons within them, every property is somehow related to some other property. Basically I'm just asking what is the speed of light related to, and how.

 

[KatamariDamacy]

"Why" questions can have answers, but to decide what would be a satisfying answer, you have to decide what you consider to be fundamental and what you consider to be derived. The modern attitude is that the c in SR is not defined as the speed of light, it's just a conversion factor between time and space. What's fundamental is not Einstein's 1905 postulates (which single out light as if it had some special role) but the Lorentz transformation, which describes the properties of spacetime.

Yes, we can arrive to amazing variety of interpretations by simply defining and re-defining the meaning of the words or mathematical symbols. That's a tricky part, indeed. But if all those theories and equations describe the same reality, then the same fundamentals should hold valid in all of them. Wouldn't they?

If you accept these foundations, then there is a reason light travels exactly at c, which is that massless particles always travel at c.

I don't think a velocity can be fundamental, time and distance are. Velocity is always a consequence, always defined or bound by something. Although possible, I'd say it's logically or mathematically wrong to qualify any kind of velocity as "fundamental" property.

 

[Drakkith]

However, combined or derived concepts can have "why" explanation, which is really only just a relation with other concepts. So although we don't know why gravity exist or why it has those proportions that it does, we still can explain planetary orbits, explain the speed of falling objects, terminal velocity, or escape velocity. Similarly I think there is reasonable hope this particular question can too have such explanation. In other words, even though the origin remains a mystery, it should still be relative to something.

It does have an explanation, which was given in post #2 and expanded on throughout the thread. Whether you like that explanation is another matter.

 

[Ich]

Although possible, I'd say it's logically or mathematically wrong to qualify any kind of velocity as "fundamental" property.

Nothing wrong here. As bcrowell explained, we're talking about a union of space and time here, called spacetime. That means space can be measured in the same units as time. But how long is a second of space or a meter of time? There must be a fundamental conversion factor "c" that tells you how many meters you have per second. That fundamental "c" obviously has the dimensions of a velocity.

So everything is logical. You don't have to accept spacetime, however, but then there's no answer to your "why?".

 

[ChrisVer]

@Katamari:
First of all, avoid in trying to find "fundamental" quantities when they are connected. Nothing is more fundamental than the other... Both velocities and spacetime points belong to some vectors. The speed of light c is a better quantity (doesn't depend on reference frame), while position and time depend on the reference frame.

Why photons can't go any slower than the speed of light, in vacuum? Or if they could, then why they don't?

Because if they would go any slower, they would have to be in some other mean and not the vacuum. So when you ask why it travels at c in vacuum, the answer is because it's in vacuum. If it was anywhere else, then the velocity is:
$u= \frac{1}{\sqrt{\epsilon \mu}}$
where $\epsilon, \mu$ the dielectric constant and magnetic constant of the mean material.
Why is that? because that's how waves work, and the electromagnetic waves follow the Maxwell eqs too...

 

[bcrowell]

It does have an explanation, which was given in post #2 and expanded on throughout the thread. Whether you like that explanation is another matter.

Well, there have been two completely different explanations discussed in the thread.

@Katamari:
Because if they would go any slower, they would have to be in some other mean and not the vacuum. So when you ask why it travels at c in vacuum, the answer is because it's in vacuum. If it was anywhere else, then the velocity is:
$u= \frac{1}{\sqrt{\epsilon \mu}}$
where $\epsilon, \mu$ the dielectric constant and magnetic constant of the mean material.
Why is that? because that's how waves work, and the electromagnetic waves follow the Maxwell eqs too...

This seems like a very unsatisfactory explanation to me. Then you would have to have a completely different explanation for why gluons travel at c, and why gravitational waves travel at c.

 

[Dale]

Basically I'm just asking what is the speed of light related to, and how.

It is related to Maxwells equations since light is an electromagnetic wave.
It is related to the invariant speed of the Lorentz transform since light is massless.
It is related to our systems of units since it is a dimensionful universal constant.

 

[Drakkith]

Well, there have been two completely different explanations discussed in the thread.

Have there?

*rubs eyes*

I think I need some sleep.

 

[KatamariDamacy]

It does have an explanation, which was given in post #2 and expanded on throughout the thread. Whether you like that explanation is another matter.

