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Aer
09-21-05, 06:50 PM
This thread is in conjunction with the Negamass thread. It's purpose is to solely demonstrate what it means for speed to be a scalar quantity.

Imagine if you will that you have negative speed. You are moving along at -s. Furthermore, if we differentiate this speed with time, we'll be able to derive the force acted upon you with the equation:

F = m d(-s)/dt.

From this equation, we see that you have a negative force acting on you just because you have a negative speed.

Now did you ever once consider that the negative sign on the speed made "speed" a vector? (i.e. velocity). I sure hope so, but unfortunately, you probably did not..

funkstar
09-21-05, 07:46 PM
But, speed isn't a scalar. Speed is defined exactly as the magnitude of the velocity. Magnitudes are non-negative, by definition. What you're demonstrating is that if we call velocity "speed", then "speed" is a vector. What's the purpose of that?

F = m d(-s)/dt

yield negative force? If your "speed" is constant wrt. time (say, constantly -s, as in that equation), you'll get a big fat zero out of d(-s)/dt, even though your "speed" was negative.

Aer
09-21-05, 08:02 PM
But, speed isn't a scalar. Speed is defined exactly as the magnitude of the velocity. Magnitudes are non-negative, by definition. What you're demonstrating is that if we call velocity "speed", then "speed" is a vector. What's the purpose of that? So now speed isn't a scalar? Do you know what a scalar is? I'll give you a hint, there are at least two definitions and one of them is synonymous to magnitude. Time for you to go review..

F = m d(-s)/dt

yield negative force? If your "speed" is constant wrt. time (say, constantly -s, as in that equation), you'll get a big fat zero out of d(-s)/dt, even though your "speed" was negative. Thanks genius. You are completely correct, if there is no force acting on you, then when you differentiate your "speed" you will get 0.. If the magnitude of your speed is increasing, you'll get a negative force, if the magnitude of your speed is decreasing you'll get a positive force. But note that this depends on the acceleration vector and not on the mass scalar.

James R
09-21-05, 09:13 PM
Speed is usually defined like this:

s = sqrt(v.v)

where v is the velocity vector.

The dot product (mathematically the inner product between two vectors) is, by definition, positive definite for the dot product of a real vector with itself. Therefore, s may be positive or negative, from the definition above. The convention is that we always take s to be positive, or zero (we take the positive square root).

It's just a matter of definition. If all speeds were taken to be negative, it wouldn't affect any of our calculations, as long as we were consistent.

Aer
09-21-05, 09:23 PM
Yes, speed is always taken as positive or 0 because speed is a magnitude. Similarly, mass is always taken as positive or 0 because mass is a magnitude. I think this thread has served its purpose. Feel free to lock up.

Pete
09-21-05, 09:44 PM
...and charge can be positive or negative because charge is a scalar.

Didja know that a vector multiplied by a negative scalar will give a vector in the opposite direction to the first?

Mathworld (http://mathworld.wolfram.com/ScalarMultiplication.html)

Aer
09-21-05, 09:50 PM
Again Pete, we are refering to separate definitions of scalar. For an object with constant mass, how can you have a negative force with a positive acceleration? explain how -F = (-m)*a makes any sense. It doesn't which goes back to what I originally said, negative mass leads to nonsense.

Pete
09-21-05, 10:09 PM
we are refering to separate definitions of scalar

For an object with constant mass, how can you have a negative force with a positive acceleration?
Physically, or conceptually?
Physically, you can't - unless you happen to find a chunk of negative mass, which I suspect just doesn't exist.
Conceptually, however, there's no problem. And it's fun to think about, which is the whole point of the Negamass thread.

On that topic:

A negative mass is ill-defined because mass is defined as a scalar quantity and a negative indicates a direction. Combine the two and you are telling me that mass is a vector quantity.
Wrong!
Combine the two and we are telling you that mass is a scalar quantity. Using the other meaning of scalar.

If F and a do not have the same vector directions, it is the result of another vector.

