I was just throwing tea leaves outside the window when an idea struck me.
If I want to measure the height of my building, I would have to only measure the time it takes for the leaves to hit the ground, and I'd know my value. But to get an accurate value for scientific accuracy, we'd have to take in many things... For human mind's sake, let me take the values upto four decimal places alone.
For example, firstly, I'd have to take into account the exact radius of the planet at the point I'm standing to derive the precise value of g. For that I'd have to take into account plate techtonics, and stuff. Going to a simpler level, I'd have to measure the time it takes for the sound to reach me as well, taking into account the speed of sound. But for that, I'd need the value of the ambient air temperature. Now, because I need this temperature, I'd have to measure the air pressure at that point as well. For the air pressure at the point, I will need the exact height of our plot from sea level.
Not only that, if I take into consideration, the air resistance, then I'll have to calculate that as well. For the air resistance, I would need to take into account several factors such as the wind direction, the humidity in the air (that would affect it's viscosity), and the surface area of the leaves themselves. Now, upon calculating that, for accuracy, I'd have to account for air pressure again. And so on.
But the value of 1 atm at sea level was derived several decades ago, since when the water levels have risen. So I'd have to measure the volume of water increased. Thus, I would need to know precisely how much ice has melted over the polar caps to get that much volume. For knowing how much ice has melted, I would need to take into account the convectional currents in our atmosphere (which, by the way is part of turbulent fluid mechanics, an impossibility at current levels of physics). For knowing the convectional currents in the atmosphere, I would have to calculate very precisely the speed of the earth's rotation about it's axis. And for calculating that, I would need to know how fast it goes about the sun (since energy has to be conserved). Then, by that logic, I would also need to know how fast the sun is revolving about it's axis.
For that, I would need to know, or calculate, how fast the stellar cloud rotated 4.5 billion years ago, for which I'd need the velocity with which the gas cloud contracted. For that velocity, I would need to know the gravitational potential of each and every particle, not to mention the electromagnetic effects in there at the time. Fast forwarding, all in all, I would need to know the exact value of the exponential constant at which the universe inflated. Which takes me right to the moment of the big bang.
And the WHOLE thing is thrown out if we take into account relativistic motion, however small, as it would, inevitably, affect the final result.
Assuming we found out ALL of these values, adding all the errors in the system would lead to a figure SO FRICKIN LARGE, that it would be mind boggling...
All in all, it's a hell lot of work to do to derive the height of my house to a hundredth of a centimeter only... It might be an interesting holiday project...
For example, firstly, I'd have to take into account the exact radius of the planet at the point I'm standing to derive the precise value of g. For that I'd have to take into account plate techtonics, and stuff. Going to a simpler level, I'd have to measure the time it takes for the sound to reach me as well, taking into account the speed of sound. But for that, I'd need the value of the ambient air temperature. Now, because I need this temperature, I'd have to measure the air pressure at that point as well. For the air pressure at the point, I will need the exact height of our plot from sea level.
Not only that, if I take into consideration, the air resistance, then I'll have to calculate that as well. For the air resistance, I would need to take into account several factors such as the wind direction, the humidity in the air (that would affect it's viscosity), and the surface area of the leaves themselves. Now, upon calculating that, for accuracy, I'd have to account for air pressure again. And so on.
But the value of 1 atm at sea level was derived several decades ago, since when the water levels have risen. So I'd have to measure the volume of water increased. Thus, I would need to know precisely how much ice has melted over the polar caps to get that much volume. For knowing how much ice has melted, I would need to take into account the convectional currents in our atmosphere (which, by the way is part of turbulent fluid mechanics, an impossibility at current levels of physics). For knowing the convectional currents in the atmosphere, I would have to calculate very precisely the speed of the earth's rotation about it's axis. And for calculating that, I would need to know how fast it goes about the sun (since energy has to be conserved). Then, by that logic, I would also need to know how fast the sun is revolving about it's axis.
For that, I would need to know, or calculate, how fast the stellar cloud rotated 4.5 billion years ago, for which I'd need the velocity with which the gas cloud contracted. For that velocity, I would need to know the gravitational potential of each and every particle, not to mention the electromagnetic effects in there at the time. Fast forwarding, all in all, I would need to know the exact value of the exponential constant at which the universe inflated. Which takes me right to the moment of the big bang.
And the WHOLE thing is thrown out if we take into account relativistic motion, however small, as it would, inevitably, affect the final result.
Assuming we found out ALL of these values, adding all the errors in the system would lead to a figure SO FRICKIN LARGE, that it would be mind boggling...
All in all, it's a hell lot of work to do to derive the height of my house to a hundredth of a centimeter only... It might be an interesting holiday project...
