Richard, there are more things in heaven and earth than are mentioned in Einstein's theory! As I first read about it, I cannot recall where, the simultaneous behavior of 'complementary' electrons in relation to each other was taken as an indication of a limit to the applicability of Einstein's tenet that nothing travels faster than the speed of light.
But Einstein's theory establishes that time is relative to speed, as illustrated in the example of the one twin who travels in outer space while the other stays on earth and who, because of the different speeds at which they travel, age at different rates. But if anything but light travelled at the speed of light, time would not affect it at all. Mind-boggling.
From: Richard Seddon <[log in to unmask]>
Reply-To: "T. S. Eliot Discussion forum." <[log in to unmask]>
To: [log in to unmask]
Subject: Warning//Quantum Mechanics/ /way off topic
Date: Thu, 26 Jul 2007 09:25:49 -0600
. I'm interested in two phenomena or facts especially: that at the speed of light there is no time, and that the response of two particles to each other at distant locations occurs faster than the speed of light, i.e., in no time. Light outrunning time appeals to my imagination! Again, thanks. Diana
Your two interests, although seemingly related, are not related. The first has to do with relativity of which I know nada. The second is one of the quantum mechanical (of which I know almost nada) paradoxes. In fact it is the basis of the EPR paradox which gave Einstein the willys. What you are referring to is “spin”. An electron can have + or – (up or down) spin. If when we determine their spin while they are in the same atomic orbit one always has one spin and the other has the other spin. The reason is bound up in the math. But, and it is a big but, as the electrons exist in the atom they must be neither until we measure them. At the moment I determine the spin of one the other simultaneously assumes the opposite spin. Note it is simultaneous. It is not faster than the speed of light, it is simultaneous. There is no speed; as one is measured to have up spin the other has down spin. Two things here. Not only does the untouched electron know what spin it should have but it knows that it should have spin. Remember the spin of both electrons was undefined until one was measured.
Distance makes no difference. The last thing I saw was two “entangled’ particles (I think they were photons) were separated by about 40 miles when one was measured. At the moment of measurement of the one the other revealed it had spin and that its spin was the opposite of its sister. Again it is not faster than the speed of light, it is simultaneous.
Another implication here which is also hard to swallow is that the electrons really don’t have spin until examined. Then all of a sudden they have it. They are identical until one is examined. When one is examined it appears to “choose” which spin to have and the other is simultaneously forced to have the opposite spin.
Gribbin goes into some depth in a non-mathematical treatment of spin. I want to emphasize that there are no contradictions in the math.
Concerning your first question. Remember the constant “C” refers to the speed of light in a vacuum. The speed of light in other mediums is quite different. Cherenkov radiation http://en.wikipedia.org/wiki/Cherenkov_radiation is an effect of charged particles exceeding the speed of light in water. IAW the charged particles are outrunning the photons in the same water. Now as far as I know both the charged particles in water and the photons in the same water are still affected by time. Why would it be different in a vacuum???
There are time paradoxes in quantum mechanics. As I recall Susskind will introduce you to some of them. Basically they involve the “stuttering” of particles between negative time and positive time.
I’ll give you a question that bothered me for a long time. Look up the mass of a photon. It is zero!!! Yet a photon has energy!!! And, energy is another way of measuring mass!!! E=MC^2!!!! So if I do the equation for a photon of energy such and such I get a mass right, wrong. ?????? BTW there is an answer it just is not very satisfying.