# Thanksgiving

This year we give thanks for a feature of the physical world that many people grumble about rather than celebrating, but is undeniably central to how Nature works at a deep level: the speed of light. (We’ve previously given thanks for the Standard Model Lagrangian, Hubble’s Law, the Spin-Statistics Theorem, conservation of momentum, effective field theory, the error bar, gauge symmetry, Landauer’s Principle, the Fourier Transform and Riemannian Geometry.)

The speed of light in vacuum, traditionally denoted by c, is 299,792,458 meters per second. It’s exactly that, not just approximately; it turns out to be easier to measure intervals of time to very high precision than it is to measure distances in space, so we measure the length of a second experimentally, then define the meter to be “the distance that light travels 299,792,458 of in one second.” Personally I prefer to characterize c as “one light-year per year”; that’s equally exact, and it’s easier to remember all the significant figures that way.

There are a few great things about the speed of light. One is that it’s a fixed, universal constant, as measured by inertial (unaccelerating) observers, in vacuum (empty space). Of course light can slow down if it propagates through a medium, but that’s hardly surprising. The other great thing is that it’s an upper limit; physical particles, as far as we know in the real world, always move at speeds less than or equal to c.

That first fact, the universal constancy of c, is the startling feature that set Einstein on the road to figuring out relativity. It’s a crazy claim at first glance: if two people are moving relative to each other (maybe because one is in a moving car and one is standing on the sidewalk) and they measure the speed of a third object (like a plane passing overhead) relative to themselves, of course they will get different answers. But not with light. I can be zipping past you at 99% of c, directly at an oncoming light beam, and both you and I will measure it to be moving at the same speed. That’s only sensible if something is wonky about our conventional pre-relativity notions of space and time, which is what Einstein eventually figured out. It was his former teacher Minkowski who realized the real implication is that we should think of the world as a single four-dimensional spacetime; Einstein initially scoffed at the idea as typically useless mathematical puffery, but of course it turned out to be central in his eventual development of general relativity (which explains gravity by allowing spacetime to be curved).

Because the speed of light is universal, when we draw pictures of spacetime we can indicate the possible paths light can take through any point, in a way that will be agreed upon by all observers. Orienting time vertically and space horizontally, the result is the set of light cones — the pictorial way of indicating the universal speed-of-light limit on our motion through the universe. Moving slower than light means moving “upward through your light cones,” and that’s what all massive objects are constrained to do. (When you’ve really internalized the lessons of relativity, deep in your bones, you understand that spacetime diagrams should only indicate light cones, not subjective human constructs like “space” and “time.”)

The fact that the speed of light is such an insuperable barrier to the speed of travel is something that really bugs people. On everyday-life scales, c is incredibly fast; but once we start contemplating astrophysical distances, suddenly it seems maddeningly slow. It takes just over a second for light to travel from the Earth to the Moon; eight minutes to get to the Sun; over five hours to get to Pluto; four years to get to the nearest star; twenty-six thousand years to get to the galactic center; and two and a half million years to get to the Andromeda galaxy. That’s why almost all good space-opera science fiction takes the easy way out and imagines faster-than-light travel. (In the real world, we won’t ever travel faster than light, but that won’t stop us from reaching the stars; it’s much more feasible to imagine extending human lifespans by many orders of magnitude, or making cryogenic storage feasible. Not easy — but not against the laws of physics, either.)

It’s understandable, therefore, that we sometimes get excited by breathless news reports about faster-than-light signals, though they always eventually disappear. But I think we should do better than just be grumpy about the finite speed of light. Like it or not, it’s an absolutely crucial part of the nature of reality. It didn’t have to be, in the sense of all possible worlds; the Newtonian universe is a relatively sensible set of laws of physics, in which there is no speed-of-light barrier at all.

That would be a very different world indeed. In Newton’s cosmos, when a planet moves around the Sun, its (admittedly feeble) gravitational field changes instantly throughout all of space. In principle, in pre-relativistic laws of physics it would be possible to imagine communication or transportation devices that took you from here to billions of light years away, in as short a time as you can imagine.

