Has C ever been derived from knowing E & M?

[Tyrannical]

Ok, I know e=mc^2, so c = √(E/m)

I know we usually use fancy laser setups to measure how fast it travels in a vacuum, but has c ever been accurately derived from knowing e & m?

 

[Drakkith]

Sure. Take a 10 kg mass. It's energy is equal to 898,755,178,736,817,640 joules.

So take that value and plug it back into the equation. E above divided by 10 = 89,875,517,873,681,764. Square root of that = 299,792,458, or c.

I don't know if that's "deriving" c, but that's how you would calculate it based on having energy AND mass already.

 

[Tyrannical]

Obviously no one has ever converted 10kg of mass into pure energy and measured it.
Have we ever been able to convert a known mass into energy and accurately measure that energy output enough? I want to know if C has ever been independently verified based solely from M & E measurements.

 

[Drakkith]

Ah ok. I believe they have been able to measure the amount of mass lost during nuclear reactions and converted into energy.

 

[Tyrannical]

Looks like MIT did something similar here solving for M. But they plug in the same old derived value of C and never solve for E.

http://web.mit.edu/newsoffice/2005/emc2.html

In the famous equation, E stands for energy, m for mass, and c for the speed of light. "In the test, we at MIT measured m, or rather the change in m associated with the energy released by a nucleus when it captures a neutron," said former MIT graduate student Simon Rainville.

The NIST/ILL scientists, led by Hans B̦rner of ILL and the late Richard Deslattes of NIST, measured E. (The speed of light is a defined and therefore exactly known quantity, so it was simply plugged into the equation.)

Specifically, the ILL/NIST team determined the energy of the particles of light, or gamma rays, emitted by the nucleus when it captures a neutron. They did so using a special spectrometer to detect the small deflection of the gamma rays after they passed through a very pure crystal of silicon.

The mass loss was obtained at MIT by measuring the difference between the mass of the nucleus before the emission of a gamma ray and after. The mass difference was measured by comparing the cyclotron orbit frequencies of two single molecules trapped in a strong magnetic field for several weeks.

 

[Drakkith]

Is there a reason the measured value of c doesn't work for you? Are you just curious?

 

[I like Serena]

Ok, I know e=mc^2, so c = √(E/m)

I know we usually use fancy laser setups to measure how fast it travels in a vacuum, but has c ever been accurately derived from knowing e & m?

Well, actually c has been derived from 'e'lectro 'm'agnetism, that is, from 'ε' and 'μ':

c = 1 / √(ε₀ μ₀).

 

[Dale]

We can measure speeds much more precisely than we can measure mass. The proposed approach doesn't make any sense. You use more precise measurements to determine less precise measurements, not the other way around.

We measure E and c to determine m. Switching that around would be possible but futile.

 

[Tyrannical]

We can measure speeds much more precisely than we can measure mass. The proposed approach doesn't make any sense. You use more precise measurements to determine less precise measurements, not the other way around.

We measure E and c to determine m. Switching that around would be possible but futile.

I think that deriving C from a measured value of E & M would help prove that no unknown forces acts upon the speed of light when we conduct terristrial laser light speed measurements.

 

[f95toli]

It is perhaps worh pointing out that it is not possible to measure the speed of light. c is defined to have a certain value and it is not possible to perform an experiment that can measure it "independently" of the other units in the SI.
This is just the way the SI works, and it will be true even after the SI is revised in a few years time (note that one consequence of this revision is likely to be that there will be an uncertainly in the value of mu).

Note that I am also referring to practical experiments here. Even if we were to pretend that we didn't know the value of c we would encounted the problem none of the other units SI can be realized with enough precision to give us a "better" value than the current definition, only a few of the other units can be realized with a precision better than 1 part in 10^9 (only two that I can think of: the second and the volt, and the latter is strictly speaking not a base unit). We can't measure mass better than about 1 part in 10^8 (and then only by referring to the artifact).

 

[Dale]

prove that no unknown forces acts upon the speed of light

Forces act on masses, not speeds. Your comment doesn't make any sense.

 

[Keep_i_real]

c is known exactly, as the metre is defined in terms of c and the second (which is defined in terms of the rate of hyperfine transitions in caesium-133 atoms).

c = 299792458 m/s exactly.

c can't be "measured" as such, as we know it exactly - when we "measure" the speed of light, we're actually measuring how long 299792458 metres is.

