two weeks ago as i filmed this derrick
over on veritasium proposed a physics
thought experiment and today i have made
that into a real experiment he proposed
a simple circuit where you have a
battery a switch and a light bulb except
the wires that connect these components
together are really really really long
and stretch far away in both directions
such that
if the power from the battery when you
flip the switch had to go all the way
down the wire and back you'd actually be
able to see a delay before the light
bulb turned on if you had to wait for
light speed effectively to make that
round trip as i watched that video i was
extremely unconvinced
i think that his answer that you don't
need to wait for the light speed delay
is technically correct if you use
his very carefully crafted definitions
like any current passing through the
light bulb constitutes the light bulb
turning on now the bulb won't receive
the entire voltage of the battery
immediately but i think that there's a
whole lot more to this question and your
intuition about the answer is probably
not quite as wrong as you've been led to
believe so i'm about to fire this
circuit up i have an oscilloscope that
can do very precise timings and i have
about a kilometer of copper wire
stretched out in both directions here
and we're going to see if there's a
light speed delay when you flick that
switch
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all right so
full disclosure i'm filming this over a
couple days and it got cold so if you
notice me wearing a coat and then
suddenly not wearing a coat and then
wearing a coat again that's why okay so
first of all i need to explain to you
how i've set up this circuit and
measurement apparatus because it's going
to look a little bit different than
derek's cartoon switch and light bulb
first difference no switch when you
actually close a mechanical switch
you've got two pieces of metal that are
attached to wires that sort of slam into
each other but when they slam into each
other they have a tendency to sort of
bounce a little bit which means that as
you flip a switch if you zoom in on that
in time it's actually going on
and it sort of bounces and it means that
your signal gets really really noisy
considering that i'm trying to see the
faintest of transients on a really long
line i wanted it to be as good and
smooth and even as possible so i'm using
an electronic switch i have a transistor
here that is going to start five volts
flowing in this wire
as soon as it receives a pulse
second change no light bulb so
i mean i'm using a resistor and to be
fair an incandescent light bulb is
basically just a resistor but more than
that by measuring the voltage across
this resistor with two oscilloscope
probes i can find out exactly how much
current is flowing through that resistor
resolved in time so i can flick this
switch start this thing recording
and
know exactly how long it takes for any
current to start flowing through that
bulb or
resistor light bulb whatever the last
critical elements here are of course the
wires themselves and i have stretched
out a kilometer of wire in two big 500
meter loops on both sides
i say a kilometer it's approximately a
kilometer i
actually the best measurements of the
length of the wire so far have come from
the oscilloscope not from the wheel that
i've been walking with if you look at
the light speed delay like how long it
takes light to move from here to here
directly through space it's you know
half a nanosecond i'm not going to be
able to see that
time delay from flipping this switch to
this thing turning on with this
oscilloscope uh because my switch itself
takes you know 20 or 30 nanoseconds to
turn on so it's just it happens too fast
to see
but
for signals to go all the way down that
500 meters of wire and come back and to
go all the way down that 500 meters of
wire and come back that takes a lot
longer and that should be on the order
of one and a half to two microseconds
which is an eternity to an oscilloscope
like this so we will be able to see
what's going on very clearly how much
current gets there right away how much
current we have to wait for how much
bouncing there is in the lines and how
long it takes for ohm's law to come into
effect like how long does it take for
steady state dc to take over so without
further ado
let's hook it up and try it out there's
so much noise
oh got it
this
is this is not how this should be done
oh look at that
so
the light bulb turns on a little bit and
then after one light speed delay the
light bulb turns on the rest of the way
let's confirm that okay so this cursor
right there when we see the
the light bulb turn on most of the way
is 1.6 microseconds 1.6 microseconds
times c
is
480 meters that's perfect we got 500
meters going out that way and we got 500
meters going out that way that is our
light speed delay
awesome okay so i am really excited
about this graph right here but i
realize that not everybody watching is
probably used to interpreting
oscilloscope traces so i'm gonna take
two minutes and i'm going to explain
what's going on here an oscilloscope
in a nutshell is really just an
exceptionally fast volt meter like a
regular multimeter voltmeter like this
you can put the probes across something
and you can see how like if a battery is
dead or something like that because you
can read how many volts there are
this is all this is doing except it's
plotting it over time all of these
graphs are a voltage or potential
plotted on the y-axis versus time on the
x-axis so if we follow this
yellow trace right here it rides along
and then at this
particular point in time the voltage
rises from zero all the way up to 5
volts this yellow trace is probing the
battery and switch together if you
imagine connecting a voltmeter across
the battery and switch with the switch
open these probes are actually attached
to the same end of the battery albeit
with a really long wire so the potential
difference between the probes is zero
however after we close this switch now
this probe is immediately connected to
this end of the battery and even
ignoring light speed stuff the wire is
resistive enough that we see the full
voltage of the battery across these
probes in this case 5 volts for the
interested this particular set of traces
was made with this complete hookup now
what's this white line that i was
specifically so excited about well
strictly speaking it's on an
oscilloscope which means that it is a
voltage plotted against time however
i've chosen this voltage in the circuit
very carefully this is actually the
voltage drop across the resistor that is
representing the light bulb at the far
end of the circuit and because i know