That seems like fun, but think about what you’re giving up. The speed of light enforces what physicists think of as locality — what happens at one point in spacetime influences what happens nearby in spacetime, and those influences gradually spread out. A universe without without the speed of light would be one that allowed for non-local influences; one where different parts of space weren’t safely separated from one another, but were potentially connected in dramatic ways. That would be convenient for some purposes — but so utterly different from the real world that it’s hard to think through all of the consequences consistently.

As soon as someone figures out that the speed of light is constant, it’s not hard to guess that someone else is going to suggest that maybe it’s secretly variable. Indeed, there has been a decent amount of investigation into what are called “variable speed-of-light” theories. Whether the idea is even sensible is somewhat a matter of taste. To many people, it’s best to think of the speed of light as something that simply can’t vary, even in principle: it’s always exactly one light-year per year. To even contemplate a varying c, you have to tell me that it’s varying with respect to something — and there aren’t any other universal speeds to compare it to.

What you mean by “varying speed of light” is that the number of meters that light travels in a second is different from place to place or time to time. Which means that you need some other objective notion of a “meter” and a “second,” or some alternative ways of separately measuring distance and time. Which is certainly possible — you can choose to measure c in units of “the number of Compton wavelengths of an electron that light travels in the time it takes a certain atomic transition to take place,” and that’s a quantity that could conceivably change from place to place in the universe. The problem with that is that you could choose any one of various different such systems of units, and generically the speed of light would change in different ways in each one. The whole game of varying-c theories, then, is to find ways that the real dimensionless constants of nature (like the strengths of the fundamental forces, or ratios of particle masses) could change in perfect harmony such as to give you the impression that what’s really changing is c. That’s a game that can certainly be played, but it’s not clear why nature would find it a worthwhile pastime.

What matters is not that light travels at a certain speed — it’s that the universe has an ultimate upper speed limit. It just so happens that massless particles, like photons and gravitons, travel at that speed. But even in a world without any massless particles, there would still be a speed limit. We wouldn’t call it the “speed of light” in such a world, but something else, like the “Einstein speed” or some such. We live in a world where it inevitably takes time for signals to travel from one place to another, and I for one am thankful for it.

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### 25 Responses to Thanksgiving

1. Anders says:

Aren’t there theories in which different wavelengths of light travel at different speeds? So you would define the “true” light speed as applying to a given wavelength.

2. stuart james says:

Hello Sean. Thank you for this. I enjoy your commentaries and your talks on these matters; as well as your insights into emergent properties of things, such as life being an emergent property of matter; and consciousness of the brain. I think this profound insight into which languages are appropriate to which scales or levels of experience is necessary in order to avoid what Gilbert Ryle called ‘category errors’ in the realm of philosophy. The concept of emergent properties was anticipated by Engels in his dialectic of nature; he referred to it as the ‘transformation of quantity into quality’. I have not the text to hand, but it’s worth a look. Politically this dialectical-materialist approach to history and nature has I think yielded useful insights; for example the idea of the class- in- itself becoming the class- for- itself, just as a complex organ such as the brain can once it has reached a certain level of complexity, become self-reflective.
Another matter that interests me is the tendency unfortunately ubiquitous, for new age thinking (sic), to indulge in backward causation. which is another instance of category error. One such instance is the popularity of the idea that ‘biophotons’ can be harnessed to do work, such as self-healing; that indeed they are a product of activity in the cells of the body. My daughter has asked me what I though of this phenomenon. I had to tell her that I didn’t know about it but suspected that it represents another instance of the backward causation and no more likely than miracles or remote spoon-bending.
I would like to be able to tell her more specifically, that low-energy photons simple are not available for this, kind of work; or work of any kind.

3. Andrew G Van Sant says:

Happy Thanksgiving, Dr. Carroll. I am a little under the weather and taking antibiotics so am unable to be at my extended family’s annual celebration.

What do you think of the emerging evidence for EM drive that, although not useful for interstellar travel, would help in exploration of the solar system?

4. Terri Cononelos says:

Thank you Sean!

5. Alan Myers says:

Thank you for blessing the universal speed limit, as we toast the 100 pilgrims who arrived 396 years ago. In principle, due to time dilation, we can travel to Andromeda (and beyond) in a single human lifetime. Of course there is the daunting engineering task of designing a rocket with a power source that accelerates (and later decelerates) the rocket at 1 g for a decade.

