Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Steve_Hardwick on 30/10/2008 09:03:39
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Steve_Hardwick asked the Naked Scientists:
Hi Chris,
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Einstein's theory of relativity stated matter can be changed into energy and vice versa energy can be changed into matter. My question is if energy is changed into matter what form of matter would be created and does this occur in nature e.g. is any matter produced when a lightning bolt discharges.
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Love the show (http://www.thenakedscientists.com/HTML/podcasts/), keep up the good work.
Â
regards
Â
Steven Hardwick
Perth, Western Australia
What do you think?
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Yes it does occur in nature notably in the effects of cosmic rays and other high energy particle processes like radioactivity.
The most common process is called pair production. (QV google).
The most common souce of pure enegy avaiable to us is electromagnetic energy and notably gamma rays very high energy photons. These are much shorter wavelength than x rays and their energy is usually expressed in millions of electron volts.
When energy is converted into matter a particle and its exact mirror image antiparticle is produced and nothing else. This happens when a high energy gamma ray passes through a very high field gradient electric field for example near the nucleus of an atom. The gamma ray photon is absorbed and an electron and a positron are produced and the nucleus reacts a bit from the shock the nucleus is much heavier so it does not recoil all that much.
The mass enegy of a stationary electron is about half a million electron volts simmilarly a positron so to create a pair a gamma ray must have more than one million electron volts of energy.
In general high energy natural processes like lightning bolts do not concentrate their large energies enough to generate gamma rays and cannot produce matter from energy. electron positiron pairs are the lowest energy ways of producing matter from energy
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Do you want a simple process? Take a coin and spin it; while it's spinning it has more mass then when at rest. The mechanical work you have made on the coin to spin it has become mass.
Or you can heat it; if you give it 1 joule of heat, its mass will increase of 1/c2 kg.
Or, maybe you want to use a spring: take a spring at rest (neither compressed nor stretched) and weigh it; then compress (or stretch) it and measure its weight again (Very sensitive scale!): it's increased.
This also explain why is sometimes incorrect to say "energy converted in mass": in the previous examples, you have an energy increase (kinetic energy of the spinning coin, thermodinamical internal energy of the heated coin, elastic potential energy of the stretched/compressed spring) and a mass increase; what have you "converted"? Nothing! In those examples, the energy increase IS the mass increase.
About the bolt: specify, as system, a region of space which remains still in some ref frame (centre of mass doesn't accelerate) and which total energy has a variation, for example a cylinder of still air through which the bolt will discharge; when the bolt discharges, that region of air will have more mass because you have given it energy. What kind of mass? The same as before. You will have the same chemicals, the same number of atoms and molecules (for sake of simplicity I'm not counting the electrons or other ions entered in the cylinder, just the energy), but that system will have more mass; it's incorrect to think that the energy has become another kind of matter.
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Light arrow; Whilst I agree that what you say is basically true. I think that our questioner was wanting to see a chunk of material that you could in effect weigh cpoming from energy in some sort of reaction and you need something like pair production to do this.
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There is no question about it happening. The point is, though, that it represents a tiny fraction of the Earth's total mass and a small factor compared with accretion of actual matter from elsewhere.
This has been going on ever since it all started.
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Light arrow; Whilst I agree that what you say is basically true. I think that our questioner was wanting to see a chunk of material that you could in effect weigh cpoming from energy in some sort of reaction and you need something like pair production to do this.
Maybe you're right. However I think it's important for people who wants to use E = mc2, to understand what it really means; I took quite a lot of time to fully understand it, just because no one had expained me well. If you only give the example you made, people (as me before) will keep thinking that:
1. There must be convertion energy --> mass, that is, that some amount of energy disappears and the same amount of mass appears. This is NOT true. Even in pair production, the total energy of the system is the same, before and after the process: E = hν before; E = 2Mec2 after, where Me = electron's (= positron's) mass.
2. Some new matter must be created. This is true, for example, in pair production, but it's not in the processes I mentioned in my previous post.
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Yes, we have seen photons being turned into electrons and vice versa. We also know due to this, there must be plenty of particles with mass being created in atmospheric collisions.