I don't see any equations in that post. I see description rather than explanation.

It is related to Maxwells equations since light is an electromagnetic wave.
It is related to the invariant speed of the Lorentz transform since it is massless.

What equation(s) are you talking about? Isn't there any equation that tells us _why does the speed of light have that particular number, and not less or more?

 

[Dale]

What equation(s) are you talking about?

These: http://en.wikipedia.org/wiki/Maxwell's_equations#Conventional_formulation_in_SI_units (see also: http://en.wikipedia.org/wiki/Maxwel...s.2C_electromagnetic_waves_and_speed_of_light )
and these: http://en.wikipedia.org/wiki/Lorentz_transformation#Boost_in_the_x-direction

Isn't there any equation that tells us _why does the speed of light have that particular number, and not less or more?

No. That is not due to any equation or any physics. That is purely due to our choice of units. You can make it be any number you want by choosing different units. Often, we even use units where it is a dimensionless 1.

 

[Nugatory]

Maxwell's equations, like any other, carry some meaning and reasons within them, every property is somehow related to some other property. Basically I'm just asking what is the speed of light related to, and how.

Have you looked at Maxwell's equations?

Among other things, they show that a decreasing magnetic field will produce an increasing electric field nearby and that a decreasing electric field will produce an increasing magnetic field nearby. That's a situation that naturally leads to wave-like oscillations: use charged particles to set up an electric field, then remove the charges so that the electric field starts to decrease to zero; as it decreases, a magnetic field is produced; when the electric field is done decreasing to zero there's nothing to produce the magnetic field any more so it starts decreasing; the decreasing magnetic field produces an increasing electric field so the cycle will repeat.

That's as good as it going to get until you actually write out and solve the differential equation describing this process. Google for "wave equation" - just about all waves of any type anywhere in nature come from situations in which one thing going up makes another thing go down, and vice versa.

 

[Nugatory]

Isn't there any equation that tells us _why does the speed of light have that particular number, and not less or more?

You accept Newton's $F=Gm_1m_2/r^2$ as an explanation of planetary orbits, escape velocity, the speed of falling objects, and the like... But there is no equation anywhere that tells you why $G$ has the particular numerical value that it does. We determined it by observation, seeing what happens to falling objects. There is no why behind its value.

Similarly, Maxwell's equation contain constants relating the strength of electric and magnetic fields, and the values of these constants were discovered by observation. But once you accept those particular values the way you've accepted the value $G$, the value of the speed of light follows as logically as the speed of a falling object follows from the value of $G$.

 

[KatamariDamacy]

So when you ask why it travels at c in vacuum, the answer is because it's in vacuum. If it was anywhere else, then the velocity is:
$u= \frac{1}{\sqrt{\epsilon \mu}}$
where $\epsilon, \mu$ the dielectric constant and magnetic constant of the mean material.

Isn't that same equation valid for vacuum as well? So the speed of light is a consequence of some electric and magnetic properties. That's good enough for me.

 

[KatamariDamacy]

These: http://en.wikipedia.org/wiki/Maxwell's_equations#Conventional_formulation_in_SI_units (see also: http://en.wikipedia.org/wiki/Maxwel...s.2C_electromagnetic_waves_and_speed_of_light )
and these: http://en.wikipedia.org/wiki/Lorentz_transformation#Boost_in_the_x-direction

I see you are pointing to that same relation of c with electric and magnetic constants. So then if these electric and magnetic properties happened to be different, the speed of light would be different as well, right?

No. That is not due to any equation or any physics. That is purely due to our choice of units. You can make it be any number you want by choosing different units. Often, we even use units where it is a dimensionless 1.

Sure, actual values are not important, only relations.

 

[KatamariDamacy]

Among other things, they show that a decreasing magnetic field will produce an increasing electric field nearby and that a decreasing electric field will produce an increasing magnetic field nearby.

To what magnitude are electric and magnetic fields increasing in say, red color EM wave, and to what magnitude they are decreasing? Do they decrease down to zero and go back, or do they go below zero, that is to say cycle from positive to negative polarity amplitude?

 

[Dale]

So then if these electric and magnetic properties happened to be different, the speed of light would be different as well, right?

