Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[wierd]

... compressed air would be significantly cheaper to build and operate.

But I admit, a magnetic omnigun would be neat all around, just not practical.

[Il Palazzo]

snip

I don't get what you're saying there. What is 'ancient newtonian stuff'?
Of course you can link Ek and p via an equation, and you can do it easily in Newtonian mechanics:
Ek=mV^2/2
p=mV
p^2=m^2V^2
Ek=p^2/2m

But that doesn't change that these two are not equivalent (one is a scalar the other a vector!), and one is not a measure of the other in the same way as force is not a measure of acceleration despite the two being linked through F=ma.

Your post following ebbor's implied that satisfying the conservation law for one automatically satisfies them for the other, which is dead wrong. The need to conserve both quantities is what constrains e.g. the CNO fusion cycle in the Sun, or pair production, or orbital motion.

Is there something I'm missing here?

[wierd]

Scalar vs vector:

This is hardly a conclusive argument, but--

 The two kinds of energy must have some degree of interchangeability, otherwise you couldn't get light pressure. (The double slit experiment shows us that light prefers to exist as waves instead of particles. It only does the particle pattern when being watched very closely. This means that if I shine a flashlight at the moon, which scatters like freaking crazy, [let's ignore the atmosphere for a moment] some percentage of the light emitted hits the moon and some percentage of that light misses it completely. Since we aren't watching the light really aggressively, it acts like waves; the photons hitting the moon are also missing the moon, simultaneously, with some percentage of the photon's energy being absorbed, and some percentage getting away.  The energy absorbed imparts a net vector away from the the flashlight's scalar field's point of origin in the form of light pressure.)

For momentum in general, you have a moving object that has mass. (scalar, we dont know what direction it is moving.) I am saying that the increase in energy needed to impart any new vector (We treat the object as if it were standing still compared to the surrounding environment; we are approaching this from the object's reference frame. Much like you feel like you are sitting still sitting in your chair, when in fact you are moving bitching fast in several vectors of movement along with the earth, with the earth/sun system, and with the earth/sun/galaxy system. You feel like you are standing still, because you have your own reference frame. In reality you are carrying some absurd amount of kinetic energy along with you in your reference frame.) to this object, the total energy you are already carrying influences how much your vector changes based on a fixed input of energy.  In this way, the energy imparted is indistinguishable from a mass term. It acts like you are heavier. This is true no matter what direction you try to alter the vector.  (To stop the object, you need to precisely counter the vector of movement with energy applied in the opposite vector. However, to accelerate the object, it takes more and more energy in the same vector to do so, with diminishing returns each time. The first unit of X joules of energy on the object will move it X meters per second, but the second addition of the same X joules of energy in the same vector will not result in the same X meters per second increase in velocity. This is expressly manifest in why you cannot accellerate to light speed using a conventional thruster; it would take infinite energy to get to that velocity.)

The kicker is that this is true no matter what the vector of motion imparted is. It would take an absurd amount of energy to alter the motion vector of an incoming cosmic ray proton, than it would to alter a similarly massed proton moving about in a beaker of acid, or a free floating one inside a magnetically contained plasma.

Moreover, the "energy as mass" feature crops up inside the LHC, and is fundamental to how the device operates.  You take two ordinary, unassuming protons and speed the living shit out of them using magnetic accellerators, then smash them into each other. You end up with particle debris much more massive than the two input proton masses; The energy you supplied to speed them up contributes the lion's share of the energy in the collision, and contributes the lion's share of the masses of the resulting particle debris. The affect on accelleration caused by this conversion to genuine mass is scalar; we dont know what direction the particles went in unless we aggressively measure them, but due to uncertainty, we can't know position on the vector, meaning we cant measure magnitude and vise versa. That's one of the reasons why particle physicists describe the particles they detect in their colliders based on their energy in GeV, and not in terms of their mass and direction of movement.  The fact that we are unable to measure it does not make the physics go away-- the particles produced by the collision have both a magnitude and a vector. We just have to pick which one we want to measure.

