# An analysis of the de Broglie equation

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#### jeffreyH

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##### An analysis of the de Broglie equation
« on: 21/05/2016 16:29:37 »
Starting from the relationship $$\lambda\,=\,\frac{h}{mv}\,=\,\frac{h}{p}$$  and the eaquation $$E\,=\,h\nu$$ we can remove Planck's constant as a component of these equations. Since $$h\,=\,\lambda\rho$$ then the energy equation can be expressed as $$E\,=\,\lambda\rho\nu$$

Since the speed of a wave can be expressed as $$c\,=\,\nu\lambda$$ then it can also be expressed as $$c\,=\,\frac{E}{\rho}$$

The interesting thing about the relationship $$E\,=\,\lambda\rho\nu$$ is that the frequency/energy relationship and momentum are on the same side of the equation which can then be used to investigate the possible mechanisms of time dilation. Since the components can vary non uniformly.
« Last Edit: 21/05/2016 16:44:05 by jeffreyH »

#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #1 on: 21/05/2016 19:23:06 »
When considering how massless particle like the photon relate can be shown by the following relationships.

$$E\,=\,\lambda\nu{m}v\,=\,0$$

Where setting mass equal to zero gives the desired result as expected. This indicates a very different relationship between the photon and time dilation.

#### alancalverd

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##### Re: An analysis of the de Broglie equation
« Reply #2 on: 21/05/2016 19:48:07 »
Your equation implies that the energy of a photon is always zero, which is obviously not the case.

Your confusion arises from assuming that momentum is uniquely asssociated with mass. Einstein's analysis of radiation pressure shows that it isn't. The fundamental relationship is p = E/v by definition for all particles at all speeds. Now a photon clearly has energy and speed, so can exert a force since F = dp/dt by definition, so an absorbed or reflected photon can transfer momentum to the absorber or reflector.
« Last Edit: 21/05/2016 19:59:06 by alancalverd »
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#### chiralSPO

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##### Re: An analysis of the de Broglie equation
« Reply #3 on: 21/05/2016 19:53:13 »
for photons p = E/c = h/λ

#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #4 on: 21/05/2016 23:59:02 »
Your equation implies that the energy of a photon is always zero, which is obviously not the case.

Your confusion arises from assuming that momentum is uniquely asssociated with mass. Einstein's analysis of radiation pressure shows that it isn't. The fundamental relationship is p = E/v by definition for all particles at all speeds. Now a photon clearly has energy and speed, so can exert a force since F = dp/dt by definition, so an absorbed or reflected photon can transfer momentum to the absorber or reflector.

There is no confusion since I already know about the above. That was not the point of this thread. I haven't finished yet.

#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #5 on: 22/05/2016 10:59:36 »
OK so as was pointed out $$\rho\,=\,\frac{h}{\lambda}$$. Therefore in the case of the photon the energy equation becomes $$E\,=\,\frac{\rho{c^2}}{\lambda\nu}$$.

If we take our wavelength as L (1 light second) then we can show that $$E\,=\,\rho{c}\,=\,\frac{hc}{L}\,=\,\frac{h}{t}$$. This 1 hertz wave then shows the direct relationship to the Planck constant.

#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #6 on: 22/05/2016 11:21:00 »
What this is meant to demonstrate is that for massless particles the Planck constant has to be included in equations. There is no way round it. For massive particles this is not the case.

#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #7 on: 22/05/2016 11:27:28 »
Starting from the relationship $$\lambda\,=\,\frac{h}{mv}\,=\,\frac{h}{p}$$  and the eaquation $$E\,=\,h\nu$$ we can remove Planck's constant as a component of these equations. Since $$h\,=\,\lambda\rho$$ then the energy equation can be expressed as $$E\,=\,\lambda\rho\nu$$

Since the speed of a wave can be expressed as $$c\,=\,\nu\lambda$$ then it can also be expressed as $$c\,=\,\frac{E}{\rho}$$

The interesting thing about the relationship $$E\,=\,\lambda\rho\nu$$ is that the frequency/energy relationship and momentum are on the same side of the equation which can then be used to investigate the possible mechanisms of time dilation. Since the components can vary non uniformly.

