Hi everyone--I got a quesiton that has been annoying me for awhile.
According to Einstein's E=mc^2 relativity theory, mass is increased as speed increases, thus explaining that fact that you cannot reach the speed of light because as you near it the mass becomes infinite. However, doesn't this contradict the Law of Conservation of Mass, which states that mass cannot be created nor destroyed? Where would this mass from speed come from? Also, if you reached absolute zero, wouldn't the mass then be 0 (because E=mc^2 and c is a constant, so m must be 0) for E to equal 0?? Again, a contradiction in the Law of Conservation of Mass.

Another question: since light is a form of energy (thus having no mass) why is it given a speed limit?? Why is there a finite speed in which it can go, and what stops it from going faster?

Thanks very much! My email address is seg1985@home.com is you want to explain it to me, or you can post here.

It's now the law of conservation of energy and mass. They're equivalent. Normally energy doesn't get converted into mass, or mass into energy, but it can happen. At usual energies, the law of conservation of energy, or the law of conservation of mass still hold, just as do Newton's laws.

In fact, some go so far as to say that you don't really increase the mass of an object by speeding it up, but that the energy itself has mass.

So are you saying that Newton's laws only work SOMETIMES, under Earth's natural circumstances? That would not make it a very good theory....

Also, you mentioned energy itself has mass. But energy is not made up of particles...
Also, if energy had mass, it would never be able to reach the speed of light, since mass becomes infinite....

Newton's Laws of motion, as described in Principia, only work under a range of circumstances. Both relativity and quantum mechanics are more general theories that include Newton's Laws as an approximation, accurate only for a range of conditions.

Newton's Laws and Maxwell's equations (which characterizes electromagnetic fields) seemed to contradict each other until special relativity came along. For example, consider two electric charges. A force couldn't propagate from an electric charge faster than the speed of light according to Maxwell's equations. However, Newton's Third Law implies that there is a reaction force immediately in the second charge, with no pause. Einstein showed that one could make a logical resolution by changing the concepts of time and space.
According to quantum mechanics, energy can be viewed as carried by particles or waves. This isn't part of relativity.

However, in pure relativity (no quantum mechanics), a field can store energy. A field is a region of space where a particle will experience a force. The strength of the field is the force on the particle divided by some numerical characteristic of the particle. By treating waves in a field as having "real" properties like mass, in other words treating the "wave" as real object like a particle, one could resolve the third law of Newton with the forces like electromagnetism.

Basically, SR presumes that waves in a field can have mass, energy, and momentum even if they aren't particles. The 1905 paper by Einstein has "field equations," which many casual readers like to skip. However, "field equations" are very important in relativity since they contain the forces that some critics say aren't in SR.

The question presumes that both quantum mechanics and special relativity are both at least partly correct. The implied assumptions are that there are photons (quantum mechanics), and that they obey E=mc^2 (SR). The mass in the "E=mc^2" formula is really called the "longitudinal mass." The longitudinal mass of a photon is NOT zero.

In SR, the "longitudinal mass" (the mass that you are talking about) is equal to the rest mass times a Lorentz factor. The Lorentz factor becomes infinite at the speed of light, and a finite number times infinity is infinity. So a particle of finite rest mass can't go at the speed of light. The rest mass is the energy that a particle would have as measured by an observer in the same inertial frame as the particle.

If the rest mass is zero, the "longitudinal mass" at the speed of light is zero times infinity which is indeterminate. It can be any number at all, so something else has to determine it. So a particle of zero rest mass has to move at the speed of light to carry energy.

One implicit assumption in SR (?) is that all observers have a nonzero rest mass. Therefore, an observer can't go at the speed of light (or else its "longitudinal mass would be infinite). Since a photon moves at the speed of light, no observer can be in the same inertial frame as a photon. So one can not measure a "zero rest mass" of a photon. Questions of the "reference frame" of the photon are meaningless because all observers have a finite rest mass.

Actually, I haven't actually read that asumption explicitly stated anywhere. Is there an implication in SR, as defined by the 1905 paper by Einstein, that all observers have a finite rest mass? Where is it written? I have seen beings of pure energy in science fiction, and even a creature made of 100% light in the old Outer Limits, but I suspect that this is impossible. However, if such a creature did exist, one would have to worry about the "rest frame" of a photon.

<font size=-1>[ This Message was edited by: Rosen1 on 2001-12-04 20:54 ]</font>

Well, it works often enough! [img]/phpBB/images/smiles/icon_smile.gif[/img]

Ok, thanks very much Rosen1, it lays it out alot more clearly now.
2 more basic questions, though:

1. What is the "Lorentz factor" exaclty? I never heard of this.
2. You say how the mass becomes infinite since energy becomes infinite, so why is the actual speed of light finite, and why can't it go faster?

Did a quick web search on it, and came up with this definition of Lorentz factor. The Mount Allison University Special and General Relativity Electronic Text looks pretty interesting, so thanks for that.