This has some radical implications, in that it means that objects with lots of kinetic energy already are harder to accellerate(change or add new vectors of motion). This means a spinning body is harder to "move" than a body that is not spinning, and a number of other interesting things.  (which you can see for yourself with reaction wheels and the like.)

For these reasons (Light pressure is a thing, Mass is created inside the LHC, reaction wheels affect changes in vector (at least in terms of orientation-- we dont know how to convert spin into a linear vector of movement, but a linear vector of movement can be converted into spin.) etc) that some degree of interchange MUST happen here.

[Radio Controlled]

light prefers to exist as waves instead of particles. It only does the particle pattern when being watched very closely.

I am no physicist by any means, but I do think this isn't really correct when stated as such. Photons (and any elementary particle, such as neutrons and protons) have the particle-wave duality, but it's not like they suddenly exhibit different properties when watched very closely. You might measure something different in different experiments, but they are the same particles/waves. And 'prefer' to exist as waves is kind of a strange way to put it, since it's not like they have an opinion on the matter: they just appear to behave as waves in some experiments (double slit comes to mind), and as particles in others (photoelectric effect).

For momentum in general, you have a moving object that has mass. (scalar, we dont know what direction it is moving.)

I thought momentum was a vector quantity? Or am I missing something?

[Il Palazzo]

snip

wierd, look. I don't mean to offend here. What you wrote is just a confused word salad, don't you know? It looks like you've made your own definitions of well-defined quantities, with properties that they don't have.
These definitions are there to facilitate communication and remove ambiguity. As it stands I don't know what you mean when you say momentum or energy or any of the other terms and I'm not sure you know what I mean when I use them.

[Dutrius]

Momentum is indeed a vector quantity.


In regards to the momentum of light:
E=mc². This is identical to E=pc (where p is momentum, equal to mc). This means that light has momentum by existing as the equivalent amount of energy.
The energy of light can be given by E=hf=hc/λ (where h is Planck's constant, f is frequency and λ is wavelength).
We can then equate the two together. E=hc/λ=pc. Thus, the momentum can be expressed as p=h/λ.
This is assuming that I haven't gone wrong somewhere.


Also, mass is not "created" within the LHC.
In the LHC, they accelerate protons to 99.99% c. This gives them huge amounts of energy (relative to the proton's rest mass). E_k=0.5mv².
Let's multiply this by 2 because we are colliding two protons together. Therefore E_k=2(0.5mv²).
When a collision occurs, the two protons are converted to pure energy, E = 2(0.5mv²). This then converts into physical particles via pair production, satisfying the conditions of E=mc².

[origamiscienceguy]

Momentum is indeed a vector quantity.


In regards to the momentum of light:
E=mc². This is identical to E=pc (where p is momentum, equal to mc). This means that light has momentum by existing as the equivalent amount of energy.
The energy of light can be given by E=hf=hc/λ (where h is Planck's constant, f is frequency and λ is wavelength).
We can then equate the two together. E=hc/λ=pc. Thus, the momentum can be expressed as p=h/λ.
This is assuming that I haven't gone wrong somewhere.


Also, mass is not "created" within the LHC.
In the LHC, they accelerate protons to 99.99% c. This gives them huge amounts of energy (relative to the proton's rest mass). E_k=0.5mv².
Let's multiply this by 2 because we are colliding two protons together. Therefore E_k=2(0.5mv²).
When a collision occurs, the two protons are converted to pure energy, E = 2(0.5mv²). This then converts into physical particles via pair production, satisfying the conditions of E=mc².

Then, doesn't the energy turn into matter and antimatter?

[wierd]

snip

wierd, look. I don't mean to offend here. What you wrote is just a confused word salad, don't you know? It looks like you've made your own definitions of well-defined quantities, with properties that they don't have.
These definitions are there to facilitate communication and remove ambiguity. As it stands I don't know what you mean when you say momentum or energy or any of the other terms and I'm not sure you know what I mean when I use them.

