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A photon’s frame of spacetime — no rest for the massless

John Healy

I’ve thought about this question for years. A FAQ. Imagine you’re traveling at the speed of light. Well, physics says that’s impossible. Mass’ gotcha. So, what can travel at the speed of light? Photons (not just the visible ones). So, imagine … does a photon “experience” space and time?

Some weeks ago I recall reading that photons do not connect with space or time. Maybe some other term than “connect.” Perhaps something written by Carlo Rovelli, but I cannot find the citation. Anyway, so I reacted when I ran across a Forbes article by Ethan Siegel [2] titled “Ask Ethan: How Does A Photon Experience The Universe?“ (December 22, 2018). 

There’s a lot written on this topic (and likely covered in physics classes as well). Siegel’s article is a good summary of the material.

… relativity declares that the laws of physics are the same and invariant for all observers, regardless of their motion. So what does this mean for a photon, which itself moves at the speed of light? 

Siegel addresses the question by characterizing three scenarios:

Let’s imagine what happens in three cases: for someone at rest, for someone moving close to the speed of light, and then that last leap, to a photon itself.

Case 1: Rest frame. The everyday case. In your surroundings, objects’ shapes and colors appear “normal” and any clocks in that scene appear to be running at the same speed as your smartphone’s (although Rovelli says this is only a blurred perspective, as the speed of time varies from point to point in space [1]).

Case 2: Relativistic frame. Typically a hypothetical case, like looking at the cityscape from inside an ultra fast railroad car. In your particular direction of motion, for things outside your frame, shapes (lengths) of objects appear contracted and clocks appear to run slower (time dilates). The color of objects directly ahead of you appear bluer and those behind you appear redder.

Things move through spacetime. Basically spacetime always balances to maintain an equality: the less motion in space, the more in time; the more motion in space, the less in time.

The effects on things become more and more pronounced — to an unreachable limit. Capture that with your smartphone, eh.

Case 3: Photon’s frame. Imagine you’re a photon. 100% motion in space. 100% contracted. 0% in time. No time, eh. Special relativity out the window. Mathematical infinities.

[All a photon] experiences are two “things” during its existence: the interaction that creates it and the interaction that destroys it. Whether there is a photon that persists after the destruction, such as via scattering or reflection, is immaterial. All that a photon experiences are those two events at the endpoints of the photon’s journey.

From an inertial frame of reference, we can calculate the distance between its emission and absorption point, but not from the photon’s reference frame. We can calculate its light-travel time, from any inertial reference frame, but not from the photon’s reference frame.

The problem is that the photon’s reference frame isn’t an inertial reference frame: In an inertial reference frame, there are physical laws which don’t depend on the motion of anything external to the system. Yet for a photon, the physical rules it obeys depend exclusively on everything going on external to it. You cannot calculate anything meaningful for it from the photon’s reference frame alone.

… rest mass is what’s required to live in an inertial reference frame … A photon cannot see the Universe at all, because seeing requires interacting with other particles, antiparticles, or photons, and once such an interaction occurs, that photon’s journey is now over.

According to any photon, its existence is instantaneous. It comes into existence with an interaction and it winks out of existence with another interaction. This could be emission from a distant star or galaxy and its arrival at your eye, and it doesn’t matter whether it’s from our own Sun or an object tens of billions of light years away. When you move at the speed of light, time ceases to pass, and your lifetime only lasts an instant.


Photons do not have a rest frame. Distance is irrelevant, whether within an atom or between galaxies. Existentialism out the window, eh.

[1] Using a constant proper time reference across an event which spans space is an approximation, eh.

Times are legion: a different one for every point in space. — Rovelli, Carlo. The Order of Time (p. 16). Penguin Publishing Group. Kindle Edition. 


[2] Ethan Siegel is a Ph.D. astrophysicist, author, and science communicator, who professes physics and astronomy at various colleges. He has won numerous awards for science writing since 2008 for his blog, Starts With A Bang, including the award for best science blog by the Institute of Physics. His two books, Treknology: The Science of Star Trek from Tricorders to Warp Drive, Beyond the Galaxy: How humanity looked beyond our Milky Way and discovered the entire Universe, are available for purchase at Amazon.

[3] Examples of other articles (Google Search “how a photon experiences space and time”)

7 thoughts on “A photon’s frame of spacetime — no rest for the massless”

  1. Here’s an interesting take on the speed of light, in an unexpected place: Business Insider, “The speed of light is torturously slow, and these 3 simple animations by a scientist at NASA prove it” (January 17, 2019).

