# Do Other Dimensions REALLY Exist?

Those of you who have been following physics for the last few decades have no doubt heard about string theory and how it requires that spacetime have 11-dimensions and not the four we are most familiar with (3 for space and 1 for time) . This has been a popular topic of discussion since the 1970s, and has spawned thousands of popularizations and lectures. I have actually written a few of these!

The difficulty is that we never experience even ordinary space directly, and as Einstein noted, space itself is more of a human mental construct than it is a physical feature of our world. When physicists need some additional dimensions to space to model our world, we find ourselves confused as our brains try to fabricate an inner model of what that might mean. The idea of ‘dimension’ is not what you might think. It is just another way of saying that some system you are modeling mathematically needs N numbers to define it uniquely in space and time. For example, economists work in ‘spaces’ where their models use N=4 unique numbers, so their universes are 4-dimensional too!

Space, as a physical idea is just our experience that we only need three numbers to locate a geometric point on Earth. We need its latitude, its longitude and its elevation above the surface of Earth. Two of these numbers are angles, but we can easily convert these angles into meters because the surface of Earth has a fixed radius and forms a sphere. The angles just represents the lengths of arcs on the surface.

Extending this into the solar system and beyond, we only need three numbers to define the location of a planet or a star. If we try to provide four numbers to locate any point in space, that fourth measurement can be replaced in terms of the previous three numbers. Because this minimum number is three, we say that our space is 3-dimensional. Similarly, all of Euclid’s geometry takes place on a flat surface where points are defined by two numbers, so it is a 2-dimensional surface. The figure above shows an example of ordinary 3-d space and its coordinate axis in the Cartesian ‘X, Y, Z’ system. But there are other possible coordinate systems we can use such as spherical (R, theta, phi) or cylindrical (R, theta, h), but they all define points in 3-d space by a unique three-number address. But wait…there’s more!

Three is not enough. Our physical world actually requires a time coordinate to define where objects are because, of course, all objects are in motion or are internally changing. Time is a fourth coordinate that helps us keep track of the complete history of an object as it moves through 3-d space. This path is called a worldline. This is why Einstein’s relativity refers to ‘spacetime’ as the fundamental arena in which all events take place. Spacetime is a 4-dimensional object with three coordinates expressed in terms of meters, and a time coordinate expressed in units of time such as nanoseconds, seconds, years etc. Spacetime is also called a manifold because every point in it can be uniquely defined by four numbers. There are mathematically an infinite number of these points. Because we have yet to find any evidence to the contrary, the manifold of all points in our physical universe, call it M, is just the same as the 4-d spacetime manifold proposed by Einstein’s relativity, call it M4, so in short-hand we can write a symbolic sentence: M = M4.

M4 is not big enough: What you need to keep in mind is that in our 4-dimensional world, we can obviously see that ‘space’ is very different than ‘time’. When physicists talk about our world or our universe having more than 4-dimensions, they also mean that additional coordinates are needed beyond (3-d) space and (1-d) time to keep track of the properties of matter and energy in their new theories. There is nothing about any of these additional coordinates that needs to have the same character as either space or time. All they need to be is numbers defining a 10-dimensional coordinate system. Some physicists, however, do think of these added dimensions as having some kind of space-like attributes.

The way that these extra dimensions are added to our world to create the M of our physical universe is that they represent coordinates in a separate kind of space, call it M6, that adjoins our M4. In string theory, this M6 space is vanishingly small. You will not find traces of it in M4, so don’t worry about somehow taking a wrong turn in M4 and suddenly ending up in M6. String theory requires that M6 be a closed, finite manifold present at every point in M4. The size of each of these new dimensions is only 10-33 centimeters, which is why these M6s are called ‘compact’ manifolds. Only quantum particles and fields have access to M6, and this access causes particles to have different characteristics.

