http://www.pbs.org/wgbh/nova/zero/hot.html
Absolute Hot by Peter Tyson
Is there an opposite to absolute zero?
Seems like an innocent enough question, right? Absolute zero is 0 on
the Kelvin scale, or about minus 460 F. You can't get colder than
that; it would be like trying to go south from the South Pole. Is
there a corresponding maximum possible temperature?
Well, the answer, depending on which theoretical physicist you ask, is
yes, no, or maybe. Huh? you ask. Yeah, that's how I felt. And the
question doesn't just mess with the minds of physics dummies like me.
Several physicists begged off of trying to answer it, referring me to
colleagues. Even ones who did talk about it said things like "It's a
little bit out of my comfort zone" and "I think I'd like to ruminate
over it." After I posed it to one cosmologist, there was dead silence
on the other end of the line for long enough that I wondered if we had
a dropped call.
I had touched a nerve, because, unbeknownst to me, the
highest-temperature question gets to the heart of current inquiries
and proposed theories in cosmology and theoretical physics. Indeed,
scientists who work in these fields are zealously trying to answer
that question. Why? Because, in some sense, nothing less than the
future course of physics rests on the answer.
Contender #1—1032 K
Certain cosmological models, including the one that has held sway for
decades, the Standard Model, posit a theoretical highest temperature.
It's called the Planck temperature, after the German physicist Max
Planck, and it equals about 100 million million million million
million degrees, or 1032 Kelvin. "It's ridiculous is what it is," said
Columbia physicist Arlin Crotts when I asked him if he could please
put that number in perspective for me. "It's a billion billion times
the largest temperature that we have to think about" (in gamma-ray
bursts and quasars, for instance). Oh, that helped.
Truthfully, when contemplating the Planck temperature, you can forget
perspective. All the usual terms for very hot—scorching, broiling,
hellish, insert your favorite here—prove ludicrously inadequate. In
short, saying 1032 K is hot is like saying the universe occupies some
space. (For a game attempt at perspective, see A Sense of Scale.)
Whatever the highest temperature is, it might be essentially
equivalent to the coldest temperature.
In conventional physics—that is, the kind that relies on Einstein's
theory of general relativity to describe the very large and quantum
mechanics to describe the very small—the Planck temperature was
reached 10-43 seconds after the Big Bang got under way. At that
instant, known as one Planck time, the entire universe is thought to
have been the Planck length, or 10-35 meters. (In physics, Max Planck
is the king of the eponymous.) An awfully high temperature in an
awfully small space in an awfully short time after … well, after what?
That's arguably an even bigger question—how did the universe
begin?—and we won't go there.
A brick wall
The Planck temperature is the highest temperature in conventional
physics because conventional physics breaks down at that temperature.
Above 1032 K—that is, earlier than one Planck time—calculations show
that strange things, unknown things, begin to happen to phenomena we
hold near and dear, like space and time. Theory predicts that particle
energies become so large that the gravitational forces between them
become as strong as any other forces. That is, gravity and the other
three fundamental forces of the universe—electromagnetism and the
strong and weak nuclear forces—become a single unified force. Knowing
how that happens, the so-called "theory of everything," is the holy
grail of theoretical physics today.
"We do not know enough about the quantum nature of gravitation even to
speculate intelligently about the history of the universe before this
time," writes Nobel laureate Steven Weinberg about this
up-against-a-brick-wall instant in his book The First Three Minutes.
"Thus, whatever other veils may have been lifted, there is one veil,
at a temperature of 1032 K, that still obscures our view of the
earliest times." Until someone comes up with a widely accepted quantum
theory of gravity, the Planck temperature, for conventional physicists
like Steven Weinberg, will remain the highest temperature.
Contender #2—1030 K
String theorists, those physicists who believe the universe at its
most fundamental consists not of particles but of tiny, vibrating
strings, have their own take on temperature. I spoke to Robert
Brandenberger, a theoretical cosmologist at McGill University in
Montreal. Along with Harvard string theorist Cumrun Vafa,
Brandenberger has proposed a model of the early universe that's quite
different from that of traditional Big Bang models. (I should note
that there are many models out there; I'm touching on only a few
here.)
Called string gas cosmology, this model posits a maximum temperature
called the Hagedorn temperature. (It's named after the late German
physicist Rolf Hagedorn.) "This is the maximal temperature which
string theory predicts," Brandenberger told me. While string theorists
don't give a specific number for the Hagedorn temperature,
Brandenberger has reasons to think it's about one percent of its
theoretical cousin, the Planck. That makes it about 1030 K, or two
orders of magnitude below the Planck.
