# Extremes in Physics

Not sure if extremes is the right word, but I've always wondered about the "negligeable" part of physics.

1) For example, water is commonly called incompressible, but it does compress some. Looking at wikipedia it says its compressibility is 4.6 E -10, whereas rock is about 3 E -10. So why do people not say rock is incompressible? They are the same order of magnitude. And is there any nulk substance that is truly incompressible? Perhaps the slush of neutrons at the center of a neutron star?

2) Another thing is the viscosity of liquid helium. Everywhere I've read has it as exactly zero. Is this a definition, or a result of the mathematics?

3) And same for the speed of light. That is defined as an exact number, but, couldn't they just change the speed of light, to say, exactly 300,000,000 m/s, then alter the definitions of meter and second? I mean, if we defined the units in the first place, couldn't we change them slightly, as along as everything worked out the same way?

4) One last thing, that's a bit more theoretical. If electrical current is merely the movement of charge. Now I realize this isn't actually the electrons literally moving, but wouldn't tiny fluctuations, even perhaps at a quantum level, induce a small current in, say, a piece of unconnected wire on short time scales? And then if you were to connect that wire to measure the current, wouldn't the Seebeck effect create a different voltage, despite how carefully the experiment was controlled?

So I guess from all of this, I want to ask what the limit of physical science could be? Surely there will be a point where the uncertainty of our instruments would be unable to be improved.

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ZapperZ
Staff Emeritus
When you lift a piece of rock with your hand, how much is the gravity from Alpha Centauri are you are accounting in your effort?

Zz.

Nabeshin
Not sure if extremes is the right word, but I've always wondered about the "negligeable" part of physics.

1) For example, water is commonly called incompressible, but it does compress some. Looking at wikipedia it says its compressibility is 4.6 E -10, whereas rock is about 3 E -10. So why do people not say rock is incompressible? They are the same order of magnitude. And is there any nulk substance that is truly incompressible? Perhaps the slush of neutrons at the center of a neutron star?
Because everyone knows rock's 'incompressible', squeezing water is a less common experience. And you can always compress something into a black hole.

2) Another thing is the viscosity of liquid helium. Everywhere I've read has it as exactly zero. Is this a definition, or a result of the mathematics?
For a superfluid, it's exactly zero: http://en.wikipedia.org/wiki/Superfluid . Similar for superconductivity. I'm not very well versed in this area, but I think that an actual superfluid will only have some percentage of the fluid existing in the superfluid state (someone can confirm or refute this please?), so the portion which is not a superfluid would produce some finite viscosity.

3) And same for the speed of light. That is defined as an exact number, but, couldn't they just change the speed of light, to say, exactly 300,000,000 m/s, then alter the definitions of meter and second? I mean, if we defined the units in the first place, couldn't we change them slightly, as along as everything worked out the same way?
This is exactly what is done. The definition of the meter is the distance light travels in 1/299,792,458 of a second. The second is defined in terms of a certain number of periods of the hyperfine transition in a Cesium atom. The point is that units are arbitrary, my favorite is when c=1.

4) One last thing, that's a bit more theoretical. If electrical current is merely the movement of charge. Now I realize this isn't actually the electrons literally moving, but wouldn't tiny fluctuations, even perhaps at a quantum level, induce a small current in, say, a piece of unconnected wire on short time scales? And then if you were to connect that wire to measure the current, wouldn't the Seebeck effect create a different voltage, despite how carefully the experiment was controlled?
Yes, you get noise because of quantum mechanics: http://en.wikipedia.org/wiki/Quantum_noise

So I guess from all of this, I want to ask what the limit of physical science could be? Surely there will be a point where the uncertainty of our instruments would be unable to be improved.
Well, you can't beat $\Delta x \Delta p > \hbar/2$