What is the significance of the speed of light squared?

joel86 · Jan 22, 2006

Hi, im a long time lurker, first time poster. I have been trying to understand Einstein's equation E= MC squared. I do not understand how Einstein figured that the mass must be multiplied by the speed of light squared to get a quantity of energy. Why the speed of light squared? I understand what the speed of light is, but why multiply it by itself? Can anyone give a non mathematical explanation of this ?

Saiph · Jan 22, 2006

Well, first the equation wasn't whipped up out of thin air. He didn't just say: And E=mc^2! It's a "derived" equation. You start with various known equations, like kinetic energy (1/2 mv^2) and others that arise in energy conservation experiments... and after about a page of math, you end up with e=mc^2 (or rather the full equation e^2=sqrt(m^2c^4 * p^2c^2) which states total conservation of energy in a system. second: why c^2? Units my friend! mass * velocity does not give you the units of energy (which are kg*m^2/s^2). <div class="Discussion_UserSignature"> --------------------SaiphMOD@gmail.com -------------------"This is my Timey Wimey Detector. Goes "bing" when there's stuff. It also fries eggs at 30 paces, wether you want it to or not actually. I've learned to stay away from hens: It's not pretty when they blow" -- The Tenth Doctor, "Blink" </div>

formulaterp · Jan 22, 2006

Well it's hard to explain without using at least a little bit of math, so bear with me. A few definitions: Mass is measured in kilograms (kg) Velocity or Speed is measured in meters per second (m/s), The speed of light is 300,000,000 m/s Force is measured in Newtons, which is (kg*m/s^2) Energy is measured in Joules, which is Newton-meters (N*m) So a Joule can be written as J = N*m If we substitute the formula for N we get J = (kg*m/s^2)*m We can further write it as J = kg*m^2/s^2 Now if we square the speed of light (c) we get c^2 = 90,000,000,000,000,000 m^2/s^2 In Einstein's formula E=mc^2, if we substitute the above, we get J = 90,000,000,000,000,000 kg*m^2/s^2 which satisfies the requirement for how we define Energy. So as you can see we must use c^2 in order for the units of measurement to work out. Now the obvious question is of course, why did we use c in the first place? We could have used any velocity, such as the speed of sound at sea level, and got the units to work. But the fact is, E is what it is. The value of E just happens to be equal to mc^2. Perhaps it has something to do with the very nature of the Universe. Perhaps it's coincidence. Maybe God just wanted it that way. Beats me, I'm no Einstein.

harmonicaman · Jan 22, 2006

And apart from mathematics; E=mc2 has some profound philosophical implications too! It states that everything in the universe (time, matter, energy, and even space itself) is all part of a grand interconnected system, and we have the ability to comprehend it! "The most incomprehensible thing about the world is that it is at all comprehensible." - Albert Einstein (1879 - 1955)

rhodan · Jan 22, 2006

second: why c^2? Units my friend! mass * velocity does not give you the units of energy (which are kg*m^2/s^2). I understand the mathematics, I did a thesis on this in highschool, so I think I have a grasp of the basics. Still, it remains puzzling to me why the speed of light is connected to how energy and mass are related, and I think that's the question of this thread. Why is it c^2 and not 6 or 13.86757^322? The relation has significance, and I too wonder if someone could explain it to me. But please dumb it down a bit, and just before you hit the continue button, dumb it down a bit again, if possible. <img src="/images/icons/smile.gif" />

Saiph · Jan 22, 2006

when I get time, I'll do what I can to dig up the derivation, and the reasoning behind it. The cheap way out is to say: Empirical evidence. We see such reactions, and the energy released vs mass loss is related by a proportionality constant equal to c^2. But i'll try to dig up the theoretical work (which came first). I'll probably get something out of it too. <div class="Discussion_UserSignature"> --------------------SaiphMOD@gmail.com -------------------"This is my Timey Wimey Detector. Goes "bing" when there's stuff. It also fries eggs at 30 paces, wether you want it to or not actually. I've learned to stay away from hens: It's not pretty when they blow" -- The Tenth Doctor, "Blink" </div>

joel86 · Jan 23, 2006

I think Rhodan worded my question better there . I think that even if I fully understood the mathematics behind the equation , I still wouldn't understand how the speed of light fits into it all. So maybe instead of asking " Why the speed of light squared ? " I should ask " Why the speed of light ? ". It may be true that thats just how the universe works, but how did Einstein discover this ? Was technology that advanced back then ? Astrophysicist Neil deGrasse Tyson says that E=MC^2 is not something that happens in your kitchen or in everyday life . http://www.pbs.org/wgbh/nova/einstein/experts.html So how did Einstein figure out how the speed of light fit into it all ?

