Does quantum mechanics conserve energy?

Daniel and Jorge explore whether basic rules of our Universe are broken at the quantum scale.

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Episode Transcript

Speaker 1 (00:08):
Hey, Jorge, are you worried about energy conservation?

Speaker 2 (00:12):
Uh?

Speaker 3 (00:13):
Not worried, but I try to do as much of
it as possible.

Speaker 4 (00:16):
Oh.

Speaker 1 (00:16):
Is that because you're very environmentally responsible?

Speaker 3 (00:19):
Nuts? Because I try to do this little exercise as possible.

Speaker 1 (00:23):
You're such an adult.

Speaker 3 (00:25):
Hey, I'm doing it for the planet, not just for me.

Speaker 1 (00:28):
Well on behalf of planet Earth. We're all very grateful
for your lazy attitude.

Speaker 3 (00:32):
Oh thanks. My body is also very grateful, although maybe
not in the long term. Hi am Jorgem, a cartoonist

(00:53):
and the author of Oliver's Great Big Universe.

Speaker 1 (00:56):
Hi. I'm Daniel. I'm a high energy particle physicist, but
I don't often feel very high energy or high. There
were times in my life when that was more true.

Speaker 3 (01:07):
Than Yeah, I seem to remember those times. Yeah. But
isn't it high a relative term at least in physics?
Like how high is high energy? Can't you always go
higher in energy?

Speaker 1 (01:18):
You can always go higher in energy? And what people
called high energy fifty years ago we now call nuclear physics.
So it doesn't even qualify what it's not low energy,
It doesn't even qualify as low energy physics.

Speaker 3 (01:32):
I guess nobody wants to be called a low energy physicist.

Speaker 1 (01:36):
Yeah, would you want to be called a low energy cartoonist?

Speaker 3 (01:40):
Well, I am, and if you call me that it
would be accurate. But I guess you can call me that,
why not?

Speaker 1 (01:47):
Yeah? Sure? Well, high energy really means highest energy. And
as we keep pushing the boundaries of what we can achieve,
then yesterday's high energy collider is today's nuclear physics.

Speaker 3 (01:59):
Mm sounds like a good slogan for the LGC. Yesterday's
high energies now today's nuclear energy. But anyways, welcome to
our podcast Daniel and Jorge Explain the Universe, a production
of iHeartRadio.

Speaker 1 (02:10):
In which we use all of our energy to help
you understand the nature of the universe. We tear things apart,
we peer inside. We try to understand at a microscopic level,
how does everything work? Is there a story we can
tell about what's happening to the littlest bits in the
universe and how it comes together to explain our reality?

Speaker 3 (02:30):
That's right. We like to explore the high energies, the
low energies, and all the energies in between that there
are in this universe to discover, to explore, to learn about,
and to blow your mind with.

Speaker 1 (02:40):
And energy is a really central concept in physics and
in people's understanding of physics. We'd like to think about
things in terms of energy, little quantum fields vibrating with energy,
energy being passed between particles, energy used to create particles.
In some sense, physics is a study.

Speaker 3 (02:58):
Of energy, and one that requires some amount of energy
to explore, right, I mean, you can't just do physics
from your couch.

Speaker 5 (03:04):
Can you.

Speaker 1 (03:06):
I don't know if it takes more energy to do
physics or cartooning, but you can sort of lie in
your couch and just think about the universe, you know,
the way the great theorists and the Greeks have done.
But absolutely to do experiments to explore the universe, to
investigate it deeply, you need to poke it, you need
to probe it, you need to interact with it, and
that does take some energy.

Speaker 3 (03:27):
Well, I feel like energy is kind of a topic,
that it's a word you learn as a kid, and
that everybody has heard of this word and we all
use it every day in our everyday lies. But to
actually define energy is kind of tricky, isn't it, Not
just from a physics point of view, but also if
you ask somebody what energy is, You don't get an
easy answer.

Speaker 1 (03:46):
Yeah, energy is a very loaded term, right. We have
a sense of like feeling like you have low energy
in the morning, or running out of energy to do
some chores or something. But it's one of these words
that physics has redefined to have a specific meaning, a
very crisp idea for what energy means. The way we
also have like meanings for force and work and other

(04:06):
words that we also use in everyday English without as
precise definitions.

Speaker 3 (04:11):
Right, But even those the simple terms have been changing
in physics over time, right, Like the word the idea
for force has changed with quantum mechanics. Isn't it Like
it used to be an invisible force that we feel
towards the Earth or the sun, But now they're talking
that maybe it's like a particle or something, it's an
exchange of particles.

Speaker 1 (04:27):
Yeah, the mechanism that explains it is definitely different. I
think the concept of force is a change in momentum
of something. Something in exchange of momentum essentially has been
pretty constant since Newton. Yeah, these things definitely can change.
And you know, for example, we've redefined gravity to not
even be a force, So what gets counted as a
force and what doesn't and how that all works definitely changes.

(04:49):
And we like to dig into these basic principles and say, like,
what does this really mean? Where does it come from?
Did the universe have to me this way? Is energy
essential to the universe? And one of the ways that
we do that is by noticing what the universe respects,
like what doesn't change in the universe, what's constant, what's conserved.
That gives you a clue about sort of what's important
to the underlying machinery of the universe.

Speaker 3 (05:11):
Right, you kind of want to know what the rules
of the universe are, or what the principles of the
universe are by which it lets things happen in it,
right exactly.

Speaker 1 (05:20):
And one of the deepest rules that people imagine in
the universe follows is conservation of energy. That energy is
somehow immutable, that it can slosh between different kinds of
energy kinetic to potential, to mass, to velocity to whatever.
But the energy has to go somewhere and has to
come from somewhere. That it's a basic component of the

(05:41):
universe itself.

Speaker 3 (05:43):
Yeah, it's a very fundamental rule that people seem to
learn about even in high school physics. But is it
actually true? Does it always happen in this universe or
does it get broken at some levels, like the quantum levels.
And so to the end the podcast, we'll be asking
the question does quantum mechanics conserve energy? Now, when you

(06:09):
say quantum mechanics, do you mean like the field or
the people who study quantum mechanics.

Speaker 1 (06:16):
The mechanics of quantum physics.

