# Why can't we go faster than 300,000 km/s?

1. Jul 5, 2008

### Desiree

According to this simple physical formula V=a*t, suppose we designed a "car" with a powerfull engine and could find a flat track long enough to conduct our test, why Einstein says our car cannot pass the 300,000 km/s limit, while we know the car's engine is capable of generating considerably high power to obtain such speed and even beyond? I just need to understand this.

I have heard that some galaxies are receding at speeds even faster than light's, is that true?

2. Jul 5, 2008

### Staff: Mentor

The simple physical formula you gave is just an approximation. The actual formula is

$$\frac{V}{\sqrt{1-\frac{V^2}{c^2}}} = a t$$

See equation 7.15 for a derivation. As you can see, the actual formula reduces to your simplified formula for V<<c. But it becomes quite different as V grows large relative to c.

3. Jul 5, 2008

### Desiree

I just want to know what happens when our "car" reaches 300,000 km/s? please provide descriptive explanations not mathematical formuals.

Suppose our test is conducted while we switched off all the "stars" in the universe so there would be no 'light' involved at all.

4. Jul 5, 2008

### Staff: Mentor

Have a closer look at the formula Dale posted. The answer is there. Descriptions via words don't really explain it. The best that can be said is that from the point of view of an outside observer, the acceleration gradually slows.

5. Jul 5, 2008

### nicksauce

As your car's speed gets closer to c, its mass increases and thus becomes more resistive to the forces applied on it, which makes it harder to accelerate.

6. Jul 5, 2008

### Desiree

Why does the mass of our 'car' increase? I just don't get it???????? (please keep in mind I'm not a physicist).

7. Jul 5, 2008

### Staff: Mentor

Mathematical formulas are the most descriptive explanations. But I will give it a shot.

Do you understand the concept of momentum?

It turns out that momentum is a non-linear function of velocity. In fact, as v approaches c momentum increases without bound. From Newton's second law, we know that a force causes a change in momentum. So your "car", which provides a constant force, causes a constant change in momentum. The car's momentum gets bigger and bigger and bigger without bound, and therefore the velocity gets closer and closer and closer to c.

8. Jul 5, 2008

### Gear300

E = mc^2 (there is actually more to it, but I'm neglecting the rest)...energy and mass are interchangeable. As the car's velocity increases in a certain direction, its mass will increase.

The reason this doesn't seem obvious is because its not really in our domain of experience. Lets say there was a range that goes from phenomenon occurring on a super small level to phenomenon occurring on the super big level. What we experience occurs somewhere in between, and we usually do not explicitly feel the effects of phenomenon occurring on more extreme scales. Our experience directs our common sense (something may seem totally awkward if its completely out of the ordinary, that is, if our experience didn't allow us to expect such a thing). But, since we do not explicitly experience things on all scales, we assume that things have the tendency to go the way we see them...and apparently, that isn't always the case.
I'm not much of a physicist either, so if I'm wrong about anything, please do so to correct me.

Last edited: Jul 5, 2008
9. Jul 5, 2008

### Staff: Mentor

The concept of relativistic mass is generally deprecated, and is unnecessary.

10. Jul 5, 2008

### Desiree

Thanks for the clarification so far. So does it mean if oneday we decide to build a spaceship and traverse the universe, we would still be bound to this speed limit forever?

Is there any possibility to actually someday build a spaceship which could somehow utilize the gravitational attraction of super massive stars to help propel itself forward and travels beyond the S of L?

Any comments on the galaxies' receding speed I pointed out earlier????

11. Jul 5, 2008

### Integral

Staff Emeritus
As we currently understand the universe it is impossible to accelerate a massive body (read that as, any body with mass) to the speed of light. This has been verified experimentally with particle accelerators. According to Newton for decades we have had particle accelerators with sufficient energy to accelerate electrons and protons beyond the speed of light. What has been observed experimentally is Einstein's relationship, not Newtons. No matter how much energy is applied the speed of the particles approach but do not reach c.

The expansion of the universe is not the same as accelerating particles. You may want to post a question in the cosmology forum about this. It, like the formation of life is a separate question and best kept separate.

12. Jul 5, 2008

### Desiree

Thanks Integral. I'll post a separate question on the galaxies receding speed on cosmology. I am aware that the tests being done at CERN and Fermi Lab have achieved speeds of 99.99995 C.

BTW, my thread on the origin of life was finally closed and blocked and my views on the Big Bang theory were considered "heresy".

13. Jul 5, 2008

### Integral

Staff Emeritus
Not heresy, but most definitely nonsense.

14. Jul 5, 2008

Staff Emeritus
You do realize you are asking for a numerical answer without a mathematical formula? That's a pretty tall order. Also, you do realize that the very first person to post a formula was you, don't you? It seems to me unreasonable to insist that nobody else posts one.

The relationship between velocity and energy is:
$$v = c \sqrt{1 - \frac{m^2c^4}{E^2}}$$

You can see that the term to the right of the minus sign is a square, which means it's non-negative. That means that the biggest the term inside the radical can be is 1, which means the biggest v can be is c.

15. Jul 6, 2008

### Fredrik

Staff Emeritus
Very distant galaxies can do that, in the sense that their distance from us is increasing by more than 299792458 meters each second (in a specific coordinate system). General relativity doesn't say that this can't happen. What it actually says (when we express things using that specific coordinate system again) is that the spatial coordinate of a particle can't change by more than 299792458 meters each second. Those "super fast" galaxies are actually staying at constant spatial coordinates in the relevant coordinate system (except for random velocities of a few hundred km/s), just like all the other galaxies. It's the expansion of space that makes the distances between galaxies increase.

16. Jul 6, 2008

### lightarrow

We would be bound...and not, it depends on what you mean. If you were in a starship travelling at very close to light's speed you would go around every locations in the known universe in a few seconds of your time. The problem (= where the light's speed finite value comes into play) is when you go back to Earth: there time has gone ahead of billions of years (probably Earth itself doesn't exist anylonger...)

17. Jul 6, 2008

### Desiree

Thanks guys. It's now clear to me. Also I posted this question on cosmology, and got good responses.

By not using mathematical formulas, I meant to reply in a simple lay people language. That's how I like explaining science and knowledge to the general public like me. If you ask me, If one can't explain their knowledge in a simple plain language and by drawing analogies, then lay people tend to not agree with or accept those views since they just don't want to go through the mathematics part of it, or are just curious to learn about the the rationale behind a phenomenon. I consider myself good at the job of drawing analogies and clarifying/simplifying things as much as I can, so I expect others as well to be able to do the same.

18. Jul 6, 2008

### Staff: Mentor

The point is that in large measure math is the language of physics. We can translate it into english, but there is always something lost in translation. If you want to really understand the greatness of Tolstoy, you have to know Russian. If you want to really understand the beauty of physics, you have to know math.

Consider all non-mathematical descriptions of physics to be forigen language translations and you will have a good understanding of the limitations of what you are asking for.

19. Jul 6, 2008

### yenchin

Regarding math and its great importance, the great Feynman has wrote the following:

Read the entire article at: http://www.collectedthoughts.com/quote.aspx?id=11305

20. Jul 30, 2008

### O.K.

If possible, maybe someone could post the formula as a graph to give a more visual explanation...if possible.