Is “the uncertainty principle basic to all reality”?
The uncertainty principle says, among other things, that one cannot (simultaneously) measure precisely both energy and time. It also says one cannot (simultaneously) measure both momentum and position.
Some people might say: “So what! The universe might look different from what it does now if it were not for the uncertainty principle, but what has that to do with reality?”
Let’s consider some basics.
On the one hand we have the ‘tangible’ stuff of the universe, which we call “matter” and on the other hand we have the ‘intangible’ stuff of the universe, which we call “space”, or “space-time”, if you prefer.
Let us assume that it is possible for matter to exist independently of space-time and vice-versa.
Since matter, we say, is tangible we can ascribe tangible properties to matter, such as energy and momentum.
But since space-time, we say, is intangible we cannot ascribe such properties to space-time.
Is this reasonable?
Well then, if space-time is intangible then it would be pointless to try to measure, for example, the energy of space-time, for how can you measure the energy of something that is intangible?
Or how can you measure the momentum of something that is intangible?
Nevertheless, according to the uncertainty principle, if we did try to measure the energy of space-time we should find that the energy is not zero!
And if we tried to measure the momentum of space-time we should find that the momentum is not zero!
How can that be?
The answer is that zero is a precise value, and therefore, the energy of space-time at some particular point in time cannot be zero.
Likewise, the momentum of space time cannot be precisely zero at some precise position in space..
So what the uncertainty principle says, in effect, is that there can be no such thing as a truly empty space-time.
The implications of the uncertainty principle extend far beyond the mere question of determinacy of properties like energy and momentum, for they go right to the heart of the question of what constitute matter and space-time.
The importance of the uncertainty principle in this connection stems from the predictive power of the uncertainty principle.
For example, the uncertainty principle predicts the existence of “virtual” particles, which are thought to be constantly popping in and out of the so-called “vacuum” of empty space.
Virtual particles resemble real particles in practically every respect except that they have such extremely short lifetimes that they (apparently) can never be observed directly.
So what, some people might say!
Well, for one thing, the virtual particles are thought to be the carriers of the fundamental forces between real particles namely, the electromagnetic, strong, weak and gravitational forces, respectively.
For example, a virtual photon is thought to be the carrier of the electromagnetic force and a gluon is thought to be the carrier of the strong force.
And though no one seems to be quite sure what virtual particle is the carrier of the gravitational force, almost certainly there must be such a particle.
Imagine what the universe might look like if there were no forces.
Then there would be no such thing as “motion” in the usual sense of the word.
Because the only way we have of defining motion is in terms of relationships between material bodies.
If there were no forces between particles of matter then there would be nothing to relate the state of one particle relative to another. And therefore there would be no way of measuring things like distances and times.
There could, in that case, be no such thing as motion through space because space itself would be undefined--it simply would not exist as we know it.
The question you might now ask is: could matter exist if space-time did not exist, or vice versa?
Well, the uncertainty principle predicts the existence of virtual particles, so presumably the uncertainty principle is fundamental to the existence of virtual particles.
As for real particles, apart from the fact that real particles have much longer lifetimes than virtual particles, there is really very little, in principle, to distinguish between real particles and virtual particles.
Even so, how can we know for sure whether, or not, the uncertainty principle is fundamental to the existence of real particles as well as virtual particles?
In trying to answer that question, let’s assume that the uncertainty principle is at least fundamental to the existence of virtual particles.
It is an observable fact that we cannot “see” virtual particles in the way that we see real particles. A table or a chair, for example, is obviously made of real particles, not virtual particles. The coffee I had at breakfast is made from real particles.
The reason why we do not see virtual particles as we see real particles, in part, is because virtual particles as a rule have much shorter lifetimes than do real particles.
We could, I suppose, define a virtual particle to be any particle which has a lifetime shorter than some arbitrary time which is shorter than can be measured directly.
Another part of the reason why we do not see virtual particles like we see real particles is that some (about half) of the virtual particles have negative energies. This means that these particles not interact with real particles in the same way as real particles interact with other real particles.
