Astronomers find cosmic golden needle buried for two decades

Discovery sheds new light on famous Einstein ring; social distance science made possible with public W. M. Keck Observatory and NASA archive data

W. M. Keck Observatory

IMAGE: Examples of Einstein ring gravitational lenses taken with the Hubble Space Telescope. view more  Credit: NASA/ESA/SLACS Survey team: A. Bolton (Harvard/Smithsonian), S. Burles (MIT), l. Koopmans (Kapteyn), T. Treu (UCSB), l. Moustakas (JPL/Caltech)

Maunakea, Hawaii – Determined to find a needle in a cosmic haystack, a pair of astronomers time traveled through archives of old data from W. M. Keck Observatory on Mauankea in Hawaii and old X-ray data from NASA’s Chandra X-ray Observatory to unlock a mystery surrounding a bright, lensed, heavily obscured quasar.

This celestial object, which is an active galaxy emitting enormous amounts of energy due to a black hole devouring material, is an exciting object in itself. Finding one that is gravitationally lensed, making it appear brighter and larger, is exceptionally exciting. While slightly over 200 lensed unobscured quasars are currently known, the number of lensed obscured quasars discovered is in the single digits. This is because the feeding black hole stirs up gas and dust, cloaking the quasar and making it difficult to detect in visible light surveys.

Not only did the researchers uncover a quasar of this type, they found the object happens to be the first discovered Einstein ring, named MG 1131+0456, which was observed in 1987 with the Very Large Array network of radio telescopes in New Mexico. Remarkably, though widely studied, the quasar’s distance or redshift remained a question mark.

“As we dug deeper, we were surprised that such a famous and bright source never had a distance measured for it,” said Daniel Stern, senior research scientist at NASA’s Jet Propulsion Laboratory and author of the study. “Having a distance is a necessary first step for all sorts of additional studies, such as using the lens as a tool to measure the expansion history of the universe and as a probe for dark matter.”

Stern and co-author Dominic Walton, an STFC Ernest Rutherford Fellow at the University of Cambridge’s Institute of Astronomy (UK), are the first to calculate the quasar’s distance, which is 10 billion light-years away (or a redshift of z = 1.849).

The result is published in today’s issue of The Astrophysical Journal Letters.

“This whole paper was a bit nostalgic for me, making me look at papers from the early days of my career, when I was still in graduate school. The Berlin Wall was still up when this Einstein ring was first discovered, and all the data presented in our paper are from the last millennium,” said Stern.METHODOLOGY

At the time of their research, telescopes around the planet were shuttered due to the coronavirus pandemic (Keck Observatory has since reopened as of May 16); Stern and Walton took advantage of their extended time at home to creatively keep science going by combing through data from NASA’s Wide-field Infrared Survey Explorer (WISE) to search for gravitationally lensed, heavily obscured quasars. While dust hides most active galaxies in visible light surveys, that obscuring dust makes such sources very bright in infrared surveys, such as provided by WISE.

Though quasars are often extremely far away, astronomers can detect them through gravitational lensing, a phenomenon that acts as nature’s magnifying glass. This occurs when a galaxy closer to Earth acts as a lens and makes the quasar behind it look extra bright. The gravitational field of the closer galaxy warps space itself, bending and amplifying the light of the quasar in the background. If the alignment is just right, this creates a circle of light called an Einstein ring, predicted by Albert Einstein in 1936.  More typically, gravitationally lensing will cause multiple images of the background object to appear around the foreground object.

Once Stern and Walton rediscovered MG 1131+0456 with WISE and realized its distance remained a mystery, they meticulously combed through old data from the Keck Observatory Archive (KOA) and found the Observatory observed the quasar seven times between 1997 and 2007 using the Low Resolution Imaging Spectrometer (LRIS) on the Keck I telescope, as well as the Near-Infrared Spectrograph (NIRSPEC) and the Echellette Spectrograph and Imager (ESI) on the Keck II telescope.

“We were able to extract the distance from Keck’s earliest data set, taken in March of 1997, in the early years of the observatory,” said Walton. “We are grateful to Keck and NASA for their collaborative efforts to make more than 25 years of Keck data publicly available to the world. Our paper would not have been possible without that.”