So what is M? The complete specification of our manifold can be written as M = M4 x M6. The address of each point in M is now given by, for example, the 4 coordinates (x,y,z,t) to define their location in M4, but to define the location of this point inside one of these compact M6 manifolds you need six additional numbers, which we can write as (a,b,c,d,e,f). The complete specification for points in the M manifold is then (x,y,z,t,a,b,c,d,e,f) or more neatly (x,y,z,t)(a,b,c,d,e,f) where we keep the two manifolds symbolically separate by placing parenthesis to group their respective coordinates.

So the question is, are the coordinates (a,b,c,d,e,f) dimensions of space like (x,y,z), are they more like the dimension of time in M4, or are they something else? As I said earlier, we already know that the time coordinate, t, is not at all like the other three space coordinates in M4, so there is no reason to believe that (a,b,c,d,e,f) should resemble either (x,y,z) or t. In fact, in string theory we already know something about the character of the coordinates in M6.

Very small: String theory proposes that they have a size of about the Planck Length, which is 10-33 centimeters. You can’t get lost in M6 because you always wind up back at your starting point after you have walked 10-33 centimeters!

Periodic: Some or all of these extra dimensions allow for the properties of physical quantities such as fields to have some periodic feature to them. An important quantity is the spin of a particle, which can be either multiples of 1 (called bosons) or 1/2 (called fermions). All elementary particles (electrons, quarks) are fermions, and all force-carrying particles (photons, gluons) are bosons.

Provides a complex topology: The number of times a quantity ‘wraps’ around a periodic extra-dimension, the more mass it has. When M6 is defined by these coordinates, the shapes of the M6 manifolds, called their topology, can have holes in them. String theory requires that these shapes be in a class called Calabi-Yau manifolds in order that the particles and fields resemble our world.

Metric signature: In special relativity, the distance between points in 4-dimensions, dS, is defined by dS2 = dx2 + dy2 + dz2 – c2dt2 where, for instance the symbol dx is the difference in the x coordinates between two points dx = x2 – x1. Notice that the space coordinates enter with a positive sign and the sole time coordinate enters with a negative sign. Physicists write this as the metric signature (+,+,+,-). In string theory, the extra dimensions are added with positive signs to make the string theory models work correctly to get something like dS2 = dx2 + dy2 + dz2 +da2 + db2 + dc2 +dd2 + de2 +df2 – c2dt2. So, the extra dimensions are taken to be space-like even though the maximum distance along any one of these 6 dimensions is only about 10-33 centimeters!

That is the mathematics of it, but do the extra dimensions really, really, reaally exist?

The truth of the matter is that we don’t know! If string theory is found to be incorrect, then there is no obvious reason to have a M6 at all, and so we are left with the M4 universe that we know and love. We cannot investigate the universe at the Planck scale, so the only way to test this idea of extra dimensions is to find that a theory like string theory is correct and accurate. We can then say that, because experiments confirm the predictions of string theory very accurately, there must be something like these M6 manifolds with their additional dimensions beyond the four we can directly measure in M4. On the other hand, it may also be that M6 is just mental ‘scratch paper’ that humans need in order to mathematically describe the particles and fields in our M4 universe, but our universe is actually doing something else entirely!

One important prediction from string theory is that gravity is a force modeled by closed strings in this 10-dimensional manifold. It also has the ability to range far and wide across these additional dimensions while the other three forces are confined to M4. This means that any gravitational interaction takes place in the 10-d arena and we only experience the part of this gravitational field that is in our ‘small’ 4-d universe. In fact, the theory says that this is why gravity is such as weak force because we are only seeing a small part of its full 10-d effects. This allows us to test at least this prediction by string theory.

Supernova 1987A: This supernova produced a pulse of neutrinos measured back on earth through the detection of about 12 neutrinos in the Super Kamiokande Neutrino Detector. These pulses arrived within seconds of the optical burst. Neutrinos are like the Miner’s Canaries and their numbers depend very sentitively on the energy of the collapsing supernova core into a neutron star. These 12 neutrinos matched the energy calculations, but only if the core of the star achieved its temperature by gravitational collapse, and with the energy determined by the action of gravity with little or no leakage into other dimensions. The tests were only able to say that the supernova data are consistent with these extra dimensions being smaller than about 1 angstrom (10-8 cm). So this result is a bit inconclusive.

