In part 1, we learned that space has three dimensions and time has one. We also saw that space and time are assumed to be homogenous, even though we have performed experiments in a tiny fraction of the space and time that make up our universe. Homogeneity of space should lead to the conservation of mass, and homogeneity of time should lead to the conservation of energy. The fact that momentum and energy appear to be conserved supports the assumption that space and time are homogeneous. But the filamentary distribution of galaxies suggests that space may not be homogenous on such large scales, or there is some undiscovered physics that causes these galactic clusters to have this structure.
Scientists also assume that space is isotropic. This means that the laws of physics are the same in every direction of space. For example, if we make a measurement with a certain apparatus and rotate the apparatus so it faces a different direction, we should get the same answer.
In the nineteenth century, scientists thought that the speed of light might change depending on the direction it traveled. They had discovered that light was a wave. Other wave phenomena known at the time required some material to travel through, such as waves traveling on water or sound traveling through air.
They postulated a medium called luminiferous aether through which light waves traveled. These scientists thought that any motion relative to the aether would cause the apparent speed of light to change. Since the Earth changes direction as it orbits the sun, scientists thought our motion relative to this aether would change and, like sound or water waves, the speed of light would change as well.
Scientists developed a very accurate apparatus that could detect very small changes in the speed of light. They oriented the apparatus to measure the speed of light along the direction of the Earth’s rotation around the sun and made a measurement. Then they rotated the apparatus 90 degrees, so it was perpendicular to the Earth’s rotation around the sun, and made another measurement. There was no discernible difference between the two measurements, demonstrating that there is no aether and space is isotropic with respect to the speed of light.
Another conserved quantity, angular momentum, is associated with the isotropy of space. Angular momentum is a measure of the inertia of rotating objects, like a planet orbiting the sun. Increasing the mass of the planet, how fast it is moving, and how far it is from the sun would increase its orbital angular momentum.
Conservation of angular momentum causes an ice skater to spin faster when they draw their arms in because the mass in their hands and arms moves closer to the axis of rotation, so the rest of their body must speed up to conserve angular momentum. In a closed system, we have always observed angular momentum to be conserved, which supports the assumption that space is isotropic.
We have seen that both space and time are assumed to be homogeneous. Since space is assumed to be isotropic, it is reasonable to ask if we can assume that time is isotropic. It turns out that time does not appear to be isotropic.
Since time has only one dimension, it can only move in two directions, forward to the future or backward to the past. However, we have always observed time moving from the past to the future. This is sometimes called the arrow of time. There is a physical quantity, called entropy, that is associated with this lack of isotropy in time. Entropy is not conserved. In a closed system, the second law of thermodynamics states that entropy can never decrease. Entropy can increase whenever work is done by an engine, a refrigerator, or any physical system that manipulates energy.
Entropy is a measure of the information required to describe a system. Entropy increases as the complexity of a system increases. This is often interpreted as an increase in disorder or chaos. But it is really the result of the available energy being used to redistribute matter into a form that requires more information to describe. Information theory is a branch of mathematics that uses the concept of entropy to describe information content. The same equation is used to define entropy in both physics and information theory.
Suppose you open a large bottle of smoke in an enclosed room. Before the bottle is opened, the smoke particles can only be found in the bottle. After the bottle is opened, you will see the smoke slowly drifting away from the bottle in little puffs or streams. If you wait a long time, the smoke will be evenly distributed throughout the room. The potential locations of smoke particles are much larger in the room than in the small bottle. The amount of information required to describe the smoke has increased, and therefore, the entropy of the system has increased.
All the smoke will not spontaneously go back inside the bottle, because that would decrease the entropy. Since each state, or arrangement of matter, is equally probable, a state with all the smoke particles back inside the bottle has a very low probability. The probability of a single smoke particle entering the bottle may be large enough that this will occur. But the probability of all the smoke particles returning to the bottle is extremely small. But if it did, there would be fewer locations of smoke molecules to keep track of, less information would be needed, and therefore it would have lower entropy. That is not allowed according to the second law of thermodynamics.
This means that time is not isotropic. If time travel were possible, we could not travel into the lower entropy past. However, we can (and are) traveling into the future. As we will learn in future posts about relativity, different frames of reference can travel into the future at different rates. This means that their clocks run at different rates. This will be our first clue about how we can see light from galaxies that are billions of light years away in a universe that is less than billions of years old.
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