# The argument of the change of units

1. Nov 2, 2012

### bloby

Hello.
I have a problem with the statement that specific values, like the speed of light, have no meaning because we can change
these values by a change of units.
For measures attached with units the value(number) has no meaning "per se", I'm ok with that. (Unlike pure numbers like
ratios of masses) But the number WITH the unit HAS a meaning: asking the question why the speed of light is 186000 mps
is the same as asking why it is 300000 km/s but different from 187000 mps.
What do you think?

2. Nov 2, 2012

### ghwellsjr

The point about the speed of light is that all inertial observers who use the same unit for length and the same unit for time (whatever those are) will determine that the speed of light is the same for each of them, even if they are moving with respect to each other. Of course the value that they determine does not have to be in mps or km/s but if they can relate whatever unit they used for length to miles or meters and whatever unit they used for time to seconds, then they will get the same answer as if they were using standard units.

Put it this way, if an ET on a far distant planet measures the speed of light without any knowledge of the units we use and then we were able to get our rulers and clocks together, we would be able to compare our units and we would agree on the speed of light.

3. Nov 2, 2012

### bloby

Ok, here is a quote from someone(no personal attack):

"As a dimensioned quantity (that is, it has units of speed, as opposed to being a pure number), the speed of light's numerical value is, to some extent, not meaningful. The speed of light takes on a whole range of values depending on different unit systems (from SI to imperial and more), and often, relativists will choose a unit system in which c=1 precisely because they are free to do so and because it is convenient. So in some ways, asking why the speed of light isn't larger or smaller is to ask why we don't use a different unit system.

Put it this way: if the speed of light were actually twice as fast, but we used a definition of the mile that were twice as large, that wouldn't yield any difference in the measured value of the speed of light."

I saw this argument several times and I think it wrong. Am I missing something?

4. Nov 2, 2012

### ghwellsjr

It looks to me like the person is saying, "If we lived in a different universe with different physics, then things could be different." But we live in this universe where the measured speed of light is now used as one of the units instead of the standard meter stick that used to be a standard.

What specifically in the argument do you think is wrong?

5. Nov 2, 2012

### bloby

"So in some ways, asking why the speed of light isn't larger or smaller is to ask why we don't use a different unit system."

Because the speed of light is independent of the unit, unlike the speed of light's numerical value.

6. Nov 2, 2012

### bloby

Then the question is: is there a reason for this specific speed? One answer could be

But units have nothing to do with that...

7. Nov 2, 2012

### Pengwuino

Let's put it this way. Let's assume you live in a country with 3 different currencies, the "dollars", the "peso", and the "cubit" (ignore the fact that the first two are real currencies, I'm too lazy to think up fun names) with a conversion rate of 1:2:3 (1 dollar = 3 cubits, for example). Let's say you're asked to do a job for someone and they say they will pay you 200 dollars. With the conversion in mind, they could just as easily pay you 600 cubits or 400 pesos. The numerical values and the "units" are all different, but they each represent the exact same amount of work. The work is the physical thing.

As for the argument you posted earlier about whether or not you'd notice if the speed of light double but the length of the mile was doubled, you WOULD notice a difference. The mile (and the second) are all part of a system of measurements. You have things like energy, temperatures, force, etc. whose standard values are all pegged against each other in a consistent manner. If all of a sudden our idea of how long a mile is changed, everything else would stop making sense in regards to our current measurements/data of everything.

8. Nov 2, 2012

### ghwellsjr

I'm really having a hard time trying to figure out what you are asking about.

Are you asking about why nature is the way it is or are you asking about something regarding our specific way of measuring nature?

9. Nov 2, 2012

### bloby

Pengwuino I agree with you,

it's not my argument, it's the argument I quoted and I think, as you do, that there is a difference

10. Nov 2, 2012

### bloby

Thank you for the effort. The general question is "why is the speed of light 300000km/s?" but it's not my question. My question is "is the argument I quoted post #3 true?". You can change
the value by changing units but there is something more in the speed, like the work in the
analogy of ghwellsjr. I don't mean to answer the question of the speed of light, just rule out
the argument "speed of light <-> unit chosen".

11. Nov 2, 2012

### PAllen

A way to look this question to see why most physicists say only dimensionless constants are fundamental:

Suppose you could communicate with an alternate universe similar to ours and wanted to determine whether the speed of light was the same there as here. How would you do it? We have two types of length measures:
- those defined using light, which will come out the same
- those related to happenstance features of earth and our size, which are incommunicable,
(unless we relate them to light, creating a tautology).

Instead, if you relate light speed to something fundamental, you can ask the question. But then you have created a dimensionless constant. You could do something direct, like 'ground state hydrogen radius per a specific measurement process'. However it is much more convenient, and works out to be equivalent, to come up with a dimensionless constant relating light speed to other constants involved in hydrogen atom behavior (Planck's constant, elementary charge, etc.). The most common one chosen for this is the fine structure constant.

Last edited: Nov 2, 2012
12. Nov 2, 2012

### pervect

Staff Emeritus
Let's say you change the definition of the meter. Every atom and structure in the universe doubles in size. Is this change a meaningful one to physics?

I would say no, it isn't. Experimentailly it wouldn't be detectablle.

Apparently there are some professional physicists who think Duff goes too far in some of his remarks. But at the minimum, one can say that changing units CAN affect dimensionful constants like the speed of light, (we can see this by just changing from miles/hour to meters/second), and that talking about quantities with no dimension is a good way to avoid such concerns.

IT's easy to change the size of atoms without even realizing it, giving rise to unintended consequences, some of which one can waste a whole lot of time arguing over the interpretation.

