Mass changes in special relativity?

Question

Could someone point to the math that explains this?

“For example, at 10 percent of the speed of light an object’s mass is only 0.5 percent more than normal, while at 90 percent of the speed of light it would be more than twice its normal mass.”

Excerpt From: Stephen Hawking. “A Brief History of Time: From Big Bang to Black Holes.”

G.Smith has already mentioned it in their answer, but the idea of mass increasing with velocity is outdated, for extended discussion you can try reading this thread. — Charlie, Sep 01 '20 at 20:27

G. Smith · Accepted Answer · 2020-09-01T21:09:17.493

7

Could someone point to the math that explains this?

So-called “relativistic mass” $m_\text{rel}\equiv\gamma m$ increases with speed by the “Lorentz factor”

$$\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}.$$

Try putting in the numbers! (And notice what happens as $v\to c$!)

However...

Today “relativistic mass” is considered an outdated concept. Physicists prefer to let mass be independent of speed and talk about the relativistic energy $\gamma mc^2$ instead. (The two concepts are obviously proportional, differing only by a factor of $c^2$. Physicists don’t care about that because they often use units in which $c=1$.) “Relativistic mass” is unfortunately still common in pop-sci explanations of physics, and some high-school textbooks, but it’s not popular with most physicists any more. I consider it pedagogical malpractice.

edited Sep 01 '20 at 21:09

answered Sep 01 '20 at 20:17

G. Smith

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Your $"PS"$ should really be the main body of your post, not some kind of afterthought. – Gert Sep 01 '20 at 20:56
@Gert I interpreted the key question as “What formula gives the numbers Hawking mentions?”, not “Does mass change with velocity?” – G. Smith Sep 01 '20 at 20:58
Be that as it may, you're inadvertently propagating the myth of relativistic mass, IMO... – Gert Sep 01 '20 at 21:03
@Gert So downvote me and write an answer of your own. – G. Smith Sep 01 '20 at 21:04
No. I just think it would have been better to make the point about RM immediately. See e.g. Einstein's own letter (in Wiki). Matter's internal structure doesn't depend on how fast it travels (that would be magical!) – Gert Sep 01 '20 at 21:08
@Gert I have been making some edits with your comment in mind. – G. Smith Sep 01 '20 at 21:09
Yes, I think that's better. +1. – Gert Sep 01 '20 at 21:12
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@Gert Thanks for helping me improve it, and for your upvote. Sorry I initially bristled. – G. Smith Sep 01 '20 at 21:14
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Oh but we all bristle! ;-) – Gert Sep 01 '20 at 21:21

Mass changes in special relativity?

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