Gravity waves: In 2017, the LIGO gravity wave detector rang out with the passing gravity wave called GW170817 from the collision between two neutron stars. The added twist was that the collision was also observed by its intense optical outburst. When detailed calculations of the energy in gravity waves and visible light were performed, the energy matched the theory exactly. The theory, based on standard general relativity, does not inlude the diminution of the gravity pulse by leakage of energy outside our M4 spacetime. The conclusion was that on this basis, gravity does not act as though there are extra dimensions! In fact, the gravity wave measurements give an observational estimate for the dimensionality of M4 of D = 4.02 +/-0.07. There is not much uncertainty to hide 6 more dimensions.

So there you have it. Those extra dimensions are probably space-like but their compact character makes them very different than either the huge space-like character of our familiar 3-dimensions to space.

Stay tuned for my next Blog in two weeks where I will be discussing the laatest Webb Space Telescope data!!!

# An Old Era Ends-A New One is Born

As the international rush to get to the moon ramps up in the next few years, it is worth noting that, just as we are losing the World War II generation, we are also losing NASA’s early astronaut corps who made the 1960s and 1970’s space exploration possible.

The Mercury, Gemini and Apollo astronauts are legends who made our current travel to the moon far less of a challenge 50 years later than it would otherwise have been. Since these missions completed their historic work, we have been able to mull over many scenarios for how to do it ‘right’ the next time, and so here we are. We have learned from our successes in science and engineering, but we have also learned from our failure of political nerve to go beyond the gauntlet thrown down by Apollo 17. Now we are in the midst of what appears to be a new Space Race, this time between the open societies of the ‘west’ and the closed and secretive society of China. Meanwhile, amidst this political hubris, the ranks of the Old Guard astronauts continue to thin out each year.

The first group of astronauts to pass, were the original Project Mercury astronauts at the pionering, and very risky, dawn of NASA (1958-1963): Scott Carpenter, Gordon Cooper, John Glenn, Virgil Grisson, Walter Schirra, Alan Shepard and Donald Slayton. With the passing of John Glen in 2016 at the age of 95, we lost irretrivably our connection to the trials and tribulations of sitting in a ‘tin can’ as big as a telephone booth and eating food out of toothpaste tubes. These were the incredably brave men who sat on top of rockets that had only been tested a handful of times without blowing up!

But more than that, these were the faces of NASA that we saw in the news media who made space travel a household word in the early-1960s. This was a HUGE transition in social consciousness because prior to Project Mercury, space travel was pure science fiction. We were a Nation obsessed by the prospects of nuclear war and Soviet spies lurking around every street corner. The adventures of the Mercury astronauts let hundreds of millions of people take a mental vacation and think about more hopeful ties to come. That plus the advent of the Jetsons TV series!

The second cohort of astronauts were those that flew with Project Gemini between 1963 and 1966. There were ten crewed missions and 16 astronauts, who conducted space walks, dockings and tested out technology and protocols for the Apollo program. Many of them went on to fly in Project Apollo having earned their ‘creds’ with Gemini.

The photo above shows, seated left to right, Edwin Aldrin (33), William Anders (30), Charles Bassett (32), Alan Bean (31), Eugene Cernan (29), and Roger Chaffee (28). Standing left to right are Michael Collins (33), Walter Cunningham (31), Donn Eisele (33), Theodore Freeman (33), Richard Gordon (34), Russell Schweickart (28), David Scott (31) and Clifton Williams (31). Additional astronauts were selected for Gemini: Frank Borman (35), Jim Lovell (35), Thomas Stafford (33), John Young (34), Neil Armstrong (33), and Pete Conrad (33). The ages of this group in 1963 spanned 29 to 35.

