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I know there is a related question, that references the Dirac Equation, that relies on relativity, but I've just watched this video:

http://www.youtube.com/watch?v=NtnsHtYYKf0

Which seems to say there is something new on this topic? What specifically has changed in our understanding?

Here is the paper he references.

In short, he (in the video) says that as mercury is large, it's electrons have to orbit really fast to not get sucked in. As they move much faster they approach c and gain mass meaning they are less able to bond with other mercury atoms.

for a start, I know that electrons fill shells and the bohr model of 'orbits' is quite naive.

The abstract of the paper says :

An old problem solved: Monte Carlo simulations using the diatomic-in-molecule method derived from accurate ground- and excited-state relativistic calculations for Hg2 show that the melting temperature for bulk mercury is lowered by 105 K, which is due to relativistic effects.

Which doesn't tell me much.

So, what new information do we have about the melting point of mercury due to relativity?

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    $\begingroup$ It's very time-consuming for people to watch a video in order to find out what your question is. Please summarize the relevant material from the video. The purpose of SE is not really to answer your question, it's to build a body of questions and answers that will be useful to other people. This question, in its present form, is unlikely to be useful to other people. $\endgroup$ – user4552 Aug 20 '13 at 21:45
  • $\begingroup$ @BenCrowell I've tried to summarise it now in my edit. I was more expecting people to go from the paper (which I can't access), and not the video which originally confused me. $\endgroup$ – Pureferret Aug 20 '13 at 22:00
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    $\begingroup$ This may be helpful: blogs.scientificamerican.com/the-curious-wavefunction/2013/07/… Cf. fourmilab.ch/documents/golden_glow $\endgroup$ – user4552 Aug 20 '13 at 22:05
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... says that as mercury is large, it's electrons have to orbit really fast to not get sucked in. As they move much faster they approach c and gain mass ...

That's not what relativity says, in short mass does not increase with velocity:

The mass (the true mass which physicists actually deal with when they calculate something concerning relativistic particles) does not change with velocity. The mass (the true mass!) is an intrinsic property of a body, and it does not depends on the observer's frame of reference. I strongly suggest to read this popular article by Lev Okun, where he calls the concept of relativistic mass a "pedagogical virus".

What actually changes at relativistic speeds is the dynamical law that relates momentum and energy depend with the velocity (which was already written). Let me put it this way: trying to ascribe the modification of the dynamical law to a changing mass is the same as trying to explain non-Euclidean geometry by redefining $\pi$!

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    $\begingroup$ How can you conclude that relativity does not effect the melting point of mercury from the fact that rest mass does not change with velocity? Just because somebody botches an explanation, it doesn't mean that the fact he is explaining isn't true. $\endgroup$ – Peter Shor Jan 8 '14 at 13:10
  • $\begingroup$ @PeterShor Okay I edited my answer so that it is more correct. $\endgroup$ – lotofdots Jan 8 '14 at 13:12
  • $\begingroup$ this doesn't really answer the interesting quesetion. $\endgroup$ – CognisMantis Aug 7 '15 at 3:47

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