This is just wrong. If the vector a is multiplied by a negative scalar, then the vector F will be in the opposite direction to a.

In other words, there is no mathematical reason that prevents mass from being both a scalar and negative.

Aer
09-21-05, 10:18 PM
I'm glad you understand me. Unfortunately I don't think you understand me.

Physically, or conceptually?
Physically, you can't - unless you happen to find a chunk of negative mass, which I suspect just doesn't exist.
Conceptually, however, there's no problem. And it's fun to think about, which is the whole point of the Negamass thread. It's also fun to think about negative speed. We still see that the direction of force is dependent on the direction of the acceleration.

On that topic:

Wrong!
Combine the two and we are telling you that mass is a scalar quantity. Using the other meaning of scalar. This is the point you keep missing: It doesn't make sense to refer to mass as a positive/negative scalar. Only the positive (i.e. magnitude) definition makes any sense, see the acceleration issue above.

This is just wrong. If the vector a is multiplied by a negative scalar, then the vector F will be in the opposite direction to a.

In other words, there is no mathematical reason that prevents mass from being both a scalar and negative. Except in the context of mass as the invariant of the 4 vector momentum. Physics Monkey has yet to show how this could be negative. It is similar to defining speed as negative.. which is what this thread is about.

Pete
09-21-05, 10:30 PM
It doesn't make sense to refer to mass as a positive/negative scalar.
Sure it does - you're just unable to figure it out. That's OK - we all have our limitations.

Except for the definition of force: F=dp/dt = dm/dt*v + m*dv/dt. We saw that if v is negative, it doesn't make dv/dt negative.
And this is supposed to prevent mass from being negative... how, exactly?

It's clear from your equation that if mass is contstant and negative, then the Force vector points in the opposite direction to the dv/dt vector.

Are you suggesting that this is mathematically impossible?

Pete
09-21-05, 10:33 PM
Except in the context of mass as the invariant of the 4 vector momentum.
I'm glad you abandoned your other argument. It really was misbegotten, wasn't it!

Physics Monkey
09-21-05, 10:44 PM
If a particle has 4 momentum p^0 = m = - |m|, p^i = 0 in its rest frame, then the invariant is still g(p,p) = -1*m*m = -m^2 (I use the metric g_00 = -1 g_ii = 1). I don't see the problem here, the invariant is insensitive to the sign of m.

Aer
09-21-05, 10:47 PM
Sure it does - you're just unable to figure it out. That's OK - we all have our limitations. No. It makes as much sense as defining speed as negative. It is your limitation that you cannot understand why.

Explain how the following makes sense: I exert a positive force on a negative mass, which way does the negative mass move? positive x direction or negative x direction? positive x is defined as the the direction in which I exert the positive force.

And this is supposed to prevent mass from being negative... how, exactly?

It's clear from your equation that if mass is contstant and negative, then the Force vector points in the opposite direction to the dv/dt vector.

Are you suggesting that this is mathematically impossible? I've always argued from a physical point of view, mathematics produces non-real results. I've allowed you to entertain your notion of negative mass in the above, explain in which direction an object moves when a postive force is exerted on it.

Aer
09-21-05, 10:58 PM
If a particle has 4 momentum p^0 = m = - |m|, p^i = 0 in its rest frame, then the invariant is still g(p,p) = -1*m*m = -m^2 (I use the metric g_00 = -1 g_ii = 1). I don't see the problem here, the invariant is insensitive to the sign of m. From the 4 momentum vector we get E<sup>2</sup>-p<sup>2</sup>=m<sup>2</sup> for c=1 so for m to be negative, p must be greater than E, correct? how is something going to have more momentum than energy? Are you suggesting faster than light travel? By the way, even if an object had greater momentum than energy, it would have an imaginary mass.. even though you seem to describe it as -m<sup>2</sup>

Pete
09-21-05, 11:04 PM
No. It makes as much sense as defining speed as negative. It is your limitation that you cannot understand why.
Impasse. We both think the other is stupid.

