Re: The speed of light is NOT a constant?! A milestone in Physics?
 

There is a constant of proportionality; in this case, with these units, it's 1. But that's a deliberate consequence of the use of SI base units. Any combination of SI base units, by definition, when equated with a different (but dimensonally equivalent) combination of base units, automatically generates this result. But if we defined E in British thermal units (BTU), m in electron volts (eV; mass as energy is a consequence of the E = mc² equation), and c in astronomical units per fortnight (AU/fortnight), there is a distinctly non-unity constant of proportionality. So it's not as if scientists and mathematicians dreamed up these units, and one day, Einstein crunched the numbers and, magically, it worked. It was defined this way, because it's convenient.

And incidentally, if we're just talking about fundamental dimensions*, then of course it works—you wouldn't have much of a physical law, if the sides of the equation were dimensionally different.

So, basically, the equation doesn't change dimensions. Energy is defined fundamentally as [M][L]²[T]^-2, and mass is [M]. And if the speed of light (in a vacuum, to be precise) changed, then any quantities derived from it would also change proportionally—but the fundamental unit [L][T]^-1 would remain the same. So the equation would still hold, with a different c, which changes with time (and more than likely spawns a horde of differential equations describing some other previously-static quantities changing proportionally with time).

*Fundamental dimensions are units such as [L], [M] and [T] (length, mass and time, respectively), which form the basis for dimensional analysis.

Re: The speed of light is NOT a constant?! A milestone in Physics?
 

Im not quite following you here. The units of time (seconds) distance (meters) mass (kilograms) and energy (speed^2 x mass or distance x force)... were all defined before Einstein made the connection that nuclear energy E = Mass x speed of light squared.

the established SI units had no relationship to the energy stored in the bonds between protons and neutron

but it was not necessary to balance Einsteins equation - as you said, K = 1

how did the speed of light just happen to fit the equation perfectly, so it was not E= 1.2783729832987 * MC^2 ? or some other correction constant?

Thats the part that blows my mind!

The established SI units were more or less arbitrary. A second is proportioal to the rotation of the earth on its axis - a meter is about the distance from someones nose to their fingertip, a kilogram is about one cubic centimeter of something or other.... so how did those arbitrary units come out perfect for nuclear energy?

Re: The speed of light is NOT a constant?! A milestone in Physics?
 

Too much confusion - ouch it's hurting my brain. Well be careful, the meter is based off of how far light travels in 1/299792458 of a second, and a kg turns out to be defined by how much of a gravitational interaction exist between the earth and said mass. So it all boils down to defining units based on time and space measurements which is what E=mc2 is really all about. And the E is not just for nuclear energy! It describes any energy!! Its just in nuclear reactions the quantities of energy are more and thus measurable. I have more mass when I'm at the top of a roller coaster than at the bottom. Unfortunately it is not a measureable amount. E=mc2 is a mass energy equivalence for any type of energy!

Re: The speed of light is NOT a constant?! A milestone in Physics?
 

Still making Physics sound simple I see.

Re: The speed of light is NOT a constant?! A milestone in Physics?
 

Simplicity is all relative :rolleyes:

Re: The speed of light is NOT a constant?! A milestone in Physics?
 

no, that is not true. The length of the meter was not altered after Einsteins discovery in order to make the equation balance. The SI units were established before mankind realized that the speed of light was not instantanious. The established length of 1 meter had nothing to do with the speed of light or the mass of the earth.

and these units were already established long before Einstein realized that matter could be converted directly into pure energy - but his equation came out exactly perfect. Theres more to the root of this than meets the eye here. The odds of that equation just happened to come out perfect, without the need for a correction factor are infinity to one.

There is some deeper connection here. Ive never heard anyone attempt to explain what it is.

Before Einstein's equation, energy and power were defined in terms of how much energy it took to raise one gram of water one degree C, or how much energy it took to raise 1 kg of mass one meter above the earth. These things have nothing to do with the speed of light, or the energy contained in the mass of an atom.

Re: The speed of light is NOT a constant?! A milestone in Physics?
 