    I’m always glad to see visualization used in communicating science.

    … light speed can be frustratingly slow if you’re trying to communicate with or reach other planets, especially any worlds beyond our solar system.

    To depict the speed limit of the cosmos in a way anyone could understand, James O’Donoghue, a planetary scientist at NASA’s Goddard Space Flight Center, took it upon himself to animate it.

    “My animations were made to show as instantly as possible the whole context of what I’m trying to convey,” O’Donoghue told Business Insider via Twitter. “When I revised for my exams, I used to draw complex concepts out by hand just to truly understand, so that’s what I’m doing here.”

    O’Donoghue said he only recently learned how to create these animations – his first were for a NASA news release about Saturn’s vanishing rings. After that, he moved on to animating other difficult-to-grasp space concepts, including a video illustrating the rotation speeds and sizes of the planets. He said that one “garnered millions of views” when he posted it on Twitter.

    O’Donoghue’s latest effort looks at three different light-speed scenarios to convey how fast (and how painfully slow) photons can be.

    Check out the videos of his animations. Tick-tock, ping-pong.

    How fast light travels relative to Earth
    How fast light travels between Earth and the moon
    How fast light travels between Earth and Mars

  2. And here’s another Space.com article by Paul Sutter on the topic: “Does Light Experience Time? And Other Riddles” (March 16, 2019).

    In order to ask the question, “How does light experience time?” you have to put yourself in a frame of reference that rides along with a beam of light. But in that frame of reference, light would appear to be stationary to you.

    That’s not allowed by our laws of physics. So there is no such frame of reference that rides along with light. And with no frame of reference, special relativity breaks down. And with no special relativity, you have no way of gauging the relationship between space and time.

    The end result of all this twisting? It’s not so much that light doesn’t experience time. It’s that our very concept of time doesn’t even apply to light.

    Light doesn’t even know what time is.

  3. My posts Imaging a light pulse? and A photon’s frame of spacetime — no rest for the massless discussed the landscape of light speed. Live Science recently posted an article “Here’s What the Speed of Light Looks Like in Slow Motion” (March 29, 2019) about a visit to the Caltech lab by The Slow Mo Guys where light pulses can be visualized at 10 trillion frames per second. The article includes Gav and Dan’s video “Filming the Speed of Light at 10 Trillion FPS” — a quick overview of the complex equipment and visualization, each of which involved hours of processing — far from instant photography.

    While the camera on your phone takes two-dimensional photos, T-CUP is a type of streak camera, which records images in a single dimension, very very quickly. Unlike prior streak cameras, which create composite images of light by recording different horizontal slices of laser over multiple laser pulses, the T-CUP is able to image an entire laser pulse in a single frame. It does this by diverting the laser beam to two different cameras simultaneously, then using a computer program to combine the two images.

    Light at 10 Trillion FPS

  4. The Science Asylum’s YouTube video “Where Does Light Come From? (Electrodynamics)” (published on Apr 15, 2019) is an excellent overview (visualization) of classical electrodynamics.

    Description:

    It’s often said that light is an electromagnetic wave, a disturbance in electric and magnetic fields, but what does that mean? How are they made? Let’s take a deeper look at electrodynamics and this history behind the discovery to see if we can find an answer.

    Quote from video:

    But, math aside, let’s just stop and appreciate something for a few seconds. This field disturbance is self-sustaining. You can stop the charge from moving and the fields will continue to do this. There’s now a disturbance in a couple fields that travels out through space. All because a charge once accelerated at some point in the past. And that field disturbance is what we call light.

    So, I’m looking for a quantum explanation of these EM laws:

    • Gauss’s law for electricity says electric fields point away from positive charges and toward negative charges. [Field gradients sort of like sources and sinks.]
    • Gauss’s law for magnetism says magnetic fields always form closed loops.
    • Faraday’s law … seems to connect the fields to each other. Basically, a changing magnetic field makes an electric field.

    History:

    Thirty years after Faraday, James Clerk Maxwell enters the conversation. … Faraday said a changing magnetic field gives us an electric field and now Maxwell’s said a changing electric field gives us a magnetic field.

    Key concept:

    If one field can make the other field, then maybe charges don’t make the fields at all. Maybe they just affect [interact with] them. Maybe they’re a thing all by themselves. I mean, we said light was a disturbance in electric and magnetic fields and light is a thing all by itself.

