Expert: Daniel Mazur - 4/24/2009

Question
QUESTION: hi daniel,
i had a few questions in physics in general this time.
1.) they say that the tides on the earth are caused due to the gravitational pull of the earth, but how can that be since the gravitational pull of the moon is used to keep the earth in a circular motion around the moon and vice versa(just like in the case of astronauts who feel no gravity)?
2.)i recently read a bit of quiantum mechanics (from feynman), and the first chapter on electron experiment amazed me. the electron first interacts and interferes as a wave and then is detected as a whole or fully at the detector as though it were a particle and if we try to look at what's going on, we end up disturbing it and it no longer behaves that way. and now we have accepted it as a basic law of nature. is it that just because presently we are experimentally or theoretically not able enough that we have given up on finding a way around the uncertainty principle? are there some people still trying to look for a way around the uncertainty principle? is there any specific branch of theoretical physics that is looking into this matter?
3.) i recently watched a lot of michio kaku videos on youtube and on discovery and all and his idea of parallel universe got me really interested. are these ideas just ideas of some great scientist or do they have some sort of a mathematical backing with them? do they have the potential of turning into scientific theories in the future?
4.) it is genrally said that the magnetic lorentz force can do no work as it's direction is always perpendicular to the velocty of the charge hence it can only change the direction of the velocity and not its magnitude and thus cann't change the K.E. but suppose if we keep two infinitely long current carrying wires side to side, then they will attract or repel each other(accordingly as current is in the same or opp. dir.) and hence the K.E. of the system will increase, which is a contradiction. i would like you to explain this contradiction.

thanks,
shikhin

ANSWER: Hello Shikhin,
nice to have you back.

1) Tides on Earth are due to the gravitational pull of the Moon (not Earth) and to see through it you need to start thinking about Earth as an elastic object, not rigid. Earth and Moon circle the Sun together and just to observe the principle of tides we can forget about the Sun. There is an attractive force between Earth and Moon, so they both circle the common center of mass. Now imagine a centrifuge on whose arm you attach not a rigid cannon ball, but an elastic gym ball filled with water. You turn the centrifuge on and as the orbital velocity of the ball increases, you'll observe a change in the ball's shape - it becomes a rotational ellipsoid.
This is what happens to Earth. It doesn't matter, what functional dependence the force has, as long as it's attractive (so that things circle and don't fly apart). It doesn't matter that Moon is the smaller of the two objects - if Moon had oceans, there would be tides on the Moon just as well. Thanks to Earth's own rotation the geographical location of the high and low tides travels around the world, but it's always the direction TOWARDS and AWAY FROM the Moon that have the high tide. Give it a thought, I will of course answer any further questions.

2) The answer is yes, some theoretical physicists are exploring the limits of observable, studying the apparent paradoxes and undoubtedly thinking about any loophole. In science things are seldom put to rest completely - even when we think something is a rock solid fact about nature, we usually make an undergraduate laboratory experiment out of it. The uncertainty principle certainly seems rock solid and seems to be the reason for our Universe to exist the way it does. For example, no atoms could exist without it. People do try to get around it, but it is very resistant.

3) I am not familiar with Michio Kaku and his theories, so I cannot judge if this is fiction or not. You will need to tell me exactly what he proposes. Creating a parallel Universe mathematically is no problem at all, the problem is finding in our Universe some physical evidence of the parallel one, not to mention any evidence of what Nature's laws work there. Generally, ANY science fiction COULD become reality, simply because it is so hard to disprove things like that. The burden of proof always lies with the defendant of the new theory, though.

4) Why do you need infinite length? Finite length wires carrying current will attract or repel each other all the same. The complete version of the nature's law you mentioned is that: "Static magnetic field cannot do work on charged particles (like electrons). An electron at rest in a magnetic field will stay at rest and an electron in motion will maintain its kinetic energy, while its trajectory is curved by the field." A wire is not a charged particle, it only contains them and therein lies the solution to your apparent paradox. When you are talking about wires, you must see that it is not the magnetic field that does the work, even though it is needed as a condition. Observe closely now:

Suppose one loose wire alone in the world. There are always free electrons in the wire and they move around and bounce off its walls. Each such bounce gives a tiny impulse on the wire as a whole to move in certain direction, but as there are good 10^15 bounces each seconds on the wire walls with EVENLY DISTRIBUTED DIRECTIONS, the net force on the wire is ZERO.

Now, let's place a magnet next to it (N-S direction oriented perpendicular to the wire direction). It is more difficult to imagine, what happens with the electrons now their paths are curved, but you can write the vector products and see that with zero net current, the bounces of electrons on walls will still give zero net force, albeit their paths inside the wire are curved by the magnetic field.

As soon as you send current through the wire, you will cause IMBALANCE between the frequency of electron bounces on the wall towards (A) the magnet and the wall away from (B) the magnet. As each one electron bounce can be approximated as delivering the same impulse, the net difference of the bounce frequencies (B-A) is directly proportional to the NET FORCE (attractive or repulsive) observed on the wire. But it is NOT the magnetic field that provides the energy for this force field, it is the electrical current you have sent into the wire! The magnetic field only curves the space for the electrons so that they start giving their energy more to the inner or to the outer wall of the conductor. Yes, I know, the magnetic field is still a culprit, but it is not causing the force by using its own energy. WE are the REAL culprits, because we send the current into the wire in one direction or the other and thereby cause imbalance between the electron bounce frequencies defined above. :-)

Let me know, if things remain unclear.

