A while back, we went to a fascinating lecture at the University of Alberta, where Professor Miguel Alcubierre of The Nuclear Sciences Institute of the Autonomous University of Mexico discussed his paper on faster than light travel (FTL). His theorized effect works via a bubble of highly warped space in which the traveler might move at arbitrarily high speeds relative to the Earth, yet never violates Einstein's Special Relativity postulate against matter reaching or exceeding the speed of light. I blogged about this under the heading “Faster than Light Travel via the Alcubierre Warp Drive”. This follow-up blog presents another way of looking at the phenomenon, namely via the manipulation of extra dimensions of space, as are theorized in various quantum gravity theories, and is based on a paper called “Supersymmetry Breaking Casimir Warp Drive” (Obousy and Cleaver, 2007).
The Speed of Light Barrier
First, here is a review of why we need some sort of fancy drive to exceed the speed of light. As noted in the previous blog, the speed of light cannot be exceeded, according to Einstein's Theory of Special Relativity (SR). Essentially, this “universal speed limit” is a postulate of the theory, but one that was necessary to make sense of certain developments in physics:
· Experimental findings such as the Michelson-Morley experiments, that showed light's speed seemed constant in all directions, as the Earth moved in its orbit, which should not have been the case under standard Galilean relativity.
· Theoretical developments, such as c (the speed of light) being derivable from Maxwell's equations of electromagnetism, implying that it was a fixed universal constant.
· The realization that allowing matter to exceed the speed of light would be equivalent to allowing time travel, in some sense, an unsettling and paradoxical possibility.
For these, and a few other reasons, Einstein decided that c must be a “universal speed limit”. That caused us to re-think a lot of things about time and space, particularly time dilation (moving clocks read slow), length contraction (moving rulers read short) and simultaneity (different observers don't agree whether events are simultaneous if they are moving at some velocity relative to each other). These odd effects have since been observed in nature (e.g. half-lives of particles moving near the speed of light that have been produced in particle accelerators are longer than those measured in laboratories that have not been accelerated).
Getting Around the Speed of Light Barrier, Part 2
The previous blog described some theoretical
methods to get around the speed of light barrier, notably the “wormhole” idea
and the “warp drive” idea, as proposed by Dr. Alcubierre. The focus of the Obousy and Cleaver paper is
on how “the manipulation of the radius of one (or more) of the extra dimensions
found in quantum gravity theories, creates a local asymmetry in the
cosmological constant which could be used to propel a space vehicle.”
The two big theories in physics are General
Relativity and Quantum Field Theory. We
know from the equations of General Relativity, that adjustments to the
Cosmological Constant can produce various warpings of the overall spacetime of
the universe, such as the accelerating expansion of the universe. Perhaps a small scale manipulation of that constant
could produce a small scale warping of spacetime that we could use for space travel.
Quantum Field Theory predicts a vacuum
energy exists, a sort of spacetime foam at the limits of the Planck scale – the
so-called zero-point energy (and experiments with the Casimir Effect have
verified its existence). Perhaps this is
what gives rise to the negative energy behind the cosmological constant, that
seems to be causing the acceleration of the universe’s expansion? Unfortunately,
a calculation that aggregates up the vacuum energy of the observable universe
results in a Cosmological Constant that is off by a factor of 10 followed by
119 zeroes. That’s rather a large error.
This embarrassing discrepancy between the two big theories of physics has led to efforts to unify them, and thus derive consistent results and predictions. This has led to a number of theories, such as String Theory or M Theory. String Theory says that the fundamental “objects” of existence are actually vibrating “strings” of energy, with different modes of vibration producing the various particles of the standard model of nuclear physics. You shouldn’t take the notion of a string too literally – these are more mathematical constructs than physical objects, as we relate to the concept.
M-Theory steps this up a bit, concluding
that our 3-dimensional universe is actually a “brane” in a higher dimensional
“bulk”. I believe “brane” is a play on
the word “membrane” – our universe exists inside this higher dimension the way
that a membrane (2-d) exists within our 3-d universe.
These brane world scenarios allow one to
decrease the predicted vacuum energy to levels much more in line with those
that we see. Essentially, the higher dimensional fields cancel out most of the
vacuum energy in our 3-d brane, thus allowing the calculation of the
cosmological constant to be much closer to that actually observed. Something
called supersymmetry plays a role in this – it is broken in our universe, but
not in the higher order universe.
