October 15, 2020 • 43 mins
Daniel and Jorge explore whether energy is actually a fundamental conserved quantity.
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Speaker 1 (00:08):
Hey, Daniel, I noticed something about physicists. I'm afraid to
hear this. I feel like all of you like to
blow things up. We do. Actually, that's what makes us
so much fun at parties. I guess. I mean you'd
like to blow up ideas. You know, you like to
think things that people think are true and then prove
that they're actually false. That's true. Actually you mean like
the Earth being the center of the universe. Yeah, I
(00:30):
like that. I like that idea, but it turns out
it's false. Or you know that people thought that the
world was nice and smooth, but actually it's quantized into
little pixels called quantum physics. Al Right, So what do
you think that means about physicists. I think it probably
means that you like to disagree with the stabich ideas.
You're basically just contrarians. No, we're not. See do you
know fun at parties? Hi am or handmade cartoonists and
(01:07):
the creator of PhD Comics. Hi. I'm Daniel. I'm a
particle physicist, and I'm very positive about new ideas. Welcome
to our podcast Daniel and Jorge Explain the Universe, a
production of Our Heart Radio in which we consider all
the crazy new ideas out there and all the old ideas.
Which ones are real, which ones are made up, which
ones are we still clueless about. We take you on
(01:27):
a tour of all of them and explain them to you. Yeah,
we like to explore the universe and talk about all
of the things that are out there and this beautiful
cosmos of ours, all the things that are true, and
all the things that might be true. And part of
the journey of physics and science in general is understanding
the universe and questioning the things we thought were true,
(01:48):
getting a deeper, more fundamental view of the way things
actually work, which sometimes is really in contrast with the
way we thought things work. Because there are a lot
of ideas out there, right, Daniel. I mean they're ideas
about how the world works, about why things are the
way they are, and how people think that it all
comes together. Yeah, And sometimes the first idea you have
(02:09):
seems reasonable and sticks around for a long time, and
then you notice small little problems with it, and when
you pull on that thread, you reveal something really fascinating
about the whole universe. Like people used to think, hey, there,
Earth is flat. It certainly looks flat from here. But
then it's sort of a mind exploding discovery to realize, Wow,
we're actually living on the surface of a huge sphere. Yeah.
(02:32):
So there are a lot of ideas out there, and
I feel like you physicists like to reserve the right
to change your mind. That's an important part of science, right,
challenging the orthodoxy. It's one of the best things about
science that sometimes we look at the very foundations of
the ideas and we say, wait a second, is that
really true? How do we actually know that? We've been
thinking that for a long time, but is it possible
(02:56):
that we were wrong. I think it's one of the
deepest virtues of science. Yeah. And if like that's maybe
your favorite part of science is proving your appears wrong
on a personal level, yes, And for me it's actually
the reason I got into science, because I'm really excited
about those moments of intellectual revolution. I feel like, when
(03:16):
you discover that the world is really different from the
way we thought it was, we've pulled the wolf from
our eyes. We've like peeled back a layer of reality.
We've discovered some truth that was hidden to us. And
what's more exciting in science than to have a moment
of discovery like that a deep revelation, you know, not
like slowly iterately building up increments of knowledge until you
(03:37):
get there, like almost like a moment of revelation where
you understand the universe differently somehow and you can never
go back to seeing it the old way. Some people
go for the Eureka moment. You like to go for
the moment. That's what I'm in for. I'm in it
for the scientific revolutions, for the Hans. You're in for
the Hans I am. And there have been lots of
(03:58):
moments in history where people have made to discoveries like this.
They've pulled on one little string and then they've unraveled
that very foundations of science, and so it's exciting to
think that there might be more of those ahead of us.
So it's exciting when a bunch of smart people's go,
never mind, I thought there was flat, but actually it's
a giant ball. Yeah, because it changes sometimes your whole
(04:18):
relationship with the universe, you know, thinking that we live
at the center of the universe everything revolves around us,
to thinking we're just a tiny little speck of dust
in an insignificant corner of the universe that really changes
the way you feel about the universe and life itself
and how you should live it. So, hey, this stuff
is actually irrelevant for how people feel about themselves and
(04:39):
their lives. Yeah. So science is all about challenging ideas,
and so today on the program will be challenging a
very core and fundamental idea and physics. I feel like
this is a very important idea that a lot of
people have kind of internalized about the universe, but that
actually might not be so true. That's right. This is
something pretty basic that if you ask folks on the street,
(05:00):
it would be pretty confident was true. But it turns
out we've learned a lot about the nature of the
universe and it might actually not be quite so fundamental.
So on the program will be asking the question is
energy actually conserved? Now, Daniel, this sort of blew my mind.
(05:22):
How can we even ask this question? What do you mean?
Is energy always actually conserved? Yeah? That's why it's such
a wonderful question because it makes you think, like, well,
why would it be conserved? How do we actually know
it's conserved? What would it be like to live in
a universe where it's not conserved? That solve all of
our energy problems. I feel like you just told me
the world is not actually a ball. It's like a
(05:43):
cube or something. We live on a donut and it's
filled with energy. It's filled with sugar, energy and sprinkles.
That's right. Just eat the glaze, man, eat the glaze.
Then then my energy will not be conserved, just an
increase or be turned into mass. Probably. I know. It's
a bit mind blowing, and that's why I was especially
(06:04):
eager to hear what folks on the internet had to
say about this question. Yes, so it's usual Daniel went
out there into the wilds of the web and ask
people the question is energy always conserved? So thank you
to these folks in advance who participated. And if you
would like to answer tough physics questions with no preparation
and have your answers broadcast thousands of people, please write
(06:26):
to us two questions at Daniel and Jorge dot com.
Think about it for a second. If someone ask you
if energy is actually always conserved, what would you answer.
Here's what people had to say. I always thought that
was one of the fundamental laws, that energy and matter
can't be created or destroyed, But the fact that you're
asking me this question makes me think I'm wrong. Yes,
(06:48):
I don't know about the energy that goes in into
a black hole, but it's somewhere there. Yes, is one
of the fundamental principles of the universe that energy is conserved.
I know that it gets a little dicey when you're
talking about black holes. Yes, it is, but I don't
know if there's any special cases where it's not. Yes,
(07:09):
energy always is conserved in some form, right, I think
ultimately everything becomes heat. But if energy does not get conserved,
where does it go? All right, not a lot of
doubters here. Everyone just said yes, no confusion. I feel
like nobody was confused about this. No, nobody was confused.
I love the person who said the fact you're asking
(07:31):
me this question makes me think I'm wrong, which is wonderful. Man,
you totally make that person. You need a doubt because
that's the process of science. We're like, we're sure that's true.
Hold on a second, how are we sure? All of
a sudden, I'm wondering, And then you've got to explore
your own intellectual framework and wonder like, do you really
(07:53):
know this or is it just something you've been assuming yeah.
Especially I guess if a physicist approaches you on the
street with my acrophone and says, do you think energy
is always conserved? I feel like, you know that automatically
makes you a little suspicious. Yeah. Actually, default answer to
a random physicist asking you a question should be no,
it should be I don't know, what do you think?
And then you flipped do you want to participate in
(08:15):
my experiment? Uh? No? Do you want to know the
deep secrets of the universe? Not? Really? So this is
I feel like this is a pretty mind blown question,
just the idea of asking this question. I feel like
the idea that energy is always conserved seems very basic
to physics, and it seems pretty internalized by most of
the public. Like I feel like, you know, it's like
(08:36):
asking which way does gravity point? Or you know, it's
space big people say yes. But there's a bit of
a history here, right. It used to be that we
thought energy was conserved and that mass was conserved. We
would watch chemical reactions and we would notice that it
was mostly a rearrangement of the atoms, like puzzle pieces
moving from one place to another, and that no actual
(08:58):
matter was destroyed or created, and so we had two principles,
conservation of energy and conservation of mass. But then we
learned conservation of mass not actually a thing, right, You
can turn mass into other kinds of energy, and energy
into mass. So then we generalized into a larger principle,
conservation of energy, which includes mass as one of its forms.
(09:20):
But that's a hint, right, that's a hint. That's something
which seems fundamental, like the existence of matter doesn't necessarily
have to be concerned. Now, this isn't just a sort
of like a semantic thing, right, Like we're not saying
that energy just transforms into mass and so it's not concerned.
We're asking kind of the bigger question, like is mass
and energy conserved? That's right now, we're asking the deep
(09:40):
fundamental question. Is total energy concerned? When you include all forms,
not just does it slip away into some other kind
of energy, but energy itself summed up over everything, is
it actually conserved? Yeah? And it turns out that the
answer is no. How can it be? No, Daniel, The
(10:01):
answer is no. He's just during my world, I feel
like democracy died last night. And now physics, well, that's
what we're here for. We are here to blow people's
minds and pull back the veil and help them understand
the way the world actually works. And so this is
kind of mind boggling. But the lesson we're gonna learn
is what's actually important about the universe, what's really fundamental?
(10:23):
What do we actually know? What really should we be
paying attention to? All Right, so I guess the short
answer is no. Energy is not always conserved. That's right,
And that's even in a closed system. Right, we talked
about energy conservation. We're usually referring to a closed system
because you know, if you have a single thing inside
a larger system, sure it doesn't have to conserve energy,
(10:44):
Like a battery inside your toy is losing energy, but
you know that energy is going to other parts of
the system. But we're talking about a closed system, or
energy doesn't escape or doesn't enter, we're talking about the
whole universe. Is energy conserved for the whole universe? And
even for that, the answer, it turns out is no, Man, Daniel,
not even for a closed system. I feel like one
(11:06):
of those celebrities. I'm ready to throw down my microphone
and walk away. Don't mic drop just yet. There are
bigger revelations to come, I see their twists. All right,
we'll step us through first, why do we think that
energy was conserved? And then maybe we'll get into why
it wasn't it's not conserved. Yeah, that's a great question.
