Massless Energy & Nothing.

[Qfwfq]

It isn't E = mc^2 + pc it's (mc^2)^2 = E^2 - (pc)^2

 

For m = 0 we get:

 

(0c^2)^2 = 0 = E^2 - (pc)^2

 

from whence E = pc.

 

For p = 0 we get:

 

(mc^2)^2 = E^2 - (0c)^2 = E^2

 

from whence E = mc^2

[Damo2600]

Right got it...

 

E = mc^2 (Rest mass)

 

E = pc (Massless momentum)

 

E = mc^2 + pc

 

or

 

(mc^2)^2 = E^2 - (pc)^2

 

(Energy of mass in momentum.)

 

So the million dollar question is:

How do you define m = 0?

 

Damien

[Qfwfq]

E = mc^2 + pc

 

or

 

(mc^2)^2 = E^2 - (pc)^2

No, these two equations are not equivalent.

 

Remember: a^2 + b^2 isn't equal to (a + :circle:^2

 

So the million dollar question is:

How do you define m = 0?

When E = pc, or E = p in natural units.

 

It might all strike you as a bootstrap argument, the way to understand is to get the 4-vector formulation of dynamics straight. If you don't want a too formal approach, such as in Landau-Lifschitz, you might prefer that in Feynman's volume II.

 

In any case, (E, p) is a 4-vector (called 4-momentum or energy-momentum) and it's "square" according to the Minkowsky metric, which is such that c is a scalar, is E^2 - p^2 and this is equal to the square of the scalar m. If you follow the whole track, the 4-momentum is equal to m times the 4-velocity; the derivative of this equation by proper time gives the analogue of Newton's F = ma. The 4-force is just the 4-momentum derived by proper time.

 

If you look it up, you'll find it takes quite a bit of getting used to, but it works.

[Damo2600]

Hi Qwfwq,

 

I looked up Feynman's volume II and saw that he once started a lecture stating that he was related to dirt.

 

But anyway I mentioned that my maths skills weren't great.

 

Energy-momentum = 4-Force (derived by proper time)

 

So energy minus mometum gives us our rest mass.

 

(mc^2)^2 = E^2 - (pc)^2

 

Which is derived with no time dilation and I can obtain the rest mass = 0. Light has no rest mass. The problem I see with this is that rest mass of light is converted (according to all I have learnt). Kinetic energy converted into purely potential energy. So light does not exist at a rest mass. This makes a compelling arguement for the assumption that light has no mass. I do not see that an absence of rest mass equates to absence of mass (due to the nature of light).

 

E = m_o gamma c^2

 

Where m_o equals rest mass.

 

So m_o gamma a = energy - momentum

 

m_o 1/sqrt 1 - c^2/c^2.c

 

E - p = m_o.1.a

 

E - p = m_o.a

 

m_o = 0

 

m = 0

 

Rest mass = mass (moving at c)

 

E = p

 

Utterly Dazzling...!

 

It appears that I could place a value in for mass as well.

 

Rest mass = 1

 

mass (moving at c) = 1

 

Why can't I just do that? There mass has a value of 1 :circle:. Or the mass of light that has been measured in a mirror box that Tormod linked?

 

The second million dollar question I see is:

 

How does energy gain mass? Say in the form of a particle. Would you be teaching us that particles have no mass next?

 

Qwfwq it does seem like a very bootstrap arguement.... However I will look into it.

 

Damien

[Qfwfq]

Indeed, the matter isn't very simple, especially if you are a bit troubled by the algebra and the calculus. There is also the unfortunate fact that these things, after a full century of being among the most widely preached scientific topics, are still taught very much without the Lorentz-covariant approach and with the unnecessary idea of the velocity-dependant mass. Terms such as rest mass or invariant mass are used only to distinguish from the E = m_o gamma c^2 which is a relic of history that would well be forgotten.

 

I'll remind you again, the sum of squares isn't equal to the square of the sum.

 

To understand better, think of the Pythagoras theorem, right-angled triangles!

 

Further, think of ordinary 3-vectors. A vector can be written as the sum of three perpendicular x, y, and z components. The length of the vector squared is the sum of the squares of all components. Choosing rotated Cartesian axes, the components change but the rule of summing squares holds.

 

The similar thing holds for space-time 4-vectors except that the squares are summed with opposite signs for space and time components, this complies with c being invariant.

 

If you can get the picture of the whole link, from electromagnetism and invariant c, to space-time geometry and Lorentz invariance, it becomes a lot less bootstrap, relativity even becomes almost obvious.

