Incompressible Rods
Most recent answer: 10/22/2007
Q:
I have often wondered about this question, but never been able to find an answer.
I take two long, lightweight, stiff, incompressible rods of very great length and place them alongside one another. I am at one end of the rods and my friend is at the other end.
I jiggle the two rods in morse code and my friend watches them. Does the information that I send him arrive faster than the speed of light? If not, why not?
picture:
ME =============== 2 very long rods =========== FRIEND
- Chris Allen (age 40)
Ipswich, Suffolk, UK
- Chris Allen (age 40)
Ipswich, Suffolk, UK
A:
This is an important fundamental question.
Obviously, if there were incompressible rods the information would be transmitted faster than c, the speed of light. However, the entire successful framework of physics would fall apart if such transmission were possible. Therefore there can be no such rods unless all of modern physics is wrong. The reason is not some engineering limit. The forces from one atom to the next are transmitted by fields, almost entirely electromagnetic fields. The speed of propagation of an electromagnetic wave (or other disturbance in any fundamental field) is c. So the effect of moving one end of the rod can't propagate down the rod faster than c. The distant end can't respond instantly, so the rod isn't incompressible.
Mike W.
Obviously, if there were incompressible rods the information would be transmitted faster than c, the speed of light. However, the entire successful framework of physics would fall apart if such transmission were possible. Therefore there can be no such rods unless all of modern physics is wrong. The reason is not some engineering limit. The forces from one atom to the next are transmitted by fields, almost entirely electromagnetic fields. The speed of propagation of an electromagnetic wave (or other disturbance in any fundamental field) is c. So the effect of moving one end of the rod can't propagate down the rod faster than c. The distant end can't respond instantly, so the rod isn't incompressible.
Mike W.
(published on 10/22/2007)
Follow-Up #1: incompressible fluid?
Q:
What about brake fluid which is said to be incompressible. When I push down the brake pedal, the master cylindre pushes the brake liquid inside the hoses which tightens the brakes immediately? So what is the speed of propagation in this scenario if it cannot be faster than c even though brake fluid seems incompressible?
- Anonymous
- Anonymous
A:
That’s a nice question. If the fluid were truly incompressible, there would be big paradoxes. In fact, the fluid is compressible, and the compressibility can be measured. One way is to directly measure the volume change under pressure. Another way is by measuring the speed of sound in the fluid. That speed is the inverse of the square root of the compressibility times the (easily measurable) density. The speed of sound is in fact the maximum speed of the propagating pressure change.
Mike W.
Mike W.
(published on 10/22/2007)
Follow-Up #2: instantaneous signals?
Q:
If the rod is compressible, is there a limit to the amount of compression possible? At some point, I would think all the atoms are going to be as close as they can get to one another. Once this happens wouldn't the movement in both ends of the rod be instantaneous?
- Mike (age 30)
Missouri
- Mike (age 30)
Missouri
A:
I think you are starting with an image of atoms as rigid impenetrable classic objects. They aren't. The atoms themselves are compressible. It is true, however, that when compressed enough they do change their behavior drastically. Under very high pressure the electrons in the fuzzy cloud of the atom combine with protons in the nucleus to form neutrons. This allows much more collapse, leading to a very dense neutron star.
Perhaps it might seem as though when the material gets dense enough it will, although still compressible, be so stiff that its sound velocity would be greater than the speed of light. Obviously that would lead to problems for relativity. Worrying about that issue was one of the clues that led to the prediction that black holes would exist. In a black hole, the material sort of falls out of our region of space-time altogether.
Mike W.
Perhaps it might seem as though when the material gets dense enough it will, although still compressible, be so stiff that its sound velocity would be greater than the speed of light. Obviously that would lead to problems for relativity. Worrying about that issue was one of the clues that led to the prediction that black holes would exist. In a black hole, the material sort of falls out of our region of space-time altogether.
Mike W.
(published on 09/25/2010)
Follow-Up #3: strictly physics
Q:
Why is physics so strict? If Physics is the study of why and how, then why can't physics be bent so that it includes these black holes that are out of our space-time? Why can't there be particles that move faster than the speed of light? Why can Physics not be bent, when it says that everything else can be(at least to an extent)? I want to know, because I want to be a physicis. I think it may be interesting to find out that in my lifetime Physics(the laws of nature) may likely be rewritten.
- anonymous (age na)
US
- anonymous (age na)
US
A:
Good question. There are lots of intellectual fields, e.g. in the social sciences, in which statements are rather fuzzy and imprecise, "laws' never are quite meant to be taken seriously, etc. In social science it's hard to see how that fuzziness could be avoided, but in physics it's not necessary. One of the drawbacks of laws that are easy to bend is that they can't ever be disproved. There's always some excuse for any discrepancy. Arguments tend to go on forever.
With our "strict" laws, we get a much sharper idea of whether they are working or not. It's precisely that strictness that allows us to say, for example, that Newton's law of gravity is not quite right. It's that same strictness that tells us that our current law of gravity, General Relativity, must break down on extremely short distance scales. People are working hard to replace it, maybe with a form of string theory. Meanwhile, more comprehensive pictures of the space-time manifold, in some sense including what are black holes from our perspective, are also being worked on.
Meanwhile, though, for events on a more familiar scale we have the strict laws of Special Relativity as an excellent well-controlled approximation. Combined with quantum mechanics, these allow the correct theoretical prediction of experimental quantities to extraordinary precision, e.g. one part in 100,000,000,000. When a theory like Special Relativity can do things like that, you don't just toss it out on a whim.
Mike W.
With our "strict" laws, we get a much sharper idea of whether they are working or not. It's precisely that strictness that allows us to say, for example, that Newton's law of gravity is not quite right. It's that same strictness that tells us that our current law of gravity, General Relativity, must break down on extremely short distance scales. People are working hard to replace it, maybe with a form of string theory. Meanwhile, more comprehensive pictures of the space-time manifold, in some sense including what are black holes from our perspective, are also being worked on.
Meanwhile, though, for events on a more familiar scale we have the strict laws of Special Relativity as an excellent well-controlled approximation. Combined with quantum mechanics, these allow the correct theoretical prediction of experimental quantities to extraordinary precision, e.g. one part in 100,000,000,000. When a theory like Special Relativity can do things like that, you don't just toss it out on a whim.
Mike W.
(published on 10/26/2010)
Follow-Up #4: New Year's Eve advice
Q:
Even if the laws of physics are strict, it doesn't mean they are absolute. You cannot say that with SR and GR : "this is how the Universe works". You can only say this : "Every experiment on SR and GR we did tends to show that this is how the Universe works" In physics, as in everyday life, never lose your skepticism and your critical thinking! Don't toss away what has been shown true many many times and don't think that if it's true, then it's absolute. Leave room for new stuff that we haven't discovered yet but greet it with skepticism and critical thinking. With that way of seeing things, you'll be a great scientist!
- Anonymous
- Anonymous
A:
I've got to disagree with your last line (too late for some of us), but other than that, thanks for the philosophical pep talk.
Mike W.
Mike W.
(published on 12/31/2011)