Can virtual particles break the law that energy cannot be created or destroyed?

[john88888]

Im new and not that advanced in science so can you try to keep your answers simple. My question is can virtual particles break the law that energy cannot be created or destroyed?
Have virtual particles been proven/observed? thanks in advance for your answers

 

[Mr.Illusion]

Hey, Virtual Particles do not break the law that energy cannot be created or destroyed. This is because Virtual Particles only "borrow" the energy for a very short amount of time. In fact, it's so short that we can't observe them. They actually arise from time/energy uncertainty principle.

 

[john88888]

I asked a particle physicst from this website http://phy.syr.edu/HEPOutreach/ lady named marina aurtuso and she said yes can somebody explain that

 

[DaveC426913]

I asked a particle physicst from this website http://phy.syr.edu/HEPOutreach/ lady named marina aurtuso and she said yes can somebody explain that

Explain what? We don't know what she said.

 

[john88888]

all she said was yes it does violate the conservation of energytheory no explanation

 

[tom.stoer]

virtial particles do not violate energy-momentum conservation. At each vertex in a Feynman diagram energy and momentum are conserved.

But the virtual particles can be off-shell. Usually for a particle with rest mass m there is the relation

E² - p² = m²

This relation can be violated, so virtual photons can have non-zero m (but this is a mathematical artefact).

 

[my_wan]

For a 'very' short time, it might be said that conservation of mass/energy is locally violated. Averaged over even a whole second, or a sufficient region of space, no such violation occurs. Virtual particles come in particle/antiparticle pairs, which quickly annihilate each other. Averaged over space and time, such particle pairs remain stable, so the total energy remains constant. The Casimir Effect is taken as the most straightforward experimental evidence. In QM a vacuum may be basically empty, but that does not mean it's 'nothing'.

 

[Phrak]

For a 'very' short time, it might be said that conservation of mass/energy is locally violated. Averaged over even a whole second, or a sufficient region of space, no such violation occurs. Virtual particles come in particle/antiparticle pairs, which quickly annihilate each other. Averaged over space and time, such particle pairs remain stable, so the total energy remains constant. The Casimir Effect is taken as the most straightforward experimental evidence. In QM a vacuum may be basically empty, but that does not mean it's 'nothing'.

I'm not unfamiliar with the argument but not the particulars. Can you give a simple example where energy conservation doesn't momentarily occur?

 

[my_wan]

It only occurs when you consider a suficiently small region of space. The vacuum fluctuations can vary as a result of the uncertainty principle. In the bigger picture this is similar to saying an air conditioner violates conservation because it decreases entopy in some limited area. It of course didn't because the area of entropy decrease is not an enclosed system, and the entire system must be considered. Which of course increases overall entropy.

Note also that there is a 3rd law of thermodynamics, which doesn't allow absolute zero. This implies that, even at maximum entropy, small local random fluctuations will remain. Classically this is a small random variations in temperature with random molecular motion, which average over to a constant. In QM this occurs as a result of the uncertainty principle. The Casimir Effect works by suppressing random fluctuations of certain wavelengths between 2 masses.

 

[tom.stoer]

It only occurs when you consider a suficiently small region of space. The vacuum fluctuations can vary as a result of the uncertainty principle.

Please show me a calculation from which violation of conservation of energy can be derived.

 

[my_wan]

Please show me a calculation from which violation of conservation of energy can be derived.

I didn't say it did. I only said it would appear that way if you restricted your description to some part of the system. I even used an air conditioner, where only the thermodynamic effects inside the building is considered, as a classical analogy. The second law applies to enclosed systems only. Thus when you only consider some subset of an enclosed system it can appear as if the 2nd law is violated, when in fact it's not.

 

[tom.stoer]

So you say that quantum fluctuations may carry away energy from a certain region of space. OK, I agree.

Please understand why I insist on energy conservation. There is this argument you can read quite frequently in some popular books that particles can borrow energy and that this indicates that energy conservation is violated at short time scales.

I agree that you can have quantum fluctuations and non-zero energy fluctuation

$$<E^2> - <E>^2$$

But at the same time you have

$$\partial_\mu T^{\mu\nu} = 0$$

as an operator identity; and you certainly have

$$<\partial_0 H> = 0$$

 

[sheaf]

So you say that quantum fluctuations may carry away energy from a certain region of space. OK, I agree.

Please understand why I insist on energy conservation. There is this argument you can read quite frequently in some popular books that particles can borrow energy and that this indicates that energy conservation is violated at short time scales.

I agree that you can have quantum fluctuations and non-zero energy fluctuation

$$<E^2> - <E>^2$$

But at the same time you have

$$\partial_\mu T^{\mu\nu} = 0$$

as an operator identity; and you certainly have

$$<\partial_0 H> = 0$$

I'm trying to learn some QFT at the moment (haven't got very far yet), and I must say that I've been a bit confused by all this talk of energy-time uncertainty relation in connection with vacuum fluctuations.