Actually, the metre is defined in terms of the speed of light in a vacuum, exactly as described above. The original definition of the metre was based on an the length of a pendulum with a period of 2 s, but that depended on the local force of gravity, and was amended instead to (an estimation of) the length of one ten-millionth of the distance between the equator and geographic north pole (which, coincidentally, was approximately the same). A bar was constructed to this dimension, and the definition was changed to use the bar itself as the standard. The definition changed over the years, as more precise ways of defining tolerances evolved (correction for temperature, deflection under its own weight, etc.). More recently, definitions based on a certain number of wavelengths of emitted radiation were adopted. Most recently, however, the metre was defined to be exactly the distance travelled by light in 1 s in a vacuum, which also depends on the speed of light, c, being defined as exactly (i.e. with no tolerance) 299 792 458 m/s.
Strictly speaking, mass isn't converted into energy. It is energy (of a different form). To convert between one representation and the other, we use a constant equal to c².
I think that the problem is a symptom of conflating the definition of energy to the definitions of the units of measurement of energy. We express energy in units that have a physical basis, because it's convenient to do so. But we define energy in terms of a variation on Einstein's famous equation. Consider this, the relativistic definition of energy:
E = γmc²
Where the Lorentz factor γ = 1 at v = 0. This equation defines all of the energy in the point mass. If this were a physical object, we'd be evaluating the sum of all sorts of energies, but here, since we're only considering a point mass at rest with respect to itself, we can exclude kinetic energy (v = 0), potential energy (w/r/t itself, no internal energy), thermal energy (no motion, so no heat), etc., since they're all zero. What we're left with is the trivial equation:
mc² = mc²
mc²/mc² = 1
Which is the unity constant of proportionality, provided that you're measuring everything in the same units. (Of course this presupposes that these relativistic equations are correct—but apart from the quantum scale, this is how it's defined.)

When incompatible units are being used, in order to maintain dimensional equivalence, you need to insert a conversion factor. But if you take your energy in J = kg·m²/s², mass in kg, and speed in m/s, your conversion factor is 1. It's all about the way the joule is defined in terms of the kilogram, the metre and the second. By definition, energy is expressed as above, and by definition, the dimensions are equivalent. The only way to reconcile these things is to set the constant of proportionality as unity.

The "trick", is, I suppose, realizing that E isn't just kinetic energy, for example—it's all of the energy. This works as long as you're consistent with the reference frame; if you have gravitational potential energy such that h = 10, then you also have to calculate (relativistic) velocity with respect to that point—and (after considering all energies present in the system) the energies will work out as Einstein and Lorentz predicted. This formulation is valid for Newtonian and relativistic mechanics, but not necessarily for quantum mechanics.

That's as deep as it gets. The bottom line is that we define the (SI) units in terms of each other, define the quantities (energy, etc.) in terms of the relativistic equations, and note that the dimensions of our equations are consistent.

Re: The speed of light is NOT a constant?! A milestone in Physics?
 

Tristan: I think you are still missing the elegance of Einsteins equation and the wonder of it coming out perfect.

1Kg of gasoline moving at 1M/S contains 1 Joule of energy.

Ok, Imagine if burning gasoline at 1 atmosphere of air pressure released an amount of energy = M * speed of sound^2. Wouldnt it strike you as odd that equation happend to come out exactly right, when the amount of energy stored in a Kg of gasoline has nothing to do with the speed of sound through the air at sea level?

Now that I think about it, I seem to recall there was something about the way Einstein derived his equation. You cannot accelerate matter to the speed of light, the amount of energy required to do so is infinite.

I vaguely remember the connection here. Now Im going to have to go look it up.

Re: The speed of light is NOT a constant?! A milestone in Physics?
 

My conclusion to all this discussion and the article is this:

There is only one constant, and that is change, which in itself varies.

AHHHHHHHHHHHHHHH!!!!!!!!! NOTHING IS EVER GOING TO BE CONSTANT!!!

:rolleyes::D

2 cents
-Joe

Re: The speed of light is NOT a constant?! A milestone in Physics?
 

You're saying 0.5 J of kinetic energy (1/2 mv²), and 0.5 J of other forms of energy, including potential (in the form of chemical energy, and maybe potential energy due to position), and rest mass (the energy stored as mass itself)?
If E_chemical = mv_sound² (which is false, but presented as an example), then it would strike me as odd for several reasons, not the least of which being that the speed of sound varies in air depending on the density (itself a function of temperature, pressure and composition). But that aside, there's a difference between the speed of sound (which is a relatively unimportant concept, as energy goes), and the speed of light (which relates to the equations that govern our definitions of energy); we can't substitute one for the other, and expect that the system will behave equivalently.