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Is that mass you add when spinning a coin or heating an object?
Weight is defined as the measurement of the pull of gravity on an object.
Mass is a measurement of the amount of invariant matter something contains.
Invariant as it is expected to contain the same 'amount' of energy and momentum no matter in what 'reference frame' you observe it.
"If the system is one particle, the invariant mass may also be called the rest mass."
I've learnt that this is a definition based on the approximation of Avogadro's number.
http://en.wikipedia.org/wiki/Unified_atomic_mass_unit
And that it's if I got it right, "still not known to the units place of significant figures."
And it's a estimation of mass to charge ratio, or a derived molar mass.
All of which are based on the agreed upon 'relative masses'.""
And then we have what we define as relative mass.
That is added 'mass' created by for example accelerating a object in space.
"and this is the total quantity of energy in a body or system (divided by c2). The relativistic mass (of a body or system of bodies) includes a contribution from the kinetic energy of the body, and is larger the faster the body moves.
So unlike the invariant mass, the relativistic mass depends on the observer's frame of reference.
However, for given single frames of reference and for closed systems, the relativistic mass is also a conserved quantity.
Because the relativistic mass is proportional to the energy, it has gradually fallen into disuse in among physicists."
http://en.wikipedia.org/wiki/Mass_in_special_relativity
And now we come to the crux of my problem:)
I can't say that I know what mass is, but this mass you are referring to as added here?
Isn't that what we would call as relative mass?
And if measured as weight only to be that..
Weight, as it is created by an influx of forces?
As compared to 'invariant mass' where weight will vary, but where its 'proper mass' always is expected to be the same.
It may sound like nitpicking but to me those definitions creates problems:)
If we have 'matter' we must have 'invariant mass'.
And that definition contrasts sharply against our other definitions of the 'same' phenomena.
Namely mass 'in general'.
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Is that mass you add when spinning a coin or heating an object?
Weight is defined as the measurement of the pull of gravity on an object.
Mass is a measurement of the amount of invariant matter something contains.
Invariant as it is expected to contain the same 'amount' of energy and momentum no matter in what 'reference frame' you observe it.
"If the system is one particle, the invariant mass may also be called the rest mass."
I've learnt that this is a definition based on the approximation of Avogadro's number.
http://en.wikipedia.org/wiki/Unified_atomic_mass_unit
Sorry, I cannot say I have completely grasped what you mean, anyway if your question was: "what kind of mass is the one you get by spinning a coin or heating it" then the answer is: invariant mass.
That is, the only meaningful mass, at least in SR. In GR there are several kinds, but we are not talking about curved spacetime, here.
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But that can't be invariant mass.
Can it?
Isn't the definition of invariant mass, that it will be the same no matter what 'reference frame' you observe it from.
Which to me means that it is what you have left without any 'forces' working on it?
If you see how I think.
To me it seems as a 'manipulation' of that invariant mass using, for example, heat?
And describing it f ex. like 'by taking this 'system'(proper mass + heat) to any frame, it will give you that same result' seems to me then as true if 'using' acceleration instead of heat.
And that is definitely not invariant mass?
Am I getting into a quagmire here:)
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But that can't be invariant mass.
Can it?
Yes it is.
Isn't the definition of invariant mass, that it will be the same no matter what 'reference frame' you observe it from.
Which to me means that it is what you have left without any 'forces' working on it?
If you see how I think
You forgot to add "Inertial" reference frame. Infact, a spinning coin's mass doesn't change from an inertial ref. frame to another.
To me it seems as a 'manipulation' of that invariant mass using, for example, heat?
And describing it f ex. like 'by taking this 'system'(proper mass + heat) to any frame, it will give you that same result' seems to me then as true if 'using' acceleration instead of heat.
And that is definitely not invariant mass?
In physics it's always necessary to give a clear definition of concepts and usually this is a mathematical definition, even if it could seem unintuitive.
In this case the mathematics is quite simple, so you're lucky [:)]:
Given a physical system in an inertial ref. frame which total energy is E, total momentum, in modulus, p and total invariant mass m, you have:
E2 = (cp)2 + (mc2)2
Now, if you heat a still coin leaving it still (in your inertial ref. frame) you have p = 0 (because it's still) so E = mc2. It means that any increase (decrease) of the system's energy becomes an increase (decrease) in its invariant mass.