The team also analyzed NASA’s archival data from the Chandra X-ray Observatory in 2000, in the first year after the mission launched.NEXT STEPS

With MG 1131+0456’s distance now known, Walton and Stern were able to determine the mass of the lensed galaxy with exquisite precision and use the Chandra data to robustly confirm the obscured nature of the quasar, accurately determining how much intervening gas lies between us and its luminous central regions.

“We can now fully describe the unique, fortuitous geometry of this Einstein ring,” said Stern. “This allows us to craft follow-up studies, such as using the soon-to-launch James Webb Space Telescope to study the dark matter properties of the lensing galaxy.”

“Our next step is to find lensed quasars that are even more heavily obscured than MG 1131+0456,” said Walton. “Finding those needles is going to be even harder, but they’re out there waiting to be discovered. These cosmic gems can give us a deeper understanding of the universe, including further insight into how supermassive black holes grow and influence their surroundings,” says Walton.


The Low Resolution Imaging Spectrometer (LRIS) is a very versatile and ultra-sensitive visible-wavelength imager and spectrograph built at the California Institute of Technology by a team led by Prof. Bev Oke and Prof. Judy Cohen and commissioned in 1993. Since then it has seen two major upgrades to further enhance its capabilities: the addition of a second, blue arm optimized for shorter wavelengths of light and the installation of detectors that are much more sensitive at the longest (red) wavelengths. Each arm is optimized for the wavelengths it covers. This large range of wavelength coverage, combined with the instrument’s high sensitivity, allows the study of everything from comets (which have interesting features in the ultraviolet part of the spectrum), to the blue light from star formation, to the red light of very distant objects. LRIS also records the spectra of up to 50 objects simultaneously, especially useful for studies of clusters of galaxies in the most distant reaches, and earliest times, of the universe.  LRIS was used in observing distant supernovae by astronomers who received the Nobel Prize in Physics in 2011 for research determining that the universe was speeding up in its expansion.ABOUT NIRSPEC

The Near-Infrared Spectrograph (NIRSPEC) is a unique, cross-dispersed echelle spectrograph that captures spectra of objects over a large range of infrared wavelengths at high spectral resolution. Built at the UCLA Infrared Laboratory by a team led by Prof. Ian McLean, the instrument is used for radial velocity studies of cool stars, abundance measurements of stars and their environs, planetary science, and many other scientific programs. A second mode provides low spectral resolution but high sensitivity and is popular for studies of distant galaxies and very cool low-mass stars. NIRSPEC can also be used with Keck II’s adaptive optics (AO) system to combine the powers of the high spatial resolution of AO with the high spectral resolution of NIRSPEC. Support for this project was provided by the Heising-Simons Foundation.ABOUT ESI

The Echellette Spectrograph and Imager (ESI) is a medium-resolution visible-light spectrograph that records spectra from 0.39 to 1.1 microns in each exposure. Built at UCO/Lick Observatory by a team led by Prof. Joe Miller, ESI also has a low-resolution mode and can image in a 2 x 8 arc min field of view. An upgrade provided an integral field unit that can provide spectra everywhere across a small, 5.7 x4.0 arc sec field. Astronomers have found a number of uses for ESI, from observing the cosmological effects of weak gravitational lensing to searching for the most metal-poor stars in our galaxy.ABOUT KOA

The Keck Observatory Archive (KOA) is a collaboration between the NASA Exoplanet Science Institute (NExScI) and the W. M. Keck Observatory (WMKO). NExScI is sponsored by NASA’s Exoplanet Exploration Program, and operated by the California Institute of Technology in coordination with the Jet Propulsion Laboratory (JPL).ABOUT W. M. KECK OBSERVATORY

The W. M. Keck Observatory telescopes are among the most scientifically productive on Earth. The two 10-meter optical/infrared telescopes on the summit of Maunakea on the Island of Hawaii feature a suite of advanced instruments including imagers, multi-object spectrographs, high-resolution spectrographs, integral-field spectrometers, and world-leading laser guide star adaptive optics systems. 

Some of the data presented herein were obtained at Keck Observatory, which is a private 501(c) 3 non-profit organization operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation.

The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the Native Hawaiian community.  We are most fortunate to have the opportunity to conduct observations from this mountain.

From EurekAlert!

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Martin Howard Keith Brumby
June 3, 2020 2:14 am

Nice to see that a few real scientists survive the politically correct and socialist activist Pandemic which has raged through Academia, unabated, for all this Millennium.