 

[Integral]

Well, actually c has been derived from 'e'lectro 'm'agnetism, that is, from 'ε' and 'μ':

c = 1 / √(ε₀ μ₀).

In the 1860's when Maxwell derived his famous set of equations, he cast them in the form of the wave equation and found this expression for the speed of Electromagnetic waves. He was surprised when he evaluated it and found it equal to the then accepted value for the speed of light. This was first real evidence that light is electromagnetic in nature. Further since it involved basic constants, it was independent of any coordinate system. This started the "great schism" in physics. It was not until Einstein's work that E&M was unified with Mechanics.

 

[Tyrannical]

In the 1860's when Maxwell derived his famous set of equations, he cast them in the form of the wave equation and found this expression for the speed of Electromagnetic waves. He was surprised when he evaluated it and found it equal to the then accepted value for the speed of light. This was first real evidence that light is electromagnetic in nature. Further since it involved basic constants, it was independent of any coordinate system. This started the "great schism" in physics. It was not until Einstein's work that E&M was unified with Mechanics.

Well, thanks for that great answer.

But I am curious to know how many decimal places that the derived speed of light differs from deriving it from the measured mass and energy. If e=mc^2 is correct, then deriving each variable from knowing the other two should give you a measure to how well you can accurately measure those three variables.

 

[f95toli]

Well, thanks for that great answer.

But I am curious to know how many decimal places that the derived speed of light differs from deriving it from the measured mass and energy. If e=mc^2 is correct, then deriving each variable from knowing the other two should give you a measure to how well you can accurately measure those three variables.

But that is a calculation that would not be very meaningful because of the uncertainties involved; it is impossible to measure m with an accuracy better than at most a few parts in 10^9 (because that is how well we know the mass of the standard kilogram) and the only measurements that involve E but not c that I can think of would have an uncertainty of a few parts in 10^8. So unless the values are off by a lot (say a part in 10^7) you wouldn't be able to detect it.
Note that there are plenty of spectroscopy experiments that would not make sense if there was a large error.

 

[Keep_i_real]

c is known exactly, as the metre is defined in terms of c and the second (which is defined in terms of the rate of hyperfine transitions in caesium-133 atoms).

c = 299792458 m/s exactly.

c can't be "measured" as such, as we know it exactly - when we "measure" the speed of light, we're actually measuring how long 299792458 metres is.

Due to how our units are defined, c is fixed - its only dependence is the rate of ground-state Cs-133 hyperfine transitions. In trying to measure the speed of light, you're actually measuring how long a metre is!


Light travels 299792458m exactly (ignoring QED) in a vacuum, per second.

A second is defined as "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom"

Therefore, the speed of light is exactly the distance that light travels relative to an inertial reference frame in the time that it takes for "9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom" to occur in an inertial frame; A metre is 1/299792458 of that distance.

Due to quantum mechanics imposing a slight uncertainty in the definition of the second, and QED imposing a slight uncertainty in the actual velocity of light, our units aren't exactly defined in the mathematical sens of exact, however its unlikely we'll ever be able to measure time/distance/speeds accurately enough for the uncertainty to be noticeable.

Could someone with a better understanding of QM/QED/SR confirm this please :)

-Mark

 

[xienohp]

You can measure c if you define m and E first, as someone before said c is defined first.
However, you may use fission to deal with that.
consider 1g of u235, you bombard a neutron into it to trigger the alpha decay. You Put the whole setup inside a water bath with temperature T,and you weight the setup. Measure T with known heat capacity you know delta E, and you now delta M. take more values until you can plot a E-M graph. Of course it is a very ideal thought, but it is more portable than measure 10g of mass totally transfrom into energy.

 

[Keep_i_real]

You can measure c if you define m and E first, as someone before said c is defined first.
However, you may use fission to deal with that.
consider 1g of u235, you bombard a neutron into it to trigger the alpha decay. You Put the whole setup inside a water bath with temperature T,and you weight the setup. Measure T with known heat capacity you know delta E, and you now delta M. take more values until you can plot a E-M graph. Of course it is a very ideal thought, but it is more portable than measure 10g of mass totally transfrom into energy.

Your problem there is that not all the converted mass becomes heat - some escapes as gamma rays. Also, the heat capacities aren't known anywhere near as accurately as they'd need to be! Nice idea though