Firstly, I should mention that I've only got as far as learning about perturbation treatments of "scattering" type scenarios, where I have some incoming particles, a few vertices, some internal lines and some outgoing particles. In these cases, for the momentum space Feynman diagrams, I have a delta function which imposes conservation of four momentum, so all is clear.

However, I'm confused about what precise QFT process the popular accounts are referring to when they talk of virtual pair creation via the energy/time uncertainty relation. The talk is usually of the vacuum as something like a "choppy sea in which particle/antiparticle pairs are constantly being created and annihilated". This is usually used in explaining effects like screening of bare charge and suchlike.

But in the more rigorous treatments of vacuum polarization I see no mention of the energy/time uncertainty relation. Am I right in saying that it's completely misleading to talk about energy/time uncertainty in this context ?

 

[tom.stoer]

... In these cases, for the momentum space Feynman diagrams, I have a delta function which imposes conservation of four momentum, so all is clear.

That's exactly the point: energy-momentum conservation at each vertex!

I'm confused about what precise QFT process the popular accounts are referring to when they talk of virtual pair creation via the energy/time uncertainty relation.

I agree, that's confusing.

But in the more rigorous treatments of vacuum polarization I see no mention of the energy/time uncertainty relation. Am I right in saying that it's completely misleading to talk about energy/time uncertainty in this context ?

Not completely, but to a large extend, yes!

 

[john88888]

So the consensus is energy is never violated at anytime

 

[Coldcall]

is not strange that nature would regulate so tightly the energy/matter resources available to the universe at any given instant? Wouldn't that perhaps suggest that the universe is finite? Why the laws of conservation if energy.matter is availabe in unlimited quantities?

 

[tom.stoer]

Why the laws of conservation if energy.matter is availabe in unlimited quantities?

Because these conservation laws are local! Not only is the total energy conserved, but even for the local energy-density there is a conservation law, namely

$$\partial_\mu T^{\mu\nu}(x) = 0$$

 

[Coldcall]

Because these conservation laws are local! Not only is the total energy conserved, but even for the local energy-density there is a conservation law, namely

$$\partial_\mu T^{\mu\nu}(x) = 0$$

thats all well and good, but it doesn't answer my question. Why would nature be so tight with resources?

 

[tom.stoer]

These conservation laws can be derived from symmetry arguments, namely Noether's theorem. For energy conservation it's rather simple: physical laws are time-independent (laws look the same at every point in time). That causes energy to be conserved.

 

[Coldcall]

These conservation laws can be derived from symmetry arguments, namely Noether's theorem. For energy conservation it's rather simple: physical laws are time-independent (laws look the same at every point in time). That causes energy to be conserved.

okay, so if the laws regulating quantum fluctuations are time-independent then in theory they exist for all universes (assuming a multiverse)?

 

[tom.stoer]

of course this depends; what do you mean by "multiverse" ? the problem is that - as multiverses are invisible to us - so are their laws ...

 

[Coldcall]

of course this depends; what do you mean by "multiverse" ? the problem is that - as multiverses are invisible to us - so are their laws ...

its actually an argument against many-worlds theories of qm. Not evidence, just a line of argument. For instance we see in our universe at almost every level of physical law (not just at quantum scale) how nature runs a very tight ship on resource allocation and efficiency. ie. virtual particles.

The point is that it would seem contrdictory for nature to be such a strict mistress only in our universe, but then spend like a drunken sailor through an infinite amount of such universes.

 

[john88888]

Sorry for posting again but
I just want to confirm this energy is never created or destroyed with virtual particles or any other circumstance and why on other topics about virtual particles on the forum does it say it can and not taking into account multiuniverses does it violate

 

[Naty1]

There is a wide ranging overview here that is pretty decent:

http://en.wikipedia.org/wiki/Conservation_of_energy

I just want to confirm this energy is never created or destroyed...

that IS the current consensus.

But I would NOT take irrevocable solace in that: over history the "consensus" have almost never been absolutely correct. But maybe we are getting better!

 

[tom.stoer]

... it would seem contradictory for nature to be such a strict mistress only in our universe, but then spend like a drunken sailor through an infinite amount of such universes.

I see what you are saying. I tend to agree, but I would not mix it up with conservation laws!

What you are referring to is a principle like Ockham's razor: If there are two theories explaining (predicting) exactly the same phenomena, the one which is simpler should be taken as the correct one. My problem with many worlds is that
- they are invisible by construction
- nevertheless they are taken to be real
- the are postulated in order to interpret QM, not to predict physical phenomena

I can't see any benefit. I have to introduce a plethora of meta-physical entities which I can neither prove nor disprove; I have to believe in them. This is obviously not physics but meta-physics - which is not wrong per se - but in the realm of meta-physics again Ockhams razor applies.

