Q & A: why constant speed of light

Why exactly is the speed of light constant in vacuum? I know that's what happens, but I want to know why. Relativity simply works under the assumption of light's constant speed, but that doesn't prove it. It's sort of like saying the product of two numbers is equal to the sum of the same two numbers just because 2+2=2x2. A proof requires more than a phenomenon.
- Bill (age 16)
vancouver, BC, Canada

This is an interesting philosophical question. In physics, we don't prove theories to be right, but we do prove theorems about the math used to hold together our theories. Which theories (whole structures, not just little fragmentary claims) are right is in the end determined by mere phenomena. Nobody gave us any book of true assertions, we have to cobble them together out of observation and mathematical logic.

The key logic behind Special Relativity was that Maxwell's equations for electromagnetism looked like exact, universal laws of physics, and their solution gives light waves with a universal speed. Now it was logically possible that those laws were only true in one special reference frame, but by 1905 no experiment (including the famous attempt by Michelson and Morley) provided any evidence that they failed to work in any inertial frame. Einstein showed that there was a logical, consistent framework (Special Relativity) in which Maxwell's equations worked in all inertial frames, and Newton's laws also almost worked for any objects moving slowly with respect to a frame. From this new framework, all sorts of other effects could be derived, and they were all confirmed. Among those many effects are the energy-dependent lifetimes of particles, the exact dynamics of fast-moving particles, the patterns of radiation from accelerating particles, the magnetism-like velocity-dependent term accompanying each fundamental force, etc.

Ultimately, the framework ran into trouble with gravity, and had to be replaced by General Relativity, which in turn probably will ultimately have to be replaced (maybe by something like String Theory) some day.

So in one sense you're right- we don't prove things the way mathematicians do, but instead have to rely a lot on what we actually see. In another sense you're wrong- we aren't generalizing from one isolated fact (like your numerical example), but fitting a huge collection of diverse observations precisely to an extended logical system.

Mike W.

(published on 10/22/2007)

Thank you for your answer. However, you’re still saying that light travels at constant speed because it’s an observation and works with all the theories. Is there a rational reasoning to this phenomenon? Also, I have another question regarding light. If light can be sucked into a black body, then it must have mass, no matter how little. Since light travels at light speed itself, wouldn’t it have infinite mass? Thank you again for your time.
- Bill (age 16)
Vancouver, BC, Canada

Bill- Right, I'm still saying that light travels at a constant speed because that's an observation and that it fits in a coherent theory with all sorts of other detailed observations of diverse phenomena. I know this point is hard to take in emotionally, but that's all the justification we have for anything. Whatever other sort of 'rational reasoning' justification you were hoping for is not something we can provide for any assertion at all. Can you deduce the existence of a table from logical first principles?
What I suspect is that you think there is something irrational about saying that light's speed is constant, but I am not claiming the right to be irrational. The sense that relativity is irrational rests on some common-sense assumptions about the nature of space and time. It turns out those common-sense assumptions are just wrong, usable only as good approximations for a limited range of phenomena. Relativity is a set of precise rules for describing how space-time looks from different viewpoints, just as objective and definite and logically consistent as common-sense, but not the same set of rules as common-sense. One is right and the other is wrong, and observation is what tells us which is which.

Your question about light's mass raises an issue we've addressed here occasionally, where some confusion arises from two different ways that different physicists use the word 'mass'. If by 'mass' you mean 'the quantity that serves as a source for gravity' or 'the thing which you multiply velocity by to get momentum' or 'the thing which is equivalent to energy' then light has mass. If you mean 'the mass something has when viewed in a frame in which the thing is standing still' (sometimes called 'rest mass' or the 'invariant mass') then it has none. There is no frame in which the light is standing still, since (as we started with) its speed is constant. Its rest mass is zero.

If you tried to imagine something that had some rest mass and was traveling at the speed of light, it would have infinite "mass' of the first kind, or infinite energy. So things like that don't exist. There are zero-rest-mass things that always travel at c, and nonzero-rest-mass things that never travel at c.

Mike W.

Comparison of observation with the predictions of theories really is about as rational as it's possible to get.  One of the reasons is that the theories may turn out someday to be wrong, and we'd have to invent new ones, but the only reason we'd ever do that is to explain some observation that the current theories disagree with.  So far, it's been good with the photon having zero mass.  Some other experimental and theoretical ingredients (which you may find also elsewhere on this site) are given below.  A small mass to the photon will cause the electrostatic force law to deviate from its standard inverse-square version (Coulomb's law), and also change the shape of Earth's magnetic field.  The current upper bound on the photon mass is m(photon)<1E-52  kilograms (from the 2004 particle data booklet, see <a href="http://pdg.lbl.gov">http://pdg.lbl.gov</a>).

