# A Machine

1. Aug 28, 2011

### nasgath

A gigantic machine that has let's say another 1000 machines inside of it. We start the primary machine to travel at 100 km/h. We send it out to space, then the machine sends the next machine inside of and kicks it to give it a boost for another 100 km/h. Now the kicked machine has an extra 100 km/h speed. So in total, we get 200 km/h. Now we have 999 machines left inside of it, so we repeat this process through outer space. Kicking and boosting every next machine giving extra speed until we reach... speed of light? Why is this not possible? Thanks.

2. Aug 28, 2011

### Staff: Mentor

3. Aug 28, 2011

### Edi

It is really the same thing as just pushing high speed matter (hot rocket stuff) out of a nozzle behind a rocket.. only, in this case, the '"hot rocket stuff" is replaced with that larger machine. (When the smaller is kicked forward, the larger is kicked backwards )

4. Aug 28, 2011

### ghwellsjr

It's not possible because after each kick, the remaining machines will still measure the speed of light to be c, just like it was at the beginning. It won't matter how many times you repeat the process, the speed of light will always be the same and you will never get any closer.

5. Aug 29, 2011

### nasgath

What exactly is c? And since speed of light will remain the same, isn't that how the machines reach the speed?

6. Aug 29, 2011

### ghwellsjr

The speed of light is represented by the letter c and is exactly 1079252848.8 km/h. Even if your plan would work, it would take a lot more than 1000 machines to get anywhere close to the speed of light. So let's talk about the speed of light in terms of km/s which is 299792.458 km/s. Most people like to round this to 300 thousand km per second. So let's say each kick of your machine can produce a speed of 100 thousand km/s. Now you're thinking that in three kicks, you will have reached the speed of light, correct? If this were true, then after the first kick, you should be able to measure the speed of light to be different than c.

So how do you measure the speed of light? Well, you put a mirror in front of you some measured distance away and then you set off a flash of light and you measure how long it takes for the light to travel to the mirror and back to you. We can also say that the speed of light is 300 meters per microsecond so let's put a mirror out there that is 300 meters away. When you make the measurement before you start out, it should take 2 microseconds for the light to make the round trip, correct? And we calculate the speed of light to be 600 meters divided by 2 microseconds or 300 meters per microsecond.

Now let's do it again after your first kick that puts you at 100 thousand k/s. First question (if your plan would work) is how long would it take the light to get to the mirror? It will take 1.5 microseconds because in that length of time, you and your mirror will have traveled 150 meters and since your mirror is 300 meters in front of you, it will be a total of 450 meters from the location where you set off the flash. The flash will have traveled 450 meters in 1.5 microseconds so that is when it hits the mirror.

Now how long will it take for the reflection of the flash to get back to you? It will take another 0.75 microseconds because in that length of time, you will have traveled 75 meters forward and the light will have traveled 225 meters back toward you to cover the total distance of 300 meters between you and the mirror.

So the total round trip time will be 2.25 microseconds which comes to an average speed of 600 meters divided by 2.25 microseconds or 266.67 meters per microsecond instead of the value of c, 300 meters per microsecond. Remember, this is if your plan would work.

Now we can give your machine another kick and the speed will be 200 thousand km/s. And when you measure the speed of light, the forward flash will take 3 microseconds because you will have traveled 600 meters and your mirror is still 300 meters in front of you which adds up to 900 meters, the distance that light travels in 3 microseconds. The reflected flash will take 0.6 microseconds because in that length of time you will have traveled 120 meters and the light will have traveled 180 meters (adds up to the distance the mirror is in front of you). So the average speed of light that you would measure after the second kick (if your plan worked) would be 600 meters divided by 3.6 microseconds or 166.67 meters per microsecond. Notice how the measured speed of light is getting even more slower as you creep up on it.

Now after the third kick, you will be going the speed of light which means that when you set off the flash, it will never reach the mirror because you and the mirror and the flash of light are all traveling at the same speed. Therefore, you will measure the speed of light to be 600 meters divided by a very large number which equals a very small number, actually zero meters per microsecond.

The whole point of this exercise is to show you that if your plan were to work, then as you get closer to the speed of light, when you measure the speed of light, it gets smaller.

But that isn't what actually happens. Whenever you measure the speed of light, you always get the same value instead of a smaller value no matter how fast you are going. That's just the way nature is. Do you believe this?

7. Aug 29, 2011

### nasgath

ghwellsjr, nice explanation there buddy. But I'm not sure I quite understand you. You're saying you'll never get close to the speed of light. Then you also didn't mention any maximum speed we can achieve? To my understanding, you're saying even if you're traveling at the speed of light, C will still be measured a lot faster. My point is to reach 300.000 KM/s but since you disproved my example, then what's the maximum speed we're talking about here?