6. Helena says:

Thank you for giving us something worthwhile to chew on during this day of feasting and gratitude.

7. vmarko says:

Hi Sean,

Happy Thanksgiving! 🙂 Let me just give two comments here.

First, it is also a common misconception that the fact that light speed is constant somehow implies that it is a maximum possible speed. Special relativity is completely compatible with faster-than-light travel, as long as it’s the tachyons that travel. Ordinary matter cannot travel faster than c due to dynamical reasons (infinite energy required to accelerate enough etc.), but this is a property of the matter surrounding us, not a property of Lorentz invariance. Of course, we haven’t discovered any tachyons in nature so far, but there is nothing in special relativity that forbids their potential existence.

Second, one builds a theory with varying c as follows. Write down the Standard Model action in natural units (c=hbar=1), insert c explicitly in all places where it should appear, and promote it into a scalar field, c(x). Then add a kinetic term for it to the action, maybe some self-interaction terms, and work out its equation of motion, coupling with other fields, etc… What you will get is a theory in which c varies (from one spacetime point to the next), i.e. a theory with a variable speed of light. Moreover, this theory can even remain Lorentz-invariant, which means that the variable-c idea is quite compatible with special relativity (and even with general relativity, but that’s off-topic).

What is nice about varying-c theories of this type is that they are very testable — work out the effective equations of motion for astrophysics, chemistry, spectroscopy, etc… , and compare the predictions to experimental data. What you’ll find is that experiments constrain the spacetime gradient of c down to zero, up to very large distances/time intervals (don’t remember the numbers, sorry). This means that c is effectively constant in the observable Universe, even if we don’t postulate it to be such.

Best, 🙂
Marko

8. David Appell says:

Is it obvious that gravitational waves should travel at the speed of light?

Do the Z and W bosons? Do gluons?

9. Sean Carroll says:

David– Massless particles (or waves in fields corresponding to massless particles) move at the speed of light, massive ones move more slowly. W and Z bosons are massive. Photons, gluons, and gravitons are massless. But gluons are always confined inside hadrons, so we never really get to see them moving at all.

10. Vincent Archer says:

I think it was the PBS-Spacetime video series that told me properly what “c” meant. It’s not the speed of light, it’s speed of “c”ausality; the fastest speed at which any information can propagate.

(I wondered for 40 years why you’d call a speed of light “c” instead of “l” or something)

11. Barry Curran says:

On this Thanksgiving clearly the Professor isn´t thinking about slow food. And give thanks to the plant kingdom for absorbing all that light at any speed they choose.

12. Benson says:

Thanks for posting this on Thanksgiving! After an afternoon of inane chatter about phone plans and stuffing recipes it’s a breath of fresh air. I appreciate your efforts to communicate science to the public. Personally, I’ve stopped watching science shows on television because I find it more informative to follow actual scientist’s blogs and twitter feeds. Love the links!

(Also bought and love The Big Picture.)

13. David says:

Limits are fascinating. You can see them everywhere in science and math. The speed of light, the uncertainty principle, Godel’s Incompleteness Theorems as well as the laws of probability. Without them, life would be boring. In fact, how could there be any life at all?

14. Tim Martin says:

Vincent: I think PBS told you *im*properly.
http://www.webcitation.org/5lLMPPN4L

15. Sir, I’ve read your books, and I’ve watched your Great Courses. They have been deeply satisfying. Thank you.

16. KC Lee says:

David,

Understood and agreed with “no limits, no life”. Just thinking a bit “in reverse”. Our classical life (brain in particular) in turn places limits on our ability to understand QM which, to us, appears to lack physical limits. (The word “physical” is emphasized for later purposes.) Locality, or conversely, the nonlocality in entanglement, is one example.

Along similar lines, Sean’s “That’s only sensible if something is wonky about our conventional pre-relativity notions of space and time” is apropos also to the above point. Instead of “wonky”, Einstein used “spooky”. Further, if the speculation of non-physical physics (Comments in Sean’s “Talking About Dark Matter and Dark Energy”) holds any water, spooky and wonky are good descriptors.

