# The Naked Scientists Forum

### Author Topic: An analysis of the de Broglie equation  (Read 21957 times)

#### alancalverd

• Global Moderator
• Neilep Level Member
• Posts: 4504
• Thanked: 138 times
• life is too short to drink instant coffee
##### Re: An analysis of the de Broglie equation
« Reply #425 on: 27/07/2016 14:37:26 »
Quote
I don't know what you mean by dimensions, sorry.

Then there is no point whatever in continuing the discussion. I might as well be writing in Martian heiroglyphics.

#### timey

• Neilep Level Member
• Posts: 1118
• Thanked: 5 times
##### Re: An analysis of the de Broglie equation
« Reply #426 on: 27/07/2016 14:53:40 »
Quote
I don't know what you mean by dimensions, sorry.

Then there is no point whatever in continuing the discussion. I might as well be writing in Martian heiroglyphics.
You have previously described dimensions as apples and oranges and pears Alan.

You cannot just say "dimensions" with a question mark and expect someone who has already given the dimensions of m and g and h to understand what you mean.

Furthermore, I have come to this site as a declared non mathematician asking for help with the maths, so if there is something that I'm missing about dimensions, then it would be polite of you to give an explanation of which dimensions you refer to and in what context.

#### Ethos_

• Neilep Level Member
• Posts: 1228
• Thanked: 10 times
##### Re: An analysis of the de Broglie equation
« Reply #427 on: 27/07/2016 15:04:56 »
You have previously described dimensions as apples and oranges and pears Alan.

Alan is making the case for Dimensional balance timey. It would be good for you to investigate "Dimensional Analysis" at Wikipedia. His point is; You can't multiply, or divide apples by oranges. All equations must be dimensionally balanced.
« Last Edit: 27/07/2016 15:26:26 by Ethos_ »

#### timey

• Neilep Level Member
• Posts: 1118
• Thanked: 5 times
##### Re: An analysis of the de Broglie equation
« Reply #428 on: 27/07/2016 16:32:37 »
You have previously described dimensions as apples and oranges and pears Alan.

Alan is making the case for Dimensional balance timey. It would be good for you to investigate "Dimensional Analysis" at Wikipedia. His point is; You can't multiply, or divide apples by oranges. All equations must be dimensionally balanced.
For goodness sake Ethos...mgh is a known calculation!

Without h, mg can describe gravity potential for individual masses at ground level and the further multiplying by h adds gravity potential energy for those masses at elevation.  h being the height of elevation.

The dimensions of this suggestion are exactly proportional to the equivalence principle, in that all relationships that exist retain their existing proportionality between each other at elevation.

I'm very sorry that I cannot express this in terms of dimensional analysis!  Perhaps this is a job for someone who is adept at mathematics - and fact is, talking to someone who is adept at mathematics is indeed the very reason for my posting on this forum...
« Last Edit: 27/07/2016 16:35:54 by timey »

#### jeffreyH

• Global Moderator
• Neilep Level Member
• Posts: 3773
• Thanked: 47 times
• The graviton sucks
##### Re: An analysis of the de Broglie equation
« Reply #429 on: 27/07/2016 18:35:42 »
You have previously described dimensions as apples and oranges and pears Alan.

Alan is making the case for Dimensional balance timey. It would be good for you to investigate "Dimensional Analysis" at Wikipedia. His point is; You can't multiply, or divide apples by oranges. All equations must be dimensionally balanced.
For goodness sake Ethos...mgh is a known calculation!

Without h, mg can describe gravity potential for individual masses at ground level and the further multiplying by h adds gravity potential energy for those masses at elevation.  h being the height of elevation.

The dimensions of this suggestion are exactly proportional to the equivalence principle, in that all relationships that exist retain their existing proportionality between each other at elevation.

I'm very sorry that I cannot express this in terms of dimensional analysis!  Perhaps this is a job for someone who is adept at mathematics - and fact is, talking to someone who is adept at mathematics is indeed the very reason for my posting on this forum...