Given this observation, we can build theories which accommodate, and even require, the photon's masslessness.  Quantum electrodynamics (QED) has at its core a U(1) gauge symmetry -- every electron's wavefunction can be multiplied by a complex function of unit magnitude and which varies smoothly in space, but is otherwise arbitrary.  From this symmetry, all of electricity and magnetism can be derived, and it has been tested to exquisite precision, particularly in the quantum corrections to g-2 for the electron.  People have worked very hard to test it, and to see if the model breaks down anywhere, but it works very very well.  If someone measures a tiny photon mass someday, it'll all come crashing down and we'll have to invent another theory.  But we have evidence from high-energy particle collisions that this theory is just embedded in another beautiful model, the electroweak interaction, which describes the weak force, and the model is also spectacularly successful there too.  We keep testing things at the edge of our knowledge, and modifying our models as we go along.

Actually, the U(1) gauge symmetry argument is a little circular, in that it assumes special relativity's geometry of space and time, as well as quantum mechanics.  But it does identify the photon as the thing that travels at the speed of light (a similar symmetry applies to gluons, the massless carriers of the strong force).  No such symmetry was identified for the neutrinos, and while we thought they, too were massless (largely because we couldn't measure their masses for a long time because we didn't have a sensitive enough experiment), there was no compelling reason to believe they are massless.  It turns out that an experiment in the late 1990's showed at least some of the neutrinos have mass, and any model explaining why they were massless is now unviable.  But now we are stuck with the problem of explaining why their masses are so small compared with everything else.

  Tom

(published on 09/18/06)

Hi Mike: Sorry to "annoy" you again. You stated that when light travels at light speed, it has zero mass. If that must be true, can you explain the reason why light, when it’s traveling, gets sucked into a black hole. If light has zero mass when it’s traveling, then 0xinfinity=undefined, which doesn’t comply with the observations of light and black body.
- Bill (age 16)
Vancouver, BC, Canada

Hi Bill- That's not quite what I wrote. I said that that a photon (a quantum of light) has zero 'rest mass', also called 'invariant mass'. Its energy (equivalent to a mass via E=mc²) is not zero. It is well defined, being hf where h is Planck's constant and f is the frequency of the light in your reference frame.  Light does serve as the source of a gravitational field. Semi-classically, then, you can think of it as having a gravitational mass and thus falling in a gravitational field.
That picture actually doesn't give the right answer, since a light beam curves by twice as much as it would if you just thought of it as a relativistic particle in a field in classical space time. The rest of the curvature of the beam comes from the non-Euclidean (curved) nature of space in General Relativity.

Mike W.

(published on 09/25/06)

Hello, I would like to know if there is any record of how the speed of light has been measured/Estimated and the method used for this purpose.The answer to this question might help in understanding why the speed of light is constant further.
- Ganesh
Bangalore,Karnataka, India

There are a number of ways to measure the speed of light.   Historically the first measurement, with several percent accuracy, was performed in 1676 by the Danish astronomer Römer who noticed discrepancies in the times of eclipses of the moons of the planet Jupiter as the earth revolved around the sun.  Earlier measurements were woefully wrong:  Galileo and others tried to compare the speed of light to that of sound, unsuccessfully.  The accuracy since Römer's time has improved by orders of magnitude.  See:http://en.wikipedia.org/wiki/Speed_of_light

The constancy of the speed of light is a different matter.  All experiments, both in the laboratory and in astronomical measurements, have verified that this is true.

LeeH

(published on 01/02/10)

Hi, Thanks for the Reply!!. I Understand that the observations show the constancy of speed of light.Now I have another question.If we take the speed of light just after the big bang and the speed of light now, Is there a difference in the value of c?
- Ganesh
Bangalore,Karnataka,India

So far as we can tell, c has been fixed at least since a very short time after the Big Bang. When you get too close to the singularity (or whatever it actually was), we don't know what sort of laws held.

Mike W.

(published on 12/12/10)

I used to believe that the speed of light was constant from all perspectives, therefore I assumed it was simple to prove. Since then, I have learned it is not constant from all perspectives, my first question is what makes light's speed different from anything else's speed. OK Im going back a few steps, but i was not satisfied with your answer of how it has been proven that lights speed is constant. First i would like to point out that the assumption that the speed of light is a constant is what allowed the present formulas and theories to be created; therefore obviously none of these formula can be used to prove the preceding presumption. That would be circular reasoning. Is there any experiment capable of demonstrating the consistency of the speed of light?
- Craig (age 20)
Kelowna, B.C. Canada

There may be two slightly different takes on what you're asking.