Speaker 3 (06:18):
Can you be a quantum mechanic like a car mechanic,
but at the quantum level.

Speaker 1 (06:23):
Yeah, bring your fields in. They need some new parts.
We'll order them.

Speaker 3 (06:26):
That's right, Your quantum carburetor needs to be swapped out, exactly.

Speaker 1 (06:31):
No, in this case, we're talking about the rules of
the smallest bits in the universe, the tiniest little things,
the electrons, the positrons of photons, all the smallest stuff
in the universe seems to operate on different rules than
the bigger stuff in the universe baseballs and basketballs and
rocks and stuff that we're familiar with. And so while
we're taught that energy is concerned very generally, we're interested

(06:53):
in whether that's always true, and whether it's true at
the smallest scale.

Speaker 3 (06:57):
Yeah, so this is a big question. Does quantum mechanics
conserve energy? And so, as usually, we were wondering how
many people out there had thought about this question, whether
this is a rule that can be broken at the
quantum level, or whether the whole universe follows it.

Speaker 1 (07:10):
Thanks very much to everybody who answers these questions. If
you would like to receive a regular dose of tough
physics questions in your inbox, right to me too, questions
at Danielandhorge dot com, and I will send them to you.

Speaker 3 (07:23):
Well, regular dose. Now do these doses make you high
in physics?

Speaker 1 (07:29):
These are microdoses, so yeah.

Speaker 3 (07:30):
Oh, I see right, it's more of a low key high.

Speaker 1 (07:34):
They're not supposed to blow your mind. They're just supposed
to color your experience of the universe a little bit.

Speaker 3 (07:39):
I see. It's more of a nuclear.

Speaker 1 (07:41):
Hit exactly, It's not a high energy dose.

Speaker 3 (07:46):
Well, think about it for a second. Do you think
quantum mechanics conserves energy? Here's what people have to say.

Speaker 5 (07:53):
I think so, or at least the rate of decay
is so minute that we are not currently able to
detect it on a cosmological scale.

Speaker 6 (08:06):
I think quantum mechanics conserves energy. I feel like it
would be big news if we found the law of
conservation of energies to be violated, though maybe it has
been and I just haven't seen that news. But the
notion of quantum fluctuations seems like it would violate that law.
Though I don't really understand quantum fluctuations.

Speaker 2 (08:22):
I'm assuming it doesn't just because I remember listening to
your podcast on how energy actually isn't conserved in the universe.
So I'm assuming that quantum mechanics follows that as well,
But I don't actually know.

Speaker 4 (08:33):
I'm not sure about this question. And like conserve in
what like in your book frequently asked questions about the universe,
you did say like there was like a quantum foam,
and like when the universe is expanding, it's just connecting
to more quantum particles, I guess. So I'm going to say,

(08:58):
I don't know, because if you mean in the universe,
like not the growing section, then no. But if we
even include all the other disconnected quantum phone then I'm
not sure.

Speaker 3 (09:13):
All right. People are on the fence about this. Some
people say it does, some people say they don't think so. Well,
they're not sure.

Speaker 1 (09:19):
Yeah, I was really surprised by this. I was expecting
people to rush to the defense of conservation of energy
and say it's a fundamental law of the universe.

Speaker 3 (09:27):
Maybe it's because we've had whole episodes where we say
that the energy is not conserving the universe that maybe
influence the answers here.

Speaker 1 (09:36):
Oh my gosh, people actually listening and absorbing the content.

Speaker 3 (09:40):
Amazing, amazing, they're learning. Well, it's great that they are
listening to us. And because we have talked about this
idea of conservation of energy in the universe, and we've
talked about how it's not actually conserved in the universe
as a whole.

Speaker 1 (09:52):
Right, that's right, And that was in the context of
sort of general relativity, thinking about the universe as it
expands and as space is changing, how we define energy
in that context, and that sort of blows a lot
of people's minds to understand that energy might not be
conserved in the universe at the biggest scales, you know,
when you zoom all the way out and think about

(10:12):
how the universe is expanding and what happens to stuff
inside of it.

Speaker 3 (10:16):
Right, Because in the other episode we talked about how
the universe is expanding due to dark energy, and basically
like there's more space being created all the time out
of nothing, which means that energy sort of being added
to the universe, created in the universe out of nothing.

Speaker 1 (10:31):
Right, Yeah, that's right, and you're coming out of nothing,
I think says a lot. You know, it implies that
energy needs to come from somewhere, and so when you
say energy is created, you have to give some explanation
for where it comes from, even if you're saying out
of nothing. But this tells us that energy isn't something
fundamental to the universe. That it can go up and
it can go down, like lots of things in the universe,

(10:51):
like the number of people in swimming pools is not
a constant number of the universe. It can go up
and it can go down.

Speaker 3 (10:56):
How do you know? Are you sure the.

Speaker 1 (11:00):
Middle of an extensive worldwide experiment to measure the number
of people.

Speaker 3 (11:04):
At any moment? Yes, Oh, you thought you were going to.

Speaker 1 (11:07):
Challenge me on that and call me out, But actually
I've been doing this in preparation for five years just
to make that casual comment.

Speaker 3 (11:13):
You know, somehow I don't believe you any.

Speaker 1 (11:16):
Away from my paper in nature. Okay, it's coming out soon,
I promise.

Speaker 3 (11:20):
Sure. Let's see the draft. Read me a poll paragraph
from the draft right now.

Speaker 1 (11:25):
Oh, I can't disembargo it because it's too high profile.

Speaker 3 (11:29):
I see.

Speaker 1 (11:30):
I signed an NBA. What am I gonna do? No,
obviously I have not done that experiment.

Speaker 3 (11:34):
A nuclear disclosure agreement, which means it's really low.

Speaker 1 (11:38):
But clearly there are things in the universe that do change,
things that are not fundamental to the universe, while there
are other things that are fundamental, like momentum. We think
momentum is conserved in the universe, and that comes from
a really deep symmetry about space and time that the
experiments you do anywhere in the universe should give you
the same answer. That doesn't matter where you put your

(11:58):
origin in space. Rules of physics don't care, and that
gives you directly as a consequence of Nuther's theorem, momentum conservation.
But energy is not in that same category, and energy
can go down and it can go up, like when
the universe expands, you get in new space, and that
space comes with energy, but also energy gets decreased because
as space expands, it reddens the wavelengths of all the

(12:20):
photons inside of it. Take for example, the cosmic microwave
background radiation from the early universe. When it was created,
it was very high energy. That plasma was super dup
or hot. It was thousands of degrees kelvin. But it's
been stretched out by the expansion of the universe to
very long wavelengths, and now it's at like three degrees kelvin.
Where do that energy go? Didn't go anywhere, it's just gone.

