# Changing the speed of light

1. Oct 7, 2004

### scariari

what would change in everyday life if the speed of light were to decrease?

2. Oct 7, 2004

Staff Emeritus
Say that c were 100 mph. Then a walking pace of 3 mph would be .03c, and the dilation factor $$\gamma = \frac{1}{\sqrt{1-.03^2}}$$ would be 1.015. Your watch and your twin's watch if he were walking would differ by 54 seconds an hour, almost a minute difference every hour, and if he walked around the block he would wind up proportionately younger than you. A car travelling past you at 30 mph = .3c would be flattened relative to you by a factor of 71%!

3. Oct 7, 2004

### Mike2

I wonder sometimes if space were more dense in the past because the universe was more compact, then wouldn't the speed of light change in a denser space? Or if space were being more tightly stretched out the older it gets, then wouldn't light travel faster?

4. Oct 7, 2004

### Cal

Hmmm. Intresting question.

I beleive that if light did suddenly become slower than there would be lag on everything. We would see things which have already happened. Almost as if looking back on time. But also, i beleive our brains would eventually adapt to it and we would not notice anything different.

Just my oppinion.

5. Oct 7, 2004

### soeren

But when you come back, both of you are of the same age. ;-)
I think that's amazing..

What's that for a formula?
$$\gamma = \frac{1}{\sqrt{1-.03^2}}$$
Is it the special dilation-formel?
I would be happy, if you explain it short for me :-)

And why do you get 1,015?

I get this, when i calculate it by mupad, here with 100 digits (i wasn't sure how much he needs to calculate this).

>> 1/(sqrt(1-0.03^2));
1.000450303977992047779634328440388770795233640457725628749815339135740539\
010530892349154310775908323

Now.. to write something On-Topic:
I think, that a life as ours is now, would be not really possible, exspecially would it be funny to make a journey, or generally drive with the car.
When you have to be somewhere and drove there with the car with 90mph,
would the dilation-factor be about 2.294157339 after your formula (Sorry, if i understand it wrong).
Does that mean that if i drive an hour in "my" time,
the clocks of me and my twin who's not in the car differ of
1.29... hours?
Does that mean, that I'm there before I leave home?

Sorry, if i do a big mistake, but i don't understand, how you get the 1,015.
Maybe thats the only obscurity.

if my thoughts are too stupid and this has nothing to do with the topic, we can clarify this via personal messages or something like that.

thanks,

Soeren

6. Oct 8, 2004

7. Oct 8, 2004

### soeren

@robphy do you mean me and my curious posting or do you mean it to the thread-owner (does this word exist?).

greets
soeren

8. Oct 8, 2004

Staff Emeritus
Yes you can make words like thread-owner in English, although just using the two words would be more usual. I am sure the Tomkins reference was directed to anybody in the discussion, since it is an instructive fantasy (a la Flatland) based on just the proposition of this thread.

9. Oct 8, 2004

### pervect

Staff Emeritus
The question isn't totally well defined - but one of the most interesting responses I've seen to it is that if the speed of light in a vacuum were ever reduced below the escape velocity of the Earth, the Earth would then be by definition a black hole and undergo gravitational collapse. Another way of looking at it - the Schwarzschild radius is R=2GM/c^2, so if you lower c you increase the Schwarzschild radius for an object of given mass (assuming that G stays constant).

10. Oct 8, 2004

### Prometheus

I assume that you mean the spatial component of the speed of light. The answer is the only thing that would change is the measured rate of the speed of light.

11. Oct 8, 2004

### Prometheus

I don't follow. If a pair of twins are walking at the same rate of speed, how will their watches differ by so much?

Is this even relevant? If one twin walks around the block now, with light at its current speed, he will age less than his brother who is stationary with respect to the earth.

12. Oct 8, 2004

### pervect

Staff Emeritus
That's really not a viable option. If you chance 'c', you have to change in addition one or more of the following three things

1) Maxwell's equations
2) The electrical permittivity of free space
3) The magnetic permeability of free space

You can't have all of the above three unchanged and a value of the speed of light other than the current value.

The fact that there are different possibilities is what makes the question somewhat undefined.

What's interesting, though, is that the expansion of the Schwarzschild radius of an object of a given mass doesn't depend on the details of how one changes 'c'. So lowering 'c' too much would turn first the sun, then the earth, into a black hole independently of the exact options one chose above.

13. Oct 9, 2004

### Prometheus

Wonderful. You are claiming that there are other metrics that would be changed as well. No surprise there. I consider that these are irrelevant to the main point, however. There is no reason to believe that the speed of light has the same rate of motion through space throughout the entire universe and for the life of the entire universe.

14. Oct 9, 2004

### pervect

Staff Emeritus
Actually we do have some data that strongly suggests that the speed of light has not changed much, if at all.

The more recent observations of the fine structure constant, for instance, show no variation with time over a period of 10 billion years.

http://www.eso.org/outreach/press-rel/pr-2004/pr-05-04.html

Previous results had suggested there might be a small variation with time (on the order of 10 parts per million) - this would be big news if it could be confirmed, but the latest results do not confirm it.

The fine structurce constant is a dimensionles quantity equal to the square of the electron charge divided by planck's constant (hbar) times the speed of light, so any change in 'c' would affect the fine structure constant unless other fundamental constants also changed.

Because it's dimensionless, a change in the fine structure constant definitely reflects a change in the laws of physics, as opposed to a trivial change in units.

See

http://scienceworld.wolfram.com/physics/FineStructureConstant.html

for more on the fine structure constant.

15. Oct 11, 2004

### pervect

Staff Emeritus
Fine structure constant and it's relation to 'c'

One thing that I've been thinking about more is the significance of the fine structure constant, and it's relation to the speed of light.

