Do Virtual Particles Travel Faster Than Light and Violate Causality?

[Dynamic Sauce]

Hi Everyone I was wondering if virtual particles travel faster than light,i ask this because i saw a video where it talks about virtual particles traveling faster than light but if that is so would that imply they travel backwards in time and causality is violated? I also ask this because there are a lot of forums on virtual particle's on this site at the moment.
EDIT:Ive been looking at other posts on here and it says that virtual particles are not real,that they don't exist,is this true?

 

[tiny-tim]

Welcome to PF!

Hi Dynamic Sauce! Welcome to PF!

I can't believe everyone missed this thread at the time!

Sorry!

I was wondering if virtual particles travel faster than light,i ask this because i saw a video where it talks about virtual particles traveling faster than light but if that is so would that imply they travel backwards in time and causality is violated?

Virtual particles appear in the maths in a long complicated multiple integral.

The variables of integration are the 4-momentums of the virtual particles.

Every integral is from -∞ to ∞ (in four dimensions).

4-momentum is the 4-vector (energy, 3-momentum), or (E,p).

The speed of that 4-momentum is |p|/|E|.

So the integral is over all values of p, and over all values of p/|E|, ie over all speeds from 0 to ∞ (and also over both positive and negative values of E, see below ).

So, yes, virtual particles (in the maths) have all possible speeds, including faster than c.

What Does it mean when virtual particles travel "Backwards in time" does it mean literally?

Ah, here we're talking about anti-particles.

An anti-particle behaves exactly the same as a particle, provided you "run the film backwards" …

eg take a film of an electron being created at 2 o'clock and destroyed at 3 o'clock, then run the film backwards: it looks exactly like a film of a positron being created at 3 o'clock and destroyed at 2 o'clock.

In the integrals I mentioned above, negative values of E are included, and an particle of energy -E is interpreted as an anti-particle of energy E; and also, in the three-dimensional integrals which are a little further back in the calculation (I didn't mention them, but they're there), the particle's creation and annihilation operators are swapped over.

For example, if the virtual particle is a virtual electron, a negative value of E (but with the same 3-momentum, p) means a virtual positron with the same velocity, but being annihilated before it is created, ie "living backwards".

This is just maths of course!

 

[A. Neumaier]

Hi Everyone I was wondering if virtual particles travel faster than light,i ask this because i saw a video where it talks about virtual particles traveling faster than light but if that is so would that imply they travel backwards in time and causality is violated? I also ask this because there are a lot of forums on virtual particle's on this site at the moment.
EDIT:Ive been looking at other posts on here and it says that virtual particles are not real,that they don't exist,is this true?

More than enough has been said in the threads
https://www.physicsforums.com/showthread.php?t=75307
https://www.physicsforums.com/showthread.php?t=460685
in the PhysicsForums Library at
https://www.physicsforums.com/library.php?do=view_item&itemid=287
and in Chapter A7: Virtual particles and vacuum fluctuations
http://arnold-neumaier.at/physfaq/physics-faq.html#A7
of my theoretical physics FAQ.

If after reading all that you still can't make up your mind whose arguments you want to believe, no amount of discussion here can help you.

 

[jtbell]

I see that DynamicSauce has already posted during the last week or so in the second thread mentioned in the preceding post, so I see no point in continuing this one.