Mass and energy

[geordief]

Hardly news shattering that there is a mass -energy "equivalence".

 

Was  Einstein the first person to  show this ?

 

Can someone perhaps give a little detail (or a rough resume) of  how the two are connected?

 

Is it interesting that c ,which is described as  a "conversion factor" between  space and time (have I got that right?) appears to  fill the same or a similar role between mass and energy?

 

 

 

[studiot]

13 minutes ago, geordief said:

 

Can someone perhaps give a little detail (or a rough resume) of  how the two are connected?

 

Is it interesting that c ,which is described as  a "conversion factor" between  space and time (have I got that right?) appears to  fill the same or a similar role between mass and energy?

 

 

 

 

Interesting yes, consistent with other areas of Physics , again yes.

The dimensions of energy are M L² T^-2 ;    of mass are M;   of c are L T^-1

 

So if you substitute these into E = Mc² (can you do this) what do you see?

 

http://www.schoolphysics.co.uk/age16-19/General/text/Dimensions_/index.html

[Sensei]

35 minutes ago, geordief said:

Can someone perhaps give a little detail (or a rough resume) of  how the two are connected?

e.g. annihilation:

You have electron with rest-mass m_e and positron (antimatter antiparticle of electron) also with rest-mass m_e:

[math]e^- + e^+ \rightarrow \gamma + \gamma[/math]

Energy prior annihilation E=2 m_e c² = 1.022 MeV

Energy after annihilation E=2 hf_c = 1.022 MeV

 

Constants:

m_e  - rest-mass of electron/positron https://en.wikipedia.org/wiki/Electron_rest_mass

h - Planck constant https://en.wikipedia.org/wiki/Planck_constant

c - speed of light https://en.wikipedia.org/wiki/Speed_of_light

f_c  - Compton frequency https://en.wikipedia.org/wiki/Compton_wavelength

 

Edited February 5, 2018 by Sensei

[geordief]

13 minutes ago, studiot said:

 

Interesting yes, consistent with other areas of Physics , again yes.

The dimensions of energy are M L² T^-2 ;    of mass are M;   of c are L T^-1

 

So if you substitute these into E = Mc² (can you do this) what do you see?

 

http://www.schoolphysics.co.uk/age16-19/General/text/Dimensions_/index.html

M L2 T-2 =M L² T^{-2  ?}

 

^{Does  mass just have one  dimension?}

[Sensei]

4 minutes ago, geordief said:

Does  mass just have one  dimension?

Studiot used wrong word. He should say UNITS, not dimensions.

Mass is scalar.

 

Edited February 5, 2018 by Sensei

[swansont]

10 minutes ago, Sensei said:

Studiot used wrong word. He should say UNITS, not dimensions.

Mass is scalar.

 

The practice is known as dimensional analysis, so while it's true that mass is a scalar and not a physical dimension, studiot was not wrong

BTW, mass is not a unit. Gram or kilogram (or slug, or ton, or amu, etc.) is a unit of mass. 

[geordief]

So mass and energy are related (dimensionally) in  a " L^2 T^-2 ^" way?

 

Edited February 5, 2018 by geordief

[Sensei]

3 minutes ago, swansont said:

The practice is known as dimensional analysis, so while it's true that mass is a scalar and not a physical dimension, studiot was not wrong

What I meant is that Studiot should say (at least to layman) "The units of energy are (...)"

https://en.wikipedia.org/wiki/Units_of_energy

Because dimension for layman means 3D, 3D+1, (geometry or geometry+time) or so..

And unnecessary debate about additional dimensions will begin once again..

 

Did not you read question from geordief  "Does  mass just have one dimension?" ....

Swansont, read between the lines.. We have seen it many times already..

 

 

[studiot]

41 minutes ago, geordief said:

M L2 T-2 =M L² T^{-2  ?}

 

^{Does  mass just have one  dimension?}

The only thing I did wrong was to write the equation E = mc2 with a capital M, sorry.

Yes you have got it (how did you get on with the link?)

 

@sensei

No I don't care what nonsense Wiki says.

Units are things like kilogrammes, metres, miles centuries etc.

Dimensions are not specific to particular units.

In particular the constant of conversion is never included in the dimensions but must be included in any comparative statement of units.

For example there are 1609.34 metres in one mile.

Both miles and metres have the dimension L

So the constant of conversion (=1609.34) is miles divided by metres which is L/L and  therefore dimensionless

 

But the point I'm making in answer to geordie is that the constant of conversion, which provides the connection he was seeking, between space and time, is a speed. In particular it is the speed of light, c

Edited February 5, 2018 by studiot

[Strange]

13 minutes ago, Sensei said:

What I meant is that Studiot should say (at least to layman) "The units of energy are (...)"

https://en.wikipedia.org/wiki/Units_of_energy

Because dimension for layman means 3D, 3D+1, (geometry or geometry+time) or so..

