How Do Virtual Particles Exist Without Violating Conservation Laws?

[putongren]

Hi

I'm trying to learn more about Quantum Foam and naturally my curiosity led me to Wiki. In Wikipedia, it says that at such small scales (Planck length) the uncertainty principle allows particles and energy to briefly come into existence, and then annihilate, without violating conservation laws.

Now, how is it that virtual particles can come in and out of existence without violating the conservation laws?

 

[starkind]

average their coming and going over some small region? As one emerges, another disappears. Net gain or loss is zero, so no violation.

 

[friend]

average their coming and going over some small region? As one emerges, another disappears. Net gain or loss is zero, so no violation.

Is the zero point energy of the quantum foam correlated to the overall curvature of spacetime?

 

[starkind]

I imagine not, friend. Spacetime, overall, is large and nearly flat. Quantum foam is very small and tightly curved.

 

[Orion1]

Since energy curves spacetime according to Einstein's theory of general relativity, this suggests that at sufficiently small scales the energy of the fluctuations would be large enough to cause significant departures from the smooth spacetime seen at larger scales, giving spacetime a "foamy" character. However, without a theory of quantum gravity it is impossible to be certain what spacetime would look like at these scales, since it is thought that existing theories would no longer give accurate predictions in this domain.

[/Color]
Reference:
Quantum foam - Wikipedia

 

[friend]

I imagine not, friend. Spacetime, overall, is large and nearly flat. Quantum foam is very small and tightly curved.

The small momentary tightly curved twists in spacetime are characteristics of individual quantum fluxuations, and there is energy associated with each individual twist. That energy can be hugh at times. But the overall curvature of space time has to correlate to the average energy density of that region. So if there is a positive zero point energy, then there has to be a curvature associated with that, right? What's that work out to be, I wonder.

 

[starkind]

As you say, within a region energy can be huge. Within another region, energy may approach zero. I imagine the difference between 'a region of spacetime' and 'all of spacetime' is some set of boundaries. As far as I know, spacetime is unbounded, would you agree?

If you wish to establish a correlation between two things, there must be some similarity between them. What similarity can there be between a thing which is totally bounded and a thing which has no boundaries? Isn't this like trying to divide any number by zero, or infinity by any number?

How much energy is there in all of spacetime? Can there be a correlation between all the energy in spacetime and all the energy in some small region of spacetime?

 

[friend]

As you say, within a region energy can be huge. Within another region, energy may approach zero. I imagine the difference between 'a region of spacetime' and 'all of spacetime' is some set of boundaries. As far as I know, spacetime is unbounded, would you agree?

If you wish to establish a correlation between two things, there must be some similarity between them. What similarity can there be between a thing which is totally bounded and a thing which has no boundaries? Isn't this like trying to divide any number by zero, or infinity by any number?

How much energy is there in all of spacetime? Can there be a correlation between all the energy in spacetime and all the energy in some small region of spacetime?

As I understand it, General Relativity equates curvature (positive curvature) to ANY kind of energy density, right? So if there exist a positive (non-zero) zero point energy due to QFT, then shouldn't there also be non-zero, positive curvature, and visa versa? However, the zero point energy is also called the cosmological constant which drives the universe into accelarated expansion. Doesn't this expansion cause a negative curvatue in spacetime? So which is it, positive curvature due to a positive amount of zero-point energy, or negative curvature due to energy of the cosmological constant?

 

[seggahme]

gravity theory with lambda term and without it - 2 different theories.

 

[starkind]

Consider the curvature of the surface of the ocean. Now consider the curvature of a single wave as it strikes the shoreline. How is the curvature of the ocean affected by the curvature of a wave along the shore?

I might cup my hand and throw a splash of water, and the drops would be even more tightly curved than the wave they came from. Does this affect the curvature of the ocean? Therefore local curvature may have negligible effect on global curvature. I might find a means to produce the finest, most tightly curved droplets of all, but the curvature of the ocean does not change in any measurable way because of my doing so.

Or imagine a sheet of some deformable metal. A ballpeen hammer might produce a local dent, but if the sheet is very large, the dent might cause no change to the flatness of the sheet at all. If the dent is very small and the sheet of metal is very large and very flat, can you say that the additon of a small dent changes the curvature overall? If you tried to calculate the change in curvature of a very large sheet with a very small dent, you would find that the change in overall curvature is so small as to be unmeasurable even in principle, since it would be drowned out in other local effects, such as thermal variations, or even the molecular scale variations in the smoothness of the sheet.

I have to conclude that the overall change of curvature caused by local deformations in a very large spacetime is too small to measure even in principle.

Now maybe you would argue that changes in overall curvature of spacetime would have some effect on the amount of local curvature caused by a given force. However, spacetime is very, very, very flat. No one has ever found any measurable evidence for an overall curvature of spacetime. Since it is so very flat, do you suppose a small change in overall curvature could have a measurable effect on the curvature of the tiny little local dimple?

The overall curvature of spacetime is a proposal from general relitivity. The curvature of spacetime due to local energetic densities is a proposal from particle physics. Yes, it would be nice to find a connection between general relativity and particle physics. In fact, it is something of a holy grail. IMHO the correspondence you propose does not lead us to the required solution.

 

[friend]

The overall curvature of spacetime is a proposal from general relitivity. The curvature of spacetime due to local energetic densities is a proposal from particle physics. Yes, it would be nice to find a connection between general relativity and particle physics. In fact, it is something of a holy grail. IMHO the correspondence you propose does not lead us to the required solution.

The questions are simple: Does there exist a non-zero zero-point-energy due to the uncertainty principle that gives an overall average energy density in any size region of space, (yes or no)? Is there a curvature associated with ANY energy density prescribed by GR, (yes or no)? If the answer is yes to both, then the conclusion is inescapable: there is a curvature associated with the zero-point-energy.

 

[seggahme]

The questions are simple: Does there exist a non-zero zero-point-energy due to the uncertainty principle that gives an overall average energy density in any size region of space, (yes or no)? Is there a curvature associated with ANY energy density prescribed by GR, (yes or no)? If the answer is yes to both, then the conclusion is inescapable: there is a curvature associated with the zero-point-energy.

zero-point energy is not observable, so no any sense to talk about its value and sign.
there are 2 contributions to curvature - from normal matter and dark one. so even without normal matter the curvature of space may be nonflat.

 

[starkind]

Friend, an association is not a correlation. So we are down to semantics.

Just for drill, IMHO a correlation means that if one goes up, the other goes up also (or down, if the correlation is inverse.) I tried to show that changing local curvature has no effect on global curvature. Then I tried to show that changing global curvature has no effect on particular local curvature. There is no direct or inverse correlation between overall curvature of space and local curvatures.

To find the overall curvature resulting from the curvature of local regions, you would have to average...how are you going to calculate an average over all of space if you don't know how many regions there are? And what do you do if the total of the regions is infinite?

I am afraid overall curvature cannot be calculated in the manner you suggest.

Unfortunately I am having power source problems with my computer, and may have to shut down indefinitely. If I don't get back here for a while, it is not that I am ignoring you.

Perhaps if you would show how you would do such a calculation it will be more evident.

Thanks for the conversation.

Richard