Bridging the Gap Part 1
Video Series: Part 1, Part 2, Part3, Part 4
Transcript
Rickey Austin
Welcome and thank you for joining our presentation today. My name is Ricky Austin and I have a PhD in Computational Science in Engineering with a focus on theoretical physics. Today, I’d like to introduce to you a concept that will bridge the effects of general relativity to the effects of quantum mechanics. Now, that’s a huge statement. So I want to caveat that this is a model, and if you follow this model, you will see that general relativity has effects that are predicted in it and that have been measured that will produce fundamental quantum effects in our world. So let’s look at see if we can sort of explain the process and direction that we’re going to be going. In this, we will be covering a scalar field. We’re going to call it preview. It’s based on a very simple concept. And I should say at this point, the lecture for this video is going to have mathematical equations in it. Nothing that’s going to go real deep. You should not really have to have beyond a high school level calculus, maybe up to calculus three if you were looking at college level, but it’s not going to go real deep. But at the same time, I also want to present some illustrations as we go through this series that will hopefully make it look and compare to things that you know and in everyday world, so that these examples in this model can be based off of something that sort of corresponds to things that you live with and are around each and every day so that they’re not foreign concepts to you. Hopefully after we introduce this scalar field, we’re going to examine, examine celestial orbits, i.e. the moon around the earth or the earth around the sun, etc. any type of orbit that is celestial and how it will work. If we did it over this scalar field, then we’re going to dive from the celestial down to the very small. So from the very large to the very small. And we’re going to examine a hydrogen atom and we’re going to model that hydrogen atom in this previous space once we get to that particular area in this series, I’ll describe a little bit more about it. But it’s going to be a classical model. It’s not the quantum theory model. It’s based on a classical model, much like those that might be familiar with it. We’ll discuss in some ways the Bohr model and how that bore derived his model, but it’s going to be basically sort of based on that, basically. Then we’re going to discuss these results of modeling the hydrogen atom in previous space. And I think that’s where this series becomes very interesting and exciting for possibilities that a simple model might actually show some of the correlation between the very large and the very small and how they might possibly interact with each other. Then in part five, the last part of this particular series, we’ll discuss other possible impacts. So we’re going to discover some things as we model this hydrogen atom, we’re going to discover some things that this model predicts. And as we discover those things, they may have an implication or an impact. On other areas. And that would be a very interesting talk as we go through that. Lastly, there are several known physical constants that we’ll be discussing throughout this lecture. Some of them have never been derived, meaning that we have to go out and measure them. We can measure them to great accuracy, but we’re not able to derive them and say that this is how they come about. We just know that nature operates this way and thus we go out and measure it and we place it in our model. Some of these constants through this model will be derived from modeling it in this previous space. That in itself I think is worth watching the series for. Just so if nothing else, it gives another frame of thought in a way of looking at something that might provide us more information. So what is a scalar field? Well, this is basically just an analogy of a way to map all the space that is around you. So imagine the room that you’re in or the location that you’re in if you’re outside the sky. If you’re inside the room, there’s a ceiling. There’s a floor. Imagine all of this area. And if every location in that area had a point that you could go to with length, height and width, you know, x, y, z, coordinates. In every location. You put a number. That would be a scalar field. Consider the temperature in a room and the thermometer is a function to determine the value of each location in that room. So if you could take that thermometer and every imaginable space in the room, write down what the temperature was. Then at every space in that room, you would have a number that represented the temperature. It should be noted that a scaler is just for layman’s terms. A a number. That’s all it is. Is is a number. And that number is 1 to 2.5, the square root of two pi, etc. It’s just a number for each location. If we’re talking about temperature, that number represents the temperature, but the number actually does not have any type of units behind it. It’s not ft. It’s not time, it’s not a temperature. It’s just a number that we’re going to assign at every place in the field. And we’re going to talk about how we assign those numbers in the next slide. Now, let’s consider if we had a candle, and if that candle is known to melt above a certain temperature, we would not want to store that candle where it would melt. We would want to store it, unless that’s what you wanted. But we normally would not want to store that in an area where it would melt. So if we took that field of the temperature. Measurements at every location. We could look at that and decide where is the best place to store a candle for it not to melt. Well, an everyday use of a field is also an expression like it gives rise to the expression like hot air rises, which means that the area of the ceiling is warmer than the air of the floor and a scalar field in a room. Means that there’s smaller numbers at the floor. And there’s larger numbers at the ceiling just to represent that gradient as it goes from cold to warmer air. We’re going to use the same type of scalar field and the same type of numbering system, but with a different function instead of a thermometer. We’re going to have a different function that gives us a number for all of these locations. So let’s introduce this privacy shield. It’s basically derived and here’s some of those equations. But these equations are fairly known and fairly common. One is kinetic energy on the left, and on the right is potential energy. Ordinarily, if you were going to measure this energy and you were going to use gravitational forces, you would use two masses, and then you would multiply those masses together down the gravitational constant g and divide it by the distance squared for force, just the distance not squared for energy. In this case, it would be potential