And essentially we thought that energy was conserved because mostly
(11:27):
it is, and so we never noticed we never saw
a counter example. And a lot of physics works this way.
We see things happening in the world and we see
them seeming to follow a rule, and so we just
sort of like we positive, well, maybe this rule is true.
Maybe this is fundamental. You know, electric charge is conserved,
or you know F equals m A. We don't always
(11:48):
have a reason for it. We don't always have like
a first principles derivation for it, which is something we observe,
we categorize, and then we elevate it to a status
and if nobody ever sees it broken, we think, well
that must be true. For some reason. We elevated to
that like a law status. We think it's a law
of the universe. Yeah, And this is the way science works,
is that we come up with a rule, we test it,
(12:10):
we check it, we explore it and lots of different ways,
and if it survives experimental tests over and over and
over again. We think, oh, it's probably true, and then
we can sometimes dig deeper and figure out the reason why.
We can sometimes later derive that law from deeper truths.
But sometimes we can reveal that it was only ever
approximately true. We haven't checked every possible scenario. That's impossible, right,
(12:35):
and so people will find a place where, look, it
turns out it's broken over here, it doesn't quite work
over there. It was the same story with conservation of mass.
If you're just doing basic chemistry, mass is mostly conserved.
It's only when you get to like higher energies where
you're destroying particles or colliding particles that you notice that
it's broken. So a lot of these conservation rules are
(12:57):
not exact. They're not like really true. They're almost true,
or they're true and lots of circumstances and so we
never notice. It's kind of like F equals m A.
I feel like that feels really fundamental and intuitive because
that's what dominates our everyday experience. But like if you
push the physics of it to extreme situations, it doesn't work.
(13:17):
It breaks, yeah, exactly. And the same is true for
things about like time. You know, we've learned that not
everybody has to agree on the order of events. We
had a whole podcast about what happens when people are
running a race and you look at it from different speeds,
and these are the kind of things you don't notice
in your everyday life. You don't approach the speed of light.
And so we never tested things in those sort of
(13:38):
high speed extremes until recently, and we noticed, whoops. Those
rules we thought were deep and fundamental and true turned
out to be a special case that are only valided
certain situations, not fundamental truths about the universe. And physics
is all about uncovering the fundamental truths about the universe,
not just the special cases. And so that's why we
thought energy was conserved because we've always seen it conserved
(14:01):
and sort of made sense. Yeah, it's conserved in most
situations that we're familiar with, right, Like, if you have
a canister of gas or something, the energy in it
is going to be mostly conserved, mostly conserved, are totally conserved,
the energy is going to be almost exactly conserved. And
thinking about when it's conserved and noticing when those rules
are broken, it's going to teach us really something fundamental
(14:23):
about the nature of space and symmetries and conservation laws
in general. But fuel, for example, is mostly conserved. All right,
let's get into some examples of when energy is not conserved,
and let's get into why it's not being the good
conservative we thought it was. But first let's take a
quick break. All right, Daniel, we are blowing up people's
(14:57):
brains here. Apparently energy is not concerned in this universe.
That's right. It's not always the same, that's right. It's
not always the same. The amount of energy in the
universe can change. And this is the kind of thing
I get email questions from listeners about all the time,
because people who have been thinking to themselves about dark
energy have come in their minds to what seems like
a contradiction. Remember, dark energy is the expansion of the universe.
(15:22):
It's not something we understand. It's not a law physics.
It's just sort of the observation that the expansion of
the universe is continuing and that it's speeding up, and
we don't understand the mechanism of it. But there is
something about dark energy that we do know, which is
that it's constant in space. So it makes more space,
and then that space has new dark energy. So every
(15:43):
cubic meter of space, for example, has its own dark energy.
And as the universe expands, you get more universe, you
get more dark energy. So these listeners right in and
they say, hold on a second, where does that energy
come from? Does that mean that dark energy doesn't concern
of energy? Right? Yeah, it's it's kind of very puzzling,
right because you're telling me that the universe is expanding
(16:05):
with more energy and acceleration, so it has to you know,
be drawing energy from somewhere, but it's sort of coming
out of nothingness, this dark energy. And so the answer
to those listeners is that no, it doesn't have to
come from somewhere. It violates the conservation of energy. As
the universe expands, you get more space, and that space
has new energy, and the energy in the universe increases.
(16:29):
So as spacetime expands, the energy can go up. And
where does that energy come from? It doesn't have to
come from anywhere, because energy conservation is not actually a
fundamental law of the universe. It's just something we never
saw broken before. I feel like that throws everything to question. Now, Daniel,
what do you mean, yes, right, Welcome to physics, questioning everything,
(16:52):
even even the idea of asking questions. Why are you
asking questions, Daniel, don't ask questions about that. That's a
zone of a wild So is that the primary example
of energy not being conserved is in space and in
this idea of the universe expanding or is it more
you know, kind of seeped into our everyday physics. It's
(17:13):
not really steeped into our everyday physics. And the cases
where energy is not conserved are really going to give
us a clue as to why it's not conserved. And
I can give you another example, which is also related
to the expansion of space. As space expands, it turns
out there's a way to lose energy. For example, a
photon photon is flying through space, and we know that
(17:35):
if a photon comes to you from far away, but
that the space between you and the source expands in
the meantime, that photon red shifts are red shifts associated
with that source having a velocity. Like a police siren
that's moving away from you, the wavelength of the sound
is stretched, and the same is true for light from
stars that are moving away from us. But there's another
(17:58):
kind of red shift, which is just the expand engine
of space between you and that light source. It will
also stretch the photon and make it redder. Won't slow
it down, it'll just shift its frequency. That will stretch it.
That's right. Photons always move with the same speed, the
speed of light, but they have different levels of energy
which correspond to their wavelength, which is equivalent to their
(18:18):
color or their frequency. It's all the same thing. And
so when you make a photon redder, effectively you're taking
away its energy. It's losing energy. So in that case,
the expansion of space disappears energy from a photon. What
could it all be the same energy, Daniel? Could dark
energy be the energy of photons getting redder. That wouldn't
(18:40):
add up to like a factor of tend to one.
There's so much more dark energy than the energy that's
being lost by photons being red shifted. But we see this.
It's a real thing. It's just kind of like a
dark red energy. I like that phrase, dark red energy.
That should be a thing. There should be a physics.
Should be the title your other sci fi novel, dark
(19:00):
red energy. All right, I'll do it just starting from
the title. I can just write the novel from there.
But yeah, So here are two examples, space expanding meaning
extra energy is created, or space expanding meaning energy is
lost by photons. And the thing that those two examples
have in common, of course, is that space is not static.
In those cases, space is expanding its dynamic and that's
(19:24):
the clue. I see. Yeah, that's kind of um, it's
like breaking a law by breaking another law, kind of
because I feel like, you know, we thought space didn't
expand we thought space was fixed before, but then we
learned that space is like malleble and bends and stretches. Yeah,
and just like thinking that Galilean transformations Newtonian physics always
worked because we had always seen it work because we'd
(19:44):
only ever checked low speeds and then discovering that they
break when you get too high speeds. This is an
example of something we never thought was possible, expanding space,
and when it happens, it challenges some pretty basic stuff
that we thought was true, but turns out only have
been true in the special scenario we ever tested it in,
which is fundamentally static space. Right, Well, then step us
(20:07):
three here, Daniel, why is an energy conserved when space expands? Well,
I think the best way to tackle that is to
think about, like, well, why should we expect it to
be conserved? Did we have a reason to think it
should be conserved. Is there some fundamental theoretical idea that
tells us it should be conserved, or is it just
something we observed and thought was true. And for that,
(20:29):
I think it's good to think about, like, what do
we mean exactly about conserved? Right to be kind of
specific about it, And by that we mean like, here's
something we calculate, Like you can measure the amount of
energy and something and then you can let it do
its thing. You know, maybe you turn on the engine
of your car or whatever, and then you calculate it again,
and you notice you get the same answer. So as
(20:50):
you said before, like you burn the fuel in your car,
but now you've added speed to your car, so energy
is moved from one part of the system to another.
And we've noticed so far that if you add up
all the energy before and you add of the energy after,
you get the same thing. And so we call that conserved,
right that there's a symmetry there that says it hasn't
changed the accounty. You can account for every cent of
(21:11):
that energy. That's right, And so people have long wondered, like,
why are things conserved at all? What does it mean
about the universe? Because it's the kind of thing that
makes a physicist scratch his or her head. It's like, well,
if this thing is concerned, does that mean that it's
a deep truth in the universe, that it's an important quantity.
