Feynman insists that ...
Hello helpful physicist
Since you seem to be a physics person I thought you could help me with a thing that bothered me for quite some time now. Nobody has been able to answer me yet. I read a series of lectures Feynman gave in New Zealand for the non-science student. In there he seems to insist that:
1) There is no need for an uncertainty principle
Now, I was talking about that with a mathematician and he said I must have misunderstood something. However, even though it was a lecture for the non scientist, Feynmam INSITED that all the information he gave was correct.
Now, who is right? Feynman or the mathematician?
1) There is no need for an uncertainty principle
(Just for completeness I mention that the uncertainty principle says that if you have two Hermitian operators A and B whose commutator is a non-zero operator C, it is true that the product of the uncertainties of A and B is greater or equal to 1/2 of the expectation value of C. The most known application of this rule is when A is the x component of the impulse p, B is the x coordinate and C is the Planck constant h (~10 to the negative 34 power joule*s) divided by i*2*pi. Then the uncertainty principle reads delta(p)*delta(x)>= h/(4*pi))
Now back to the statement 1. The answer is that it is 100% true for your everyday life, i.e. for macroscopic objects. Indeed, the uncertainty principle does not effect macroscopic measurements. As an example I show the measurement of the position and speed of a volleyball ball. The mass of the ball is 200 grams, and in order to hit it very precisely, you need to measure its position with a precision let us say of 1 mm , than the TV cameras should be in principle able to measure its speed with the precision delta(v)>= 10^(-34)/(2*0.2*0.001)=~2*10^(-31) meters/s which none of the known electronics would be able to do, their errors are much bigger then the above value. However, in the microscopic world, serious limitations apply, because of the uncertainty principle, for example, we cannot construct very precise microscopes which would use light, or we cannot measure the speed of electrons in an atom, because their position is very well know, therefore their speed must be uncertain.
2) Photons can travel slower or faster than lightspeed (and indeed do) (I know they can go slower, but faster???)
Yes, photons can travel faster then the speed of light, and you will be surprised, not only photons, but elementary particles too!!! The trick is , that in certain mediums ( described by a number called index of refraction which depends on the wavelength of the traveling light), light travels with a speed which is less than the speed of the light in vacuum. This speed can be substantially less then 300 000 km/s. Since the index of refraction depends on the wavelength, other kinds of photons, for example X-ray photons, could in principle travel with a higher speed then the speed of the light in that given medium. The same holds for elementary particles. In fact, we use this phenomena to detect and distinguish particles here at Fermilab. This effect has it own name, and is called Cherenkov effect, or Cherenkov radiation. We use mediums made out of silicon. The light speed there is roughly 1.33 times less than the speed of the light in vacuum. Sometimes we have very fast electrons ( with a speed very close to the speed of the light in vacuum) entering this silicon medium. Since they travel faster then the speed of the light in silicon, they shine out light, which we can actually see and analyze and get some crucial information about those electrons.
3) Photons reflect from a mirror in ALL angles (equally) and not only in the one that is the same to the incoming angle.
Yes, this statement is also true, as long as we specify, what "equally" means. One thing is obvious from everyday life, in the mirror of your car, you do not see all objects on the road such as cars in front of you, ... , but you see only objects which shine light under the proper angle in order to get it to your eyes. Therefore, this statement 3. needs a little thought, which Feynman luckily did for us :-) To be precise, his statement says, that photons reflect in all existing directions, but NOT with EQUAL PROBABILITY. This was his basic input and observation, when he invented the notion of PATH INTEGRAL as a very successful tool for calculations in quantum field theory. The most probable trajectory for the reflected light WILL be the one which obeys the law of having the same reflecting angle as the incoming angle. All other trajectories will have extremely small probabilities to happen, and in most of the cases will cancel out. Similarly, when you throw a football ball you predict its motions by calculating its path from the Newton's equations of motions. However, Feynman's input to the calculations was, that he postulated that all PATHs of the football ball are possible, but they have various PROBABILITIES to happen and moreover he gave us a prescription, how to calculate these probabilities for a given path.
You gave me very nice questions, I had fun to think them over. Hope my answers helped you. If you have any further questions, or I used scientific words that you do not understand please do not hesitate to ask.
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