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Of course, things only got much better and clearer from reading Einstein's own words on his theories.
Now, more up-to-date dissertations on this subject can be found on some of our more recent pages: )

New for November 6, 2017: How well do modern scientists really know their Einstein? How many of the popular oft-recited mantras actually CONTRADICT his theories? Cosmos 8: "Journeys in Space and Time" The Universe: "Light Speed"

The Unraveling of E=mc²

E = m c²

As much as his ideas may have been a break-away from then-traditional "Newtonian physics", E=mc² by itself does not transcend Newtonian Physics. In fact, the equation can easily be derived from other equations basic to Newtonian Physics, where its meaning seems to be rather less than what was intended.

Of course the intended meaning is to show the relationship between energy and mass, and how much of one you can get from the other. I've always wondered exactly what the speed of light had to do with the conversion. That has also led me to question exactly what kind of energy Einstein sees the mass converting into through this equation. The tendency is to assume kinetic energy: the energy of movement, and to wonder whether the mass has "disappeared" by accelerating itself to the speed of light.

Let's dig into the math for a moment, to see where we end up if we don't transcend the easier-to-understand Newtonian Physics. What light it can shed on this equation? As you will see, it looks promising for a while, but then all falls apart....

(Or click on this link to skip the math and continue with the concepts).

A Newtonian Derivation

E = W

E = F d

E = m a d

E = m v v

E = m v²

But finally I stumbled upon what may be a good or partial answer, which I will talk about below. However, it really does require you to look beyond Newtonian Physics, specifically the speed involved in kinetic energy, for the more we truly understand the meaning of relativity, the less meaning speed has at all.

So what did we manage to wring out of Newtonian Physics? What is E=mv²? The kinetic energy of a mass moving AT a certain velocity? Not quite. To understand it as we've derived it, we have to back up a bit:

E = m

d t t

d

It is essential that we be able to square the d and t values separately, in order to simplify this equation to E=mv². The t values are simple. Both values are the same, and typically 1 second each, because we derived them from acceleration which is measured in metres per second squared. The t values came to us squared already. But what about the d values? The first d describes the value of the acceleration, the second the distance through which the force necessary for that acceleration must operate. These two values are not necessarily the same, and if they're not the same, we can't square them.

Of course, we could arbitrarily make them the same, as Einstein seems to have done. In that case we could square them, and get E=mv². If our identical d values were 10 metres, let's say, what would our equation describe? The energy required to accelerate a mass at 10 metres per second per second, over a distance of 10 metres.

Note that we're not actually describing a speed here. In fact, if our object started at rest, what speed would it reach after 10 metres? Well, it's not going to cover 10 metres in the first second, because it's still accelerating from zero up to 10 metres per second in the first second. So this acceleration through this distance will last more than 1 second, therefore the velocity will increase more than 10 m/s.

But what if our object doesn't begin at rest. What if it's already moving at 20 m/s when it enters the area of distance that we're measuring? It could cover our 10 metres in half a second at that speed alone, and it's accelerating on top of that. If it spends less than half a second in our measuring zone, it won't have time to increase its speed even by as much as 5 metres per second.

So, not only does E=mv² not describe a speed, it cannot either describe a specific change of speed independently of its "measuring zone", or frame of reference. Doesn't sound like E=mv² is a very useful equation, does it?

It does, however, prove one thing. If v is substituted with the speed of light, and we write E=mc², this now refers to the energy required to accelerate a mass either BEYOND the speed of light, if it began at rest at the beginning of our measuring zone, or a mass that was going faster than the speed of light to begin with and has gone yet faster still. Fascinating....

But we've still got an unchanging mass, and we're measuring the energy as a function of that mass's movement: kinetic energy. The Newtonian law of conservation of mass is satisfied. And the Newtonian way of satisfying the law of conservation of energy is to say that, well, if it wasn't actually moving with that amount of kinetic energy, it could be, therefore when it's at rest, it has an equal amount of potential energy.

What's the maximum amount of potential energy any old lump of matter could have? Depends on how fast it can go, according to Newtonian physics. It could be anything. It could be infinite. And E=mv² has not given us any reason to limit this; quite the reverse in fact.

But Einstein tackled this in his conversion theory, then gave us E=mc². And perhaps a finite mass, if it is converted into energy, should produce a finite amount of energy. Does that then limit its top speed to the speed of light?

It shouldn't. Remember, E=mv² is not about converting mass into energy. It's about measuring the amount of energy required to accelerate it smoothly over a given distance.

If E=mc² is true as a mass-energy conversion principle, then we must recognize that it's not really about the KINETIC energy of anything moving at the speed of light. But the speed of light has since become a bizarre lightning rod for theories and scientific thought for the past century, and is long overdue for a lot of extra scrutiny.

Now, what's interesting is that I wrote down the above theory of mine that I've had for some time, supposedly as an argument against one of the popular interpretations of Einstein's Theory of Relativity, then I went and visited http://leiwen.tripod.com/theory.htm to further my understanding of Einstein, relativity, E=mc², and the speed of light. Lo and behold, I seem to have independently come up with one of the two fundamental postulates upon which Einstein's Theory of Relativity is based. In fact, this is the idea behind the name "Relativity".