So, Making sure you change only dimensoinless quantites MAY be over-conservative. (It isn't if you believe Duff). But it's certainly a very simple way of being _sure_ that you've actually changed the fundamental physics, and not simply relabeled standard physics with a unit change and called it "new and improved".

Regardless, a lot of the serious discussion of what could be interepted as "changing speed of light is going to occur in a place where one might not expect to look for it - in discussion of changing the fine structure constant. So it's good to know where the issue is discussed, I think, so one can reseearch it properly.

Last edited: Nov 2, 2012
13. Nov 2, 2012

### bloby

In this analogy I see someone ask "why does the light earns 200\$?" I find the question interesting but someone else say 200 is not meaningful, depends on currencies. But I think what is interesting is "is there a reason the work(analogy) done by light have this value?"

14. Nov 2, 2012

### ghwellsjr

Yes, it is true--provided that you understand what is being said. He's saying that if there was another universe side-by-side to ours in which the speed of light were doubled what it was in our universe and it happened that people in that universe happened to have defined a unit of length called the mile that was double what our mile was, but their unit for seconds was the same as ours, then they would also measure the speed of light to be 186000 mps. He's not addressing how anything else would be effected which is what Pengwuino was talking about.

15. Nov 2, 2012

### bloby

16. Nov 2, 2012

### bahamagreen

The question is not about the numbers (which could be anything), it is about the magnitude... that light moves at a certain speed in any set of units.

Imagine you were as big as a galaxy... the Milky Way and Andromeda are like two dinner plates only 20 feet apart with light taking 200M years to cross... light would seem to move very slowly.
If you were the size of a molecule, light would seem to go very fast.

The "feeling" about how fast light travels is pretty much determined by your size.
The anthropomorphic principle suggests that you have to be some size, so asking why c is what it is becomes the same as asking why you are a particular size, rather than smaller or larger.
All conscious intelligent things we know of so far seem to require certain physical, chemical, electrical, and mechanical conditions that operate at our scale of size; so it's not just convenient that we are the size for which that stuff works; it looks like we have to be this size in order to be here and ask about it. Along with that size comes the relative magnitude of c and many other things.

17. Nov 2, 2012

### bobc2

The question of the speed of light has to do with the fundamental structure of the 4-dimensional universe.

Consider all objects, including a photon of light, to be 4-dimensional objects having very small X1, X2, and X3 measurements while extending some 10^13 miles along their 4th dimensions. These long time-like paths through the 4-dimensional universe are often referred to as world lines.

And along with that, consider the strange and curious way in which nature has worked out the instantaneous 3-D cross-section views of the universe experienced by observers moving about at various speeds relative to each other. The sequence of space-time diagrams below shows observers (blue coordinate inertial frames) moving at ever increasing relativistic speeds relative to the black rest frame (increase in clockwise rotations corresponds to increasing speed along the black X1 axis--time increasing along the X4 axis). The slanted X4 axes represent the world line paths through 4-D space while the X1 axes represent the instantaneous cross-section views across the 4-D space experienced by the observers (the 3-D worlds the observers live in at a given instant of time).

The photon is always represented by a world line slanted at a 45-degree angle with respect to the black rest frame. It always bisects the angle between the X4 and X1 axes for any observer (no matter what his speed, i.e., the slant of his X4 axis). Thus, the 4-dimensional photon has THE unique orientation among all 4-dimensional particles. It's angle-bisecting slant is unique--giving a ratio of dX4/dX1 = 1 in the inertial frame for any and all observers.

The arbitrary accidental calibration assignment of clocks (sec, min, hours, days, years, etc.) along the X4 axis results in our numerical value for c.

Why and how did nature manage to work out such a rule of rotating X1 axis to provide the 3-D world that an observer should experience? Who knows. But, one thing that is accomplished by that (in addition to having the same c for all observers) is that the laws of physics then are naturally the same in all inertial frames (no matter how X4 is slanted).

18. Nov 2, 2012

### grav-universe

One could let light travel some arbitrary distance and define that as a unit distance per unit time, or one could let light travel twice as far and define that as a unit distance and unit time instead in the same way, so there is no absolute distance or time that light travels, just as there are no absolute units of distance or time to begin with, only as they are quantified as defined. With any arbitrary quantity of units applied, since light speed is finite rather than infinite, some ratio of units of distance to units of time will be found, right, but in any case, it is better and simpler to think the other way around, that light travels at a finite maximum unit speed, the limiting speed c, without any absolute numerical quantity applied except perhaps unity, and all other bodies travel at some fraction of c between 0 and 1.

Last edited: Nov 2, 2012
19. Nov 2, 2012

### Staff: Mentor

I am sorry that you have a problem with it, but it is correct. The question is whether dimensionful numbers are physically meaningful or not, and if not, how to make them meaningful.

So, I can say that something has a velocity of 5 farks. Does that statement have any meaning? Clearly not. I can give it some meaning by telling you that the air-speed velocity of an unladen swallow is 1 fark. However, once I do that, I have actually provided not a dimensionful number, but a dimensionless quantity. It turns out that any way you attempt to give meaning to the quantity 5 farks requires that you provide such a dimensionless quantity.

20. Nov 2, 2012

### bahamagreen

I think this misses the point of the question. It's not about the numbers, but the proportions at a scale of reference...
Take an example; light traveling radially from the Earth's surface... the light travels about 25 Earth diameters per second. Don't think about the units or numbers, just visualize any handy sphere (like a globe, an orange, a pea) and notice the apparent speed in relation to the sphere at that scale.

For a globe one foot in diameter it takes light one second to go 25 feet - holding the scale of the globe as the Earth. That is the meaning of the question... why that proportion - why the particular scale we observe?