Speaker 3 (12:42):
Well, it's not gone, it's just gonna spread out, is it.

Speaker 1 (12:44):
No, there's less energy in those photons. Those photons have
gone from high energy to low.

Speaker 3 (12:49):
Energy because they got stretched out.

Speaker 1 (12:51):
But the total energy is also different. It's not just
the energy density.

Speaker 3 (12:55):
But they're longer now, that's what those are longer. Yeah,
isn't where the energy went.

Speaker 1 (13:01):
The energy of those photons is less. They're also longer,
but the energy of those photons is less. If you
stretch space, the photons get redder, which means they have
less energy.

Speaker 3 (13:09):
Well, I guess this is what I mean. Because the
idea of energy, the concept of energy can really vary
into a lot of these arguments about whether it can
can be conserved or not. I feel like maybe they
depend on a good definition of energy, and so maybe
for folks we should talk about what energy actually is,
how to physicists define it.

Speaker 1 (13:26):
Yeah, I wish I knew what energy was.

Speaker 3 (13:29):
Wait, what.

Speaker 1 (13:32):
Energy is a really slippery topic. It's something we've been
struggling with over the last few decades to really define.
We have some very crisp but unsatisfying definitions of energy.
You know, in some cases you can say energy is
the thing that's conserved over time, you know, so you
can define it to be something that's conserved. Really, I
think a better way to define energy is to talk
about like the forms it can take. You know, like

(13:54):
there's kinetic energy, which means energy of motion. Something is
moving that has energy. There's potential energy, this energy of configuration.
Like a book is sitting on the shelf, there's energy
stored in that. You know, it takes energy to put
the book on the shelf. Mass, for example, is a
representation of internal stored energy. Put a bunch of photons
into a box, they have energy. That box now has

(14:16):
more mass. All these are different ways you can calculate energy,
and if you add them all up, you get the
total energy. And so that's sort of how we define energy,
but you know it's a little hand wavy.

Speaker 3 (14:26):
Wait wait, wait, So I was right earlier when I
said that I don't really know what energy kind of is,
but you made it seem like we did know.

Speaker 1 (14:32):
We don't really know what energy is in the broadest sense,
but we can define something and say this is what
we call energy. I don't know if it really captures
our full experience of energy, but yeah, we can write
down a formula for what energy is.

Speaker 3 (14:45):
But I guess the question is what did those things
have in common? And why do you use the same
word for all of them? The kinetic energy, potential energy,
you know, energy of mass. Why do you use the
same word for all of those things?

Speaker 1 (14:57):
Yeah, great question, And the reason is that in classical
mechare at least, you know, things moving around at our
scale at or fairly low speeds. We notice that they
can turn back and forth into each other. Like you
take that book on the shelf. It has potential energy
and no kinetic energy. You push it off the shelf.
Now it's speeding up towards the ground. It's losing potential
energy and gaining kinetic energy. So we notice that these

(15:17):
things can turn into each other, and therefore we group
them together into one big category. And we notice that,
at least in classical mechanics, the total the sum of
them all does stay constant. So like if you're add
of all the potential energy and all the kinetic energy
at one moment, and you do it again later, you
find you get the same answer.

Speaker 3 (15:36):
And how does that relate to the energy of a
photocon which you mentioned earlier.

Speaker 1 (15:40):
So now we're departing classical mechanics a little bit. We're
talking about a quantum object, but we can still think
about the energy of a photon. A photon has kinetic
energy because it's in motion, it's always in motion. It
has only kinetic energy. So photons definitely have energy.

Speaker 3 (15:55):
Well, it seems like maybe the common factor is the
idea of motion, like things moving have energy to them,
and things that can move in the future or can
cost things to move, or like the potential to cost
something to move, is what maybe you would call energy.

Speaker 1 (16:09):
Maybe I think that puts kinetic energy in a more
primary position than potential energy, which I'm not sure is justified.
I think there really are at its core two different
kinds of energy. There stored energy potential energy and kinetic energy.
I'm not sure which one would be more fundamental.

Speaker 3 (16:24):
And so are those the only two kinds of energy?
So you have in classical physics kinetic and potential.

Speaker 1 (16:30):
Yeah, those are the two forms. People might think, what
about mass? What is mass? Is that kinetic energy or
potential energy? It's sort of a special case. It's just
sort of a label we give some kinds of energy
if they're stored internally, Like if you have gluons inside
of proton, they have a bunch of kinetic energy they're
zooming around. They also have potential energy of their bonds.
All that energy is inside the proton, so we call

(16:52):
that mass. So mass is sort of a label we
give to some energy, but it's not on the same
level as like kinetic and potential it's not its own
kind of energy.

Speaker 3 (17:01):
So then if an eight year old asked you, hey,
doctor Whitson, what is energy? What would you answer?

Speaker 1 (17:07):
I would say, I've had this nightmare scenario many times
and I have no idea how to respond.

Speaker 3 (17:12):
You would spring in their face, Ah, run away, No, seriously, like,
what would you say, you have to say something? What
would you say, I'll get you started. It's a quantity that.

Speaker 1 (17:27):
I'd say, energy is something that makes things move, but
it's also something you can store. That's my best shot.

Speaker 3 (17:34):
It's almost like a liquid or something.

Speaker 1 (17:36):
You know, for a long time people did imagine that
energy in the form of heat was a liquid that
flowed between things. But it's not a physical quantity in itself.
It's a description of the physical state of other quantities.
Like a liquid can have energy, but so can solids.
It's not like when energy flows from one thing to another,
there's some physical substance that moves between it. It changes

(17:58):
the state of those objects.

Speaker 3 (18:00):
Well, I guess I'm a little surprised you're having so
much trouble just defining energy, which is pretty interesting. But
as you said, I think one thing that we do
sort of know about it is that in some cases
it's conserved and maybe in some cases it's not.