Earlier in this thread, we addressed the question of why we don't try to pick a special frame to call "at rest" and say that light only travels at c with respect to that frame. The reason is that we would end up saying that nature has conspired to change all sorts of other variables in exactly the way needed to prevent us from ever measuring anything that could tell us whether we're using that frame or not. (Poincare said just that.) If we try to define speed by using any physical objects at all to measure distance and time, the same physical objects give the same light speed for light going by us in any direction. Our neighbor who is moving past us tries the same measurements with identically constructed meter sticks and clocks, and gets the same speed. These sorts of measurements have been done repeatedly, starting with the famous Michelson-Morley experiment.

We could stubbornly insist that only one of those frames is the "correct" one, but that assertion would tell us nothing new and correct about anything we observe. Or we could postulate with Einstein that all laws of physics, including ones to be discovered, will look the same in each frame. That was a spectacularly successful prediction for the many laws that have been discovered since 1905.

Perhaps you're asking more about why we can't pick among some much broader set of coordinate choices, if we allow that light speeds in different directions don't have to be equal. I've heard that it is possible to construct such coordinates (here I'm discussing on small patches of spacetime, not the coordinates of General Relativity). Then obviously basic laws such as Maxwell's equations (from which the speed of light is derived) would need some messy form in which the spatial derivatives in different directions are multiplied by different factors and/or various extra terms are added in. Why would anybody choose such major complications, when the much simpler choice of having laws that are independent of spatial orientation works perfectly well?

To repeat a philosophical point- yes all of science involves some circular logic. There's no set of unquestionable axioms from which you can derive the whole thing. You try to find simple self-consistent rules and see which fit the phenomena.

Mike W.

(published on 03/10/11)

Hi,I want to ask, Is it possible that the speed of light is zero and what we assume "speed of light is constant" is just expanding speed of our universe?.As we know that matter is deeply connected to space as a result we feel gravity,likewise light is also connected to space and when it is created it accelerates with the speed of expanding space because atoms are way too heavy when compared to light and light probably has the mass somewhat equivalent to that of space.(Just a hypothetical thought).
- syd
Hyderabad,Andhrapradesh,India

It's hard to see how you could make a consistent description with the speed of light being zero, since in any one region you have light rays going all different directions. How could each ray have speed of zero?

Mike W.

(published on 07/29/11)

Still unsatisfied with the initial answers to the question: has light mass?. it is confusing the mixture of observation and concepts--term such as semi-classically. If light would has mass, agrees with light being sensitive to the space curvature or a black whole. However, this idea conflicts with the initial assumptions: Why then speed of light is constant? and why this is the maximal speed in the universe?
- LEGO (age 50)
solon

To the best of our knowledge, the standard picture we've presented is fully self-consistent. Light which is traveling in a particular direction has no invariant mass, i.e. E=pc, where E is energy and p is momentum. The E and p of the light enter into the General Relativistic gravity equations just like any other E and p. There's also a pressure term in GR, also directly obtainable from the dependence of E of light on a coordinate stretch.

The geodesic paths followed by light are just the limiting paths for any particles whose velocity approaches c. By "semi-classically" we just meant "pretending that space is Euclidean". It isn't, so that's why the real answer comes out different.

Could you follow up with an explanation of what inconsistency you believe you see?

Mike W.

(published on 12/18/11)

Thanks so much for your answer on this fascinating topic. I was unsatisfied with the idea of formulating two separate concepts of mass that are not intuitive. '..the quantity that serves as a source for gravity' vs. 'the thing which you multiply velocity by to get momentum'. Are these supposed to be equivalent? ( a principle in general relativity?). We know that in the universe nothing is “still� but only in a reference frame; example: we are moving at the earth & galaxy speed of rotation & translation although we do not notice. Is such a movement part of an object momentum? Accordingly, I can understand that light moves faster because its momentum is much lower. However light is sensitive to gravity, for example light follows the geodesics in space. It is possible that neutrinos have even less mass, so they interact less with space curvature (gravity) and, therefore, they do not follow the earth warping space. Will this explain the fact that neutrinos may travels faster than light?
- LEGO (age 50)
Solon, OH, USA

Yes, the mass that appears in the gravity source term and the one that appears in the velocity-momentum ratio are the same thing. As you say, this equivalence is at the heart of General Relativity.

