Hello. First time I have ever posted, but this question has bothered me for a while.
Premise 1:
In one of my physics classes, I understood that as an object approaches the speed of light, its mass approaches infinity. Which is why traveling at light speed is impossible.
Premise 2:
Light has mass. Gravity affects it; as seen near a singularity as it bends light.
Question:
How can light ever achieve its own speed without achieving an infinite mass?
IIRC light has NO mass, even at light speed. As long as something has NO mass, I don’t see why It cannot travel the speed of light without violating any laws.
Light has to have mass. Using the formula E=mc^2, we would reaarange this to c^2=E/m. Since we know light has Energy, it has to have mass otherwise you are dividing by 0; which cannot be done.
Hi Hodge,
The “c” in the equation isn’t “light”, it is the “velocity of light” and is a conversion-constant in the equation, not a variable.
What it means is that mass is directly proportional (or equivalent) to energy with c^2 as a constant of proportionality.
And while light doesn’t have mass, it does have energy and can be converted into mass in certain instances.
E = mc[sup]2[/sup] gives the energy equivalent of the rest mass only, i.e. the energy an object/particle has when sitting still. Photons do not sit still, thus they have no rest mass, and no energy equivalent to their rest mass.
The full relevant equation for a free particle is
E[sup]2[/sup] = p[sup]2[/sup]c[sup]2[/sup] + m[sup]2[/sup]c[sup]4[/sup]
where E is the total energy, p is the momentum, and m is the rest mass. You can see where E = mc[sup]2[/sup] comes from; if one only wants the rest energy, one sets p = 0, and gets back the more famous equation.
For a photon, m = 0, and the equation reduces to E = pc. Photons do indeed have momentum, but they do not have a rest mass, and thus it’s not a problem that they travel at c.
Just to confuse things a little, while an individual photon does not have mass a system of photons whose momentum is zero can have mass. You can see this from Philbuck’s relativistic equation:
E[sup]2[/sup] = p[sup]2[/sup]c[sup]2[/sup] + m[sup]2[/sup]c[sup]4[/sup]
But there are obviously some people here that can answer my question:
What is the purpose of the c squared (sorry, don’t know how to make a superscript) in the equation? The speed of light squared is a constant and therefor doesn’t really change the equation E=m, other than to make E a really big number, which was probably the intention.
Daemon wrote:
What you’re missing is the units of measure. You could define a unit of energy, called the “daemon,” and set it equal to the energy that one kilogram of mass has. Then your equation would be E=m, where E is measured in daemons and m in kilograms.
But Einstein’s equation gives us the energy in units of measure that we’re used to thinking of. For example, if you express c as 300,000,000 meters per second, and m as kilograms, then the energy comes out with the units of “kilogram-meters squared per second squared,” also known as joules. Energy is normally expressed in the metric system as joules, so the equation presents the answer to you in units that are useful to you. And the number happens to be large, because the speed of light is large value the way we generally measure it.
You could also express the speed of light as feet per second, and mass as slugs, and come out with an energy expressed in the English system, but I don’t know physics well enough in that system to figure out what it would be.
Think of it this way:
Gravity bends space/time. Imagine a marble sitting on a paper towel held between your hands. The marble will dent the paper towel where it rests. A light ray travelling along the paper towel will dip in as it crosses the dent made by the marble. If looked at from above (straight down) the light ray traces a straight line (this has us in 3D). If looked at from the perspective of a 2D creature living on the paper towel the light ray appears to bend as it crosses the dent (our 2D guy will be looking at it from the side).
In our case the light ray travels a straight line in 4 dimensions that appears curved (or bent) in 3 dimensions. As you can see this requires no mass on the part of light to get bent. It’s merely following the contours of space/time.