Speaker 1 (18:13):
So.

Speaker 3 (18:13):
Well, let's dig into the question and when it's conserved,
is it conserved at the quantum level or is it not.
So let's dig into that, But first let's take a
quick break. All right, we are mustering up the energy

(18:37):
to talk about something that apparently physicists can't define energy,
such a basic word that even little kids use, everyone
uses their in their daily lives. But it seems Daniel,
that it's something physicists can't really define very well. Maybe
only mathematically you can define it. Is that kind of
the case.

Speaker 1 (18:56):
Yeah, And as you'll see, when we get into the
quantum system, this is going to be even trickier. And
physicists disagree about how to define energy and whether we
can even define it in terms of quantum systems.

Speaker 3 (19:08):
Well, it seems like we don't even need to get
through you already don't know how to define it exactly.

Speaker 1 (19:12):
And that's why I want to be upfront about how
complicated and confusing this topic is, even in the easy case,
because when we get to the hard case, it's going
to get even trickier. So I did my best to
give you like my understanding of energy, but if you
look at the official definition of energy, I find it's
even less satisfying. Like if you just google energy and
you ask Wikipedia or chat GPT, like, what is energy?

Speaker 3 (19:34):
Well, it's you know, legit sources.

Speaker 1 (19:36):
Legit sources. They say energy is the quantitative property that
is transferred to a body, and that doesn't really even
tell you what it is. It's like Okay, well, it
can move from one thing to another, but what is it? Man,
it doesn't really answer that question.

Speaker 3 (19:50):
Well, that's kind of what I meant before, is that
it's a quantity. Is basically kind of the only way
you physicists know how to define it, right, it's a
it's a quantity. It's something that can measure, that can
be a lot or a little, which you seem to
be able to measure about things, and that sometimes seems
to be conserved.

Speaker 1 (20:09):
So mathematically, we can write down a formula that defines it,
and then it's defined in terms of things we can
measure like velocity and position and stuff like this. And
it turns out that if you write it in certain ways,
then that number doesn't change. The internal values can slash
back and forth, but the total doesn't change. That's sort
of like the crispest most mathematical definition. But I think

(20:30):
what we're proving forward is like what does it mean philosophically?
Like what are the implications of that? And that's much trickier.

Speaker 3 (20:36):
Well, you seem to not want to give primacy to
kinetic energy, but in a way, that's kind of like
our most direct experience of energy, which is motion, right,
Like if something has a lot of energy to either
moving fast, or it's hot or it's exploding. For us,
in our experience of the universe, energy is basically things
moving fast or things that can make things move fast.

Speaker 1 (20:57):
Yeah, if you're talking about the experience of it, then
you more directly experience motion than stored energy. It's energy
you don't really experience when it's stored because it's just
being stored. It's when it's transformed into kinetic energy that
you're experiencing it. Like if you zap yourself on a battery,
it's the motion of those electrons being transformed from the
potential into their kinetic energy that's zapping you.

Speaker 3 (21:19):
All right. So then you said that sometimes it's conserved
and sometimes it's not. So when is energy conserved in
a classical way?

Speaker 1 (21:27):
In classical sense, energy is only conserved when space time
is not curved and when space time is not changing.
So if space time is fixed, like you have flat
space time, meaning you shoot two photons and they stay
parallel to each other, then you can expect energy to
be conserved. But if that space is changing, like it's
expanding the way our universe is, then the general relativity,

(21:49):
energy is not conserved. Even more generally, anytime you have
curved space in general relativity, you do not have conservation
of energy. So, for example, black holes colliding do not
conserve energy.

Speaker 3 (22:01):
Wait, what what do you mean.

Speaker 1 (22:02):
When two black holes collide? You have the collision of
two curved bits of space, and what comes out of
that is not the sum of what goes into that.
You're not guaranteed that in general relativity.

Speaker 3 (22:11):
But is in space always curved like uncurving space around me,
and yet I don't seem to have infinite energy.

Speaker 1 (22:18):
That's right, you do not have infinite energy and you
are curving space around you. But the total amount of
energy in the system changes in time in general relativity,
and it gets really fuzzy and weird because general relativity
is really hard to think about in some reference frames.
According to generalativity, energy is conserved in others, it's not.
Depends sort of on how you're looking at things.

Speaker 3 (22:37):
Okay, it sort of sounds like you're saying like, if
you don't think about general relativity, then you can assume
that energy is being conserved. If you assume that there's
general relativity and things are being space is being bent
like around black holes or the expansion of the universe.
Then you can't assume that energy is being conserved.

Speaker 1 (22:54):
As long as we're above the quantum level.

Speaker 3 (22:56):
Right, So it's mostly like whether or not you ignore
the bunding of space exactly.

Speaker 1 (23:00):
If you can ignore the bending or expansion of space time,
then classically you can think of energy as conserved.

Speaker 3 (23:06):
Right. And so we talked about that the universe is
expanding and so therefore energy is not being concernedd and
we talked about two black holes colliding. Energy is not
being conserved there So now the question of the episode
is when you get down to the quantum level, is
energy still conserved even though maybe there's no space time
bending at the quantum level. If you assume there's no
bending at the quantum level, does energy get conserved.

Speaker 1 (23:30):
Yeah, And we have to assume there's no space time
bending at the quantum level because we don't know how
to do quantum mechanics when space is curved and you
have gravity, and gravity for particles is something we don't understand.
So let's assume space is totally flat and we have objects,
you know, like baseballs and rocks for which we think
energy is conserved and then zoomed down to the quantum
level and try to understand when you have photons and

(23:52):
electrons instead of rocks and baseballs, is energy still conserved?
And really the deep question is like, is energy conservation
something that's through in through the universe at every scale
or is this something that emerges only at the scale
we experience it out of something that operates totally differently,
because remember, quantum mechanics breaks all the rules of classical physics.
It says things don't actually have well defined positions and locations,

(24:14):
and lots of the things that emerge at our level
are not true at the quantum level. So it's not
guaranteed that everything about our experience will be translated down
to the quantum level.

Speaker 3 (24:23):
All right, So then let's answer the question, does quantum
mechanics can serve energy or not?

Speaker 1 (24:27):
So the short answer is we don't know.