[Qfwfq]

The second million dollar question I see is:

 

How does energy gain mass? Say in the form of a particle. Would you be teaching us that particles have no mass next?

Good question! :)

 

Whether the mass of an electron, for instance, may be seen as internal energy is still somewhat open to debate, it isn't currently observable. However a pair, e- e+, can annihilate producing a pair of photons with the same total 4-vector of energy-momentum.

 

This does not mean a particle "has no mass" because, whether or not you can see the internal details, it is mass. Mass is just a name for rest energy. If you warm a piece of iron it will have more rest energy, which means more mass.

 

If you throw the same piece of iron, without warming it, it will have kinetic energy for your frame of reference but this does not mean it has a greater mass, it means instead that E will be greater than m (times c^2 if you prefer) in your frame.

 

Why does the iron have a greater mass when it is hotter? At a greater temperature, the constituent particles have a greater kinetic energy, for a frame of reference in which the iron is at rest. Each particle doesn't have a greater mass but the total energy is greater, again for the same frame in which the iron is still. This means greater rest energy: greater mass.

[Damo2600]

Hi Qwfwq,

 

I am very interested in your posts they are always thought inspiring. I have to read them very slowly and look up any or usually all terms you are using to see what exactly you are talking about. So I learn.

 

However I am not sure I understand the reasoning for how this proves energy has no mass. I seem to have a misunderstanding about electro-magnetism. A magnet, gravity, electron and photon all exhibit electromagnetic force. A magnet, planet and electron all exhibit mass. Where as you are saying of the three it's the photon that does not have mass. In the next post you are suggesting that a photon is basically an electron or positron (I'll discuss this more in the next post - I told you webfeet) .The force gravity creates is described as the curvature of spacetime. Now spacetime does not, as far as I am aware, have mass nor is it energy. Am I right? A magnet has mass and electro-magnetic force. If you polarise the charges within a metal then either pole of the magnet will attract another peice of metal or another magnet. As far as I was concerned magnetic fields, which are exhibited by electrons as well, are not energy. I would be interested if you could correct this notion if I am incorrect.

 

The spacetime 4-vectors you describe map out points in space and time. Just like a 3-d movie character is mapped out using vectors. You can make the character look real, i.e. solid with mass and form, but inside the character on the screen has no mass. Einstien-tensor, as is my understanding, maps out the vectors so you can see exactly what is happening in the space around the planet or star over time and describes the curvature of spacetime.

 

Electromagnetism is an effect of electrons and you are saying they are the thing.(edit -the 'same' thing, that should be)

 

It is still 'bootstrap' to me and I'm not convinced.

 

Josephine

[Damo2600]

(edit: snipped the quote sorry Tormod)

 

The fact that e- and e+ annihilate when they meet was known to me. I was told that the energy is absorbed by a near by proton. The person who explained this to me has been studying electrons for a 'long' time and feels that electrons having wave and particle function is not exactly true. So they did not explain that e- & e+ will from two photons. We will leave this person out of the conversation and go with your explanation. So a photon and electron appear to be the same thing according to you and an electron is a photon energy at rest.

 

We will leave the kinetic energy out of it aswell. Rest energy is mass. More Rest energy more mass. It appears you are describing that which I have already suggested in a previous post (which was not accepted well). That mass is merely a measurement of how energy reacts to other energy. My body is energy and the Earth is energy. When I weigh myself on the scales (which I hate to do) It shows not how much weight I have but how much energy I have and the attractive forces between my energy and the Earth's energy.

 

That is fair enough to me. Energy has mass. But mass is merely a measurement of the attractive quatity of mass (edit: 'quality of energy' that should be). Are we in agreeance?

 

The fact that photons have zero mass to me is uncertain. It appears that it has no inertial mass. It appears that it does exhibit gravitational mass. It appears that redshift has something to do with energy being altered by the electro magnetic field. If an electron is a photon (in a different form) then it appears it has a rest mass.

 

It does appear that you can look at the situation either way and to say that the opposite viewpoint is incorrect is in itself incorrect.

 

Well anyway thanks again,

Josephine

[WebFeet]

I seem to have a misunderstanding about electro-magnetism. A magnet, gravity, electron and photon all exhibit electromagnetic force.

Close, but no cigar.

A magnet and an electron exhibit electromagnetic force. Gravity is a force, but it is not electromagnetic and a photon is the force carrier for electromagnetic force, but does not exhibit a field of its own.

 

In the next post you are suggesting that a photon is basically an electron or positron (I'll discuss this more in the next post - I told you webfeet) .

A photon Can have the same energy, but is not an electron or a positron. The characteristics of the electron/positron, charge/mass, disappeared when they annihilated each other.