It's like a clue about how the universe works. If
(21:32):
this thing doesn't change, right, it's like a constraint or
a law. And if you're on the hunt for figuring
out the fundamental rules of the universe, that seems like
an important clue, right, Yeah, well, I guess maybe it's
it's it feels fundamental because it's kind of it feels
logical for it to be conserved. I know we're trying
to question it here, but it's like, you know, if
you have some money, it has to go somewhere. Can't
(21:52):
just like disappear, and it can't just pop out of
the nothingness. I think that's just your intuition. You're just
used to having a conserved and actually money is a
great example because money is also not conserved. You know,
if I take a painting by Picasso and I just
set it on fire. Where does the value of that
painting go nowhere? Or if I am Picasso, when I
(22:13):
make a new painting, right I've created a hundred million dollars,
Where does that come from? Right? I wasn't worth a
hundred million dollars. It didn't seep out of me. Or
one day people decide that some kind of rock is
now the most valuable thing in the world, and we
will all pay five d dollars an ounce for this
kind of rock. Then we've created value. So money is
(22:35):
not conserved at all. It's a great example, right, But
I feel like money is kind of it's like a
psychological concept, money and value. But we're talking about like physics, right, yeah, exactly,
Like you know, if if I have something here, it
can't just disappear, or I can't just suddenly appear another
whore in front of me, although it would be cool
because then I could go to sleep. Well, there are
(22:59):
actually really interesting fundamental insights about why some things are
conserved and some things are not conserved. And this comes
from a law from a real genius of physics who
have been long overlooked and only recently been appreciated a
mathematical physicist from the early part of this century, I
mean Utah, and she wrote down a really interesting law,
and she says that there's a conservation. There's something that's conserved,
(23:22):
like energy or momentum, every time the universe has a symmetry.
But there's this deep connection between something being conserved and
the universe having some sort of balance or symmetry to it.
From a language point of view, that makes sense. If
there's a symmetry means there's like an equation, which means
things are balanced and conserved. But I'm guessing you mean
(23:42):
more like the mathematical idea of symmetry. And there's lots
of really fascinating examples before we get to energy. And
one of my favorites is momentum. So why is momentum
conservad at all? You might ask that, Well, it turns
out that momentum is conserved because the universe has no
preferred location called this translation symmetry, Like something that happens
(24:03):
here in space could equally well happen ten ms to
the right or a hundred up or whatever. The laws
of physics don't change based on where you are in
the universe. That's we call a translation symmetry, and that
translation symmetry directly implies conservation of momentum. Like if you
didn't know momentum was conserved, but you knew that, you
(24:24):
didn't matter where you were in the universe, you could
derive conservation of momentum mathematically, How would you, I guess,
derive it? Can you give us like an in twitter sense,
like you know, the equations can be reduced to like
you know, momentum and equals momentum out. Yeah, there actually
is a mathematical procedure. That's what Newtis theorem does. It
tells you what conservation law comes out of a specific symmetry.
(24:49):
If the universe is symmetric to changes in some quantity X,
then you can derive the quantity why that is conserved.
For those listeners who want a little bit more gory
Dta hills, you take the quantity that's conserved, and then
you have to take the derivative of the lagrange in
of the universe with respect to the derivative of that
(25:09):
thing that's conserved, and so it gets a little bit
hairy mathematically, but there is a relationship between the quantity
that has symmetry. In this case, position in space and
the thing that's being conserved in this case mass times
the velocity, which is the derivative of your position in space.
And so that's the nuts and bolts of the mathematical
genius of Emily Nuther. But the idea is that there's
(25:31):
a symmetry here, and I think you can understand it intuitively. Like,
think about, for example, just a single rock floating in space,
and that could be anywhere. Right, you push on that rock,
you've given it momentum. It flies off with a certain momentum.
It makes sense for momentum to be conserved, your momentum
flowing to the momentum of the rock. If nothing pushes
on you, you're going to keep coasting at the same speed. Yeah, exactly.
(25:54):
And that's true here, or it's true to the left,
or it's true to the right, or it's true somewhere else.
As law is, space is the same everywhere, The same
results come from the same experiment. But what is space
isn't the same everywhere? What if, like, you're near a
really massive planet and so space is curved, for example,
and so it kind of does matter how close you
are to that planet, because if you get a push
(26:17):
when you're close to the planet, or you get a
push when you're far from the planet, you get very
different outcomes, right, And so in that scenario, the momentum
of the rock is not conserved because space is not
the same everywhere. The answer you get depends on where
you are in space. But in that case, now you're
sort of expanding your system. Now your system is the
rock and the planet, and momentum is conserved between them,
(26:39):
isn't it exactly? If you include the planet in the system,
then momentum is conserved anywhere because you can move the
rock plus planet system to anywhere in space. And the
reason momentum is conserved is that now the whole system
can be shifted anywhere in space, and it as an ensemble,
does the same thing. And so the key is that
your system can be translated anywhere in space, and then
(27:01):
momentum is conserved if it matters where in space your
system is. If your system is just the rock, then
momentum is no longer conserved. All right. It's something to
do with this idea of symmetry and the equations of
physics and symmetry. I feel it's a tricky concept because
you know, I think we're all familiar with the idea
of symmetry, like if something looks the same in front
(27:22):
of a mirror, or you know, if I take a
piece of paper and folded the ink kind of like
copies from on both sides of the paper, and it
looks symmetric. But in the equations, it's it's a little
bit different, right. It sort of means kind of what
you said in me is, which means it's more about
conserving or having the laws be the same in different situations. Yeah,
exactly if you made a change, would you get the
(27:45):
same outcomes? Right? Do the same laws apply here and there?
And so for the example of the rock in space,
you know, the rules of the universe shouldn't depend on
where you are, right, So then it kind of seems
to sort of make sense that if you have a symmetry,
then that thing is conserved, right, Like that sort of
makes intuitive sense. That's kind of interesting. Yeah, there's a
(28:07):
connection between the symmetry and the thing that's conserved. In
this case, space is the symmetry, and momentum motion through
space is a thing that's conserved, right, So momentum is conserved,
but then for energy it's different. It has a different symmetry.
That's right. The idea of the conservation of energy comes
from symmetry in time. If the universe is the same
(28:28):
going forwards and backwards, if there's a symmetry in time,
then you get conservation of energy. And here's a little
bit trickier to understand the connection between energy and time,
but it's there, and quantum mechanically, I think it's actually
the clearest. We have the Shorting Air equation, which is
what tells us how like a quantum mechanical system changes.
(28:50):
It says, if you have this quantum wave function, now
what quantum wave function will you have in the future.
That's the Shorting Air equation and solutions to the Shorting
equation are things that work in the universe, but it
tells us how things move forwards in time. Well, turns
out the Shorting Your equation is just an expression for
the energy of the system. Like if you actually look
(29:11):
at the mathematics of it, it's kinetic energy plus potential energy.
That's just a total energy of the system. And so
if the universe is symmetric in time, then energy is
conserved in your system for served in time. Kind of
like I feel like you're telling me that there's a
symmetry in time means that what I have now she's
gonna be equal to the things that I have later.
(29:33):
So in a way, that sort of translates into you
don't lose or gain energy. It has to kind of
be the same here and after. Yeah, exactly. This is
sort of a conservation there, this conservation of probability. Also
in quantum mechanics, it says that things are transformed and
they slash around, but they don't disappear. And what is
the thing that doesn't disappear. Well, it's the solution to
(29:54):
the Shortinger equation, which is really just the sum of
all the energies in the system. And so in some sense,
it's sort of like asking what is energy. Well, energy
is the thing that's conserved if you have time symmetry
in your system. And it's something we just sort of noticed.
We're like, well, you add all these things up kinetic
(30:14):
energy and potential energy here, and you add it up later,
we notice we get the same answer. And that's something
we've noticed because we've mostly been doing experiments in systems
where time doesn't matter. Where if you do the experiment
now or a hundred days or in a thousand years,
you get the same answer. So whenever time is symmetric,
and it has basically always been for our experiments, then
(30:34):
energy is conserved. So I feel like you're saying that
energy is just an illusion of times, and yes, exactly,
that's the message, is that energy is connected to time.
And we know that already from quantum mechanics. Right. We
know quantum mechanics tells us you can't measure the position
and momentum of a particle at the same time. Those
two concepts are connected, right, And it also connects energy
(30:55):
and time, and it's for the same fundamental reason that
there's a connection between those two basic quantities. They're really
two sides of the same thing. One symmetry leads to
a conservation law. All right, I feel like we're set
up now to break the conservation of energy and talk
about why that's really true and what it means. But
now it's time for us to take another quick break.
(31:29):
All right, Dan, we're talking about the conservation of energy,
and it turns out that energy is not always conserved,
which blows my mind. You're telling me it has something
to do with the symmetry of times. If time is symmetric,
then energy is conserved. And so I'm guessing what you're
gonna say now is that time is not always symmetric,
and it's actually a little bit larger than that. It's spacetime.
(31:50):
If the universe in which you're doing your experiment is fixed,
if spacetime is fixed, it's not changing, then yes, energy
is conserved. And so if spacetime is flat and it's
not changed, you can do your experiments. You can fuel
your car, you can drain your battery, you can collide particles,
you can do chemistry, and energy will be conserved. But
as soon as you break the symmetry of spacetime, as
(32:11):
soon as spacetime is changing, right, the shape of space
and the shape of the universe. As soon as that
is changing, energy is no longer guaranteed to be conserved
because it only was conserved because space time was not changing.