Speaker 3 (24:29):
Surprise, surprise, But let's talk about it anyways.

Speaker 1 (24:32):
The slightly less short answer is it depends on what
you think is happening at the quantum level, mostly about
what happens when you try to measure energy.

Speaker 3 (24:40):
What do you mean? So I guess, because it's quantum mechanics,
you have to measure things. That's very importing quantum mechanics.
So you're saying, we have to answer this question with
this idea in mind.

Speaker 1 (24:50):
Yeah, exactly. So let's start off the easy case without
measurements and have a picture in our minds or what's happening.
You know, quantum mechanics tells us that there are probabilities
for various things to happen, and we can calculate those
probabilities using the rules of quantum mechanics, and those probabilities propagate.
You have two electrons heading towards each other, they might
scatter off each other and go that way, they might

(25:11):
pass right through each other. All those probabilities are sort
of live until somebody actually asks the question and makes
a measurement using a classical object and you know, tries
to take a picture of it. Until then sort of
have all the possibilities live. So that's quantum mechanics without measurement.
You know, that's what we're imagining is happening when we're
not looking. And in that scenario we can ask, well,

(25:34):
is energy conserved? Like when all those probabilities are slashing around,
the electrons are maybe bouncing off each other and maybe
not is energy conserved there? And already we kind of
run into trouble because we don't really know how to
define energy here. Like, what if you have a quantum
system and has a few different possible states, a low

(25:54):
energy state and a high energy state. How do you
define the energy of it? Is it like the way
average of the probabilities of the various states? Is it
something else. I've had conversations with a bunch of physicists
this week to try to sort out what people think
energy is, and some people say, you can't define energy
in that context, and other people say, no, it's definitely
the weighted average of the various probabilities.

Speaker 3 (26:16):
Right, I think, meaning maybe for people who are not
super familiar with quantum mechanics. So in quantum mechanics, particles
and things like that aren't just in one state, like
a baseball sitting on your table. It's like it's doing
multiple things at the same time. It's here, it's a
little bit there, it's moving in this direction a little bit,
but it's also has the probability to be moving in
this other direction. And so you're saying that maybe one

(26:37):
way to measure its energy, or to think about its
energy is like, if it has a fifty percent probability
of going this way, then you take that energy and
multiply by a half. And if it has a certain
probility that it's moving this way with that velocity, like
a twenty five percent probability, then you maybe multiply that
energy by a quarter, and then you would add it
all up and maybe that would kind of give you

(26:58):
an average of it energy.

Speaker 1 (27:00):
Yeah, exactly, Like if it has a fifty percent chance
of having twenty five jewels of energy and a fifty
percent chance of having seventy five jewels, then you say, well,
I'm going to average those two. I'm gonna say its
energy is fifty jewels because on average that's what it has.
And here allowing the particle to still have both probabilities
to say, oh, maybe it's in the lower energy state,
maybe it's in the higher energy state.

Speaker 3 (27:20):
Right, it's in a superposition, it's with a life and dead.
Then you said, some of your physicist friends said, you
can't do that, like that's not even that doesn't make sense.

Speaker 1 (27:27):
Yeah, And they say, you can't do that because you
can't measure that, right, you never measure the fifty Like
if you went and asked the question, all right, we
have the particle in this state, go measure the energy.
You're gonna get twenty five or you're gonna get seventy five.
You're never going to get the average. It's like saying
the average number of children in the US is two
point four, but nobody actually has two point four children, right,

(27:48):
and so in the same way, you'll never see this
particle have that energy. So in what sense is that
the energy of the particle? That's sort of the complaint.

Speaker 3 (27:55):
That's kind of a fundamental problem with quantum mechanics. Like
it's you know, the cat is alive and dead. Obviously
the cat can't be alive if you see the cat.
It can't be both. But in a quantum sense, it
is both.

Speaker 1 (28:06):
In a quantum sense, it is both. In quantum sense,
we need a new idea for what these things mean,
Like what does position mean in a quantum sense, Well,
you know, for a particle that you haven't measured, it's
not really well defined. There's only a probability where is
the particle Actually, well, it's not anywhere. Actually, So these
concepts that are so important to us at the macroscopic

(28:26):
scale have to take different meanings. We have to do
this like philosophical extrapolation, and this is a problem with energy.
For example, say we have the particle and has two
different possibilities, the twenty five jewel and the seventy five jewel.
Then you go and you measure and it turns out
it has seventy five jewels. Well, if a minute ago
you said it had fifty jewels because that was the average.
Now you've measured it and you said you have seventy
five jewels. Where did that twenty five jewels come from?

Speaker 3 (28:49):
Right?

Speaker 1 (28:49):
And so boom right there, you have a violation of
conservation of energy. If that's how you define energy before
you measure it.

Speaker 3 (28:56):
Wait, say it again. It is energy suddenly appear.

Speaker 1 (28:59):
So if you start out the particle we were just
talking about, it has a fifty percent chance of having
twenty five jewels and a fifty percent chance of having
seventy five jewels. So we say, okay, we define the
energy of it to be fifty jewels because that's the average.
Now you go and you measure it, and you measure
it to have seventy five jewels for example, Then according
to our definition of energy, it's gone from having fifty
jewels to having seventy five jewels, and so where did

(29:20):
that energy come from?

Speaker 3 (29:22):
It didn't come from anywhere, it just said before it
was a guess about what its energy was. It was
kind of like the expectations of it or the average
of what we think its energy was. But then in
the second instance, is what we measured its energy. So
they shouldn't be a surprise if it's more or less,
should it?

Speaker 1 (29:37):
So you're saying, those are really two different things. One
is an actual energy because you've measured it. The other
is just some estimation of what we might measure, but
not really the energy.

Speaker 3 (29:46):
Well, and it is in the quantum sense right like
it's alive and it's dead before I look at the
cat in the box and then I wanted to open
the box. It's alive with it. It's not like the
cat suddenly came back to life.

Speaker 1 (29:59):
And I think this comes down to a question of
like interpretation, You know, what is really happening there? It
does the particle secretly already have seventy five jewels and
now we're measuring it and discovering it. You know, is
the uncertainty there or reflection of our lack of knowledge
about something that's actually already determined or something that really
isn't determined until we measure it. The particle really is

(30:20):
in a superposition of those two states. If it really
isn't determined until we measure it, then we do have
to kind of ask, like, where does the energy come
from when the universe decides to make that seventy five
jewel particle instead of the twenty five jewel particle.