    In fact, that’s exactly how we imagine fields these days. Notice the arrows in this graphic remain in the same place as the charge moves. They’re attached to the space, not the charge. If there aren’t any charges around, we like to imagine the fields are still there and just have a value of zero. We wouldn’t really get confirmation of this though until the 1860s.

    Vocabulary: Field arrows (vectors)

  5. So, this is a question about photons that’s always fascinated me: Can photons interact? This Live Science article “Inside Giant Atom Smasher, Physicists See the Impossible: Light Interacting with Light” by Paul Sutter (April 25, 2019) discusses some recent experiments by the ATLAS collaboration at the Large Hadron Collider.

    [Photons] aren’t supposed to interact with each other, …

    In high-energy experiments, we can … get two photons to strike each other, though this happens very rarely [“… after trillions upon trillions of collisions, the team detected a grand total of 59 potential intersections. Just 59.”].

    Photons so rarely interact with one another because they connect only with particles that have electric charges.

    The answer lies in one of the most inscrutable and yet delicious aspects of modern physics, and it goes by the funky name of quantum electrodynamics [1].

    In the case of photons, as they travel, every once in a while (and keep in mind that this is extremely, extremely rare), … it can become a [virtual] pair of particles, a negatively charged electron and a positively charged positron that travel together [extremely briefly].

    Well, I don’t know about that. The arxiv.org PDF paper discusses the experiments for 7 pages and then has 21 pages of acknowledgments, references, and the ATLAS Collaboration list. It’s a fascinating and quite technical presentation of the selection criteria for detection / photon reconstruction and the methods used to exclude background and other signatures. One has to trust the “high priests” of physics on that score.

    This letter describes the observation of the light-by-light scattering process … in [heavy-ion] Pb+Pb collisions at √sNN = 5.02 TeV [how hard the ions are being collided together]. The analysis is conducted using a data sample … collected in November 2018 by the ATLAS experiment at the LHC. Light-by-light scattering candidates are selected in events with two photons produced exclusively, each with transverse energy … > 3 GeV and pseudorapidity … < 2:37, diphoton invariant mass above 6 GeV, and small diphoton transverse momentum and acoplanarity. After applying all selection criteria, 59 candidate events are observed for a background expectation of 12  ± 3 events. The observed excess of events over the expected background has a significance of 8.2 standard deviations. ...

    Light-by-light scattering … is a quantum-mechanical process that is forbidden in the classical theory of electrodynamics. In the Standard Model (SM), the … reaction proceeds at one-loop level at order … (where … is the fine-structure constant) via virtual box diagrams involving electrically charged fermions (leptons and quarks) or W± bosons. However, in various extensions of the SM, extra contributions are possible, making the measurement of … scattering sensitive to new physics. Light-by-light scattering graphs with electron loops also contribute to the anomalous magnetic moment of the electron and muon.

    … Exclusive light-by-light scattering can occur in these collisions at impact parameters larger than about twice the radius of the ions. The strong interaction becomes less significant and the electromagnetic (EM) interaction becomes more important in these ultraperipheral collision (UPC) events. The EM fields produced by the colliding Pb nuclei can be described as a beam of quasi-real photons with a small virtuality …

    The paper also references two other processes in which photon-by-photon scattering has been measured.

    In fact, I recall reading here that photons can interact in the presence of (nearby) atomic matter.

    [2015] Now quantum electrodynamics allows not only 𝑒+𝑒−→𝛾+𝛾 but also the reverse process 𝛾+𝛾→𝑒+𝑒− . The former process you can nowadays observe with some tabletop equipment as an undergraduate lab. The latter has so far not been observed in the lab.

    So, it’s not like two ultra pure (coherent single frequency) laser beams (in an ultra clean vacuum cavity) were directed at each other and a few photons interacted / scattered — something that might be simpler to visualize.

    Wiki: Two-photon physics

    [1] Wiki: In technical terms, QED can be described as a perturbation theory of the electromagnetic quantum vacuum. Richard Feynman called it “the jewel of physics” for its extremely accurate predictions of quantities like the anomalous magnetic moment of the electron and the Lamb shift of the energy levels of hydrogen.

  6. Sean Carroll answered some questions about light in this recent video.

    YouTube > Think Inc. > “‘The Speed Of Light’ Is Wrong! Ft. Sean Carroll | Think Inc.” (June 29, 2020) – [Caltech physics] professor Sean Carroll dives into why “The Speed of Light” has stuck around for so long when it should really be called “The Speed of Causality” [and] why we use meters and seconds when measuring the speed of light, and much more!