Oh I see, So maybe to match up our intuitions
to this new idea, we have to maybe expand our
idea of conservation of energy. Like maybe it's not a
(32:33):
conservation of energy for a closed system. It's like we
have to think about conservation of energy being true for
like the same spacetime or a static spacetime. But if
you change that, if you change spacetime, then you can't
say that energy is conserved anymore. Exactly. We have to
add a qualifier. We say energy is only conserved when
(32:54):
time symmetry is respected, which happens when space time is
not changing. But you know, we live in a universe
where spacetime is changing. The expansion of the universe is
not just things moving through space. It's the stretching of
space itself. It's the creation of new space. So we
live in dynamic space time, which means energy fundamentally is
(33:16):
not conserved. It means that energy is not the deep,
true quantity that we thought it was. It means it's
not the important thing to be thinking about. So it's
expansion of space that destroys the conservation of energy. Or
is it the expansion of space time? Are you do?
You use it as the same shorthand? Yeah, Well we're
talking about the expansion of space time, right, or the
expansion of space through time. You can think about it
(33:38):
like that because the space in which we're doing our
experiments is changing as a function of time. And remember,
to have conservation of energy, you need to have symmetry
and time. But the universe is not the same today
as it was a thousand or a billion years ago.
It's a different universe. It's expanded. The space in which
we're doing our experiments is different, and so it changes
(34:00):
the results of the experiments. And it means energy is
not conserved from one moment of space to another moment
of space. And that would also work here at the
local level too, right Like, if I had a canister
of gas and I expanded the space time it was in,
I would see energy not conserved. That's true. You would
(34:20):
create more dark energy because you've expanded space and every
new unit of space has dark energy in it. So yeah,
you would have created more energy whether or not there
was a canister of gas there. And the thing for
people to understand is remember the expansion of the universe
seems dramatic. The universe is big, it's expanding super fast,
but locally it's not very quick, Like the expansion of
(34:41):
space is not something you notice day to day, and
it's actually pretty weak. It's pretty small quantity in a
small piece of space. It only adds up to be
most of the universe because the universe is already so big.
There's so much empty space out there that if you
add up all the dark energy becomes a huge number.
So this violation of energy something that's very, very small.
(35:02):
It's very hard to notice because the expansion of space
is a very gradual, tiny effect. I see, it's conserved mostly,
but if you think about the whole universe, it's not
actually insignificant. Yeah, exactly, it's a small violation, and an
individual unit of space added up over the whole universe
becomes kind of a big deal. But for me, it's
not as much about like the size and the number
(35:24):
as the fact of it, Like, whoa this thing we
thought was a deep truth in the universe turns out
to be a coincidence or just a product of where
we happen to be. You know. It's like if you
grow up eating toast for breakfast and they butter it
on the top side, you think, well, toast has to
be buttered on the top side, and then you go
visit your friend you discover what they eat butter on
the bottom side of their toast. That's even possible. It
(35:45):
opens your mind a whole new way of thinking about
the universe. And that's what this does. It says energy
is not the important thing. Right. Energy is something we
thought was deep and fundamental, but it's actually important to
cosmologists are things like curvature and expansion. Those are the
fundamentally interesting things about the universe, not the energy. I
guess maybe what would trip people up is thinking about
(36:07):
where that energy comes from, right, I mean that's sort
of the origin of the original question. If the universe
is expanding and there's more energy being created, where does
it come from? Are you saying that energy can just
be created out of the blue. Yes, that's exactly what
we're saying, is that we've discovered that it doesn't have
to come from anywhere. That's sort of the wrong question.
It's like asking where does the value come from when
(36:30):
Picasso paints a new painting, Right, it didn't come from anywhere.
It wasn't and now it is. It only has to
come from somewhere if it's conserved, and there are things
that are universe that are conserved, like electric charge. Right,
you can't just create an electron because it's charged, has
to come from somewhere, has to come from previously charged particles.
(36:51):
Or you can start with a photon and create an
electron but then you have to create an anti electron also,
so you have balance of charge. There are things that
are fundamental that have to be conserved to have to
come from somewhere, but energy is not one of them.
It should be like demoted from that list of like
super important fundamental conserved quantities because it's just sort of
like an accident of where we live that we never
(37:13):
noticed that's not actually conserved. Man, first you demote pluto,
and now you're demoting energy. Who's the next matter? That's right,
We are pulling back the veil. Man. We are discovering
new deep truths. Matter that was like a hundred years
ago demoted matter the same matter doesn't matter. Matter, it
doesn't matter. And you know, I think it must have
been equally bewildering a hundred years ago to think what
(37:35):
you can create matter? Do you think you're some sort
of divine being? Right? Matter is you can't where did
it come from? When you make new matter, and it
doesn't have to come from anywhere. It's transformed from energy.
But the matter itself didn't exist, and matter can disappear,
It can exist and then just not exist anymore. It
doesn't have to be conserved all right, Well, it sort
(37:56):
of blows my mind. But it turns out that this
is actually a little bit controversial in physics, Like not
everyone agrees with this conclusion that energy is not conserved.
Is that right? Yeah, that's right. There are some folks
who find this very uncomfortable and they don't like this idea,
so they try to patch up energy and say, well,
let's think about energy in a slightly different way so
that it is concerned, and that's totally valid. It's like, well,
(38:19):
let's find a different symmetry or a different thing, you know,
energy prime or energy two point oh, so that it
actually is conserved, because maybe that will give you some
deep insight into the universe. And the way they do
this is a little bit controversial. I would say like
three out of four cosmologists and dentists I asked would
say that energy is not conserved. But there's some people
out there that try to patch it up by folding
(38:41):
this energy back into the gravitational field. Meaning like maybe
they think that maybe you're just doing the accounting wrong.
They might say that a costs of paintings are conserved
in value, is just that you know, you're accounting for
people's happiness when they purchase a costs or something like that,
right exactly. And they say, there's another category of energy
(39:03):
that we're not accounting for, and that's the gravitational energy,
and that as the universe expands, it actually gets more
and more negative gravitational energy. That the expansion of the
universe creates negative energy in the gravitational field that offsets
the positive energy from dark matter. And they do some
calculations and show that boom, it all adds up to zero,
(39:23):
and so energy is actually conserved. According to these folks,
is it kind of like the photon that loses energy
Like when you grow space you're pulling things apart, which
means you're losing gravitational energy, right, or you're gaining you're
losing you're gaining when when you're pulling things apart, it
takes energy to separate objects, right, So that's negative work
(39:45):
and so you're losing energy. You're creating a negative energy
situation in the gravitational field. But there's a problem with
this and the other folks on the other side of
the divide that say the energy is not conserved, they
quibble with the way this calculation is done, and they
think it's not actually technically correct that you can't actually
just measure the energy of a gravitational field, because gravity
(40:07):
is a really complicated thing. It's not just like, here's
a fixed gravitational potential and you can measure the energy. Remember,
gravity is dynamical, it's responding to space, it's shifting, it's changing.
And so, for reasons that I think are a little
too technical to dive into, there's not really a good,
well defined way to calculate the gravitational energy of the
whole universe, or even the gravitational energy more importantly of
(40:29):
a part of the universe, the gravitational density. So they
say that doesn't really count. You can't include it in
the calculation. Energy is not concerned. So it's still in progress.
People are still talking about it. People are still talking
about it, but I think the consensus is energy is
not conserved, despite these efforts to try to patch it
up and fix it and to say that there's a
way to look at energy such that it is concerned.
(40:52):
And then what do the dentist thing that if you
maybe do a root canal, you consider bypass s base.
They think we shouldn't eating fruit loops late at night
you should be flossing more often. You'd be flossing your
theory is more often because you know you can get
gun accumulating. But to me, I think it's fascinating. It's
a great investigation into like what's real about the universe,
(41:13):
what's deep, what's true. The reason that we try to
identify conservation laws is not just because we need a
better energy policy, but because we're trying to understand the
way the universe works, and finding these things that are
conserved or turns out to be not conserved are ways
that we get clues as to the way the whole
machinery works deep down. Yeah, I think what I'm getting
is that physics is maybe as fickle and sensical as
(41:36):
the art world. I think is what you're saying, and dentistry.
Your theory is genius, it's fundamental. Actually, no, it turns
out it's worth nothing. It's like cubism itself, makes no sense.
That's right, But there's a real beauty here to this inside,
this connection between symmetries and conservation laws, and it tells
(41:57):
you that every time you find something symmetric about the universe,
there's something out there being conserved. And that's really cool
and beautiful to me. Well, I think the takeaway is
that we can say that energy is conserved in space time,
but that spacetime itself is not always conserved. Yeah, if
spacetime is fixed, then energy is definitely conserved. In a
(42:17):
situation any universe like ours, where spacetime is expanding, then
there's no guarantee of energy conservation. Energy actually increases as
space time increases, and it doesn't come from anywhere, which
is hard to grapple with, but it is our reality.
And that's the job of physics is confronting us with
hard to understand truths, things that don't make sense to
(42:37):
our intuition, but that we figured out through science. Right,
that's why we have science and not just intuition, to
confront us with these things which are in conflict with
what we thought but turned out to be actually true.
All right, done, I won't walk away from the interview.
I'm staying. I'm staying for the rest of it, which
is about ten seconds. All right, Well, I conserved some
(42:59):
energy for this last bit. Well, we hope everyone enjoyed. Dad,
Thanks for joining us, and think a little bit more
about what do you think is true about the universe
and what might be an idea that Daniel and his
dentists wrong in the future, hopefully everything. Thanks for joining us,
see you next time. Thanks for listening, and remember that
(43:25):
Daniel and Jorge explain the universe is a production of
I Heart Radio. Or more podcast from my heart Radio
visit the I heart Radio app, Apple Podcasts, or wherever
you listen to your favorite shows.