Speaker 3 (30:32):
Well, I guess in the same way that you can
ask if you find that the cat is alive, how
did the cat come alive? It was if it was
alive and dead before you open the box.

Speaker 1 (30:40):
Right, But the difference between the two states of the
cat doesn't violate the conservation of energy, which we thought
was maybe a fundamental rule in the universe. That violates
the conservation of the number of dead cats, which nobody
really thinks it's a.

Speaker 3 (30:52):
Conservation I hope not well or well, And this says
that we think that it's impossible for a cat to
go from being dead to being alive.

Speaker 1 (30:59):
Right, I think if we're going to make the analogy
to the shorten your cat experiment, and then you want
to ask the question, is the cat alive before it's measured,
And the answer I think a lot of people would
give is it's neither alive nor dead. It has the
probability of being both. And then to extrapolate that philosophically
back to our particle, you'd say, well, the particle doesn't
really have twenty five or seventy five jewels, It just
has a probability of being both. And energy is not

(31:21):
really well defined. So I think one answer there is
to say, well, energy is not really defined without measurements,
so you can't answer this question, and the others to say, no,
that's the definition of energy, and there is violation of
conservation of energy, So you either have to give up
an understanding of what energy means for quantum particles or
you have to give up energy conservation.

Speaker 3 (31:40):
All right, So it seems like the moment you measure
a quantum particle is super important because it's so fuzzy
before you measure it, and it's so crisp after you
measure it, and so you kind of fall into a
trap to try to compare the energy before that moment
and after that moment, you know, you could interpret it
as saying that energy is not conserved or could interpret
it saying, well, you know, there's no definition of energy

(32:04):
before you measure it, and so therefore don't even worry
about energy classivation exactly.

Speaker 1 (32:10):
But there's really important loophole that we're overlooking here, and
that's the measurement itself. Some people argue that energy isn't conserved,
that this extra energy must come from the measurement, that
we're only violating conservation of energy because we're not including
the full system. Right. Energy is only conserved inside a
closed system where you don't have energy transfer anyway. Right,

(32:30):
Like energy is not conserved for a battery. As you
use it, it's energy is decreasing, but if you include
where that energy is going, usually it is concerned. So
some people argue, ah, what about the measurement. In order
to measure something, you have to like poke it, you
have to interact with it. Maybe you're adding that energy
when you're making that measurement and things do balance out
in the end.

Speaker 3 (32:50):
Wait what that was very confusing? Can you give me
an example.

Speaker 1 (32:54):
So let's say you want to measure this particle and
you want to say it doesn't have seventy five jewels
or twenty five jewels, How do you measure things about
a quantum particle, you have to bounce another quantum particle
off of them. So shoot this electron with a photon,
then measure where that photon goes and use that to
detect what the energy of your particle was. Well, now
you're shooting your electron with a photon, which is going
to change its energy. And so people argue, when you're

(33:17):
doing this, the energy that gives that electron seventy five
jewels comes from that photon somehow.

Speaker 3 (33:22):
But then wouldn't you measure that the overall energy went
down because you would measure the photon after it hits
the electron, and you would see that it was had
less energy exactly.

Speaker 1 (33:32):
So this is the game people try to play in
order to recover conservation of energy for quantum mechanics. They say,
this argument is flawed because you're not taking into account
the energy of the measurement. So there's a whole cottage
industry and a bunch of paper. It's recently about whether
it's possible to recover it using the measurement or whether
that's a red herring.

Speaker 3 (33:48):
Well, the whole thing could be a red herring, right,
Like it could be that it just doesn't make sense
to talk about energy before the measurement.

Speaker 1 (33:54):
It could be and that actually depends also on your
interpretation of quantum mechanics. We're talking right now in the
Copenhagen interpretation, which has this whole idea that there's a
superposition and when you make a measurement it collapses to
one of those options. That's just one view of quantum mechanics,
and our argument about the energy non conservation depends on
that view. It turns out in other views of quantum

(34:15):
mechanics they tell a whole different story.

Speaker 3 (34:18):
All right, well, let's get into what these other views
of quantum mechanics are and what they say about the
conservation of cat energy or not. So let's dig into that.
But first let's take another quick break. All Right, we're

(34:43):
talking about energy, whether it's conserved in the universe, is
it conserved at the quantum level? And I think we've
established that it's a minefield of confusion for everybody. Some
people might say, does it even make sense to talk
about energy before you measure something? And you know, it
doesn't make sense to talk about whether the cat is

(35:03):
alive or dead before you open the box. And some
people might say that it does kind of matter, right,
or that if you discovered the cat to be aliver
before or after, maybe you killed the cat when you
open the box. That's kind of what you're saying exactly.

Speaker 1 (35:17):
And it's amazing to me that this is a topic
of recent discussion. This is not like something that Bore
and Heisenberg argued about and figured it out in nineteen
thirty seven their papers about this. Like last year, you know,
people are still debating what energy even means in quantum mechanics. Like,
sort this out, folks. You had it for one hundred years.
You think that would be enough time to figure out

(35:37):
basic stuff about quantum mechanics.

Speaker 3 (35:39):
Yeah, can't you just run an experiment to figure this out?
Like if measuring an electron somehow adds energy to it
or creates energy, can't you just measure that cad you
just design an experiment where you should a photon at
an electron.

Speaker 1 (35:52):
So people are trying to design experiments, and the crucial
thing is designing an experiment where you think the measurement
will not influence the energy of the system. That's the goal,
because then you can have an internal system and an
external system, and you can isolate it and say this
is the whole system. So you want to try to
separate your measuring device from the energy of the system.

Speaker 3 (36:11):
Wait, wait, do you mean like they're trying to come
up with how to measure something without measuring it.

Speaker 1 (36:14):
Well, they want to measure it without changing its energy,
so they want a energy independent measuring system.

Speaker 3 (36:21):
But I guess, if you shoot a photon at an electron,
don't you know how much energy the photon had when
you shot it so that you can take it into
account later when it comes out? Like, why is this
problem so hard?

