# Conceptual questions: Limit of energy?

1. Oct 29, 2013

### tolove

Starting with this equation,

$E^2 = p^2c^2 + m^2c^4$

With a photon, m = 0... what happens when E starts to get large? Very large. As E approaches infinity, do strange things happen? Will a singularity form?

If we let our photon have a mass, something very small, will the picture change at all?

A very open question, since I'm having trouble here... What's the difference between mass and energy?

2. Oct 29, 2013

### Staff: Mentor

For a photon? No. It has no mass and will never collapse into a singularity.

Instead of letting our photon have mass, let's just look at a massive object. We have two ways of increasing E. We can either add momentum, or we can add mass. If we add momentum, then the picture is still the same as the photon. It will never collapse into a black hole because it has no momentum in its own rest frame.

However, if we add mass, then we CAN have it collapse into a black hole once we get it sufficiently massive enough.

An easy way to think of it is that mass is energy in a form that all observers will agree upon. What I mean is that the mass of a baseball is the same no matter what your motion is relative to the baseball. The energy of it, is not, however. The total energy changes depending on if you (or the ball) is moving relative to one another. If I fly by the ball at 0.5c then it's going to have an enormous amount of energy as seen from my point of view compared to if I'm sitting in the stands and watching it fly into left field.

You may be saying, "But energy has mass!"
And you'd be right. However, while the mass of the BALL ITSELF does not change, the mass of the system as a whole does change. As a simple example, let's say I have a system of two ships out in space at rest relative to one another. Let's say the combined mass of the system is 10,000 kg. Now, I have another system with two spaceships identical to the ones in the first example. However, in this system, they are moving at 0.5c relative to one another. The total mass of the system is MORE than 10,000 kg due to the extra kinetic energy.

Make sense?

3. Oct 29, 2013

### tolove

Ah, I was moved to the relativity subforum. Didn't want to to be strictly related to relativity. Would like to ask a question along the lines of: Does anything interesting happen with particle creation/annihilation when a photon approaches infinite energy? If the question even makes sense! I'm just curious what happens at the extremes, if anything.

Just regurgitating something my professor said today, it's what confused me so much! Photons might carry a very small amount of mass.

I didn't know about relativity affecting mass. We only hop scotched over the subject so far, mentioning length and time. Moving objects gain mass? We can observe a black hole from one reference frame, while in another it's not? This.. doesn't sound right. Resting mass demands distinction? I don't understand why.

4. Oct 29, 2013

### Staff: Mentor

With very large amounts of energy the photon can interact with another particle and create new particles.

The possibility exists, but as far as we know, they are massless.

The mass of the object itself never changes. The mass of a SYSTEM of objects is what increases. For example, the mass of a box of marbles that aren't moving is less than the mass of a box of marbles that are bouncing around everywhere. But the mass of the first box of marbles is the same in its own rest frame as it is in the frame of an observer who sees that box in motion. The motion of the box as a whole doesn't affect its own mass. (Rest mass if you want to use that term)

So an object that isn't a black hole in its own frame of reference can never become one by accelerating it to any velocity.

5. Oct 30, 2013

### mrspeedybob

So while a photon in and of itself cannot become a black hole it could, in principal, be of such high energy that when it comes into proximity of a massive particle that the particle/photon system would become a black hole. Is this correct?

What about a 2 photon system where the 2 photons come from opposite directions? In this case any observer who sees one photon red shifted would see the other blue shifted so all observers should agree on the total energy. Does that make it mass?

6. Oct 30, 2013

### Staff: Mentor

I would say yes to both of those questions. That's how I understand it at least. But the required energy would be so extreme that I'm not sure it's actually realistic.

7. Oct 30, 2013

### Naty1

No single particle, mass or massless, will form a black hole because of high speed. That's because the gravitational curvature is given by the stress energy tensor in the frame of the particle; speed has no effect. You can think of it this way: as you go faster and faster nothing happens in the frame of the moving particle....it's clock tick normally, it's mass remains invarient, its size remains constant.

For collisions, see here:
http://en.wikipedia.org/wiki/Black_holes#High-energy_collisions

Even colliding electromagnetic waves could in principle produce a black hole.....

8. Oct 31, 2013

### dauto

Yes to most of your points except that the total energy is always frame dependent. There is no way to create a system where the total energy is an invariant.

9. Oct 31, 2013

### tolove

The first thing you said here is "... because of high speed." When I say "A photon with high energy" am I also saying "A photon with high speed?" Isn't the energy of a mass-less thing is determined by frequency alone, and the speed is fixed? Is frequency similar to velocity?-- just like an isolated system can't determine its own velocity, an isolated energy wave is unable to determine its own frequency?

Also, could you please elaborate on colliding EM waves producing a black hole? Enough mass in one spot will collapse, why doesn't enough energy in one spot collapse? What's significant about collision?