Explain how the following makes sense: I exert a positive force on a negative mass, which way does the negative mass move? positive x direction or negative x direction? positive x is defined as the the direction in which I exert the positive force.
No no! I'll not be drawn into the physical implications here!
I believe that physical consequences do in fact lead to the conclusion that negative mass can not be physically realised.

I've always argued from a physical point of view
Except when you incorrectly reasoned that if mass can be negative, it must be a vector, which is the point of my foray into this thread.

Aer
09-21-05, 11:10 PM
I believe that physical consequences do in fact lead to the conclusion that negative mass can not be physically realised. That is what I've said all along. You get nonsensical results.. perhaps in a day or two you'll get it.

Aer
09-21-05, 11:11 PM
Except when you incorrectly reasoned that if mass can be negative, it must be a vector, which is the point of my foray into this thread. You still don't see how speed is a scalar and velocity is a vector.

Physics Monkey
09-21-05, 11:16 PM
Aer, you are totally confused. The point is that it is the mass squared that enters into the equation E^2 - p^2 = m^2 so even if m is negative, m^2 is still positive. In order to have m^2 negative, you would need m to be imaginary.

Pete
09-21-05, 11:19 PM
That is what I've said all along. You get nonsensical results.. perhaps in a day or two you'll get it.
Your unsupported assertions are unimpressive, regardless of whether they are true or not. Show me a rigorous derivation, and perhaps I'll be impressed.

You still don't see how speed is a scalar and velocity is a vector.
:bugeye:
Your attempt at mindreading is oddly timed and an empirical failure. I think it's just a red herring to divert attention from your embarrassing suggestion that if a quantity can be negative, it must be a vector.

Aer
09-21-05, 11:37 PM
Your unsupported assertions are unimpressive, regardless of whether they are true or not. Show me a rigorous derivation, and perhaps I'll be impressed. I stated why your negative mass is nonsensical, I did not just assert it.

:bugeye:
Your attempt at mindreading is oddly timed and an empirical failure. I think it's just a red herring to divert attention from your embarrassing suggestion that if a quantity can be negative, it must be a vector. Tell me what direction means to you. If a force is defined as positive, what does that mean? If an acceleration is positive, what does that mean? If a mass is positive what does that mean? I'll give you a hint, for mass it doesn't mean that the mass is in the positive direction, and why? because mass is a scalar quantity, without direction. Show me how a force can be positive and an acceleration can be negative.

Show me how when two objects collide, one with positive mass, the other with negative mass, that momentum is conserved.

Explain how negative does not denote a negative direction when dealing with forces and accelerations. Go on, explain how mass can be a negative scalar and contain no direction information.

Good luck trying..

Pete
09-21-05, 11:43 PM
I stated why your negative mass is nonsensical, I did not just assert it.
I rank armwaving explanations on the same level.

I'm glad to see that you are now presenting meaningful physical arguments. I look forward to ironing out the details in the negamass thread (assuming you're capable of participating without abuse).

I just think it's funny that you're pretending that you never said that if a quantity is negative, it must be a vector. It's OK - I can see that it would be embarrassing for you. :D

Explain how negative does not denote a negative direction when dealing with forces and accelerations. Go on, explain how mass can be a negative scalar and contain no direction information.
Do I need to remind you again that multiplying a vector by a negative scalar changes the direction of the vector?
In that limited sense, direction information does not imply that the quantity is a vector.

Do you think that charge is a vector quantity?

Aer
09-21-05, 11:56 PM
I rank armwaving explanations on the same level.

I'm glad to see that you are now presenting meaningful physical arguments. I look forward to ironing out the details in the negamass thread (assuming you're capable of participating without abuse).