Hey, Daniel, I noticed something about physicists. I'm afraid to
hear this. I feel like all of you like to
blow things up. We do. Actually, that's what makes us
so much fun at parties. I guess. I mean you'd
like to blow up ideas. You know, you like to
think things that people think are true and then prove
that they're actually false. That's true. Actually you mean like
the Earth being the center of the universe. Yeah, I
(00:30):
like that. I like that idea, but it turns out
it's false. Or you know that people thought that the
world was nice and smooth, but actually it's quantized into
little pixels called quantum physics. Al Right, So what do
you think that means about physicists. I think it probably
means that you like to disagree with the stabich ideas.
You're basically just contrarians. No, we're not. See do you
know fun at parties? Hi am or handmade cartoonists and
(01:07):
the creator of PhD Comics. Hi. I'm Daniel. I'm a
particle physicist, and I'm very positive about new ideas. Welcome
to our podcast Daniel and Jorge Explain the Universe, a
production of Our Heart Radio in which we consider all
the crazy new ideas out there and all the old ideas.
Which ones are real, which ones are made up, which
ones are we still clueless about. We take you on
(01:27):
a tour of all of them and explain them to you. Yeah,
we like to explore the universe and talk about all
of the things that are out there and this beautiful
cosmos of ours, all the things that are true, and
all the things that might be true. And part of
the journey of physics and science in general is understanding
the universe and questioning the things we thought were true,
(01:48):
getting a deeper, more fundamental view of the way things
actually work, which sometimes is really in contrast with the
way we thought things work. Because there are a lot
of ideas out there, right, Daniel. I mean they're ideas
about how the world works, about why things are the
way they are, and how people think that it all
comes together. Yeah, And sometimes the first idea you have
(02:09):
seems reasonable and sticks around for a long time, and
then you notice small little problems with it, and when
you pull on that thread, you reveal something really fascinating
about the whole universe. Like people used to think, hey, there,
Earth is flat. It certainly looks flat from here. But
then it's sort of a mind exploding discovery to realize, Wow,
we're actually living on the surface of a huge sphere. Yeah.
(02:32):
So there are a lot of ideas out there, and
I feel like you physicists like to reserve the right
to change your mind. That's an important part of science, right,
challenging the orthodoxy. It's one of the best things about
science that sometimes we look at the very foundations of
the ideas and we say, wait a second, is that
really true? How do we actually know that? We've been
thinking that for a long time, but is it possible
(02:56):
that we were wrong. I think it's one of the
deepest virtues of science. Yeah. And if like that's maybe
your favorite part of science is proving your appears wrong
on a personal level, yes, And for me it's actually
the reason I got into science, because I'm really excited
about those moments of intellectual revolution. I feel like, when
(03:16):
you discover that the world is really different from the
way we thought it was, we've pulled the wolf from
our eyes. We've like peeled back a layer of reality.
We've discovered some truth that was hidden to us. And
what's more exciting in science than to have a moment
of discovery like that a deep revelation, you know, not
like slowly iterately building up increments of knowledge until you
(03:37):
get there, like almost like a moment of revelation where
you understand the universe differently somehow and you can never
go back to seeing it the old way. Some people
go for the Eureka moment. You like to go for
the moment. That's what I'm in for. I'm in it
for the scientific revolutions, for the Hans. You're in for
the Hans I am. And there have been lots of
(03:58):
moments in history where people have made to discoveries like this.
They've pulled on one little string and then they've unraveled
that very foundations of science, and so it's exciting to
think that there might be more of those ahead of us.
So it's exciting when a bunch of smart people's go,
never mind, I thought there was flat, but actually it's
a giant ball. Yeah, because it changes sometimes your whole
(04:18):
relationship with the universe, you know, thinking that we live
at the center of the universe everything revolves around us,
to thinking we're just a tiny little speck of dust
in an insignificant corner of the universe that really changes
the way you feel about the universe and life itself
and how you should live it. So, hey, this stuff
is actually irrelevant for how people feel about themselves and
(04:39):
their lives. Yeah. So science is all about challenging ideas,
and so today on the program will be challenging a
very core and fundamental idea and physics. I feel like
this is a very important idea that a lot of
people have kind of internalized about the universe, but that
actually might not be so true. That's right. This is
something pretty basic that if you ask folks on the street,
(05:00):
it would be pretty confident was true. But it turns
out we've learned a lot about the nature of the
universe and it might actually not be quite so fundamental.
So on the program will be asking the question is
energy actually conserved? Now, Daniel, this sort of blew my mind.
(05:22):
How can we even ask this question? What do you mean?
Is energy always actually conserved? Yeah? That's why it's such
a wonderful question because it makes you think, like, well,
why would it be conserved? How do we actually know
it's conserved? What would it be like to live in
a universe where it's not conserved? That solve all of
our energy problems. I feel like you just told me
the world is not actually a ball. It's like a
(05:43):
cube or something. We live on a donut and it's
filled with energy. It's filled with sugar, energy and sprinkles.
That's right. Just eat the glaze, man, eat the glaze.
Then then my energy will not be conserved, just an
increase or be turned into mass. Probably. I know. It's
a bit mind blowing, and that's why I was especially
(06:04):
eager to hear what folks on the internet had to
say about this question. Yes, so it's usual Daniel went
out there into the wilds of the web and ask
people the question is energy always conserved? So thank you
to these folks in advance who participated. And if you
would like to answer tough physics questions with no preparation
and have your answers broadcast thousands of people, please write
(06:26):
to us two questions at Daniel and Jorge dot com.
Think about it for a second. If someone ask you
if energy is actually always conserved, what would you answer.
Here's what people had to say. I always thought that
was one of the fundamental laws, that energy and matter
can't be created or destroyed, But the fact that you're
asking me this question makes me think I'm wrong. Yes,
(06:48):
I don't know about the energy that goes in into
a black hole, but it's somewhere there. Yes, is one
of the fundamental principles of the universe that energy is conserved.
I know that it gets a little dicey when you're
talking about black holes. Yes, it is, but I don't
know if there's any special cases where it's not. Yes,
(07:09):
energy always is conserved in some form, right, I think
ultimately everything becomes heat. But if energy does not get conserved,
where does it go? All right, not a lot of
doubters here. Everyone just said yes, no confusion. I feel
like nobody was confused about this. No, nobody was confused.
I love the person who said the fact you're asking
(07:31):
me this question makes me think I'm wrong, which is wonderful. Man,
you totally make that person. You need a doubt because
that's the process of science. We're like, we're sure that's true.
Hold on a second, how are we sure? All of
a sudden, I'm wondering, And then you've got to explore
your own intellectual framework and wonder like, do you really
(07:53):
know this or is it just something you've been assuming yeah.
Especially I guess if a physicist approaches you on the
street with my acrophone and says, do you think energy
is always conserved? I feel like, you know that automatically
makes you a little suspicious. Yeah. Actually, default answer to
a random physicist asking you a question should be no,
it should be I don't know, what do you think?
And then you flipped do you want to participate in
(08:15):
my experiment? Uh? No? Do you want to know the
deep secrets of the universe? Not? Really? So this is
I feel like this is a pretty mind blown question,
just the idea of asking this question. I feel like
the idea that energy is always conserved seems very basic
to physics, and it seems pretty internalized by most of
the public. Like I feel like, you know, it's like
(08:36):
asking which way does gravity point? Or you know, it's
space big people say yes. But there's a bit of
a history here, right. It used to be that we
thought energy was conserved and that mass was conserved. We
would watch chemical reactions and we would notice that it
was mostly a rearrangement of the atoms, like puzzle pieces
moving from one place to another, and that no actual
(08:58):
matter was destroyed or created, and so we had two principles,
conservation of energy and conservation of mass. But then we
learned conservation of mass not actually a thing, right, You
can turn mass into other kinds of energy, and energy
into mass. So then we generalized into a larger principle,
conservation of energy, which includes mass as one of its forms.
(09:20):
But that's a hint, right, that's a hint. That's something
which seems fundamental, like the existence of matter doesn't necessarily
have to be concerned. Now, this isn't just a sort
of like a semantic thing, right, Like we're not saying
that energy just transforms into mass and so it's not concerned.
We're asking kind of the bigger question, like is mass
and energy conserved? That's right now, we're asking the deep
(09:40):
fundamental question. Is total energy concerned? When you include all forms,
not just does it slip away into some other kind
of energy, but energy itself summed up over everything, is
it actually conserved? Yeah? And it turns out that the
answer is no. How can it be? No, Daniel, The
(10:01):
answer is no. He's just during my world, I feel
like democracy died last night. And now physics, well, that's
what we're here for. We are here to blow people's
minds and pull back the veil and help them understand
the way the world actually works. And so this is
kind of mind boggling. But the lesson we're gonna learn
is what's actually important about the universe, what's really fundamental?
(10:23):
What do we actually know? What really should we be
paying attention to? All Right, so I guess the short
answer is no. Energy is not always conserved. That's right,
And that's even in a closed system. Right, we talked
about energy conservation. We're usually referring to a closed system
because you know, if you have a single thing inside
a larger system, sure it doesn't have to conserve energy,
(10:44):
Like a battery inside your toy is losing energy, but
you know that energy is going to other parts of
the system. But we're talking about a closed system, or
energy doesn't escape or doesn't enter, we're talking about the
whole universe. Is energy conserved for the whole universe? And
even for that, the answer, it turns out is no, Man, Daniel,
not even for a closed system. I feel like one
(11:06):
of those celebrities. I'm ready to throw down my microphone
and walk away. Don't mic drop just yet. There are
bigger revelations to come, I see their twists. All right,
we'll step us through first, why do we think that
energy was conserved? And then maybe we'll get into why
it wasn't it's not conserved. Yeah, that's a great question.