rhodan · Jan 23, 2006

But i'll try to dig up the theoretical work (which came first). I'll probably get something out of it too. I'm looking forward to it, thanks Saiph.

newtonian · Jan 23, 2006

Saiph - thank you and I also look forward to it. Rhodan - Yes, it is puzzling why c^2 - I asked the question on this forum but got no satisfying answer. The ratio is real, not simply a human invention - although units, which are human concepts, are involved, as Saiph noted. I think this has to do with the fine tuning of our universe to favor the existence of stars and life - the many fine tuned ratios, including the ratios of the 4 forces of physics and the rate of universal expansion are extremely precisely fine tuned to allow stars and life to exist. To me, it indicates God is a scientist and a math genius far beyond the genius of discoverers of these math ratios - e.g. Einstein.

harmonicaman · Jan 23, 2006

In a famous footnote written in 1905, Einstein calculated precisely how much "E" (energy) was being converted into mass when "m" (mass) is accelerated to "c" (the speed of light), in a few simple lines he demonstrated that E = mc2. This also proved that a small bit of "m" held enormous "E" potential -- which led to the development of the atomic bomb! ...and that everything in the universe is relative, (based on the perspective of the viewer), which led to the TOR!

newtonian · Jan 23, 2006

harmonicaman - Yes, and the awesome amount of energy compared to mass means there was an awesome amount of energy incorporated into the big bang! Astronomers generally conclude our universe began with only energy - e.g. that it was too hot for matter to exist! Have you heard any estimate on the actual amount of energy incorporated into the big bang?

CalliArcale · Jan 23, 2006

<blockquote>In reply to:<hr />In a famous footnote written in 1905, Einstein calculated precisely how much "E" (energy) was being converted into mass when "m" (mass) is accelerated to "c" (the speed of light), in a few simple lines he demonstrated that E = mc2.<hr /></blockquote> Aha! Now I, too, understand how he came to use the speed of light to arrive at this equation. <div class="Discussion_UserSignature"> "People assume that time is a strict progression of cause to effect, but actually from a non-linear, non-subjective viewpoint it's more like a big ball of wibbly wobbly . . . timey wimey . . . stuff." -- The Tenth Doctor, "Blink" </div>

joel86 · Jan 23, 2006

Thanks harmonicaman , it now makes sense to me. I thought it was just a theory at the time , I didn't know Einstein proved it through experimentation. I thought that came later.

abhinavkumar_iitr05 · Jan 24, 2006

Dear harmonicaman Does your statement means that Einstein arrived at the equation after performing the experiment as joel86 consider then I am totally dissatisfied.As far as the term E=mc^2 is considered it came into existance only mathematically.The experiments on this was done after about 15-20 years in the form of development of ATOM BOMB. As far as I know Einstein came across the following equation only mathematically while seeing the effect of change of mass wrt velocity in the calculation for total enegy which comes out to be the sum of square root of p^2*c^2 and m^2c^4 where m is the rest mass.I had done the derivation. Einstein was no doubt a Great Mathematician but he never had performed the experiment before giving the theory.

rhodan · Jan 24, 2006

Actually, Einstein was a great thinker, but he sometimes needed help with the math work. He was just very good in theorizing about things. <img src="/images/icons/wink.gif" />

harmonicaman · Jan 24, 2006

Rhodan is right! Einstein relied on the equasions of Maxwell and Lorenz (and others) because he wasn't the sharpest tack in the box when it came to maths. The actual experimental proofs came later and continue even to this day! So far no one has been able to poke a hole in Einstein's theorems... His explanation as to how our universe works has withstood the test of time and current experimentation and observation have only verified his original ideas!

larper · Jan 24, 2006

<blockquote>In reply to:<hr />Einstein was no doubt a Great Mathematician but he never had performed the experiment before giving the theory. <hr /></blockquote> Relativity came about only through thought experiments. The one that led to E=mc2 is this: If I drop a ball from a height, it gains kinetic energy (K) as it falls. But energy must be conserved. This is accomplished by introducing the concept of potential energy (P) that indicates how much energy the ball has when it is at rest. This classic physics: E=P+K. So, I drop the ball. The potential energy is converted into kinetic energy. Now, I accelerate myself so that I am moving at velocity that the ball has after, say, 10 seconds. At that moment, the ball is at rest to me. It has no kinetic energy as far as I am concerned. But, it starts to accelerate away from me, gaining kinetic energy. This must come from its potential energy, or rest energy. But wait, 10 seconds ago I saw some of its potential energy converted into kinetic energy. Now it is starting over again...... He continued to think through this experiment until he derived the full equation that expresses the total amount of energy in a system, which is always E=P+K. E=mc2 is simply what is true when K=0. It was all theory until someone actually saw mass being converted into energy, and the amount of energy was exactly what is predicted by E=mc2. <div class="Discussion_UserSignature"> Vote Libertarian </div>