Whenever I look at this photo, I see these astronauts as being 10 years older than their actual age. I was a teenager during this time and anyone older than 25 or 30 looked pretty old to me. I guess for these astronauts, a military life, and the dress styles of the narrow-tie, conservative, early-60s does that to you.

At the present time, January 2023, the only survivors of the Mercury and Gemini groups are Edwin Aldrin (92), William Anders (89), Russell Schweickart (88) and David Scott (91). We just lost Walter Cunningham (90).

Finally, we have the Program Apollo astronauts. They were actually drawn from the Project Gemini group, but because of the premature deaths of Roger Chaffee, Ed White, Charles Bassett, and Theodore Freeman, additional astronauts were added to this project: Charles Duke, Harrison Schmitt, Ken Mattingly, Fred Haise, Wally Schirra, Edgar Mitchell, Jack Swigert, James Irwin, Alfred Wordon, James McDivitt, Ronald Evans, and Stuart Roosa.

Each Apollo mission had three astronauts. Two would take the LEM to the surface for a walk-about, while the third astronaut remained behind in the Command Module. A total of 12 Apollo astronauts actually walked on the moon between Apollo 11 and 17: Neil Armstrong, Buzz Aldrin, Pete Conrad, Alan Bean, Alan Shepard, Edgar Mitchell, David Scott, James Irwin, John Young, Charles Duke, Eugene Cernan and Harrison Schmitt. Of these, the survivors by January, 2023 are Buzz Aldrin (92), David Scott (90), Charles Duke (87) and Harrison Schmitt (87).

So, the surveying astronauts in January 2023 from the Mercury, Gemini and Apollo programs are, in order of age:

Buzz Aldrin (92: Gemini 12, Apollo 11),

David Scott (90: Gemini 8, Apollo 9, Apollo 15),

William Anders (89: Apollo 8),

Fred Haise (89: Apollo 13),

Russell Schweickart (88: Apollo 9),

Charles Duke (87: Apollo 16)

Harrison Schmitt (87: Apollo 17).

Ken Mattingly (86: Apollo 16, STS-4, STS-51C),

We are entering something of a race against time for these survivors to be present for the launch of Artemus III. Artemis III is planned as the first crewed Moon landing mission of the Artemis program. Scheduled for launch in 2025, Artemis III is planned to be the second crewed Artemis mission and the first crewed lunar landing since Apollo 17 in 1972. Buzz Aldrin (92: Gemini 12, Apollo 11) was one of the first astronauts to set foot on the lunar surface, while Harrison Schmitt of Apollo 17 was one of the last. With Buzz Aldrin and David Scott, we even have survivors from the Gemini Program who laid the groundwork for EVAs (Gemini 12) and docking maneuvers (Gemini 8).

The odds are pretty good that many of these Old Guard astronauts will still be with us to see the Artimus III lunar lander called Starship HLS reach the lunar surface, and oh what a celebration it will be at NASA!

# This is Not Your Father’s Universe!

When I was learning astronomy in the 60s and 70s, we were still debating whether Big Bang or Stady State were the most accurate models for our universe. We also wondered about how galaxies like our Milky Way formed, and whether black holes existed. The idea that planets beyond our solar system existed was pure science fiction and no astronomers spent any time trying to predict what they might look like. As someone who has reached the ripe old age of 70, I am amazed how much progress we have made, from the discovery of supermassive black holes and exoplanets, to dark matter and gravitational radiation. The pace of discovery continues to increase, and our theoretical ideas are now getting confirmed or thrown out at record pace. There are still some issues that remain deliciously mysterious. Here are my favorite Seven Mysteries of the Universe!

1-How to Build a Galaxy: In astronomy, we used to think that it would take the universe a long time to build galaxies like our Milky Way, Thanks to the new discoveries by the Webb Space Telescope, we now have a ring-side seat to how this happens, and boy is it a fast process!

