Oh, hello there. I'm the Doctor... well a
doctor... of physics, and this is the TARDIS:
Time And Relative Dimension In Space.
Come in, yes it is bigger on the inside.
It's Time Lords technology which allows
the Doctor and his companions to
travel... well why don't we listen to the
man himself. "All of time and space,
everything that ever happened or ever
will. Where do you want to start?" Now one
thing you should know about the TARDIS
is it can be a bit rubbish, that or the
Doctor doesn't always know how to use it
properly. He frequently turns up at the
wrong place or time again and again and
again. "Doctor" "Yes, what is it? What you want?"
"Don't steal that one, steal this one. The
navigation system's knackered but you'll have
much more fun." Basically it happens a
lot! But even with all these mishaps the
TARDIS, if real, would be by far the
most precise machine ever. First let's be
clear by what we actually mean by
precision, because it's not the same as
accuracy. Accuracy is also known as a
trueness, bias or systematic error
concerns how far away from the correct
value of quantity is. How good your aim
is essentially. Precision on the other
hand is the statistical error, the spread
of possible values and outcomes that you
might actually get. What we care about
here is the relative precision, which
compares the smallest thing you can
measure on an instrument with the
largest thing it can cope with, because
whilst you might measure your waist with
a tape measure you certainly wouldn't
measure the length of the equator with
one. Now a metre ruler can measure down to
just one millimeter and of course it's a
metre long which is 1,000 millimetres so
it's relative precision is 1 in 1,000.
From here on I'm only going to be
calculating to the nearest order of
magnitude, the nearest power of 10,
because
as you'll see we're going to cover
some pretty big numbers. Before tackling
the TARDIS I thought we should first
have a look at our very best machines
for measuring space and time, let's actually
start with time. Currently the second is
defined as nine billion, 192 million, 631 thousand,
770 complete cycles of microwave
radiation produced by the transition
between two hyperfine levels of the
ground state of caesium 133 atoms at
Absolute Zero. Phew, what a mouthful! To measure a
second you basically need to count up to
some nine billion, so you'd think the
highest precision we could ever achieve
would be about a hundred trillionths of a
second, but no you're wrong. By using Ytterbium
atoms German physicists were
able to build our best clock to date. But
why is it better than a caesium clock?
Well the atomic transition it uses isn't
in the microwave part of the spectrum
but some 10,000 times higher in
frequency in the visible. That higher
frequency means a shorter time period
for each complete cycle giving this
clock a relative uncertainty of a bit
less than one in ten to the 18, that's one
with 18 zeros after it or a billion
billion. But it turns out we're even
better at measuring space. You probably
heard about our first direct detection
of gravitational waves by the advanced
LIGO instrument. It measures the
absolutely tiny changes in distances
between points in space that are caused
by gravitational waves, ripples in space
and time sent out by the most extreme events
in the universe like two black holes
merging. It does this using an
interferometer, a sort of ruler based on
interfering two beams of laser light.
Now those beams are some eight kilometres
long, that's four kilometres one way
another four kilometres back, but the
instrument can pick up changes along
that distance sometime ten
thousand times smaller than a proton. And
depending on the frequency of the
gravitational waves, advanced LIGO can
get up to sensitivities of one in 10 to
the 23. A similarly impressive machine is
Spektr-R, a radio space telescope. Now
by combining its observations with 15
different ground-based radio telescopes
our highest resolution astronomical
image to date has been produced. The
combination of all that data gives you
an image equivalent to having a single
telescope eight times the diameter of
the Earth, or to put that in terms of
numbers an angular resolution of a few
millionths of an arcsecond, where there are
3,600 arcseconds in just a single
degree. So in terms of the fraction of
the entire sky that equates to again one
in 10 to the 23. It seems like we're
living in the age of the 10 to the 23. So
now that we know how good we are, let's
have a look at how good time lords are
with the TARDIS. Remember the TARDIS can
travel anywhere in all of time and space,
so what is its relative precision
bearing in mind it often doesn't turn
up when and where it's expected? Let's
tackle space first, so how big is the
entire universe? That's not an easy
question to answer. The observable
universe, the limit to how far away
we can see from here on Earth or indeed
how far away any vantage point in
the universe could see, is currently ten to the
27 metres in diameter. This limit exists
because the speed of light is finite and
the universe had a beginning, so the
earliest light in the universe, the
cosmic microwave background, is only now
just reaching us here on earth from that
distance in space when also factoring in
the expansion of the universe. Yeah it's a bit
mind-bending at times.
So let's say the doctor limits his
travels for the current observable
universe, given his tendency to hang
around in the anthropocene, or the
era of humans. The Earth has a radius of just
over 6,000 kilometres so taking the
ratio of that to the ratio of the
observable universe and then cubing it
because we've got three spatial
dimensions to move around in, simply
landing on the planet Earth equates to
one in ten to the seventy relative
precision. Now while we don't know
exactly how big the universe extends
beyond the observable, we can place some
limits on it. The curvature of the
universe seems to be consistent with
zero, completely flat. This could mean
that space is actually infinite but
because of the sensitivity of our
measurements so far, the universe could
have some curvature so long as it's just
incredibly small. Assuming that the universe
is a four dimensional hyper sphere where
we live on its surface, the smallest its
radius of curvature can be given our
measurements is around 10 to the 28
metres. So in that case the TARDIS
would be at least as good as one part in
10 to the 74. But it is time where the
TARDIS really comes into its own.
Currently the universe is some 13.8
billion years old, but in the grand scheme
of things its pretty much still a newborn.
Eventually all the stars, planets and
galaxies will die; all protons and
neutrons will decay; and once the
universe is some ten to the 100 years
old even all of the supermassive black
holes will have evaporated via Hawking
radiation and all that will be left is a
dilute gas of photons and neutrinos at
some non zero temperature. From that
point onwards nothing more can happen, it
is the heat death of the universe. But if
we factor in random quantum fluctuations
or quantum tunneling,
the end of the universe could be
postponed to something like 10 to the 10
to the 10 to the 56 years in the future.
That is a stupendously large number! Now
given that when the TARDIS turns up at
the wrong time it's usually only a few
years or decades off at most, that means
we're talking about a machine that's
good to one part in at least 10 to the
100 and maybe as much as 10 to the 10 to the 56. I can
be almost certain we will never see
anything as precise as that within the
lifetime of the human race. So don't diss
the TARDIS when it gets things slightly
wrong, because in the grand scope of all
of time and space it's doing better than
well you can possibly imagine.
Thanks so much for watching all of this
Doctor Who video. For more mind-bending
physics subscribe to my channel and I'd
love to see your comments and likes down
there. See you next time.
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