Why does the vacuum of spacetime have energy? How much energy does it have? What prevents us from using it to do anything useful? I discuss these questions and more in today’s Ask a Spaceman!

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EPISODE TRANSCRIPTION (AUTO GENERATED)

It's Friday. Late afternoon. You're at work, and you've got that major deadline due at the end of the day. Your boss is breathing down your neck. Your whole team is on edge.

They're all counting on you to finish this final task. Put a bow on it and get it out the door. You've had 10 cups of coffee today, maybe more. You've lost count. Your hands are jittery.

You can feel your heart racing in your chest. Your mind is going a mile a minute, and you can feel the energy inside of you, but nothing comes out. Despite the intensity of your thoughts, it's almost like they're too sluggish to turn into anything meaningful. You're awake, but exhausted. You're energized, but unfocused.

You're keyed in, but you have nothing left to give. This is the state of the vacuum in our universe. An overly caffeinated worker who can feel the energies inside them, but can't tap into them to get anything useful done. And if that's all you need to answer the question of today's episode, which is why can't we get free energy from the vacuum, then please stop the episode, go home, and take a nap. But this is more than a mere analogy.

Well, okay. It's literally an analogy, but I chose the words here on purpose. Full of energy, but unable to be used. That's physics. The vacuum of space time has energy.

It's impossible to say exactly how much energy. It's anywhere from a tiny amount to literally infinity, but it's definitely not zero. But no matter how much energy the vacuum of space time has, it's not useful energy. It's not energy we can turn into work. It's not energy that we can transform into something else or transfer somewhere else.

It's just there. Existing. All around us. Always present, but always in the background. Now the idea of the vacuum having energy in the first place might be a bit strange.

And to be perfectly honest, it is strange. We're used to thinking of energy in terms of objects. A hot cup of coffee has thermodynamic energy. A baseball speeding towards your face has kinetic energy. The mass of the Earth has gravitational potential energy.

We attach energy to things. And in physics, energy is a property of objects. Just like objects have other properties like position or momentum or color, they also have this property called energy. Some of that energy is internal and intrinsic to the object. Some of it is dependent on its situation.

So, like, thermal energy depends on the temperature of that object. So if you have a temperature, you also have thermal energy associated with you. And if I place that same object up on a high shelf, it now gains potential energy depending on its situation. There are so many different forms of energy that objects can take. There's not just thermal or kinetic or gravitational potential.

There's chemical. There's nuclear binding energy. There's electric energy, magnetic energy. There are so many different kinds of energy that objects can have. And this energy, this quality of objects, this property of objects that we call energy, allows the object to do things.

It can make the object move. It can make the object transform. It can make the object do work on something else. It can make the object contribute to Patreon. That's patreon.com/pmsutter.

It is your energetic contributions that keep this show possible. Thank you so much. That's patreon.com/pmsutter. With energy, an object gets to interact with the rest of the universe. And we use this language of energy in physics to explain just about every scenario that happens in the entire universe, including up to and including the evolution of the universe.

Energy is neither created nor destroyed. It only changes from one form to another. And in the process, it allows physics to proceed. And energy is the enabler here. It is the thing that allows objects to do stuff.

They can expand inside of container and press on, a piston, for example. And pressing on that piston, doing work on that piston drives a a turbine. It drives the engine in my car. I can capture energy in the form of chemical bonds and then release that energy later to push things around inside of cells or to generate heat to to get other processes going. There is energy everywhere and we use this the concept of energy is so central to all of physics because it is how we understand objects interacting with each other and the ability for objects to interact with each other.

And you can follow these threads of energy transformation in one object influencing another through surprising and sometimes ridiculous connections that you would have never thought of. Like, atoms have nuclear binding energy. This can be released in the core of the sun through fusion reactions. Now that energy transforms, and it becomes electromagnetic radiation, electromagnetic energy that is then transported through the plasma of the sun and then out into space. Then those electromagnetic rays strike certain special molecules in plants, which shifts them around, and that transforms that energy into chemical binding energy.

