# Speed of light

1. Jun 9, 2012

### jedd

Hello. I'm not very educated in the field of physics but I do like to let my mind wander at times and contemplate the nature of gravity and the speed of light. I had this thought today over morning coffee and thought I would share it with someone who has a much better understanding of these things

Has anyone ever accelerated an object to near the speed of light and detected an actual increase in it's mass? Just curious because Einstein states that any object with mass that is accelerated to the speed of light would gain infinite mass requiring infinite energy. However, is it all relative to the observer? To an outside observer doing the math, the object would appear to gain infinite mass, but to an observer inside the object, perhaps the rest of the universe appears to lose all mass, allowing for instantaneous travel anywhere. The universe losing all mass to the observer inside the object seems no more bizarre than the object gaining infinite mass to the outside observer.

Be kind and explain my fallacy. Thanks ahead of time.

2. Jun 9, 2012

### Chopin

Imagine you have a rocket that puts out a constant force. According to basic physics, that means that it will accelerate with a constant rate (i.e. its speed on a speedometer will climb at a constant rate). That's what normal non-relativistic physics says. That's a problem, because if you wait long enough, you can expect it to eventually go faster than light.

What relativity says is that this is not what actually happens. Instead, if you shoot off this rocket, and watch it from the ground, you will not see it accelerate at a constant rate. Instead, it will accelerate at slower and slower rates as it goes along. This is because time and space contract for an object as it moves faster, so even though it is accelerating at a constant rate from its point of view, time and space stretch out, making it appear that it's not accelerating as fast as you would expect. The net result is that it will continue to get faster and faster, but at an increasingly slow rate. So it will get infinitely close to the speed of light, but never quite reach it.

Since force equals mass times acceleration, if the force stays constant, and the acceleration is decreasing, one interpretation of this phenomenon is that the mass is increasing. That's kind of an illusion, though--the mass is still the same as it always is, but time and space are increasing, so our interpretation of what acceleration means is really what's changing. Therefore, I think most modern relativity books don't advise thinking of this as the mass actually increasing--it leads to lots of questions about what is the "real" mass, and how inertia is different in the direction of travel and perpendicular to the direction of travel, etc. Instead, it's usually easier to think of the mass as staying constant, and its observed effects in the world as changing due to the object's velocity.

3. Jun 9, 2012

### Staff: Mentor

Yes. I've done it myself with high-energy electrons.
But you may find the FAQ at the top of this forum on the experimental basis of special relativity to be more convincing.

That's not how it works. If you're the observer inside the object, you see yourself at rest and the rest of the universe moving relative to you.

Let's make the picture a bit simpler by just considering our two observers and not worrying about rest of the universe for now. Observer A is sitting in his spaceship and watches B zoom past him at a high rate of speed V. A sees B's mass to be increased, exactly as predicted by relativity (and also sees B's clocks run slow and B's lengths contracted).

Now consider what B sees: As far as B is concerned, he's at rest and A is zooming away from him at the same speed V, but in the opposite direction. So B sees A's mass to be increased (and also sees A's clocks run slow and A's lengths contracted).

So....
So it's not a matter of mass being "lost" by one observer and transferred to another observer - everyone sees the mass of the objects moving relative to them as increasing, and no one sees their or anyone else's mass decreasing.

Also, be aware that all of this talk of infinite mass when at the speed of light is itself an oversimplification. If you look at the equations (I'm not going to post them here because there's another thread on this exact topic going right now), you'll see that what they actually say is that the mass becomes arbitrarily large as the velocity becomes arbitrarily close to c. There's never any infinity in them, and no matter how hard you accelerate an object, it never quite gets to the speed c.

4. Jun 9, 2012

### Staff: Mentor

That FAQ is actually at the top of the Relativity sub-forum (which is where this thread should probably be moved).

5. Jun 9, 2012

### Navdeep201

this discussion brings some questions to my mind,

chopin used length contraction to justify the statement "no object can ever attain the velocity of light" now my question is, speed of light is constant in any frame of reference (i hope this is true). so, there is no way to know which of the two observers are at zero velocity, furthermore velocity of light varies with its medium (slowest recorded was 19 m/s in some super cooled atoms) so does this means an object moving through that medium cannot surpass that velocity? and if we ever create a system which is true vacuum (space is not true vacuum) and gravitation free, will this system have a greater velocity of light?

6. Jun 9, 2012

### jedd

Great answers! I have some understanding of what you are explaining. Much appreciated! This is a nice forum. I'm glad I found it though you all may grow tired of my ignorant questions lol! Again, thank you all for your answers so far.

7. Jun 9, 2012

### jedd

Great explanation. This really helped my understanding. Thank you.

8. Jun 9, 2012

### jedd

And that is the million dollar question. Why not? What prevents it? If not an infinite build up of mass then it is because of the energy required?

I really appreciate you guys indulging my silly questions!

9. Jun 9, 2012

### Chopin

The concept of "infinity" in mathematics means something a little different than what it is often taken to mean in pop culture. You can't actually treat it like a concrete number, such as "I'll pay you infinity dollars", etc. Instead, you can only treat it as a direction that can be moved closer to, for instance "as x tends to infinity, f(x) tends towards zero". This just means that f(x) gets closer and closer to 0 as x gets bigger and bigger, but it never gets there no matter how big x actually gets. This kind of limit at infinity is called an asymptote.

Using this language, the way to phrase the idea we've been discussing here is to say that the speed of an object under uniform acceleration will asymptotically approach the speed of light, but will never reach it. For a more thorough discussion of the concept of an asymptote, see http://en.wikipedia.org/wiki/Asymptote.

Last edited: Jun 9, 2012
10. Jun 9, 2012

### harrylin

Yes, in fact both: a particle of infinite inertia ("mass") also has an infinite momentum. It would require an infinite amount of energy to reach that speed.

BTW, physicists generally worry less about using the word infinite than mathematicians. For example Einstein wrote simply: "Thus, when v=c, W becomes infinite."

11. Jun 9, 2012

### Staff: Mentor

The speed of light in vacuum is indeed the same in all frames. This is a postulate of special relativity, but also is supported by much experimental evidence and is strongly suggested by the laws of electricity and magnetism.

Pretty much correct, although it would be more accurate to say that there is no such thing as a "zero velocity" that's not relative to some observer - so the problem isn't that we have no way of knowing which observer is really at "zero velocity", it is that the question is meaningless.

Velocity of light in a non-vacuum medium is a whole different situation, because when there's a medium you can have a distinguished "really at zero velocity" frame, namely one that has zero velocity relative to the medium. There's nothing wrong with moving faster through a medium than light itself can travel through that medium - but you still can't exceed c, the speed of light in vacuum.

12. Jun 10, 2012

### arindamsinha

There are some well-known experiments that provide apparent proof of this - not directly, but showing the counterparts to this phenomenon - (a) velocity of light being independent of the velocity of the source and (b) time dilation (note caveat below). For (a), Alvager et.al. [1964] showed that velocity of light is independent of the velocity of the source, and for (b) Bailey et. al. [1977] showed that time dilation for a fast moving particle in an accelerator/muon ring reaches a time dilation factor of 29.3 (i.e. they live 29.3 times as long as normally expected in a rest position).

Caveat: these experiments were conducted with sub-atomic sized particles in the relatively massive gravity of Earth and in the presence of huge magnetic fields. Whether the conclusions can be generalized to all cosmic physical phenomenon is something to think about.