I just think it's funny that you're pretending that you never said that if a quantity is negative, it must be a vector. It's OK - I can see that it would be embarrassing for you. :D
Too bad for you, I've asked you to explain how mass cannot be a vector and behave in the manner you describe. I've said all along that it is nonsensical - in fact that is the very first thing I said! Then I said that if mass was in fact negative, it would have to be a vector, otherwise you cannot get around the nonsensical stuff. But at last, given what we know about mass, it is nonsense to say that mass is a vector as well - so all around, we have one big nonsensical crap-ola.

Do I need to remind you again that multiplying a vector by a negative scalar changes the direction of the vector?
In that limited sense, direction information does not imply that the quantity is a vector. Again, you are bringing up negative scalars as if I never told you that the mass scalar is a magnitude quantity. What is a negative magnitude?

Do you think that charge is a vector quantity? No, and I don't consider charge to be a magnitude either. + and - charge are inherently different and the + and - signs denote this. You wouldn't state that a + charge has a + direction.

Pete
09-22-05, 12:02 AM
as if I never told you that the mass scalar is a magnitude quantity.
I chose to ignore your unsupported assertion :D

You wouldn't state that a + charge has a + direction.
Of course not. Just like I wouldn't state that a negative charge has a negative direction, or a negative mass has a negative direction. It would be stupid, wouldn't it, to think that applying a sign to a quantity gives it direction!

It's OK, Aer, I'm done goading you now. Bye!

Aer
09-22-05, 12:10 AM
I chose to ignore your unsupported assertion :D You conviently ignore a lot of things such as my first paragraph: Too bad for you, I've asked you to explain how mass cannot be a vector and behave in the manner you describe. I've said all along that it is nonsensical - in fact that is the very first thing I said! Then I said that if mass was in fact negative, it would have to be a vector, otherwise you cannot get around the nonsensical stuff. But at last, given what we know about mass, it is nonsense to say that mass is a vector as well - so all around, we have one big nonsensical crap-ola.

Of course not. Just like I wouldn't state that a negative charge has a negative direction, or a negative mass has a negative direction. It would be stupid, wouldn't it, to think that applying a sign to a quantity gives it direction! You really do not get that mass is a magnitude quantity do you? Attributing a negative sign to a magnitude is paramount to defining it as a vector as I'ved stated repeatedly. If you give speed a negative sign, what does that mean? Essentially: your "speed" is a velocity vector.

It's OK, Aer, I'm done goading you now. Bye! I see you've run out of cop-outs on how mass can be a negative scalar when I told you that it cannot in the context of Newton's equations. You just have not written out the mathematics yet to fully understand the implications. But that is all right, because after a day or two, you'll finally realize what I've said all along - mass is a magnitude and as such, attributing a negative sign is nonsensical.

funkstar
09-22-05, 05:04 AM
So now speed isn't a scalar?

Well, yeah, but it's non-negative. By definition. You know, s = |v|.

That's why it's silly to bullshit about negative speed, while it's not so for negative mass. There's a sound reason to dismiss negative speed (the concept is inherently meaningless, and requires you to redefine what speed stands for) and this simply isn't the same as with negative mass. There's nothing about the math which makes negative mass impossible. It's certainly not analogous to speed, which seems to be your point here.

funkstar
09-22-05, 05:14 AM
You really do not get that mass is a magnitude quantity do you?
Ok, Aer. What is it a magnititude of then? Which vector has length mass, such that the very concept of negative mass is meaningless? When I see

F = m a

I don't see anything suggesting that m is a magnitude.

Aer
09-22-05, 11:50 AM
Well, yeah, but it's non-negative. By definition. You know, s = |v|. Or as James R said:
s = sqrt(v.v) Similarly, from the 4 vector of momentum, mass is defined to be:

m = sqrt(<b>P</b>.<b>P</b>)

we only take the positive root for s, so why wouldn't we only take the positive root for m? Like I said, the negative root is a non-real / non-physical.

That's why it's silly to bullshit about negative speed, while it's not so for negative mass. Wrong, that is why it is silly to bullshit about negative speed and negative mass.

