Virtual particles in space.

[Little Bang]

Can anyone tell me how many virtual particles might be found in one cubic meter of space in any given amount of time? Or maybe where I could find such information.

[sebbysteiny]

I don't have an answer, but I have a physical explanation for virtual particles that might help.

 

dE * dt = h/(2pi).

 

What this means is that a virtual particle (and anti particle) of energy E can only exist for a time t = h/((2pi)*(2E)).

 

This also means that virtual particles are absolutely everywhere because if there was a spot with no virtual particles, the uncertainty between time and energy would be 0.

 

I'm not sure how to use that to calculate an actual number of virtual particles.

[Little Bang]

Ok, if each cubic meter of space is filled with virtual particles for some finite amount of time, would they not also exhibit the properties of mass while they were there? If that is true they could possibly be the dark energy we are looking for because the very minimum volume of the milkyway is 10^40 cubic meters. Multiplied times even a small number of particles being in each cubic meter thats a sizable chunk of mass.

[Erasmus00]

What you are suggesting, in fact, is the reason that the calculated cosmological constant from the standard model (which depends on the energy density of space) is very, very high. Meanwhile, the observed cosmological constant is small, but non-zero.

 

This is one of the problems people have when trying to make quantum field theories and general relativity play together.

-Will

[sebbysteiny]

Ok, if each cubic meter of space is filled with virtual particles for some finite amount of time, would they not also exhibit the properties of mass while they were there? If that is true they could possibly be the dark energy we are looking for because the very minimum volume of the milkyway is 10^40 cubic meters. Multiplied times even a small number of particles being in each cubic meter thats a sizable chunk of mass.

 

If my understanding is correct, you cannot be right here because dark energy has the OPPOSITE effect of matter (dark or otherwise). It serves to accellarate the universe's expansion rather than slow it down.

 

Also, the virtual particles will exist for such a small amount of time that gravitational effects are negligable. Further, since they are everywhere, the effects should cancel each other out.

[Erasmus00]

Also, the virtual particles will exist for such a small amount of time that gravitational effects are negligable. Further, since they are everywhere, the effects should cancel each other out.

 

The virtual particles are everywhere, and hence they increase the energy density of free space( so called vacuum energy). It can be shown (though I won't do it here) that in general relativity, the energy density of the vaccuum leads to a repulsive effect. As I mentioned above, the standard model value for the vaccuum energy is orders of magnitude higher than the observed cosmological constant would indicate.

-Will

[Little Bang]

How about this as a possiblity, the virtual particle density of intergalactic space may be far less than galactic space. The same CMB differences that created galaxies might also apply to virtual particle density. This might also explain the observed rotation curve of galaxies.

[sebbysteiny]

It can be shown (though I won't do it here) that in general relativity, the energy density of the vaccuum leads to a repulsive effect

No do show it hear. I never heard that in general relativity. If true, I'd love to see it. Then we don't need to talk about 'dark energy' to explain why the Universe's expansion is accellarating. However, finding this out completely stunned cosmologists as they were completely clueless as to how this could happen.

 

And since the vacuum is uniform in all space, you would have to explain why there is an overrall force at all.

 

 

Back on virtual particles, what velocity do these virtual particles appear? Surely that's depends on your frame. But since the laws of physics is independant of your particular frame, they should be produced with a range of velocities going all the way from c to -c.

 

Yeah, combining relativity and quantum mechanics can be a right *****.

 

However, I have done it, just not with virtual particles. I think a particle physics knowledge is the key to this problem but I never studied that option.

 

Has anybody on this sight studied particle physics in detail?

[Erasmus00]

No do show it hear. I never heard that in general relativity. If true, I'd love to see it. Then we don't need to talk about 'dark energy' to explain why the Universe's expansion is accellarating.

 

Except the calculated cosmological constant is (minimally) several orders of magnitude higher than observed.

 

As to the cosmological constant being related to the energy of free space, thats pretty standard in GR, if you don't have Misner/Thorne/Wheeler try here The Cosmological Constant

 

And since the vacuum is uniform in all space, you would have to explain why there is an overrall force at all.

 

See the above references. In short: a uniform energy will cause a uniform curvature.

