Physics questions...please help!

Ok…so I’m having a discussion tonight about relativity. And the topic came up discussing the equation:

M=M0 /(the square root of) (1-(v2 xc2)

Or to put it in english since I can’t figure out how to actually put the equation in here, its:

Mass=the mass at rest divided by the square root of 1 minus the product of the velocity squared times the speed of light constant squared.

Ok. Basically the disagreement is that one of us thinks that the velocity V squared is the representation of Energy, since Energy equals Mass time the speed of light constant squared. The other of us basically thinks that the velocity is NOT representing energy in the equation, that this is simply another way to express mass, and velocity is simply velocity. I being the one saying that velocity does NOT represent energy in the equation, though conceeding that velocity and energy are related, or are a function of each other. So, my questions are:

  1. Who is right (or are we both wrong as I suspect)? IS the v in the equation representing energy? Can mass be defined or specified without talking about energy?

  2. Can someone please tell me how both velocity, mass and energy are represented in some kind of definition that makes sense to a layman? I THINK that velocity is distance over time, mass is the weight over the gravitational constant (I think) and energy is related to work and power, but its been over a decade since I was in college.

  3. The root of the discussion was one of particles in a specific experiment. Basically, the real question that drove all this was: If a small particle (say an electron) is passing through some material going basically at the speed of light and it encounters a nucleus or other particle, why does the nucleus deflect the moving particle? The way the other person was looking at it, basically, was that the mass increases as the particle approaches the speed of light (becoming very large, relative to the initial mass of the particle)…so how does it get deflected? Is it by the charge of the particle only, or is it the potential energy of the stationary particle acting in basic Newtonian ways (i.e. action reaction, an object in motion stays in motion, unless acted upon by another object/force, etc etc)?

  4. Can someone explain how mass increases as a particle approaches the speed of light? I always just thought it was the energy that increased as a particle or object approached the speed of light, but appearently, looking at the equation I listed and the E=MC2 equation, mass ALSO increases. Can any physics types kind of give a good laymans explaination of this?

Really appreciate any help you can give to clear this up. I’m SO rusty at this crap that I can barely get my brain around it anymore.

-XT

The way I read it, your equation is wrong.

The term (v[sup]2[/sup] x c[sup]2[/sup]) should read (v[sup]2[/sup] / c[sup]2[/sup]).

This means that for low velocities the value of (v[sup]2[/sup] / c[sup]2[/sup]) is small and M is very close to M[sub]0[/sub] because the value of root(1-(v[sup]2[/sup] / c[sup]2[/sup])) is very close to 1.

As v approaches c, the value of (v[sup]2[/sup] / c[sup]2[/sup]) rises and M[sub]0[/sub] becomes much bigger than M as the value of root(1-(v[sup]2[/sup] / c[sup]2[/sup])) falls.

Yes, I mis-typed in the equation. My bad. :slight_smile: Yes, as V squared approaches C squared (i.e. as the velocity approaches the speed of light) then the equation becomes the square root of 1-(1/1)…or zero. That means that you have the initial mass divided by the square root of zero…which is zero. So, its the initial mass divided by zero…or an infinite number, correct? M0/0

Sorry about that…it was nearly 2am and I was more than slightly drunk when posting. Any one have any thoughts on the other questions?

-XT

Yes, the equation in special relativity is:

m = γm[sub]0[/sub]

or as in special relativity γ = 1/√(1 - v[sup]2[/sup]/c[sup]2[/sup])

m = m[sub]0[/sub]/√(1 - v[sup]2[/sup]/c[sup]2[/sup])

  1. v[sup]2[/sup] represents v[sup]2[/sup], it is clear that mass, energy and velocity arer closley related in special relativity, but it is the whole gamma term that relates to the mass and therefore enrgy increase, not just the v term (see below)

  2. The equation:

E = γm[sub]0[/sub]c[sup]2[/sup]

clearly follows on from mass-energy equivalcne and the above equations

  1. An electron can’t travel at the speed of light, but if it is moving at a relativistic speed it’s momentum can be found from the following equation

p = γm[sub]0[/sub]v

Whenb it collides with a another particle, it will b deflected according to the exchange of enrgy and momentum with the other particle.

  1. I’m not sure what you mean, if your looking for a mechanism then mass-energy equivalnce is the only one I can give you, but if you want to know how mass dialtion was derived it’s not quite as easy as showing how lenght contraction or time dialiton was derived, but basically it can be shown thta in order for memntum to be conserved mass must increase in this manner.

v is velocity, and I think this has already been cleared up. But, no, one cannot really seperate mass and energy if one is using relativistic equations.

Mass is an intrinsic quantity of matter. You are thinking of converting mass to weight, for which one needs the gravitational constant. But mass and weight are only interchangeble in a constant gravitational field (like on the surface of the earth). Weight is actually force.

There are electrical forces as well as gravitational forces at work.

