Speed of Light - Highest Possible Speed?

Well the other day I was thinking about the speed of light and how physics says that nothing can go above the speed of light and that you need infinite energy to go at the speed of light. But take this example: Imagine this example, you're on a train going at 99% the speed of light (therefore energy required is < infinity) and you put a race car on top of the last wagon on the train and have it go at 2% (once again energy required is < infinity) of the speed of light, wouldn't you technically be going at 101% of the speed of light? Is the speed of light truly the limit?

Answers and Replies

gb7nash
Homework Helper
Well the other day I was thinking about the speed of light and how physics says that nothing can go above the speed of light and that you need infinite energy to go at the speed of light. But take this example: Imagine this example, you're on a train going at 99% the speed of light (therefore energy required is < infinity) and you put a race car on top of the last wagon on the train and have it go at 2% (once again energy required is < infinity) of the speed of light, wouldn't you technically be going at 101% of the speed of light? Is the speed of light truly the limit?

Shouldn't matter. The racecar is initially going 99% the speed of light, since it is on this train. It would need an infinity amount of energy to go 1% faster.

jtbell
Mentor
you're on a train going at 99% the speed of light (therefore energy required is < infinity) and you put a race car on top of the last wagon on the train and have it go at 2% (once again energy required is < infinity) of the speed of light, wouldn't you technically be going at 101% of the speed of light?

No. Velocities don't "add" the same way in relativity that they do in classical physics:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel.html

K^2
Science Advisor
Somebody needs to make a nice animation with hyper-rotations of world lines to show how velocity addition works due to a non-positive definite metric.

Other than that, what you need to keep in mind is that everything is always traveling at the speed of light, but through both space and time. An object at rest propagates only along the time axis. An object in motion can then have at most the speed of light as its observed local velocity. In observer's rest frame, time axis is always pointing along the observer's own world-line. Hence the need for rotations to explain velocity addition.

Read Feynman's Six Not So Easy Pieces, it has a very nice solution to this
You can't just add the speeds, you have to put it twice through the equation for special relativty, and as long as the components don't equal the speed of light, how they relate won't either.

Well the other day I was thinking about the speed of light and how physics says that nothing can go above the speed of light and that you need infinite energy to go at the speed of light. But take this example: Imagine this example, you're on a train going at 99% the speed of light (therefore energy required is < infinity) and you put a race car on top of the last wagon on the train and have it go at 2% (once again energy required is < infinity) of the speed of light, wouldn't you technically be going at 101% of the speed of light? Is the speed of light truly the limit?

Well, actually, that is exactly why Einstein said time slows down. When time in the racecar slows down, the racecar cannot go at 2% of the speed of light, so relative to the time outside, the racecar is going slower than 2% of the speed of light, but I have proven that there is a commonly known mysterious massive particle (don't worry its not the tachyon) that can go at any speed it wants and have given my reasoning with gravity.

Somebody needs to make a nice animation with hyper-rotations of world lines to show how velocity addition works due to a non-positive definite metric.

I've seen one you might be interested in. The www.lerner.org web site has the old The Mechanical Universe series, which has some excellent (basic) graphicals on relativity theory, amongst a wealth of other fields. The web link is this ...

http://www.learner.org/index.html" [Broken]

You'll be asked to register, but it's all free. The videos may be viewed on your PC screen, and in full screen if selected. The Mechanical Universe & Beyond series is at this shortcut ...

http://www.learner.org/resources/series42.html" [Broken]

The episodes that relate to relativity theory are these ...

41 The Michelson-Morley experiment

42 The Lorentz Transformation

43 Velocity and Time

44 Mass, Momentum, Energy

It's either episode 42 or 43, I think 43, that presents the animation on relativity's Composition of Velocites.

GrayGhost

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