The mathematics of hypothetical extraction of energy from the vacuum

Wouldn't it be great if we could get "free energy"? I put "free energy" in quotes to indicate that it doesn't simply mean energy which is free, which I guess you could claim solar power is once you have your solar collectors. I'm talking about the "energy from the vacuum" and similar claims.

I have read some of the threads about that topic on ATS. While I don't rule out the possibility completely, it seems pretty unlikely that if vacuum energy is the lowest possible energy state of a system, that we can extract energy by making it go below its lowest possible energy state, because if we could do that, then we could reasonably claim that it wasn't at its lowest possible energy state to begin with.

But I started wondering what the math would look like if we could extract energy from the vacuum, and I haven't seen anyone else do the math I wanted to see, so I decided to do the math and thought I'd share it with you here.

How much energy is in the vacuum? We aren't 100% sure but recent measurements by the Wilkinson Microwave Anisotropy Probe and many other experiments seem to be converging on a positive cosmological constant, equal to roughly 7 × 10^-27 kilograms per cubic meter. This corresponds to a positive energy density of about 6 × 10^-10 joules per cubic meter.

So the question I wanted to answer, is, if the vacuum energy COULD be extracted, how much "space" with this "vacuum energy" in it would I need to power my home's electrical needs? The average home uses an average of 1020 watts of electrical power.(I picked the middle of the three figures). I use slightly less than that but it's close enough for me and probably more relevant to everyone else if I just use the average.

Watts are joules per second, so this means if your home is typical, it uses 1020 joules per second.

1020 J/s divided by 6x10^-10 J/m^3 equals about 1.7 trillion cubic meters per second.

An olympic sized swimming pool has a volume of about 2500 cubic meters.

So, 1.7 trillion cubic meters per second divided by 2500 cubic meters equals 680 million olympic pool volumes per second.

There are 84,400 seconds per day, so you'd need 680,000,000 x 84,400 olympic pool volumes per day to power your home with that amount of vacuum energy if the energy was even extractable, which it probably isn't.

So, you'd need to extract 100% of the vacuum energy from about 57.4 trillion olympic pool volumes per day to power the average home.

I don't know about you, but I can't even fit ONE olympic sized pool in my back yard, they are 50 meters or about 165 feet long by 25 meters or about 82 feet wide, and 2 meters deep. So even if we COULD extract this vacuum energy, where would you get the 57.4 trillion olympic sized pool volumes per day needed to power your home? If you could only extract say 10% of the energy you'd need 574 trillion of those huge pools of space, every single day.

It just doesn't sound very practical to me even if we could extract energy from the vacuum, which I suspect we probably can't.

Now compare this with solar power for example. if you adjust the figures in this source for the average power of 1020 watts, then you'd need 44 square meters of solar panels to power the average home. I believe the average home in the US probably has that much space on the roof.

So even if you could extract the energy from the vacuum, wouldn't putting solar panels on your roof still be more practical? The solar panels are kind of expensive now but I think the costs will come down in the future, and the efficiencies might go up too which means you might need less than 44 square meters of solar panels.

reply to post by Arbitrageur

Personally I think solar power in its current form/technological state sucks. It is so inefficient and expensive and I believe the panels eventually need replacing after 20 years or so. (I could be wrong). But solar power is not much use without some serious (and probably expensive) batteries. It wouldn't surprise me if the cost of panels are dictated not by production cost plus a "reasonable" profit but more by current energy prices. Here it takes at least 10 years to get the money you invested in the panels back, if it's not 20 years.

I think wind power might be better but here at least, I think you aren't allowed to place such structures on your property without permission.

Energy is a monopoly and I don't see that changing anytime soon. Sigh...

ETA You made some impressive calculations though.

Originally posted by Arbitrageur

...if vacuum energy is the lowest possible energy state of a system...

Someone's been reading my definitions

So, you'd need to extract 100% of the vacuum energy from about 57.4 trillion olympic pool volumes per day to power the average home.

Certainly does sound like a lot, but let's consider it a bit further. Let's take into account the fact that the Earth is moving through that vacuum. In fact, it's moving through the vacuum at about 370,000 m/s. 1.7 x 10^12 m^3/s divided by 370,000 m/s gives an area of 4,594,594.6 m^2. That's 2143.5 m by 2143.5 m (1.332 miles by 1.332 miles). For each home. And that area always has to be perpendicular to the Earth's direction of travel.
So, yeah, no matter how you look at it...it's a ridiculous amount of "free energy."

reply to post by CLPrime

Thanks for the great contribution CLPrime, I always enjoy reading your posts.

So hypothetically I'd just need a collector 1.3 miles by 1.3 miles after accounting for our movement through the vacuum?

Hey, I already said I can't even fit a 165 foot long olympic pool in my back yard!

OK, when I buy my next house, I'll look for a lot that's at least 1.3 miles squared just in case (just kidding).

reply to post by LightSpeedDriver

I think those are all valid points. By comparing solar energy to vacuum energy, I wasn't trying to imply solar power is ready for residential use, though I do think there are good commercial applications now.

I do think the cost needs to come down and the efficiency needs to go up to make solar power more viable for residential use, and I think that will happen, but I don't know how long it will take.

