How confident can we be that light’s speed across the universe is really constant, as I assumed in a recent post? Well, aspects of that idea can be verified experimentally. For instance, the hypothesis that light at all frequencies travels at the same speed can be checked. Today I’ll show you one way that it’s done; it’s particularly straightforward and easy to interpret.
LHAASO and Photons
Light’s speed in empty space is widely thought to be set by a universal cosmic speed limit, c, which is roughly 300,000 km [186,000 miles] per second. Over time, experiments have tested this hypothesis with ever better precision.
A recent check comes from the LHAASO experiment in Tibet — LHAASO stands for “Large High Altitude Air Shower Observatory” — which is designed to measure “cosmic rays.” A cosmic ray is a general term, meaning “any high-energy particle from outer space.” It’s common for a cosmic ray, when reaching the Earth’s atmosphere, to hit an atom and create a shower of lower-energy particles. LHAASO can observe and measure the particles in that shower, and work backwards to infer the original cosmic ray’s energy. Among the most common cosmic rays seen at LHAASO are “gamma-ray photons.”
Light waves vibrating with slightly higher frequency than our eyes can detect are called “ultra-violet”; at even higher frequencies are found “X-rays” and then “gamma-rays.” Despite the various names, all of these waves are really of exactly the same type, just vibrating at different rates. Moreover, all such waves are made from photons — the particles of light, whose energy is always proportional to their frequency. That means that ultra-high-frequency light is made from ultra-high-energy photons, and it is these “gamma-ray photons” from outer space that LHAASO detects and measures.
A Bright, Long-Duration Gamma-Ray Burst
In late 2022, there was a brilliant, energetic flare-up — a “gamma-ray burst”, or GRB — from an object roughly 2 billion light-years away (i.e., it took light from that burst about 2 billion years to reach Earth.) We don’t know exactly how far away the object is, and so we don’t know exactly when this event took place or exactly how long the light traveled for. But we do know that
- if the speed of light is always equal to the cosmic speed limit, and
- if the cosmic speed limit is indeed a constant that is independent of an object’s energy, frequency, or anything else,
then all of the light from that GRB — all of the gamma-ray photons that were emitted by it — should have taken the same amount of time to reach Earth.
This GRB event was not a sudden flash, though. Instead, it was a long process, with a run-up, a peak, and then a gradual dimming. In fact, LHAASO observed showers from the GRB’s photons for more than an hour, which is very unusual!
As discussed in their recent paper, when the LHAASO experimenters take the thousands of photons that they detected during the GRB, and they separate them into ten energy ranges (equivalent to ten frequency ranges, since a photon’s energy is proportional to its frequency) and look at the rate at which photons in those energy ranges were observed over time, they find the black curves shown in the figure below. LHAASO’s data is in black; the names “Seg0”, etc, refer to the different ranges; and the vertical dashed line was added by me.
In units of 1 TeV (about 1000 times the energy stored in the E=mc2 energy of a single hydrogen atom, and about 1/14th of the energy of each collision at the Large Hadron Collider), LHAASO was able to observe photons with energy between roughly 0.2 TeV and 1.7 TeV. Looking at the rate at which photons of different energies arrived at LHAASO, one sees that the peak brightness of the GRB occurred at the same time in each energy range. If the photons at different energies had traveled at different speeds, the peaks would have occurred at different times, just as sprinters with different speeds finish a race at different times. Since the peaks are roughly simultaneous, we can draw some conclusions about how similar the speeds of the photons must have been. Let’s do it!
Light’s Speed Does Not Depend on its Frequency
We’ll do a quick estimate; the LHAASO folks, of course, do a much more careful job.
From the vertical dashed line, you can see that all ten peaks in LHAASO’s data occurred at the same time to within, say, 10 seconds or better. That means that at the moment the GRB was brightest, the photons in each of these energy ranges
- left the source of the GRB,
- traveled for about 2 billion years, and
- arrived on Earth within 10 seconds of each other.
Since a year has about 30 million seconds in it, 2 billion years is about 60 million billion seconds (i.e. 6 times 1016 seconds.) And so, to arrive within 10 seconds of one another, these photons, whose energies range over a factor of about 5, must have had the same speed to one part in 6 million billion. Said another way, any variation in light’s speed across these frequencies of light can be no larger than, roughly,
- 10 seconds / 2 billion years = 10 seconds / ([2 x 109 years] x [3×107 seconds/year])
= 10 seconds /(6 x 1016 seconds) = 2 x 10-16 !
Notice we do not need a precise measurement of the photons’ total travel time to reach this conclusion.