Re: The speed of light is NOT a constant?! A milestone in Physics?
 

I'd be careful with your comparison of the burning gasoline. E=mc2 is not implying that anything is done with the mass (True there may be a mechanism out there that can do this - but that's for another thread). Simply that mass and energy are equivalent. Experimental evidence is everywhere, but a common example is of a high speed particle moving relative to us. If we deliver some energy to that particle so it gains KE, instead of it going into its speed it winds up gaining mass since, as you mentioned, it can't never reach the speed of light. Those chaps at SLAC (Stanford linear accelerator) know this all too well, their electrons are 100's of times more massive than when they at rest.

Getting back to the units... How do we measure the speed of light? Well we have to use some units of distance and time, right? Not necessarily... We can also look at it from Maxwell's point of view consider only the electric and magnetic fields - which end up just using the permitivity and permeability constants of a vacuum. How are those defined? Teslas, meters, Amps, Newtons, Coulombs,... I bet I can throw some of those together and get Joules too. I guess I'm losing where I'm going here, but hopefully you get my drift.

I don't want to sound like a know it all - because I really don't!! This is just some of my take on it and I sadly enjoy having this keep my up at night.

Re: The speed of light is NOT a constant?! A milestone in Physics?
 

I think the way Einstein put it is "energy and mass are two forms of the same thing"

E=MC^2 is saying that a given amount of mass can be converted (translated? released...) into a specific amount of energy.

When uranium fission occurs the uranium atoms change into lead atoms. Only one proton or neutron is lost in the process, but the mass of that one proton is where all the 'nuclear energy' comes from. That proton is gone, converted into pure energy.

I thought I had an article that explained how Einstein's reasoning led him to the equation, but I cant find it. It might be something I read in a book. It had something to do with how matter warps space, and how matter cannot reach the speed of light. Thats why the equation comes out perfect with no correction constant needed. This is going to bug me until I can find the explaination.

Re: The speed of light is NOT a constant?! A milestone in Physics?
 

Nuclear reactions most definitely do not convert single protons or neutrons into energy.

When a nucleus of uranium (we'll use 235 for this example) becomes 236 and fissions, only the mass of the binding energy within the nucleus is lost and converted to energy.

The products for this reaction are 3 neutrons (which may continue the reaction) and two products that account for the remaining mass (a common example would be Krypton 89 and Barium 144).

However, even though the example shows that the mass in AMU's of a 236 uranium should equal that of (3 + 89 + 144), a small fraction of the mass is lost to energy (the energy between the 89, 144, and 3 that was once the 236 nucleus).

Re: The speed of light is NOT a constant?! A milestone in Physics?
 

some subatomic particle is lost in the conversion - at the moment I cannot find the equations

from Wikipedia:

http://en.wikipedia.org/wiki/E=mc^2

Re: The speed of light is NOT a constant?! A milestone in Physics?
 

I've to agree with you. I'm at work, i really can't access anything except CD ;) .
But i do have the papers that explain E=mc^2.
There is still a lot of research going on about this topic. I actually read the whole thread and now my mind is full of random questions too. But I'll try to make it as simple as possible and try not to raise anymore questions.
I do agree the fact that there is a relationship between the speed of light and the gravity. Although our astronomy is strong enough to see the planets, but i don't think its strong enough to justify the relationship between gravity and light, especially in space, yet. Everything can have a constant speed in Vacuum, but what if there is a resistance in the Vacuum. Yes I'm referring to a black hole here. Light cannot escape Black hole, and thats a well known truth. now the question is does it changes it speed when it approaches the black hole. It might it might not. There is no way to prove it as of now.

So the bottom line is

Anything in Vacuum can go in a constant Speed. Even light can.
But if theres a resistance in Vacuum (aka energy, I'm mainly talking about gravitational here) it can change. It might be a slightest change, but it does matter.

Please try not to confuse it with other rays, because there is a lot of difference between the frequency of each and every ray, and we are talking about visible light here.
And now heres something for you guys to think about.
Theoretically it is possible for a human hand to cross a wall, only if the frequency of the particles in human hand is same as the wall or vise versa :ahh: .