Edit: with a spinning coin is the same, if it's centre of mass is still in your frame: total momentum p is equally zero.
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It's strange.
i think you are right in your definition, but didn't you by using that coin introduce 'motion' as being 'mass' here.
Or it being acceleration, depending on where your coin is on 'a time scale/curve':)
If one treat it as 'events' inside an accelerating system (red / blue shift in our spaceship)
Then it seems that there will be an infinite amount of events here, all with their own 'invariant mass'?
"The invariant mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference."
momentum is one of the parameters here, and that only 'express itself' as a result of a velocity, right?
Otherwise we would define it as 'inertia':)
Then invariant mass can only be said to be invariant as a 'event'.
It seems then a abstract description, not acting as a unchanging entity, described in time, inside spacetime?
Strange but reasonable.
I've always had problem with what I thought to be the definition of 'invariant'.
But i can't see how it differ accelerating from non accelerating systems?
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Lightarrow you wrote
"Edit: with a spinning coin is the same, if it's centre of mass is still in your frame: total momentum p is equally zero."
Are you saying that the added 'invariant mass' seeks itself to the 'still' center of that coin as it is added by the coins centrifugal 'motion/acceleration'.
This is deeper than I thought.
(into that quagmire I mean:)
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Lightarrow you wrote
"Edit: with a spinning coin is the same, if it's centre of mass is still in your frame: total momentum p is equally zero."
Are you saying that the added 'invariant mass' seeks itself to the 'still' center of that coin as it is added by the coins centrifugal 'motion/acceleration'.
This is deeper than I thought.
(into that quagmire I mean:)
Don't know exactly what you mean. However the essence of the concept is this:
mass (when I write mass I always intend invariant mass, unless we are talking about curved spacetimes) is nothing else than "energy confined in a given space".
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Lightarrow, it seems that my idea of what invariant mass is and how it expresses itself is sadly befuddled here.
I would have expected both that spin of the coin and the added heat to be an expression of some sort of relativistic mass, not invariant mass?
And you will swear on your... ah?
Sort of.
Do you have any good links discussing types of mass?
I looked but can't find pages discussing this.
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I can see why momentum is there.
First of all we have no objects being in rest anywhere.
the only definition we have about 'rest' is relative something having the same velocity.
That's why I had trouble with 'invariant mass' as I saw it before.
But now 'invariant' seems to be defined as whatever properties acting on a object as long as it is not accelerating?
That seems to create frames that might have extremly small 'time-slices'.
Think about that spinning coin for an example, acting in 'gravity' it will, seen in time, change its rotation.
And there is nothing hindering me to speed it up or down (the coins rotations) in time.
Think now of our experiment with the light-bulbs inside an accelerating spaceship.
------------>
o----X----o
I'm standing in the middle (X) of that ship accelerating.
What does the ship do here when accelerating?
I saw it as the ships acceleration created an 'gravity well' (¤) placed behind its tail.
This is the direction in where you will feel that 'gravity' as well as the direction your porcelain will fall when dropped.
¤ <----
...........................................
Travel direction
-->-------> ------------ship---------->
¤ <- Gravitys direction <- o----X----o
............................................
Inside the ship, looking at the light bulbs from our position in the exact middle, we will find that the light bulb situated at the front will have a blueshift as compared with the lightbulb coming from the rear who will present a red shift.
Graphically it should be like this
-->-ships --> acceleration-->
¤ ----RS--> X <-BS--
That as the light coming from the rear is 'climbing' uphill
And the light from the front is going 'downhill'
"In physics, light or other forms of electromagnetic radiation of a certain wavelength originating from a source placed in a region of stronger gravitational field (and which could be said to have climbed "uphill" out of a gravity well) will be found to be of longer wavelength when received by an observer in a region of weaker gravitational field.
