# Faster Than the Speed of Light

*Most recent answer: 10/22/2007*

Q:

My physics teacher said that it is imposible to go faster than the speed on light, but if you were standing on a train going at the speed of light and you walked from one end of the train to the other, then would’nt you be going faster than the speen of light relative to the ground? and what would happen if you were going at the speed on light or faster? Theoretically

- Daimhin (age 17)

Unley High School , Australia

- Daimhin (age 17)

Unley High School , Australia

A:

Daimhin -

It may seem like should happen that way. The problem with physics is that it doesn't always work the way that it seems like it should.

You've probably learned that the speed of light is a constant (c). But what if you looked at it from different points of view? For instance, if you're standing on the Earth, then the speed of light is c. But what if you're standing on the train that's moving at half the speed of light? Shouldn't it look like the light is moving at half speed? Well, for all that it certainly seems like it should, it doesn't. The light moves at the same speed whether you're standing on the Earth, or on a speeding train.

But whoa! How can the light move at the same speed from the Earth's perspective as from the train's? Because velocity is equal to distance divided by time, and it seems like everybody should agree on the distance traveled and the time elapsed. But do they? According to special relativity (Einstein's work), distance and time don't work the way that we think they do either, and that get's really important when you're talking about speeds close to the speed of light.

I know that this wasn't exactly what you were asking, but I wanted to emphasize to you how things don't always happen according to the rules that you're used to. One of the basic rules of space and time is that no object can travel faster than c. That might seem ridiculous, because if you can get a train going at 0.9999999999c , you could then walk on it at 0.0000000002 c relative to the train, and that would add up to 1.0000000001 c. However, velocities don't add that way because time and space intervals aren't the same as seen from the ground and the train. Somebody on the train says that you're walking at 0.0000000002 c. Somebody on the ground thinks that your steps are much smaller than you or your friends on the train think, and that it takes you much longer to take those steps than you think. So they still end up thinking that you're traveling at less than c.

You might think that if you could just keep applying force to something it would accelerate to greater than c. However, that assumes that F=ma, which turns out to be false. The effective 'm' in the expression mv for the momentum (v is velocity) increases for bigger v! When you exert a force, as v gets near c you end up mainly increasing that 'm', not v.

The kinetic energy grows more rapidly as v increases than classical physics would say. As v gets close to c, the energy grows toward infinity. So to get to the speed of light, it would take an infinite amount of energy.

-Tamara (and mike)

It may seem like should happen that way. The problem with physics is that it doesn't always work the way that it seems like it should.

You've probably learned that the speed of light is a constant (c). But what if you looked at it from different points of view? For instance, if you're standing on the Earth, then the speed of light is c. But what if you're standing on the train that's moving at half the speed of light? Shouldn't it look like the light is moving at half speed? Well, for all that it certainly seems like it should, it doesn't. The light moves at the same speed whether you're standing on the Earth, or on a speeding train.

But whoa! How can the light move at the same speed from the Earth's perspective as from the train's? Because velocity is equal to distance divided by time, and it seems like everybody should agree on the distance traveled and the time elapsed. But do they? According to special relativity (Einstein's work), distance and time don't work the way that we think they do either, and that get's really important when you're talking about speeds close to the speed of light.

I know that this wasn't exactly what you were asking, but I wanted to emphasize to you how things don't always happen according to the rules that you're used to. One of the basic rules of space and time is that no object can travel faster than c. That might seem ridiculous, because if you can get a train going at 0.9999999999c , you could then walk on it at 0.0000000002 c relative to the train, and that would add up to 1.0000000001 c. However, velocities don't add that way because time and space intervals aren't the same as seen from the ground and the train. Somebody on the train says that you're walking at 0.0000000002 c. Somebody on the ground thinks that your steps are much smaller than you or your friends on the train think, and that it takes you much longer to take those steps than you think. So they still end up thinking that you're traveling at less than c.

You might think that if you could just keep applying force to something it would accelerate to greater than c. However, that assumes that F=ma, which turns out to be false. The effective 'm' in the expression mv for the momentum (v is velocity) increases for bigger v! When you exert a force, as v gets near c you end up mainly increasing that 'm', not v.

The kinetic energy grows more rapidly as v increases than classical physics would say. As v gets close to c, the energy grows toward infinity. So to get to the speed of light, it would take an infinite amount of energy.

-Tamara (and mike)

*(published on 10/22/2007)*

## Follow-Up #1: relative velocities

Q:

Wouldn’t you observe that you were moving faster than the speed of light because time had slowed so much? (i.e. It would take almost no time, relative to you, to cover vast distances)

- Mark

Atlanta

- Mark

Atlanta

A:

According to you, you're moving at speed zero. So the question is how fast you say the other stuff is going past. It turns out that, when you take into account all the effects in which your time and space measurements differ from those of your neighbors, if they say you're going by them at velocity v, you say they're going by you at velocity -v. It's one of the few results of Special Relativity that happen to just match common sense.

Mike W.

The two effects in SR are length contraction and time dilation. The lengths of the "vast distances" contract by the same factor the time dilates by, producing this remarkable (but not coincidental) happy situation.

Tom

Mike W.

The two effects in SR are length contraction and time dilation. The lengths of the "vast distances" contract by the same factor the time dilates by, producing this remarkable (but not coincidental) happy situation.

Tom

*(published on 10/22/2007)*

## Follow-Up #2: assertions about velocity

Q:

if you were on a glass trian going 99% at the speed of light, and you ran forward at 2% of the speed of light(just pretend you can) then someone from outside the train would see the person move faster than the speed of light..... if there was a face between a light ray and the person on the train the person would win...

- Physics is stupid (age 16)

Preston, Lancashire, England

- Physics is stupid (age 16)

Preston, Lancashire, England

A:

That's not a question but an assertion. It's wrong.

Mike W.

Mike W.

*(published on 04/19/2013)*