Word salad?

A vector quantity has a magnitude and a direction. (that's why it is a vector)
A scalar quantity just has a magnitude.

How does this differ from the established definitions?

When you can conserve the vector to a null definition, it becomes scalar, because direction is meaningless after that. (EG, I have a fast moving object in space. I apply additional energy to it to curl it's trajectory into a tight circle, and continue to reduce the radius of this circle until that radius equals zero. The energy in the fast moving object is not "Gone", but it is no longer moving in a straight line. It is now spinning around a point at its baricenter. It still has all of its momentum. It does not matter which direction it is spinning in- It no longer has net velocity in any direction, except circular around the baricenter point. The rate of rotation conserves the momentum.) If you compress the object beyond the schwartzchild radius, it becomes a singularity point. It still has mass, and still has the rotational energy, but the velocity is now unmeasurable. Would you say this is a vector quantity still, or has it become scalar?


An example of a scalar quantity at work here would be the higgs field interaction. We have successfully isolated the Higgs boson now. The Higgs field is totally a thing.  This field fills the entire universe, and Interactions with this field are scalar. They have a magnitude, but no direction. When you accelerate an object, the interaction changes, as it takes more and more energy to accelerate, because the object becomes harder and harder to accelerate. One way of looking at this, is that the object causes more and more drag on spacetime as its inertial reference frame interacts with the surrounding space-- Frame dragging is also a measured, real thing. Adding energy to a moving object seems to increase the magnitude of this interaction.

Another way to put this-- Shining a light beam into a black hole-- what changes, it's rotation or its mass? If you say mass, then you are converting a vector (EM radiation) into a scalar (gravitation) quantity.

[Sheb]

If you keep applying acceleration to your mass, it won't conserve its momentum...

[wierd]

Sheb-- The momentum will increase with the added energy, not go away. However, the object's velocity will appear to diminish. That was the point.

[Il Palazzo]

I've got work to do on a tight deadline, so I'll respond later. Unless you don't care, which is fine too.

[wierd]

That's fine, take your time.

[LordBaal]

I quite like how civilized discussions are here.

[Zrk2]

It's a pleasant change from reddit. This is really interesting, as I know most of this, but haven't thought about it in a while. I should be better at all the relativity, as I've had multiple classes go over it. But then, all my relativity/non-Newtonian mechanics was with respect to mass-defects and nuclear physics, not this particular application.

[Il Palazzo]

Word salad?

A vector quantity has a magnitude and a direction. (that's why it is a vector)
A scalar quantity just has a magnitude.

How does this differ from the established definitions?

That's not what I was talking about.

First, let me explain why I applied such an epithet.

The discussion started because you've made a statement about energy and momentum that I've found faulty. That's all it is about.
You said that one is an expression of the other. I tried to address how that's not the case, also pointing out to how one is a scalar the other is a vector.

Your response begins with

The two kinds of energy must have some degree of interchangeability

and you lost me there already. I don't know what two kinds of energy you mean.
Assuming a slip of mind, and that we're still talking about momentum and kinetic energy...

You then go on on a tangent about light pressure and wave-particle duality that doesn't support your contention that the two qualities are interchangeable. Light pressure obeys both energy and momentum conservation laws. You say that

The energy absorbed imparts a net vector away from the the flashlight's scalar field's point of origin in the form of light pressure

which it doesn't. The energy doesn't 'do' anything. It's just a quantity conserved in the interaction. The thing that does affect the motion directly is the momentum.
The energy conservation means that the energy of the absorbed light must go somewhere, the momentum conservation that the total momentum must remain the same. So while just with the first all the energy could have gone into heat or chemical reactions, with the second a specific change in motion is also required.