And essentially we thought that energy was conserved because mostly
(11:27):
it is, and so we never noticed we never saw
a counter example. And a lot of physics works this way.
We see things happening in the world and we see
them seeming to follow a rule, and so we just
sort of like we positive, well, maybe this rule is true.
Maybe this is fundamental. You know, electric charge is conserved,
or you know F equals m A. We don't always
(11:48):
have a reason for it. We don't always have like
a first principles derivation for it, which is something we observe,
we categorize, and then we elevate it to a status
and if nobody ever sees it broken, we think, well
that must be true. For some reason. We elevated to
that like a law status. We think it's a law
of the universe. Yeah, And this is the way science works,
is that we come up with a rule, we test it,
(12:10):
we check it, we explore it and lots of different ways,
and if it survives experimental tests over and over and
over again. We think, oh, it's probably true, and then
we can sometimes dig deeper and figure out the reason why.
We can sometimes later derive that law from deeper truths.
But sometimes we can reveal that it was only ever
approximately true. We haven't checked every possible scenario. That's impossible, right,
(12:35):
and so people will find a place where, look, it
turns out it's broken over here, it doesn't quite work
over there. It was the same story with conservation of mass.
If you're just doing basic chemistry, mass is mostly conserved.
It's only when you get to like higher energies where
you're destroying particles or colliding particles that you notice that
it's broken. So a lot of these conservation rules are
(12:57):
not exact. They're not like really true. They're almost true,
or they're true and lots of circumstances and so we
never notice. It's kind of like F equals m A.
I feel like that feels really fundamental and intuitive because
that's what dominates our everyday experience. But like if you
push the physics of it to extreme situations, it doesn't work.
(13:17):
It breaks, yeah, exactly. And the same is true for
things about like time. You know, we've learned that not
everybody has to agree on the order of events. We
had a whole podcast about what happens when people are
running a race and you look at it from different speeds,
and these are the kind of things you don't notice
in your everyday life. You don't approach the speed of light.
And so we never tested things in those sort of
(13:38):
high speed extremes until recently, and we noticed, whoops. Those
rules we thought were deep and fundamental and true turned
out to be a special case that are only valided
certain situations, not fundamental truths about the universe. And physics
is all about uncovering the fundamental truths about the universe,
not just the special cases. And so that's why we
thought energy was conserved because we've always seen it conserved
(14:01):
and sort of made sense. Yeah, it's conserved in most
situations that we're familiar with, right, Like, if you have
a canister of gas or something, the energy in it
is going to be mostly conserved, mostly conserved, are totally conserved,
the energy is going to be almost exactly conserved. And
thinking about when it's conserved and noticing when those rules
are broken, it's going to teach us really something fundamental
(14:23):
about the nature of space and symmetries and conservation laws
in general. But fuel, for example, is mostly conserved. All right,
let's get into some examples of when energy is not conserved,
and let's get into why it's not being the good
conservative we thought it was. But first let's take a
quick break. All right, Daniel, we are blowing up people's
(14:57):
brains here. Apparently energy is not concerned in this universe.
That's right. It's not always the same, that's right. It's
not always the same. The amount of energy in the
universe can change. And this is the kind of thing
I get email questions from listeners about all the time,
because people who have been thinking to themselves about dark
energy have come in their minds to what seems like
a contradiction. Remember, dark energy is the expansion of the universe.
(15:22):
It's not something we understand. It's not a law physics.
It's just sort of the observation that the expansion of
the universe is continuing and that it's speeding up, and
we don't understand the mechanism of it. But there is
something about dark energy that we do know, which is
that it's constant in space. So it makes more space,
and then that space has new dark energy. So every
(15:43):
cubic meter of space, for example, has its own dark energy.
And as the universe expands, you get more universe, you
get more dark energy. So these listeners right in and
they say, hold on a second, where does that energy
come from? Does that mean that dark energy doesn't concern
of energy? Right? Yeah, it's it's kind of very puzzling,
right because you're telling me that the universe is expanding
(16:05):
with more energy and acceleration, so it has to you know,
be drawing energy from somewhere, but it's sort of coming
out of nothingness, this dark energy. And so the answer
to those listeners is that no, it doesn't have to
come from somewhere. It violates the conservation of energy. As
the universe expands, you get more space, and that space
has new energy, and the energy in the universe increases.
(16:29):
So as spacetime expands, the energy can go up. And
where does that energy come from? It doesn't have to
come from anywhere, because energy conservation is not actually a
fundamental law of the universe. It's just something we never
saw broken before. I feel like that throws everything to question. Now, Daniel,
what do you mean, yes, right, Welcome to physics, questioning everything,
(16:52):
even even the idea of asking questions. Why are you
asking questions, Daniel, don't ask questions about that. That's a
zone of a wild So is that the primary example
of energy not being conserved is in space and in
this idea of the universe expanding or is it more
you know, kind of seeped into our everyday physics. It's
(17:13):
not really steeped into our everyday physics. And the cases
where energy is not conserved are really going to give
us a clue as to why it's not conserved. And
I can give you another example, which is also related
to the expansion of space. As space expands, it turns
out there's a way to lose energy. For example, a
photon photon is flying through space, and we know that
(17:35):
if a photon comes to you from far away, but
that the space between you and the source expands in
the meantime, that photon red shifts are red shifts associated
with that source having a velocity. Like a police siren
that's moving away from you, the wavelength of the sound
is stretched, and the same is true for light from
stars that are moving away from us. But there's another
(17:58):
kind of red shift, which is just the expand engine
of space between you and that light source. It will
also stretch the photon and make it redder. Won't slow
it down, it'll just shift its frequency. That will stretch it.
That's right. Photons always move with the same speed, the
speed of light, but they have different levels of energy
which correspond to their wavelength, which is equivalent to their
(18:18):
color or their frequency. It's all the same thing. And
so when you make a photon redder, effectively you're taking
away its energy. It's losing energy. So in that case,
the expansion of space disappears energy from a photon. What
could it all be the same energy, Daniel? Could dark
energy be the energy of photons getting redder. That wouldn't
(18:40):
add up to like a factor of tend to one.
There's so much more dark energy than the energy that's
being lost by photons being red shifted. But we see this.
It's a real thing. It's just kind of like a
dark red energy. I like that phrase, dark red energy.
That should be a thing. There should be a physics.
Should be the title your other sci fi novel, dark
(19:00):
red energy. All right, I'll do it just starting from
the title. I can just write the novel from there.
But yeah, So here are two examples, space expanding meaning
extra energy is created, or space expanding meaning energy is
lost by photons. And the thing that those two examples
have in common, of course, is that space is not static.
In those cases, space is expanding its dynamic and that's
(19:24):
the clue. I see. Yeah, that's kind of um, it's
like breaking a law by breaking another law, kind of
because I feel like, you know, we thought space didn't
expand we thought space was fixed before, but then we
learned that space is like malleble and bends and stretches. Yeah,
and just like thinking that Galilean transformations Newtonian physics always
worked because we had always seen it work because we'd
(19:44):
only ever checked low speeds and then discovering that they
break when you get too high speeds. This is an
example of something we never thought was possible, expanding space,
and when it happens, it challenges some pretty basic stuff
that we thought was true, but turns out only have
been true in the special scenario we ever tested it in,
which is fundamentally static space. Right, Well, then step us
(20:07):
three here, Daniel, why is an energy conserved when space expands? Well,
I think the best way to tackle that is to
think about, like, well, why should we expect it to
be conserved? Did we have a reason to think it
should be conserved. Is there some fundamental theoretical idea that
tells us it should be conserved, or is it just
something we observed and thought was true. And for that,
(20:29):
I think it's good to think about, like, what do
we mean exactly about conserved? Right to be kind of
specific about it, And by that we mean like, here's
something we calculate, Like you can measure the amount of
energy and something and then you can let it do
its thing. You know, maybe you turn on the engine
of your car or whatever, and then you calculate it again,
and you notice you get the same answer. So as
(20:50):
you said before, like you burn the fuel in your car,
but now you've added speed to your car, so energy
is moved from one part of the system to another.
And we've noticed so far that if you add up
all the energy before and you add of the energy after,
you get the same thing. And so we call that conserved,
right that there's a symmetry there that says it hasn't
changed the accounty. You can account for every cent of
(21:11):
that energy. That's right, And so people have long wondered, like,
why are things conserved at all? What does it mean
about the universe? Because it's the kind of thing that
makes a physicist scratch his or her head. It's like, well,
if this thing is concerned, does that mean that it's
a deep truth in the universe, that it's an important quantity.
