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Is it only the higgs field that stops me from accelerating up to the speed of light or is there other restriction concerning the increase in mass? In other words if I had a Higgs field shield on my spacecraft could I get close to the speed of light without an increase in mass?

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Nope. The majority of the mass of protons and netrons is from binding energy which isn't affected by the Higgs field. – Brandon Enright Nov 12 '13 at 8:06
Does that mean there are 2 reasons why mass increases when you accelerate? Is there another higgs like field that causes the binding energy to increase? – Jitter Nov 12 '13 at 8:19
Interesting but I still don't know if it's the higgs field that increases that small part of the mass or if it's something else. Does the mass that the Higgs field is responsible for increasing during acceleration increase to infinity as you approach c? or is it finite? – Jitter Nov 12 '13 at 8:40
A question for science fiction writers: what would a Higgs field shield be made out of? – DarenW Nov 13 '13 at 4:37

Courtesy of the question Bound State of Only Massless Particles? Follows a Time-Like Trajectory? the answer to your question is no.

If you take the example of a glueball formed from two gluons, although the gluons are massless the glueball has a rest mass. In his answer to the above question Ben Crowell argues that the glueball must move on a timelike trajectory i.e. slower than the speed of light. So we have an example of a bound state of massless particles that moves slower than $c$.

So even though removing the Higgs contribution to the mass would render the elementary particles massless, QCD bound states would remain massive and travel on timelike trajectories.

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