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

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1. Aug 7, 2014

### KatamariDamacy

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

2. Aug 7, 2014

### Staff: Mentor

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.

3. Aug 7, 2014

### KatamariDamacy

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?

4. Aug 7, 2014

### Staff: Mentor

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.

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.

Last edited: Aug 7, 2014
5. Aug 7, 2014

### 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!

6. Aug 7, 2014

### KatamariDamacy

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.

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

7. Aug 7, 2014

### PAllen

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

8. Aug 7, 2014

### Staff: Mentor

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".

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9. Aug 7, 2014

### bcrowell

Staff Emeritus
"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.

10. Aug 7, 2014

### KatamariDamacy

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.

11. Aug 7, 2014

### KatamariDamacy

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?

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.

12. Aug 7, 2014

### Staff: Mentor

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.

13. Aug 7, 2014

### Ich

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?".

14. Aug 7, 2014

### 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...

15. Aug 7, 2014

### bcrowell

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

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.

16. Aug 7, 2014

### Staff: Mentor

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.

Last edited: Aug 7, 2014
17. Aug 7, 2014

### Staff: Mentor

Have there?

*rubs eyes*

I think I need some sleep.

18. Aug 7, 2014

### KatamariDamacy

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

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?

19. Aug 7, 2014

### Staff: Mentor

and these: http://en.wikipedia.org/wiki/Lorentz_transformation#Boost_in_the_x-direction

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.

Last edited: Aug 7, 2014
20. Aug 7, 2014

### Staff: Mentor

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.

21. Aug 7, 2014

### Staff: Mentor

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 $G$.

22. Aug 7, 2014

### KatamariDamacy

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.

23. Aug 7, 2014

### KatamariDamacy

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?

Sure, actual values are not important, only relations.

24. Aug 7, 2014

### KatamariDamacy

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?

25. Aug 7, 2014

### Staff: Mentor

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.