One of the first things we notice about space and time is their dimensionality. Space has three dimensions, and time has one dimension. The dimensions of space or time are simply the number of coordinates needed to specify a location. A point in space requires three numbers, or coordinates, to specify it.
In the U.S. we are accustomed to specifying locations in terms of address, city, state, and zip code. Suppose you were invited to a party, and instead of an address the host specified the latitude and longitude of the location. You can enter a latitude and longitude in Google Maps and, if you enter enough digits, it will find the location just as well as if you used an address. Now suppose the party is in a skyscraper. In addition to latitude and longitude, you would also need altitude, specified by the floor number, to find the location. These are the three dimensions we use on or near the earth; latitude, longitude, and altitude.
Time is one-dimensional. It flows from the past through the present, and into the future. Your party invitation will also include the date and time of the party. You only need one number, or dimension, to specify the date and time. Most computer systems use a single floating-point number to specify date and time. The number of days after a certain date are on the left of the decimal, and fractional days, or time of day, is specified to the right of the decimal. The party is an example of an event, something that occurs at a specified location and time. Four dimensions are needed to specify an event, three spatial dimensions and one time dimension.
An experiment is generally a sequence of events. It can take place in various locations over a particular sequence of times. Would the results of the experiment differ if the locations or times changed? Scientists cannot test every point in space at every time for every experiment. So, they perform tests at many different locations and times and make some very reasonable assumptions about the results at different locations and times.
Scientists assume that space and time are homogeneous. This means that the laws of physics act the same at every point in space and time. This does not mean that every point in space and time is the same. Some may contain more, less, or different forms of matter than others but the laws of physics are assumed to be the same.
Homogeneity of space means that the same physical laws apply at all points in space. We need to make this assumption because we have not confirmed that all our physical principles work the same at every location on the earth, let alone the entire universe. We have sent robotic probes to the edge of the solar system. Even so they are only about fourteen billion miles, or 0.0024 light years away from our home planet, compared to the billions of light years required to reach the most distant objects we can observe. We have sampled the laws of physics in a very, very tiny portion of our universe.
Homogeneity of time means that the same physical laws apply at every time coordinate, past, present, and future. Just like space, we have not confirmed that all our physical principles and laws apply at every moment of time. If we go sufficiently far into the past, we will find that at some point there were no humans present to make any observations. Likewise, there are no guarantees that the laws of physics will still apply at some distant time in the future.
When astronomers observe light from some distant object, they need these assumptions about space and time to move beyond the mere observation of the light and develop theories about the source. They will also assume that the light was produced by processes that operate in our little region of space and time and that it traveled at the speed of light to reach us. They also assume that the light may have changed during the long trip through space, because of processes that we have observed here and now.
These properties of space and time are related to the conservation of certain physical quantities (https://en.wikipedia.org/wiki/Noether%27s_theorem ). You may have heard of the conservation of energy or the conservation of momentum. The conservation of momentum is associated with the homogeneity of space. We can think of momentum as the inertia of objects traveling in a straight line. It is generally equal to the mass of an object multiplied by its velocity. However, even objects with no mass such as light can have momentum.
The conservation of energy, also called the first law of thermodynamics, is associated with the homogeneity of time. Thermodynamics is the study of heat, work, temperature, and energy. Energy can exist in several different forms, such as kinetic energy, which is the energy of moving objects. Potential energy is the “potential” of producing energy through the action of a force. For example, an object falling under the influence of gravity converts gravitational potential energy into kinetic energy as it picks up speed. Other forms of energy include thermal energy (or heat), and electrical energy.
These conservation laws apply to a closed system, which means all outside influences such as matter, light, or forces have been accounted for. In closed physical systems, we always observe that momentum and energy are conserved. This suggests that space and time are indeed homogeneous. However, when we look at the large-scale structure of matter in the observable universe, such as large clusters of galaxies, we see that it is not distributed uniformly but in filaments (https://www.nao.ac.jp/en/news/science/2021/20210910-cfca.html ). This suggests that space may not be homogeneous on such large scales, or there is some undiscovered physics that causes these galactic clusters to have this structure.
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