The oldest galaxies discovered with the Hubble Space Telescope date back to between 400 and 500 million years after the Big Bang. A few weeks ago, Webb spotted a galaxy that seems to have formed only 300 million years after the Big Bang. Rather than the massive galaxies like the Milky Way, these young galaxies resemble the dwarf galaxies like the Large Magellanic Cloud, perhaps only 1/10 the mass of our galaxy and filled with enormus numbers of massive, luminous stars. The above image from Hubble is a nearby galaxy called M-33 that has a mass of about 50 billion suns. There were lots of these smaller galaxies being formed during the first 300 million years after the Big Bang.

It looks like the universe emerged from the Dark Ages and immediately started building galaxies. In time, these fragments collided and merged to become the more massive galaxies we see around us, so we are only just starting to see how galaxy-building happens. Our Milky Way was formed some 1 billion years after the Big Bang, so the galaxy fragments being spotted by Webb have another 700 million years to go to make bigger things. Back in 2012, Hubble had already discovered the earliest spiral galaxy seen by then; a galaxy called Q2343-BX442, camping out at 3 billion years after the Big Bang. In 2021, an even younger spiral galaxy was spotted, called BRI 1335-0417, seen as it was about 1.4 billon years after the Big Bang.

So we are now watching how galaxies are being formed almost right before our eyes! Previous ideas that I learned about as an undergraduate, in which galaxies are formed ‘top-down’ from large collections of matter that fragment into stars, now seem wrong or incomplete. The better idea is that smaller collections of matter form stars and then merge together to build larger systems – called the ‘bottom-up’ model. This process is very, very fast! Among the smallest of these ‘galaxies’ are things destined to become the globular clusters we see today.

2-Supermassive Black Holes: The most distant and youngest supermassive black hole was discovered in 2021. Called J0313-1806, its light left it to reach us when the universe was only 670 million years old. Its mass, however, is a gargantuan 1.6 BILLION times the mass of our sun. Even if the formation of this black hole started at the end of the Dark Ages ca 100 million years after the Big Bang, it would have to absorb matter at the rate of three suns every year on average. That explains its quasar energy, but still…it is unimaginable how these things can grow so fast! The only working idea is that they started from seed masses about 10,000 the mass of our sun and grew from there. But how were the seed masses formed? This remains a mystery today.

3-The Theory of everything: The next Big Thing that I have been following since the 1960s is the search for what some call the Theory of Everything. Exciting theoretical advancements were made in the 1940s and 1960s to create accurate mathematical models for the three nongravity forces, called the electromagnetic, weak and strong forces. Physicists call this the Standard Model, and every physicist learns its details as students in graduate school. By the early 1980s, string theory was able to add gravity to the mix and go beyond the Standard Model. It appeared that the pursuit of a unified theory had reached its apex. Fifty years later, this expectation has all but collapsed.

Experiments at the Large Hadron Collider continue to show how the universe does not like something called supersymmetry in our low-energy universe. Supersymmetry is a key ingredient to string theory because it lets you change one kind of particle (field) into another, which is a key ingredient to any unified theory. So the simplest versions of string theory rise or fall based on whether supersymmetry exists or not. For over a decade, physicists have tried to find places in the so-called Standard Model where supersymmetry should make its appearance, but it has been a complete no-show. Its not just that this failure is a problem for creating a more elegant theory of how forces works, but it also affects astronomy as well.

Personally, when string theory hit the stage in the 1980’s I, like many other astronomers and physicists, thought that we were on the verge of solving this challenge of unifying gravity with the other forces, but this has not been the reality. Even today, I see no promissing solutions to this vexing problem since apparently the data shows that simple string theory is apparently on a wrong theoretical track.

One cheerful note: For neutrinos, the path from theoretical prediction to experimental observation took 25 years. For the Higgs boson, it took 50 years. And for gravitational waves, it took a full 100 years. We may just have to be patient…for another 100 years!