You need to keep your reference frames straight. An object travelling at high velocity appears (to an observer) to gain mass, but in its own reference frame, it has the same mass it had at rest. In fact, the observer will appear to have gained mass from the reference frame of the particle. This is all a simple* consequence of the fact that the speed of light is constant when measured from any reference frame. The rest of the phenomena (eg, mass gain) just comes out of the equations once you assume this.

*simple, that is, once Enistein made the brilliant observation that the speed of light is constant.

To the mod…sorry, I figured this thread was pretty well dead, thats why I re-packaged my OP to something a bit more coherent (as I was more sober for the second one). WOn’t happen again.

Last things from the other thread were:

From MC Master of Ceremonies

From John Mace

From XT

Hopefully people will be interested enough to continue to fight my ignorance on mass at relativistic speeds.

-XT

In pure maths a postive real (which m[sub]0[/sub] must be in special relatvity) divided by 0 is usually taken as undefined. In physics quite often a postive real number divided by zero is described as ‘infinity’ as a/x, where a is a postive real tends to zero as x tends to infinity. Howver when such an infinity occurs it usually in breach of the boundary conditons and hence refers to an unphysical (impossible) situation.

correction: “as a/x tends to infinity as x tends to zero”

MC Master of Ceremonies…ok, dim light bulb is going off. So, would it be accurate to say that an object with mass, accelerating towards the speed of light would CHANGE its mass (and shape, etc) but would not necessarily get larger or, er, more massive? Is THAT what the equation means? Am I at least getting close?

-XT

Only length contraction (l = l[sup]0[/sup]/γ) would effect it’s size/shape, but it would for example exert a greater graviational pull.

Remember no matter what your proper accelration you can’t get to the speed of light

Sorry; l = l[sub]0[/sub]/γ

The object would exert a greater external gravitational force because…its mass relative to an outside observer increases as it approaches the speed of light? It makes sense based on the math…but in real world terms, why would, say, a cue ball accelerated towards the speed of light (say at 99.999% of the speed of light) exert a larger gravitational effect than the cue ball at rest?

No particles with actual mass (I seem to remember that photons are massless) have ever been observed traveling at the speed of light?

-XT

xtisme,

You’re stuck on the idea that size and mass are someow connected and that they are intrinsic properties of an object.

Both those ideas are flat wrong. I know, I know, that’s how the world seems to all of us everyday. But that’s only because we’re going so slowly.

To understand this stuff you, and I, and everyone else, has to get rid of the idea that mass, or size, or time are fixed properties of matter. Here’s a very stretched analogy that may help you get your mind bent around this stuff. Warning: I’m not an expert, although I do read a lot on the topic.

If you ask me where my house is, I’ll tell you. You won’t ask again tomorrow, because you assume location is a fixed property of houses; they don’t move. If you do ask again, I’ll tell you the same location again, over and over and over. “Location” is a fixed property of houses.

But if you ask me where my dog is, my answer will be different from time to time. And the fact that I give different answers for the same dog doesn’t surprise you a bit.

Why not? Because “location” is not a fixed property of dogs. Name, yes; breed, yes; size, more-or-less yes, but not location. You understand and accept that very easily.

The mass of an object is (very roughly) like the location of a dog; it varies based on the circumstances. In particular, like everything else in relativity, the mass of something depends on who’s measuring and what their relative speeds are.

The big jump is for you / me / anyone to start thinking of “mass” and "size"and hence “shape” as more like dog-location than house-location. They are not fixed vaules, period, amen.

So when somebody zooms by at nearly light speed, you’ll measure him/her as having nearly infinite mass, nearly zero length along the axis of relative motion and no change in size in the other two directions. Hence their shape is all squashed-looking.

Meanwhile the person who zoomed by thinks they’re of normal mass and size and shape, while you look to them like you’re of nearly infinite mass, nearly zero length, and all squashed-looking.

Mass and length are not fixed quantities. Why? Because that’s how the universe works. I’m not sure anyone can give a qualitative explanation that really sinks in. It just turns into a wall of equations and “Because the math works out, that’s why.”

LSLGuy
p.s. If I sounded critical that wasn’t my intent; I was trying to be exhortational, not confrontational. Sometimes you just gotta take a leap of faith to “get” a radical new idea.

no no, LSLGuy, I appreciate any and all input on this. :slight_smile: I’m trying to slog through stuff I learned over a decade ago and probably forgot 5 min. after my final, and discuss this with a friend who is just starting to learn this stuff. We are having a lot of disagreements on the subject, mostly because of BOTH of our ignorance on the subject.

From LSLGuy

[/QUOTE]

Actually, I do understand that size and mass are not connected. From Newtonian physics, I remember that mass was a combination of Force and Acceleration (i.e. M=F/A), and also that you can measure mass in a gravitational field using weight and the gravitation constant. I remember that Mass in Einstinean physics is a function of energy and velocity.

I actually DO understand the concept of different frames of reference, and how things change based on which space frame you are using. I also understand that the change in mass is relative to the observer. What was confusing me was, the math SEEMED to be saying one thing, that didn’t make sense to me…namely that as a particle approaches the speed of light, it seemed (again from the math) to become of infinite mass (to an outside observer).