Wrong! The h is required to produce an energy equation. This is why dimensional analysis cannot be ignored. Mg is kg m s^-2. Not correct.

#### timey

• Neilep Level Member
• Posts: 1118
• Thanked: 5 times
##### Re: An analysis of the de Broglie equation
« Reply #430 on: 27/07/2016 18:50:55 »
You have previously described dimensions as apples and oranges and pears Alan.

Alan is making the case for Dimensional balance timey. It would be good for you to investigate "Dimensional Analysis" at Wikipedia. His point is; You can't multiply, or divide apples by oranges. All equations must be dimensionally balanced.
For goodness sake Ethos...mgh is a known calculation!

Without h, mg can describe gravity potential for individual masses at ground level and the further multiplying by h adds gravity potential energy for those masses at elevation.  h being the height of elevation.

The dimensions of this suggestion are exactly proportional to the equivalence principle, in that all relationships that exist retain their existing proportionality between each other at elevation.

I'm very sorry that I cannot express this in terms of dimensional analysis!  Perhaps this is a job for someone who is adept at mathematics - and fact is, talking to someone who is adept at mathematics is indeed the very reason for my posting on this forum...

Wrong! The h is required to produce an energy equation. This is why dimensional analysis cannot be ignored. Mg is kg m s^-2. Not correct.
Mass on the ground can be considered either as a part of the greater mass of earth, or as individual masses that are subject to the gravity of the greater mass.

Sure - use mgh, where h is ground level.  Problem solved.  Any further elevation is just adding value to h and therefore adds energy as to height. Equivalence principle is upheld.

...and - dimensional analysis of the gravity potential equation already exists.

#### jeffreyH

• Global Moderator
• Neilep Level Member
• Posts: 3773
• Thanked: 47 times
• The graviton sucks
##### Re: An analysis of the de Broglie equation
« Reply #431 on: 27/07/2016 19:29:26 »
Valid values for h fall within a set range. The gravitational field needs to be able to be considered uniform within this defined range. It would be meaningless to measure from the surface of the earth with a value for h in the hundreds of thousands of metres range. Since the value for g varies significantly over such a distance. Your value for energy would be in significant error. This is not a trivial point. All things are relative.

#### timey

• Neilep Level Member
• Posts: 1118
• Thanked: 5 times
##### Re: An analysis of the de Broglie equation
« Reply #432 on: 27/07/2016 20:34:26 »
Valid values for h fall within a set range. The gravitational field needs to be able to be considered uniform within this defined range. It would be meaningless to measure from the surface of the earth with a value for h in the hundreds of thousands of metres range. Since the value for g varies significantly over such a distance. Your value for energy would be in significant error. This is not a trivial point. All things are relative.

In the instance of measuring the change in gravity potential energy between the potential energy at h=ground and h=17inches, the equation does just fine.
Where h=radius then I understand that a different equation can be used...

...and when one states mgh, I assumed that this included the factor of g being at h.  Doesn't it?

Mass size of different process can vary, but if g and h are constant for all mass size per reference frame, then the equivalence principle is upheld as all energy, relationships between particles, atoms, molecules, etc remain proportional to each other.

The fact that the equivalence principle can be derived in this way is what is relevant here.

#### alancalverd

• Global Moderator
• Neilep Level Member
• Posts: 4504
• Thanked: 138 times
• life is too short to drink instant coffee
##### Re: An analysis of the de Broglie equation
« Reply #433 on: 27/07/2016 22:47:49 »
then the equivalence principle is upheld as all energy, relationships between particles, atoms, molecules, etc remain proportional to each other.

So there is no change in the emitted energy of the mossbauer photon or the frequency of an atomic clock. Face it, if the quantised energy levels of an atom were to change with gravitational potential, space would be occupied by plasma, not atoms and molecules, but it ain't.

#### timey

• Neilep Level Member
• Posts: 1118
• Thanked: 5 times
##### Re: An analysis of the de Broglie equation
« Reply #434 on: 27/07/2016 23:01:39 »
then the equivalence principle is upheld as all energy, relationships between particles, atoms, molecules, etc remain proportional to each other.