The speed of light depends upon the curvature of space, in general relativity. In flat space, where special relativty is valid, it is limited--otherwise, energy from one event could reach a second event in the first one's future, and energy from the second event could reach the first one in the second one's future!

By the way. Short correction.
A photon always has a nonzero longitudinal mass. I knew what I wanted to say, but it came out wrong.


I made the phrase up, assumming that you knew the basic formula and would understand it in context. The Lorentz factor that
I was talking about a factor F where:
F = 1/sqrt(1-(v/c)^2).

Note that according to SR,
m = F times m_0
where m is longitudinal mass and m_0 is rest mass.

You can see that if v=c, F becomes infinity. Well, actually, the precise way of saying this is that as v goes to c, F goes to infinity. There is a very fine distinction between equality and going to a limit which I don't want to get into until I absolutely have to.

The longitudinal mass of a photon does not go to infinity. The longitudinal mass becomes infinite only if the rest mass is nonzero. For the reasons that I stated (infinity times zero is an indefinite number), the longitudinal mass is indeterminate only if the rest mass is zero and thus doesn't have to be infinite. What we measure isn't infinite, it is a finite longitudinal mass greater than zero.

The photon has a longitudinal mass greater than zero. The photon has inertia, characterized by the longitudinal mass. That is why there is radiation pressure.

A lot of Einstein's work was based on the apparent descrepancy of Newton's third law (for every action on a particle, there is instantly an equal and opposite reaction on another particle) with the fact of radiation pressure (if a particle emits light, the force it exerts isn't felt by the particle until later). He tried to resolve this. He didn't at the time know about photons (he later introduced the concept, for which he won the Nobel prize). However, most people at that time didn't know that light had mass. So where does the radiation pressure come from? Well, E=mc^2. Light contains energy, and energy has mass, so light has mass and can exert radiation pressure.

As some people will tell you, the formula E=mc^2 has a history before Einstein. However, they don't mention some caveats. Einstein worked it out in a different way and in a far more useful context. However, it is true as far as it goes. He wasn't the first. Nor did he get a Nobel prize for THAT particular formula.


A photon has a rest mass of zero, but a longitudinal mass greater than zero. The longitudinal mass goes into E=mc^2, not the rest mass. Unless they are the same thing, which only happens when v=0. If v=0, there is no difference between a rest mass and a longitudinal mass. Newtons Laws in their simplest form work well only when v is much less than c.


<font size=-1>[ This Message was edited by: Rosen1 on 2001-12-05 06:52 ]</font>

Einstien is said to have gotten the inspiration for reletivity by imagining he was on a motorcycle.

Imagine a surfer. The wave he is riding is infinitly wide, 20 feet long, 100 feet high, perfectly straight, perfectly rigid, and and moving towards a perfectly straight, infinite shore at 4000 miles per second at an angle of one degree. The board he rides has zero friction with the wave and all is happening in a vacum. How fast does the surfer go?

Sine of one degree 0.0174524064 times speed of wave 4,000 miles per second equals surfer speed 229,194 miles per second.

Speed of light 197,000 miles per second.

Just a msecond. Are you saying that the surfer is moving at an angle of one degree with respect to the wave? That doesn't seem plausible. [img]/phpBB/images/smiles/icon_smile.gif[/img]

You do say that the wave is at an angle of one degree with the shore, so the place where the wave is breaking on the shore is moving at an angle of one degree with respect to the wave.

I seem to recall that a photon does not have mass because it would violate SU1 symmetry if it had mass. So I guess if you really want to know, it will take a couple of years of study of abstract algebra [img]/phpBB/images/smiles/icon_smile.gif[/img]

Rob

It's true, Newtonian physics breaks down when you get into the realms covered by relativity theory, but it works very well for most applications. As a perfect example, let's look at the Apollo program. Three men were sent to the moon and back, with a lot of nifty calculations involved, without going beyond Newton's theories, along with the calculus he gave us. To put that in perspective, it means that spaceflight was a scientific possibility 300 years ago! All it took after that was the engineering end of things to catch up.

And puhleeeeze, don't anybody give me agro about engineering being a science too.

;^)

_________________
Free speech; exercise it or shut up!

<font size=-1>[ This Message was edited by: The Rat on 2001-12-05 09:08 ]</font>

There is no law of conservation of mass, and there never was. However, there was a law of conservation of matter in chemistry, and there still is. There is no conflict with relativity here. The law of conservation of matter only reflects the evident fact that all of the atoms which go into a chemical reaction, come back out. Hence, the matter in the reaction is "conserved".

It was common in Newton's day, and is probably still common in the popular view of science, to equate the "amount of matter" to the "amount of mass", but that is wrong. If you look at Newton's F = ma you can see that m is just a proportionality factor between F and a. It was assumed to be constant only because no body knew at the time how to vary m without also varying the amount of matter. But there are a number of interesting classical problems that involve a varying m, suchg as a sandbag pendulum losing mass, or the ballistic problem of a siege gun cannon ball attached to a chain.