8. Aug 29, 2011

### ghwellsjr

There is no maximum speed that we can achieve, there's only a maximum speed that we can't achieve and that's the speed of light. Anything less than that is achievable. But even when you got to that speed if you then measured the speed of light, it would still be exactly c, just like it was before you started, it wouldn't be faster and it wouldn't be slower. The speed of light is exactly 299792458 m/s so you could go 299792457.99999999999999999999... m/s (throw in as many 9's as you like to get closer to c).

So now that I have answered your questions, will you please answer mine? Do you believe that no matter how fast you are going, you will always measure the speed of light to be the same constant value, 299792458 m/s?

9. Aug 29, 2011

### Ryan_m_b

Staff Emeritus
Technically the maximum speed would be 0.99999.....c pretty much ad infinitum. You can never travel at the speed of light as this required infinite energy for objects with mass. At any speed we measure the speed of light in a vacuum to be the same. So if I am on Earth and I have a devise to measure the speed of light in a vacuum and you are on a spaceship heading to the centre of the galaxy at 99.99% of the speed of light we would both get the same measurement. You would also experience 20 minutes for every day I experience (i.e. a day for you means that over two months have past on Earth).

10. Aug 29, 2011

### DrGreg

To be pedantic, technically there is no maximum but there is a supremum i.e. lowest upper bound.

11. Aug 29, 2011

### ghwellsjr

If you are defining clock rates according to a Frame of Reference in which the Earth is stationary, then what you say is true, but if you are defining clock rates from a FoR in which the spaceship is stationary, then the opposite is true--time on Earth is going slower. There is no a priori reason to say that one of these two FoR's is preferred over the other--or any other FoR for that matter.

Last edited: Aug 29, 2011
12. Aug 30, 2011

### Ryan_m_b

Staff Emeritus
True, I should have stipulated something along the lines of "and then the ship comes back to Earth and they compare clocks"

13. Aug 30, 2011

### ghwellsjr

But even that stipulation doesn't make the Earth rest frame preferred, it just makes that frame the easiest one in which to conclude that when they reunite the spaceship clock has less time on it than the earth clock. Every other frame will also come to that same conclusion and many of these frames will have the earth clock running slower during the outbound portion of the trip.

The whole point of this "exercise" is to emphasize that every observer will experience the same thing in terms of their own measurement of the speed of light no matter how many times they have been kicked up to a higher speed as you pointed out in your first post.

14. Aug 30, 2011

### MrNerd

A particle with mass will never be able to reach light speed because it would take an infinite amount of energy. Why is this? Einstein's E = mc^2 is the answer!

Essentially, the formula states that mass IS energy. Inputting energy into an object will increase an object. Therefore, it becomes more and more massive as it accelerates, and the same force acting on it will accelerate it less and less. An object can approach the speed of light(with a truly enormous amount of energy required to do so, especially if it has a large mass), but it can never actually reach it. It's like the equation y = 1/x. As x gets larger and larger, y will become smaller and smaller, becoming ever closer to 0. However, it will never actually reach 0, since 1 divided by any number is always greater than 0.

If you want the actual equation for kinetic energy on a relativistic scale:

K(kinetic energy) = (mc^2)/sqrt(1-((v/c)^2)) - mc^2

Notice that as v approaches c(the speed of light), (v/c)^2 will become closer and closer to 1. As a result, the square root of 1 - (v/c)^2 will approach 0. At this point, you will be dividing by 0(which is impossible unless you're Chuck Norris or hallucinating). If v were to exceed c, then (v/c)^2 would be greater than 1. This would mean 1 - (v/c)^2 would be less than 0, and since it is square rooted, you can't do this. Therefore, you can consider this "imaginary".

Additionally, if you could truly get close enough to the speed of light with a probe or machine, it would be highly unlikely you would get to see it finish its task in your lifetime, with the enormous amount of time dilation. The object could take, say, 1 hour to perform the task. If the object is to go fast enough, then that hour experienced by the object would take thousands of years for the base to observe the results.

15. Aug 30, 2011

### ghwellsjr

But the OP wasn't asking about how the base observes the traveler and the traveler is completely unaware of any increase in mass that the base may attribute to the traveler, just like the base is completely unaware of any increase in mass that the traveler may attribute to the base or any time dilation the traveler attributes to the base. Neither viewpoint is any more "correct" or preferred than any other. I thought I just pointed that out.

The point the OP needs to understand is that it doesn't matter what your past history of speed is, everything will still seem the same to you as it did before you started. You will be completely unaware of any of your clocks running at any different speed. You will be completely unaware of any of your rulers having different lengths. You will be completely unaware of any change in mass. When you get another kick in speed, you will respond to it exactly like you did the first one. And most importantly, when you measure the speed of light after any kick in speed, you will get the same answer, instead of a lower answer, which is what would happen if the OP's assumptions were true. That is why I am asking him if he believes this important concept.