# Necessity of Constant c.

1. Jan 30, 2009

### matheinste

Hello all.

While browsing Lorenz and Poincare Invariance - 100 Years of Relativity, I came across the followng:- -----The meter is the length of path traveled by light in vacuum during a time interval of 1/299,792,458 of a second----- This is, i believe, the generally accepted definition. Then the following-----As stressed by Leon Hsu, "The Principle of Relativity implies that the speed of light is a universal constant if and only if time is measured in units of meters"------

Two questions.

Firstly: Is this a respectable source? It seems authoritative if perhaps somewhat unconventional in that other derivations of Relativity are discussed.

Secondly: If the quote can be taken seriously why should it be the case that the units used for light speed matter?

Matheinste.

2. Jan 30, 2009

### Staff: Mentor

Leon Hsu is wrong. The above definition of the meter came 78 years after Einstein proposed the postulates of relativity.

3. Jan 31, 2009

### matheinste

I don't quite see how your second statement is relevant to your first statement.

Matheinste.

4. Jan 31, 2009

### The Dagda

The second is defined as the time it takes a caesium atom to go through a set number of perturbations. Does that really sum up why 1sec=1/3600 of an hour? I'm not sure what you are asking here, we have two constants in this case, the second and the speed of light, yes using that standard the measure is correct.

If 299,792,458 mps^-1 is measured in m and s? Isn't that like asking why ten centimetres should be measured in centimetres?

5. Jan 31, 2009

### Staff: Mentor

How could the principle of relativity be limited to a specific definition of the meter when that definition of the meter came 78 years later? It is an absurd assertion.

What would be correct to say is "if you measure time in seconds and distance in meters then the postulate becomes a tautology". But just because it is a tautology in one system of units does not mean that it is not also valid in other systems of units.

6. Jan 31, 2009

### matheinste

Hello DaleSpam and The Dagda

I think we are at cross purposes. I understand the definitions of the meter and the second and light speed and their intrelationship. I have no problem with them. The definition of the meter was included in the quiote because it seemed appropriate and in context. This is the quote without my comment.

Quote.
The meter is the length of path traveled by light in vacuum during a time interval of 1/299,792,458 of a second. As stressed by Leon Hsu, "The Principle of Relativity implies that the speed of light is a universal constant if and only if time is measured in units of meters"
Unquote

The bit i was worried about is

Quote
As stressed by Leon Hsu, "The Principle of Relativity implies that the speed of light is a universal constant if and only if time is measured in units of meters".
Unquote.

It seems odd to me and i was seeking clarification. It may be making a point that is beyond me or it may be plain nonsense. Is it nonsense, or, if it is not nonsense, what does it mean. That was what i was asking.

If it is nonsense i will be quite happy and there is no more to be said.

Matheinste.

7. Jan 31, 2009

### The Dagda

Well I think you can measure light speed in any length you chose, that is arbitrary, whether it's chains per second, or furlongs per second or whatever. I think it might be a misunderstanding with the text. If the metre is defined as x, and light speed as c, then by definition it must be cx/t. But you could substitute x with anything and t likewise, provided it agreed with what we observe, and what we observe are observed in terms or related to d and t, the units are arbitrary, you could use $\sigma$ and $\tau$ if you wanted, whatever you wanted them to be. c however is a constant, so we assume it is constant regardless of x and t, it could change over time, but there's no way of knowing that.

8. Jan 31, 2009

### Staff: Mentor

It is nonsense. First, in the SI system of units time is measured in units of seconds, not meters. Second, although the principle of relativity is a tautology for the SI system (using today's definition of the meter) it applies for all systems of units (including older versions of the SI system).

9. Jan 31, 2009

### matheinste

Thankyou both for clearing that up.

I am glad that someone else thinks it is nonsense.

Matheinste.