Go to https://brilliant.org/ArvinAsh to get a 30-day free trial + the first 200 people will get 20% off their annual subscription. Be sure to check out the course called "Special Relativity" to get a deeper understanding of the concepts discussed in this video. TALK TO ME on Patreon: https://www.patreon.com/arvinash REFERENCES Visualizing 4D spacetime (Arvin Ash): https://www.youtube.com/watch?v=ZfR1Jc6Zglo Minkowski spacetime calculations: https://tinyurl.com/2bft4pw6 What is spacetime article: https://tinyurl.com/23mzynkj Paul Ehrenfest paper on more than 3 dimensions: https://tinyurl.com/27jma7j6 Why we are stuck with 3 dimensions: https://tinyurl.com/23oseuup Sean Carroll video on spacetime: https://tinyurl.com/27srn5ez CHAPTERS 0:00 The most important concept in Physics? 2:00 Defining spacetime 3:15 The math of space vs math of spacetime 7:41 Let's answer your questions 8:41 How the heck can you add time and space in the formula? 10:12 The implications of combining space and time 11:10 Why not more than 3 spatial and 1 time dimension? 13:27 How to learn spacetime more deeply SUMMARY What is Spacetime? Are space and time the same thing? Space was thought to be nothing, an empty void with no matter in it. In 1908, Hermann Minkowski postulated that time could be thought of as a 4th dimension along with the three dimensions of space. Einstein later showed that this spacetime is a kind of geometry that can bend, affecting the trajectory and passage of time for objects. How can space and time be part of the same canvas? Space is measured in meters, while time is measured in seconds. How are the two interchangeable? The definition of spacetime is the set of points in space and time, located with 4 numbers. This would be the location in 3 dimensional space and a time. You can also call these events. In ordinary Euclidean space, the distance between two point A and B is fairly simple to figure out. The straight line between them is the shortest path. And it’s obvious also that any other path, from A to B will be longer. If we change one of the coordinates to time, the math that we need is not based on Euclidean geometry, but Minkowskian geometry (or Minkowski Geometry). The straight line between A and B does not represent distance but time elapsed between two events. A straight line represents traveling at a constant velocity between the two events, and is the MAXIMUM duration. So for example, in spacetime, if you took a curved path from event A to event B, or a zig zag path, then the elapsed time would be lower compared to the straight line between A and B, because you will have traveled more in space than in time. Einstein showed that there is no such thing as absolute time, and so that’s why we have a new formulation. But how do you add time and distance together, since the units are completely different? The key is that there in important conversion factor between time and space, that allows us to convert one to the other. And that conversion factor is, the maximum speed limit of the universe, that is, as far as we know, is the speed of light. The speed of light is the key to uniting space and time. We call this maximum speed “c” in physics. And c is 299,792,458 meters per second. As you know speed is distance over time. If we multiply this speed by time, we get a distance. So now we can convert time in the same equation to distance – distance = c*t. Thus, the equation works by using this conversion factor. This formulation for a 2 dimensional spacetime can be extended to the real 4 dimensional spacetime we live in. And that 4 dimensional geometry is the foundation for understanding General Relativity, with the addition that this spacetime is no longer flat, but can curve and contort. So the math gets complicated in General Relativity. The consequence of a curving spacetime is that this results in gravity. Why do we have only 3 dimensions, why not more? And why not more than one time dimension? First, large spatial dimensions probably don’t exist because we would have detected them if they did. And more than one dimension of time could result in closed time-like loops, in other words it would allow travel to the past. This is considered an impossibility because it would break causality. More than 3 spatial dimensions would also likely have fatal consequences. In 1920 Paul Ehrenfest showed that our orbit around the sun would be impossible if we had an additional spatial dimension. Other problems have also been identified, for example the orbit of the electron in atoms would become unstable. #spacetime If we had fewer spatial dimensions, then spacetime would be too simple for life. For example if we had only one spatial dimension, then orbits could not form. Two dimension would also probably be too simple to result in life.