There's a sound reason to dismiss negative speed (the concept is inherently meaningless, and requires you to redefine what speed stands for) and this simply isn't the same as with negative mass. Yes it is the same, mass is inherently positive as well.

There's nothing about the math which makes negative mass impossible. It's certainly not analogous to speed, which seems to be your point here. Speed and mass are similiarly defined, there is nothing about any math that doesn't allow you to obtain non-physical results. Just as negative speed is thrown out, so is negative mass.

Ok, Aer. What is it a magnititude of then? Which vector has length mass, such that the very concept of negative mass is meaningless? When I see

F = m a

I don't see anything suggesting that m is a magnitude. I gave it to you above, from the 4 vector momentum, mass is defined to be:

m = sqrt(<b>P</b>.<b>P</b>)

This is also why "mass" refers to "rest mass" and not "relativistic mass" because it is an invariant quantity.

Physics Monkey
09-22-05, 01:48 PM
Aer, mass is not defined in terms in terms of the invariant square of the four momentum. Mass is defined in terms of the measured energy of an object as observed in its rest frame. You are confusing the fact the the invariant square is the mass squared, which is true, with the your notion that the mass is defined as the positive square root of the invariant square, which is not true.

Let me give you an example. Consider two ordinary three vectors with comonents v = (1,0,0) and u = (-1,0,0). Note that if these two vectors represent velocity, then they have the same magnitude, or in other words, the same speed. However, a knowledge of the square of the quantity is not equivalent to a knowledge of the original quantity. These two velocities are not the same vector even though they have the same square. The same is true is for the four momentum. If I have two hypothetical particles, one with mass m>0 and the other with mass -m<0, then they have the same invariant square four momentum but different mass. I hope this makes it clear why we don't define the mass in terms of the positive square root of the invariant square.

Aer
09-22-05, 02:22 PM
Physics Monkey, m=E/(&gamma;c<sup>2</sup>) and m=sqrt(<b>P</b>.<b>P</b>) will yield the same result. In both cases you can get a negative result from the mathematics and in both cases, that result is a non-physical result.

Trilairian
09-22-05, 02:24 PM
Actually AER is right. See the new thread on modern relativity. It is not inconsistent to define mass as rest energy but everywhere I have seen this done the authors have run into problems with circularity.

Aer
09-22-05, 02:43 PM
Just to clarify, you are stating that mass is invariant, correct? You aren't saying anything about whether negative mass is physical or not.

I think Physics Monkey and James R agree that mass is invariant. 2inquisitive and Billy T on the other hand do not.

Trilairian
09-22-05, 02:50 PM
Just to clarify, you are stating that mass is invariant, correct? Correct.

You aren't saying anything about whether negative mass is physical or not.

I wasn't, but I might as well - I'll think about believing in negative mass when I see it. As far as I am conserned it doesn't exist.

Physics Monkey
09-22-05, 04:11 PM
Trilairian,

I am afraid that Aer (and you) are not right. In quantum field theory, the single particle states are defined as irreducible representations of the Lorentz group. Note that the possibility of negative mass (eigenvalue of P^0 in rest frame) is not in any way excluded based on the algebra of the Lorentz group.

It is an experimental fact that negative mass particles do not exist. In fact, this observation is intimately connected with the stability of matter in quantum field theory.

Trilairian
09-22-05, 05:28 PM
Trilairian,

I am afraid that Aer (and you) are not right. ... It is an experimental fact that negative mass particles do not exist. ... Are you just trying to be contradictory or do you not realise that what you just said amounts to: you are not right but experimentally its a fact that you are right ?

Physics Monkey
09-22-05, 05:53 PM
I am, of course, not being contradictory. Aer stated that mass is defined to be positive (a claim which you supported), and I simply indicated that this not the case. Please not that I never claimed that negative mass exists, and I even gave, in my previous post, a physical reason why we expect it not to exist.