Using David’s point of the uncertainty principle to illustrate if I may, physical-only physics provides us with only physical rulers so to speak. Using these rulers to measure anything non-physical (QM possibly, for example) naturally returns uncertain read-outs.

KC

17. Mark K. Debe says:

Prof. Carroll,
Thank you for your interesting and enlightening posts. As an old, retired experimental physicist, I find your method of teaching wonderful and exciting. I don’t know if this is the appropriate place to submit what I am about to ask, as I have never responded to a blog post before, so I don’t know whether my comments will be too long, or whether this is the correct place for this particular comment, as it is really more specific to the one you wrote when the LIGO discovery was announced. But I am not sure that if I added comments now on that older blog, whether you would see it. So here goes. When the LIGO Scientific and Virgo Collaboration results were announced in the Abbott et al. paper, I was as amazed as anyone with the achievement. But something bothered me in the way that achievement was presented to the world, and nit-picking here, with a claim made in the Abbott paper and their repetition in many literature accounts, e.g. in the April, 2016 issue of Physics Today, or the March 2016 issue of APSNEWS. Specifically, the claim I am referring to is the first half of the last sentence of the abstract of the Abbott paper, viz. “This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.” Without question it is the first direct detection of extra-terrestrially generated gravity waves, but for reasons I give below, I don’t think it is the first detection of gravity waves. So on April 22, I submitted a letter to the editor of Physics Today, hoping to get some clarification as to why my reasons are wrong or might have some truth to them. However, it appears that the letter was cast into the 70% pile that they choose not to publish, since seven months later, I have not been notified yea or nay on the subject. But I am keen to know what I am misunderstanding if my reasoning below is faulty, and believe that you are the one to know immediately. (I have not been able to find anything in your textbook, Spacetime and Geometry, that persuades me otherwise, but that could easily be corrected by you too.)
“4/22/16 Letter to the Editor of Physics Today-submitted by Mark Debe
Sung Chang’s Search & Discovery article, “LIGO detects gravitational waves,” Physics Today, April, 2016, like most other heralding articles in the scientific and non-scientific social media outlets (see e.g. the headline article in the APSNEWS letter of March 2016, Vol. 25(3), “Gravitational Waves Caught in the ACT,” ) certainly reflects the incredible achievement for which the LIGO and Virgo teams deserve the highest recognition. As an experimental physicist, what was accomplished there is truly mind-boggling, and the references above cannot be faulted for repeating the claim in the B. P. Abbott et. al. paper that two firsts were achieved; “the first direct detection of gravitational waves and the first observation of a binary black hole merger.” (1). That they are the first to directly detect extra-terrestrially generated gravity waves, as opposed to detection by inference from pulsar orbital decay is without question, and the word detection is certainly an understatement when one looks at the sophistication of their measurements and comparisons to their models. I suspect that much like an overused trademark name, the meaning of the words gravitational waves has become synonymous only with the predictions of general relativity in the dynamic and relativistic strong-field regime, thus implying only non-terrestrial sources can produce gravity waves.
I am in no position to know, or care for that matter, who was first on something of this magnitude. But I wonder if in so consistently implying that gravity waves are extraterrestrial and rare, the reports are losing a teachable moment, not only for young physicists, but for the public as well: that gravity waves in the most general sense, albeit vanishingly small ones, are constantly enveloping us and everything else just as are electromagnetic waves of all types, and that one does not require big-science detectors to show their existence. What I am suggesting is that there is a prior example of gravitational wave generation and detection in a laboratory setting, first demonstrated by Robert L. Forward and Larry R. Miller, in the mid-1960’s (2). Robert Forward was a student of J. Weber, who is widely credited as the originator of gravitational wave detection (in the extra-terrestrial sense) in the 1960’s. Forward, well known in the history of gravity wave detection and ultimately a writer of 11 science fiction novels, went to work at Hughes Research Laboratories on a program to develop rotating gravitational mass sensors that could be used on spinning spacecraft to map the mass distribution of the moon or measure the mass of astroids, by quantifying the gradient of their gravitational field at any orbit position. In order to develop, measure and calibrate the sensor structures without having to go into space, they turned the problem around and built in their laboratory “a rotating generator of dynamic Newtonian gravitational-force-gradient fields” coupled to a non-rotating static detector. The essence of their generator was a rotating mass quadrupole moment derived from pairs of metal cylinders, or cylinders and voids, arranged across from one another on axes perpendicular to the axis of rotation. They were able to show excellent agreement using classical Newtonian force-derived equations for the effective gravitational force coupling strength to the dynamic field-gradient induced vibration of the cruciform-shaped sensor having piezoelectric strain gauges on its mechanically tuned arms. As Abbot et al. (1) state in the first paragraph of their introduction, Einstein showed that his linearized weak-field equations had transverse wave solutions that travel at the speed of light due to time variations of the mass quadrupole moment of the sources. Assuming that the linear and weak gravitational-field limiting equations of Einstein’s general relativity theory are consistent with the more approximate equations of Newton’s classical theory of gravity, it would seem to follow that any rotating mass quadrupole moment would be generating a gravitational wave. This is a simple explanation for the energy coupled to the vibrational modes of the sensor from the motor driving the rotating quadrupole masses in Forward’s and Miller’s apparatus, despite the iron plates and other intermediary chamber walls of their experiment that isolated the sensor and rotating masses.
During the summer before I started graduate school in the physics department at the University of Wisconsin, Milwaukee, in 1969, I had the opportunity to help develop a senior undergraduate physics lab experiment, in which we reproduced the apparatus of Forward and Miller, with some non-essential minor differences, (3). It was a wonderful experience that taught me invaluable lessons in ultra low-level signal retrieval, electronics of precision motor control, elementary vacuum technology and particularly acoustic and vibrational isolation techniques. It especially brought to memory my amazement the first time I saw a Cavendish balance mounted up in the far corners of the hall used for my freshman physics lectures; to think that there was a static gravitational field attraction between such small objects for one another that could be measured, in the classroom no less. So I wonder why a “dynamic Cavendish balance” such as Forward’s and Miller’s rotating quadrupole-generator of time varying gravitational field gradients would not qualify as generators of gravitational waves? If so it amazes me further to think of the broader implications this may have for the generation of gravitational waves by any time-changing mass distribution with a quadrupole moment. Even gravity coupled systems as mundane as an automobile moving in a straight line past a building, or a boulder rolling down a slope, could probably be expressed in an expanded series of terms of mass distribution-moments, one of which is a time changing quadrupole, producing waves rippling through space-time at the speed of light with a vanishingly small, but non-zero amplitude.
Such waves and their sources may not be as fascinating to read about as those from massive astronomical objects that push the extremes of relativistic gravity and allow direct tests of Einstein’s general theory of relativity. But on the other hand, they suggest to me the even greater significance of relativity in general, how mass-energy and space-time mutually interact – on any scale, all the time, everywhere.