Reply to  Martin Howard Keith Brumby
June 3, 2020 2:30 am

That is what makes this sort of science article so interesting and rewarding to read in comparison with the spew of nonsense pumping forth, daily, on the subject of ‘Climate Change’.

Ron Long
June 3, 2020 3:22 am

Good work and good story. Also another reference to the agile mind of Albert Einstein. As I understand it his IQ was high (165 or so?) but what really set him up was the interconnection between right and left hemispheres of his brain. This apparently allowed him to visualize experiments, in an artistic sense, then analyze the thought for accuracy. He also had visual reference memory (not photographic) and well-developed pre-frontal cortex so lots of introspection, probably on display as he reluctantly supported the Manhattan Project. A scientist with a conscience? I don’t think they exist in the CAGW crowd.

Reply to  Ron Long
June 3, 2020 3:49 am

Hmm interesting in a commentary on science. You mention IQ.. essentially a SOCIAL “Science??” construct, and Einstein was NEVER tested so we don’t know… and… left right brain bulshit that was debunked many many many years ago… very scientific I must say… NOT

Reply to  Slyrik
June 3, 2020 4:11 am

I have a most uninteresting IQ AND no brain to speak of (let alone Left or Right), so what bloody chance do I have?

Reply to  toorightmate
June 3, 2020 5:01 am

Hard work can make up for lack of ability. 😇

Reply to  toorightmate
June 3, 2020 2:42 pm

For success discipline matters more than intelligence.

Reply to  Slyrik
June 4, 2020 12:00 pm

The major brain division is not left and right, but Conscious and Unconscious. It is said that 90% of the personality is in the Unconscious. But we digress. We need a brain thread to pick up these pieces.

Ron Long
Reply to  John Tillman
June 3, 2020 5:51 pm

John, also: Sciencedaily, 4 Oct. 2013 “the left and right hemisphere of Albert Einsteins brain was unusually well connected”, and BRAIN: A Journal of Neurology, Sept. 21, 2013 “Einstein…extraordinary pre-frontal cortex…”. Remember, Einstein never performed an actual experiment after graduating university, he visualized everything, and analyzed the visualization by math and further thought.

Steve Keohane
Reply to  Ron Long
June 3, 2020 4:51 am

‘Eidetic mind, one that thinks in pictures.

Reply to  Ron Long
June 3, 2020 5:57 am

I have a son who see’s sounds in colors along with hearing them. We initially found this out when he was very young and said certain sounds were red, green, yellow or a mix of them and the bad sounds were blue and black. He is also can play every instrument by ear and all self taught. He currently has a band and produces music and videos/animations for others. He is all image and sound based but really has an issue spelling, writing and math. The brain is quite amazing.

Gordon A. Dressler
Reply to  rbabcock
June 3, 2020 7:50 am

Hi, rbabcock,
If you and/or your son have not already read it, I highly recommend the book “Born On A Blue Day: Inside the Extraordinary Mind of an Autistic Savant” by Daniel Tammet (also available on Kindle and as audiobook and MP3 CD). Daniel Tammet describes himself as “seeing” numbers as different shapes/outlines, sizes and colors and has performed incredible math-based feats, such as reciting pi from memory to 22,514 digits in five hours and nine minutes.

(ref:,been%20translated%20into%2018%20languages. )

Reply to  Ron Long
June 3, 2020 5:55 pm

Einstein invented, nothing, save for a refrigerator that required no electricity. I don’t know anyone who uses one, though.

Crispin in Waterloo
Reply to  Karim Ghantous
June 4, 2020 8:47 am

People don’t invent, they discover. Einstein discovered much.

Gordon A. Dressler
Reply to  Karim Ghantous
June 4, 2020 11:37 am

Karim Ghantous, it sure sounds like you are referring to the “thought experiment” involving a thermodynamic demon created by James Clerk Maxwell, not Albert Einstein (see ).

If not, please advise what particular invention of Einstein’s you are referring to in you post.

June 3, 2020 4:44 am

That Berlin Wall was pulled down because the world found it disgusting.

Today’s Climate Scientists are assisting in BUILDING a new Berlin Wall around the entire world. That’s even more disgusting.