From LSLGuy

[QUOTE]
Mass and length are not fixed quantities. Why? Because that’s how the universe works. I’m not sure anyone can give a qualitative explanation that really sinks in. It just turns into a wall of equations and “Because the math works out, that’s why.”

You are probably right. From vague memory, I recall that its very dificult to describe all this stuff WITHOUT the math. I was hoping someone could come up with some good ways to illustrate all this stuff that a layman could comprehend.

I didn’t take it the wrong way at all…I KNOW that I’ve forgotten a hell of a lot of this stuff, and that my half remembered fuddle is very spotty, full of holes and errors. :slight_smile: I appreciate your input and help to get me up to speed on this.

-XT

XT:

There are many things in Quantum Physics and Relativity that we humans have no intuition for. The idea of what an electron actually looks like, what “spin” means, or the idea that mass increases with velocity are simply things that don’t (and can’t) occur in our everyday lives.

When an object “gains” mass in relativity, what is happening is that every electron, proton, and neutron in every atom of the object is increasing in mass. Nothing is added to the object. It simply has a different value for “m”.

John,

I’m sure you are right…this stuff is not intuitive to every day life. Its probably impossible to visualize this stuff without the math, unfortunately.

PLEASE correct me if I’m totally wacked here: As an object with mass approaches the speed of light, that to an outside observer the object APPEARS to get larger, as well as to become longer, and time seems to slow down for anything inside the object with respect to the outside observer (my rememberence is that time stops for the person inside the even as the object achieves the speed of light). To a person inside the object though, everything appears normal. Time moves normally, the object and person inside appear to be the same mass as when at rest, in reference to themselves.

I guess one of my confusions was maybe that I thought the object only APPEARED to change mass in reference to an outside observer, but this was more due to the distortions of traveling at relativisic speeds…dopler effect, red shift, etc . I DID remember that time actually DOES slow down though for the person inside the event, even though s/he percieves it as moving naturally with reference to themselves. I suppose that mass ALSO would physically change, not just with reference to an outside observer.

What was throwing me though, was the infinite thing which MC pointed out I had wrong. It was blowing my mind, not so much that the mass was changing with velocity (I could grasp that), but that, when the velocity of the object reached the speed of light, mass would be infinite. THAT was the main thing that really had me confused.

-XT

Yes to all, except the object does not appear to get larger. In fact, it looks smaller, overall, as al linear dimensions in the axis of travel get shorter.

The error you are making (I think) that you are assuming there is some “absolute” reference frame against which you can compare what is “really” happening with what is happening in the reference frame of the moving object. Time does not slow down. We simply measure it differently. The person travelling at high speed does not think he has gained any extra time. Time is simply experienced differently in the two reference frames (relative to the other).

The way that time “catches up” in the famous twin paradox is that the slowly aging twin must experience acceleration to get to the high speed and also to return to the original reference frame.

What is throwing you is that you are thinking that the object can reach the speed of light. It cannot. It can get real close, but it cannot reach the speed of light. To ask “does the mass go to infinity” is to ask an unanswerable question, since the object cannot ever get to that point in the first place.

The most intuitive way to think about it are in terms of four-vectors in spacetime as you find that rather than thinking of velocity as changing dimensions you can think of velocity as a rotation in spacetime.

Thanks John. :slight_smile: I think you hit it completely on the head there.

From John Mace

Its VERY difficult to get your mind around some of this stuff, as its not intuitive at all. I don’t think our brains are quite wired right to do this…and its amazing to me that members of our species were able to concieve all this. True ‘thinking outside the box’ IMO.

I’m not sure I have gotten my mind around the fact that there isn’t an absolute frame of reference to all this. I can concieve it intellectually, but part of me is still rebelling. I suppose you just have to condition yourself that its the way it is.

I really appreciate the time and effort you guys all put into this. For what its worth to you guys, you really helped a lot. A lot of this I didn’t really get when I was IN college studying this stuff. Oh, I could do the differential equations and work the math…but it seems appearent I didn’t GET it, even then.

Thanks,
XT

XT:

This stuff is hard to grasp. I studied phsysics in college (undergrad and grad), and after awhile you learn to accept the concepts without really understanding them-- that is, not understanding them on an intutive level. I remember my QM prof once turning to us as he was writing some complicated equation on the board and saying: “This must really blow away you guys who got tricked into majoring in physics by studying inclined planes and pendulums.” And then later: “Don’t worry. Nobody understands this. You just get used to the equations after awhile.”

If you can get your hands on Relativity for the Million
by Martin Gardner, that’s probably the best non-mathematical explanation you’ll get. I read it many, many years ago.

BTW, on a seperate note, I just picked up Wizard’s First Rule and look forward to a peaceful night reading at home (after several very late nights in a row of heavy drinking). Thx for the recommendation in the Ayn Rand thread a few weeks ago.