abhinavkumar_iitr05 · Jan 26, 2006

In reply to the statement Rhodan is right! Einstein relied on the equasions of Maxwell and Lorenz (and others) because he wasn't the sharpest tack in the box when it came to maths. Dear harmonicaman here I would like to tell you that Einstein was not only a great thinker but also a legendary mathematician too.The greatest proof of this can be easily seen when we go through the Theory of Relativity both Special as well General.What the theory is nothing but only the a total mathematical work.This is also probably a reason that he was not given the all important Noble Prize for this. So far ur statement The actual experimental proofs came later and continue even to this day! So far no one has been able to poke a hole in Einstein's theorems... His explanation as to how our universe works has withstood the test of time and current experimentation and observation have only verified his original ideas! is concerned I totally agree with u.There is ofcourse no holes in Einstein theorems.

jhawk648 · Apr 2, 2007

Here are my thoughts as to why the speed of light is used as a relationship between mass and energy. First of all... I can think of no situation where a release of energy DID NOT cause a movement of mass. And remember, creation of heat and propogation of electromagnetic waves is still movement of mass... even though people don't tradionally think of these processes as movement of mass. So one could therefore practically define energy as simply the movement of mass. If you assume that no object can travel faster than the speed of light... then you could therefore assume the maximum ammount of energy it would possess would be its energy at the speed of light. And since E=MC^2 is the direct conversion of mass into energy... this would make sense. However, I am still confused as well as why this quantity is squared. Could it be that Speed by itself is a two dimensional quantity.... and energy can only exist in four dimensions... therefore needing to square the two dimensional quantity to make it a four dimensional quantity... I do not know. Very confusing questions. Very confusing.

spacester · Apr 3, 2007

The classic equation describing an orbit in terms of kinetic and potential energy is called the 'Vis-Viva' equation. It dates from the 17th century, formulated by Leibniz, who was a very influential philosopher in his day. From the latin: 'vis' = power 'viva' = life So Leibniz named his equation 'The Power of Life'! This was a rather mystical equation and had the same sort of effect on contemporary thought as Relativity does today. A lot of people pondered this equation for a long time. One of the keys to the equation is the demonstration that velocity squared is specific energy. Specific energy is the energy of an object divided by the mass of the object. It allows you to treat all objects orbiting the same parent body the same, just like with deltaV calculations. So I'm thinking that Einstein started from the vis-viva equation at some conceptual level. Another thing worth mentioning is that the definition of kinetic energy: K = 1/2 m * v^2 is very similar to E = m * c^2 So I guess my answer is that people had been squaring the velocity for over 200 years. But going from Newton's equation for kinetic energy to Einstein's equation is still quite a leap forward. <div class="Discussion_UserSignature"> </div>

yevaud · Apr 3, 2007

Ah, actually it's "Vis-Visa," not Viva. <div class="Discussion_UserSignature"> Differential Diagnosis: "I am both amused and annoyed that you think I should be less stubborn than you are." </div>

spacester · Apr 3, 2007

Um, I don't see an emoticon. You're serious? Google is your friend. <div class="Discussion_UserSignature"> </div>

yevaud · Apr 3, 2007

He referred to it as several things: Anima Motrix (Motive Soul), Vis Motrix (Life Force), and yes Vis Viva. And, from Moons and Planets (Hartmann, 3rd edition - standard college text), "Vis Visa." <div class="Discussion_UserSignature"> Differential Diagnosis: "I am both amused and annoyed that you think I should be less stubborn than you are." </div>

spacester · Apr 3, 2007

Well, you said it was NOT Vis-Viva, but I can come up with a dozen web links to that term, whereas I only find one reference to 'vis-visa'. And that's a Wikipedia page with what looks to be a typo. Google really is your friend <img src="/images/icons/laugh.gif" /> Textbooks can have mis-prints, you know. Do you have the errata sheet for that book? <div class="Discussion_UserSignature"> </div>

yevaud · Apr 3, 2007

I still possess the book, used in Solar, Planetary and Space Science 202. Thanks for your "correction." <div class="Discussion_UserSignature"> Differential Diagnosis: "I am both amused and annoyed that you think I should be less stubborn than you are." </div>

What is the significance of the speed of light squared?

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