What exactly are uncertainty and virtual particles?

[Jake1]

So, as I understand it, virtual particles can exist because they exist for such a short period of time, so as uncertainty in time decreases, uncertainty in energy increases, creating enough energy for a particle to exist for that time increment. But why does uncertainty in time decrease as the length of time decreases? Is uncertainty equal to change? Is that why uncertainty and change are both represented by delta? I'm very uncertain about what uncertainty actually is.

[Implicate Order]

So, as I understand it, virtual particles can exist because they exist for such a short period of time, so as uncertainty in time decreases, uncertainty in energy increases, creating enough energy for a particle to exist for that time increment. But why does uncertainty in time decrease as the length of time decreases? Is uncertainty equal to change? Is that why uncertainty and change are both represented by delta? I'm very uncertain about what uncertainty actually is.

 

Hi Jake1

 

This handy set of brief FAQ's should help.

[Jake1]

Yes, I've already read that FAQ, and it does a nice job of explaining virtual particles, but I'm still confused as to what uncertainty is. Does uncertainty in time decrease as change in time decreases, because the particle can only exist in a shorter interval of time, so its position in time is less uncertain? And this is what causes uncertainty in energy to increase, resulting in virtual particles?

[Implicate Order]

It's probably best to initially compare and contrast the notion of a 'particle' from a classical and then quantum mechanical perspective.

 

Classical particle physics talks in terms of 'point' particles which descxribe the properties of particles without any spatial dimension. In this way we may have a point mass property, a point charge property and so on and so forth.

 

In QM there is a distinction placed between a 'point particle' property also called an elementary particle (eg. electron, quark and photon) and a composite particle (eg. proton or neutron). The distrinction is based on how many properties we are defining. When defining single properties we refer to elementary particles and when defining multiple properties we refer to composite particles. Note here that when talking in terms of single properties, a single wave description of an electron for example is fully described but exists as a superposition of states. To be clear I am not combining a wave description of charge, a wave description of spin and a wave description of rest mass to produce this electron wavefunction as fundamentally the electron wave description is as small as we can go from a particle perspective. The wave description needs to include all this information and the possible superposition statesw of this description.

 

In QM (without first taking into account HUP) an elementary particle with a single property is a 'delocalised wavepacket' which is in a superposition of states and can be 'exactly localised' on wavefunction collapse and hence approximates a classical notion of a particle with no spatial extent. However a composite particle (comprising multiple properties) can never be 'exactly' localised on collapse due to the inability to make a single coherent superposition of states of its component properties. As a result, the composite particle has extent in space in QM. Now we unfortunately have to add the Heisenbergy Uncertainty Principle to this perspective which therefore renders both descriptions in terms of uncertainty.

 

When dealing with uncertainty it is best to not talk in terms of gradating scales in resolution of time or space. I see your confusion in dealing with a diminishing time interval, but I am thinking in your description that you may be falling into this trap which is very easy to do.

 

It is a phenomenon that arises at a particular scale referred to as the planck scale. Many of us think that this scale arises from the inability of our measuring instruments to specifically define a particles location or momentum, but importantly the uncertainty principle is not a measuring instrument accuracy problem. It is a fundamental limit at a particular scale that prevents us from ever determining the exact position and momentum simultaneously of a particle. It is not a progressively fuzzy nature of things as we increase our magnification (the fuzziness is referred to as the observer effect and simply is a resolution problem in our equipment). The HUP however is an additional fuzzy effect that hits us like a brick wall a particular scale resolution.The HUP is an inherent fundamental feature of all wave like systems and arises on any interaction event occurring between a classical measurement of a quantum system.

 

What HUP says is that it is not a problem of the specificity of our measuring instruments, but at a fundamental level there is an actual limit to which certain pairs of physical properties (known as complementary variables) can be known simultaneously. An example of a complementary pair is position and momentum. For example, the more precisely the 'position' of some particle is known, the less precisely it's momentum can be known, and vice versa. This obviously throws a spanner in the works for classical physics using notions such as a smooth and continuous spacetime. Now you may say that this is not a problem if we could freeze the entire universe in time at an instant (and therefore sacrifice our knowledge of each particles momentum) as we would then be able to determine the position of every particle contained theirein, but that is not how nature seems to work. QM says that every physical system 'must' have some residual energy, and we literally cannot freeze the universe even when the temperature is absolute zero. At this point we are left with residual energy known as 'zero-point energy' or the energy of the vacuum. This zero-point energy allows the sudden appearance of particles to pop into existence and then annihalate each other (provided they do so within the finite limits allowed by HUP).

Even at the smallest scales (as energy is equivalent to mass) of spacetime, this energy-mass equivalence produces space-time curvature. This spacetime curvature causes fluctuations in the distance between points in spacetime resulting in stochastic behaviour and resulting in distances in spacetime becoming ill-defined. The problem with this notion is that when we look at an infintesimally small region, our calculations yield infinite energy answers which clearly does not seem to be the case with nature suggesting that perhaps there is a fundamental limit to how small we actually can go with spacetime to avoid this conundrum.

Work in QM derived a theoretical 'natural' limit referred to as the Planck length which neatly utilised universal consants in its definition thereby avoiding relativists demands that space and time canot be considered seperate but can only be invariant when considered together as spacetime. Some believe that the Planck length (being derived from universal constants) retains its value in all reference frames (this however may lead to doubly special relativity) but my opinion is otherwise. I am thinking that the scale referred to as the planck boundary is where classial properties emerge from a fundamentally quantum realm....but that is just philosophical mumbo jumbo so take no heed.

 

Jake1, this is the best explanation I can give without setting forth into philosophical territory. You are right to be confused about the causative factors of HUP and vacuum energy as dependent on your interpretation taken, you have different viewpoints. I could share my viewpoint with you on this but the thread would probably need to be re-located from mainstream physics. I hope the above helps at least a bit with your ponderings.

Edited February 11, 2014 by Implicate Order