# Need help explaining light speed limit to younger brother

1. May 11, 2010

### MasterZoran

Hi everyone - I am having trouble getting my brother to wrap his head around why you cannot move faster than the speed of light.

My little brother has said that he believes eventually we will have technology that will allow FTL travel - I agree with this but I told him that IF it happens it will not be because of us literally moving FTL, it will be because we figure out how to bend space to allow us to cover great distances in a short time (think of the ant and the thread, then folding the thread - this is how I believe FTL travel *may* work)

I tried to explain to him E=MC2 and diminishing returns - how the more energy you put into an object the more mass it has, so even if you could come up with an "infinite" energy supply and were to pour "infinite" amount of energy into an object the object's mass would increase proportionately with diminishing returns so you would never actually reach light speed -

he seems to think that eventually - some day we will overcome this limit - I told him the universe would probably break

can anyone link me to a good article or help me come up with some way to explain why light speed is a hard limit - why it cannot ever be exceeded by objects with mass

-ps, I'm sure many of the terms / idea's I am using are not perfectly accurate - I'm just generalizing some advanced concepts for the sake of explanation based on my limited understanding of special relativity - I am no scientist

I might even be the one who is wrong - but I would love to learn why/why not.

thanks!

Edit: The gist of what I am getting at is in the definition of "Traveling faster than light speed" - If you define it as moving from one place to another quicker than light would get there I do believe that possible.

If you define it as accelerating too and past the speed of light I believe that is not possible, now or ever

Last edited: May 11, 2010
2. May 12, 2010

### daisey

If your question is "why can an object with mass physically not exceed the speed of light", I think you have already answered it. It would take an infinite amount of energy.

If your asking "Why is the speed of light the limitation that it is in our world", as opposed to, "why the limitation is not one mile-an-hour faster", I'm not sure anyone can answer that one yet, at least I have not read a good answer.

I have read one theory as to why there has to be some type of limitation (as opposed to no limit) on movement through space. If I understood the explanation correctly, it is because time is (according to this theory) like a concatenation of individual "moments" - similar to a motion picture. And this speed limitation (light speed) determines the maximum amount of difference there can be between the individual "frames" of time. Otherwise, time would not appear to us to flow smoothly, and would appear erratic. It made sense to me, at least.

Daisey

3. May 13, 2010

### Tantalos

4. May 15, 2010

### starthaus

No, you won't. It is very easy to disprove your statement:

$$v=\frac{at}{\sqrt{1+(at/c)^2}}$$

Calculate $$v$$ for $$t->oo$$.

5. May 15, 2010

### map19

starthaus. You haven't disproved anything.
you are referring back to the start point or reference frame because these relativistic formulae always do.
If you are inside a ship and it accelerates at a constant rate, eventually, by your own calc of constant speed increase x time you will see that you have exceeded c.
Observers in other frames will see that you get ever closer, but never reach c.

Where's my post gone ?

6. May 15, 2010

### starthaus

You must be reading too much sci-fi.

which means precisely that the ship will NEVER reach c.

Another way of proving that is by obeserving that the mechanical work necessary to get to $$v=c$$ starting from $$v=v_0$$ is:

$$\Delta W= m_0c^2(\gamma(v=c)-\gamma(v=v_0))=oo$$

Last edited: May 15, 2010
7. May 15, 2010

### matheinste

So what is your calculated superluminal speed relative to?

Matheinste.

8. May 15, 2010

### Lsos

I'm not going to do the math here...but let's say you DO accelerate at 5g for 20 or so years, and then slow down at 5g for another 20 years. You'd probably end up at the other end of the universe...if not beyond it. You then look back at the distance you covered, and look down at your watch/ calendar....wouldn't YOU be able to say, with a clear conscience, that you WERE traveling faster than the speed of light? (I understand that millions/ billions of years will have passed for the universe, but bear with me here....)

9. May 15, 2010

### Integral

Staff Emeritus
Your post was deleted because it is simply wrong. You can calculate what ever you want but that does not mean that you have actually calculated your correct speed. To get your actual speed you must measure it with respect to some point. It does not matter what point you choose to be stationary with respect to your motion you will never measure a speed greater then c.