Mark K. Debe
Stillwater, Minnesota
Refs.
1. B. P. Abbott et. al. (LIGO Scientific Collaboration and Virgo collaboration), Phys. Rev. Lett. 116, 061102 (2016).
2. Robert L. Forward and Larry R. Miller, J. Appl. Phys. 38, 512 (1967).
3. M. K. Debe, D. E. Bethlendorf and R. H. Dittman, American J. of Phys. 39(10), 1142-1144 (1971).”

Finally, yesterday, I looked back at your Oct. 13, 2015 post on “The Universe Never Expands Faster Than the Speed of Light,” and found it to express concerns with properly communicating physics so as to better, rather than worsen “people’s appreciation for how the universe works,” perhaps not unlike the one I think is my issue above. If you are willing to point out a problem with the nitpicking issue I raise above, perhaps you could also explain Larry Krauss’s comment in the 6th paragraph of his “The Back Page article of the 8-May, 2016 issue of APS NEWS, where he states “One hundred years ago, Albert Einstein used his newly discovered general relativity (which implies that space itself responds to the presence of matter by curving, expanding or contracting) to demonstrate that each time we wave our hands around or move any matter, disturbances in the fabric of space propagate out altho speed of light, as waves travel outward when a rock is thrown into a lake.” Despite the irony of using “a hand waving” argument, there is no mention of the requirement of a quadrupole moment when doing so?