One way to change the "speed of light" is to change the defintion of the meter. But this is just a "units change". So let's determine the speed of light in some fundamental units that arise from the properties of matter.

This means that we take the view that the properties of matter are constant with time. It is possible to imagine that the universe is not expanding, but rather that atoms are shrinking. But this leads us into an endless circle if we want to talk about speeds. Since we are made out of atoms, it is a reasonable idea to take the size of atoms as defining our distance and time scales.

The length scale is easy - let's use the Bohr radius, the radius of the hydrogen atom.

The time scale turns out to be a little bit tricker, but not much. The hydrogen atom has several characteristic frequencies of emission. The reciprocal of a frequency of emission is a time. So the first thought is to use the reciprocal of some characteristic "emission line" for our time unit.

We start off with the Balmer formula for the spectral frequencies of hydrogen

http://scienceworld.wolfram.com/physics/BalmerFormula.html

We quickly find that the important constant here is the Rydberg constant

http://scienceworld.wolfram.com/physics/RydbergConstant.html

The Rydberg constant is in inverse meters - the characteristic time associated with it is just 1/(R*c). The Rydberg constant turns out to already incorporate the speed of light, since it is measured in units of inverse meters. We can see the 'c' inside the defintion of the Rydberg constant, our characteristic time scale is 1/(R*c) which does not involve the symbol 'c' at all.

So we conclude that the bohr_radius / (1/R) = bohr_radius * R is a truce constant of nature, which we can think of as determining 'c' in units related to the basic properties of hydrogen, the Bohr radius, and the Rydberg constant.

We modify this formula just slightlly, by using Rinf rather than R, which eliminates a factor of the mass ratio of the proton to the sum of the mass of the proton and the electron.

When we work out the value of the bohr radius * Rinf, we get a multiple of the fine structure constant.

bohr_r = $$\frac {4 \pi \epsilon_0 \bar h ^2}{m_e e^2}$$

Rinf = $$\frac {m_e e^4} {8 c \epsilon_0 ^2 \bar h ^3}$$

I want to repeat myself here, and point out that the natural "time scale" associated with heavy hydrogen-like atoms is 1 / (Rinf *c). This is

$$\frac {8 \epsilon_0 ^2 \bar h ^3} {m_e e^4}$$

Note that this expression for the "natural time scale" does *not* include c!

[end edit]

Now we have argued that the bohr radius * Rinf is a constant, this value is

bohr_r * Rinf = $$\frac {\pi e^2} {2 \epsilon_0 \bar h c}$$

It's closely related to the fine structure constant, but differs by a multiplicative factor. The actual fine structure constant as it's usually defined is

http://scienceworld.wolfram.com/physics/FineStructureConstant.html

fine_structure_constant = $$\frac {e^2} {4 \pi \epsilon_0 \bar h c }$$

Let's put this another way - if we take the time interval that it takes a light beam to transverse a hydrogen atom (specifically the amount of time it takes light to traverse a bohr radius), and multiply this time interval times the emission frequency of some spectral line of hydrogen, we will get a constant. This constant is a multiple of the fine structure constant.

Last edited: Oct 11, 2004
16. Oct 11, 2004

### Prometheus

If the speed of light has been recognized to have changed not much, then it has been recognized to have changed. The amount of change is completely irrelevant.

You are operating under the assumption that 10 billion years is extremely significant in the life of the universe. What evidence do you/we have that this is definitely so?

17. Oct 11, 2004

### pervect

Staff Emeritus
You'd better go back and re-read what I wrote. The current experiments find no change.

See for instance Ned Wright's cosmology tutorial

http://www.astro.ucla.edu/~wright/age.html

(Theory + three separate experiments are discussed).

Speaking about evidence, why don't you try and present some? So far you've been making totally unsupported statements, and demanding that they be disproven.

18. Oct 11, 2004

### Prometheus

Notice the phrase "not much, if at all" in your post. If you re-read what you wrote, you left open the possibility of change.

He is making the assumption, which I consider faulty, that time in the entire universe is moving at the same rate. Why must this be so?

I agree that I have been making unsupported statements. You have been making statements with support. I reject your support. You need not accept my rejection. I have not demanded that you disprove anything. If you think that I have, please cite where I told you that you must disprove something.

We have estimated the age of the universe, here, in this part of the universe. Why should we consider that this is the age everywhere in the universe? If the speed of light were not constant, the then age of the universe could be considerably greater than we now believe; not here, but elsewhere in the universe. What evidence might support this? We recognize that we can only see some 4% of the universe. The rest is "dark", a euphemism for stuff that we do not understand. If the speed of light were not constant, the missing mass could be "hidden" at vast distances between here and the site of the Big Bang, even though we think that we can see the site of the Big Bang 14 billion years ago, according to our time frame.

19. Oct 12, 2004

### pervect

Staff Emeritus
OK, if you do decide to support your statments, let me know. Right now, I can't get very excited about your ideas because they seem to come out of the blue sky, like some sort of personal visonary experience, rather than being based on any observational evidence that can be the topic of a fruitful discussion.

20. Oct 12, 2004

### chronon

Note that if you are suggesting that the speed of light is different at different times/places, then you should make sure that what you are suggesting is a physical effect, rather than just a coordinate change. Look at the section on Manipulating Space-Time Diagrams in Ned Wright's cosmology tutorial http://www.astro.ucla.edu/~wright/cosmo_03.htm. In most of them the past lightcone (red line) curves, suggesting a changing speed of light, but this is just due to the selection of coordinates. The only one where it is straight is actually a pretty weird coordinate choice.