The Nature of the Universe - Part IV - The Great Duality

 

Force Fields

In a previous post, I talked about the Fundamental Forces which govern every single interaction in the Universe. It is useful to think of a Fundamental Force manifesting itself as a directional field. Think of a magnet - it has a magnetic field. The direction of the field depends on the pole of the magnet - north or south. The strength of the field is the Electromagnetic Force that is felt by an object in that field depending on the distance it has from the magnet based on the inverse square relationship described earlier.

Just the way a magnet creates a magnetic field, all matter creates a gravitational field. You and I are held to the Earth by its gravitational field. Earth and all the other planets in our Solar System are held to the Sun by its gravitational field. Similarly there are fields associated with the Strong and Weak Nuclear Forces.

All these fields are directional, and have different strengths at different points. If you sprinkle iron filings around a magnet, they will align themselves in circular lines going from pole to pole. These lines are called Field lines. You will find more iron filings closer to the poles than in the middle - it is because near the poles the field is stronger.

While on a macro level, this concept of force fields seems obvious enough, if we examine these fields at very small, subatomic levels, they turn out to be very interesting. To understand them better, we need to understand the nature of Light itself.

 

Light is not What it Seems!

For a long time, people thought that light travels infinitely fast and is like sound - that it behaves like a wave. Just the way sound moves in a medium by disturbing it and creating a wave, light travels in a medium by setting up some kind of disturbance which moves infinitely fast. Both these beliefs are not just inaccurate, their true nature goes a long way in understanding the nature of  our world.

For starters, light does have a finite speed - it travels at 300,000 km / second. The interesting part is that nothing can travel faster than light in vacuum. Recall that light is made of Photons which are massless. So what we are saying here is that massless particles like Photons travel at 300,000 km / sec in vacuum and nothing can move faster than this speed.

This is more interesting than it sounds - let me illustrate with an example. Let us suppose you are driving a car at 60 km / hr. On the same road, another car moving at 40 km / hr in the opposite direction passes your car. To you, the apparent speed of that car would not be 40 km/hr, it would be 100 km/hr. All of us have experienced this  - cars coming from the opposite direction seem to move faster. Now assume that another car moving at 65 km / hr is trying to overtake you. As you look towards the driver of the car - he is not moving much fast - he seems to move slowly ahead - actually at exactly 5 km / hr. This is not just an illusion - the car overtaking your car crosses the length of your car in more time as compared to the car coming from the opposite direction. This is the law of addition of velocities - you add when they are opposite and you subtract when they are in the same direction.

However, when an object is moving very fast, things are different: if your car was moving at the speed of light and another car came from the opposite direction at the speed of light, to each other, they would still seem to be traveling at the speed of light to each other. This is very counter-intuitive, but actually true. The reason is that the law of addition of velocities is not a simple addition - it is a bit more complicated than that. The math is such that it reduces to simple addition if the velocities are small. Scientists have done experiments on this, and found this to be true - nothing can ever move / seem to move faster than light. This is the reason that science fiction writers need to come up with warp drives and wormholes to create situations where the space-opera hero is able to fly across the galaxy to destroy evil aliens! Of course it does not apply to situations where there is no real movement of anything physical - for example, a shadow can move across a distant surface very fast, and can move faster than even the speed of light. But of course that movement of the shadow is not really the movement of anything physical.

If you thought that was weird enough - you will be astounded on the other aspect of light - depending on how you want to think about it, light can behave either as a wave or as a particle. Realize that a particle is at a given point in space, whereas a wave is spread out in space. Light is peculiar in the sense that it seems to be spread out in space as well as behave like it is made up of particles. Recall that light is a form of electromagnetism - one of the four fundamental forces. So it is really these photons which seem to behave as if they are waves. How can a particle behave as a wave? This is explained by the Uncertainty  Principle.

 

The Uncertainty Principle

Take a book and give it a little push - depending on how big it is, it may move a bit, or may not move at all. Now think about giving the same push to - let's say a matchbox - it moves a lot more. That is because when we push an object, we transfer some of our energy to that object. As objects get lighter and lighter, the amount of energy it takes to move them reduces.

