# I Is it really possible that relativistic mass tends to reach infinity?

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1. Feb 25, 2017

### Thalooth Bin Khalid

I have seen at many places that if ever matter travels more faster than light, it's relativistic mass will reach nearly infinity. Some says it's the inertia, so very high energy is required to accelerate. But since it is traveling with the velocity above 3×10^8 m/s, i believe that the high energy is required only to stop these mass motion. And if mass tends to infinity, shouldn't a black hole be created and and is it anything that tells why light bends in a black hole?

2. Feb 25, 2017

### Staff: Mentor

Do you have a peer reviewed reference which supports this belief?

Nothing with mass can even reach c, let alone travel faster.

No, John Baez has a great FAQ on this topic

3. Feb 25, 2017

### Thalooth Bin Khalid

I admit that there is no peer reviewed reference in support of this .

4. Feb 25, 2017

### Simon Bridge

Welcome to PF;
... what places? Nobody can know what you are talking about if you do not provide a context. Maybe those places are filled by crackpots who don't know what the are talking about?
... if it has mass and is travelling faster than light, then it is obeying an unknown kind of physics, so I don't see how anyone has any basis for saying they know anything about what is going on. If you are thinking of tachyons - they have imaginary mass. Nobody knows what that means.
... you believe? On what basis? You seem to be talking about an object with regular mass, doing something no mass has ever been observed to do, that is not obeying known laws of physics. (Cosmological speeds do not count as "travelling" in this context.)
I am kinda thinking you are trying to discuss tachyons here though...
... to make the object stationary with respect to you yes - there is no such thing as absolute rest.

You really do seem to be thinking of tachyons: hypothetical particles that are the result of proposing FTL within the framework of relativity. Within that framework, you would expect to have to do work to slow the particle towards lightspeed. It is one of the problems with the idea.
That sort of question is one of the reasons relativistic mass is not used any more: it leads people to think that you can just substitute relativistic mass for the mass term in gravity equations instead of using general relativity. It also suggests that the presence of a black hole can be observer dependent: ie I can make a star into a black hole by speeding up.
With regard to tachyons, they already have imaginary mass so the concept of relativistic mass works differently for them, and is not actually useful.

Sooo... clear this up for me: are you talking about tachyons?

Last edited: Feb 25, 2017
5. Feb 25, 2017

### Thalooth Bin Khalid

But what does it mean by mass tends to infinity?

6. Feb 25, 2017

### Thalooth Bin Khalid

Thank you . You were right. I have mixed up between mass of objects and relativity mass. But can you tell me why we cannot accelerate an electron in a cyclotron?

7. Feb 25, 2017

### Staff: Mentor

Are you familiar with mathematical notation. $$\lim_{v\to c} E =\infty$$

Last edited: Feb 26, 2017
8. Feb 25, 2017

### Thalooth Bin Khalid

Yes limit

9. Feb 25, 2017

### Thalooth Bin Khalid

No no iam not familiar (didn't notice the last part)

10. Feb 25, 2017

### Staff: Mentor

You yourself are moving right now, at 99.99% of c with respect to something somewhere in the universe, e.g. a high-energy cosmic-ray proton zipping past the solar system. Are you a black hole? Do you notice the "relativistic mass" that you would have with respect to that proton?

11. Feb 25, 2017

### Thalooth Bin Khalid

Yes

12. Feb 25, 2017

### Thalooth Bin Khalid

Not a black hole but like having a very high inertia

13. Feb 25, 2017

### Simon Bridge

But we can accelerate an electron in a cyclotron... it's just impractical.

Without referring to relativistic mass, the cyclotron frequency is given by: $$\omega = \frac{qB}{\gamma m} = \frac{1}{\gamma}\omega_0$$ ... where m is the invariant mass of the charge and gamma indicates the Lorentz factor.

This equation can be derived from how the magnetic field looks in the particle frame... the effect is the same maths as relativistic mass in the lab frame so most books find it convenient to go from the non-relativistic formulation to the relativistic one by that route.

That approach does not work in every situation... for instance, you cannot just go: $F=\gamma GMm/r^2$ or $r_s = (\frac{2G}{c^2})\gamma M$ for gravity.

Did you read the article I pointed you to? That clears this up for you.

Sooo... clear this up for me: are you talking about tachyons?
jtbell seems to be tackling the whole high relative speed = black hole thing.

Last edited: Feb 25, 2017
14. Feb 25, 2017

### Simon Bridge

What physical test would you do to tell if your inertia had changed with respect to the proton?
jtbell would probably want to ask this too...

15. Feb 26, 2017

### Thalooth Bin Khalid

I know about tachyons but I was not talking about that . I don't know the difference between relative mass and mass of matter

16. Feb 26, 2017

### Thalooth Bin Khalid

Each time I hit a meteor or any kind of space rock, i never stop moving.