Trilairian
09-22-05, 06:06 PM
I am, of course, not being contradictory. Aer stated that mass is defined to be positive (a claim which you supported), and I simply indicated that this not the case. Please not that I never claimed that negative mass exists, and I even gave, in my previous post, a physical reason why we expect it not to exist.
No he/ we didn't. You are just being contradictory. He said
"m=sqrt(P.P) will yield the same result. In both cases you can get a negative result from the mathematics and in both cases, that result is a non-physical result".

Aer
09-22-05, 06:09 PM
Trilairian,

I am afraid that Aer (and you) are not right.Trilairan never said anything incorrect. Whether you want to say that I am right or wrong about mass being positive appears more semantical than anything else. You are willing to admit that negative mass is not physical:
It is an experimental fact that negative mass particles do not exist. But you hesitate to define mass as positive when in fact, we could make negative mass mathematically unless you define mass to be postive.

Let's review what you have learned here: Negative mass is not physical by your own admission. So what is the point of attributing something to have negative mass?

Physics Monkey
09-22-05, 06:18 PM
Your claim was that the mathematical machinery of physics would break down if we suddenly discovered a particle with negative mass. Newton's law would make no sense, etc. This is incorrect. The equations can handle negative mass just fine, it is experiment that says negative mass particles are unphysical. This sort of generality is encountered often in physics. Another example is the notion of a magnetic monopole. Maxwell's equations can handle magnetic monopoles no problem (in fact they are more symmetric with magnetic charges included), but it is an experimental fact (so far) that the magnetic charge density is zero.

Aer
09-22-05, 06:41 PM
No, I never said anything about the "mathematical machinery" you have just brought up. I said from the start that negative mass was non-physical and as example put forth the nonsensical predictions that come out of Newton's equations.

It is you who mistaken claim that the mathematics are always physical when we know this is not true. There are many mathematical solutions to many equations, yet all of the solutions are not always physical.

Physics Monkey
09-22-05, 06:59 PM
You claimed Newton's 2nd law made no sense for a particle with negative mass when in fact it does. You based this claim on the silly notion that putting a negative sign on mass changes its scalar nature. How is this not a claim that the mathematical machinery (Newton's 2nd Law in vector form) breaks down for negative mass?

You are arguing a silly point. There are plenty of good reasons why mass shouldn't be negative. Pick any of them you want and waffle on about it all day long. Note, however, that the mathematical structure of the theory is not one of those good reasons.

Also, I have, of course, never said that the mathematics is always physical. In fact, if you look at my post, I said that while the mathematics allows negative mass, there are plenty of good physical reasons why negative mass shouldn't exist. I have clearly made a distinction between the mathematics and the physics. I know everyone here knows this, but I just thought I would state it one more time for completeness.

Aer
09-22-05, 07:08 PM
You claimed Newton's 2nd law made no sense for a particle with negative mass when in fact it does. You based this claim on the silly notion that putting a negative sign on mass changes its scalar nature. How is this not a claim that the mathematical machinery (Newton's 2nd Law in vector form) breaks down for negative mass?
No Monkey, I said that mass was a magnitude and as such making it negative didn't make any sense.

You are arguing a silly point. No, you are arguing a silly point. You are arguing that negative mass isn't physical and is well defined. Wrong, it is not well defined because of the fact that it is not physical.

Also, I have, of course, never said that the mathematics is always physical. Good, it appears you are learning something.

James R
09-22-05, 09:02 PM
I said that mass was a magnitude and as such making it negative didn't make any sense.

In what sense are you using the term "magnitude"?

Is temperature a magnitude? What about a temperature of -23 degrees Celcius?

Or do you mean that mass is the magnitude of a particular vector? If so, which vector?

Aer
09-22-05, 09:11 PM
In what sense are you using the term "magnitude"?

Is temperature a magnitude? No.

What about a temperature of -23 degrees Celcius? That is not a magnitude either.

Or do you mean that mass is the magnitude of a particular vector? If so, which vector? No, as a mass-vector would be non-physical as well. Though, I'll point you to physicsforums if you want to discuss vector masses as they seem to like that kind of thing.