However I can say that as oil and other energy prices continue to rise, the economics for solar panels tend to compare more favorably than they do when fossil fuels are cheap.

reply to post by Arbitrageur


You could have a million stars and flags and a Nobel Prize. This is idiotic.

Call that guy Page, he is the resident expert of nowhere.---------------------

Which begs the question ...

If you could (somehow) instantaneously extract ALL the energy from a cubic metre of vacuum, what would happen to the state of that volume of vacuum ? Nothing ? ... or would it possibly collapse in on itself ? ... or an unknown end result ?
Just had a thought. Maybe the energy content within the vacuum serves as a positive pressure to prevent vacuum collapse ?
That's the trouble with the universe ... too many questions and not nearly enough answers

reply to post by tauristercus


Extracting the energy collapses the vacuum state to a lower energy level. It doesn't really do anything tangible to the vacuum, itself...it just releases a bunch of energy. Other than the release of a bunch of EM radiation, we wouldn't notice any change to the vacuum.

Just as a thought, the earth is spiraling like a corkscrew at thousands of miles per hour. This is how the space needed could be lightened, as if you were putting a sail to the never ending wind that is our movement through space and time. Wait this is starting to sound like Michelson-Morley

reply to post by JibbyJedi


Here I am all serious trying to keep up with this thread and along you come with the Turbo Encabulator with perfect timing to have me laughing so hard I got tears in my eyes.

I'm still laughing.

reply to post by Arbitrageur

I hear you but here's another conspiracy, oil is not quite the finite resource we have been lead to believe it is. It appears to be literally gushing out of the ground still and production does not seem to be decreasing one bit, despite what "experts" might be trying to tell us. Should that be a wrong assumption (which I personally now highly doubt) I am sure there is plenty of new tech that can be whipped out all of a sudden. For example, have you seen any governmental attempt at seriously reducing the dependence on oil? Sure they are posturing with fracking and tar sands and other nasty things but OPEC is as strong as ever.

Another question might be, just how much did Tesla really know? Obviously in relation to your original post.

reply to post by Arbitrageur

Or put more simply a tea mug contains enough vaccuum energy to boil of all the water on this planet. Extracting the vaccuum energy is imposible with our technology and current understanding of the universe. To get the energy you need to build a container that can block all particles from penetrating its exterior. Things like neutrinos which are said to be ghostlike and pass through anything

reply to post by LightSpeedDriver

I've seen the theory that oil isn't a finite resource, what i haven't seen is the proof for it.

Some countries are dragging their feet more than others in pursuing alternate energy sources. Germany seems to be doing a lot in this regard. I can't say why other countries aren't doing as much as Germany, but they probably should be doing more of what Germany is doing.

Regarding Tesla, he was a bright guy. We can actually extract energy not from the vacuum, but from the invisible TV and radio waves we are constantly bathed in. The closer you live to a television or radio broadcast antenna, the more energy you can extract from it.

I didn't do all the math on that but my guess is that if I did the math, the energy you can extract from radio and TV waves in the air is far greater than the amount of vacuum energy. But it's still a pathetically small amount measured in microwatts, as discussed in this thread:

Power from the Air: Device Captures Ambient Electromagnetic Energy to Drive Small Electronic Devices

Chances are you'll never power your house with it in the foreseeable future, but as the article suggests, it sure could power some little sensors and it probably will do that eventually, outside the lab.

reply to post by Aletheia007

That's one theory, but I've seen no evidence the vacuum contains that much energy. I think the best evidence we have comes from measurements like those from the Wilkinson Microwave Anisotropy Probe.

I think to approach this topic one needs to look for evidence. The theory that vacuum energy is small has evidence to support it. I have yet to see evidence the vacuum energy is as high as you claim it is, but like I said I did see a theory about that, with no evidence specifically showing a high level of vacuum energy.

If you've got evidence of that, please post it,because I'd like to see it.

reply to post by Arbitrageur


en.wikipedia.org...
www.calphysics.org...

reply to post by Aletheia007

If you had looked at the source in my OP, you'd see it already contains those same theories.

I asked for evidence like measurements from the the Wilkinson Microwave Anisotropy Probe which I used for my calculations.

I see no evidence like that in your sources.

reply to post by Arbitrageur

Unless I am completely wrong, did Tesla not extract huge amounts of power just from the "air" and not "the vacuum"? That tower that J P Morgan funded then retracted support for once he realised its true potential and damage to his monetary grip?

reply to post by Aletheia007


So, are you using the observed 6×10⁻¹º J/m³ or the theoretical 10¹¹³ J/m³? 'Cause there's a big difference. Personally, I'd think the observed value would be preferred.

reply to post by Arbitrageur

At a quantum level particles are constantly being created and annihilated. Surely that means that there is no limit to the energy potentially available from a vacuum?

reply to post by Pimander


Humans are constantly being created, as well, but that doesn't mean there's an unlimited supply of them at any given time. Just like humans, vacuum energy has a density. This density is most basically determined by the number of particles per cubic meter, but, since these particles are energy, their density is given in terms of that energy - their energy density. This limits the amount of energy we can extract at any given time. The source, itself, is unlimited, since particles are, as you say, constantly being created, but they are being created at a rate too slow to be of any practical use.