# Does mass become infinite near the speed of light?

1. Oct 12, 2014

### avito009

I read somewhere that at 90% the speed of light the mass doubles. So does mass only nearly double at the speed of light and does mass not become infinite at the speed of light? I thought nothing with mass can travel at the speed of light because mass would become infinite at light speed.

Also as per my understanding the relativistic mass increases at higher speeds but this increse in mass is temporary and when at rest the mass again returns to the normal value. Is this correct?

2. Oct 12, 2014

### Matterwave

The concept of relativistic mass has largely fallen into disuse over the past years. It tends to lead to confusions more than it leads to any genuine physical insight. What can be said is the kinetic energy of a massive object approaches infinity when that object approaches (but it can't reach) the speed of light. The "relativistic mass" as defined as $m_{rel}\equiv\gamma m$ where $m$ is the invariant mass of the object, also approaches infinity when the object approaches the speed of light.

3. Oct 12, 2014

Correct.
In simple words, at nearly the speed of light (speed of light can not be attained), the energy required to accelerate a body further becomes quite awfully large. To explain this phenomena, it is said that the mass of the body increases near the speed of light, but in actual the kinetic energy approaches infinte.

4. Oct 12, 2014

### vanhees71

As Matterwave said, it's the energy which becomes infinite, not the mass, which stays constant, i.e., independent of the speed of the particle (as long as there are no intrinsic excitations of the particle involved).

5. Oct 12, 2014

### A.T.

To understand this, it helps to consider a relativistic wind up car:

Does its relativistic mass (energy) increase, as it accelerates?

6. Oct 12, 2014

### vanhees71

This is a very interesting example. The mass decreases here. Remember again that mass is always "invariant mass", i.e., the mass of the object as measured in its momentary restframe. In the beginning some spring inside the car is tensioned and thus has potential energy which you provided winding it up. Thus there is more energy saved in the car at rest than when the spring is not tense, and thus there's an additional mass given by $\Delta m=\Delta E/c^2$. Now you relaease the car and it gets accelerated. It gains kinetic energy and looses the potential energy. At any moment thus its mass decreases while its kinetic energy increases by the corresponding amount according to the famous mass-energy relation. At the end it has lost the mass $\Delta m$.

7. Oct 12, 2014

### ShayanJ

I think textbook authors should abandon the concept of relativistic mass. Its of almost no use and produces too much trouble. I'm sure there can be other explanations for why nothing with mass can reach the speed of light. One thing that seems fine to me is to say that in SR, Newton's second law changes from $\vec a=\frac{\vec F}{m}$ to $\vec a=\frac{1}{\gamma m}(\vec F-\frac{\vec v \cdot \vec F}{c^2}\vec v)$.

8. Oct 12, 2014

### harrylin

1. As already clarified by others, although the "rest mass" stays the same ("invariant"), indeed the "relativistic mass" increases with speed; and this increase in inertia can be measured in for example cyclotrons*. But what you perhaps did not realize is that this increase is very non-linear; "doubling at 90%" and "infinite at 100%" are not in disagreement with each other! The related non-linearity of speed increase as well as the increased kinetic energy were nicely illustrated in a demonstration video:
https://www.physicsforums.com/threa...and-video-bertozzi-the-ultimate-speed.770488/

2. Your second question: yes, at rest we simply measure the rest mass. Note that if the mass is for example a ball that travels with you inside a high speed rocket, and you try to throw it away from you, you would also not feel any effect as relative to you the object is in rest (that's "relativity").

*See https://en.wikipedia.org/wiki/Cyclotron#Relativistic_considerations

9. Oct 12, 2014

### A.T.

Does the inertia of the wind up car increase as it accelerates? Does it require more force to accelerate, the faster it goes?

The point of this wind up car example is to constrain this very common way of putting it:

And to provide a better understanding: The increase in inertia comes from external energy input, not from speed itself. If all the energy for acceleration is stored on board, there is no increase in inertia during acceleration.

Last edited: Oct 12, 2014
10. Oct 12, 2014

### harrylin

That's an an interesting one! :) I assume that the relativistic synchrotron equations do not apply to the car in your example (if it could go fast enough of course) - the constraint for the usual equations and discussions is that the object's rest mass (and thus also its rest energy) remains constant (ceteris paribus as one used to say in old days).

:
Right - while I fear that that example could make matters overly complex for the OP, your precision about external energy input may be helpful indeed!

Last edited: Oct 12, 2014
11. Feb 21, 2016

### Ducatidoug

Well a question concerning life at the speed of light. Since no object with any mass can reach the speed of light then only objects or waves of 0 mass exist there which I would assume to mean that only pure energy exists at that realm. Also time and distance do not exist correct? So if there is no mass is there any gravity? Of course we have gravity and it does affect light by bending it. So matter does interact with mass less photons and neutrinos. Is it possible that the big bang is the result of massive amounts of pure energy slowing down (for whatever reason) to the point of becoming an explosion of matter and also creating the dimension of time and space?

12. Feb 22, 2016

### Ibix

"Pure energy" and "realm" don't really have a meaning in physics. Also you appear you appear to beusing "dimension" in its science fiction sense of "a separate universe" rather than its trchnical sense of "direction". The existence of matter or energy pre-supposes the existence of spacetime as the background on which they exist, at least in our current physical models. Finally, there is no way to slow anything that travels at the speed of light.