If applied to optical wave-lengths this manifests itself as a change in the colour of the light as the wavelength is shifted toward the red (making it less energetic, longer in wavelength, and lower in frequency) part of the spectrum. This effect is called gravitational redshift and other spectral lines found in the light will also be shifted towards the longer wavelength, or "red," end of the spectrum. This shift can be observed along the entire electromagnetic spectrum."
http://en.wikipedia.org/wiki/Gravitational_redshift
But when looked at as a consistent structural frame (space ship) the question I ask is why this can't be seen as a infinite (yes:) number of frames all resting inside spacetime.
And that brings me back to that coin, and the definition of what may be invariant?
Is there anything we can prove to be 'invariant' other than (possibly) geometrically?
Like, we do have geometric shapes defining 'matter' in 3D but that's about it?
So is 'invariant mass' everything except acceleration?
And where is the difference between that coin spinning and acceleration
If one define the 'time slices' per frame as infinitively many in both?
Yep, now I'm confusing, but I am:)
Sorry about that.
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Lightarrow, it seems that my idea of what invariant mass is and how it expresses itself is sadly befuddled here.
I would have expected both that spin of the coin and the added heat to be an expression of some sort of relativistic mass, not invariant mass?
And you will swear on your... ah?
Sort of.
Yes.
Do you have any good links discussing types of mass?
I looked but can't find pages discussing this.
http://en.wikipedia.org/wiki/Mass_in_general_relativity
<<If two objects have the same mass, and we heat one of them up from an external source, does the heated object gain mass? If we put both objects on a sensitive enough balance, would the heated object weigh more than the unheated object? Would the heated object have a stronger gravitational field than the unheated object?
The answer to all of the above questions is yes. The hot object has more energy, so it weighs more and has a higher mass than the cold object. It will also have a higher gravitational field to go along with its higher mass, by the equivalence principle. (Carlip 1999)>>
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But now 'invariant' seems to be defined as whatever properties acting on a object as long as it is not accelerating?
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Invariant means that doesn't change from a ref frame to another, even without acceleration. Example. An object's velocity is not invariant: from Earth a passing train has velocity 100 km/h, from another train, moving at 80 km/h in the same direction, it has velocity 20 km/h. For the same reason, kinetic energy is not invariant. The same for an object's coordinates. The same for momentum. In special relativity, not even time is invariant.
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But now 'invariant' seems to be defined as whatever properties acting on a object as long as it is not accelerating?
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Invariant means that doesn't change from a ref frame to another, even without acceleration. Example. An object's velocity is not invariant: from Earth a passing train has velocity 100 km/h, from another train, moving at 80 km/h in the same direction, it has velocity 20 km/h. For the same reason, kinetic energy is not invariant. The same for an object's coordinates. The same for momentum. In special relativity, not even time is invariant.
Yes, we talk about the same thing here.
But my own:) definition was.
That by calling some kind of mass (matter) 'invariant' we were referring to that property of matter that defines it reducible, when all forces/actions acting on it had been 'counted away'.
And that made me confused as we couldn't define 'at rest' as being anything more than a relation between two frames of reference.
I should have checked it up.
My understanding was..
Invariant=Persistent in occurrence and unvarying in nature.
This new definition of 'invariant' seems to me more of.
"A feature (quantity or property or function) that remains unchanged when a particular transformation is applied to it"
So to me it does not define the reducible 'stuff' matter is made of, it's more of defining a 'invariant' relation between whatever energy state a object in spacetime might have 'in that exact 'time' and frame' and then states that this 'relation of energy' will be valid for all other frames (except acceleration).
Do I make sense here?
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Looking at your link which btw is very nice (don't know how I missed it) I read this about invariant mass.
"
The only difference between the "hot" and "cold" systems in our last question is due to the motion of the particles in the gas inside the pressure vessel. Doesn't this imply that a moving particle has "more gravity" than a stationary particle?
This remark is probably true in essence, but it is difficult to quantify.
Unfortunately, it is not clear how to measure the "gravitational field" of a single relativistically moving object. It is clear that it is possible to view gravity as a force when one has a stationary metric - but the metric associated with a moving mass is not stationary. "
That 'ambiguity' was what I thought that this 'new' definition was trying to do away with?
Am I wrong in understanding it as being applicable to all situations except acceleration?
