Einstein's C is for Constant, but what the @#$ is it?

[PJay_A]

I think one of the biggest mysteries of the Universe is Einstein's "constant", casually referred to as "c", as in E=Mc2 and the countless other very important equations in physics it found its way into thereafter. Other than an explanation of what exactly is "c" (constant), the best I ever hear as to what exactly it actually really is all comes down to the fact that it's a variable that makes equations in theoretical (and practical) physics work.

Yes, I know "c" also happens to be the speed of light, etc., etc., and so on, but why.... or how.... or what.... or even where and when is "c"? I challenge anyone here to come up with an explanation that could provide a tangible definition explaining what it is. We know many measurements depend on it and so much of what we know about the physical world requires its very existence. But what is it? We know what is affects, we see its footprints, we see how things are related to it, but, again, what is it?

Take two objects born moments after the Big Bang. At first they appear close, but (assuming they don't move) eventually are pulled far apart as the expanding Universe inflates the space between them. Though the two objects do not move, the expanding space between them give an illusion that the two are speeding away from one another faster than the speed of light, but neither is moving. In fact, if these objects could "see", neither would ever see one another - ever - because the light from the other could never catch up.

Where would "c" apply to the above example? Would "c" only be applied to the radiating light from the two objects? I think there's a lot more going on than we see, and that "c" plays a big role in whatever is actually happening.

 

[ramparts]

Well, c doesn't "happen to be" the speed of light. c is the speed of light. It was long before Einstein. I don't know who's telling you "it's a variable that makes equations in theoretical (and practical) physics work", but they're wrong (it's not even a variable - remember, it's a constant).

So what is it? Well, it's a speed. It tells you how fast something (light, or in fact any massless particle) travels, in units of length divided by time - so the length that something travels in a given interval of time. So asking what c is is kind of like asking what 90 mph is. It's the speed I'm driving on the highway as I type this post on my iPhone, but I don't think there's really a Platonic form of "90 miles per hour" that we can get at, so the question is perhaps poorly phrased.

Moreover, c is a fundamental constant of nature, which is why it appears in so many equations (including E=mc^2). Keep in mind that on both sides of any equation, the units have to be the same, so that tells you what kind of constants you have in an equation like E=mc^2. The units of energy are joules, or mass times length^2 (length squared) divided by time^2 (time squared). So in order to turn m (which has units of mass) into E, you need a constant with units of length^2 divided by time^2. Why is that constant the speed of light? Well, there are some fairly deep reasons for that, many of which unfortunately require a significant amount of study. But it has to do with the fact the speed of light is the fastest speed there is (in fact, I think that that fact comes from the speed of light being this fundamental scaling constant, rather than the other way around, but you can look at it either way). The speed of light is fundamentally engrained in the fabric of our spacetime.

If you're asking why it has its particular value rather than, say, 20 miles per hour, that's a question to which we don't have an answer, and may never have a satisfactory answer (besides the anthropic one - if it were significantly different, we wouldn't be here to see it).

 

[ramparts]

Also: we're not sure if "c" originally stood for "constant" (there are lots of other constants of nature, many of which we knew about before we started using "c"). It might have, but some also think it was used to mean "celeritas" - the Latin word for "speed". Here's an interesting Wiki article on the history: http://en.wikipedia.org/wiki/Celeritas. One of the nifty tidbits there is that Einstein used "V" to represent the speed of light. Oh well, it's a letter :lol:

 

[thebigcat]

All Albert did was take Sir Isaac's classic equation of F=mv^2 , force equals the mass times the square of the velocity, and do some substitution. The velocity in this case is the speed of light. We are inserting a constant, c, in place of a variable, v, so we need a different variable, E, to express the outcome. Energy instead of force because we are not dealing with Newtonian concepts any longer, even though the equation is derived from Newton. That's why Einstein originally had v in his equation instead of c.