Then those chemicals get chewed up and reconstituted as new chemical arrangements, which then get combined with oxygen to release that chemical energy and become heat and motion, which powers my voice to create pressure waves in the atmosphere, which hit a device in my microphone, which converts that to electrical energy, which drives a speaker to turn it back into pressure waves which hits your eardrum which causes vibrations that cause new electrical and chemical signals of their own which exist as the experience you're having right now of listening to me. All powered by some starting point of energy, in this case nuclear binding energy, transforming again and again with objects acquiring this energy in some form and then using that energy to influence their environment to transform themselves, to get work done, to transfer that energy somewhere else. And we follow these chains all across the universe, and that is the game of physics. It's all energy. Sloshing and zipping and transforming everywhere.

And all of these require entities, objects, things, atoms, pressure waves, whatever it is, there's a thing that has energy. Just like there are things that have shape or size or temperature or color. They have energy. It is a property of objects. But what if there's nothing?

What if you have a vacuum? A region of space with nothing in it at all. How can that nothingness have an energy associated with it? I mean, it doesn't have a color. It doesn't have a temperature.

But here we are talking about the energy of the vacuum, and I know this is such a commonly replayed phrase in science fiction and and science communication, pop sci, all that. You know, vacuum energy. Like, let's take a step back and appreciate how wild that sentence that phrase even is. If you were to go back in time four hundred years ago and say, yeah. So the vacuum energy, I don't know.

Maybe they'd burn you at the stake just out of a precaution. How can the nothingness of the vacuum have energy connected to it? This question should have a very simple, very reasonable answer. The answer should be, that's not possible. There should be no energy in the vacuum.

But as usual, quantum mechanics has to come barging in, uninvited to the party, always eager to awkwardly interject a well actually into the conversation and make things complicated. Empty space if you take a box and get rid of everything in it, even the photons, all of it. Get out of here. Even the neutrinos, you're not invited. Get out of here.

And it's totally empty. There should be no energy in the box. We should not be able to talk about the energy in an empty patch of space. But here comes quantum mechanics. Well, actually, empty space isn't really empty.

Empty space can indeed be very empty of particles, radiation, sound waves, all the usual stuff. But there is one more component, one more ingredient to the universe that you just can't get rid of. And those are the quantum fields. Quantum fields are a not nearly talked about enough, and I think I mention that every time I mention quantum fields. They do not get nearly enough airplay in popular science communication, so here I am trying to fix that.

Quantum fields are nonintuitive, weird, a little bit spooky, also really fun. Quantum fields arise from our understanding of what when we combine quantum mechanics with special relativity, when we, you know, when we get quantum mechanics, we get Schroedinger's equation and Heisenberg uncertainty principle, and we're, like, feeling really good. And then Einstein comes around and he says, well, what about special relativity? What about the connection between space and time, the ability to transfer from energy to mass and how mass itself is just concentrated energy? You know, how does that play with Schrodinger's equation, Heisenberg uncertainty principle, all the juicy stuff we love about quantum mechanics?

When you try to fit those two pieces together, you end up creating an entirely new theory of physics that we call quantum field theory. One of the big points of quantum field theory is that particles aren't really particles. In fact, they're not really all that important at all. The real fundamental object in quantum field theory and indeed in all of modern physics is the field. This is an entity.

It's a thing. It's not a normal thing like you normally think of things. It's it's own kind of thing. But it's a thing. It's an object that exists all through space and time.

And this is what we believe to be the primary physical object of reality. Every single kind of particle that you can think of is really an expression of an underlying field. So you think of a photon, you think of a little tiny little packet of light, really, that's an expression of an underlying field, something we call the electromagnetic field that exists all through space and time. Sitting alongside that field are fields for all the other particles. There's a field for the electron.

There's a field for the top quark. There's a field for each of the neutrinos. There's a field for the Higgs boson. When you see that particle zoo and list of all the fundamental particles, there is a field attached to each one of those or associated with each one of those particles. These fields, like I said, exist through all of space and time.

The analogy I love to use because you know me in food metaphors. It's like dipping a piece of bread in olive oil and balsamic vinegar. They mix together. They both soak the bread of space time with their delicious essence. I should have had lunch before recording this.