I will have to reread that wiki to see what exactly 'invariant' it defines
'A relation' or a 'reduction' :)
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My understanding was..
Invariant=Persistent in occurrence and unvarying in nature.
This new definition of 'invariant' seems to me more of.
"A feature (quantity or property or function) that remains unchanged when a particular transformation is applied to it"
Bingo! [:)]
So to me it does not define the reducible 'stuff' matter is made of, it's more of defining a 'invariant' relation between whatever energy state a object in spacetime might have 'in that exact 'time' and frame' and then states that this 'relation of energy' will be valid for all other frames (except acceleration).
Here what do you mean with "reducible"?
Looking at your link which btw is very nice (don't know how I missed it) I read this about invariant mass.
"
The only difference between the "hot" and "cold" systems in our last question is due to the motion of the particles in the gas inside the pressure vessel. Doesn't this imply that a moving particle has "more gravity" than a stationary particle?
This remark is probably true in essence, but it is difficult to quantify.
Unfortunately, it is not clear how to measure the "gravitational field" of a single relativistically moving object. It is clear that it is possible to view gravity as a force when one has a stationary metric - but the metric associated with a moving mass is not stationary. "
That 'ambiguity' was what I thought that this 'new' definition was trying to do away with?
Am I wrong in understanding it as being applicable to all situations except acceleration?
Here you are mixing at least three different concepts: invariant mass in special relativity, gravitational mass and general relativity. If you only want to talk about special relativity (even because I know little of GR) then you only need to know a system's energy and momemtum, nothing else.
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Oh yoron, would you like my explanation, which is no more correct than his, but might help yo?
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"Here you are mixing at least three different concepts: invariant mass in special relativity, gravitational mass and general relativity."
Well thank you Mr Lightarrow.
Is it ok if I lay down to die now?
Awhh, just joking:)
I had hoped that the definition of 'invariant' would be more intuitive to me.
But it's not.
Yet it is thought as giving a better definition of 'mass' if I understood the intention rightly.
But don't give up on me yet Lightarrow, I will try to understand.
(Reducible, as I was thinking before, was to me relating to some smallest constituent of, and defining primary, 'matter' as invariant in all frames.)
Embarrassingly naive, as I now find out.
This coin, if rotating.
Won't its highest 'gravity'(angular momentum?) be at its rim?
I know, mixing again:)
It's just that I would have wanted gravity and mass to be a simpler relation.
Highly subjective of me I admit.
And...
Yes Mr S, if you please:)
Go for it, if you can pound some more sense in my head?
Lightarrow have tried:)
And partly succeded.
I know as I now have a headache..
But that can only become better
( bigger? :)
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This coin, if rotating.
Won't its highest 'gravity'(angular momentum?) be at its rim?
If you treat it as a rigid body, then you can talk of the entire system's angular momentum, so you just have a unique one. If the system is not rigid, or you want to consider just a small portion of it (e.g. a single particle) then, yes, the angular momentum is higher for those particles at greater distance from the centre. However, it's not angular momentum which makes the mass in this case, but rotational kinetic energy and elastic potential energy of the stretched bonds between the particles (because of centripetal force). Usually the second one is neglected in ordinary (non-relativistic and however for not very high angular velocities ω) problems, so you are left with rotational kinetic energy. For a rigid body this energy is:
Er = (1/2)Iω2
where I = moment of inertia (for an homogeneus disk I = MR2/2, M = disk's mass, R = disk's radius).
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Awh.
Lightarrow you instill ever new definitions for me.
'Rigid body' you say?
(Would that have anything to do with dreaming of Christina Aguilera:)
But I like it very much.
Exact definitions help me see how things are defined.
So now I will have to read up on that.
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"but rotational kinetic energy and elastic potential energy of the stretched bonds between the particles (because of centripetal force)."
Nice.
'Rotational kinetic energy'.
How does that differ from 'angular momentum'?
Is it in the geometric direction of 'force'.
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Awh.
Lightarrow you instill ever new definitions for me.
'Rigid body' you say?
(Would that have anything to do with dreaming of Christina Aguilera:)
ROTFL [:D]
But I like it very much.