Now consider things in motion. Let us say that you are standing on the road and a car passes you by. Assume that you push against the car as it passes you (please do not try this in real life, you may hurt yourself)  Do you think it would change its path? Unlikely. For a bus full of passengers, it is even more unlikely. This is because the mass of a bus is more than that of a car. However, if you were to push against a bike, it would certainly change its path, it may even get unbalanced and fall. This is because the mass of a bike is less than that of a car or a bus. Again the same issue of transferring energy comes in - it takes less energy to change the path of a moving object that is heavier, than the energy it takes to change the path of a lighter object. It is the same idea that it take more heating to boil a cup of water as compared to a bucketful of water. So the key point is that as the mass of an object increases, it takes more energy to change its state - temperature or position or velocity.

With that established, let's come to a different point - how do we see things? We see things when light strikes an object, gets reflected back, is received by our eyes and creates an image on the retina. So to see things, light must strike an object. Now we know that light consists of photons, and a photon of visible light has energy of 9 x 10^-20 calories. What if the particle we want to see, has such little mass, that when a photon of light hits it, the energy transferred is enough to move the particle? That means that the instant we see the particle at a point, it has moved from that point. It turns out that at subatomic level, particles like electrons actually have that small a mass. So when we try and observe a particle, the very act of observation changes the position or the velocity of the particle. If we try and observe the particle sharply, the energy of the light it takes is higher, and the change in the velocity of the particle is even higher. If we use less sharper light, we do not change the velocity of the electron, but then we do not get to know its position accurately either. It turns out that we can determine with precision one of the quantities - position or velocity - but not both.

This is called the Uncertainty Principle - we cannot determine with certainty the complete state of a particle in terms of its position, velocity, etc. because the act of observation itself would change that state on one or more dimensions - there is always some minimum uncertainty involved in determining the full state. This uncertainty applies not just to subatomic particles, but also to real world objects. But at the scale of larger objects the uncertainty is negligibly small and we can routinely determine with full accuracy the position and velocity of a ball in mid-flight in a game of football.

 

Wave-Particle Duality

The example I gave above is a useful way of understanding the Uncertainty Principle, but is also slightly misleading. It may seem that the uncertainty we talked about arises on observation, but if we were not to observe, the particle would have both an exact position and velocity. This, however, but is not correct. The reality is that irrespective of whether you observe the particle or not, there is never a precise position or velocity associated with a particle. Particles are not like the solid point concrete particles we think them to be, they are like waves - a wave is spread out and not at a specific point. Similarly, a particle is spread out like a wave.

This seems very un-intuitive - how can particles behave like waves? One way of trying to visualize this is to think of a particle rapidly moving about. If we were to somehow plot its position over a period of time, we would get a fuzzy spherical cloud of points which would be denser in the center and rarer towards outside. The probability of the particle being towards the center is higher, but it can be towards the outer side too, but the probability is smaller. So you get this fuzzy spherical cloud like image with a denser center and a rarer boundary. It is like the rotating blades of a fan - you cannot see the blade coz it is moving too fast. A particle behaves in a somewhat similar manner, except that it is not really moving, it is occupying all those spaces simultaneously - it is like a wave. I talked about Force Fields earlier. This "wave-like" nature of a particle can be interpreted as a particle field. So, much the way the smallest constituent of a electromagnetic field is the photon, the smallest constituent of an electron field is the electron.

All matter has this wave-particle duality, but the effects of this are only visible at sub-atomic levels. At macroscopic levels, the "wave effects" of matter are so small as to be completely negligible. This is why things around us are solid and we can see and touch and feel them. However, this is still a matter field. When you touch a ball, you can think of the "touch" as an act where two matter fields are interacting with each other!

In an earlier post, I had talked about how Fundamental Forces are conveyed thru Force Carrier Particles. A photon is an example of a Force Carrier Particle - it carries the electromagnetic force. Even these Carrier particles for the Fundamental Forces have this same dual character wave-particle character. You can think of a Force field as being made of Carrier Particles at every point in the Field. A Fundamental Force Field is the summation of its carrier particles each of which has a dual particle-wave character. So both matter and Fundamental forces are just summations of the dual effect of the fundamental particles. While the summation of the fundamental particles of matter - quarks and mesons - is such that it leads to matter which has mass and occupies space, the summation of the carrier particles of fundamental forces - Photon, Graviton and Bosons - manifests as a force field.