17. Feb 26, 2017

### Staff: Mentor

I strongly suggest that you start by reading: What is relativistic mass and why it's not used much, which @Simon Bridge linked to earlier. This explains what "relativistic mass" is, and why it is a concept that is largely discarded by modern scientists.

Yes, this would be evidence of large momentum, you would collide one object with another and study the change in momentum. When scientists say momentum (or energy or relativistic mass) tends to infinity, what they mean is that momentum increases without bound as the velocity approaches c. In other words, pick any momentum you like, say 10^100 kg m/s, there is some v<c such that the momentum is greater than that! It doesn't matter how large a momentum you pick, there is always a momentum larger than that for some v<c. Similarly for energy. Since momentum and energy are conserved, this means that no massive particle can ever reach c.

18. Feb 26, 2017

### SiennaTheGr8

$m_{rel} = \dfrac{E}{c^2} = \dfrac{\gamma E_0}{c^2} = \gamma m$.
• $m_{rel}$ is relativistic mass
• $E$ is relativistic energy or "total energy" (sum of rest energy and kinetic energy)
• $E_0$ is rest energy (the energy of a body as measured when it's at rest, aka "proper energy" or "invariant energy")
• $m$ is rest mass (same as $m$ in Newtonian physics, aka "proper mass" or "invariant mass")
• $\gamma = (1 - (v/c)^2)^{-1/2}$
Because $c$ is a constant, it serves as nothing but a conversion factor here. Thus, $m_{rel}$ and $E$ are the same exact quantity, but expressed in different units. The same goes for $E_0$ and $m$: they are the same quantity, but expressed in different units.

So there are only two concepts here: total energy/mass, and rest energy/mass. It's redundant to use all 4. We only need 2.

Today, most people use total energy $E$ and rest mass $m$ (but we just call it "mass," in keeping with Newtonian terminology):

$E = \gamma m c^2$.

Nothing with (rest) mass can ever be accelerated to the speed of light. And anything without mass (like light) always travels at $c$.

As for gravity and black holes:
• in Newton's theory, the only "mass" that matters is $m$. "Relativistic mass" (total energy) has nothing to do with it. You can replace $m$ with $E_0 / c^2$ if you'd like, but kinetic energy $(E - E_0)$ plays no role in Newtonian gravity. But of course, there are also no black holes in Newtonian gravity, so this is all beside the point.
• in Einstein's theory (general relativity), mass is no longer the source of the gravitational field. Instead, gravity is nothing but the curvature of spacetime, and that curvature is caused by something called the stress–energy tensor. "Relativistic mass" (total energy) does play a role here, but not in a simple way.
The answer to your question about black holes is no: a black hole does not form if "relativistic mass" (total energy) is large enough. You can convince yourself of this by considering that right now, as you read this, your own total energy is arbitrarily large in other frames of reference (because your kinetic energy depends on relative velocity). And you certainly haven't formed a black hole! On the other hand, a black hole will form if rest energy (mass) is large enough within a given volume of space.

Hope that helps.

19. Feb 26, 2017

### Mister T

Let's start with the ordinary mass $m$. You can multiply this by the factor $\gamma$, where $$\gamma=\frac{1}{\sqrt{1-(\frac{v}{c})^2}},$$ and get $\gamma m$. Notice that when the speed $v=0$, $\gamma=1$ so $m$ and $\gamma m$ are equal to each other. But also notice that as $v$ gets closer and closer to the speed of light $c$, $\gamma$ increases beyond all bounds (approaches infinity, in the jargon of mathematics). Thus $\gamma m$ approaches infinity, but $m$ stays the same.

Now, if you think of $\gamma m$ as the inertia, then you can see that the inertia approaches infinity, meaning it gets harder and harder to increase the speed $v$ the closer it gets to the speed of light $c$. But the problem with that line of reasoning is that $\gamma^3 m$ is a better measure of that property, and $\gamma^3 m$ is called the longitudinal mass. In this terminology scheme $\gamma m$ is called the transverse mass, but of course it's also called the relativistic mass. These terms are all old out-dated concepts that were used to describe the physics before our modern understanding of the concepts was developed.

It was in the past considered a good idea to call $\gamma m$ the relativistic mass and make use of the concept, but most people no longer agree that it's a good idea to use the concept. Thus it's probably a good idea to stop calling $\gamma m$ the relativistic mass, and simply have only one kind of mass $m$. It avoids a lot of confusion.

Now, let's address the black hole thing. It's based on the notion that $\gamma m$ is the source of gravity, like $m$ is the source of gravitation in the newtonian approximation. That notion is false. In modern physics gravitation is a far more complex interaction than it is in newtonian physics.

20. Feb 26, 2017

### SiennaTheGr8

Mister T, check PM.