So... maybe it is a good opportunity to introduce people to the wider meaning of dimension.

[geordief]

1 minute ago, studiot said:

The only thing I did wrong was to write the equation E = mc2 with a capital M, sorry.

Yes you have got it (how did you get on with the link?)

 

 

The link felt like a resume of things I had come across in the past but with more detail.

 

It seems to me like a good way of double checking  equations and making sure you are  not "comparing apples with pears"

 

As well as other practical uses it seems.

[studiot]

12 minutes ago, geordief said:

The link felt like a resume of things I had come across in the past but with more detail.

 

It seems to me like a good way of double checking  equations and making sure you are  not "comparing apples with pears"

 

As well as other practical uses it seems.

 

Hopefully it was helpful.

 

It is important to get this because this thread is posted in relativity and when you move to spacetime, you need the conversion.

Spacetime is not three spatial axes plus one time axis.

It is four equivalent axes, so the added time part must be 'converted' to a spatial axis.

At the risk of introducing one more difficulty, the easiest way is to use the imaginary number

[math]i = \sqrt { - 1} [/math]

 

Because the pythagorean theorem about distance distance in ordinary space

[math]{\rm{distance}} = \sqrt {{x^2} + {y^2} + {z^2}} [/math]

 

becomes

 

[math]{\rm{Interval = }}\sqrt {{x^2} + {y^2} + {z^2} + {{\left( {ict} \right)}^2}} [/math]

 

When the (ict) bit is squared the necessary negative sign appears naturally due to the square root of minus 1

 

In ordinary space the distance is the same in all coordinate systems (frames). That is it is invariant.

The becomes the interval is the same in all coordinate systems (frames). That is it is invariant for spacetime.

 

Edited February 5, 2018 by studiot

[geordief]

20 minutes ago, studiot said:

 

Hopefully it was helpful.

 

It is important to get this because this thread is posted in relativity and when you move to spacetime, you need the conversion.

Spacetime is not three spatial axes plus one time axis.

It is four equivalent axes, so the added time part must be 'converted' to a spatial axis.

 

 

I had  not come across that use of the word "conversion" (as a way of ensuring that all 4 axes  were units of length).**

If that is the accepted use of the word I am happy with it though as it is  very simple and understandable (in theory any speed quantity would do in that case ,wouldn't it ?)

 

 

** I was actually struggling to understand what "conversion" meant as I had heard it employed on quite a few occasions ( as in perhaps " c is the conversion factor between space and time")

 

Edited February 5, 2018 by geordief

[studiot]

Conversion / connection / some other word.

I suppose different people have used different words for much the same thing.

Here is a simple example.

 

A 3/4 hp (750 watt) motor runs at full power for 4 hours.
How much energy does it ouput? (ignoring efficiency considerations)

Well power x time gives energy

So in units the output is (3/4 kilowats-hours) x 4 = 3 kilowatt-hours of energy on your meter or 3 units of energy.

In dimensions we have

Power x time = energy

(ML²T^-3 ) x (T) = MLT^-2

Would you call that converting power to energy usage?

Edited February 5, 2018 by studiot

[geordief]

n

42 minutes ago, studiot said:

Conversion / connection / some other word.

I suppose different people have used different words for much the same thing.

Here is a simple example.

 

A 3/4 hp (750 watt) motor runs at full power for 4 hours.
How much energy does it ouput? (ignoring efficiency considerations)

Well power x time gives energy

So in units the output is (3/4 kilowats-hours) x 4 = 3 kilowatt-hours of energy on your meter or 3 units of energy.

In dimensions we have

Power x time = energy

(ML²T^-3 ) x (T) = MLT^-2

Would you call that converting power to energy usage?

Yes,analytically/mathematically **  as both sides of the equation  are presumably expressing the same thing in different ways( perhaps  they can be broken up mathematically in different ways and so the verbal description would have to adapt)

 

I guess verbal descriptions are a blunter tool in this regard(when I came across the word applied to spacetime I  must have subconsciously supplied my own meaning  as I didn't get the proper context-even if my own meaning made no good sense)

 

Maybe I fell into the trap of confusing   the mathematical model with some kind of "entity" -it's not unknown

 

**I mightn't be able to comment on the verbal  description as I am out of the way of  the subject of work,power energy as basic as it probably is.

 

 

[studiot]

3 hours ago, studiot said:

A 3/4 hp (750 watt) motor runs at full power for 4 hours.

I owe you an apology.

A silly error crept in there.

 

A 1hp motor is 3/4 of a kilowatt  silly me.

 

The rest is correct.