 

As far as I was concerned magnetic fields, which are exhibited by electrons as well, are not energy. I would be interested if you could correct this notion if I am incorrect.

The force carrier of electromagnetic fields is the photon, energy. You can determine the size of a magnetic field. This is not a single photon, but a concentration of photons. A single photon does not have mass, but a group of photons does.

 

The fact that e- and e+ annihilate when they meet was known to me. I was told that the energy is absorbed by a near by proton.

All the energy from the e- and e+ is accounted for in the resulting photons.

 

That is fair enough to me. Energy has mass. But mass is merely a measurement of the attractive quatity of mass (edit: 'quality of energy' that should be). Are we in agreeance?

Look at what you have written very carefully.

In one statement you are saying, after the edit, that mass is the measurement of the attractive property of energy. In the previous statement you are saying that Energy has Mass.

If Energy already had Mass, why would it also need a method of measuring mass?

[Damo2600]

'A magnet and an electron exhibit electromagnetic force. Gravity is a force, but it is not electromagnetic and a photon is the force carrier for electromagnetic force, but does not exhibit a field of its own.' WebFeet

 

I see..

So Earth has poles like a magnet and they both attract yet they are different effects. Could I ask you to please explain this further to me as I do not understand the difference other than a magnet will attract metal and gravity will attract anything. Please don't explain this if you do not wish to.

You are stating that photons and eletromagnetic force are intrinsically related. IT seems you are stating that a photon does not have it's own eletro magnetic field, rather, it acts as the feild. In other words an electromagnetic force has no effect on other metals without the photons to act as a carrier.

 

'A photon Can have the same energy, but is not an electron or a positron. The characteristics of the electron/positron, charge/mass, disappeared when they annihilated each other.' WebFeet

 

If a car smashes into another car and two motorbikes are produced wouldn't this suggest that the car and motorcycle are intrinsically related.

 

A single photon does not have mass, but a group of photons does.' WebFeet

 

It appears there is a contradiction here which you have not explained.

 

'All the energy from the e- and e+ is accounted for in the resulting photons.' WebFeet

 

Except for the mass and electromagnetic field which has somehow dissapeared.

 

'In one statement you are saying, after the edit, that mass is the measurement of the attractive property of energy. In the previous statement you are saying that Energy has Mass.

If Energy already had Mass, why would it also need a method of measuring mass?' WebFeet

 

I will restate. Mass is merely a measurement of the attractive quality energy has with respect to other energy. Does that sit better with you?

 

Thanks Josephine

[paultrr]

Einstein's field equations are

 

G_(uv) = 8 pi T_(uv)

 

The entity on the left, Tuv, is the stress energy tensor. The entity on the right is a measure of the curvature of space-time.

 

The stress energy-tensor is nothing but the density of energy and momentum per unit volume. When you multiply the stress-energy tensor by a vector representing a volume, the result you get is the total energy and momentum in that volume as described by the energy-momentum 4-vector. Tuv describes in tensor form the mass, momentum and stress intensities of a system at any point in a field. That tensor for electro-magnetic radiation takes a particular form and when you perform a tensor operation on it, called 'taking the trace', you end up with zero. It is therefore described as being trace-free. This tensor then tells space-time how to curve through another tensor called the Einsteinian Guv, which in turn then tells matter and radiation how to move. As such both kinetic energy and rest mass all add to the curvature of spacetime. Around any mass or energy, spacetime is curved. The Energy-Momentum-Tensor does not have anything to do with the actual mass of the body. Gravity depends on the objects energy, not on the mass. The reason mass comes into play is mass and energy are related via the equations that have been raised here before. All positive energy curves spacetime. In the quantum aspect so does negative energy. However, one curves spacetime in a positive fashion while the other curves spacetime oppositely.

 

 

Photons have no rest mass. But they do have kinetic energy which does play into this equation. They are the force carrier of the EM field. By theory, the force carrier of gravitation is the graviton, a spin 2 particle. It too by theory would have no rest mass. The force carrier of the strong force and the weak force are themselves Bosons. But these force carriers have mass and in the weak force the three carriers have charge of the normal type(+W,-W,and Neutral W) while those for the strong force have charge of what is termed the color type(Red, Blue, Green and their anti-matter counter parts) which is a whole other issue for another discussion.

[Qfwfq]

Hi Damo, unfortunately I couldn't begin to give a whole course in theoretical physics here although I like to help people learn and I'm pleased that you learn something by looking up what I say and thinking about it. It's actually a good method for those who take the challenge, that's why I sometimes step in with some witty remark, hoping it will stirr up thought. To prove all these things properly, so that you could be convinced, would take a bit of doing, along the lines of a good university degree in physics, so I can only touch upon things and help you to see where you want to go.