It's like a clue about how the universe works. If
(21:32):
this thing doesn't change, right, it's like a constraint or
a law. And if you're on the hunt for figuring
out the fundamental rules of the universe, that seems like
an important clue, right, Yeah, well, I guess maybe it's
it's it feels fundamental because it's kind of it feels
logical for it to be conserved. I know we're trying
to question it here, but it's like, you know, if
you have some money, it has to go somewhere. Can't
(21:52):
just like disappear, and it can't just pop out of
the nothingness. I think that's just your intuition. You're just
used to having a conserved and actually money is a
great example because money is also not conserved. You know,
if I take a painting by Picasso and I just
set it on fire. Where does the value of that
painting go nowhere? Or if I am Picasso, when I
(22:13):
make a new painting, right I've created a hundred million dollars,
Where does that come from? Right? I wasn't worth a
hundred million dollars. It didn't seep out of me. Or
one day people decide that some kind of rock is
now the most valuable thing in the world, and we
will all pay five d dollars an ounce for this
kind of rock. Then we've created value. So money is
(22:35):
not conserved at all. It's a great example, right, But
I feel like money is kind of it's like a
psychological concept, money and value. But we're talking about like physics, right, yeah, exactly,
Like you know, if if I have something here, it
can't just disappear, or I can't just suddenly appear another
whore in front of me, although it would be cool
because then I could go to sleep. Well, there are
(22:59):
actually really interesting fundamental insights about why some things are
conserved and some things are not conserved. And this comes
from a law from a real genius of physics who
have been long overlooked and only recently been appreciated a
mathematical physicist from the early part of this century, I
mean Utah, and she wrote down a really interesting law,
and she says that there's a conservation. There's something that's conserved,
(23:22):
like energy or momentum, every time the universe has a symmetry.
But there's this deep connection between something being conserved and
the universe having some sort of balance or symmetry to it.
From a language point of view, that makes sense. If
there's a symmetry means there's like an equation, which means
things are balanced and conserved. But I'm guessing you mean
(23:42):
more like the mathematical idea of symmetry. And there's lots
of really fascinating examples before we get to energy. And
one of my favorites is momentum. So why is momentum
conservad at all? You might ask that, Well, it turns
out that momentum is conserved because the universe has no
preferred location called this translation symmetry, Like something that happens
(24:03):
here in space could equally well happen ten ms to
the right or a hundred up or whatever. The laws
of physics don't change based on where you are in
the universe. That's we call a translation symmetry, and that
translation symmetry directly implies conservation of momentum. Like if you
didn't know momentum was conserved, but you knew that, you
(24:24):
didn't matter where you were in the universe, you could
derive conservation of momentum mathematically, How would you, I guess,
derive it? Can you give us like an in twitter sense,
like you know, the equations can be reduced to like
you know, momentum and equals momentum out. Yeah, there actually
is a mathematical procedure. That's what Newtis theorem does. It
tells you what conservation law comes out of a specific symmetry.
(24:49):
If the universe is symmetric to changes in some quantity X,
then you can derive the quantity why that is conserved.
For those listeners who want a little bit more gory
Dta hills, you take the quantity that's conserved, and then
you have to take the derivative of the lagrange in
of the universe with respect to the derivative of that
(25:09):
thing that's conserved, and so it gets a little bit
hairy mathematically, but there is a relationship between the quantity
that has symmetry. In this case, position in space and
the thing that's being conserved in this case mass times
the velocity, which is the derivative of your position in space.
And so that's the nuts and bolts of the mathematical
genius of Emily Nuther. But the idea is that there's
(25:31):
a symmetry here, and I think you can understand it intuitively. Like,
think about, for example, just a single rock floating in space,
and that could be anywhere. Right, you push on that rock,
you've given it momentum. It flies off with a certain momentum.
It makes sense for momentum to be conserved, your momentum
flowing to the momentum of the rock. If nothing pushes
on you, you're going to keep coasting at the same speed. Yeah, exactly.
(25:54):
And that's true here, or it's true to the left,
or it's true to the right, or it's true somewhere else.
As law is, space is the same everywhere, The same
results come from the same experiment. But what is space
isn't the same everywhere? What if, like, you're near a
really massive planet and so space is curved, for example,
and so it kind of does matter how close you
are to that planet, because if you get a push
(26:17):
when you're close to the planet, or you get a
push when you're far from the planet, you get very
different outcomes, right, And so in that scenario, the momentum
of the rock is not conserved because space is not
the same everywhere. The answer you get depends on where
you are in space. But in that case, now you're
sort of expanding your system. Now your system is the
rock and the planet, and momentum is conserved between them,
(26:39):
isn't it exactly? If you include the planet in the system,
then momentum is conserved anywhere because you can move the
rock plus planet system to anywhere in space. And the
reason momentum is conserved is that now the whole system
can be shifted anywhere in space, and it as an ensemble,
does the same thing. And so the key is that
your system can be translated anywhere in space, and then
(27:01):
momentum is conserved if it matters where in space your
system is. If your system is just the rock, then
momentum is no longer conserved. All right. It's something to
do with this idea of symmetry and the equations of
physics and symmetry. I feel it's a tricky concept because
you know, I think we're all familiar with the idea
of symmetry, like if something looks the same in front
(27:22):
of a mirror, or you know, if I take a
piece of paper and folded the ink kind of like
copies from on both sides of the paper, and it
looks symmetric. But in the equations, it's it's a little
bit different, right. It sort of means kind of what
you said in me is, which means it's more about
conserving or having the laws be the same in different situations. Yeah,
exactly if you made a change, would you get the
(27:45):
same outcomes? Right? Do the same laws apply here and there?
And so for the example of the rock in space,
you know, the rules of the universe shouldn't depend on
where you are, right, So then it kind of seems
to sort of make sense that if you have a symmetry,
then that thing is conserved, right, Like that sort of
makes intuitive sense. That's kind of interesting. Yeah, there's a
(28:07):
connection between the symmetry and the thing that's conserved. In
this case, space is the symmetry, and momentum motion through
space is a thing that's conserved, right, So momentum is conserved,
but then for energy it's different. It has a different symmetry.
That's right. The idea of the conservation of energy comes
from symmetry in time. If the universe is the same
(28:28):
going forwards and backwards, if there's a symmetry in time,
then you get conservation of energy. And here's a little
bit trickier to understand the connection between energy and time,
but it's there, and quantum mechanically, I think it's actually
the clearest. We have the Shorting Air equation, which is
what tells us how like a quantum mechanical system changes.
(28:50):
It says, if you have this quantum wave function, now
what quantum wave function will you have in the future.
That's the Shorting Air equation and solutions to the Shorting
equation are things that work in the universe, but it
tells us how things move forwards in time. Well, turns
out the Shorting Your equation is just an expression for
the energy of the system. Like if you actually look
(29:11):
at the mathematics of it, it's kinetic energy plus potential energy.
That's just a total energy of the system. And so
if the universe is symmetric in time, then energy is
conserved in your system for served in time. Kind of
like I feel like you're telling me that there's a
symmetry in time means that what I have now she's
gonna be equal to the things that I have later.
(29:33):
So in a way, that sort of translates into you
don't lose or gain energy. It has to kind of
be the same here and after. Yeah, exactly. This is
sort of a conservation there, this conservation of probability. Also
in quantum mechanics, it says that things are transformed and
they slash around, but they don't disappear. And what is
the thing that doesn't disappear. Well, it's the solution to
(29:54):
the Shortinger equation, which is really just the sum of
all the energies in the system. And so in some sense,
it's sort of like asking what is energy. Well, energy
is the thing that's conserved if you have time symmetry
in your system. And it's something we just sort of noticed.
We're like, well, you add all these things up kinetic
(30:14):
energy and potential energy here, and you add it up later,
we notice we get the same answer. And that's something
we've noticed because we've mostly been doing experiments in systems
where time doesn't matter. Where if you do the experiment
now or a hundred days or in a thousand years,
you get the same answer. So whenever time is symmetric,
and it has basically always been for our experiments, then
(30:34):
energy is conserved. So I feel like you're saying that
energy is just an illusion of times, and yes, exactly,
that's the message, is that energy is connected to time.
And we know that already from quantum mechanics. Right. We
know quantum mechanics tells us you can't measure the position
and momentum of a particle at the same time. Those
two concepts are connected, right, And it also connects energy
(30:55):
and time, and it's for the same fundamental reason that
there's a connection between those two basic quantities. They're really
two sides of the same thing. One symmetry leads to
a conservation law. All right, I feel like we're set
up now to break the conservation of energy and talk
about why that's really true and what it means. But
now it's time for us to take another quick break.
(31:29):
All right, Dan, we're talking about the conservation of energy,
and it turns out that energy is not always conserved,
which blows my mind. You're telling me it has something
to do with the symmetry of times. If time is symmetric,
then energy is conserved. And so I'm guessing what you're
gonna say now is that time is not always symmetric,
and it's actually a little bit larger than that. It's spacetime.
(31:50):
If the universe in which you're doing your experiment is fixed,
if spacetime is fixed, it's not changing, then yes, energy
is conserved. And so if spacetime is flat and it's
not changed, you can do your experiments. You can fuel
your car, you can drain your battery, you can collide particles,
you can do chemistry, and energy will be conserved. But
as soon as you break the symmetry of spacetime, as
(32:11):
soon as spacetime is changing, right, the shape of space
and the shape of the universe. As soon as that
is changing, energy is no longer guaranteed to be conserved
because it only was conserved because space time was not changing.