The key to understanding m is to see its true role in classical physics. It is not a measure of how much matter you have. Rather, it is a measure of the inertia of whatever matter you do have. Once you move your concept of m from "matter" to "inertia", things get conceptually easier.

So, the increase of mass with speed only says that inertia increases with speed, reaching infinity in the limit as speed approaches that of light. The "amount of matter" remains invariant, but the "amount of inertia" does not.

The common way to express this is by using a velocity dependent mass in Newton's equations, but it is not the proper treatment. The problem is that in Newtonian equations the laboratory ("coordinate") time is used. If you recast the equations to use "proper" time, mass once again becomes invariant. The variablity of mass is just another of those illusion induced by the relativistic confusion over reference frames (see Spacetime Physics by Taylor & Wheeler).

<font size=-1>[ This Message was edited by: Tim Thompson on 2001-12-05 10:16 ]</font>

And, as a matter of fact, didn't Newton first formulate the law as force = time derivative of momentum, or f = d(mv)/dt?

Then, when m is assumed constant, it can be taken outside the derivative so f = m*dv/dt which is f = m*a.

Some people still talk about the law of conservation of mass. Here's a website at SLAC that does--and there are many more as any search will tell you. The SLAC site does explain the consequences of relativity, though.

I recall a physics teacher (professor?) saying exactly what you said, except formulated in another way, i.e. derivative of the "quantity of movement" (please remember I am not a native english speaker and hence don't have classes in english! That a litteral translation) with respect to time.

Tim, thanks for that explanation. I had never considered it quite that way, that mass is a measure of inertia, not matter. Wow, that makes some sense.

David Simmons, yes, Newton did in fact use the time derivative of momentum. It only simplifies to F=ma in most cases. However, one place it definitely does not is in the rocket equation. Basically any time you're burning fuel for acceleration, mass is not constant.

Mr. X, "quantity of movement" - thinking about that phrase, I would come up with displacement, or distance. Quantity means amount, and movement indicates changing location. The first derivative of displacement is velocity, second derivative is acceleration.

SEG9585, another way to consider the relativistic mass problem is to think of it as increasing kinetic energy, not increasing mass.

Quantity of movement I seem to recall is exactly what... that guy... has said is, the mass scalar multiplied by the velocity vector, in other words mv with a little arrow on top of the v (that's a joke, thank you very much), and we used that, which was written as P (vector) to illustrate conservation of quantity of movement during collisions. Now what did we do that with...

Isn't that basically the equivalence principle?

Try this URL http://news.bbc.co.uk/hi/english/sci...00/1695390.stm



<font size=-1>[ This Message was edited by: David Simmons on 2001-12-07 22:45 ]</font>

This is wrong as stated. I think that you meant something else. I believe that current usage of the word "mass" by physicists usually means the "longitudinal mass," and that you are probably thinking of mass as the "rest mass." I will make a painfully long winded explanation of the difference.

When physicists today speak of mass, they are usually speaking about what Einstein called the "longitudinal mass" in his 1905 paper. This is defined assumming an observer in an inertial frame who sees a particle or closed system move relative to him at a velocity v. By "system" moving at v, I am talking about a set of particles and waves where the center of mass is moving at v. Both Newton's Laws and Maxwell's equation apply to the observer, albeit in a highly modified manner.

One of the modifications to Newton called mass or inertia is anistropic. That is, there is one "mass" for the moving system in the direction of motion called the "longitudinal mass," and another "mass" for the system in the direction perpendicular to the direction of motion (the "transverse mass)." The equation:
F = ma
still applies. However, if the force is in the direction of the velocity v then "m" is the longitudinal mass, and if the force is perpendicular to v then the "mass" is the longitudinal mass.I don't remember the formula for transverse mass right now, but it isn't very important for this discussion. The equation for longitudinal mass m_L of a particle or system
m_L = m_0 /sqrt(1-(v/c)^2)
where m_0 is a parameter known as the "rest mass." Now, in these terms, the famous formula can be written as:
E = m_L c^2
where E is total energy of system, as measured by an inertial observer, and c is the speed of light.

One place the use of longitudinal mass can be seen is in a closed system. Imagine an almost rigid box (i.e., as rigid as SR allows) where the is a mixture of particles bouncing back and forth near the speed of light, in addition to light particles (photons) bouncing back and forth at the speed of light. Consider an inertial observer in the rest frame of the center of mass of the box.

To this observer, the box is standing still (i.e., |v|=0). He can examine it by pushing or pulling it. For him, the longitudinal mass of the box is exactly the same as the rest mass. He can used Newton's Laws up to the point that the center of mass goes close to the speed of light.

However, suppose he does experiments to find out what the inside of the box is like. The par