See also Einstein Online - Principle of Relativity, this is a nice and succinctly written piece insisting that all space time motion is relative, and that there are no absolutes. Notice however, how the next page Einstein Online - The Relativity of Space and Time completely contradicts this by saying that moving clocks move slower than stationary ones - even after establishing that we have no way of knowing which ones would be stationary and which would be moving - we could only know that they all move relative to each other. Also grossly neglected are limitations of perception, where the time we think things happened is affected by the speed of light bringing sight to our eyes, versus the speed of sound bringing noise to our ears. (Note how many times the page uses the phrase "appears to be" instead of "is", which is quite typical of most in-depth explanations of relativity.) Then there's the whole mystery surrounding the speed of a nerve impulse traveling from the sense organ to the brain, and whether or not some kind of quantum superposition or time reversal occurs allowing the brain to perceive a sensation before the nerve impulse could possibly have transmitted it. These are factors. Special Relativity, however, ignores them to equate perception with fact.

So don't let anyone tell you that Einstein said that traveling faster than light was impossible. His work on relativity actually proves the opposite.

Gravity Holes

The whole concept of a black hole in space seems to depend on this idea. A star that becomes so massive that it collapses in on itself, concentrates its gravitational pull so much that light can no longer escape it, that's what a black hole is. The speed of light basically slowed down so much within it that it reversed itself. No light can come out of it, or pass through from behind it. It sucks it all in. Spooky. Dark. Completely black. A hole in the backdrop of space.

All gravitational bodies must be doing this to a small extent then. Not stopping light completely and more, but at least slowing it down a little. All stars are doing this now. Ours must be doing it.

I don't know how they're measuring the speed of light these days, but the first attempt to do so is neatly chronicled in the book E=mc² by David Bodanis, under the section "c is for celeritas". Basically they measured differences in the time it took for light to reach the Earth from the moons of Jupiter at different times of the year. In other words, that difference was based on a distance from one side of the Earth's orbit around the sun to the other. Their point of reference, or stationary marker, was the center of our solar system, the sun itself.

David Bodanis' "Biography" of the world's most famous equation is a great read about the history of many of the physicists, ideas, and other contributions leading to the formation of the equation, and its subsequent uses.

How much was the sun's gravitational pull affecting that speed? Have we ever been able to measure the speed of light without the gravitational pull of our own sun affecting that speed? Could we ever be able to measure the speed of light without the gravitational pull of the center of our galaxy affecting it? Are scientists taking these factors into account?

Perhaps the speed of light can be infinite, when free of gravity. Perhaps there is no real environment totally free of all gravity. Who knows. But these are the questions and concepts that fascinate me.

The Hyperspace Factor

The truly bizarre phenomenon that has been observed and must be accounted for, is that no matter what speed you travel at, light can always be found traveling at "c" relative to your frame of reference. The explanation offered that I don't buy is to suppose that the time/space continuum stretches or contracts to compensate.

Has anyone ever thought this: Perhaps light is always moving around us at every imaginable speed, but we can only perceive, with our eyes and instruments, the light that travels at c relative to ourselves. Anything else won't trigger our sensors and receiving apparatuses. (And if a black hole has gotten in the way, perhaps it's already "eaten" those photons that would have been traveling at the right speed to allow you to see it.)

Perhaps this sheds some light on what seems to be the real reason for the inclusion of "c" in Einstein's equation. The speed of light may operate like something of a 90-degree right angle in interspatial geometry, allowing one dimension to interact with another. "C" seems to have been an important element in the "Lorentz transformations" dealing with trans-dimensional geometry. Three or four physicists came up with these same transformations independently, including both Lorentz and Einstein even though neither of them were the first to do so, so they must have some validity.

Einstein's theories soon insisted on looking at more than just the three dimensions of space and one dimension of time that we all experience daily. Personally, I'm always keen to add one or more dimensions of choice (leading to parallel universes) to my own space-time continuum. Was Einstein laying the basis for these in physics when he proposed that there were actually nine dimensions in space, of which we only perceive three? His new physics takes into account movements and forces operating through all those dimensions, the ones we can't see being referred to as hyperspace. And perhaps you need the speed of electromagnetic radiation (a.k.a. light) in the Lorentz transformations to find out how a force or movement in a hyperspace dimension affects a force or movement or electromagnetic aggregation of energy into matter in the dimensions we're accustomed to. That's my best understanding of it at the moment. It feels unproven, and I'm not totally convinced yet.

In the best tradition of Stephen Covey's principles and 7 habits, we don't like this early draft view of the universe either, because it doesn't yet include your input. We want to hear your comments! You may contact Lyratek Arts and the author from this page:

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And yes, there is a bizarrely often-forgotten answer to my favourite fundamental question:
"The speed of light is constant relative to... what?"

Of course, it only got much better and clearer from reading Einstein's own words on his theories.
We discuss it in greater depth on some of our newer pages:

New for November 6, 2017: How well do modern scientists really know their Einstein? How many of the popular oft-recited mantras actually CONTRADICT his theories? Cosmos 8: "Journeys in Space and Time" The Universe: "Light Speed"

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