 

[ramparts]

All Albert did was take Sir Isaac's classic equation of F=mv^2 , force equals the mass times the square of the velocity, and do some substitution. The velocity in this case is the speed of light. We are inserting a constant, c, in place of a variable, v, so we need a different variable, E, to express the outcome. Energy instead of force because we are not dealing with Newtonian concepts any longer, even though the equation is derived from Newton. That's why Einstein originally had v in his equation instead of c.

Except the equation you're referring to has a 1/2 in front (kinetic energy = 1/2 mv^2), is most certainly not the equation for force and that's not at all what Einstein did. First of all, Newton's classic equation for force is F=ma. mv^2 doesn't even have the right units for force, so it certainly can't be force. Moreover, force and energy are completely different things and have completely different units, so you can't just substitute one for another.

Now, the equation E = 1/2 mv^2 is the classical equation for kinetic energy - that is, the energy a body has in motion. The whole point of E=mc^2 is that it's a rest energy - objects always have energy, even when they're not moving (in fact, E=mc^2 no longer holds when an object is in motion). If it were just substituting c in for v, then that would be the kinetic energy from moving at the speed of light, which E=mc^2 absolutely isn't.

Finally, please don't use Einstein and Newton's first names if you have no understanding of their theories. That's Herr Doktor Professor Einstein to you, bud.

I'm not sure what physics class you've taken, but I think I need to have a chat with your teacher :lol:

 

[drwayne]

Dimensional analysis is a usefull skill to be sure. It doesn't show that you are right, but it
is very good at showing when you get things badly wrong.

(Like when you write something like F = m * v ^2, instead of F = m * a)

Wayne

 

[ramparts]

Exactly. On the other hand, dimensional analysis (that is, checking the units on both sides of an equation) won't do you much good for deciding, say, whether or not there's a factor of 1/2 in front of the mv^2 in the kinetic energy equation, or whether to use v^2 or c^2

 

[drwayne]

Exactly. On the other hand, dimensional analysis (that is, checking the units on both sides of an equation) won't do you much good for deciding, say, whether or not there's a factor of 1/2 in front of the mv^2 in the kinetic energy equation, or whether to use v^2 or c^2

Exactly. That is what I was mumbling about when I referred to a test that can tell you for usre whether
there is something wrong, but not whether what you have derived is "right".

The MKS units for force are kg m/sec^2, so if what you have derived as a force has units of kg m^2/sec^2,
you did something wrong.

Wayne

p.s. Regular readers have heard this before, but F = ma is actually a special case of Newtons law, which is

F = dp/dt

 

[dryson]

[quoteWell, c doesn't "happen to be" the speed of light. c is the speed of light. It was long before Einstein. I don't know who's telling you "it's a variable that makes equations in theoretical (and practical) physics work", but they're wrong (it's not even a variable - remember, it's a constant).

So what is it? Well, it's a speed. It tells you how fast something (light, or in fact any massless particle) travels, in units of length divided by time - so the length that something travels in a given interval of time. So asking what c is is kind of like asking what 90 mph is. It's the speed I'm driving on the highway as I type this post on my iPhone, but I don't think there's really a Platonic form of "90 miles per hour" that we can get at, so the question is perhaps poorly phrased.

Moreover, c is a fundamental constant of nature, which is why it appears in so many equations (including E=mc^2). Keep in mind that on both sides of any equation, the units have to be the same, so that tells you what kind of constants you have in an equation like E=mc^2. The units of energy are joules, or mass times length^2 (length squared) divided by time^2 (time squared). So in order to turn m (which has units of mass) into E, you need a constant with units of length^2 divided by time^2. Why is that constant the speed of light? Well, there are some fairly deep reasons for that, many of which unfortunately require a significant amount of study. But it has to do with the fact the speed of light is the fastest speed there is (in fact, I think that that fact comes from the speed of light being this fundamental scaling constant, rather than the other way around, but you can look at it either way). The speed of light is fundamentally engrained in the fabric of our spacetime.

