# Is Relativistic Mass Plausible?

1. Oct 15, 2009

### planck42

I've read contrasting sources concerning the concept of an object increasing in mass at relativistic velocities. Some of my older calculus texts mention this as being accepted by physicists, while a newer(by comparison) textbook called Principles of Physics: A Calculus-Based Text by Serway and Jewett claims that relativistic mass is outdated. Normally, the newer book would be correct, but I don't think there is any other reasonable explanation of the momentum of photons. Can the good people at PF please shed some light on this matter?

2. Oct 15, 2009

### keniwas

Its really becomming a very outdated concept as you say.

As for the momentum of photons, its actually not a relativistic result at all. Classical electromagnetism predicts the momentum of electromagnetic waves. This relation is carried over into the quantum world (which is where photons live) when you quantize the radiation field (or more simply, when you postulate as planck did that the energy in light had to exist in discrete quantities). In the end you get the photon momentum without any mention of relativity.

3. Oct 15, 2009

### planck42

Thank you for that explanation

4. Oct 16, 2009

### Wallace

Note that what is changing/has changed is just the terminology that people see as being most helpful. The underlying physical theory hasn't changed. Just making that clear.

5. Oct 16, 2009

### JANm

Hello planck42
So you are easily satisfied. I think that to say that mass-velocity relation is outdated is not a scientific statement. Science should be timeless. Theories are prooved true or false. So do you think that Serway and Jewitt mean in their book that there is no such thing as relativistic mass depending on velocity?, or is it depending on velocity in another way?
greetings Janm

6. Oct 16, 2009

### Wallace

JANm, as stated in my post above, the scientific theory hasn't been changed, just the prevailing view on the clearest way to think and talk about the concepts. The answer to any question that relates to what an observer would actually measure (which relates to what can be experimentally verified) hasn't changed.

7. Oct 16, 2009

### Naty1

As noted above it's all relative....rather than "right" or "wrong"

Wikipedia actually has a good discussion regarding your question....and these quotes:

For more try here: http://en.wikipedia.org/wiki/Relativistic_mass#The_relativistic_mass_concept

Last edited: Oct 16, 2009
8. Oct 16, 2009

### Naty1

In the prior Taylor and Wheeler quote, am I supposed to find it easier to relate an increase in momentum with the geometries of spacetime rather than an increase in mass? Why?

Or is it that an increase in mass relates somehow to the time component of the four vector and that is supposedly a less plausible relationship?

I think the above might imply that because we think we have a fundamental concept of mass, a structure we think we understand that we lack with momentum, for example , then it's more difficult to relate to a purported change in that structure.

I wonder if maybe it's plausible our understanding of mass needs some updating...that, for example, maybe we only have a low energy understanding of mass and are not even aware of that limitation....just as Newtonian physicsts were unaware their understanding was a low velocity picture. To say it another way, if time and space and energy change at high velocity why not mass??

9. Oct 16, 2009

### Klockan3

Because it is much cleaner to say that mass is a kind of energy and that all kinds of energy have properties we normally associate with mass than to add mass to every object containing energy. Relativistic mass might be easier to understand but it usually gives people extremely bad understanding of what actually happens.

10. Oct 16, 2009

### Staff: Mentor

I think this is actually reasonably accurate. The point, IMO, is that we think of mass as being an inherent property of an object itself, rather than a relationship between it and some observer. That means that the intuitive idea (or as you put it "fundamental concept") of mass must be relativistically invariant.

11. Oct 16, 2009

### Fredrik

Staff Emeritus
I think you're missing their point, which is that we intuitively connect the word "mass" to internal structure. It doesn't sound strange to say that the particle's energy is different in different frames (because energy depends on velocity), but it sounds very strange to say that the particle's internal structre is different in different frames.

12. Oct 16, 2009

### JANm

With this "extremely bad understanding" some physici mean: getting of the track of believing in relativity. It could also mean it is pedagogically better not to speak of it because it can get you of the track of Klassical Mechanics, which used to be an exact science next to mathematics itself.
Janm

13. Oct 17, 2009

### Fredrik

Staff Emeritus
What are you talking about? Special relativity is a more exact science than non-relativistic classical mechanics. (The theory is just as well-defined, and it makes much more accurate predictions about the results of a much wider range of experiments).