4-Dark Matter: The biggest missing ingredient to the cosmos today is called dark matter. When astronomers ‘weigh’ the universe, they discover that 4.6% of its gravitating ‘stuff’ is in ordinary matter (atoms,. stars, gas, neutron stars etc), but a whopping 24% is in some other ‘stuff’ that only appears by its gravity. It is otherwise completely invisible. Putting this another way, it’s as though four out of every five stars that make up our Milky Way were completely invisible.

Because we deeply believe that dark matter must be tracable to a new kind of particle, and because the Standard Model gives us an accounting of all the kinds of elementary particles from which our universe is built, the dark matter particle has to be a part of the Standard Model…but it isn’t!!!! Only by extending the Standard Model to a bigger theory (like string theory) can we logically and mathematically add new kinds of particles to a New Standard Model- one of which would be the dark matter particle. String theory even gives us a perfect candidate called the neutralino! But the LHC experiments have told us for over a decade that there is nothing wrong with the Standard Model and no missing particles. Astronomers say that dark matter is real, but physicists can’t find it….anywhere. Well…maybe not ALL astronomers think it’s real. So the debate continues.

Personally, I had heard about ‘missing mass’ in the 1960s but we were all convinced we would find it in hot gas, dim red dwarf stars or even black holes. I NEVER thought that it would turn out to be something other than ordinary matter in an unusual form. Dark matter is so deeply confounding to me that I worry we will not discover its nature before I, myself, leave this world! Then again, there isnt a single generation of scientists that has had all its known puzzles neatly solved ‘just in time’. I’m just greedy!!!

5- Matter and Antimatter: During the Big Bang, there were equal amounts of matter and anti matter, but then for some reason all the antimatter dissappeared leaving us with only matter to form atoms, stars and galaxies. We don’t know why this happened, and the Standard Model is completely unhelpful in giving us any clues to explain this. But next to dark matter, this is one of the most outstanding mysteries of modern, 21st century cosmology. We have no clue how to account for this fact within the Standard Model, so again like Dark Matter, we see that at cosmological scales, the Standard Model is incomplete.

6- Origin of Time and Space: Understanding the nature of time and space, and trying to make peace with why they exist at all, is the bane of any physicists existence. I have written many blogs on this subject, and have tried to tackle it from many different angles, but in the end they are like jigsaw puzzels with too many missing pieces. Still, it is very exciting to explore where modern physics has taken us, and the many questions such thinking has opened up in surprising corners. My previous blog about ‘What is ‘Now’ is one such line of thinking. Many of the new ideas were not even imagined as little as 30 years ago, so that is a positive thing. We are still learning more about these two subjects and getting better at asking the right questions!

7-Consciousness: OK…You know I would get to this eventually, and here it is! Neuroscientists know of lots of medical conditions that can rob us of consciousness including medical anesthesia, but why we have this sense about ourselves that we are a ‘person’ and have volition is a massively hard problem. In fact, consciousness is called the ‘Hard Problem’ in neuroscience..heck…in any science!

The ‘Soft Problem’ is how our senses give us a coherant internal model of the world that we can use to navigate the outside world. We know how to solve the Soft Problem, just follow the neurons. We are well on our way to understanding it thanks to high-tech brain imaging scanners and cleverly-designed experiments. The Hard Problem is ‘hard’ because our point-of-view is within the thing we are trying to undertand. Some think that our own ‘wet ware’ is not up to the task of even giving us the intelligence to answer this qustion. It will not be the first time someone has told us about limitations, but usually these are technological ones, and not ones related to limits to what our own brains can provide as a tool.

So there you have it.

My impression is that only Mysteries #1 and #2 will make huge progress. The Theory of Everything is in experimental disarray. For antimatter, there has been no progress, but many ideas. They all involve going outside the Standard Model. Dark matter might be replaced by a modification of gravity at galactic and cosmological scales.

Beyond these ‘superficial’ mysteries, we are left with three deep mysteries. The origin of space, time and consciousness remain our 21st century gift to children of the 22nd century!

Check back here in a few weeks for the next blog!