# Mass of objects moving at the speed of light

1. Mar 25, 2013

An object moving at the speed of light will be mass-less or will it have infinite mass??

2. Mar 25, 2013

### Staff: Mentor

Yes, if by "mass-less" you mean "zero rest mass". Only objects with zero rest mass can move at the speed of light.

No; objects moving at the speed of light have zero rest mass (as above), and finite energy. Objects with non-zero (finite) rest mass will move at less than the speed of light. There are no objects with infinite mass, whether you intepret "mass" as meaning rest mass or total energy.

3. Mar 25, 2013

### 1977ub

If you attempt to move an object with mass up to the speed of light, it will put up increasing resistance as if its mass were increasing toward infinity. A photon, with no mass, could not be slowed down by you from the speed of light.

4. Mar 25, 2013

The second answer gave an interesting information about resistance building up until it reaches near infinity, if the first answer was the correct one how do you reply to the building-up-infinite-resistance answer.

5. Mar 25, 2013

### 1977ub

The photon is a completely different kind of beast from other constituents of matter.

6. Mar 25, 2013

Oh, OK.
So a non-photon object moving at the speed of light has no mass, but photons have infinite mass?

7. Mar 25, 2013

### Staff: Mentor

No, we're just using different definitions of the word "mass". The mass I referred to is "rest mass" (I used that term in my post, you'll note), and it is an invariant, fixed property of an object (at least, it is for the cases we're talking about here); it doesn't change when the object's state of motion changes. An ordinary object like a rock or you or me has nonzero rest mass and can only move slower than the speed of light; a photon has zero rest mass and can only move at the speed of light.

The mass that 1977ub refers to is "relativistic mass"; but that is really just another word for "total energy". What 1977ub is really saying is that the more energy an object with nonzero rest mass has, the more force it takes to accelerate it by a given amount; or, conversely, the less its velocity changes in response to a fixed amout of force. A photon, with zero rest mass, can't change its speed in response to a force at all; it always moves at the speed of light. That's what 1977ub meant when he said that photons are a different kind of thing.

I'm not sure how you got this from either my or 1977ub's posts. It should be evident from what we've said and what I clarified above that neither of these statements is true: a "non-photon object" (by which I think you mean an object with nonzero rest mass) can't travel at the speed of light at all, and a photon has zero rest mass and finite total energy, so it does not have "infinite mass" in any sense.

8. Mar 25, 2013

I feel so stupid. I should have mentioned that I'm a student in high school, I don't know much about physics, I just really really like it !!
You shouldn't explain again, I'll do more research, if I had any questions Physics Forums will be the first thing I go to.

9. Mar 25, 2013

### Staff: Mentor

No need to. The questions you are asking are good questions, and relativity is counterintuitive, so it's not always easy to process the answers.

That's good!

Glad to hear it! Another useful online resource is the Usenet Physics FAQ:

http://math.ucr.edu/home/baez/physics/

10. Mar 25, 2013

### m4r35n357

Is this really true? AIUI if you push on an object you are pretty much in its frame of reference, so it will not appear to get heavier, shorter, or experience any time shifts relative to you. So how does it put up increasing resistance?

11. Mar 25, 2013

### Staff: Mentor

Not necessarily. For example, suppose you push on it with a big laser that pushes on a laser sail attached to the object. You can stay stationary as you fire the laser, while the object moves faster and faster relative to you.

12. Mar 25, 2013

### m4r35n357

Point taken, but as you probably realize I was really thinking along the lines of using a jet pack ;) Your suggestion is more like a particle accelerator, and that is a very different situation I agree.

13. Mar 25, 2013

### 1977ub

Let's say there is a giant slingshot. You've used classical calculations to determine how to set it up so that you can accelerate a bowling ball to the speed of light. As it speeds up, it seems to you that it is responding to the pressure of the device as if it had become somehow more massive, and when it leaves the slingshot, it is some % of c.

14. Mar 30, 2013

### apurvmj

protons have mass, when we accelerate them in large colloidal hydron like thing, does protons gains mass?
thanks.

15. Mar 30, 2013

### HallsofIvy

"colloidal hydron"? I think you mean "hadron collider"! And yes, protons gain mass. That has been measured (indirectly by measuring the motion of objects the protons hit) and the mass gained is what is given by relativity.

16. Mar 30, 2013

### vanhees71

Well, nowadays we mean "invariant mass" (or "rest mass", if the particle has non-zero invariant mass) when we talk about mass (at least in high-energy physics). Then the proton always has one and only one mass, namely $938 \; \mathrm{MeV}/c^2$, no matter how fast it moves. This has the advantage that mass is a Lorentz scalar.

What you label as "relativistic mass" simply is energy divided by $c^2$. Energy is the temporal component of the energy-momentum four-vector.

As already mentioned in the thread, it's just a question of convention, but I'd advise anybody to use the modern definition, which makes everything much simpler!

17. Mar 30, 2013

### Staff: Mentor

You have to be a little careful with mass. In relativity there are two different definitions of mass which are in common use. So you can get different answers when different respondents use different definitions.

First: invariant mass. This mass is given by the equation $m^2 c^2=E^2/c^2-p^2$. Because of the way energy and momentum transform between reference frames in relativity, all reference frames will agree on this quantity. It is also sometimes called the "rest mass" because it is the mass as measured in a reference frame where its momentum is 0. When most physicists use the term "mass" this is the mass they mean. Also, when anyone says that a photon has zero mass, this is the mass they mean.

Second: relativistic mass. This mass is given by the equation $m=E/c^2$. Because energy is different in different frames, different frames will disagree on this quantity. When people talk about "mass increasing" this is the mass that they are talking about. However, because it is just another name for E this meaning is dying out and is deprecated by most modern physicists. Unfortunately, you still see it in pop-sci and in older texts.