You also ask if GR effects on neutrino travel might give the apparent faster-than-light travel reported by the group from CERN. The answer is no. The total GR effects on the coordinates near Earth are only around one part per billion, much smaller than the discrepancy reported for neutrino speeds. Now it may be that there was some subtle problem with clock synchronization involving GR effects as a clock was slowly transported from the neutron source to the detector. However, no such effect on the fast-traveling neutrinos themselves could be nearly large enough to account for the reported anomaly.

Mike W.

(published on 12/25/11)

The first questioner Bill asked a question which might be interpreted as: can one derive the speed of light, and the fact that it is constant in all inertial frames, from theoretical first principles (rather than simply measuring it). You mentioned later that the velocity of light can be derived from Maxwell's equations, but this uses classical wave theory based on measured values and mathematical relations between charge density, current, and magnetic flux density, and also involves an implicit assumption of a "medium" or single inertial frame. In some sense, that Maxwell's equations work at all is kind of a coincidence, a classical approximation, because it doesn't take into account the underlying principles of relativity or quantum mechanics. Given these considerations, my question is: is there a way to derive the speed of light, and the fact that it is the same in all inertial frames, using only the notions of space, time, matter, and energy that are consistent with quantum theory?
- Jeff (age 52)
Clovis, NM, USA

There are really two questions there. One is whether the particular value for the speed of light can be derived from something deeper than Maxwell's equations, with their empirical constants. The current answer is no. In fact, it would hardly even mean anything to derive c, since it has units (e.g. m/s) and the number depends entirely on the units. What physicists ask is whether various dimensionless numbers (e.g. the fine structure constant) involving c can be derived from some deeper rule. The answer to that is still no, at last for now..

Your other question is whether there's a way to derive that c is constant in all inertial frames. At heart, that amounts to deriving the rules for transforming coordinates between the different frames. I believe the answer to that is also no currently. Perhaps a deeper theory will be developed from which the rules of relativity (such as the Lorentz transforms) will emerge.

Mike W.

(published on 03/21/12)

Hi Mike! I don't have a follow up question, but I found this page searching for answers and just wanted to thank you for taking the time to answer the questions.
- Aaron Von Gauss (age 38)
Boynton Beach, FL

Aaron- we always publish notes like yours.

Mike W.

(published on 11/02/12)

Mike, I find that physics is easier to understand if you separate it into two distinct components. (1) There is an objective reality which we observe through phenomenon. (2) The mathematics of Physics, which are used to *model* and *simulate* the actual objective reality. I find that physicists assert (directly or indirectly) that the mathematics *is* the objective reality. This is tantamount to confusing a doll house with an actual home. The dollhouse is a *model* of the house, accurate in many details, but it can never be mistaken for an actual house. A dollhouse can be used to predict traffic patterns and determine furniture placement, but you will never eat in its kitchen nor sleep in the bedrooms. It is a place to play and tinker. One must always keep in mind is that the mathematics of physics is NOT objective reality. That is to say that Physics is the DOLLHOUSE that allows us to tinker with the math in order to describe and predict what is happening in the actual house of objective reality. So is the speed of light constant? Who knows what is happening in the objective reality? However, that assumption, allows for much simpler mathematics, the extension of relativity to electrodynamics, and the mathematics provides a better tool for predicting and modeling objective reality. Michael
- Michael J. Schreck (age 51)
Danbury, CT, USA

Thanks for the philosophical musings. I don't have definite views on those general questions, so I'll just pass yours on to other readers.

On the particular application to the question of relativity, you ask "...is the speed of light constant? Who knows what is happening in the objective reality?" Here I sort of disagree. Even asking the question of what something's speed is implicitly assumes some particular type of mathematical framework. So once you've gotten that far, I think it's ok to answer "yes".

Mike W.

(published on 12/26/12)

Q1: Lots of fundamental constants in physics/mathematics end up being related to each other. Does the speed of light c enjoy any such reputation? Is there a beautiful power series expansion or a continued fraction expansion for c ? Q2: So when the light gets sucked into a black hole, it accelerates, but the acceleration doesn't change its speed? Q3: Do we ever talk of rate of change of acceleration (or may be other higher derivatives of distance) in special/general theory of relativity? If not, why not? Q4: Thought experiment 1: How does a photon see the rest of the universe? Does it observe different speeds, accelerations, etc? Q5: Thought experiment 2: Does a photon in a light beam sees a photon in another light beam tavelling at a constant speed c? What about the relative speed of two photons in the same beam of light? Q6: If light is never at rest, how do we define it? We still haven't been able to define motion (refer Zeno's arrow motion paradox), though certain people claim that calculus has settled it, but it hasn't.
- Amarpal Singh (age 38)
Thousand Oaks, CA, USA

Q1: Not really. "c" is usually given as a number in some arbitrary units, in which case the numerical value has no deep significance at all.  In fundamental units, we define c=1, which is special but not in a complicated way.