energy. But to map our field, what we’re going to do is we’re going to create this virtual point mass called M V and that MV is going to equal in every way the mass M, except that it’s only used to map the number in the field. Just like we use the thermometer, we’re going to use this MV mass to map all the points in our field and we’re going to use initially this e t as the total energy, as this kinetic energy minus this potential energy. And then we’re going to ask then we’re going to add to that because we’re still just dealing with energy. And we didn’t want to have any units. We didn’t want to have energy or temperature or FT or time or anything behind it. We want just a number. We want just that scalar to come out. So to do that, we’re going to set the function and we’re going to call it a to equal one. Plus that total energy, the kinetic minus the potential divided by what is called the rest energy of the mass that is generating this gravitational field. So over in this side is what our actual equation looks like. It’s just going to be one plus this ratio of the total energy to the rest energy. Notice that since MV and M have the same value, they cancel. And over here the same they cancel when we put them over each other and we come up with this particular equation right here that we’ll use. Now, this provides us a number at every location in the field, much like the thermometer provided as a number for a temperature at every place in the field. This function is going to provide us a number at every location in our field. Next. How would we want to look at this? Well, let’s think about the that the preview value represents a dilation of time at a local point compared to where. There’s no gravitational effect at all. And there’s a clock there. What is the time there? Sort of think about it as if we had currency conversion between two countries. I think about if I’m at my location right now and I pull out and I have $10 in my pocket, what is the value of that $10 in another country, say, Canada or Mexico? I have to take what I have locally in my pocket and I’m going to convert it to what it would be at a different country or a different location. That’s what we’re doing here. We’re taking the clock that a person has and we’re going to convert it. The time rate that it takes from that location they’re at in a field that’s caused by gravity to a location to where there is no gravitational effect, no big mass causing any type of gravity. And how does the clock tick there? So we have this area that’s called infinity is where there’s no gravitational effect at all. And that clock right there ticks at our scalar number that we came up with, time, whatever our clock tick is. So if we had one second on our clock, our a value was two, then two time one second is 2 seconds. So an infinity 2 seconds would equal one second locally. Which means the clock actually ticks faster at infinity than it does here. And our gravitational well now unit distance is also measured locally, just as if I was measuring the money in my pocket or I was looking at the clock here, I may have a unit of measure, maybe it’s a tape measure or a little ruler, and I’ll measured it where I’m standing. I don’t go to another location and figure it out. I look right where I’m standing and this unit of measure is going to be determined by how far the speed of light goes in one unit of my time. And I’m going to convert that to what that same length would be to where there was no gravitational effect. And that’s how we come up with this length that infinity is equal to the distance. The speed of light travels at infinity, which is equal in a unit of time, is equal to the distance. The speed of light travels locally. Time are scalar and that gives us what it is, an infinity and terminology, so that if we want to mention it later on, so I don’t have to keep saying where there is no gravitational effect, etc. We’re going to call a space where there is no gravitational effect, just exemplar space. So anytime I say exemplar of space, we know we’re talking about an area that has no gravitational effect on a location. There’s nothing special about that value except that it represents an area where there’s no gravitational effect. And at that place I equals one because there’s no mass causing any type of effect in that. Now let’s consider a clock in that previous space. We go back to the clock in our pocket and we have a clock at a certain height in one location and another height and another location under Newtonian laws, original classical physics that he produced and changed the world with, the clock would tick the same weathers at the bottom of a mountain or the top of a mountain. Whether it was setting and the ground or if it’s up in space on a satellite, the clock would always tick at the same rate. But in our model. That may not be the case. We need to actually sort of put it in, test it, and then see how that may measure up to others. Think of it this way. I have a I have two friends in two countries. One friend is in Canada. One is in Mexico. One has a Canadian dollar in their pocket. The other one has a mexican peso in their pocket. They call me up and they need me to tell them how much an item I’m selling. Cost. And they’re. Rate of exchange or their money. That’s sort of what we’re going to do here. We’re going to look at a clock that is in one person’s pocket and a clock that is in another person’s pocket, but they’re just at a different height away from a massive object. And we’re going to figure out how does that in this previous space, how does it show the time rate is for each one of those? So we have a clock one, an exemplar space. Remember, exemplar is no gravitational effect. So clock one is equal to a as defined locally by our first person and the clock of the first person. Clock to an exemplar space is. A as measured by our second person in clock two. That’s measured by our second person to evaluate in previous space from our previous equations. We have these equations. Here’s the fun and interesting part of this Schwarzschild solution to Einstein’s field equations. And now I welcome you to look that up. If you want more information given to a first order, which means the first order is in a series and we’re just going to take the part that’s not squared as it goes down, it gets more and more and more accurate. But we really just want to look at this first order series right now. What this tells us is that our field is working to at least a first order. Of Einstein’s known solutions. That’s pretty exciting. That is going to be hit for this first part, just introduce you to the field, what the field is and how some of the time dilation might work. And the next part, we’re going to venture out and look at planetary orbits and how planetary planetary orbits will traverse in this field and analyze the results of that.