[cripplecreek]

The one thing I've always had trouble with is my own little question that many have tried to answer but "no" just doesn't do it for me.

If you're travelling on a train moving at 99.9999% the speed of light and you get up and walk to the front of the train, didn't you just surpass the speed of light?

[PatrickHenry]

If you're travelling on a train moving at 99.9999% the speed of light and you get up and walk to the front of the train, didn't you just surpass the speed of light?

Not in your own frame of reference. And to a "stationary" observer watching your train go by, the answer is no.

[Tijeras_Slim]

At that speed you're gonna miss your stop.

[Gay State Conservative]

If you're travelling on a train moving at 99.9999% the speed of light and you get up and walk to the front of the train, didn't you just surpass the speed of light?

Given the speed of light,a walk at .0001% of that speed would have to be a fairly brisk one.

[Lunatic Fringe]

For you, perhaps. But to an outside observer, you would never get up from your seat.

[VadeRetro]

Straightforward Newtonian addition of velocities doesn't work to get you past c. If you plug the problem you propose into the Lorentz transformations Einstein adopted, you don't get over c. No observer anywhere thinks you're going faster than light, not even one going near the speed of light the other way.

[Larry Lucido]

If you're travelling on a train moving at 99.9999% the speed of light and you get up and walk to the front of the train, didn't you just surpass the speed of light?

No, the speed of light is how fast my cat takes my chair when I get up.

[RedStateRocker]

What the 'Relative' in Relativity means is that there is no absolute frame of reference in the universe except for the speed of light. Before relativity there was the question of the ether; in other words, EVERYONE thought that there MUST be a medium for light to propagate through since light was a wave and waves mus move through something. But there were many problems with the ether, for instance measurements should show it, and the earth would be moving through it first one way and then another as it circled around the sun, etc- science went to great lengths to try to imagine the properties of this thing that light moved through.

Relativity changed all of that. It stated that ALL rules of the universe applied everywhere equally. In other words, what is "movement"? Are you moving? and relative to what?.
your train moving 99% of the speed of light relative to what? earth? the center of a galaxy? another train headed away, also at 99% of the speed of light?
So what relativity states is that neither light nor this train not the passenger on it can exceed speed 'C'.
What would be happening in your instance is that yes, you would move to the front of the train at what you would think was say 2% lightspeed, but to an observer anywhere else the train and you still do not exceed the speed of light. The reason is that *TIME* is NOT a constant.
Time *IS* a constant to us here moving at tiny non relativistic speeds but as you near the speed of light, since 'C' can't change, time does. It is a very hard concept to wrap the brain around. That train going 99% of the speed of light is not moving at all to the person riding on it. But if you rode it for a few days your time you would find your twin brother months or years older.
Who says God doesn't have a sense of humor?

[Boot Hill]

cripplecreek:   "If you're travelling on a train moving at 99.9999% the speed of light and you get up and walk to the front of the train, didn't you just surpass the speed of light?"

You walk at 671 mph?

[wideminded]

If you're travelling on a train moving at 99.9999% the speed of light and you get up and walk to the front of the train, didn't you just surpass the speed of light?

No. even if you walked up the aisle at 99.9999% the speed of light, to an external observer it would appear that your net velocity was only about 99.99999999995% the speed of light. This is because of the hyperbolic geometry of spacetime.

This is somewhat analogous to when you see a scene through a fisheye lens. Objects off to the side seem to be compressed together. If you move to the side, some of the objects you can see will expand as they get closer to the center of your field of view. As they get close to the center their expansion will slow down. Objects that are at wide angles don't seem to expand much.

In spacetime, it is the apparent set of velocities that is distorted for each observer. Each time one attempts to speed up to a new velocity, the speed of light seems just as far off.

For example let us suppose that in a certain direction you can see objects that appear to be moving away at velocites in the range of 60% to 70% times the speed of light (60% c to 70% c), a range of 10%. If you then speed up to half the speed of light (50% c) toward them, they will now appear to be moving away at velocities of 14.3% c to 30.8% c, a range of 16.5% c.

For velocities that originally seemed to be moving away from you between 80% and 90% the speed of light (also a 10% range), these objects will now seem to have relative velocities between 50%c and 72.7% c, a range of 22.7% c.

So in a sense, as one speeds up, more velocities have appeared by the expansion of initially narrow velocity ranges. All observers see the same range of relative velocities from -c to c, just as all viewers using fisheye lenses see a range of angles from -90 to 90 degrees.

[LibWhacker]

If you're travelling on a train moving at 99.9999% the speed of light and you get up and walk to the front of the train, didn't you just surpass the speed of light?

Remember, for an outside observer who measured your train's speed to be 99.9999% the speed of light, your clock would run extremely slowly. That's one of the main features of relativity. So while you would swear that you were advancing toward the front of the train at 3mph (4.4 ft/sec), the outside observer wouldn't see you doing that at all. Instead, he would see you advancing toward the front of the train at 3 in/sec, say. That's because your seconds are not the same as his seconds. Any attempt by you to go faster (by running, jumping on a bicycle, etc.) would only result in the outside observer noting that your clock was running even slower than before, such that you could never exceed the speed of light no matter how fast you advanced toward the front of the train.

[gomaaa]

If you're travelling on a train moving at 99.9999% the speed of light and you get up and walk to the front of the train, didn't you just surpass the speed of light?

Wow! This post generated a LOT of responses! I don't have much to add except to say that your question is ALMOST EXACTLY the original problem that got Einstein thinking about the subject. Specifically, he asked what would happen if you were traveling in a train at a significant fraction of the speed of light and turned on a flashlight. The answer (as has already been described several times apparently) is that you can't simply add speeds when dealing with relativistic velocities. The math is more complicated.

[reagandemo]

If two objects pass by each other each traveling .75% of the speed of light would then a each object in relation to one another be traveling faster than the speed of light?