Reply to  DocSiders
June 3, 2020 10:12 pm

The world was quite happy with the Berlin Wall for a long time. It was Ronald Reagan and Meg that tore it down, not the world. I lived behind that disgusting thing for 20 years before I escaped in 1981. The world doesn,t care about the junk science now. It is not disgusting, in fact it is celebrated.
Just like with the Berlin Wall it is up to the individuals (you and me included) to tear it down.

Hal DeSaussure
June 3, 2020 5:00 am

This bit of scientific detective work is pretty remarkable. During the shutdown, I took to participating in the Zooniverse project which allows ordinary folks like me to classify galaxies in a very basic way. It’s a very tedious but weirdly fascinating time-wasting exercise. One quickly realizes doing this that there is so much out there that trying to find these needles is a major undertaking. The fact that the authors were able to find these out of the vast quantity of data is remarkable. I can’t imagine the days and weeks spent in looking at images and other data accumulated of the thousands upon thousands of galaxies that must be archived.

June 3, 2020 5:02 am

This looks like science to me but what do I know?….

June 3, 2020 5:43 am

I doubt they were able to get the mass “with exquisite precision”.

Reply to  mkelly
June 3, 2020 6:25 pm

In astronomy, galaxy mass within 100 orders of magnitude is exquisite precision. Anything less takes unicorns and fairy godmothers.

Reply to  mkelly
June 4, 2020 8:00 am

mkelly, I assume what they meant about the mass determination was relative.

Gordon A. Dressler
June 3, 2020 7:36 am

A prime example of the incredible capabilities and inventiveness of the human mind when devoted to greater understanding of our universe and its physics.


Sal Minella
June 3, 2020 7:52 am

Enlighten me. How does the following quote resemble the facts.

“With MG 1131+0456’s distance now known, Walton and Stern were able to determine the mass of the lensed galaxy with exquisite precision and use the Chandra data to robustly confirm the obscured nature of the quasar, accurately determining how much intervening gas lies between us and its luminous central regions.”

The distance is not known, the quasar is 10 billion light years away. Wait, maybe it is. Wait maybe it’s not. Maybe it was, 10 billion years ago. Maybe it doesn’t even exist. Maybe it hasn’t existed for billions of years.

Gordon A. Dressler
Reply to  Sal Minella
June 3, 2020 11:24 am

Astronomers frequently refer to astronomical objects having distances relative to the speed of light, equivalent to looking back in time (e.g., a “light year”).

For example the Sun is 8.317 light minutes away from Earth, and in fact no one can state with 100% certainty that the Sun didn’t cease to exist, for example, 7 minutes ago.

Scientists can only deal with observations as they are made. There is no issue with the general understanding in the astronomy/cosmology communities that reported observations are based on events that happened billions, millions, thousands or even minutes prior to recording the data being analyzed.

The bottom line: the scientific method does NOT require the observation of the current status of the universe, and certain physics is based on the assumption of time-invariant behavior.

Sal Minella
Reply to  Gordon A. Dressler
June 3, 2020 1:32 pm

I’m taking exception to the phrase “distance now known”. We know where it was 10 B years ago, but relative to what. Not Earth for sure as our solar system would not exist for some 6 B more years. I am not unfamiliar with spacetime, but it is not made clear in most astrophysics treatises that the time relative to us is not “now”.

For example, the commonly stated idea that the Universe is expanding (now) and that objects farther away are expanding faster never includes the time component. It could be stated that farther back in time the Universe was expanding faster. It could also be noted that galaxies within 100 M light years from Earth are collapsing toward one another. The interpretation might then be that the Universe started to contract 100 M years ago. Instead it is presented as a mystery (why are galaxies moving away from one another and why do they move faster the farther away they are). In order to support the Expanding Universe, all form of magic dark stuff (invisible matter and energy) and magic numbers (constants that aren’t constant) had to be invented. Not so for the Contracting Universe theory.

Gordon A. Dressler
Reply to  Sal Minella
June 3, 2020 7:17 pm

“. . . why are galaxies moving away from one another and why do they move faster the farther away they are . . .”

This is a common misperception. It is not so much that galaxies having intrinsic motion relative to each other over mega-light years distances as it is the fact that spacetime itself is expanding.