To me the conclusion is as follows: I have two alternatives:
1) QM which works physically but which can't be interpreted meta-physically
2) QM + MW which is physically the same as QM but which adds not observable, not understandable, ... entities.
All what I achieve by alternative 2) is to shift my ignorance from QM to MW.

So by Ockhams razor I reject the many-worlds interpretation.

 

[born2bstar]

yes:

 

[Coldcall]

I see what you are saying. I tend to agree, but I would not mix it up with conservation laws!

What you are referring to is a principle like Ockham's razor: If there are two theories explaining (predicting) exactly the same phenomena, the one which is simpler should be taken as the correct one. My problem with many worlds is that
- they are invisible by construction
- nevertheless they are taken to be real
- the are postulated in order to interpret QM, not to predict physical phenomena

I can't see any benefit. I have to introduce a plethora of meta-physical entities which I can neither prove nor disprove; I have to believe in them. This is obviously not physics but meta-physics - which is not wrong per se - but in the realm of meta-physics again Ockhams razor applies.

To me the conclusion is as follows: I have two alternatives:
1) QM which works physically but which can't be interpreted meta-physically
2) QM + MW which is physically the same as QM but which adds not observable, not understandable, ... entities.
All what I achieve by alternative 2) is to shift my ignorance from QM to MW.

So by Ockhams razor I reject the many-worlds interpretation.

Good point.

Yes i was going to mention ockhams razor as another reason i am dubious of theories which deal with both biocentric coincidences and quantum interpretations by suggesting an infinite amount of universes.

It seems we have used the idea of many-worlds or multiverses as a way to explain away various oddities regarding qm and the existence of life in the universe.

 

[john88888]

sorry for posting again just another question if you take away the many theory is energy still conserved and in the future will there be an uncertainty principle

 

[Coldcall]

sorry for posting again just another question if you take away the many theory is energy still conserved and in the future will there be an uncertainty principle

Im not sure what you are asking. But if MWI is false, it has no siginificant effect on either energy conservation or the HUP. MWI is just an interpretation, a foundational way of imagining what is going on with quantum mechanics.

 

[daisey]

Going back to the original question, since these virtual particles are continually appearing and disappearing, is it possible that the appearance of one pair of particles is "borrowing" the energy from another pair of particles somewhere that just disappeared? In that sense, energy is really not even being "borrowed", but simply transferred. In either case, total system energy is not increased or decreased.

- Daisey

 

[tom.stoer]

... energy is really not even being "borrowed", but simply transferred. In either case, total system energy is not increased or decreased.

Exactly!

If you look at Feynman diagrams (which are the key ingredient when talking about virtual particles - I will come back to that in a final comment) every theory like QED, QCD, MSSM, SUGRA, ... has a uniquely defined set of rules, a set of "elementary Feynman graphs", namely external particle lines, internal particle lines = propagators and vertices.

By combining these elemenatry graphs you can construct arbitrarily complex graphs. The (infinite) set of all graphs is equivalent to the full perturbation theory of the quantum field theory (I do not say "full theory" as it's only a perturbative treatment which misses certain features, so-called non-perturbarive effects which we know are relevant e.g. in QCD for chiral symmetry breaking and confinement).

Basically the Feynman diagrams are a method of book-keeping and a starting point for calculations. But in popular books they are presented w/o the corresponding mathematical rules (where these come from and how the results are calculated). So let's do the same here.

If you only look at the Feynman graphs diagrammatically you see that different types of particles are converted into each other. One can also equip each line with a "label" for the flow of energy and momentum. (just like an electric current in a wire). At each vertex the flow of energy and momentum is conserved; so along with the particles interacting and changing there is a flow which is conserved meaning that energy and momentum is transferred between the particles at the verices.

One final comment regarding virtual particles: it is not the case that virtual particles do exist in nature and Feynman invented his diagrams in order to describe them. It is more or less the case that virtual particles are "created" by drawing Feynman diagrams. If one would be able to do all the math w/o these diagrams directly and w/o any approximation (perturbation expansion) nobody wouldcare about virtual particles.

 

[sheaf]

One final comment regarding virtual particles: it is not the case that virtual particles do exist in nature and Feynman invented his diagrams in order to describe them. It is more or less the case that virtual particles are "created" by drawing Feynman diagrams. If one would be able to do all the math w/o these diagrams directly and w/o any approximation (perturbation expansion) nobody wouldcare about virtual particles.

I've seen different opinions expressed on the "reality" of virtual particles. I've always argued, as you say, on the side that the particles don't exist - they're only intermediate calculation artifacts. The way I've always tried to explain it is that the diagrams they appear in are a bit like terms in a Taylor series - the full sum of the series is what's important, not the individual terms.