Thank you so much for your time,

Mark

18. marten says:

@ Anders

Like Lee Smolin for instance. The observation of the simultaneous arrival on earth of rays of light/radiation with different wavelengths, years ago from a supernova burst of energy long time ago, proved him wrong, at least in situations of ceteris paribus, the circumstances being the same for all the rays during the time they were travelling together. Apparently their average speeds were the same over the total period of time. This observation does not prove that rays with different or the same wavelengths have the same speed during different circumstances.

19. Kolyo says:

Why the hell theories with constant speed of light and variable space-time dimensions are widely accepted and theories with variable speed of light and constant space and time dimensions are absolutely disregarded and placed into the trash. On basic logical level they are absolutely the same in the results they offer, but nobody tell that light may change speed and may not be isotropic in moving reference frame. I am really curious about that scientific misfortune?? I am interested in your opinion prof. Caroll! Can you give a brief explanation why you and everybody else don’t analyse the other possibility?

20. Dr John G Mark says:

Hi Sean,
I have been a fan for some time. I am a retired scientist/engineer and some time ago I taught my Grandson about special relativity. As an example I created an example of a trip to Pandora. Pandora is the mythical planet in the movie Avatar 4 lt. years from earth.
I noted that if an Observer on earth saw the space ship traveling @ .8c he wold say it would arrive in 5 years. From the travelers point of view he will arrive in 3 years. He would claim he was traveling at 4/3c. The Lorentz contraction is relevant to time NOT space.
Almost all treatments of Special Relativity are from the Observers Point of view but the Traveler lives in a much more Newtonian World. Velocity is unlimited. Mass does not increase with velocity etc. AM I SANE?

21. Jim Birch says:

I wish tachyons would go away and die. They are basically a pretty dumb “schoolboyish” interpretation of one of the Special Relativity equations. There is zero evidence that there is anything in the actual universe like it. And, there are other very good reasons for believing that c is the upper limit, eg, causality and locality . (I too am thankful for this.)

22. John B says:

I think it is a shame that the government cut the original experiment to detect tachyons short by cutting its funding after only a couple of months, which is irregular or we might have detected faster than light particles. It seems like if an object was traveling at a constant speed of 99% the speed of light, it could just say it is at rest and then it could start traveling up to 99% the speed of light again, because it could never actually measure closing in on a difference of 1% between the speed of light and itself.

If there was a variable speed of light, then there would be no need for spacetime dilation or relativity. If I didn’t know any better, I would say Sean has been visiting SciForums…

23. arch1 says:

Sean, sincere thanks for this wonderful tradition you’ve started (kind of like the Royal Institution Christmas Lectures minus a couple of centuries and the BBC).

I have this feeling topic nominations aren’t open yet for Thanksgiving 2020. (Actually, I have this feeling that topic nominations aren’t open at all, but then I had this feeling that I was getting a real spaceship for my birthday one year, and boy was *that* wrong).

So, I nominate “the scientific enterprise” as the Thanksgiving topic for 2020. (Why 2020? It’s a pun. Also, if my feeling *is* right, four years should be long enough for Sean to forget he didn’t think of the topic, even as its merits percolate indelibly into his subconscious:-)

24. Tom I says:

But why is c = 299,792,458 meters per second. Not a bit more, not a bit less.
Further why is it a constant? A constant anywhere in the Universe. (?)
All goes back to the creation of photon, which has no mass. Without mass it moves, and moves at a certain maximum but fixed speed. But why?
Calling it fundamental, or the result of ‘initial condition’ simply skip the answer. After all, during the inflation period (if this theory is proven) the Universe expanded much faster than c.
My guts tell me the photon is not fundamental. It is the interactions of what make up a photon that gives it a c.

25. Moe says:

“All goes back to the creation of photon, which has no mass. Without mass it moves, and moves at a certain maximum but fixed speed. But why?”

Have you considered that movement is not actually what you are thinking about? A photon ‘moving’ somewhere is just a way to say that an interaction occurred between two space-time points, from your point of view.

From the standpoint of a photon, nothing even moved at all, and no time has passed. It is basically an interaction between two totally overlapping space-time points, and is completely reversible.