Think of the analogy of massive 3D ball of cookie dough, with randomly embedded chocolate chips, put into an oven in a weightless environment (like aboard the ISS). As the dough (the analogue for the spacetime of our universe) expands due to the dough generating carbon dioxide and being heated during the baking process, the individual chocolate chips (the analogue for galaxies in our universe) are moved away from each other by the expanding dough. And since the absolute rate at which the dough expands is assumed to be constant over a fixed distance (say, one mm/sec over each cm) the further apart two chocolate chips are, the faster they will be carried away from each other at any given moment . . . so for the hypothetical constant rate of one mm/sec per cm, two chocolate chips only two cm apart would be moving away from each other at about 2 mm/sec, whereas two chocolate chips six cm apart would be moving away from each other at about 6 mm/sec.

Note that the chocolate chips themselves are NOT moving through the dough, but are instead being carried along by it as the whole ball of dough expands . . . same concept with galaxies in an “open” universe, one that will keep on expanding forever (albeit, the rate of expansion might be variable, as long as it stays positive).

It is this fundamental expansion of spacetime comprising our universe (with its changing volume being mostly empty anyway) that produces the universal—pardon the pun—Doppler shift from the blue toward the red part of starlight’s spectrum for the most distance galaxies that we observe . . . this is not speculation but is supported by a tremendous amount of empirical data. This spacetime expansion is consistent with (actually, inseparable from) the theoretical concept of the Big Bang.

You are correct in speculating that some localized groups of galaxies can be “contracting” toward each other . . . this is the result of gravitational attraction within said groups. But at tens of gig-light years distances, the combined forces of all the galaxies in the universe appear to be insufficient (due to gravity’s 1/r^2 dependence and the very low density of matter in the universe) to counteract the expansion of our universe’s spacetime continuum that was forced by the Big Bang (and you can read up on “cosmological inflation” if you want some of the more gory details of what we think we know about our universe and its future).

Gordon A. Dressler
Reply to  Gordon A. Dressler
June 3, 2020 7:29 pm

Of course, that should be “giga-light year” (not “gig-light year) in the last paragraph of my post above.

Reply to  Sal Minella
June 3, 2020 1:07 pm

If it was a 10bn light years away a 10bn years ago, in an expanding universe, how far away is it now ?

William Astley
Reply to  Sal Minella
June 3, 2020 4:20 pm


Proving Einstein’s theory of general relativity is correct, is not a discover. Proving GR incorrect would be a discovery.

If science is working, when there is an observational paradox, there should be a breakthrough. This has not occurred in astronomy.

The following is a summary of some of interesting ‘quasar’ observations which are a paradox for the theory that the complex set of observations about a thing in space which we call a ‘quasar’…

The Big Bang theory assumes everything is made from infalling clouds of gas.

A Quasar was assumed to be a black hole (massive object, gravity drives/powers what makes the weird spectrum at the quasar) and a large cloud of gas that falls into the black hole

It has been found that active galaxies, are emitting massive jets into space from their core, and the jets that are emitted from the quasars have from time to time, bright ‘knots’ that are emitting x-rays.

“Quasar’ emit non thermal radiation.

With the majority of the Quasar radiation being caused by massive jets of gas that are emitted out of each pole of the galaxy, through a galaxy sized magnetic field that it appears is attached to the massive object.

A Galaxy is called an active galaxy, if the galaxy’s massive ‘black’ hole is …. is ejecting stuff out of its poles.

There is no accepted explanation as to how infalling gas, into a black hole, could create any significant magnetic field.

The new X-ray telescopes can look through the massive clouds of dust that surround Active galaxies, and infrared observational also can observed through dust, and lower frequencies show the location of the massive clouds of gas that have been ejected from the active galaxy.

So we have found a great deal more quasars and we have found that these objects are connected.

… As Halton Arp noted, 40 years ago, there are clouds of gas connecting, active galaxies to the ejected quasar like objects …..

… and the quasar like objects appear to be at the same redshift as the active object based on the connecting gas clouds.

However based on redshift the ejected quasar like objects are billions of light years more distant than the active galaxy which is an observational paradox. At that time it was assumed that there could not be clouds of gas that extend for billions of light years….

Evidence that quasars and quasar like objects are close is this evidence of quasar clustering and quasar alignment.
Spooky Alignment of Quasars Across Billions of Light-years

“The first odd thing we noticed was that some of the quasars’ rotation axes were aligned with each other — despite the fact that these quasars are separated by billions of light-years,” said Hutsemékers.
The team then went further and looked to see if the rotation axes were linked, not just to each other, but also to the structure of the Universe on large scales at that time.

