Create a Matlab Movie Showing the Growth of a Spacetime Warp Bubble

Copy and Paste the Following Code into Matlab to create a nice movie.

I modified the original Alcubierre metric to include an ‘engine parameter’ which simulates the gradual creation of a warp bubble after the engine is activated.

% Formation or Alcubierre Warp Bubble

% Richard Obousy. Oct 2007

% Create Mesh

[x, y] = meshgrid([-15:.5:15],[-15:.5:15]);
% Prepare for Movie
axis tight
set(gca,’nextplot’,'replacechildren’);

% Record the movie

% CYCLE 1 – The generation of the Bubble
for k = 1:75     % k embodies the ‘Engine Paramter’
   
 x=x-.001*k    ;  
for i=1:length(x);
    for j=1:length(x);
z(i,j)=-1/2*(tanh (1*sqrt(abs(x(i,j)^2+y(i,j)^2-58)-10)+2.5)-tanh(1*sqrt(abs(x(i,j)^2+y(i,j)^2-58)-10)-2.5))…
*tanh(16)*(exp(k/75)-1)*x(i,j);
    end
end

% Plot

mesh(x,y,z)
axis([-12 12 -12 12 -15 15 -7 7])       % Adjust Perspective
view([133,22])
colormap(jet)
F(k) = getframe;
 pause(.05)
end

% CYCLE 2 – The Motion of the Bubble

[x, y] = meshgrid([-15:.5:15],[-15:.5:15]);

for kk = 1:75
   
 x=x-.0013*kk    ;   % Term encodes ‘acceleration’
for i=1:length(x);
    for j=1:length(x);
z(i,j)=-1/2*(tanh (1*sqrt(abs(x(i,j)^2+y(i,j)^2-58)-10)+2.5)-tanh(1*sqrt(abs(x(i,j)^2+y(i,j)^2-58)-10)-2.5))…
*tanh(16)*(exp(75/75)-1)*x(i,j);
    end
end
 

axis tight
set(gca,’nextplot’,'replacechildren’);
mesh(x,y,z)
axis([-12 12 -12 12 -15 15 -7 7])
view([133,22])
colormap(jet)
G(kk) = getframe;
 pause(.02)
end

movie2avi(F,’warpmotion3′,’compression’,'cinepak’)
movie2avi(G,’warpmotion4′,’compression’,'cinepak’)

%———————————————————————-

You can see the interior region of the bubble remains flat throughout the generation of the bubble. Any spacecraft located within this region would experience no acceleration effects. Hypothetically a craft and its crew could reach unprecedented speeds whilst escaping the ultra-high g-forces such an acceleration would normally produce.

This assymetric warp at the front and aft of the ship reflect the ’shrinking’ and ’stretching’ of space respectively. This interstellar propulsion proposal works by effectively expanding and contracting spacetime locally to reach the destination. To read more about this take a look at the following paper here which is written for the educated laymen (no equations). For the more mathematically inclined you can take a look at the paper which includes the calculations here.