# Travelling at the speed of light

1. Jan 14, 2010

### Eddy 7

This is my first topic and I do not have a physical education degree.

How can I put this...I´m only a curious guy who loves physics and mechanics!

So, what brings me here...

Travelling at the speed of light (SOL) is only possible in our most inspired dreams and sci-fi movies but let´s pretend we can do it.

Imagine a space-ship capable of reaching SOL.

We are the crew.
Can we survive the rush of acceleration?!
In order to let us survive the acceleration, it would be necessary to bring it to a rising-speed (or G-force) that we can outlive.
7 G´s is quite confortable.

So...here is where I need your help.

How much time do we need to reach SOL, accelerating at 7 G´s?!

And how far are we from the starting point when we reach SOL?

2. Jan 14, 2010

### sylas

If you build a spaceship with some engine able to give thrust to accelerate the ship at 7G, it will never get to the speed light.

That is because the acceleration actually experienced on board the space ship is different from the acceleration measured by an observer at rest outside the space ship. This is a direct consequence of the time dilation and Lorentz contraction effects, or better, of the Lorentz transformations switching between the frame of an observer on board the ship, and an observer at rest outside.

You can never get to the speed of light with any finite acceleration, no matter how great, as measured by people on board the space ship.

If you have a constant acceleration from the perspective of people on board, the perspective of an outside observer has the ship approaching but never reaching the speed of light.

Cheers -- sylas

3. Jan 14, 2010

### Staff: Mentor

So, you know the laws of physics prevent us from reaching c and yet you want us to tell you what the laws of physics would predict if the laws of physics were wrong?

4. Jan 14, 2010

### DocZaius

I think the OP thinks the reason why we can't reach the speed of light is insufficient technology, rather than the laws of physics.

5. Jan 15, 2010

### Matterwave

Well, to give the OP some look into the speeds involved, let's just say constant acceleration at 7Gs to accelerate up to .5c.

At that speed, relativistic effects are still roughly ignorable. (gamma~.87)

It would take 2.14 million seconds or about 25 days at a constant CONSTANT 7Gs. I mean, you'd feel like you weighed 7 times more than now for 25 straight days...I don't think you can take it. Instead of 60kg, I'd weigh 420kg (almost half a ton!) for 25 days. As you get closer to c, it gets harder and harder as the relativistic effects set in.

6. Jan 15, 2010

### sylas

The real question is... 7G according to whom? If you are an observer at rest, and you see a vehicle with velocity v and accelerating at dv/dt, then you can conclude that passengers on board are experiencing a pseudo-gravitational field of (1-v2/c2)-3/2.dv/dt.

As Nabeshin reminds us both, the gamma is actually 1.15; 0.87 is 1/γ. In any case, the acceleration experienced on the ship will not be 7G, but about 10.63G.

Alternatively, if the ship has a gamma of [strike]0.87[/strike] 1.15 and the people on board are experiencing 7G acceleration, then the acceleration you observe from outside is about 4.61 G.

Cheers -- sylas

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

### Nabeshin

For one, gamma is always greater than one, and for two, I get gamma as 1.15 for v=.5c.

8. Jan 15, 2010

### sylas

Quite so. The 0.87 was actually 1/γ, and I just used the same number but divided instead of multiplying. Thanks for the correction; I shall fix the post to make the numbers consistent with the formula. Thanks for picking this up!

Cheers -- sylas

9. Jan 15, 2010

### HallsofIvy

You should at least understand that "physical education" is NOT physics!

Traveling at the speed of light is not possible in relativity even in "dreams" (or, classier, "thought experiments"). "Pretending we can do it" is saying "suppose relativity is not correct". You cannot then say "what would relativity say about this situation"!

No, 1 g is comfortable. Even lying on a couch feeling like I have a 7(150)= 1050 pounds = a half ton weight on me may be survivable but not what I would call "comfortable"!

Assuming classical mechanics, since you have already denied relativity, 1 g is 9.81 m/s2, approximately, and, after t seconds, our speed will be gt= 9.81t= c= 300000 m/s gives t= 300000/9.81= 30581 seconds= 510s minute= about 8 and 1/2 hours. A surprisingly short time!

In that time we will have gone (1/2)gt2= (1/2)(9.81)(30581)2= 4587155963 meters which is about 4587156 km or about .0000005 light years.

Of course, none of that is real. We are just "dreaming".

10. Jan 15, 2010

### sylas

You've missed three orders of magnitude, by using the value appropriate to km/sec. The time to get to the speed of light under this classical assumption is just under a year at 1g

Cheers -- sylas

PS. By the way... the formulae for a spaceship that has an engine capable of constant acceleration in its own frame of reference are the hyperbolic functions. Suppose your acceleration is "a" m/s2. Suppose also you have a clock on board the ship.

Consider an inertial frame of reference from which the ship launches out at constant acceleration (according to the ship) with the on board clock reading 0 at launch. Consider the event of the onboard clock reading the value u. Then, in the intertial launch frame:
• The location of the ship is c2/a (cosh(au/c) - 1)
• The time in the launch frame is c/a sinh(au/c)
• The velocity of the ship is c tanh(au/c)

So, with c = 3*108 m/s, and a = 9.8 m/s2, after one year of ship time (u = 31556736 sec) we have:

• Ship has traveled about 0.53 of a light year.
• The time in the launch frame is 1.19 years.
• The velocity of the ship is about 0.77 the speed of light.

Last edited: Jan 15, 2010