    (from transcript) …but the point is that it’s more fundamental than just the speed of light. it’s also the speed of gravitons, the speed of gravity, for example, and most importantly it’s just the cosmic speed limit [built into the fabric of space-time] …

    … if I poke the universe right now, the influence from that poking (as far as we know) cannot travel faster than the speed of light. so the fact that it’s the speed of causality – the speed of influence – propagating through the universe is indeed the important fact. but historically, before anyone was thinking that way, they were thinking about light …

    … there is a way of measuring distances in space-time and intervals. so intervals of time distances in space, and the way that works out in space-time is that the curve along which a photon travels has zero space-time interval. ok, so if you could talk about it experiencing time, it would experience zero time; and when you say to a physicist a photon experiences zero time, they know what you mean …

    —

    I was glad Carroll talked about the pitfalls of explaining the twins paradox scenario:

    Yeah, you know I really I try to be careful about this. I don’t always succeed.

    I do not like to talk about clocks or time flowing at different rates because from your perspective on that journey to Alpha Centauri, every time you look at your clock, it’s ticking at one second per second. okay, the time that you feel never feels like it’s … [changing speed].

  7. How did the fact that light has a speed arise? Something that (hopefully) all of us take for granted. Evidently in ancient times the question was debated [1].

    Empedocles (c. 490–430 BC) was the first to propose a theory of light and claimed that light has a finite speed. He maintained that light was something in motion, and therefore must take some time to travel. Aristotle argued, to the contrary, that “light is due to the presence of something, but it is not a movement“. Euclid and Ptolemy advanced Empedocles’ emission theory of vision, where light is emitted from the eye, thus enabling sight. Based on that theory, Heron of Alexandria argued that the speed of light must be infinite because distant objects such as stars appear immediately upon opening the eyes.

    In the early 17th century, Johannes Kepler believed that the speed of light was infinite, since empty space presents no obstacle to it. … Descartes speculated that if the speed of light were found to be finite, his whole system of philosophy might be demolished.

    So, when was the speed of light first quantitatively measured? The credit goes to astronomer Ole Rømer in 1676. But, as Wiki notes, the “theory” was controversial, a saga about more than just collecting data and calculation.

    In 1865 Maxwell’s theory of electromagnetism framed light as an electromagnetic wave, traveling at the associated speed. But how likely is a Jay Leno-like “Jaywalking” survey to find that commonly understood?

    Paul Sutter discusses the more modern frame of reference in this article:

    Space.com > “Why is the speed of light the way it is?” by Paul Sutter (July 16,2020) – Why does the speed of light have the value 299,792,458 meters per second? Why isn’t it some other number? And why do we care so much about some random speed of electromagnetic waves? Why did it become such a cornerstone of physics?

    And this was all well and good until Einstein came along a few decades later …

    Einstein found that there was a single constant, a certain speed, that could tell us how much space was equivalent to how much time, and vice versa.

    Einstein’s theories didn’t say what that number was, but then he applied special relativity to the old equations of Maxwell and found that this conversion rate is exactly the speed of light.

    Of course, this conversion rate, this fundamental constant that unifies space and time, doesn’t know what an electromagnetic wave is, and it doesn’t even really care. It’s just some number, but it turns out that Maxwell had already calculated this number and discovered it without even knowing it. That’s because all massless particles are able to travel at this speed, and since light is massless, it can travel at that speed. And so, the speed of light became an important cornerstone of modern physics.

    Then, because units of measure are arbitrary, Sutter considers how we might explain the speed of light to an alien civilization.

    Notes

    [1] In contrast to the ancient consensus about sound as a movement of air; and any movement requiring time. Yet without our modern frame of reference of speed (or waves).

    Stack Exchange > History of Science and Mathematics > “When was it first realized that sound travels with finite speed?”

    However, nothing resembling the expression “finite speed” was used anywhere in antiquity to describe either light or sound. Leonardo is credited with suggesting c.1500 that sound travels in waves in the modern sense (“we see the waves running across the field while the grain remains in place”). This allows one to make sense of speed and frequency. However, first measurements of the speed of sound were only attempted in 1630s by Mersenne and Gassendi, the first “authoritative” one was the one performed by the Florentine Academy in 1660.

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