# Homework Help: Speed of light

1. Jun 10, 2006

### meemosewa

This question has been driving me crazy all night.

If the speed of light were smaller than it is, would relativistic phenomena be more or less conspicious than they are now?

Honestly, i do not have a clue as to what the question is asking, and without understand thing the question, i have no way to answer it. I have read and reread the section in my book on the speed of light, and i do not understand it in the least bit... ANY HELP WOULD BE LOTS OF HELP!

THANK YOU!

2. Jun 10, 2006

### Saketh

Take some non-classical relativity equations, and look at what would happen if you made $$c$$ a smaller number. For example:
$$p = \frac{m_{0}v}{\sqrt{1-\frac{v^2}{c^2}}}$$.

What if $$c$$ were a smaller number - say, 0.5? Take it to the extreme! The change in momentum is an example of a relativistic phenomenon - would a large change in c have an impact on this phenomenon?

Take a look at some other equations of special relativity, and plug in ridiculously small values of $$c$$.

3. Jun 11, 2006

### Tide

This may not be within the scope of the question you were given but in order for the speed of light to be different both $\mu_0$ and $\epsilon_0$ would need to be changed thereby changing other things like the Bohr radius and electromagnetic quantities. Our scales of time and length would thereby change accordingly.

4. Jun 11, 2006

### meemosewa

unfortunately my class is material based, and not equation based. i should have mentioned this before, but do you have an explaination that is a little easier to understand? i appreciate the help, i just do not know what the equations and symbols represent... thanks!

5. Jun 11, 2006

### illwerral

The speed of light in a vacuum is a constant value in any non-accelerating frame of reference, and it is a very high speed. To illustrate this, think of someone with a tube that bounces photons around vertically, who is on a train moving at 20 m/s. To the guy on the train the photons move only vertically, but to an observer on the ground they also move horizontally, making their total distance moved greater. Since speed is distance divided by time, and since light moves at the same speed for both of these peope, we can calculate the time it takes for a round trip from the top of the tube, to the bottom and back up for each observer. For the guy on the outside, the light travelled a greater distance at the same speed, so time happened faster for him than the guy on the train.

Using similar ideas, we can generalize by saying that as an object approaches the speed of light, its length decreases, its mass increases, and time slows down for it.

Now consider if the speed of light were walking speed, and tell us what you think would happen in your everyday world.

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6. Jun 11, 2006

### meemosewa

If the speed of light were represented by a guy walking with a tube of protons that bounce vertically, then:

time would slow down. the length of each bounce would increase (because of relativity?) and the mass would be smaller?

i think i have it now, thank you for the visualization and easy to understand explaination!

7. Jun 11, 2006

### illwerral

Unless your everyday world consists of guys who walk around with tubes of photons, I was getting at something slightly different

Since nothing can move faster than light, and you know the effects of moving near the speed of light, and if the speed of light were all of a sudden 10 km/h.... what would happen to you if you went for a run. What is the fastest you could run then? How would your length, mass, and perception of time change?

8. Jun 11, 2006

### Saketh

Mass increases as you reach the speed of light, and the speed of light is the maximum speed. If the speed of light became 10 m/s, then nothing could move faster than 10 km/s, and mass would increase much faster.

Increasing Mass Equation - notice that if the speed of light is smaller then your mass increases more.
$$m = \frac{m_{0}}{\sqrt{1-\frac{v^2}{c^2}}}$$

The tube of protons (photons?) is a complicated way to think about it. Think about the increase in mass as you approach the speed of light, and how it would change if the speed of light were smaller.

9. Jun 11, 2006

### illwerral

I think I said photons?

10. Jun 11, 2006

### meemosewa

Then i would not be able to run very quickly at all. Everytihng would slow down to an extreme, including the speed of cars, and planes. My perception of time would chage in dramatic ways. Everything would take so long to complete. A trip to the grocery store would take days... I think this is an interesting way to view the concept. I understand the time portion... as for the rest, i guess my mass would increase and my length would be shorter??? errr...

i think i get the concept of the speed of light about as much as i can. Thank you for all of your help!! I now understand that if the speed of light were slowed down it would have a HUGE impact on everything.

I DO APPERCIATE IT!

11. Jul 6, 2006

### MeJennifer

Not quite.
Mass would not increase much faster since it would be just as hard to go to say 50% of the speed of light is it was 10 m/s as it is when it is 299,792,458 meters/sec.

The speed of light is not always the same (in a vacuum). Inside a black hole light can go faster than 299,792,458 meters/sec.

By the way the speed of light in vacuum is exactly 299,792,458 meters/sec by definition!