Then you talk about momentum:

For momentum in general, you have a moving object that has mass. (scalar, we dont know what direction it is moving.)

While mass is a scalar, velocity is a vector, and the product of the two is still a vector. So when talking about momentum of an object, we do know (or must know) which direction it's moving.

Next, you say:

(We treat the object as if it were standing still compared to the surrounding environment; we are approaching this from the object's reference frame. Much like you feel like you are sitting still sitting in your chair, when in fact you are moving bitching fast in several vectors of movement along with the earth, with the earth/sun system, and with the earth/sun/galaxy system. You feel like you are standing still, because you have your own reference frame. In reality you are carrying some absurd amount of kinetic energy along with you in your reference frame.)

Which uses some confused terminology.
Objects don't 'have a reference frame'. There exist (an infinite number of) reference frames in which any given object is at rest (rest frame is what I think you meant). A reference frame should not be treated as a physical thing. It's just a coordinate system used for description of motion.
Assuming you meant 'a rest frame'...
When you say:

In reality you are carrying some absurd amount of kinetic energy along with you in your reference frame

it's another case of confused terminology. It's incorrect to say that objects carry kinetic energy in their rest frame. They don't, that's why it's a rest frame. The correct thing to say is that kinetic energy (and momentum too) are frame-dependent. It doesn't mean that 'in reality' there's some energy somewhere out there - it means that kinetic energy has no absolute value and can be only discussed by first specifying a reference frame.
I think I know what you're getting at here, but it's rather sloppy and not very relevant to the discussion so why bring it?

In the light of the above, the following:

I am saying that the increase in energy needed to impart any new vector to this object, the total energy you are already carrying influences how much your vector changes based on a fixed input of energy. In this way, the energy imparted is indistinguishable from a mass term. It acts like you are heavier. This is true no matter what direction you try to alter the vector.

suggests that your kinetic energy in some reference frame affects changes in motion in your rest frame. I don't know if that's what you mean. I hope not.
Again, I think I understand what you're getting at (on that later), but it's not the way to do it. Again terminology. You use 'your vector' without qualifiers as if it meant anything.

I don't want to go on quoting your post bit by bit, since I've always found that not very conductive to discussion and this post already looks nitpicky and combative. I hope I've made my case in the support of perceived deficiencies in clarity, uh, clear enough already.


What I'd want to talk about is what I think you're getting at.

You're trying to say that given the two quantities, Ek and p, a change in the one necessitates a change in the other.
This is something nobody argues with! The two are functions of the same base quantities of mass and velocity, so it's obvious that it's going to happen.
But, they are separate quantities, that tell you different things about the system. If you analyse a system trying to keep only one of the quantities conserved, you'll get different results than if you do it with both.
Nuclear reactions look like they do because both quantities must be conserved, so it's not just sufficient to supply the right amount of energy to make new particles pop up - you need to allow for the momentum to be conserved.
This is what makes it easier to create particles from scattering photons off a heavy nucleus than it is from two photons interacting.
It's why you rarely have nuclear reactions that produce only one daughter particle despite nothing prohibiting it energetically - you need something to carry away the excess momentum.

In your example with light pressure, the need to conserve momentum is what causes it, even as all the energy could be just reflected. That's what the momentum is for - to account for such effects!
Why would you invent your own personal ways to get to the same place only without having it as a separate quantity? What does it accomplish apart from confusing your interlocutors?


Lastly, I just have to comment on these two points in your later post:

When you can conserve the vector to a null definition, it becomes scalar, because direction is meaningless after that.

You can't change a vector to a scalar by taking a limit. Even an infinitesimally small vector is still a vector. A limit doesn't mean that something becomes zero - it approaches zero.

Another way to put this-- Shining a light beam into a black hole-- what changes, it's rotation or its mass?

Why present only these two options there? Both mass and momentum change.


Again, I apologise if it looks combative. It's hard to point out what one sees as mistakes without assuming vaguely patronising airs.