 

First, let's agree that, since you do catch on to things, we can simplify some things by choosing, as I have mentioned, the same unit of "length" for space and time: the unit for velocity will then be this length divided by itself... velocity is dimensionless in space-time and c = 1. What does E = mc^2 become? It becomes E = m and this means that mass id energy. This equation is for a body at rest, no kinetic energy (nor other forms such as potential) so mass is one form of energy and a body's mass is the energy which is "internal to it" in a sense.

 

There has historically been some confusion about these things, they have been quite cleared up for some time, to the enlightened physicist but they still aren't taught very well to the common folk, despite a full century of wide preaching since Einstein's initial publication in April 1905. Exactly how is mass "one form of" energy? It could be a long discussion. A friend of mine took the historic branch and graduated with a thesis on this confusion and how it arose. That took quite a bit of doing! It added very good marks to her graduation. The idea of writing mass dependent on velocity was an easy conclusion to draw from Einstein's first works, especially before Minkowski sorted things out mathematically better, a few years later. The often quoted m_0 Gamma is really just the energy component of the 4-momentum, modern physicists use 'mass' to denote the length of this 4-vector according to Minkowski's metric, for a body at rest the 4-momentum is (m, 0, 0, 0).

The spacetime 4-vectors you describe map out points in space and time.

Remember: :) there aren't only purely geometrical vectors!!!!! The magnitude of force and momentum aren't lengths.

 

e- e+ --> g (I'll use g for photons, they're usually called gamma)

 

This reaction can't conserve the energy-momentum. Why? The following two can:

 

e- e+ --> 2g

 

e- e+ p --> p g

 

Instead of a proton p, it could be any massive charged particle. The second is much like the first, in field theory the EM field is like an extra photon, just like the second g in the first example. It isn't easy to work these things out, but these two can conserve 4-momentum while the one with only one photon can't. If two bodies have 4-momentum (E, p) and (E', p'), the total is (E + E', p + p'). I can remember Feynman's vol II has an example or two about this type of thing, might be helpful.

[Damo2600]

Hi Qfwfq,

 

So basically light has a rest mass which is not the same as saying that a photon is sitting in mid-air. Either light energy is; absorbed within a black hole; absorbed within a proton (edit: or other massive particle) or is the rest energy is existent as an electron (Just for interest my friend who I have spoken about has an OPINION that electrons are a black hole. Food for thought).

 

I'm fine with that.

 

When a photon is moving at the speed of light energy has no mass. Perhaps I agree with that.

 

E = mc^2

 

c = 1, or, m=1

 

E = c^2

 

or

 

E = m

 

^ With the invariant speed of group velocity that leaves you with only two choices.

 

If c = 1, and m = 0, then E = 0

 

m=c^2

 

^Would this be the next logical conclusion? It doesn't makes sense to me however E = m, c

 

(mc^2)^2 = E^2 - (pc)^2

 

^ This does seem needlessly confusing in this case.

 

e- e+ --> 2g

 

e- e+ p --> p g

 

In this second case where is the second g? I am assuming the p has it...

 

Thanks heaps

Josephine

 

Thanks Paultr I will try to grasp your post however I am really tired right now and it seems really complicated for me.

[Qfwfq]

So basically light has a rest mass which is not the same as saying that a photon is sitting in mid-air.

A photon has zero mass, which means zero rest energy. It has kinetic energy: E = p.

 

m^2 = 0 = E^2 - p^2 <=> E^2 = p^2

 

Apart from signs, this means E = p.

 

Since Newton people were saying that mass has inertia and gravity. Now we say that energy has these. Some have continued to say that hence all energy is mass but it's more appropriate to use the word 'mass' for the scalar quantiy in the above equation, iow only for the rest energy. For p = 0, a body at rest:

 

m^2 = E^2 - 0^2 = E^2.

[Damo2600]

When m = 0

 

E = c

 

When p = 0

 

E = m

 

I see

 

An electron has rest energy and mass. When it is annihilated it becomes E = p

i.e. a photon.

 

A photon has no rest energy nor rest mass.

 

Conservation of energy...

Conservation of mass...

 

I do not wish to question you on this. My education is obviously limited.

 

Thanks

Josephine :xx:

[WebFeet]

Conservation of mass...

Where did you get this from ?

[Damo2600]

Here I guess. Although I don't really know enough to discuss this further.

 

http://www.iop.org/EJ/abstract/0031-9120/31/4/018/

 

Thanks guys.

Josephine