So there is no change in the emitted energy of the mossbauer photon or the frequency of an atomic clock. Face it, if the quantised energy levels of an atom were to change with gravitational potential, space would be occupied by plasma, not atoms and molecules, but it ain't.
Yes there is a change in emitted energy and frequency, but all masses of any size are experiencing the same shift.

*

As I understand it g diminishes with increased h, and both gravity potential and gravitational time dilation tail off in deep space.
No danger of excessive energy levels in space under those circumstance.

#### alancalverd

• Global Moderator
• Neilep Level Member
• Posts: 4504
• Thanked: 138 times
• life is too short to drink instant coffee
##### Re: An analysis of the de Broglie equation
« Reply #435 on: 28/07/2016 07:52:18 »
There is no mass involved in the Fe57 transition. Nor are the masses of the electrons and nuclei relevant to the Cs133 hyperfine transition.

Gravitational potential increases as you move away from the source of gravitation. V(x) = -GM/x by definition. So it is zero in deep space and tends to minus infinity as you approach a massive body.

#### timey

• Neilep Level Member
• Posts: 1118
• Thanked: 5 times
##### Re: An analysis of the de Broglie equation
« Reply #436 on: 28/07/2016 21:59:30 »
There is no mass involved in the Fe57 transition. Nor are the masses of the electrons and nuclei relevant to the Cs133 hyperfine transition.

Gravitational potential increases as you move away from the source of gravitation. V(x) = -GM/x by definition. So it is zero in deep space and tends to minus infinity as you approach a massive body.

I 'was' creating a really long and convoluted post, (chuckle), but it occurs that I should just ask this:

http://physics.info/standard/

If the masses of all the particles were individually calculated as mgh, where the potential energy is additional to the energy of the mass, would the same proportionality of energy differences between the masses be retained at any given h?

Or will the calculation escalate the energy of larger masses disproportionally to the energy increase the calculation gives to smaller masses?
« Last Edit: 28/07/2016 22:05:28 by timey »

#### alancalverd

• Global Moderator
• Neilep Level Member
• Posts: 4504
• Thanked: 138 times
• life is too short to drink instant coffee
##### Re: An analysis of the de Broglie equation
« Reply #437 on: 28/07/2016 22:31:32 »
The potential energy of any particle of mass m at height h in a uniform gravitational field is mgh.

#### timey

• Neilep Level Member
• Posts: 1118
• Thanked: 5 times
##### Re: An analysis of the de Broglie equation
« Reply #438 on: 28/07/2016 23:02:07 »
The potential energy of any particle of mass m at height h in a uniform gravitational field is mgh.

Oh, OK... I had assumed h being  height is variable, and indicated a change in gravity field...?

#### alancalverd

• Global Moderator
• Neilep Level Member
• Posts: 4504
• Thanked: 138 times
• life is too short to drink instant coffee
##### Re: An analysis of the de Broglie equation
« Reply #439 on: 29/07/2016 20:07:50 »
If you want to include variations in g with h, by all means, but it turns a simple linear equation into an integral and doesn't shed any light on the subject at all. The variation over 100 feet or even 1000 feet from the earth's surface is not worth worrying about.

#### timey

• Neilep Level Member
• Posts: 1118
• Thanked: 5 times
##### Re: An analysis of the de Broglie equation
« Reply #440 on: 02/08/2016 13:59:12 »
If you want to include variations in g with h, by all means, but it turns a simple linear equation into an integral and doesn't shed any light on the subject at all. The variation over 100 feet or even 1000 feet from the earth's surface is not worth worrying about.
A mathematician and an engineer are subjects of a psychology experiment; first they are separately shown into a room where there is an empty bucket, a trashcan, and a faucet. The trashcan is on fire. Each of them first fills the bucket with water from the faucet, then dumps it on the trashcan and extinguishes the flames. Then the engineer is shown to another room, where there is again a faucet, a trashcan on fire, and a bucket, but this time the bucket is already filled with water; the engineer takes the bucket, empties it on the trashcan and puts out the fire. The mathematician, when introduced to the exact same situation, takes the bucket, and empties it on the floor, and then says "which reduces this to a previously solved problem."