14. Oct 17, 2009

### JANm

Hello Fredrik
PLease don't think I want to go back to the days of classical mechanics. But there were two laws of conservation then: the one of mass and the one of Energy. It seems to me that if relativity theory wants to be right there would be one combining these two laws in one conservation-law. So it is not the prediction part of relativistics I am judging, but rather the theoretical part in which i miss something...
greetings Janm

15. Oct 17, 2009

### Staff: Mentor

There is, it is called the conservation of four-momentum. It combines the classical conservation laws of energy, momentum, and mass into one unified law.

16. Oct 17, 2009

### JANm

Hello DaleSpam
Wow that is nice. Could you elaborate a little more about this. I know mass and energy are somewhat bounded by E and mcpower2 and that they are in someway scalar functions. I suppose the momentum comes in as a vector function or what.
Ýou got me interested
Greetings Janm

17. Oct 18, 2009

### Klockan3

In relativistic theory you let time and length have the same units, so velocity is unit-less meaning that mass, momentum and energy can all be put on the same diagram without getting anything strange.

Anyway, to get the momentum 4 tensor you take the velocity 4-tensor and tacks on mass on it. This gives the normal relativistic momentums in the spatial dimensions while in the time dimension you get energy. Also since all of these needs to be rotational symmetric you need the length of this to be invariant you get that this is the invariant mass. (This is assuming c=1, otherwise you need to tack on a few c's, like E/c and mc)

Though, note that Minkowski space have a strange norm where time is seen as negative distance so you wont get the result I mentioned above if you do not use that.

Last edited: Oct 18, 2009
18. Oct 18, 2009

### Staff: Mentor

In relativity I am sure that you have heard that time is fourth dimension. This is represented mathematically using four-vectors: $(ct,x,y,z) = (ct,\mathbf{x})$. See the http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/vec4.html#c1" page (on both pages be sure to follow the links to further details).

Taking this approach you can do a couple of things that are mathematically very elegant and can give some physical insight. First, you can represent the Lorentz transform as a matrix. When you do so you notice that it has the form of a peculiar sort of a rotation matrix. Second, you can look for a norm which does not change under this rotation. This is the http://en.wikipedia.org/wiki/Spacetime_interval#Spacetime_intervals" $s^2 = -c^2 t^2 + x^2 + y^2 + z^2 = -c^2 t^2 + \mathbf{x}^2$ it can be considered the "length" of a four-vector and all reference frames will agree on it.

Now, if you work through it you will find that the four-vector that contains momentum in the spacelike part has the form $(E/c,p_x,p_y,p_z) = (E/c,\mathbf{p})$ which is called the four-momentum. This means that energy and momentum have the same relationship to each other as time and space do. Now, if you take the "length" of this four-vector you find that it is the rest mass, aka the "invariant mass" or just "mass". All observers agree on this quantity, and it simplifies to the famous E=mc² equation for an object at rest.

Now, you can get to the part that you were interested in, the conservation law. Analogously to Newtonian mechanics, the four-momentum of a system is the sum of the four-momenta of its constituent particles, and the four-momentum of the system is conserved across any interaction, including particle anhilation and creation interactions. This means that a system's energy (timelike component of four-momentum), momentum (spacelike component of four-momentum), and mass ("length" of four-momentum) are also conserved and you get one conservation law which unifies three separate conservation laws from classical mechanics. To me it is one of the most elegant and compelling facets of relativity.

Last edited by a moderator: Apr 24, 2017
19. Oct 18, 2009

### Naty1

PLanck: a general feature of physics is that as you learn more and more, different insights begin to emerge...for example Dalespam said above :

That's enough to rock me back on my heels still and I've know about it for a while ...and while not smart enough to extrapolate that relationship further, I know enough to realize it's hinting at other things we likely don't understand fully yet. Just like E = Mc2...two pieces of a puzzle with many other pieces still missing....

I can't help but wonder if time and mass and energy and space all popped out, apparently togther in some sort of a bang, that we'll ultimately understand how they are all related at a fundamental level....maybe a fundamental constitutent from which these emerge, perhaps like quantum vacuum fluctuations...

Last edited: Oct 18, 2009
20. Oct 18, 2009

### matheinste

That is a very enlightening presentation. Seeing how all these things knit together is, to me, far more interesting and worth the effort of learning before worrying about some of the more often discussed esoteric topics such as time travel, wormholes, black holes etc.

Matheinste.

Last edited by a moderator: Apr 24, 2017