Cheers,
Daniel

---------- FOLLOW-UP ----------

QUESTION: hi Daniel,
thanks a lot for clearing things up, but the first question is still kind of unclear to me. it was a typing mistake (as you also rightly pointed out), that tides are caused due to pull of the moon. now, suppose if we station ourselves on the moon and observe the earth, the earth will be going around the moon in a circular orbit, i.e. the gravitational force of the moon on the earth is being entirely used to keep the earth rotating around the moon, a case similar to astronauts. the force that the astronauts experience due to the earth is being completely used to provide the centripetal force, or in other words being used to keep them in a circular orbit around the earth. so in the same sense if the entire pull of the moon is being used to keep the earth going around the moon, how can the earth experience any force from the moon and also vice-versa?
also another question,
2.) I've attached an image for this. R is the contact force and G vector is the sum of the weight and the external force F applied on the body of mass m and N is the normal force. now the friction has a maximum limit beyond which it becomes constant i.e. uN, where u is the coefficient of friction. but if suppose we keep on increasing the force F so that it crosses the limit of maximum frictional force, the magnitude as well as direction of G vector keeps on changing but R vector remains constant, so the force applied by the block on the surface (sum of its weight vector and F) is G vector and the force applied by the surface on the block is R vector which remains constant after a certain limit. within a certain limit, R vector equals G vector, that is, newton's third law is satisfied, but beyond the limit of max. friction, G and R vectors aren't equal and opposite. does it mean that newton's third law isn't valid all the time?

thanks,
shikhin  

Answer
Hello Shikhin,

the followup and the new question are very much related as they both concern Newton's 3rd Law of mechanics. The crucial point of this law is that it speaks about forces on two DIFFERENT objects being equal.

1)Consider the first problem. Gravity means that two massive objects attract EACH OTHER. That is the definition of gravitation: It does not say there is only ONE force acting in the system, it says that there are TWO forces, but one acts on Earth, the other on Moon. And as Nature made it so via Newton's 3rd Law, the two forces have the same magnitude and have orientation always aligned with the straight line to the other object.

An astronaut orbiting the Earth attracts Earth with a force of the same magnitude as the one with which the Earth attracts him. The effect of the force acting ON Earth (the acceleration due to this force) is tiny, due to the huge Earth's mass and by comparison small human mass, so the change of Earth's motion cannot be perceived. To sum up: the number of forces between N objects is N*(N-1), while the number of different interacting pairs is N*(N-1)/2. Earth-Moon system has N=2, so here is 1 pair and 2 forces acting (this is very important) on the different members of the system.

2) Thank you for the image, it would have been better if you posted this as a separate question as I now have to scroll up and down the whole length of our communication to see it :-). The result force G is not defined the way you describe. Force F is never applied at the floor, because they are parallel. What acts on the floor is the pressure of the block and the "mirror of the friction force". The latter is the Newton's 3rd Law reaction force to the friction - if floor holds the block by friction, then block holds the floor by the same friction. The "mirror" has the same magnitude as the friction force acting on the block. But as this mirror acts on the floor, it has the opposite orientation. This "mirror" LOOKS like the FRICTION-COMPENSATED PART of force F, but as F acts on the block and the "mirror" acts on the floor, we must NOT mix them. It seems to me that you have drawn all the forces in the system as if they acted on the block, whille some of them really are applied BY the block ON the floor. Let's sort this out.

The force F acts on the block. Gravity mg acts on the block as well, but it is entirely compensated by the normal force N=-mg, so the net force of these two is ZERO. The interaction between the block and the floor, however, results in friction force FF(!), which will be a) FF = -F (compensating the force F down to net zero force), if this one is |F| < |fmg|, or b) FF = -fmg when |F| >= |fmg|. Here and below I use the convention that orientation of force F defines the positive horizontal direction, the weight mg defines the positive vertical direction. The result force Ftot acting on the block is a) Ftot=F+FF=0 or b) Ftot=F+FF=F-fmg depending on the above conditions.

Now, the forces acting on the FLOOR are the vertical pressure by the block's weight mg and the horizontal friction force -FF (note the "minus") applied by the block. If I use the symbol (+) for vector summation then the force acting on the floor is a) mg(+)-FF=mg(+)F or b) mg(+)-FF=mg(+)fmg, see conditions above. Beware: the force F appears in the equations HERE only as a magnitude and direction of the friction force, NOT as F itself, again because F itself acts only on the BLOCK. The vector sums have the orientation of the force G that you drew in the picture, but they are subject to the upper limit (condition b)) G<=mg(+)fmg.

If you want to judge the action-reaction relationship, you need to vector-add the friction acting on the block and the normal force N acting on the same. You don't include force F itself(!), because to evaluate action-reaction relations you must neglect all forces coming from outside the system block-floor. The force F is present only as an agent that gives rise to the friction tension between the block and floor. Then R=N(+)FF and this translates as a) R=N(+)-F=-mg(+)-F and b) R=N(+)-fmg=-mg(+)-fmg. Here you can finally see that Newton's 3rd Law holds. Let me summarize:
a) condition |F|<|fmg|: G = mg(+)F, R = -mg(+)-F = -G;
b) condition |F|>=|fmg|: G = mg(+)fmg, R =-mg(+)-fmg = -G.

We can discuss it more, but I think I wrote it the clearest way I am capable of. The key is to realize what is each force done BY and what does it act ON and never mix the two. I was lucky enough in my 15 years of age that my high school physics teacher took the trouble to force the understanding of the 3rd Law into us. He knew that it is the key to solutions of many problems.

I hope you enjoy the solution.
Cheers!
Daniel