the resistance of that resistor it's one
kilo ohm and i know ohm's law v equals
ir or in this case i equals v over r i
can calculate the current flowing
through the light bulb as a function of
time and that's basically what this is
plotting now current is literally a
measure of how many electrons per second
are flowing through a particular
electrical component so in this case we
see that after about a microsecond
there's somewhere in the vicinity of a
fifth of a volt across this one kiloohm
resistor which equates to a current of
about 200 microamps which might not
sound like very much but it's somewhere
in the vicinity of
quadrillion electrons per second
traveling through that resistor now that
makes it sound like a lot but if we wait
another few microseconds until the
circuit reaches steady state we get a
significantly larger current 1.7
milliamps or 10 quadrillion electrons
per second so if you were watching the
video just to find out if derek was
wrong and you made it this far
here's the data you get a tiny little
bit of current
immediately
almost immediately probably not quite as
fast as he said
but
after you wait for the signal to go all
the way down the wire and all the way
back you get a much larger signal that
shows up and actually turns the light
bulb on in my mind if a light bulb is
capable of turning on with this much
current it's probably going to you know
burn out and explode with this much
current so if this is your situation you
can turn on a light bulb with that
little current you've done a terrible
job at designing your circuit but the
fact remains there is a tiny little bit
of current right there and it's flowing
and it's flowing almost immediately
which is weird so to help imagine this
bonus current let's take a look at the
circuit from the top down when you flip
the switch you start current flowing in
the wire and the electrons in the wire
start moving around in a loop that's
what electricity is but if we account
for the light speed delay you could
imagine that all of these electrons
don't start moving at the same time
there's a wave that travels through them
that gets each electron started on its
way and only when that wave reaches the
light bulb do the electrons and the
light bulbs start moving and turn the
light bulb on this extra current that we
see immediately then can't come from
this primary wave down the wire it
doesn't have time to get there it has to
be something else it's actually a second
wave that starts at the light bulb
almost immediately flowing a very small
amount of current through that light
bulb and then it travels down the wire
to meet the first wave but only once the
first wave makes it all the way back to
the light bulb does the bulb turn on all
the way so how does current flowing in
this wire start current flowing in this
parallel but effectively disconnected
wire i'd say that there are two
possibilities capacitance and induction
and because most transmission line
models ignore the cross inductance at
least for today i will too but to
understand how these wires act like a
capacitor we need to know a little more
about why electrons flow
yes when you have a wire like this
that's just a bare wire hanging out in
the air
the power that is being transmitted
through this wire is being transmitted
through the
electric field around the wire you can't
just have a battery that flows current
out into nothing and then somewhere else
you're drawing power out and a light
bulb turns on because of the magic of
the pointing field like wires are
important wires are the guides for
electrons and for our power i actually
really liked the chain in a tube example
that derrick used in his video
because you need to make
almost no changes to that to make it
extremely accurate so i have this set up
here i've covered a bunch of things with
paper so it's a little easier to see
these wires are basically invisible when
you stretch them out over a field which
makes it one hard to set up and two very
hard to film if you see this whole bunch
of stuff you should see battery and
switch and this you should just imagine
as light bulb and everywhere these
probes show up really accurate clock
other than that we just have these wires
that stretch out
two this way in a big loop and two that
way in a big loop so for a moment
entertain the idea that electrons are
actually little charged hard spheres i
know that that's not technically what
they are if you want to go into the full
wave function but
for a lot of cases you can gain a lot of
intuition by thinking about them as
actual physical particles so if we
imagine that this wire right now is full
of electrons say it's like one line of
electrons the trick to metals
is that in metals due to some really
cool solid state physics electrons are
actually able to move long distances and
when i say long distances i don't mean
like down a transmission line i mean
like millimeters because
most electrons in most solids even most
of the electrons in a metal are actually
restricted to moving within a few
angstroms you know every atomic nuclei
is only spaced out by a couple
nanometers and if an electron is never
allowed to leave its own atomic nucleus
then you know it's it's hardly going to
move at all so to move millimeters is
enormous and that's what we're
leveraging when we use wires to transmit
electric power now when i connect this
circuit up again imagine that this is
just battery and switch when i flip that
switch the battery starts pumping
electrons from one side to the other
that's all a battery does is basically
remove an electron from this wire and
set it at the end of this wire then
we've got too many electrons over here
this electron that we just placed the
battery pumped into this wire is going
to repel
the next electron in the chain the next
negatively charged thing and then that
electron is going to be it's going to
move a little bit and it's going to
repel the next electron which is going
to move a little bit
and
all of them are going to start moving at
once you know once that that ripple that
wave of motion reaches the end of the
line over here we're actually doing the
opposite we're pulling electrons out of
this wire so that we can put them over
here which means that we don't have
enough electrons over here so it
actually ends up taking on a positive
charge because there aren't enough
electrons to shield out the positive
static electric fields from all of the
atomic nuclei and that means that nearby
electrons are actually attracted to this
region
another way to think about it is that
this electron used to be repelled
equally by both of these electrons on
both sides of it and when we take this
one away it's only being pushed from