 

Back on virtual particles, what velocity do these virtual particles appear? Surely that's depends on your frame. But since the laws of physics is independant of your particular frame, they should be produced with a range of velocities going all the way from c to -c.

 

Of course virtual particles appear across the momentum spectrum. And, obviously, higher energy particles are shorter lived.

 

Yeah, combining relativity and quantum mechanics can be a right *****.

 

However, I have done it, just not with virtual particles. I think a particle physics knowledge is the key to this problem but I never studied that option.

 

Combining quantum mechanics and special relativity is doable, its known as quantum field theory and is essentially what we are discussing (apart from GR). If you have combined quantum field theory and general relativity, you would have a nobel prize on your hands. Its an unsolved problem.

 

Has anybody on this sight studied particle physics in detail?

 

I have.

-Will

[sebbysteiny]

Of course virtual particles appear across the momentum spectrum. And, obviously, higher energy particles are shorter lived.

 

That's what I thought. Except what stopped me from being immediately convinced by it is that energy measurments depend on what frame you are in. On frame's 'high energy' may be another frames 'stationary'. So relativity calculations are necessary before one can agree with this.

 

Lastly, is the energy density of free space ENTIRELY in the form of virtual particles? Because if it is, then it can only have an attactive force and cannot actually repulse. I'm not quite sure how energy works for gravitation.

[Little Bang]

Question sebby, how do we know that all space is uniform?

[sebbysteiny]

Question sebby, how do we know that all space is uniform?

 

On the microscopic, it isn't. But when averaged over, say, a square meter, there are no equations or laws I know that predict a non-uniform distribution. Are you aware of any?

[Farsight]

I am.

 

The law of gravity.

 

:)

[sebbysteiny]

I think you've seen something I havn't. You should explain how the theory of gravity predicts a non-uniform vacuum density.

[Erasmus00]

That's what I thought. Except what stopped me from being immediately convinced by it is that energy measurments depend on what frame you are in. On frame's 'high energy' may be another frames 'stationary'. So relativity calculations are necessary before one can agree with this.

 

But you can always formulate things in terms of the covariant energy/momentum 4-vector. This is, in fact, just what is done in any good relativisticly covariant theory.

 

Lastly, is the energy density of free space ENTIRELY in the form of virtual particles? Because if it is, then it can only have an attactive force and cannot actually repulse.

 

First, no one knows what the energy density of free space actually is. The quantum field theory/standard model calculation is FAR too big to match the observed constant.

 

Second, if the energy density of free space WAS entirely virtual particles it would not imply an attractive force. I again refer you to the reference I posted above on the cosmological constant and the energy density of empty space.

-Will

[sebbysteiny]

Second, if the energy density of free space WAS entirely virtual particles it would not imply an attractive force. I again refer you to the reference I posted above on the cosmological constant and the energy density of empty space.

 

A quick qualitive summary would help me a great deal.

[Erasmus00]

A quick qualitive summary would help me a great deal.

 

Well, to build up the standard "toy model" of such things: consider a real scalar field with Lagrangian

 

[math] \mathcal{L}=\frac{1}{2}g^{\mu\nu}\partial_{\mu}\ph\partial_{\nu}\phi -V(\phi)[/math]

 

where g is the metric tensor and V is some potential energy.

 

Now, our stress energy tensor is

 

[math]\frac{\delta S}{\delta g^{\mu\nu}} = T_{\mu\nu} = \frac{1}{2}{\partial_{\mu}\phi\partial_{\nu}\phi + g^{\lambda\rho}\partial_{\rho}\phi\partial_{\lambd}\phi g_{\mu\nu}-V(\phi)g_{\mu\nu} [/math]

 

Now, for our minimal action solution, we don't have non-uniformities. This is because of the gradient term in the Lagrangian. Hence, the only surviving bit of the energy/momentum is

 

[math] T_{\mu\nu} = -V(\phi_0)g_{\mu\nu} [/math]

 

Obviously the uniform energy V is simply the energy density of the vaccuum, so this is

 

[math] T_{\mu\nu} = -\rho_{vac}g_{\mu\nu} [/math]

 

Now, this is simply the stress energy tensor of a perfect fluid, so we see Pressure from the vaccuum is simply [math]-\rho_{vac}[/math] So, a uniform positive energy density leads to a negative pressure.

-Will