Q2: The speed as locally measured in a standard reference frame doesn't change. Whether you want to say the light "accelerated" or not is a matter of word choice, or more precisely on choice of coordinate system. In one standard coordinate system the light falling into a black hole slows down on the way in due to the gravitational redshift.

Q3. Even in classical physics the time derivative of the acceleration, called the "jerk", is sometimes referred to. In general relativity, I believe that it comes up as an important quantity in understanding the radiation from particles in reference frames in which there's a uniform gravitational acceleration. Choosing such a reference frame doesn't make a charged particle radiate, but a first look at the expressions for radiation makes it seem that any accelerated particle does radiate. So I guess that the jerk becomes useful in these descriptions.

Q4. Our coordinate transforms (Lorentz transforms in special relativity) don't include transforms to frames moving at c with respect to the initial frame. So I don't think there's a real answer to this.

Q5. The speed of light remains c in any of the special relativistic frames. Thus in the limit as you get close to the speed of light, according to the initial frame, it should remain c. It's not clear what it means to say two photons are in the same beam, but so long as you don't insist on knowing how things truly look from the photon's point of view, in that limit any other photon you look at is traveling at c.

Q6. I don't understand here what you're asking. What is it you want done? What do you mean by "define"?

Mike W.

(published on 01/20/13)

what is that pressure that you mentioned in follow up #7?
- Bassem (age 18)
ramboland

This pressure comes from the decrease in energy of photons when their wavelengths are stretched. It is just 1/3 of the photon energy density for an isotropic photon gas. That's because the energy is proportional to the magnitude of the momenta which go as the inverse of the wavelengths, which go as the cube root of the volume.

For a gas of slow-moving massive particles, the pressure is 2/3 the kinetic energy density. That's because that energy goes as the momenta squared.

Mike W.

(published on 02/06/13)

You have addressed various questions about light, here's mine. How can the QM properties of light result in the "real world" phenomenon of image reflection observed in a mirror or window or flat surface of water? Here is a microscopic blob of energy - with wavelike properties measured in nanometers - traveling at incredible speed - that was initiated by my light bulb - and it "bounces off" of glass or some other reflective surface - at exactly the right angle - and forms an image of me shaving? If nothing else, the "bouncing off" of glass isn't the redirection of something moving at the speed of light, is it? Instead, reflection would seem to require an incoming photon being absorbed by a silicon or oxygen atom and then being reemitted again in a different direction, right? That process alone looks like it would result in a randomization of the outgoing photon direction, not precise reflection angles. So how can there be images formed? Also, is there a maximum number of photons that can exist in a given (small) volume of space? And why don't photons interact with each other? How can a photon travel for billions of years in a straight line and never get struck by another photon (or gas molecule, for that matter) and get deflected off course in a way that would spoil the ability of Hubble to form an image from it?
- Ricky (age 57)
Huntsville AL 35803

1.  "the "bouncing off" of glass isn't the redirection of something moving at the speed of light, is it?"
Yes, it is.

2. "reflection would seem to require an incoming photon being absorbed by a silicon or oxygen atom and then being reemitted again in a different direction, right?   That process alone looks like it would result in a randomization of the outgoing photon direction, not precise reflection angles.  So how can there be images formed?"
Absorption/re-emission processes (fluorescence) do indeed scramble the directions and thus ruin images. So that is not what happens in reflection. "Bouncing" is a much more accurate way to think of it.

3. "Also, is there a maximum number of photons that can exist in a given (small) volume of space? "
Yes, there are limits involving quantum gravity and black holes. Those limits are far above any photon density with which we ever expect to deal.

4. "why don't photons interact with each other? "
They do, but weakly.

5. "How can a photon travel for billions of years in a straight line and never get struck by another photon (or gas molecule, for that matter) and get deflected off course...? "
The photon-photon interactions are extremely weak for visible photons. The gas molecules and atoms are very sparse. Since the main ones around are hydrogen and helium, they  also interact quite weakly with visible light.

Mike W.

(published on 03/05/13)