Exact definitions help me see how things are defined.
So now I will have to read up on that.
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"but rotational kinetic energy and elastic potential energy of the stretched bonds between the particles (because of centripetal force)."
Nice.
'Rotational kinetic energy'.
How does that differ from 'angular momentum'?
Is it in the geometric direction of 'force'.
They are different concepts, even because they have different units and one is a scalar while the other is a (pseudo) vector.
Given a system of N particles, you have:
Angular momentum (pseudo vector) = K = ∑i ri Λ mivi units: Joule*second
ri = position vector of the i-esim particle
mi = mass of the i-esim particle
vi = velocity of the i-esim particle
Λ = vectorial product
Rotational kinetic energy (scalar) = Er = ∑i (1/2)mi(viG)2 units: Joule
where viG is the velocity of the i-esim particle with respect to the centre of mass G. For a rigid body such velocities viG are all perpendicular to the vector radius from the axis of rotation; for this reason it could be demonstrated that
Er = (1/2)Iω2
Edit: Indicating with Ku the component of angular momentum along the axis of rotation, the following equation is valid:
Ku = Iω
so you also have:
Er = (1/2)Kuω
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Thanks Lightarrow.
I will ask you more things, I'm sure.
But first I will need to assimilate what you already shown me.
Considering the average density of my head.
Quite thick I'm afraid.
It will take me some time:)
But, as they say in sunny California...
"I'll be back"
--------Quote-------
They are different concepts, even because they have different units and one is a scalar while the other is a (pseudo) vector.
Given a system of N particles, you have:
Angular momentum (pseudo vector) = K = ∑i ri Λ mivi units: Joule*second
ri = position vector of the i-esim particle
mi = mass of the i-esim particle
vi = velocity of the i-esim particle
Λ = vectorial product
Rotational kinetic energy (scalar) = Er = ∑i (1/2)mi(viG)2 units: Joule
where viG is the velocity of the i-esim particle with respect to the centre of mass G. For a rigid body such velocities viG are all perpendicular to the vector radius from the axis of rotation; for this reason it could be demonstrated that
Er = (1/2)Iω2
--------------------End - Quote --
Yes, I can see that one is scalar and that the other describing the whole 'system / coin' of scalar 'bonds' will be seen as a vector (magnitude and direction)
Is there anywhere one can download the most common expressions of 'symbolic' expressions and their definitions?
Or do they change depending on what you use them for?
Often when I see those mathematical symbolic formulas they don't get explained.
And sometimes they don't seem to be bound to any 'definite description'
So doing like you do makes me want to put numbers into your formulas to see if I really understands them.
And that's why I will need to go slow.
This is a new language for me.
I've done some boolean logic, Computers and Philosophy, but that is the nearest I've ever cometh :)
So I do enjoy the care you take in explaining your concepts and math here.
Cheers.
yoron.
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If you google rotational kinetic energy you find many links, e.g.:
http://theory.uwinnipeg.ca/physics/rot/node6.html
About vectorial product, the rule is the following. Given the two vectors:
A = (Ax,Ay,Az)
B = (Bx,By,Bz)
then:
AΛB = (AyBz-AzBy,AzBx-AxBz,AxBy-AyBx)
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What?
Only joking:)
Thanks..
And I'm goggling.
Or should it be ogling?
:)
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What?
Only joking:)
Thanks..
And I'm goggling.
Or should it be ogling?
:)
Actually, there is a little picture which helps remembering that rule: write the symbols x, y, z in this order, clockwise in a circle. So you understand that the x component of the vectorial product is given by the product of the y component of the first vector by the z one of the second (from y to z you go clockwise) minus the z component of the first by the y one of the second (because now you go anti-clockwise): AyBz-AzBy.
The same rule for the other components.
[ Invalid Attachment ]
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Ahem, perfectly understandable.
With some thought?
perhaps?
And yes, we are talking density here.
(between my ears:)
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The first one was easier on my mind than this second ::))
But that may have to do with my English?
There is only one conclusion can I draw after reading your explanation over, some times.
You are right no matter what sense I will make.
I will never forget that little picture:)