Oh I see, So maybe to match up our intuitions
to this new idea, we have to maybe expand our
idea of conservation of energy. Like maybe it's not a
(32:33):
conservation of energy for a closed system. It's like we
have to think about conservation of energy being true for
like the same spacetime or a static spacetime. But if
you change that, if you change spacetime, then you can't
say that energy is conserved anymore. Exactly. We have to
add a qualifier. We say energy is only conserved when
(32:54):
time symmetry is respected, which happens when space time is
not changing. But you know, we live in a universe
where spacetime is changing. The expansion of the universe is
not just things moving through space. It's the stretching of
space itself. It's the creation of new space. So we
live in dynamic space time, which means energy fundamentally is
(33:16):
not conserved. It means that energy is not the deep,
true quantity that we thought it was. It means it's
not the important thing to be thinking about. So it's
expansion of space that destroys the conservation of energy. Or
is it the expansion of space time? Are you do?
You use it as the same shorthand? Yeah, Well we're
talking about the expansion of space time, right, or the
expansion of space through time. You can think about it
(33:38):
like that because the space in which we're doing our
experiments is changing as a function of time. And remember,
to have conservation of energy, you need to have symmetry
and time. But the universe is not the same today
as it was a thousand or a billion years ago.
It's a different universe. It's expanded. The space in which
we're doing our experiments is different, and so it changes
(34:00):
the results of the experiments. And it means energy is
not conserved from one moment of space to another moment
of space. And that would also work here at the
local level too, right Like, if I had a canister
of gas and I expanded the space time it was in,
I would see energy not conserved. That's true. You would
(34:20):
create more dark energy because you've expanded space and every
new unit of space has dark energy in it. So yeah,
you would have created more energy whether or not there
was a canister of gas there. And the thing for
people to understand is remember the expansion of the universe
seems dramatic. The universe is big, it's expanding super fast,
but locally it's not very quick, Like the expansion of
(34:41):
space is not something you notice day to day, and
it's actually pretty weak. It's pretty small quantity in a
small piece of space. It only adds up to be
most of the universe because the universe is already so big.
There's so much empty space out there that if you
add up all the dark energy becomes a huge number.
So this violation of energy something that's very, very small.
(35:02):
It's very hard to notice because the expansion of space
is a very gradual, tiny effect. I see, it's conserved mostly,
but if you think about the whole universe, it's not
actually insignificant. Yeah, exactly, it's a small violation, and an
individual unit of space added up over the whole universe
becomes kind of a big deal. But for me, it's
not as much about like the size and the number
(35:24):
as the fact of it, Like, whoa this thing we
thought was a deep truth in the universe turns out
to be a coincidence or just a product of where
we happen to be. You know. It's like if you
grow up eating toast for breakfast and they butter it
on the top side, you think, well, toast has to
be buttered on the top side, and then you go
visit your friend you discover what they eat butter on
the bottom side of their toast. That's even possible. It
(35:45):
opens your mind a whole new way of thinking about
the universe. And that's what this does. It says energy
is not the important thing. Right. Energy is something we
thought was deep and fundamental, but it's actually important to
cosmologists are things like curvature and expansion. Those are the
fundamentally interesting things about the universe, not the energy. I
guess maybe what would trip people up is thinking about
(36:07):
where that energy comes from, right, I mean that's sort
of the origin of the original question. If the universe
is expanding and there's more energy being created, where does
it come from? Are you saying that energy can just
be created out of the blue. Yes, that's exactly what
we're saying, is that we've discovered that it doesn't have
to come from anywhere. That's sort of the wrong question.
It's like asking where does the value come from when
(36:30):
Picasso paints a new painting, Right, it didn't come from anywhere.
It wasn't and now it is. It only has to
come from somewhere if it's conserved, and there are things
that are universe that are conserved, like electric charge. Right,
you can't just create an electron because it's charged, has
to come from somewhere, has to come from previously charged particles.
(36:51):
Or you can start with a photon and create an
electron but then you have to create an anti electron also,
so you have balance of charge. There are things that
are fundamental that have to be conserved to have to
come from somewhere, but energy is not one of them.
It should be like demoted from that list of like
super important fundamental conserved quantities because it's just sort of
like an accident of where we live that we never
(37:13):
noticed that's not actually conserved. Man, first you demote pluto,
and now you're demoting energy. Who's the next matter? That's right,
We are pulling back the veil. Man. We are discovering
new deep truths. Matter that was like a hundred years
ago demoted matter the same matter doesn't matter. Matter, it
doesn't matter. And you know, I think it must have
been equally bewildering a hundred years ago to think what
(37:35):
you can create matter? Do you think you're some sort
of divine being? Right? Matter is you can't where did
it come from? When you make new matter, and it
doesn't have to come from anywhere. It's transformed from energy.
But the matter itself didn't exist, and matter can disappear,
It can exist and then just not exist anymore. It
doesn't have to be conserved all right, Well, it sort
(37:56):
of blows my mind. But it turns out that this
is actually a little bit controversial in physics, Like not
everyone agrees with this conclusion that energy is not conserved.
Is that right? Yeah, that's right. There are some folks
who find this very uncomfortable and they don't like this idea,
so they try to patch up energy and say, well,
let's think about energy in a slightly different way so
that it is concerned, and that's totally valid. It's like, well,
(38:19):
let's find a different symmetry or a different thing, you know,
energy prime or energy two point oh, so that it
actually is conserved, because maybe that will give you some
deep insight into the universe. And the way they do
this is a little bit controversial. I would say like
three out of four cosmologists and dentists I asked would
say that energy is not conserved. But there's some people
out there that try to patch it up by folding
(38:41):
this energy back into the gravitational field. Meaning like maybe
they think that maybe you're just doing the accounting wrong.
They might say that a costs of paintings are conserved
in value, is just that you know, you're accounting for
people's happiness when they purchase a costs or something like that,
right exactly. And they say, there's another category of energy
(39:03):
that we're not accounting for, and that's the gravitational energy,
and that as the universe expands, it actually gets more
and more negative gravitational energy. That the expansion of the
universe creates negative energy in the gravitational field that offsets
the positive energy from dark matter. And they do some
calculations and show that boom, it all adds up to zero,
(39:23):
and so energy is actually conserved. According to these folks,
is it kind of like the photon that loses energy
Like when you grow space you're pulling things apart, which
means you're losing gravitational energy, right, or you're gaining you're
losing you're gaining when when you're pulling things apart, it
takes energy to separate objects, right, So that's negative work
(39:45):
and so you're losing energy. You're creating a negative energy
situation in the gravitational field. But there's a problem with
this and the other folks on the other side of
the divide that say the energy is not conserved, they
quibble with the way this calculation is done, and they
think it's not actually technically correct that you can't actually
just measure the energy of a gravitational field, because gravity
(40:07):
is a really complicated thing. It's not just like, here's
a fixed gravitational potential and you can measure the energy. Remember,
gravity is dynamical, it's responding to space, it's shifting, it's changing.
And so, for reasons that I think are a little
too technical to dive into, there's not really a good,
well defined way to calculate the gravitational energy of the
whole universe, or even the gravitational energy more importantly of
(40:29):
a part of the universe, the gravitational density. So they
say that doesn't really count. You can't include it in
the calculation. Energy is not concerned. So it's still in progress.
People are still talking about it. People are still talking
about it, but I think the consensus is energy is
not conserved, despite these efforts to try to patch it
up and fix it and to say that there's a
way to look at energy such that it is concerned.
(40:52):
And then what do the dentist thing that if you
maybe do a root canal, you consider bypass s base.
They think we shouldn't eating fruit loops late at night
you should be flossing more often. You'd be flossing your
theory is more often because you know you can get
gun accumulating. But to me, I think it's fascinating. It's
a great investigation into like what's real about the universe,
(41:13):
what's deep, what's true. The reason that we try to
identify conservation laws is not just because we need a
better energy policy, but because we're trying to understand the
way the universe works, and finding these things that are
conserved or turns out to be not conserved are ways
that we get clues as to the way the whole
machinery works deep down. Yeah, I think what I'm getting
is that physics is maybe as fickle and sensical as
(41:36):
the art world. I think is what you're saying, and dentistry.
Your theory is genius, it's fundamental. Actually, no, it turns
out it's worth nothing. It's like cubism itself, makes no sense.
That's right, But there's a real beauty here to this inside,
this connection between symmetries and conservation laws, and it tells
(41:57):
you that every time you find something symmetric about the universe,
there's something out there being conserved. And that's really cool
and beautiful to me. Well, I think the takeaway is
that we can say that energy is conserved in space time,
but that spacetime itself is not always conserved. Yeah, if
spacetime is fixed, then energy is definitely conserved. In a
(42:17):
situation any universe like ours, where spacetime is expanding, then
there's no guarantee of energy conservation. Energy actually increases as
space time increases, and it doesn't come from anywhere, which
is hard to grapple with, but it is our reality.
And that's the job of physics is confronting us with
hard to understand truths, things that don't make sense to
(42:37):
our intuition, but that we figured out through science. Right,
that's why we have science and not just intuition, to
confront us with these things which are in conflict with
what we thought but turned out to be actually true.
All right, done, I won't walk away from the interview.
I'm staying. I'm staying for the rest of it, which
is about ten seconds. All right, Well, I conserved some
(42:59):
energy for this last bit. Well, we hope everyone enjoyed. Dad,
Thanks for joining us, and think a little bit more
about what do you think is true about the universe
and what might be an idea that Daniel and his
dentists wrong in the future, hopefully everything. Thanks for joining us,
see you next time. Thanks for listening, and remember that
(43:25):
Daniel and Jorge explain the universe is a production of
I Heart Radio. Or more podcast from my heart Radio
visit the I heart Radio app, Apple Podcasts, or wherever
you listen to your favorite shows.
Hosts And Creators
Daniel Whiteson
Kelly Weinersmith
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