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

1. Jun 4, 2010

### 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?

2. Jun 4, 2010

### 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.

3. Jun 5, 2010

### john88888

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

Last edited by a moderator: May 4, 2017
4. Jun 5, 2010

### DaveC426913

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

Last edited by a moderator: May 4, 2017
5. Jun 5, 2010

### john88888

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

6. Jun 5, 2010

### 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).

7. Jun 5, 2010

### 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'.

8. Jun 5, 2010

### Phrak

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

9. Jun 5, 2010

### my_wan

It only occurs when you consider a suficiently small region of space. The vaccuum 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.

10. Jun 5, 2010

### tom.stoer

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

11. Jun 5, 2010

### my_wan

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.

12. Jun 6, 2010

### 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

$$<\partial_0 H> = 0$$

13. Jun 6, 2010

### sheaf

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 ?

14. Jun 6, 2010

### tom.stoer

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

I agree, that's confusing.

Not completely, but to a large extend, yes!

15. Jun 6, 2010

### john88888

So the consensus is energy is never violated at anytime

16. Jun 6, 2010

### 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?

17. Jun 6, 2010

### tom.stoer

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

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

18. Jun 6, 2010

### Coldcall

thats all well and good, but it doesnt answer my question. Why would nature be so tight with resources?

19. Jun 6, 2010

### 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.

20. Jun 6, 2010

### Coldcall

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