For example, a positive energy electron interacts with a positive energy positron (a positively charged anti-electron) by a process in which the total mass-energy of these particles is converted into pure (massless) energy. So what we see in this case is the particles vanish (as such) in a burst of radiation (a pair of photons). Since the positron is the antiparticle of the electron, total charge, spin etc. are conserved. Energy and momentum also are conserved, which is why we see a burst of radiation rather than total annihilation (into nothingness).
By contrast, when a positive energy electron interacts with a negative energy anti-electron, provided that the energies and momentum are equal in magnitude, the electron simply vanishes into nothingness; no flash of light, no puff of smoke, nothing to indicate that the electron ever existed.
As before, energy, momentum, spin, etc. are conserved but because total energy and total momentum are zero annihilation in this case is total.
You might be wondering at this point, what makes some particles real and some particles virtual? Why aren't all particles real, or why aren't all particles virtual?
To gain some understanding of why that is so, imagine that you are travelling in a space ship through (seemingly) empty space.
Let us suppose, for the moment that, although the space ship has an engine, the engine, for the present is turned off.
And so, according to Newton’s first law of motion, the space ship is drifting through space at uniform velocity, that is to say, without acceleration.
As you might expect, from your vantage point in this freely-floating spaceship, space appears to essentially empty (despite the presumed presence everywhere in space of virtual particles galore).
But suppose you turn the engine on and set it to full blast.
Suddenly see a glow in front of you as though half the sky were lighting up.
This glow, you find, consists not only of photons (particles of light) but particles of all kinds, such as electrons, neutrinoes, protons etc.
[I hasten to add that you would have to be accelerating at a truly tremendous to see the more energetic particles in this radiation, for the effect in question is very, very weak, at ordinary rates of acceleration).
The effect you would be seeing is called the Unruh Effect. It is an effect which results purely from acceleration.
[Note that a non-accelerating observer would not observe the particles due to the Unruh Effect; in that sense particles which appear real to one observer need not necessarily appear real to another.]
In effect, the fact that you are seeing these particles means that, from your perspective, there is an excess of positive energy (virtual) particles over negative energy (virtual) particles, because if there were an equal number of both kinds of particles the net energy would be zero and you would not be seeing any particles at all.
Therefore, some of the virtual particles which previously were invisible to you now have become visible because of your acceleration.
But acceleration, as Einstein pointed out, is equivalent to gravity.
Therefore you could say that the particles which previously were virtual particles, have become real by virtue of the gravitational field generated by your acceleration.
Can you see the similarity here between the radiation resulting from the Unruh effect and another effect: black hole (Hawking) radiation?
Black hole radiation is caused by the gravitational acceleration of virtual particles near the event horizon of a black hole, which causes some of the virtual particles in that region to become real.
In that sense black hole radiation and the radiation resulting from the Unruh effect are analogous.
All of which bring me to the point that I am trying to make here.
We live in a universe which is dominated by matter. Matter has mass and therefore it has gravity.
And gravity, as we have just seen, causes virtual particles to become real.
Can gravity exist without matter?
Can matter as we know it exist without space-time?
No because space-time is intimately related to gravity and matter cannot exist independently of gravity.
So put together the uncertainty principle and gravity and what have we got?
What we have got is this:
We started out with the uncertainty principle which predicts the existence of virtual particles.
We have seen that the virtual particles are the carriers of the fundamental forces. One of those is the gravitational force.
We have seen that the gravitational force turns virtual particles into real particles.
We have seen that the forces allow us to define relationships between the real particles.
We have seen that the relationships between the real particles allow us to define space and time; in effect space and time derive from those relationships.
And finally, those relationships are expressed in the uncertainty principle, which is what we started off with.
And so we come full circle, starting off with the uncertainty principle and ending with the uncertainty principle.
Would you say that the uncertainty principle is fundamental to reality?
I think I would.