*

mgh as a linear equation is calculating the gravity field as a positive calculation, but the gravity field is reducing by the inverse square law at h.  (As an integral we would see the Riemann geometry that forms part of GR.)

https://en.m.wikipedia.org/wiki/Gravitational_potential

Quote:
" In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be done by the force of gravity if an object were moved from its location in space to a fixed reference location. ***It is analogous to the electric potential with mass playing the role of charge.***  The reference location, where the potential is zero, is by convention infinitely far away from any mass, resulting in a negative potential at any finite distance."
Unquote:

So a positive calculation is describing a negative potential.

My theory of this proposed additional inverted gravitational time dilation states that g, g being 9.807m|s^2, (for Earth), is 'mostly' due to the weak force of gravitational attraction being accelerated near bodies of mass by the contracting of the time period of unit's of time in the increasing strength of gravity field...

...and looks to the weak force of gravitational attraction itself being of a far lesser value, where this link in relation to the *** mass analogous to charge *** is interesting, in that this link is describing the magnetic moment of an electron.

https://en.m.wikipedia.org/wiki/Gravitational_coupling_constant

The Lorentz transformations describe length contraction, and in their inverse form they describe time dilation.

Can I ask please if the time dilation the Lorentz transformations describe is gravitational, or motion related?

#### Ethos_

• Neilep Level Member
• Posts: 1228
• Thanked: 10 times
##### Re: An analysis of the de Broglie equation
« Reply #441 on: 02/08/2016 15:38:29 »

Can I ask please if the time dilation the Lorentz transformations describe is gravitational, or motion related?
According to Wikipedia: "The term "Lorentz Transformations" only refers to the transformations between inertial frames usually in the context of SR."

#### alancalverd

• Global Moderator
• Neilep Level Member
• Posts: 4504
• Thanked: 138 times
• life is too short to drink instant coffee
##### Re: An analysis of the de Broglie equation
« Reply #442 on: 02/08/2016 17:08:06 »

mgh as a linear equation is calculating the gravity field as a positive calculation, but the gravity field is reducing by the inverse square law at h.  (As an integral we would see the Riemann geometry that forms part of GR.)

Not sure what you mean by a positive calculation, but g(h) = g(0) (R/(R+h))^2 where R is the radius of the earth. So substituting R = 6,371,000 and h = 25 we get g(h)/g(0) = 0.999992 for a 25 meter height increase, 1 part in 10^6 difference. Compare this with the measured Pound-Rebka frequency shift of 2.5 x 10^-15 and I think you will see that there is a bit more to it than merely variaton of g with h.

#### timey

• Neilep Level Member
• Posts: 1118
• Thanked: 5 times
##### Re: An analysis of the de Broglie equation
« Reply #443 on: 02/08/2016 21:10:47 »

mgh as a linear equation is calculating the gravity field as a positive calculation, but the gravity field is reducing by the inverse square law at h.  (As an integral we would see the Riemann geometry that forms part of GR.)

Not sure what you mean by a positive calculation, but g(h) = g(0) (R/(R+h))^2 where R is the radius of the earth. So substituting R = 6,371,000 and h = 25 we get g(h)/g(0) = 0.999992 for a 25 meter height increase, 1 part in 10^6 difference. Compare this with the measured Pound-Rebka frequency shift of 2.5 x 10^-15 and I think you will see that there is a bit more to it than merely variaton of g with h.
Generally, all the most useful physics books I've read provide explanation of maths in word format as a given... I'm not sure why your h is in brackets, so on, but I think I get overall jist...

However... (If calculating g as 9.807m|s^2,)... g*h 'adds' only positive value, when the gravity field is reducing, which should result in a partial subtraction of a negative value.

