Relativistic mass and Hubble constant

[student1307]

Student here, please forgive...

I have a question about relativistic mass in galaxies. Is the mass of far away galaxies affected by expansion of universe? That is: Is mass of a far away galaxy is different for observer there compared to the observer here? Let's say there is a galaxy identical to Milky Way, at the far end of the red shift spectrum. What is the mass of this galaxy (black hole included) from my perspective? Do I get expansion velocity from distance and Hubble constant and plug to relativistic mass equation?

Thanks!

student1307

 

[Chalnoth]

Student here, please forgive...

I have a question about relativistic mass in galaxies. Is the mass of far away galaxies affected by expansion of universe? That is: Is mass of a far away galaxy is different for observer there compared to the observer here? Let's say there is a galaxy identical to Milky Way, at the far end of the red shift spectrum. What is the mass of this galaxy (black hole included) from my perspective? Do I get expansion velocity from distance and Hubble constant and plug to relativistic mass equation?

Thanks!

student1307

We no longer consider velocity to have an effect on the mass of an object. Apparently this formulation led to a number of mistakes, and has fallen out of favor as a result. Today, mass is simply defined as the energy in the internal degrees of freedom of an object (or, equivalently, its non-kinetic energy). So if the far away galaxy was the same as the milky way, its mass would also be the same, no matter where it was or how fast it was moving with respect to us.

 

[student1307]

Thank you,

Does this mean that gravity forces inside the fast moving galaxy are stronger, because masses are the same, but the galaxy for a lack of better word is smaller?

 

[Chalnoth]

Thank you,

Does this mean that gravity forces inside the fast moving galaxy are stronger, because masses are the same, but the galaxy for a lack of better word is smaller?

No, not at all. The galaxy is the same as our galaxy, as you said. So the distances and forces between the stars (and other stuff in the galaxy) are the same.

 

[chroot]

Hello student1307!

Try not to think about motion in absolute terms. You can't define the velocity of one thing all by itself; you can only define the velocity of two objects in relation to each other. So, a "fast-moving galaxy" isn't a good way to put it. Galaxies are just galaxies, no matter how they're moving with respect to other galaxies. Galaxies here and galaxies there will have the same mass, when defined in the modern way. They will appear to us to behave differently when they're moving fast, but that is just a result of the motion, not something actually happening to the galaxy.

Think about looking at a tall building from different places in a city. Its apparent height, maybe compared to the size of your hand at arm's length, will be totally different from different vantage points. In the same way, a single galaxy can appear differently to observers moving with different velocities.

I hope this helps!

- Warren

 

[Tanelorn]

What is the reasoning behind dropping relativitic mass at galactic scales?
Do gravitational fields propagate at the speed of light?
Are relativistic particles in galactic halos a candidate for dark matter?

http://en.wikipedia.org/wiki/Mass_in_special_relativity

 

[student1307]

Hello student1307!

Try not to think about motion in absolute terms. You can't define the velocity of one thing all by itself; you can only define the velocity of two objects in relation to each other. So, a "fast-moving galaxy" isn't a good way to put it. Galaxies are just galaxies, no matter how they're moving with respect to other galaxies. Galaxies here and galaxies there will have the same mass, when defined in the modern way. They will appear to us to behave differently when they're moving fast, but that is just a result of the motion, not something actually happening to the galaxy.

Think about looking at a tall building from different places in a city. Its apparent height, maybe compared to the size of your hand at arm's length, will be totally different from different vantage points. In the same way, a single galaxy can appear differently to observers moving with different velocities.

I hope this helps!

- Warren

Ah So when I am sitting here, my Milky Way has mass M, radius R, angular momentum L etc. If I warp speed to the other(which runs away at some significant velocity), it would be identical. But When I look from here, I observe it as being redshifted (for sure), with smaller radius? but same mass, same total energy and same angular momentum, hence orbiting faster? So the only relativistic correction is contraction of time and length, but not mass (due to the definition).

Did I get it?

 

[chroot]

Hey student1307,

Yes, I think you've got it, with one small exception. If you observe a highly redshifted galaxy, one that is moving away very rapidly, you will actually see it rotating more slowly than if it were stationary. Keep in mind that the angular size (the apparent size on the sky) of a galaxy is not necessarily related to its actual size. Nearby galaxies generally appear larger on the sky than distant ones just because of their different distances.

- Warren

 

[Chalnoth]

What is the reasoning behind dropping relativitic mass at galactic scales?

People think of mass as an intrinsic property of matter. A formulation which allows the mass of a particle to depend upon the motion of the observer is quite contrary to this perception of mass. This incongruence led to a number of errors, and so it has fallen out of favor.

Do gravitational fields propagate at the speed of light?

Well, certain changes in gravitational fields propagate at the speed of light. If you have, for example, a star moving through the galaxy, its gravitational field will move right along with it. It has to, if you think about it, because you know what the gravitational field of it is if it's standing still compared to you, so you can simply calculate the gravitational field if it's in motion by doing a coordinate change to a moving observer. But if you suddenly change the motion of the star (e.g. it's moving with respect to us, and we stop it suddenly), then the gravitational field around the star will sort of ring with gravitational waves, which propagate at the speed of light, eventually relaxing into the new field configuration.

Are relativistic particles in galactic halos a candidate for dark matter?

Nope. Not only would we see them (due to the emission of synchrotron radiation), but we also see the effect of dark matter before any galaxies formed, in the cosmic microwave background.

 

[Chalnoth]

Ah So when I am sitting here, my Milky Way has mass M, radius R, angular momentum L etc. If I warp speed to the other(which runs away at some significant velocity), it would be identical. But When I look from here, I observe it as being redshifted (for sure), with smaller radius? but same mass, same total energy and same angular momentum, hence orbiting faster? So the only relativistic correction is contraction of time and length, but not mass (due to the definition).

Did I get it?

It's not correct to say the radius is reduced. A galaxy moving away from us is compressed along the line of sight. If we see a spiral galaxy face-on, there will be no change in apparent radius. If we see a spiral galaxy edge-on, then the galaxy will no longer appear to be circular.

Though in practice, this difference of thickness along the line of sight is immaterial, because in practice we just can't measure the thickness of a galaxy along the line of sight in the first place. These objects are simply too far away, and we infer all of our information about the size of the galaxy from its angular size, which does not change due to its cosmological motion.

As far as the energy, that really depends upon what you mean. In the simple special relativistic sense, its energy will be essentially equal to the relativistic gamma factor times the mass. But this statement doesn't really have any physical significance, so we don't usually bother with it.

 

[student1307]

Hey student1307,

Yes, I think you've got it, with one small exception. If you observe a highly redshifted galaxy, one that is moving away very rapidly, you will actually see it rotating more slowly than if it were stationary. Keep in mind that the angular size (the apparent size on the sky) of a galaxy is not necessarily related to its actual size. Nearby galaxies generally appear larger on the sky than distant ones just because of their different distances.

- Warren

I understand the issue of geometric perspective and apparent size. I am talking about the other MW having smaller (lineal, not angular) radius as measured from Earth. And why rotating more slowly?

 

[Chalnoth]

I understand the issue of geometric perspective and apparent size. I am talking about the other MW having smaller (lineal, not angular) radius as measured from Earth.

Well, we can't observe that, though, because the smaller dimension is along the line of sight, which we are almost completely insensitive to.

And why rotating more slowly?

Time dilation.