The speed of light (giving me a headache)

[ziggwarth]

Hi.

I'm trying to understand a few things about the speed of light.
From what I've read, nothing can travel faster than the speed of light.
If anyone takes a spaceship and accellerates it to the speed of light © (which I've read is not possible with anything that has a mass, but let's just pretend it is possible), the time outside slows down (from the persons inside the spaceship's point of view) and would reach its destination immediately, but for an observer outside the ship would still travel at 300000km/s.
Ok, I think I got this.

But now for the questions:
1. First of all, how did we figure out the speed of light in the first place? Did we measure its velocity in some way or...? If we did not measure it, how do we know the light actually travels at 300000km/s, and that this number is just a constant we use that has nothing to do with the actual speed of light?

2. From what I've read, when matter accellerates towards the speed of light, more and more energy are required to push it just a little faster because the mass of the traveling object is getting higher and higher until it reaches infinity at the speed of light. Ok, this is WHAT that is happening, but why is it so? How can an object gain mass "just by" accellerating towards the speed of light? Isn't the mass of an object constant (assuming there's no outside interference)?

3. I've also read that first when matter reaches approximately 1/3 of light speed, it starts to gain mass and needs more and more energy to accellerate it any more (like I mentioned above). Why this particular speed? Are the "time dilation" that comes with objects moving at near the speed of light present also at lower velocities, but the effects are so small that they are just insignificant before 1/3 of light speed?

4. Everything is moving at a speed relative to an other object, right? But what about the speed of light: Let's say we got TWO space ships that are capable of travelling at the speed of light. We place them at the opposite end of our solar system, and they accellerate to the speed of light towards eachother. When they meet, both ships are travelling at 300000km/s. But then, if you take one of the pilot's point of view, you are moving towards the other ship at 600000km/s, because that ship also travels at 300000km/s towards you. But what then happens to the "nothing-can-travel-faster-than-C"-rule?

I hope someone can enlighten me a little on these questions, as I really do wonder.. I've read a little about this subject, but the more I understand of it, the more questions seems to pop up :P

Well, thanks in advance for any answers.

[piersdad]

1 speed of light
i dont know the exact way but it was some sort of mirrors reflecting the light back anf forth and by increasing the speed of turning it on and off till the light does not hit the last mirror and measuring the distance it took to get to the last mirror and multiply it by the speed the light was turned on and off and that would be a primitive way of measuring it.

2 once we split the atom we realised that energy and mass were interchangeable
a kilogramm of hydrogen is also a heap of pure energy. (the hydrogen bomb )
so once you get to the speed of light and the speed of the the electrons in the piece of mass they gain weight/energy and it will be a sort of kinetic energy store

as for the rest of the questions im a bit out of my depth here

[Sp1ke]

OK, I'll try to answer some of these big questions. I'm sure some others will add to or correct my comments:

1) Yes, the speed of light can be measured. It's fast but it can be measured experimentally. Why it's 300,000 km/s (186,000 miles/sec) and not some other value, I don't know. Note: these figures are for the speed of light in a vacuum. It is slower in other mediums.

2) Why do moving objects gain mass? This is a tricky one. Einstein's theory of relativity predicts this and experiments demonstrate it. I don't understand the mechanism myself but, hey, it works. And that's the main thing that stops things moving at c as they'd need infinite energy to accelerate them to that speed.

3) I think 1/3c is probably quoted as a point when there are noticeable effects on mass. Any motion will produce an increase in mass but at the speeds we're familiar with, it is a very small effect.

4) This last question is one of the many ways in which relativity is counter-intuitive. When two objects approach each other, the velocities are not added like in classical mechanics. Another way to look at it is when your spaceship is moving at 90% of lightspeed and you turn the headlights on, do they send light out at 190% lightspeed? Well, no. Everything is based on what frame of reference you use. Again, it's a tricky one to explain and I'm sure someone else can explain better how it works. But I think your headlights will be red-shifted so that they won't have a velocity greater than c.

Note: there is only one way I know of that any velocity can exceed c and that's the expansion of the universe itself that, in theory, can be at any speed and, as you get further from us, the universe can be expanding at c or beyond.

[TheThorn]

Let me take a shot too. I'll probably just confuse you more

1) You can measure the speed of light directly. I did it in a second year university course, 35 years ago, so I bet they do it in high school now. What we did was send a beam of light through a slit in a piece of paper (I bet they use lasers now), then to a mirror that was mouinted on a motor so that we could make it rotate on it's vertical axis (but it was kept stationary to set up the apparatus). We arranged it so that the beam reflected off that mirror to another mirror a long (but measured) ways away, which reflected it back to the rotating mirror, and then back to the source, where it showed up projected on the piece of paper that the slit was in. Two mirrors and a motor, simple. When you turn the motor on so that the first mirror rotates really fast, the projected light on the paper starts to flicker, because most of the time the mirror isn't lined up right any more. And the flickering light moves off to one side, because, when it is lined up right, in the time that the light takes to go from the rotating mirror to the distant mirror and back, the mirror has turned a little bit, so it doesn't reflect it right back where it came from. You can measure the amount it moves to the side, and the rest is just geometry. I think we got the answer within 25% or so that way. Not the greatest accuracy, but they have much better ways with more sophisticated equipment too.