And the most important thing about the fields is that they all always exist. No matter where you go in space, no matter where you go in time, the fields exist. They are simply everywhere. What we call particles, if I see an individual electron, the particles are really just traveling, stable, well behaved ripples in that field. If you take a little bit of that field and you give it a little bit of extra energy, and you stabilize it, and you allow it to travel, propagate from a to b, we call that a particle.

We we had to invent this entire language because we realized very early on that particles could be created and destroyed at will, and that seemed kinda weird to be able to create and destroy particles, but now it makes sense because we're not creating and destroying particles. We're just adding energy and taking energy away from the field. And when there's extra energy, we call that a particle. When there's not so much energy, there are no particles there, but the field is still there. Just like I can have waves in a pond, and I call those waves, and I can see them moving across the pond.

But if I get rid of all the waves, if I lower the energy of the pond so that there are no disturbances, no waves at all, I can't get rid of the water itself. The pond is still there, it just doesn't have waves on it. Each of these quantum fields still exist. It's still there even if there are no particles being expressed by the field in that moment. And without any particles around, these fields are in what's called their ground state.

Their lowest energy state also known somewhat weirdly as the zero point state which is going to introduce a little bit of a headache in a bit. We're gonna navigate it. Don't worry. In the ground state or zero point state, these fields are in their barest possible, lowest possible, most stable possible state of existence. It's as boring and plain and neutral as a field can get, which turns out to not be boring, plain, or neutral at all.

If you add energy to a field or a patch of a field, you get a particle there. And if you remove it, the field is still there, and it's definitely not boring. And that's because quantum mechanics puts a limit on just how stable, plain, boring, and neutral any ground state can be. Any lowest energy state. If I take a bowl and I put a marble in it and I just drop the marble in, it's gonna start off with a lot of energy.

It's gonna be rolling around, rattling around, and its energy will transform. It will turn into sound waves. It will turn into heat from friction, and eventually, the marble will settle at the bottom of the bowl, and it will be still and motionless. It will be in its ground state. I say, this marble in this bowl is in its ground state.

It's in its lowest energy configuration. It's in its most stable configuration. It's just there. It doesn't move. It can't get any lower energy situation than that.

It is like a teenager on a lazy summer afternoon, lowest possible energy state that can still claim to be existing barely. But instead of a marble or a teenager, put something more quantum mechanic y in like an electron. If I drop an electron in a bowl, the electron will slosh around, maybe it'll make tiny little sound waves, a little bit of electromagnetic radiation, a little bit of friction. Eventually, that electron will reach its lowest energy state, its most stable, boring state, its ground state, its zero point state, but it won't stay still. And that's because of the Heisenberg uncertainty principle.

The Heisenberg uncertainty principle, also affectionately known as HUP, says that we can't know the precise position and momentum of a subatomic particle. And so if this electron is in its ground, say, you know, the marble I can say, look, the marble is right there. I'm pointing to it right now, and it's not moving around. I know both its position and its momentum. Heisenberg uncertainty principle, Hub, says you can't do that with an electron.

You can't point at the electron and say, hey, that electron's not moving, and it's right there. You can't know both to infinite precision. There's a limit to how well you can know where an electron is and how quickly it's moving. There must always be a little bit of uncertainty, and we can think of this little bit of uncertainty as a little vibration. The ground stable state of an electron in a bowl has a little bit of wiggle to it.

It's constantly moving around, buzzing like a little trapped bee. It's just not quite exactly in the center of the bowl the whole time, and it's not quite perfectly at rest the whole time. It's just jittering around just a little bit due to the uncertainty principle. So even though the electron is at the bottom of the bowl, even though the electron is in its ground state, even though it's in its zero point state, there's still a little bit of motion associated with that electron. And if there's a little bit of motion, there's a little bit of energy.

This electron, in its ground state, in its zero point state, in its lowest energy state, has an energy associated with it due to the fundamental uncertainty of quantum mechanics. This means that quantum mechanic objects like electrons do not have zero energy in their ground state. In an ironic and unfortunate clash of jargon, we can also say that the zero point state of the electron does not have zero energy, which means there must be zero point energy. In general, I'm not a big fan of the term. You may have heard the term zero point energy.