Your questions don't make much sense, I'm afraid.

13. Feb 23, 2016

### Idunno

According to observers watching a spaceship get close to the speed of light, the mass of the ship gets greater, making it harder to accelerate, thus it cannot go faster than light, as the energy needed to accelerate approaches infinity. Fine.

However, what about the people in the ship? According to them, their mass is still the same, the rest of the universe is travelling close to the speed of light, and the mass of the rest of the universe has increased. According to the people in the ship, what is the problem with using a bit more fuel and accelerating a little bit more?

14. Feb 23, 2016

### PAllen

None. They can apply 1 g acceleration (for example) forever (until running out of propulsion). They will see Doppler increase without bound. An object they throw out of the ship will always move away 1 g acceleration initially, no matter how long they've been firing their rockets. However, If they stop accelerating periodically to have inertial basis to measure speed of objects going by, they simply find that they are ever close to c, but never reaching it. This is part of the limitation is using 'increasing mass' as the explanation of the c as a limiting velocity.

The way to see algebraically what happens is suppose when already .9c with respect to stars, the rocket drops a space buoy and continues accelerating till that space buoy is moving at .9 away from the rocket. This is perfectly possible. You might think that means the stars are moving at 1.8c. That is wrong. velocities don't add that way. The correct rule (for collinear motion) is (u+v)/(1 + uv/c2). Thus, when the buoy is moving .9c away from the rocket, the stars are moving away at .9945c. Understood as a feature of spacetime, with non-Galilean rules of algebra and geometry, you see that increasing 'relativistic mass' is completely irrelevant.

Last edited: Feb 23, 2016
15. Feb 23, 2016

### ZapperZ

Staff Emeritus
See, this is one of the many reasons why we try to refrain from using the term "relativistic mass", because it creates this kind of confusion and this kind of problems where people seems to think that this is REAL mass that can cause real gravitational effects. In fact, the questions in this thread are the POSTER CHILD on why this term should not be used.

Please read our FAQ on why this is really not an accurate description (it is more accurate to consider relativistic momentum), and why, even Einstein, stopped using this term later on in his life.

Zz.

16. Feb 23, 2016

### Idunno

Thank you very much for your answer. I've been wondering about this for awhile. To paraphrase you, the explanation that you cannot go faster than light because the mass is increasing is a limited explanation, as it is not the explanation that observers on the accelerating spaceship would use... That fair?

17. Feb 23, 2016

### PAllen

Fair enough. Personally, I wouldn't use the increasing mass explanation at all, but some great physicist have used it, within its limitations (e.g. Richard Feynman). Einstein, however abandoned relativistic mass soon after 1905.

18. Feb 24, 2016

### vanhees71

I don't know, how often one has to repeat this argument. Today, we define mass as a scalar. Sometimes one emphasizes this by calling it "invariant mass". Relativistic mass was an idea from the very beginning of the development of relativity before its full mathematical structure has been understood. This idea of a velocity-dependent mass is an unnecessary confusion. Everything related with it is fully described by the total energy of a system, which is the time component of the four-momentum vector.

19. Feb 25, 2016

### Mister T

An excellent way to explain the mass-energy equivalence!

20. Feb 25, 2016

### Mister T

That's certainly a valid reason, but the real reason is more general. Consider the equation $E=\gamma mc^2$ where $\gamma$ is defined as the ubiquitous $(1-\frac{v^2}{c^2})^{-\frac{1}{2}}$. The quantity $\gamma m$ increases beyond all bounds as $v$ appraoches $c$. Choosing to call $\gamma m$ the mass is a just that, a choice. It is not a consequence of the postulates, but the introduction of an arbitrary re-definition of the word mass. Einstein used it briefly after 1905 but then quickly abandoned it. Unfortunately it was favored in some but not all arenas for almost the following 90 years or so, at which time it started disappearing from the lexicon.

21. Feb 25, 2016

### DrStupid

What was the original definition?

22. Feb 25, 2016

### Mister T

The original definition of mass? I don't know. In Newton's time it was "quantity of matter". The modern definition involves comparison to a standard body.

23. Feb 26, 2016

### vanhees71

Mass is a Casimir operator of the Poincare group, i.e., a scalar. Any other historical definition (in the early days before Minkowski they even had "longitudinal" and "transverse" masses and all kinds of very confusing quantities, which are of no other use than to confuse the students) is obsolete. I don't know, why so many people insist on making physics even more complicated than it is in its most natural form ;-).

24. Feb 26, 2016

### DrStupid

That wasn't a definition but Newton's name for mass. The definition was mass=density*volume but that isn't very helpful. It is used the other way around as a definition of density. Alternatively mass could be defined implicit by other laws and definitions. But in special relativity such a definition would result in relativistic mass.

The reference is required for the measurement (in addition to the definition).

25. Feb 26, 2016

### PAllen

No it wouldn't unless you choose a definition that leads to this. For instance, if I want mass to be invariant, I define it operationally as resistance to acceleration measurd in the MCIF of the body; or in relation to a unit mass, I define it s the ratio of momentum of the given mass to a comoving unit mass. The latter idea is simply that mass is the contribution to momentum due to the 'content of the body' and not its speed.

[edit: or mass is what give 4-momentum from 4-velocity. You only get 'relativistic mass' with what I would consider definitions that are ill conceived in the context of SR.]

Last edited: Feb 26, 2016