From the linked publication: “A localized suppression of vacuum entropy near the hull creates dS/dx > 0 outward”.
I don’t understand this part. My naive view is that localized suppression means S<S0 (surrounding entropy), or some local minimum. S0 is the same on both sides far away from this minimum. This means the gradient dS/dx is positive on one side of this localized suppression region, and negative on the other side, possibly in an asymmetrical way. But after you integrate dS/dx over x to calculate the total force acting on the region, it will be exactly 0. The same reasoning applies to the other side of the craft, where you have a local peak of vacuum entropy. The total “push” will be 0 + 0.
Mike, thank you so much for catching that error! You are absolutely right. That is describing the situation where a “static” magnetic field is used to suppress vacuum fluctuations in both the front and the back of the craft at the same time and that is not what we want. As you point out, that will not result in the asymmetry we require.
In order to get an asymmetric dS/dx profile we would only suppress the vacuum fluctuations in the front of the craft and leave the back “off”. We’d also need to apply a “pulsed” magnetic field to the front—not a “static” magnetic field. I tried to show this in my simple diagram, but I didn’t do a very good job of conveying that idea.
I am grateful that you caught my mistake. It’s been 45 years since I did any calculus so my math skills are really rusty. It may take me some time to work out the correct equations, but this kind of feedback is invaluable. This is exactly what I’m looking for. What I was hoping for.
From the linked publication: “A localized suppression of vacuum entropy near the hull creates dS/dx > 0 outward”.
I don’t understand this part. My naive view is that localized suppression means S<S0 (surrounding entropy), or some local minimum. S0 is the same on both sides far away from this minimum. This means the gradient dS/dx is positive on one side of this localized suppression region, and negative on the other side, possibly in an asymmetrical way. But after you integrate dS/dx over x to calculate the total force acting on the region, it will be exactly 0. The same reasoning applies to the other side of the craft, where you have a local peak of vacuum entropy. The total “push” will be 0 + 0.
Mike, thank you so much for catching that error! You are absolutely right. That is describing the situation where a “static” magnetic field is used to suppress vacuum fluctuations in both the front and the back of the craft at the same time and that is not what we want. As you point out, that will not result in the asymmetry we require.
In order to get an asymmetric dS/dx profile we would only suppress the vacuum fluctuations in the front of the craft and leave the back “off”. We’d also need to apply a “pulsed” magnetic field to the front—not a “static” magnetic field. I tried to show this in my simple diagram, but I didn’t do a very good job of conveying that idea.
I am grateful that you caught my mistake. It’s been 45 years since I did any calculus so my math skills are really rusty. It may take me some time to work out the correct equations, but this kind of feedback is invaluable. This is exactly what I’m looking for. What I was hoping for.
Thanks again!