In general, I'm not a big fan of it because it's so dang confusing. What's the zero? What's the point? What's the energy? Hard to untangle.

So hopefully, that's the last we hear of that today. No promises though. And this is the key key concept for understanding the energy of the vacuum. Is that because of quantum uncertainty, the lowest energy state of a quantum mechanical thing is not zero energy. If I look at that at marble, I can say I that's zero energy.

It's not moving. No kinetic. It's at the bottom of the bowl, so it's a zero potential. I can zero everything out. And I can say the ground state of the marble is at zero energy.

But the ground state of a quantum mechanical electron does not have zero energy. It has some positive energy associated with it. And the fields, the quantum fields, as their name suggests, are very, very quantum mechanic y things. You can't get rid of a field. You can empty out a box of all the particles, all the radiation, which means in that is the exact same thing as saying I'm going to take the fields, the quantum fields in this box, and I'm going to bring their energy down as low as possible.

I will get rid of all the extra excitations and vibrations. I'm going to bring everything down, chill everything out to its lowest energy state possible. That means the vacuum of space time, even though it's empty of particles and radiation, is still filled with quantum fields because I can't get rid of the quantum fields. And the quantum fields have an energy associated with them in their ground state because of the uncertainty principle. There's a little bit of jitter.

There's a little bit of static. There's a little bit of noise. There's a little bit of wiggle. The the fields themselves are vibrating just a little bit. Not enough to make, a wave.

Not enough to make a big particle showing up. They're just there, humming in the background. It's like a pond not having any waves on it, but countless tiny little ripples and vibrations. Or I like to think of it as the as a static that fills up reality all around us. We all exist on top of the static, and normally, we don't notice it.

But when you reach a quiet space and you eliminate all the particles, you bring those fields down to their lowest energy configuration possible. There is an energy with that. There is a static with that. The the fields are not still. So how much?

If the fields have an energy, even in their lowest energy state, If their lowest energy state is not zero, it's something else. What is it? What's the number? Well, this is the point that I reach in pretty much every episode involving quantum mechanics where I let out an exasperated sigh. So here we go.

The problem is that the fields exist everywhere. Literally everywhere. Not just all throughout space, but all within space. No matter how small you look, no matter how refined your microscope, no matter how detailed your measurement, you'll never reach the bottom end of the field. It's kind of a weird squirrely concept to get across.

But, yeah, if you take a box, a meter on a side, you have that much field. Okay. I have field filling up this this meter size box. If you take a smaller box, say it's, I don't know, a femtometer across, then you have a femtometer's worth of field. If you take a fraction of a femtometer, you have that much field.

Okay. There's no matter how small you get, no matter how small your divisions, how much you zoom in to the fabric of space time, you are always going to encounter fields. There are just fields covering everything. But no matter the volume, there are always an infinite number of points within that space. You may remember from geometry that points, geometric points have have no space whatsoever.

They have no volume. They have no extent. They're infinitesimally tiny. They take up no space whatsoever. So no matter my volume, I can always have an infinite number of points within that volume.

If I have a volume a meter across, and I ask, well, how many geometric points can I put in this box? The answer is infinity Because each point takes up no space. I can keep subdividing the box as much as I want. And if I take a a femtometer sized box, really, really, really tiny box, I ask, hey, how many geometric points are in that box? The answer is infinity.

Because I can take that femtometer size box and chop it up as much as I want. No matter how much I chop it up, I don't reach the end of the field. I don't reach the the the resolution limit of the field. The field is continuous. The field is infinite.

It's always there. It occupies every single point, real point in space time, which means there are always an infinite number of points within any volume. And each one of those parts of the field contribute an energy to the vacuum. When I look at this field and I say, how much energy does it have? Okay.

My first job is to subdivide the field into little chunks, and then ask how much each of these little chunks contribute to the overall energy in my volume. And just chopping it up. Okay. So we're gonna cut the box in half, and then quarters, and then eighths, and then sixteenths, and then thirty seconds. I'm gonna chop it up, and I'm going to say, okay.