As noted, these theories posit many more
dimensions than those that we observe.
They are thought to be too small (compactified is the term often used)
to see, however, with current technology.
Out of the Brane, and Into the Bulk
The principle of using this theory to produce locally warped spacetime, is that the “size” of these extra dimensions can be manipulated locally, thus affecting the local vacuum energy. This then affects the “local cosmological constant”, thus warping the local spacetime. A spacecraft can then take advantage of the warping, to break the universal speed limit, the speed of light. Presumably this would take the ship “out of the brane and into the bulk”. That’s my phrase, not theirs. I think it would make a cool verse in Neil Young’s “Rust Never Sleeps”, which would help in fund-raising for further research. :)
The paper posits one extra dimension, and runs through some equations to show how the vacuum energy can be related to the size of this dimension. Actual string theories posit more than one extra dimension (sometimes 10, sometimes 26, depending on the theory), but I believe that the paper sticks to one, to keep the math simpler. There is a fair bit of mathematical physics in the paper to back up these assertions, but frankly it exceeds my B.Sc. in physics, so I’ll have to take their word for it. Besides, it is peer reviewed, so it should be accurate. More adept readers, of course, can check the equations out for themselves.
The tricky part, of course, is how do you manipulate the radius of a hidden dimension? Basically, the paper gives this problem to “a more advanced civilization”, though it is clear that it would probably require injecting a lot of energy into the nearby spacetime, where the hidden dimension is to be de-compactified. They conclude by encouraging further theoretical research in this area, to determine the actual energies likely to be involved.
2. Herzburg Memorial lecture, June 15 2015.
3. The Warp drive: hyper-fast travel within general relativity (M.
Alcubierre, Class. Quantum Grav. 11
4. Supersymmetry Breaking Casimir Warp Drive, 2007 Space Technology and
Applications International Fourm.
5. Warp Field Mechanics 101, Dr. Harold “Sonny” White, NASA Johnson
Here is an explanation of FTL travel given
in Dodecahedron Books SF novel: The Witches’ Stones: Rescue from the Planet
of the Amartos:
Inside the ship, Steph and the servant settled Sarah on the
couch. Dian stood nearby, curiously
looking around the ship.
“Your ship - it is circular in shape. Is that because the circle is the perfect
shape, a reflection of the divine?”
Coryn realized that this must be the first time the young
woman had been on board a spacecraft. He
was surprised by her interest – Kordean witches usually projected a studied
disdain for Terran technology. He
suppressed a fleeting desire to tour her about the ship, explaining the
technological wonders of Terran civilization.
Dian’s eyes told him that he would have had a receptive audience for
such a demonstration.
Coryn smiled. “I don’t
know much about the divine, or about spaceship engineering for that
matter. Sarah was - ” he corrected
himself quickly “ - is the expert on that.
But I think the shape’s got to do with the particle accelerators that
are at the heart of the ship. They are
circular in cross-section.”
“What do they do?”
“As far as I know they generate some sort of exotic fields
that warp space and propel the ship. If
the ship’s near an omega coordinate, they can be used to pull the ship into
higher dimensional space – we call that omega-space. That shrinks distance, so that ships can
travel the galaxy without breaking the laws of special relativity.”
“How do they shrink distance?”
“Terrans only partially understand it – the machinery was
invented by a different species and gifted to us. But we think we understand the mathematical
theory behind it – well, sort of, anyway. I have had it explained as dimensions
being folded up inside of each other. If
you go from one dimension to two dimensions, you shrink distance by the square
root of two. If you go to three
dimensions, it’s the square root of three.
If you go up to a hundred dimensions, you shrink distance by a factor of
ten. Some people think omega-space has infinite
dimensionality, so you can shrink distance all you like. That doesn’t seem
right to me, too much fooling around with infinity, but then I’m not a
Dian smiled. “Your
explanation sounds as mystical as anything a Kordean Witch could come up with.”
Coryn smiled and shrugged.
“Maybe Terrans have more in common with Kordeans than we usually
think. At least the mathematicians do.”
That last bit is a stretch, but it reads easier than trying to make sense of string theory, especially if one is attempting to explain it to a member of an alien species who spurns human technology in favor of their own psychic abilities. By the way, Helena Puumala came up with “Omega Space” long before she ever heard of string theory. :)