Well, you have to be careful what you mean by different. The numbers for the electric and magnetic properties are also just due to the units you use. So you have to decide if that is what you mean by different, and if not then you have to think about what you do mean.

 

[KatamariDamacy]

You accept Newton's $F=Gm_1m_2/r^2$ as an explanation of planetary orbits, escape velocity, the speed of falling objects, and the like... But there is no equation anywhere that tells you why $G$ has the particular numerical value that it does. We determined it by observation, seeing what happens to falling objects. There is no why behind its value.

That's fine. I'm not asking why are those constants the way they are, I'm just asking what constants define the speed of light constant.

Similarly, Maxwell's equation contain constants relating the strength of electric and magnetic fields, and the values of these constants were discovered by observation. But once you accept those particular values the way you've accepted the value $G$, the value of the speed of light follows as logically as the speed of a falling object follows from the value of $G$.

I accept. Mystery solved.

 

[ChrisVer]

This seems like a very unsatisfactory explanation to me. Then you would have to have a completely different explanation for why gluons travel at c, and why gravitational waves travel at c.

Well this explanation is the "classical" one given from studying the EM waves in Electrodynamics... it's not a pure answer though,so I tried to make you happy with my next post.
And it can also explain why light travels with different velocities in different materials and not only vacuum ...
The rest you are saying for gluons is answered by relativity itself since they are massless..

 

[ChrisVer]

Isn't that same equation valid for vacuum as well?

yes it is and
$u_{vac}= \frac{1}{\sqrt{\epsilon_{0} \mu_{0}}}= c$
but I'm talking for EM waves and not photons
The photons as massless always travel at c (property of special relativity). However, as I pointed out, the Maxwell Eqs when written for light in the vacuum give the velocity c. In other means, the velocity changes and the light can travel slower (from c down to some very small values).

Now for the photons, they travel at c because they are massless. That's due to the fact that (since they are massless) the 4-momentum squared would have to be zero $p^{\mu}p_{\mu}=0$ and that should be true for any reference frame...
So in any case it should be: $p^{\mu}= (E/c, \vec{p})$
and always $c^{2}|\vec{p}|^{2} = E^{2}$
The velocity in this case is $v=c=1$ (when you go to the appropriate units)
because the velocity is given by $\beta=v/c=|p|/E=1$
And that is true for every reference frame just because $p^{\mu}p_{\mu}$ is a lorentz invariant quantity (is the same for all ref frames).
Even if photons go through any material, they remain massless (we can consider an exception for Superconducting materials) so they always travel at c... what happens is that they can be scattered or absorbed/re-emitted and so on, so the light propagates slower...
https://www.physicsforums.com/showthread.php?t=565739

 

[bcrowell]

Well this explanation is the "classical" one given from studying the EM waves in Electrodynamics... it's not a pure answer though,so I tried to make you happy with my next post.
And it can also explain why light travels with different velocities in different materials and not only vacuum ...
The rest you are saying for gluons is answered by relativity itself since they are massless..

I wasn't asking you to give a different explanation, I was saying why I preferred my explanation in #9 to yours.

Now for the photons, they travel at c because they are massless. That's due to the fact that (since they are massless) the 4-momentum squared would have to be zero $p^{\mu}p_{\mu}=0$ and that should be true for any reference frame...
So in any case it should be: $p^{\mu}= (E/c, \vec{p})$
and always $c^{2}|\vec{p}|^{2} = E^{2}$
The velocity in this case is $v=c=1$ (when you go to the appropriate units)
because the velocity is given by $\beta=v/c=|p|/E=1$
And that is true for every reference frame just because $p^{\mu}p_{\mu}$ is a lorentz invariant quantity (is the same for all ref frames).
Even if photons go through any material, they remain massless (we can consider an exception for Superconducting materials) so they always travel at c... what happens is that they can be scattered or absorbed/re-emitted and so on, so the light propagates slower...
https://www.physicsforums.com/showthread.php?t=565739

Comparing this with my #9, it seems like we're on the same track, but approaching the argument in different ways. In your approach, you seem to be taking $v=p/E$ as given. What foundational principle do you use to show that this is an identity? Note that you can't get this identity by dividing $p=m\gamma v$ by $E=m\gamma$, because those are indeterminate forms in the case of m=0.