Speaker 1 (36:32):
Well, every quantum object has an uncertainty to it, and
so you shoot a photon at it. You try to
generate photons with a specific energy, but those photons will
also have an uncertainty to them, and that uncertainty propagates
through your whole experiment. So what you want to try
to do is set up a scenario where the uncertainty
you're adding by your measurement is smaller than the difference
in the energy between the two states of the thing

(36:52):
that you're measuring. So you want to try to use
something really low energy to measure a really big difference.

Speaker 3 (36:58):
I guess it's kind of like you know, you're trying
to figure out if the cat is alive or dead
in the box, and you're sending it in a cat
to do it. But it turns out that the scientist
cat is also a quantum object, so it could also
be a live or dead, in which case you don't
really know the scientist cat is killing the other cat exactly.

Speaker 1 (37:13):
So what you want to do is try to send
in like a tiny miniature kitten that you can argue
is going to not influence whether your cat is alive
or dead as much.

Speaker 3 (37:21):
As possible, or that you know for sure if it's
alive or dead.

Speaker 1 (37:25):
Or the uncertainty on it is smaller than the uncertainty
on the thing you're trying to measure. So people come
up with these crazy clever experiments where you try to
use really low energy device to measure a very high
energy difference in the possible states of the object. So
the thing you're measuring is not influencing the state enough
to change the answer.

Speaker 3 (37:44):
Oh I see, yeah, Like you said, like you want
to send in a scientist kitty whose state whether the
kitty is a live or dead is not really going
to influence whether the big cat is a live or
dead exactly.

Speaker 1 (37:56):
And so there's these folks that come up with its
really clever experience where you take a box and you
put low energy photons inside of it, and under some
almost magic like wave mechanics mathematics, there's a place in
the box where the photon wavelengths add up in a
special way to wiggle at a really high energy. So
waves can add up and they can cancel each other out.

(38:17):
This is constructive and destructive interference, where it turns out
if you put a bunch of low energy photons into
a box, there's one portion of the box where they're
wiggling really really fast where all those photons added up
kind of make a higher energy photon than the sum
of all the energy of the photons you put in.
And they came up with this way to try to
reflect that one part of the photon out of the

(38:39):
box by slipping a mirror in really quick. And so
it's sort of like putting a few low energy photons
in a box and then getting out a really high
energy photon. So this is the experiment they propose would
prove violation or conservation of energy and quantum mechanics. But
there's a lot of controversy about what this experiment might
mean and whether you could actually do it.

Speaker 3 (38:58):
Oh, I see, because if you measure a really big
photon coming out of this corner of the box, you
have to wonder where that energy came from.

Speaker 1 (39:05):
Yeah, how did the universe make this high energy photon
out of just a few very low energy photons? Where
did it come from? Just like the example we were
talking about before, how did the particle get seventy five
GeV when the expected value of the energy was fifty
Where did that energy come from? And you can only
really ask that question where did it come from if
you believe it should come from somewhere, which implies that

(39:25):
it's conserved, that it has to come from somewhere, that
it's like flows around in it's a limited amount. But
if energy is not conserved, it can just like go
up or down, like the number of dead cats in
the universe. Then that's not really a problem.

Speaker 3 (39:36):
But couldn't you just say that the energy of that
right photon in the corner came from the little photons
or would it come out with a much bigger energy
than the if you add up the little smaller photons.

Speaker 1 (39:46):
Yeah, in this case, the energy is much bigger than
the sum of the energies of all the photons you
put in, So you can't explain it by just like
having added up those photons. It's a really cool experiment.
It's called super oscillation if you want to check out
more details about it.

Speaker 3 (40:00):
Well, but then you said that this is all just
base on one interpretation of quantum mechanics. What did the
other interpretations say or how can they help us?

Speaker 1 (40:08):
Yeah, because a big part of the issue is what
happens when you make a measurement. Right if you go
from a state that has on average fifty jewels of energy,
then you make a measurement, how do you end up
in one of those states? And where does that energy
come from? And other interpretations of quantum mechanics tell a
very different story about what's happening there. For example, the
Many Worlds or ever Ready in quantum mechanics says that
there is no collapse of the wave function. That if

(40:31):
you have a superposition of two possibilities that has alive
or dead, the particle has twenty five or seventy five
jewels of energy, that when you make a measurement, the
universe just branches and now there's one branch that has
one option and another branch that has the other option.
And so in that sense, if you're like averaging over
the branches, nothing has really changed. You know, the total
energy in the universe hasn't changed. One individual branch might

(40:53):
see seventy five jewels, so they might think they're seeing
violation of conservation of energy. But averaged over all the branches,
including the ones that don't see, nothing has really changed.
There's still just a distribution of different energies.

Speaker 3 (41:05):
I feel like you just skipped over a humongas concept
which is just throwing the multiverse.

Speaker 1 (41:11):
Yes, exactly, in the multiverse.

Speaker 3 (41:12):
Quantum multiverse. So you're saying, like, one way to interpret
quantum mechanics is that things don't collapse. You know, if
something if the cat is alive and dead, it means
that there's a universe where the cat is alive and
there's a universe where it's dead, and so overall energy
is still conserved. That's kind of the idea.

Speaker 1 (41:28):
Yeah, energy is just unevenly distributed among those quantum multiverses.
One of them gets more, another one gets less. Overall
it all balances out across the multiverse. But in an
individual universe, an observer does see a violation of energy.
So that's a pretty different story than what's being told
by the Copenhagen group.

Speaker 3 (41:47):
Let me see if I get this, so, like, I
have the cat in the box, and I open the
box and I find that the cat is alive, and
I think, oh my god, this is a violation of
cat aliveness in the universe because before the cat was
only fifty percent and now it's fully alive.

Speaker 1 (42:01):
Sure.

Speaker 3 (42:02):
Yeah, And you're saying, if you think that the actually
there's a multiverse, is a quantum multiverse, then there's no
real violation because if you consider my universe where the
cat is alive and your universe where the cat is dead,
then it makes sense for me to see that the
cat is alive, and it makes sense for you to
see that the cat is dead. There's no violation here.

Speaker 1 (42:21):
Yeah, because across the quantum multiverse it's still fifty percent
alive and fifty percent dead.

