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I have been reading a book about quantum mechanics ( In search of Schrodinger's cat by John Gribbin ) and on page 196, it states

An electron does not exist in isolation, because it can borrow energy from the uncertainty relation, for a short enough period of time, and use it to create a photon. The snag is, almost as soon as the photon is created it has to be reabsorbed by the electron, before the world at large 'notices' that energy conservation has been violated. The photons exist only for a tiny fraction of a second, less than 10-15 seconds, but they are popping in and out of existence around electrons all the time.

My limited knowledge of physics makes me think, 'Couldn't you build a machine that can harness the energy from those photons and turn it into electricity?' I know it would be very difficult, but would it be possible? Have I just stumbled upon the green energy of the future? Or am I missing a critical piece of this puzzle?

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    $\begingroup$ Did you overlook the bit about "as soon as the photon is created it has to be reabsorbed by the electron"? $\endgroup$
    – WillO
    Commented Aug 10, 2023 at 14:52
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    $\begingroup$ "Have I just stumbled upon the green energy of the future? Or am I missing a critical piece of this puzzle?" No and yes, respectively. $\endgroup$
    – hft
    Commented Aug 10, 2023 at 14:53
  • $\begingroup$ @WillO It says they last up to 10⁻¹⁵ seconds; if you separate the photon from the electron in that time, it can't get reabsorbed through a wall, thus giving you extra time to retrieve its energy $\endgroup$
    – Pazzel
    Commented Aug 10, 2023 at 15:09
  • $\begingroup$ The fact you think you could accomplish something in $10^{-15}$ s is itself very concerning. The reality of this situation is that there is no physical photon ever even present. This is alluding to a complicated constructed in the path integral formulation of quantum field theory called “virtual photons,” which don’t properly exist at all and are merely a mathematically required contributor to the various energies of a particle system. The reasons are far too technical for a comment. $\endgroup$
    – Matt Hanson
    Commented Aug 11, 2023 at 5:33

2 Answers 2

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When a ball propagates inertially from point A to point B, it takes a straight line at constant speed, which minimizes the action. For a quantum particle, all possible paths contribute to the amplitude…with the paths around the minimum action dominating due to coherence.

For an interacting quantum field, such as the electron field, you have to include all possible field configurations and sim the amplitudes. This includes interactions with the electromagnetic field.

This is a difficult problem and is treated with perturbation theory, which is possible because the EM field isn’t too strong.

The 1st order perturbation is the emission and absorption of a virtual photon. Note that this is not what happens, rather it is a picture that describes an approximation to the field configuration.

This used to be done in old fashioned perturbation theory, in which energy is not conserved for a time less than $E/\hbar$. Basic scattering amplitudes were long complex calculations that were important achievements at the time.

In 1948, OFPT was superseded by QED, a fully relativity treatment that conserved energy and momentum all the time. The amplitudes were represented as Feynman diagrams, and first order calculations took minutes.

Nevertheless, ppl still talk about borrowing energy from the bubbling vacuum, which just causes confusion and offers little to no insight.

As an exercises: consider a sole electron emitting and reabsorbing a photon in a manner that conserves both energy and momentum: what do the frequency and wavelength of that photon look like?

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  • $\begingroup$ +1 But to just play devil advocate, I would like to say that, even when we are dealing with free EM fields (so no perturbation theory), the expectation value of E/B fields are zero in vacuum state, but their variance isn't. In fact, it diverges! So how do we explain this phenomena? Virtual particles paired with uncertainty principle can give an intuitive explanation. They can even exert finite force on extended "classical" large objects, the so called Casimir effect. So they are as real as holes, or phonons, not just some artifact from an old approximation. $\endgroup$
    – Paradoxy
    Commented Aug 11, 2023 at 1:39
  • $\begingroup$ I look at is as low frequency modes are cutoff between the plates, and the closer the plates, the more are missing. It’s then energetically favorable for the plates to be closer. I think the experiment that needs to be done is to measure the fluctuations in the force, but idk if that has been done. $\endgroup$
    – JEB
    Commented Aug 26, 2023 at 16:12
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Well let's play a game.

I toss a coin. When it is head, I give you 1€. If it is tail, you give me 1€. Can you make a profit by playing this game with me? Yes, and No! Yes, it might so happen that in the first few coin flips we get head again and again. So you do make a profit or maybe the reverse happens and you loss some money. But in a long run, you lose all your profits, or you recover from your losses.

It might so happen that a photon come to existence out of nowhere. If you capture it you make a profit, no? (insert stonks meme) But It might also so happen that, a photon in your pocket disappear to nothingness. No matter how much you try, the number of photons in your pocket remains the same in long interval.

P.S: Be very skeptical about non mathematical physics books. They hide a lot of important information, such as concept of variance and uncertainty and they make everything look interesting (well to sell their book, obviously), but the reality is different.

I would be thankful if I know why I was down voted, I might as well throw away my master degree in physics.

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  • $\begingroup$ thank you for the simple but useful answer. Often, the answers are very confusing for my tiny brain, but yours is simple to understand and helpful. $\endgroup$
    – Pazzel
    Commented Aug 11, 2023 at 8:38
  • $\begingroup$ @Pazzel if your brain was tiny you wouldn't have asked this question, don't let others discourage you from asking. As a bonus point, note that we, as macroscopic objects, whether we want to not, interact with a lot of quantum objects at the same time. So it is not really meaningful to isolate one virtual photon and talk about it. It is always a set of many interactions at the same time, and they happen in a such way that we cannot exploit them for our benefits, well even we could, still in a long run we couldn't profit. $\endgroup$
    – Paradoxy
    Commented Aug 11, 2023 at 17:56

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