 

[KatamariDamacy]

Comparing this with my #9, it seems like we're on the same track, but approaching the argument in different ways. In your approach, you seem to be taking $v=p/E$ as given. What foundational principle do you use to show that this is an identity? Note that you can't get this identity by dividing $p=m\gamma v$ by $E=m\gamma$, because those are indeterminate forms in the case of m=0.

Zero can not define any numbers but zero itself. Zero mass may allow it, but it can not define the speed of light and explain why it is c and not more or less. A non-zero constant velocity must be defined by non-zero numbers that are constants themselves, there is no other way. So that some constant electric and magnetic properties define constant speed of electromagnetic wave propagation makes prefect sense.

But I knew that before, I was hoping there is more that can be said about it. I have to mention now what actually inspired this question. In another thread someone made what seems to me to be an amazing discovery. They tried to figure out at what velocity would magnetic Lorentz force match the magnitude of electric Coulomb's force. And guess what, it's the speed of light.

q2/(4πεR2)=μq2v2/(4πR2)
v0=1/√(ε0μ0),

The simplicity of it strikes me as profound, and it's amazing because even though the relation is rather obvious no one seems to have paid any attention to it before. Unfortunately, as usual, it's not quite clear what it really means or whether it is a part of the reason or just a consequence itself. Still, it actually tell us more about the whole thing, not much perhaps, but it's something.

Can anyone make some more sense out this relation and explain why would these two forces "need" to be balanced in an electromagnetic wave, and whether this could be a part of the reason for the speed of light or just a consequence of it and a side-effect itself?

 

[ChrisVer]

Why are they undetermined? You can always use them, even if you have to take the limit of $m \rightarrow 0$,afterall it's independent of m... These expressions are not good for defining the energy and momentum of the photon, but they seem fine in defining the velocity extracted from SR.

 

[Dale]

The simplicity of it strikes me as profound, and it's amazing because even though the relation is rather obvious no one seems to have paid any attention to it before.

I think many people have noticed it. In fact, it is something that we occasionally talk about here and sometimes try to get people to calculate on their own:

https://www.physicsforums.com/showthread.php?t=719625
https://www.physicsforums.com/showthread.php?t=589457

I am sure that there are other examples. I remember calculating it, being surprised, and then realizing that it was a necessary consequence of the Lorentz transform.

If you are interested in that, then I would definitely focus on the Lorentz transform stuff more than the magnetic/electric properties stuff. The Lorentz transform part is probably more fundamental anyway.

 

[bahamagreen]

...I was hoping there is more that can be said about it.

"For doubt can exist only where a question exists,
a question only where an answer exists,
and an answer only where something can be said." (original emphasis)
Ludwig Wittgenstein, 1921 Tractatus 6.51 2nd paragraph

 

[256bits]

q2/(4πεR2)=μq2v2/(4πR2)
v0=1/√(ε0μ0),

The simplicity of it strikes me as profound, and it's amazing because even though the relation is rather obvious no one seems to have paid any attention to it before. Unfortunately, as usual, it's not quite clear what it really means or whether it is a part of the reason or just a consequence itself. Still, it actually tell us more about the whole thing, not much perhaps, but it's something.

Can anyone make some more sense out this relation and explain why would these two forces "need" to be balanced in an electromagnetic wave, and whether this could be a part of the reason for the speed of light or just a consequence of it and a side-effect itself?

It means that when charge distribution changes, the effect cannot be felt instantaniously, but spreads out as a wave at the speed of light.

 

[KatamariDamacy]

I think many people have noticed it. In fact, it is something that we occasionally talk about here and sometimes try to get people to calculate on their own:

https://www.physicsforums.com/showthread.php?t=719625
https://www.physicsforums.com/showthread.php?t=589457

I don't think a thread on a forum has any official significance. When Maxwell derived the speed of light from his wave equation it was a revolution in physics. Surely then this other and more direct derivation deserve more serious attention and treatment in some published peer review paper.

If you are interested in that, then I would definitely focus on the Lorentz transform stuff more than the magnetic/electric properties stuff. The Lorentz transform part is probably more fundamental anyway.

I don't see Lorentz transformation has anything to say about the connection between the speed of light and equality between electric and magnetic force.