2) Why do moving objects gain mass? This one is really easy. No, really.

Energy and mass are equivalent. That's what e=mc^2 means. When you add energy to something you increase its mass. It's obvious in nuclear energy, where we take energy out of Uranium, and decrease its mass. And its also true of moving objects, when we put kinetic energy into them, we increase their mass. By exactly the amount that equation says.

So the question is really self explanatory. Motion is energy, and energy IS mass. they are the same thing.

3) Nothing magic about 1/3 c. Objects gain mass as soon as they start to move. But that equation (e=mc^2) means that they gain very little mass until they reach pretty high speeds. At the velocities we experience in every day life we can ignore the effect. At 1/3 c (or so) the effect becomes big enough to make a significant diffrerence.

4) Relativistic velocities don't just add arithmetically. They add using something called the Lorentz transformations. If you can stand the math, this page gives a reasonable explanation. If you can't stand the math, special relativity will probably remain a mystery. It really is counter intuitive.

[rahuldandekar]

Ok, here's a link:

http://www.marxists.org/reference/archive/.../relativity.pdf

This is a book by Albert Einstein on his Thoery of Relativity. (It's pdf). Right click and click "Save target as" to download. It is very simple.

[ziggwarth]

Thanks a lot, everybody, for such great answers.
I even understand most of it after I read them.
TheThorn and rahuldandekar: Thanks for the links. I will definitly check them out when I get home from work.

But then I got another question for Sp1ke: How can the universe expand faster than c when nothing else can travel faster than c? Isn't the expansion of the universe just "everything" moving away from each other?

Again, thanks for great and simple answers.

[Ola D.]

Originally posted by TheThorn@May 2 2005, 02:06 AM
What we did was send a beam of light through a slit in a piece of paper.. then to a mirror that was mouinted on a motor so that we could make it rotate..

Not the greatest accuracy, but they have much better ways with more sophisticated equipment too.

Another way to measure "c" is using an oscilloscope to time how long it takes a flash of light to travel from a transmitter, to a distant mirror and back to a receiver. The oscilloscope times light pulses travelling from the transmitter to the receiver, find the distance travelled, and use these data to find the speed of light.

I'm sure this method calculates "c" with a greater accuracy.

[Nereid]

But then I got another question for Sp1ke: How can the universe expand faster than c when nothing else can travel faster than c? Isn't the expansion of the universe just "everything" moving away from each other?

This is one of the most popular misconceptions about General Relativity, Cosmology, and the Big Bang!

If you can get hold of it - buy, or borrow from a library, the March 2005 edition of Scientific American has an excellent article by Charles Lineweaver on just this topic (here is a more technical version). To get an overview of cosmology (and how GR is applied to the Universe), check out New Wright's cosmology tutorial.

[Ola D.]

Originally posted by Nereid@May 17 2005, 12:14 PM
If you can get hold of it - buy, or borrow from a library, the March 2005 edition of Scientific American has an excellent article by Charles Lineweaver on just this topic.

Here's the article Nereid is pointing to.

I posted this article a while ago, but I think it's worth posting again since you're discussing it.

[DannL]

Here's an excellent (short) article on the subject . . .

Speed of Light

[Ola D.]

Thanks for the article, DannL. Welcome to UT forum!

[DannL]

Ola D.,

Thank you for the grand welcome.

To add . . . I have proven may times that the speed of light (velocity of a photon) is not limited to 299,792.4588 kilometers/second . . . if I can get home after work, accomplish everyone's "want lists" and still get a couple hours of telescope time in before midnight . . . I was "faster" than the speed of light. That would be more on the order of "c" cubed. So, there you have it. :blink:

[ziggwarth]

Thanks for the articles.
I've read through both of them, and I found the article Nereid mentioned (which Ola D. was kind enough to give me a link to) especially interesting.
Makes one wonder how big the universe really is (considering we can "only" see about 14 million light years into it).

[antoniseb]

Originally posted by ziggwarth@May 19 2005, 07:26 AM
Makes one wonder how big the universe really is (considering we can "only" see about 14 million light years into it).

Yes it does. As to the size... we have no idea, except that it is at least 13.7 billion lightyears in radius (and probably MUCH bigger).