How accurate is this polar mechanism for the Diels-Alder reaction?
Disclaimer: This is not a full answer. I was just too long for a comment.



I think the suggested mechanism is not entirely wrong, it might be a contributing factor of the whole process, but not a very important one. In the last fifty years, the mechanism has been discussed in almost countless publications. One of the more recent ones by Goldstein et. al. concluded that a concerted pathway is the most economical.[1] 
They also included possible diradical pathways and the similar. Of course there is no uniformly applicable mechanism, it is very dependent on the substrates. Many of the reactions can be effectively described by frontier molecular orbital theory, so it is also possible to do so for the simplest Diels-Alder reaction. 

There might be many more publications out there discussing the whole mechanism in pretty exhausting detail, but for a start I thought the cited one will do just fine. Just to name some more, see [2] through [4].

The electrostatic interpretation is tempting, as it is simple and it explains the simplest case very well. I believe it explains it too well for the wrong reasons:
 I would not expect the polarisation, i.e. induced dipole, in ethylene and butadiene be strong enough to make this happen at all. Both are colourless gasses at room temperature. If there were more induced dipoles, they would be liquid, which means that these molecules are basically unpolarised. 

In a publication by Gian Franco Tantardini and Massimo Simonetta it was stated, that the contribution of the polarised Valence Bond Structure is very little, see [5]. If I read it correctly, the contribution is less than 1%. This alone should suffice to disregard a mechanism purely based on electrostatic considerations. In the same publication it is stated, that ethylene has quite a significant contribution from its polarised structure (about 25%). However, these consideration would in most cases not be able to describe streospecific reaction products, that are obtained from different substrates.

As another aspect, one must not forget, that the ground state of 1,3-butadiene is trans and it requires just a bit of energy to rotated it to the necessary cis formation, which should be about 10 times less present. So what are the odds having a well polarised ethylene hitting a polarised cis-butadiene in the right angle at the right speed. There has to be more to it...


E. Goldstein, Brett Beno, and K. N. Houk; J. Am. Chem. Soc., 1996, 118 (25), 6036–6043. 
R.B. Woodward, and Thomas J. Katz; Tetrahedron; 1959, 5 (1), 70-89. Mirror at znu.ac.ir.
Michael J. S. Dewar, Santiago Olivella, and James J. P. Stewart; J. Am. Chem. Soc., 1986, 108 (19),  5771–5779.
J. Sauer; Angew. Chem. Int. Ed., 1967, 6 (1), 16-33. 
Gian Franco Tantardini and Massimo Simonetta; Int. J. Quant. Chem., 1978, 14 (S12), 131-141.