Contender #3—1017 K
I learned of yet another highest possible temperature from
Brandenberger's former graduate student, Stephon Alexander. Now an
assistant professor of physics at Penn State, Alexander is one of many
physicists who are eagerly awaiting the day that officials at CERN on
the Swiss-French border switch on the Large Hadron Collider, the
world's largest particle accelerator.
One reason why they're excited has to do temperature. As Alexander
told me, "It may be that the [highest possible] temperature is—as I
believe—the temperature or the energy right around the energy that the
LHC will be probing." The LHC will operate at 14 trillion electron
volts, or terra electron volts, designated TeV. Fourteen TeV equals
1017 K, thus 15 orders of magnitude below the Planck.
Why could the LHC help determine this? As Brandenberger explained to
me, string theory predicts that space-time has more than four
dimensions, either 10 or 11. "Now, the other dimensions, which are
hidden to us, could either be very, very tiny—they could be strings or
Planck scale—or else they could be TeV scale." And if these extra
dimensions prove to be TeV scale, he says, then the topmost
temperature will be TeV scale too.
If there is a hottest temperature, whatever it is, how about something
even hotter? No problem!
I asked Alexander what it would mean for physics if the Planck
temperature turned out to be TeV scale. "Oh my God, this would be one
of the biggest breakthroughs of our species—you know, Einstein stuff,"
he said. "It'd be as big as the discovery of relativity and quantum
mechanics itself." Brandenberger, for his part, thinks it's a "very,
very long shot" that temperature's upper terminus is TeV scale.
Regardless of who's right on this score—if, in fact, either is—it will
be nail-bitingly suspenseful to see what arises from the LHC, which is
slated to begin operation in 2008. Says Alexander: "I've got my stock
invested."
Contender #4—0 K
As if at least three different possible opposites to absolute zero
weren't pause-giving enough, what Alexander told me next really set my
head spinning. Whatever the highest temperature is, he said, it might,
just might be essentially equivalent to the coldest temperature. "In
other words, zero temperature is the same, in a sense, as the Planck
temperature."
Come again?
Alexander described two potential ways the universe began. Either it
was at the Planck temperature and then inflated and cooled to create
what we see today. Or it started off at zero temperature and speeded
up as it expanded. "So one of two situations could have happened," he
said, "and it would be interesting if, indeed, both situations are
really the same underlying phenomenon."
That is, could the physics of the coldest possible temperature be
equivalent to the physics of the hottest possible temperature?
Considering that beyond both limits—below one and above the
other—space and time start to do those strange, unknown things,
Alexander believes it's "a logical conclusion, a logical possibility.
Why not?"
Beyond the beyond
Why not, indeed? After chatting with Alexander and others in his
rarefied field, I was up for anything. How about something
theoretically hotter than the Planck? Sure! I asked Jim Gates of the
University of Maryland. "All we know is that above the Planck
temperature, the rules change, but … we don't know what the rules
change to," he said. "If someone figures out such consistent rules,
then yes, it's conceivable that there will be hotter temperatures."
How about a boundlessly high temperature? Great! After all, classical
general relativity calls for an infinitely high temperature at the
very start of the universe, as well as in the centermost point, the
singularity, of black holes.
Or, if there is a hottest temperature, whatever it is, how about
something even hotter? No problem! In theory, a hotter temperature
than a hottest temperature can exist—it's a negative temperature. As
Charles Kittel and Herbert Kroemer write in their classic text Thermal
Physics, "The temperature scale from cold to hot runs +0 K, …, +300 K,
…, +? K, -? K, …, -300 K, …, -0 K."
Almost giddy now, I again turned to Arlin Crotts for help. If,
theoretically speaking, you go above the Planck to an infinitely high
temperature, the next step beyond infinity is minus infinity? "Well,
you're not talking about thermal distribution anymore," he said, "but
if you keep pushing it, you basically go through infinity over to
minus infinity and then come around on the other side." Wow! "What you
really should be paying attention to," he added, "is 1 over T [where T
is temperature], because one over infinity and one over minus infinity
are basically the same thing." Totally!
Contender #5—Who the heck knows?
As you might have guessed, by this point the physicists had lost me—if
not at the very beginning. I was way out of my comfort zone.
In the end, perhaps the best answer to my question came from Lee
Smolin of the Perimeter Institute for Theoretical Physics in Waterloo,
Ontario. "It may be that the most you're going to be able to say is
that there's a possibility that there's a highest possible
temperature," he told me. "But let me mull it over…."
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