The LHAASO experimenters do a proper statistical analysis of all of their data, including the shapes of the ten curves, and they get significantly more precise results than our little estimate. They then use those results to constrain specific speculative theories that propose that the speed of light might not, in fact, be the same for all frequencies. If you’re interested in those details, you can read about them in their paper (or ask me more about them in the comments).
Bottom Line
LHAASO thus joins a long list of experiments that have addressed the constancy of the speed of light. Specifically, it shows that when light of various high frequencies (made up of photons of various high energies) travels a very long distance, the different photons take exactly the same amount of time to make the trip, as far as our best measurements can tell. That’s strong evidence in favor of our best guess: that there is a cosmic speed limit that holds sway in the universe, and that light traveling across the emptiness of deep space always moves at the limit.
And yet… it’s not final evidence. Grand scientific principles can never be permanently settled, because all experiments have their limitations, and no experiment can ever deliver 100%-airtight proof. Better and more precise measurements are still to come. Maybe one of them, someday, will surprise us…?
15 Responses
Apologies – I’m a little late to the party, but I have a question about light travelling over that vast distance for 2 billion years: isn’t vacuum space actually full of other radiation that would interact with that light? I understand that earth is constantly being bombarded by all sorts of energetic particles which I presume pervade the universe (like the gamma ray burst itself but from other sources, solar wind from our star and others, and perhaps a sea of neutrinos…) – is the light not impacted by those particles? Or perhaps only the light that finally reaches us isn’t impacted? I was just curious if the very minor difference of < 10 seconds or so might be a result of such particles. I have no knowledge of physics, but just thoroughly enjoy your blog and the fact that I learn cool new stuff from it all the time. Thanks!
Very good question.
Most likely the “minor difference of less than 10 seconds” is due to statistical fluctuations in the arrival of the photons — i.e., to random chance. There are always differences when you measure two identical things, because measurements are intrinsically imperfect. All one can say is that any effects such as those you suggest are much less than 10 seconds; one cannot attribute the discrepancy to any particular thing.
Could there be any such effects? Yes and no. First, no. It is true that light does slow down in materials. For instance, light slows considerably in water and even a bit in air. Radio waves *do* slow down as they cross the galaxy, because of the small amounts of material between the stars. What slows radio waves down are electrically charged particles, especially electrons, wandering through space. The effect on the radio waves is measurable though small — but it decreases rapidly as the wavelength of the light decreases, especially once that wavelength is smaller than the average distance between one electron and the next. The wavelength of the gamma rays observed by LHAASO is roughly a billion billion times shorter than the wavelength of typical radio waves… and so the effect on the gamma rays’ speed due to electrons is negligible.
Second, also no: the gamma rays photons could individually scatter off individual particles wandering the cosmos. The probability per photon for this to happen is small, and it doesn’t lead to photons arriving late; those photons don’t arrive at all. The only impact would be that slightly fewer photons would reach LHAASO than would do so were the universe truly empty.
But third, yes: To my surprise, I learned today (from this paper) that for gamma ray photons, there is a larger effect, from scattering off the microwave cosmic ray background [CMB] photons. For the standard CMB, the effect is still tiny, measured in billionths of a second. But if there were regions where the density of such photons is unusually high, and if those regions were more widespread than we think, then perhaps they could have a measurable effect if one or more such regions stood between us and the source of the photons. The observation by LHAASO implies that this effect, if present, must indeed be very small, at least for this particular gamma ray burst.
So rather than viewing the small differences of <10 seconds as possible evidence of an effect, you should view it as concrete but limited evidence against any such effect: had it been there and been larger than a few seconds, LHAASO would have detected it, so if it is present in the universe, it must be smaller than that.
Conversely, suppose that, in the future, an experiment does measure such an effect. Then we will have to decide whether the effect is due to (a) an impact on the photons due to material in the universe, or (b) a non-constant speed of light. With only one measurement from only one gamma-ray burst, we may not know right away, though we may have a prejudice. But with multiple measurements, the regularities/irregularities of the pattern of time differences versus frequency will almost certainly allow scientists to figure out whether the effect is due to (a) or (b).
My velocity-addition-formula blog:
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Einstein once said that a hundred experiments may prove hos theory of relativity as correct but it only takes one to prove it wrong. So far so good.
This is true of all theoretical ideas in science. Disproof is easy; one experiment is enough in principle — though any one experiment can be in error, so it has to be confirmed by multiple versions of the same experiment and often by supplementary experiments. Proof, however, is never achieved. When a long series of attempts to disprove fail, confidence gradually grows, but it never reaches 100%.
Did Einstein really say this, though? He is quoted as saying so many things… of which many were in fact said by other people, while others are flat out wrong. This quotation is a correct statement, but really doesn’t sound like Einstein; unless you have a confirmed source, I would tend to be suspicious.