If you're asking why it has its particular value rather than, say, 20 miles per hour, that's a question to which we don't have an answer, and may never have a satisfactory answer (besides the anthropic one - if it were significantly different, we wouldn't be here to see it).][/quote]

Perhaps a new revision to E=MC^2 needs to be put into play. We all know that light or ultraviolet radiation interacts with different mediums, whether that medium be a solid, liquid or gas where the UV light will penetrate the medium to a certain depth. Another medium that light travels through and is the biggest defining characterstics of light speed is gravity.

 

[ramparts]

Hi dryson - the speed of light doesn't actually change in different media - it just looks that way because it interacts with atoms, gets bounced and scattered around, so it appears to go a bit slower. But if you look deep down, on a microscopic level, the light is still just travelling at good ol' c

 

[Planet_Lubber]

The actual value of c depends on the units we use for time and distance. If we measure distance in light years and time in years, then c = 1.

Most of the units we have invented for measuring time and those for distance have nothing to do with each other. But if we want to think of time as a 4th dimension, there has to be a conversion factor. The most convenient is c, the speed of light, because then we get a metric for spacetime that has the nice property that physically meaningful quantities are invariant with respect to it.

The example with the two particles moving apart just after the Big Bang doesn't make sense because it is phrased in terms of things "not moving" and has an implicit assumption of simultaneity, both of which are heresies in relativity.

 

[drwayne]

Of course, you could simply ignore C and keep everything in terms of epsilon and mu,

 

[arkady]

I believe the OP is confusing C with Einstein's constant or Einstein's gravitational constant. The cosmological constant used in his field equations. It's denoted with the greek letter kappa though and not C.

It's the one he referred to as his biggest blunder, because it's based on the idea of a static universe. An idea he had to abandon when a certain mr. Hubble came along and showed us that other galaxies appear to be receding away from us, and that the Universe is in fact expanding. This cosmological constant is to this day still a subject of much debate and may in fact end up being Einstein's greatest legacy.

 

[ramparts]

Hi arkady,

Actually, the Einstein's constant you link to (though you should be aware, no one today actually calls it that, since it's not really a fundamental constant, but a combination of them) is not the cosmological constant. Einstein's constant has always been and will always continue to be perfectly valid - without it, there is no general relativity

Also, the OP is as far as I can tell referring to neither of those constants; he's talking about the constant c in E=mc^2, which is the speed of light.

 

[arkady]

though you should be aware, no one today actually calls it that, since it's not really a fundamental constant, but a combination of them) is not the cosmological constant.

Ah yes. Thanks for pointing that out. Maybe it would've helped had I actually read the article I linked.

he's talking about the constant c in E=mc^2, which is the speed of light.

Yes, hence the word "confusing". Just thought that the whole thing made more sense if he was talking about the cosmological constant. Rereading the OP I'm actually not so sure anymore. Never mind then.

 

[ramparts]

Well, it's true that the cosmological constant is one of the biggest mysteries of the universe right now So maybe his post would have made more sense if that's what he had been talking about.

 

[origin]

All Albert did was take Sir Isaac's classic equation of F=mv^2 , force equals the mass times the square of the velocity, and do some substitution. The velocity in this case is the speed of light. We are inserting a constant, c, in place of a variable, v, so we need a different variable, E, to express the outcome. Energy instead of force because we are not dealing with Newtonian concepts any longer, even though the equation is derived from Newton. That's why Einstein originally had v in his equation instead of c.

Reminds me of that classic Gary Larson comic.

 

[MeteorWayne]

:lol: :lol:

 

[Oxize]

Offtopic: Is the formula E = hf still being used in some physics?

 

[drwayne]

I assume you are talking about

E = hv where v = nu

Which provides the energy of a photon of a given frequency. If so, yes, as is the form

E = hc/lambda

Wayne

 

[ramparts]

The short answer is yes - come on, Dr. W., it's totally legit to use f for frequency