Neutron Stars & SR: Explained for Discovery Channel

[TheTuringTester]

I saw a thread that asked the same basic question as I'm asking, but the explanation was beyond my current knowledge. Please consider answering my question as if you were being interviewed for a Discovery Channel special and had to make it comprehensible for a general audience. Thanks!

For me, the most confusing concept in relativity, so far, is if there really is only one version of an object and accelleration can really add mass to that object and any object can be declared to be accellerating in relation to another object, how do objects avoid having a whole range of masses and thereby cause a range of gravitational fields to distort spacetime around them?

I thought about observing a neutron star that was just under the limit of density to collapse into a black hole being pushed over that limit to observers who had a relative motion near the speed of light relative to the neutron star.

 

[PeterDonis]

if there really is only one version of an object

By which I assume you mean, any object can be described by invariant quantities, which do not depend on who is observing them, correct? If so, yes, this is true.

accelleration can really add mass to that object

It can't, at least, not in the appropriate sense. See below.

I thought about observing a neutron star that was just under the limit of density to collapse into a black hole being pushed over that limit to observers who had a relative motion near the speed of light relative to the neutron star.

No, this won't happen. If it's not a black hole to someone at rest relative to it, it's not a black hole to anyone; being a black hole is an invariant--all observers agree on it.

What this shows is that what you are thinking of as "mass", which is more precisely termed "relativistic mass", is not an invariant; different observers disagree on how much relativistic mass an object has. (One of the reasons the term "relativistic mass" is not used much any more is that it invites confusion, because "mass" seems like it should be an invariant. The appropriate term to use is just "energy", which at least reduces the chance of confusion, since energy is observer-dependent even in Newtonian physics.) The appropriate invariant description of an object, such as a neutron star, involves something called the stress-energy tensor, which represents the energy, momentum, pressure, and other stresses inside the object in a proper relativistic way. Using this description, it can be shown that an object that is a stable neutron star in one frame will be a stable neutron star in any frame.

 

[TheTuringTester]

Thank you for your reply. I want to make sure I'm clear on this. Regular mass distorts spacetime and we call that gravity. Relativistic mass does not distort spacetime and increase the gravitational field. If so, I vote we stop calling both of those properties mass. We can call one mass and the other something totally different.

 

[PeterDonis]

Regular mass distorts spacetime and we call that gravity.

No; stress-energy distorts spacetime and we call that gravity. See below.

Relativistic mass does not distort spacetime and increase the gravitational field.

No; "relativistic mass" is just energy, and it does distort spacetime, because it's part of the stress-energy tensor. But you can't just look at one component of the stress-energy tensor to see how spacetime is distorted; you have to look at all of it. That's why just looking at "relativistic mass" doesn't work. When you look at all of the stress-energy tensor, you see that it transforms when you change frames in a way that keeps the spacetime curvature (distortion) that is produced the same.

I vote we stop calling both of those properties mass.

"We" mostly have; the term "relativistic mass" is not used much any more, as I said in my previous post. Most physicists just say "energy", which, as I noted, makes it clearer what it is and why it isn't an invariant.

 

[TheTuringTester]

Thanks again. I'm just beginning my learning on the subject (as a middle-aged adult) and I now see I am going to have to undo all those hours of science television and popular physics books that I'm sure have led to a head full of oversimplifications and incomplete analogies.

 

[PeterDonis]

I now see I am going to have to undo all those hours of science television and popular physics books that I'm sure have led to a head full of oversimplifications and incomplete analogies.

Unfortunately, yes, TV and pop science books are seldom good places to actually learn the science. My personal opinion is that they're not really intended for that anyway; they're intended to get the audience to say "oh, wow!" and then move on to the next sound bite.

Fortunately, there are places like PF where you can come to get a better perspective.

 

[phinds]

I very much agree w/ Peter on the pop-sci stuff. I watch a lot of it as idle entertainment so I know that while they often get things right, the very often get them wrong, sometimes in egregiously awful, cringe-worthy, ways. They DO have great graphics and stuff, which makes them entertaining in a pop-corn-eating kind of way, but as Peter said they are absolutely not to be taken seriously as far as learning actual science.

 

[DrGreg]

To summarise the terminological issues:

<br /> \begin{array}{|c|c|c|}<br /> \hline<br /> \textbf{Unambiguous} &amp; \textbf{Name used by} &amp; \textbf{Pop science} \\<br /> \textbf{name} &amp; \textbf{most professionals} &amp; \textbf{name} \\<br /> \hline<br /> \text{rest mass} &amp;\text{mass } &amp; \text{rest mass }\\<br /> \hline<br /> \text{relativistic mass} &amp; \text{energy} \div c^2 &amp; \text{mass } \\<br /> \hline<br /> \text{rest energy} &amp; \text{mass} \times c^2 &amp; \text{rest energy } \\<br /> \hline<br /> \text{total energy} &amp;\text{energy } &amp; \text{energy } \\<br /> \hline<br /> \end{array}<br />

(And professionals often work in units where c = 1, e.g. one light-second per second, which simplifies the table even further.)