When astronomers look at the distribution of galaxies on scales of billions of light-years they find that they are not evenly distributed.

They form a cosmic web of filaments and clumps around huge voids where galaxies are scarce. This intriguing and beautiful arrangement of material is known as large-scale structure.
Alignment of quasar polarizations with large-scale structures, September 23, 2014

This is a complete different Big Bang paradox.

It was assumed that galaxies were formed from small proto galaxies.

Based on that assumption there should be a swarm of small galaxies (roughly 100,000 and spherically distributed) around every large galaxy.

What was found is there are roughly 400 small galaxies around the Milky Way and those small galaxy are not randomly located and….

… but rather located in a plane about the Milky Way with orientation and orbit consistent with the origin being from Milky Way galaxy ejection out of the poles of the galaxies. And it has been found that other galaxies also have a disc of dwarf galaxy about them.

and those small, ‘dwarf’ galaxies contain a type of stars, in their Globural clusters, that are not found in the Milky Way. This fact is paradox as it requires the Dwarf galaxies to be formed from a different gas than the gas that formed the large galaxy.

And in addition, it has been found that the small galaxies contain 30 times more ‘Globural Clusters’ than do the larger galaxies.

The number of these ‘Globural Clusters’ mysteriously scales with galaxy mass. The larger the galaxy is the more globural clusters there are. Except there are 30 times more globular clusters when galaxies are small.
Mysterious dance of dwarf galaxies may force a cosmic rethink
The discovery that many small galaxies throughout the universe do not ‘swarm’ around larger ones like bees do but ‘dance’ in orderly disc-shaped orbits is a challenge to our understanding of how the universe formed and evolved.

The researchers believe the answer may be hidden in some currently unknown physical process that governs how gas flows in the universe, although, as yet, there is no obvious mechanism that can guide dwarf galaxies into narrow planes.

Velocity anti-correlation of diametrically opposed galaxy satellites in the low-redshift Universe
Recent work has shown that the Milky Way and the Andromeda galaxies both possess the unexpected property that their dwarf satellite galaxies are aligned in thin and kinematically coherent planar structures1, 2, 3, 4, 5, 6, 7. It is interesting to evaluate the incidence of such planar structures in the larger galactic population, because the Local Group may not be a representative environment. Here we report measurements of the velocities of pairs of diametrically opposed satellite galaxies. In the local Universe (redshift z 7σ confidence). This may indicate that planes of co-rotating satellites, similar to those seen around the Andromeda galaxy, are ubiquitous, and their coherent motion suggests that they represent a substantial repository of angular momentum on scales of about 100 kiloparsecs.

Gordon A. Dressler
Reply to  William Astley
June 3, 2020 7:24 pm

William Astley posted; “The Big Bang theory assumes everything is made from infalling clouds of gas.”

Err . . . sorry, but no.

I didn’t read further.

J Mac
June 3, 2020 9:19 am

A really interesting bit of ‘detective work’ on a ‘cold case’ here!

Peter Pandemic
June 3, 2020 8:33 pm

How can space warp, when space is only a mathematical construct? You can’t observe space, can you, only the objects and energy in it.
Wouldn’t it be more correct to say that light deviates from a straight line, due to gravitational fields?
Wouldn’t this imply light has some slight mass, as yet undiscovered?

Reply to  Peter Pandemic
June 4, 2020 8:10 am

Wouldn’t this imply light has some slight mass, as yet undiscovered?

Light still travels in a “straight” line — the space itself is curved & light travels along the curved lines of the space-time fabric.

Gordon A. Dressler
Reply to  beng135
June 4, 2020 12:05 pm

A photon of light has the equivalent of mass by dint of its energy (the old E=m*c^2 thing)—therefore it follows geodetic paths in spacetime—as well as it also having sensible momentum (a physical reason that light sails for spacecraft are practical for producing thrust).

However, a photon of light, always traveling at the speed of light in the local medium, cannot and does not have a rest mass.

More broadly, “vacuum space” is not only a mathematical construct . . . is creates real world effects that have been measure to great precision. I invite you to research “Casimir effect” and quantum field theory: ref:

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