It is in (more or less) A Brief History of Time.
https://books.google.com/books?id=G_iziBAPXtEC&pg=170#v=onepage&q&f=false
The actual quote was “ No amount of experimentation can ever prove me right; a single experiment can prove me wrong.”:I just paraphrased it from memory. My bad. Attributed to Einstein. Quoted in Alice Calaprice, The Quotable Einstein (1996).
That does indeed sound more like Einstein! He almost never spoke in hyperbole or in flippant ways, as in “A hundred experiments…”, and instead spoke very precisely, as in “No amount of experimentation…”
Again, it’s important to keep in mind that his remark reflects a completely general statement about the relation between theoretical ideas and experimental tests of those ideas, and is not special to Einstein and/or his work.
I vaguely remember learning at school that light travels slower in media such as glass or water. I imagine too that it might have a different speed in the presence of a strong gravitational field, but how can we be sure that it has the same, empty space, vacuum speed in different parts of the universe, or even at different epochs in the universe?
First, yes, light does travel slower in media that are made from atoms; the material, made from electrically charged subatomic particles, interacts with the light, with the effect that it doesn’t move as quickly.
Gravitational fields do not slow light down, but they do make space curved enough that light’s path is not straight, which may mean that it takes longer to get from A to B than you might naively guess if you didn’t account for that.
There are two interesting and related questions folded into your last question. There are two hypotheses here: first, there is a cosmic speed limit, c; second, photons, like all particles with zero rest mass, travel at that speed. (1) The cosmic speed limit directly affects properties of atoms. If it varied, we’d see different atomic emission lines from stars in distant galaxies than we do from the Sun, with some lines affected more than others. But other than an overall redshift that affects the entire galaxy, and is interpreted as due to the expansion of space, we see no effect at all. (2) Might it be the case that the speed of light is not always the same as the cosmic speed limit? If that were the case, we would expect a variety of different effects, including (a) variation of the speed of light during the Earth’s yearly orbit; (b) odd timing effects involving communication with distant spacecraft such as Voyager and New Horizons; (c) effects such as LHAASO doesn’t observe; (d) unexpected effects in gravitational lenses, which sometimes show light coming around an object in different directions; (e) bad predictions for the behavior of light from near black holes; etc, etc. Now, any one of these effects might be absent even if the speed of light weren’t constant and the same as the cosmic speed limit; but the absence of *any* of them does provide support for the basic hypothesis.
Still, we keep looking and checking, just in case either or both hypotheses is only approximately true.
Dr.Strassler:
Would like to ask a question about red shift. There are three types of redshift. Red shift associated with the expansion of the universe, red shift associated with objects actually moving thru space, gravitational redshift.
I realize that energy is not conserved for the cosmological red shift, as this deals with the expansion of space itself. For objects actually moving thru space, energy is conserved….for instance a light sail. Photons bouncing off the light sail are red shifted, as the photons energy & momentum are transferred to the sail & attached spacecraft.
But what about gravitational redshift? as I believe energy is conserved for this redshift, as photons climb their way up out of the gravitational well, they lose energy (redshift) does the lost photon energy get transferred to the gravitational field itself?
This question is a bit subtle even in Newtonian physics. As a upwardly-thrown ball flies away from the Earth’s surface, it loses kinetic energy and slows down. Where does the energy go? It goes into potential energy, we all learn… but *where* is that potential energy? And what has it? [Same issue for electromagnetism, as when an electron moves away from a positively charged object.]
At the beginning of first-year physics, we attribute the potential energy to the ball. But later we realize that can’t be true, and instead the potential energy is stored in the Earth-ball system as a whole. Still later, usually in electromagnetism, we learn that this potential energy can be viewed as stored in the electric field between objects, and that similarly potential energy can be viewed as stored in a (Newtonian) gravitational field. But when we do that, we are looking at the gravitational field of the whole system, not the gravitational field caused by its most massive member…. i.e., the potential energy of the ball is not stored in the gravitational field of the Earth, which hasn’t changed as the ball rises, but in the combined gravitational field of the Earth-ball system.
Now, GR is complicated, and I’m not expert enough to be certain there isn’t a subtlety that I’m unaware of. With that caveat, I expect we can view the photons’ energy as transferred to the gravitational field, but only if we keep track of the correction to the gravitational field from the departing photon.
You are assuming you know the distance from the source to the detector.
I am assuming that I know it to within a factor of 2 or so. But we do know distances in the universe to much better than that. However, I know that you personally don’t believe any of that. Let me ask you a question: if a galaxy has a redshift of 0.15, how uncertain would you estimate its distance to be?