Speaker 3 (42:26):
But in the single universe version of quantum mechanics, the
cat aliveness went up from one half to one if
I see that the cat.

Speaker 1 (42:34):
Is alive exactly. So in the collapse theory where measuring
it forces the universe to choose one of these branches
instead of maintaining all of them, then somehow the number
of live cats in the universe goes up from half
to one, violating the well known principle of the number
of living cats in the universe.

Speaker 3 (42:51):
Yeah, or people in swimming pools, which I'm going to
wait for that paper from me. Okay, hold your breas, yeah,
to under the pool. Yes, Okay. So then I feel
like maybe I wonder, like you're saying, if we require
energy to be conserved in the universe for real, for sure,
then maybe I wonder if that's proof that the multiverse exists,

(43:15):
because that's the only way that this is going to work.

Speaker 1 (43:17):
Right, That's a cool perspective I hadn't thought of. Yeah,
I suppose if you define energy that way as across
the multiverse and you insist that it's conserved, then Copenhagen
interpretation of quantum mechanics does violate that. But that's not
something you can test, right. You can never access these
other branches of the multiverse. You can never know if

(43:37):
they exist, and if other people are measuring other things,
then you can only ever access our branch.

Speaker 3 (43:42):
We think, maybe, right, maybe you can this. I think
we've talked about this before and in our books, like
you could maybe discover something about the mathematics of our
universe that maybe points to the necessity of other universes.

Speaker 1 (43:55):
No, we definitely argue in our book that it might
be that the only consistent explanation of the universe is
the multiverse. So you can prove the multiverse exists without
ever experimentally verifying it, though that takes a lot of
confidence to say that there's no other explanation out there.

Speaker 3 (44:11):
That would take a high amount of confidence, not a
nuclear amount of confidence.

Speaker 1 (44:15):
So extrapolining that argument, if you can somehow prove that
a complete theory of the universe has to satisfy conservation
of energy at the quantum level, then yeah, that might
require the existence of the multiverse. But I don't know
how you would prove that requirement because energy is not
even necessarily well defined at the quantum level.

Speaker 3 (44:33):
I wonder if that means that some of the other
places that we've seen energy conservation being violated, like the
expansion of the universe. I wonder if that can mean that,
you know, as our universe expands and gains energy, maybe
there's another universe out there losing energy and being compressed.

Speaker 1 (44:48):
It's a great question and one of the reasons I
really like this question zooming down to the microscopic scale
and trying to understand what is conservation of energy there
is because we're really interested in what it means at
our scale, Like where does energy come from? Why is
it conserved for us? Is it because it's required at
the quantum level, or is it because it emerges somehow?
And so yeah, maybe energy non conservation in general relativity

(45:10):
could eventually be derived from some deep quantum gravity, some
explanation of the nature of space time at the quantum
level that has these consequences at our scale or at
the scale of the whole universe. So that would be
really fascinating.

Speaker 3 (45:24):
Yeah, or maybe vice versa, right, Like, if you prove
energy conservation at the grand level, it must might have
some consequences about you know, what we think is happening
at the quantum level.

Speaker 1 (45:34):
It could be although sometimes conservation laws cannot be exact.
They can just emerge, so they don't have to always
hold true at the quantum level to hold true at
the classical level. But there are some things that are
truet the quantum level, Like we think conservation momentum is
rock solid at the quantum level, and the reason we
have it at our level is because everything is made
out of these quantum bits which follow these rules. So

(45:55):
we don't know basically whether conservation of energy is exact
the way conservation momentum is because it comes out of
the quantum level, or if it's something that emerges somehow
when you get classical physics.

Speaker 3 (46:06):
I guess maybe your people in a pool experiment is
going to conclusively prove that.

Speaker 1 (46:10):
Then give me one hundred years. It's going to take
a lot of data.

Speaker 3 (46:15):
What do you Why do you need five years to
do this?

Speaker 1 (46:19):
Oh man, because the I RB you know, you're doing
experiments on people. You got to sign the papers. It's
the whole thing.

Speaker 3 (46:27):
I see. Yeah, And then there's a pool, so the
forms get wet. It's all a big mess. What does
this have more implications for our understanding of quantum mechanics
or understanding of energy conservation in the universe.

Speaker 1 (46:38):
I think it has consequences for our understanding of what
energy is. As we drill down to see what the
universe really is like at the microscopic scale, we learn
about things that turn out to just be features of
our existence. They're not generally true at every level of
the universe, you know, like there's no equivalent to ice
cream at the quantum level, for example, there's no equivalent

(46:59):
to cats. Those things only exist at our level. And
so I love that as we keep looking deeper into
the universe, we discover things about our experience that turn
out to just be part of our experience. They're not
generally true about the universe, Like our sun is unusual,
and maybe our planet is weird, maybe our way of
life is weird. And the same way, we discover that

(47:19):
the way we experience the universe and the things we
think are fundamental about it actually aren't. To me, that's
really cool and opens up questions about like other conservation
laws are other things that we thought were hard and
fast and true about the universe actually just sort of
like emergent approximate things, and at a quantum level they're
not preserved. That would be kind of scary.

Speaker 3 (47:38):
Well for me, I'm getting the sense that maybe, like
even if we do discover that energy is conserved or
not in our universe, that wouldn't maybe really tells what
the real truth is because we wouldn't have access to
maybe the multiverse in other universes, which would maybe cancel
out what we think is the rule of the universe.

Speaker 1 (47:56):
Yeah, that's right. We could see what we think is
energy non conservation and bigger picture, it all balances out,
and so we might never really know these answers.

Speaker 3 (48:04):
Well, I'll just take comfort in the fact that even
if I don't exercise today, maybe there's a quantum Woorge
in another universe who is doing double the exercise for
the tour that both us and in some way you
can say that I exercised today.

Speaker 1 (48:18):
Yeah, that's true, and that quantum Hohoge will live longer
than you and on average, you know, some fractionales across
the teams, this will be alive or not.

Speaker 3 (48:27):
Yeah, there you go. There you go, playing with some
kittens and counting people in a swimming pool. All right, Well,
we hope you enjoyed that. Thanks for joining us. See
you next time.

Speaker 1 (48:42):
For more science and curiosity, come find us on social
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