A bit of a confusion regarding light, speed of it

1. Aug 1, 2010

andyarok

I have a doubt regarding the speed of light. What makes it impossible to achieve it. Why cant we have a relative velocity greater than that of C. Some say you should not apply common physical world logic in these fields.

But, Consider we have 2 laser sources separated by 2c distances. Say we switch it on at the same time. Why is the relative velocity between these 2 light (not the sources) be not more than c. Common logic says for laser emitted from source A light from source B is coming at it at 2c speed. I myself had an answer for it in my younger days, but now seems to forget it. I want to know why.

Many may be fed up with this question coming up again and again. But sure if you help me now some other day I would help others who post the same question later.

Sorry just now realized there are similar threads in the forum already. But none had a discussion regarding what prevents us from reaching light speed.

Last edited: Aug 1, 2010
2. Aug 1, 2010

Staff: Mentor

The closing speed of the two beams would be 2c, as seen by you. Despite that, nothing is moving faster than c.

I'm sure there are many threads dealing with this question--it's probably one of the most-asked!

One way of answering it is to say that it would require an infinite amount of energy to accelerate a massive body to the speed of light, which is another way of saying that it's impossible.

Another way is to say that velocities do not add like you think they do. Say a rocket was moving at 0.5c with respect to earth. Then that rocket shoots another small missile at a speed of 0.5c with respect to the rocket. What's the speed of the missile with respect to earth? Our 'common sense' (based on our low-speed experience) would say that the speed should be 0.5c + 0.5c = c. But no, relativity tells us that speeds need to be added using the relativistic addition of velocity formula:

$$V_{a/c} = \frac{V_{a/b} + V_{b/c}}{1 + (V_{a/b} V_{b/c})/c^2}$$

So the speed of the missile is only 0.8c, not c.

3. Aug 1, 2010

andyarok

relative speed can be calculated by V_ab+V_ac/(1+V_ab*V_ac/c2). Then we will get the value as C. But my question is what made us to keep the speed of light as the limit.

I understand that we need infinite energy to speed up a massive object to the speed of light. But in relativistic speed calculation we again use c to calculate relative speed. But I dont get it why we use it. Thats my question sorry for not being clear.

Last edited: Aug 1, 2010
4. Aug 1, 2010

Staff: Mentor

I guess I don't really understand the question. Why is the structure of space-time such that the universal 'speed limit' equals the speed of light? Beats me!

Or are you asking how we came to accept that fact? If that's your question, the most important answer is that the predictions of relativity were confirmed by experiment. That's the best we can do.

Ah.... are you asking "how did the speed of light get into that equation?". If so, you'll need to learn some of the basics of special relativity theory. One of the postulates of special relativity is that the speed of light is the same for all observers. That ends up making the speed of light a fundamental constant that appears in all sorts of relativistic equations.

5. Aug 1, 2010

andyarok

We have defined these relative speed equations such that we can never breach the speed of light. Why is that.

Last edited: Aug 1, 2010
6. Aug 1, 2010

Staff: Mentor

No, we've derived the relative speed equation (the addition of velocity equation) based on principles that have been confirmed by experiment.

It is a very counter-intuitive and surprising result, but it's not simply true 'by definition'.

7. Aug 1, 2010

andyarok

Now in Einstein's train paradox, lightning strikes at the ends of the train but the observer sees the light at the front end of the train first and then sees the light from the end. Why is that. if speed of light is constant no matter whatever frame of reference, both lights should be seen simultaneously by the observer at the center of the train, am I right?

8. Aug 1, 2010

Staff: Mentor

No, not right.

The lightning strikes the front and back of the train at the same time according to the platform observers. By the time the light reaches the observer at the middle of the train, the train has moved. The light flash from the front of the train reaches that observer first.

Since the speed of light is the same for all observers, the conclusion is that according to the train observers the lightning strikes were not simultaneous.

9. Aug 1, 2010

andyarok

Based on what you say, consider A and B traveling in opposite direction, there is a light source switched on from the side to which A is traveling to. Now wont A receive the light first followed by B after some time delay.

10. Aug 1, 2010

D H

Staff Emeritus
First as seen by whom? Simultaneity is also relative, which, to steal Doc Al's words, is yet another one of those "very counter-intuitive and surprising results" of relativity. The important thing to remember is that the driving impetus behind relativity, that the speed of light is constant in all reference frames, was motivated by other Maxwell's theory of electromagnetic radiation and by observation.

One of the deep problems in physics during the latter part of the 19th century was the obvious conflict between Maxwell's theories and classical mechanics. That the speed of light is the same to all observers is an integral part of Maxwell's theories. The Michelson-Morley experiment was set up to prove that classical mechanics was right and that that whippersnapper Maxwell was wrong. That didn't work. What the Michelson-Morley experiment did do was to prove that classical mechanics was wrong.

Einstein's 1905 paper on special relativity started with the surprising consequence of Maxwell's equations that the speed of light is the same to all observers as one of two axioms. His other other axiom: The laws of physics are the same in all inertial reference frames. These two axioms led to all kinds of "very counter-intuitive and surprising results." So, the key is to test those axioms. That the speed of light is the same to all observers has been tested, retested, re-retested, and so on. This is one of the most well-tested concepts of all of physics. That the laws of physics are the same to all inertial observers is intuitively obvious -- and is surprisingly a bit suspect. It depends on what you mean by an inertial frame of reference. The concept of an inertial reference frame in Newtonian mechanics is itself flawed. Einstein later dealt with the issues that arose from this apparently obvious axiom in his development of general relativity.

11. Aug 1, 2010

andyarok

As the thread goes on I seem to understand it more and more. Now am almost satisfied. I had the same satisfaction some 10 years back. But somehow forgot everything as I have been away from physics for sometime.

As you said the confusion arose when I messed up the frame of reference.

THANK YOU both of you.

Now why many people try to break it. I mean the theory of Relativity. Do you think that it is fool proof no matter what or do you think, that based on what we know till now, we cannot disprove which means some day we might find something new that might add some variations to this concept.

Last edited: Aug 1, 2010
12. Aug 1, 2010

Staff: Mentor

Experiments that assume a variable speed of light started failing when a high precision was used in the measurements and mathematical inconsistencies between other theories started to be noticed. So a new theory had to be developed that could account for these observations and correct these inconsistencies.
By definition, no theory is ever considered "fool proof". A theory is just an explanation that works based on what we know now. But remember that regardless of whether/how much it is changed in the future, it will always need to explain all of the observations made to date. So as the body of evidence and precision of experiments grows, the magnitude of the possible error goes down.

13. Aug 1, 2010

Staff: Mentor

Obviously it is possible that some future observations will be in conflict with SR and a new theory will be needed to explain those observations. However, one feature that new theory will need to have is that it must reduce to relativity in the appropriate limit, the same way that relativity reduces to Newtonian mechanics in the limit v<<c.