Once I'm done chopping, I'll take this chunk by chunk, and I'll take a look at that chunk and say, hey, you. How much energy do you have due to the Heisenberg uncertainty principle? I'll write that number down. Then I'll go to the next chunk after that. Write that down.

Then the chunk after that, and write that down. And then I'll add up all the chunks throughout the volume, and I'll get the total amount of energy. But the thing is, I never run out of chunks. I can always make my chunks smaller. I never reach a limit where my chunks, like, stop.

So if I take any volume, no matter the size, I can always divide it into an infinite number of chunks. And each one of these chunks is contributing a little bit of energy to the vacuum, which means there's an infinite amount of energy in the vacuum. So by strict accounting of the nature of quantum fields, when I ask, hey, how much energy does the ground state of these quantum fields have? The answer is infinite. There's an infinite amount of energy in the fields.

We can attempt to arrive at approximations, like, not get infinity. We can cut off our calculations at some size scale. Like, like, okay. I know it's infinite points all the way down. We heard you, Paul.

But but, you know, I'm gonna smooth things out at, say, I don't know, a typical proton's radius or whatever. I'm gonna say maybe below that scale, we're misunderstanding the nature of quantum fields, and we'll just skip over that. And so we'll make we'll make our chunk size, like, a a a proton's width. And then when we add up all these little proton widths in the box, we'll get a total amount of energy. We get a ridiculously large number.

It's not infinite. It's just it's just very, very large. So, you know, there's there's some debate here whether there's infinite energy in the vacuum, significant energy in the vacuum, or maybe not a lot of energy in the vacuum at all. Maybe we're misunderstanding something about this very basic calculation. But no matter the accounting, the energy in the vacuum is definitely not zero.

Whether it's small, medium, big, or infinite, it's not zero, and it's right there. You and me are existing in it. We're swimming in it. We're living in it. It surrounds us and infuses us.

I know I sound like I'm talking about the force from Star Wars, but I swear I'm not. Even a perfectly empty box, completely devoid of particles, is filled with fields and therefore, filled with this energy. And for those of you keeping score at home, it is exactly this energy that we think is also the dark energy that is causing the expansion of the universe to accelerate, but that was last episode. Now I need to pause here and make an aside. I don't really want to because this is already a thick episode and I hate interjecting random jargon, but we need to clear the air here or more accurately, clear the vacuum.

In many, if not most discussions of the vacuum energy, ground state energy, zero point energy, whatever you wanna call it, in most of those discussions, you're more likely to encounter not vivid descriptions of the fields and vibrations and the Heisenberg uncertainty principle, But instead, this picture based on virtual particles that pop in and out of existence that, if you look at the vacuum of space time, there's this roiling mass of particles that briefly appear. They steal energy from the nothingness of space, which should violate everything we know about conservation of energy. But it's okay because of the Heisenberg uncertainty principle. And if they they if they disappear soon enough, then it's okay because they borrow their energy for only a little bit, and they put it back before anyone notices. And then if you zoom in at at subatomic scales, you'll see this frothing mass of of electrons and and and photons and and quarks and neutrinos all popping in and out of existence, and we call these virtual particles.

And, yeah, this picture isn't necessarily wrong, but virtual particles are neither virtual nor particles. They're more mathematical trick for calculating the effects of the field vibrations. So I don't I'm not gonna say you can't use that picture, but it's not the picture that's closest to the actual physics. The actual physics is this picture of quantum fields that have have inherent vibrations to them, not in terms of particles popping in and out of existence. So like I said, I'm not gonna get in your way.

If you still want to think about virtual particles when it comes to the quantum vacuum, just remember that you're doing yourself a disservice. So that bit of, pop sci imagery placed in its appropriate corner, let's get back to the vacuum and its very large amount of energy. This is where we get to all the sci fi applications. I mean, it's in the name. Vacuum energy, zero point energy, quantum energy.