In order to make this argument stronger, if I could argue that the perturbation expansion is not unique, then it would be much harder for people to put the counter argument that the individual terms represent physically real processes. So, my question is (sorry if this is a bit dumb - I'm a novice at this): Is it possible to perform alternative perturbation expansions of an amplitude, that are in some way term by term inequivalent, but sum to the same answer ?

 

[john88888]

one of the physicist I asked said yes it does violate that energy cannot be created or destroyed within the limits of Heisenberg uncertainty principle I assume this is just crap I just want to confirm sorry this is a little over my head but I just curious

 

[tom.stoer]

Is it possible to perform alternative perturbation expansions of an amplitude, that are in some way term by term inequivalent, but sum to the same answer ?

Not really (afaik).

But this is comparable to a Taylor series: the theory of holomorphic functions tells you that the series (that means every term in the series) is uniquely defined, provided the series exists at all and provided you consider the same point x for the expansion.

But based on Taylor series we can consider examples of functions that help to understand the limitations. Consider e.g.

$$f(x) = e^{-1/x^2}$$

For this function we known that the function itself as well as all its derivaties satisfy

$$f^{(n)}(0) = 0$$

That means that when constructing the Taylor series we get a sum of zeros. That seems to mean that the radius of convergence is exactly zero. Looking at the same function in terms of a complex variable z=x+iy and investigating

$$f(x=0, y) = e^{1/y^2}$$

we see that now the function diverges at y=0. So the function does not have a single pole of finite order but a more complicated singularity.

Now let's come back to perturbation theory. What can happen:

• we can start from different vacua resulting in different concepts what a "virtual particle" is.
• there can be non-perturbative effects (e.g. solitons, instantons, ...) which contain something like 1/g (g: coupling constant) for which a Taylor series at g=0 is not well-defined; or which are not visible in perturbation theory because they are eliminated by the approximation.
• there are regimes which cannot be described perturbatively, e.g. confinement in QCD; we know it's there, we can calculate it in lattice gauge theory, but we know for sure that we cannot describe it perturbatively; in this case it's not the concept of virtual particles that ceases to exist, but the concept of real particles in the asymptotic states (plane waves); they do not exist because of confinement.
• we can have a non-trivial fixpoint in the renormalization group flow; in QCD we know that it has a Gaussian fixed point g=0 which means that the theory is asymptotically free; this is the reason why perturbation theory makes sense in QCD; that need not be the case in other theories, which means that g=0 may even be an unphysical point and expansions at g=0 are nonsense.
• we can have a perturbation series which is (after renormalization) finite order-by-order, but which diverges when summing up all terms; btw.: this seems to be the normal behaviour of perturbation series, even for well-established theories like QED and QCD.
• we can have a theory which has some sort of duality; e.g. in two dimensions one can show that certain fermionic theories can be mapped one-to-one to bosonic theories (bosonization, Schwinger model) which are strictly identical in the sense that for an amplitude there are two (numerically identical) expressions, one containing only bosons, one containing only fermions; so what is the particle content of this theory? bosons or fermions?

 

[sheaf]

• we can start from different vacua resulting in different concepts what a "virtual particle" is.
• there can be non-perturbative effects (e.g. solitons, instantons, ...) which contain something like 1/g (g: coupling constant) for which a Taylor series at g=0 is not well-defined; or which are not visible in perturbation theory because they are eliminated by the approximation.
• there are regimes which cannot be described perturbatively, e.g. confinement in QCD; we know it's there, we can calculate it in lattice gauge theory, but we know for sure that we cannot describe it perturbatively; in this case it's not the concept of virtual particles that ceases to exist, but the concept of real particles in the asymptotic states (plane waves); they do not exist because of confinement.
• we can have a non-trivial fixpoint in the renormalization group flow; in QCD we know that it has a Gaussian fixed point g=0 which means that the theory is asymptotically free; this is the reason why perturbation theory makes sense in QCD; that need not be the case in other theories, which means that g=0 may even be an unphysical point and expansions at g=0 are nonsense.
• we can have a perturbation series which is (after renormalization) finite order-by-order, but which diverges when summing up all terms; btw.: this seems to be the normal behaviour of perturbation series, even for well-established theories like QED and QCD.
• we can have a theory which has some sort of duality; e.g. in two dimensions one can show that certain fermionic theories can be mapped one-to-one to bosonic theories (bosonization, Schwinger model) which are strictly identical in the sense that for an amplitude there are two (numerically identical) expressions, one containing only bosons, one containing only fermions; so what is the particle content of this theory? bosons or fermions?

Thanks very much Tom, there are some very persuasive arguments in that list !