This equation 'could perhaps' work with the idea of inverted time dilation because as the gravity field reduces, the time period of a unit of time is gravitationally dilated. (lengthened).  Therefore the negative value of g at h becomes the positive value  (ie: g*h), and by subjecting the acceleration of g to the speed distance time formula, (on basis that speed of gravity is equal to speed of light), a time value can be extracted and added to the value of a standard time unit... We can now see that time periods are extended as gravity field is reduced, and that the difference between the linear and the integral calculations 'are' inverted time dilation related, and another gravitational constant is responsible for an attractive force, while accelerations of gravity are time related.

m*g*h then calculates mass at h inclusive of inverted time dilation, and the additional potential energy due to the mass of the object will increase the frequency of the object or process of the object being measured.

Now both calculations can be said to describe that an increase in energy will cause an increase in frequency.  An increase in strength of gravity field will cause an increase in frequency for massless particles due to the increased energy of the gravity field, and an increase in gravity potential energy will cause an increase in frequency for anything with mass raised into the weaker gravity field.

The gravity field will shift energy for all mass sizes proportionally, but it will shift energy in the gravitational field equally for massless entities, and we observe that frequency changes are related to Planck's h constant (energy associated), via wavelength.

Then...because my theory states the phenomenon of time itself as energy related - Planck's h constant, being a per 'standard' second squared measurement, the measured phenomenon itself is subject to an increase in energy, causing an increase in time for that phenomenon.  Increases of joules per second squared, can then be transposed to being a linear consideration and quantum is not quantised.

These being an entirely mathematically proportional, (I think), alternative means of considering the same observations.

In the PR, the man made Doppler shift was matched by 'something' in the gravity field...

#### alancalverd

• Global Moderator
• Neilep Level Member
• Posts: 4504
• Thanked: 138 times
• life is too short to drink instant coffee
##### Re: An analysis of the de Broglie equation
« Reply #444 on: 02/08/2016 23:55:49 »
I'm not sure why your h is in brackets, so on, but I think I get overall jist...
For some reason the forum software doesn't allow subscripts at the moment. g(h) is the alternative shorthand for "the value of g at height h" compared with g(0) which pretty obviously means "the value of g at ground level"

Quote
m*g*h then calculates mass at h inclusive of inverted time dilation, and the additional potential energy due to the mass of the object will increase the frequency of the object or process of the object being measured.
a moment's reflection on the dimensions of mgh will show that it doesn't calculate mass, but potential energy.

Quote
and we observe that frequency changes are related to Planck's h constant
except that they are not. Again, dimensional analysis will show that the ratio of frequencies is dimensionless whereas h has dimensions ML^2/T

Quote
Planck's h constant, being a per 'standard' second squared measurement,  the measured phenomenon itself is subject to an increase in energy, causing an increase in time for that phenomenon.  Increases of joules per second squared, can then be transposed to being a linear consideration and quantum is not quantised.
except that h is joule.seconds, not joules per second squared.

#### timey

• Neilep Level Member
• Posts: 1118
• Thanked: 5 times
##### Re: An analysis of the de Broglie equation
« Reply #445 on: 03/08/2016 00:42:35 »
I'm not sure why your h is in brackets, so on, but I think I get overall jist...
For some reason the forum software doesn't allow subscripts at the moment. g(h) is the alternative shorthand for "the value of g at height h" compared with g(0) which pretty obviously means "the value of g at ground level"

Quote
m*g*h then calculates mass at h inclusive of inverted time dilation, and the additional potential energy due to the mass of the object will increase the frequency of the object or process of the object being measured.
a moment's reflection on the dimensions of mgh will show that it doesn't calculate mass, but potential energy.