this side so it ends up moving in
towards the battery and both of those
waves of motion travel down the line at
approximately the speed of light because
the interaction between electrons is
actually modulated by photons by light
like how does this electron right here
know that this electron is too close to
it so it wants to start moving that way
it knows because of the electromagnetic
field and the electromagnetic field is
modulated by photons and information
about the electromagnetic field travels
at the speed of light so what does this
say about the chain in a tube model well
i
i would say that the chain in the tube
model can be made extremely accurate if
you say that the the chain links are
actually bigger than the tube the tube
still constrains the motion of the chain
links like you can't have an electron
leave the wire
but the electron the
sphere of influence of the electron is
actually much larger than the wire so
this electron need not only interact
with the one right next to it you can
draw
if you if you drew all these electrons
as dots you could draw springs between
all of them and considering that they're
only allowed to move in a line here you
know the farther away springs are weaker
and and so on but they all really do
still interact with each other
which begs the question
can this electron right here interact
with an electron in this wire
and the answer to that is yes and that
is
the absolute core of this thought
experiment now real experiment and why
we just saw the effects that we did
if you think about this top down view
again the spot where this wavefront
lives actually has too many electrons in
it electrons are moving towards this
point from one side but they aren't
moving away from this point on the other
side so we must be accumulating a little
bit of negative charge right here and
that little pocket of negative charge is
going to have a net electric field
likewise on the other side we have a
region that's depleted of electron
meaning that this little spot is
actually positively charged and it emits
its own net static electric field now
imagine an electron sitting on this wire
it's free to move and it's
simultaneously repelled from this pocket
of negative charge and attracted to this
pocket of positive charge so it
accelerates this way and passes through
the light bulb it's not a lot of current
but it's almost immediate because as
soon as these waves leave the battery we
get this charge imbalance that reaches
across the air gap with electric fields
and pushes electrons around without the
far ends of the wire even knowing
okay so i just ran all the way down this
is the end of the line
this is the wire that goes to the light
bulb
this is the wire that goes to the switch
two empty wires down here without
changing any of the triggering or
anything i'm gonna fire this again
and i would expect that we still see
this blip but then it drops back down to
zero
now
yep there we go
yeah it sort of fluctuates around and
then it drops back down and the current
through the uh near side also drops down
once it charges up the capacitor that is
the two wires it stops that's really
cool so for the first 1.6 microseconds
of this circuit being on it is bound by
the laws of relativity to look exactly
like the trace from when the wires were
fully connected we have to wait 1.6
microseconds for the oscilloscope and
the resistors and all the bits that
we're measuring to be able to learn that
the end of the wire doesn't exist and
then they start behaving differently but
there's a bunch of stuff that happens
after that light speed delay that is
really interesting so this green trace
right here is showing the current
through one of the resistors that's
right next to the battery and switch and
that says that there's some current
flowing at the beginning but then that
current actually sort of dies off after
a while so here we have the battery
tirelessly pumping electrons from one
side to the other except eventually all
those electrons pile up because we've
cut the end of the wire they have
nowhere to go and the battery stops
being able to pump electrons the most
interesting thing about this plot is
actually the fact that the white trace
reverses briefly that means that we push
a whole bunch of current through the
light bulb but then when it runs into
the ends of the wires that are cut that
current actually sort of sloshes back
and we get electrons that are bouncing
back and forth on the line like a wave
through a slinky i don't want to get
into how electronic resonators work
because i don't know enough to do that
topic remote justice but i do know that
you need both capacitance the ability to
basically store charge and resist
changes in potential and inductance the
ability to give charges inertia and
resist changes in current and the
combination of those two things can
actually result in a circuit that
bounces back and forth and back and
forth and that's what we're seeing right
here but yeah without um calling up
einstein and saying that we found that
information can go faster than light we
are always going to have the first 1.6
microseconds look exactly the same i
think that's really cool
okay so if you disconnect both ends of
the wire you still get that transient
and then it sort of bounces around and
eventually goes away to zero but it
never actually turns on the light bulb
all the way because you can't flow
current through a wire that's
disconnected
now i want to see what happens when the
two loops of wire are different lengths
okay i'm sorry i really honestly hate to
do this i
also just because i want to be done
editing but i've been editing and
editing and it looks like it's going to
be some 45 minute monstrosity so i
decided to break the rest of the
experiment variants off into their own
part 2 video i had
so much fun with this project and i
actually learned a lot by
fiddling with the geometry of the wires
and trying out different things and
different variations on the experiment i
got some results that i really
wasn't expecting like at all and i want
to be able to take the time to properly
explain all of those weird results in a
second video as one of the now many
replies to derek's thought experiment i
hope that this video has been more
enlightening than confusing there are
a lot of things going on here it is a
deceptively complex problem and there
are a bunch of pieces of physics that i
think are important that didn't even
make it into this video so i hope that
the capacitive wires hypothesis that i
have proposed here makes sense and i
hope that you'll stick around and join
me for the part 2 video i will plan to
see you there
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you