Energy is what I use to get things done. And if energy is just sitting around like an untapped reservoir, then why can't we, you know, tap that reservoir and power spaceships and laser beams and spaceships with laser beams? It's because the vacuum is like you. 4PM on a Friday, vibrating from over caffeination, but unable to transform that energy into useful work. The trouble with the ground state energy isn't that it's energy, It's that it's the ground state.

It's the bottom of the barrel. It's the end of the line. It doesn't matter what value it is. It doesn't matter how much energy is in the vacuum, even an infinite amount of energy because the rest of physics happens on top of that background. It's not just energy that matters.

It's it's energy differences. I drop a ball onto the floor, the amount of kinetic energy it picks up depends on its height off the floor. It doesn't matter if I'm at sea level or three stories up or in an airplane. What matters is the difference between the height of the ball when I drop it and its final height when it hits the floor. If it drops five feet, that's it.

It dropped five feet. End of story. The differences in energy matters. And if I'm at the ground state, if the ball is already on the floor, I can't get any energy out of it because it's in its ground state. It doesn't matter if that ball sitting on the floor is at sea level or three stories up or in an airplane.

If it's on the floor, it's spent. It's done. It has no more energy to give me. If I put a marble in a bowl and it's in its ground state, I can't get energy out of the marble because it's, by definition, in its lowest energy state. It has to be in a higher energy state for me to extract energy from it and use it to get something done.

If it's something is in its ground state, by definition, that is the way ground states work. You can't get energy out of it. The quantum fields of space time are in their ground state. It doesn't matter what that value is. It doesn't matter what that the absolute value number of the energy is.

If it's in its ground state, I can't extract energy. I can't do anything with it. In other words, there's no way to pull energy out of the vacuum because there's nowhere else to put it. No matter what you do, no matter where you go, you're always surrounded by an infinite sea of energy. There are no differences in that sea that you can exploit to get work done.

The vacuum energy is there, but it's unreachable. You can't dig it out because there's nothing underneath it. You're at the bottom of the tub of ice cream. You can't scoop any more ice cream out. That's the definition of being at the bottom.

You can't go lower than the Ground Floor. And don't think you can get clever with this analogy and start talking about basements. That's not how this works. Okay. Fine.

We'll go back to virtual particles if you want. But just this last time, if you think about instead of vacuum fields vibrating with energy, if you think about virtual particles popping in and out of existence, they exist because of the Heisenberg uncertainty principle. They can pop into existence, borrow energy from the vacuum, but they can only do that if they return to the vacuum in a short enough amount of time. If you were to pluck one of them out of the vacuum and make it permanent, then you violated the Heisenberg uncertainty principle because the particle is sticking around longer than it should. You truly have stolen energy from the vacuum of space itself, and we know that energy can't be created or destroyed, so you're stuck.

There's a debt owed to the universe and like a mob boss from a corning gangster movie, the universe always finds a way of getting paid its debts. I'm sorry everyone, but in this universe, there's no such thing as a free lunch. And there's no such thing as free usable vacuum energy. Maybe it's time for a vacation. Thanks to Paul and Julia s, at kellan richards one, Roger b, Robert k, and Mahale e for the questions that led to today's episode, and thank you, of course, to all my Patreon contributors.

That's patreon.com/pmsudder. All of you deserve so much thanks. I have so much gratitude for all of you. I'd like to thank my top contributors this month. They're Justin g, Chris l, Alberto m, Duncan m, Corey d, Michael p, Nyla, Sam r, John s, Joshua, Scott m, Rob h, Scott m, Louis m, John w, Alexis, Gilbert m, Rob w, Jessica m, Jim l, David s, Scott r, Heather, Mike s, Pete h, Steve s, Wat Wat Bird, Lisa Aracuzzi, Kevin b, Michael b, Eileen g, Dante, Steven w, Brian o, Deborah a, and Michael j.

Thank you so much. Please keep those questions coming. Leave a review on your favorite podcasting platform. It really helps to show visibility, but nothing matters more than more questions. Please keep sending questions to askaspaceman@gmail.com or just go to the website, ask a spaceman dot com.

And I will see you next time for more complete knowledge of time and space. Knowledge of time and space.

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