Quote
and we observe that frequency changes are related to Planck's h constant
except that they are not. Again, dimensional analysis will show that the ratio of frequencies is dimensionless whereas h has dimensions ML^2/T

Quote
Planck's h constant, being a per 'standard' second squared measurement,  the measured phenomenon itself is subject to an increase in energy, causing an increase in time for that phenomenon.  Increases of joules per second squared, can then be transposed to being a linear consideration and quantum is not quantised.
except that h is joule.seconds, not joules per second squared.
Yes - as I said, I got the jist.
*
Yes - I know.  Clearly it is potential energy that is being calculated, not mass.  Why would you think that I think otherwise?
*
Wavelength = h|p
Frequency = E|h
Where h is Planck's h constant.
*
Sorry, my mistake... The per and squared factor is not important to the overall concept, in fact its a good deal less complicated. Joules 'times' a standard second then.

#### alancalverd

• Global Moderator
• Neilep Level Member
• Posts: 4504
• Thanked: 138 times
• life is too short to drink instant coffee
##### Re: An analysis of the de Broglie equation
« Reply #446 on: 03/08/2016 08:34:07 »

*
Yes - I know.  Clearly it is potential energy that is being calculated, not mass.  Why would you think that I think otherwise?
because you said so!
*
Quote
Wavelength = h|p
Frequency = E|h
Where h is Planck's h constant.
and frequency divided by frequency is dimensionless
*
Quote
Sorry, my mistake... The per and squared factor is not important to the overall concept, in fact its a good deal less complicated. Joules 'times' a standard second then.
Fred Hoyle made such a statement once, but went down in history for saying it.

#### timey

• Neilep Level Member
• Posts: 1118
• Thanked: 5 times
##### Re: An analysis of the de Broglie equation
« Reply #447 on: 03/08/2016 14:25:46 »

*
Yes - I know.  Clearly it is potential energy that is being calculated, not mass.  Why would you think that I think otherwise?
because you said so!
*
Quote
Wavelength = h|p
Frequency = E|h
Where h is Planck's h constant.
and frequency divided by frequency is dimensionless
*
Quote
Sorry, my mistake... The per and squared factor is not important to the overall concept, in fact its a good deal less complicated. Joules 'times' a standard second then.
Fred Hoyle made such a statement once, but went down in history for saying it.

How can m*g*h calculate mass?  You must think me a total idiot if you think I thought that.  I certainly didn't say that by any stretch of the imagination... I said that for mass m*g*h. (ie: potential energy for mass)
*
Where does frequency divided by frequency come in?  I didn't introduce that notion!
*
What Fred Hoyle said?  ...is wholly irrelevant to the concept being proposed here.

Sorry, but I really cannot understand the purpose of this post... (scratches head)

#### Ethos_

• Neilep Level Member
• Posts: 1228
• Thanked: 10 times
##### Re: An analysis of the de Broglie equation
« Reply #448 on: 03/08/2016 15:49:06 »

Where does frequency divided by frequency come in?  I didn't introduce that notion!
*

Dimensionless numbers are very important in the mathematical construction of physical realities and when one understands their importance, they are on track to seeing the importance of Dimensional Analysis. Consider the fine structure constant "a" as one example.

#### timey

• Neilep Level Member
• Posts: 1118
• Thanked: 5 times
##### Re: An analysis of the de Broglie equation
« Reply #449 on: 03/08/2016 16:44:00 »

Where does frequency divided by frequency come in?  I didn't introduce that notion!
*

Dimensionless numbers are very important in the mathematical construction of physical realities and when one understands their importance, they are on track to seeing the importance of Dimensional Analysis. Consider the fine structure constant "a" as one example.

Yes - I was entirely aware that in mentioning the gravitational coupling constant that this constant comprises of a dimensionless number, and that a dimensionless number has no dimensions to be analysed, and that dimensional analysis subsequently has very little to say about these dimensionless quantities...
(do I really have to fully describe every obvious factor in order that a reader understand that I understand the obvious?)

...the fact of point being the *** It is analogous to the electric potential with mass playing the role of charge *** ...quoted from the gravity potential link - in relation to the magnetic moment of an electron.

#### The Naked Scientists Forum

##### Re: An analysis of the de Broglie equation
« Reply #449 on: 03/08/2016 16:44:00 »