10. May 15, 2010

### map19

"you will never measure a speed greater then c." as seen from other frames. I was careful to say that.
You all seem to be missing the point.
If locked inside a ship experiencing acceleration you can only rely on acc. x time to calc your speed.
What distant observers see is irrelevant to you.
You will think you have exceeded c.

You have also deleted the interesting reference to the Wiki article on the Alcubierre method.
Be careful what you delete. I guarantee that I have been doing physics longer than anyone on this forrum. retired from Uni. a couple of years ago.

11. May 15, 2010

### Nabeshin

Right back at you. What is this acceleration measured with respect to, hm? The starting point? Well then assuming it is a constant acceleration is folly, as an observer at the starting point will not corroborate.

12. May 15, 2010

### Integral

Staff Emeritus
We hear that a lot, 90% of the time it it pure BS. All we have to go one is post content.

Again, you can compute what ever you want, it does not make it your speed. If you attempted to use that computation for navagation you would be lost.

13. May 15, 2010

### Passionflower

Wrong!

First of all an object does not have an intrinsic speed. An object can have a proper acceleration with any rate and any duration but it will always measure the speed of light to be c. It has absolutely nothing to do with a lack of energy.

At the same time, the speed between two objects (that have mass) [ remember this is relativity: there is no such thing as an intrinsic speed of an object ] is always less than c.

If you understand hyperbolic spaces you would realize that the limit of this speed does not exist, e.g. it is not c.

14. May 15, 2010

### Passionflower

I do not know your level of comprehension but do you perhaps think that acceleration is relative?

15. May 16, 2010

### Nabeshin

You think it is not?

Will fellow passengers on the spaceship measure an acceleration between themselves and, say, the other passengers on the ship? Okay, well this is true of coordinate acceleration so we should explicitly state that we're talking about proper acceleration which is indeed invariant. Very good.

So our spaceship man feels some proper acceleration. However, if he wants to find a displacement he must obviously specify a reference point. In doing so, he chooses a second reference frame and can make the transformation from his proper acceleration to the coordinate acceleration his reference observer sees. Now he should be able to find out his speed with respect to this observer, and find it is in fact less than c.

MasterZoran or map19, do you take any issue with this? I believe that is all there is to say on the topic...

16. May 16, 2010

### Passionflower

I am glad you know that.

You are not quite right on that one. While it is true that acceleration can change the observed distance and relative clock rates between two (point) objects with mass it does not cause a displacement as that would obviously violate the clock postulate. Displacement is caused by relative motion not by acceleration.

17. May 16, 2010

### Nabeshin

What I mean is he wants to start writing down equations of motions, so he needs to start with displacement (x) in order to get velocity (v). Were I the guy on the spaceship, this is the way I would do it at least. Are you suggesting something differently, or just making caveats?

18. May 16, 2010

### Passionflower

But have you thought that through?

Suppose you go in such a spaceship and travel to a place 100 million light years away. Now what would be the practical information you want to know? ...... Right, how long is it going to take me to get there. Then they tell you it will take 10 days.

So there you go, you covered 100 million light years in only 10 days, 10 million light years per day. Pretty fast wouldn't you say? So then what is your speed, well that all depends on how you define speed.

Now if you are in that ship would it really be of practical interest making calculations using some, what you called, reference point that is utterly irrelevant since time will evolve at least 200 million years for the quickest round trip? Right, I would not think so either!

Last edited: May 16, 2010
19. May 16, 2010

### DrGreg

Velocity is distance divided by time*, where distance and time are both measured by the same observer.

In your example, the distance is measured in the "stationary" frame, but the time is measured in the "moving" frame. When we mix frames like that, we call it "celerity" or "proper velocity"**. There is no upper limit on celerity: the celerity of light is infinite.

_________________
*well, actually the derivative of displacement with respect to time, but I'll use simpler language here

**I don't like the term "proper velocity" because it's incompatible with other uses of "proper" in relativity, and it may mislead some people towards an incorrect definition of "proper acceleration".

20. May 16, 2010

### starthaus

Great post. In other words:

$$\phi=\frac{a\tau}{c}$$ is unbounded
but
$$v=c*tanh \phi$$ is always <c.