I wish you would write an index to your maths so people understand your representation,  what is h etc?

Anyway I have some clue of what you are trying to express, I express

E=c delta F?

C = speed of light, rho (p) = momentum, lambda = wavelength, nu (v) = frequency of wave in hertz and h = Planck's constant.

#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #8 on: 22/05/2016 11:37:56 »
OK so as was pointed out $$\rho\,=\,\frac{h}{\lambda}$$. Therefore in the case of the photon the energy equation becomes $$E\,=\,\frac{\rho{c^2}}{\lambda\nu}$$.

If we take our wavelength as L (1 light second) then we can show that $$E\,=\,\rho{c}\,=\,\frac{hc}{L}\,=\,\frac{h}{t}$$. This 1 hertz wave then shows the direct relationship to the Planck constant.

Energy = momentum c = planck constant c divided by length = planck constant divided by ?

What is the last symbol and is that what you said?

Yes that is what I wrote. The last symbol is t for time. The Planck constant is in units of joule second so to get energy in joules you have to divide by a time factor. You should read up on dimensional analysis. It is very interesting and can clear up a lot of confusion.

#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #9 on: 22/05/2016 11:43:54 »
Ok Thebox think about this. There has to be a link between the acquisition of mass and time dilation. Question, does interaction with the Higgs field have a direct relationship to relativistic time dilation? Answer that one and stay fashionable.

#### Thebox

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##### Re: An analysis of the de Broglie equation
« Reply #10 on: 22/05/2016 11:59:34 »
acquisition
Sorry Jeff I am reading  your post ambiguously, can you please rephrase and  also use a better word than acquisition?

''There has to be a link between the acquisition of mass and time dilation. ''

What is acquiring  mass?  I don't understand your sentence sorry it seems incomplete.

#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #11 on: 22/05/2016 12:45:46 »
Quarks are the components of protons and neutrons. Do they have mass? Yes but a very tiny amount. Where does it come from. Quarks are fermions and so should have left handed and right handed components. The left handed has charge and the right handed doesn't. They switch between both states via interaction with the Higgs field becoming one particle out of two components during this process they gain mass.
« Last Edit: 22/05/2016 12:48:01 by jeffreyH »

#### Thebox

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##### Re: An analysis of the de Broglie equation
« Reply #12 on: 24/05/2016 18:27:16 »
Quarks are the components of protons and neutrons. Do they have mass? Yes but a very tiny amount. Where does it come from. Quarks are fermions and so should have left handed and right handed components. The left handed has charge and the right handed doesn't. They switch between both states via interaction with the Higgs field becoming one particle out of two components during this process they gain mass.

what you think ''mass' is Jeffrey? Mass=kg=G=N, mass and Newton's ''are'' the same thing....

#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #13 on: 24/05/2016 18:44:50 »
Quarks are the components of protons and neutrons. Do they have mass? Yes but a very tiny amount. Where does it come from. Quarks are fermions and so should have left handed and right handed components. The left handed has charge and the right handed doesn't. They switch between both states via interaction with the Higgs field becoming one particle out of two components during this process they gain mass.

what you think ''mass' is Jeffrey? Mass=kg=G=N, mass and Newton's ''are'' the same thing....

http://www.mathsisfun.com/measure/weight-mass.html

The difference between weight and mass is not trivial.

#### Thebox

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##### Re: An analysis of the de Broglie equation
« Reply #14 on: 24/05/2016 18:50:05 »

The difference between weight and mass is not trivial.

The link you provided is incorrect, a 100kg mass in space is not 100kg, the object has no mass.

Mass is relative to the object at relative rest in an inertial reference frame, the inertia frame being the provider of how much mass the object has.  If the Earth had half the gravity strength, the object would only ''weight' 50kg.  Mass is a product of gravity and not in itself a ''thing''?

added- Mass is relative to the inertia reference frame.

« Last Edit: 24/05/2016 18:54:19 by Thebox »

#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #15 on: 24/05/2016 18:59:34 »

The difference between weight and mass is not trivial.

The link you provided is incorrect, a 100kg mass in space is not 100kg, the object has no mass.

Mass is relative to the object at relative rest in an inertial reference frame, the inertia frame being the provider of how much mass the object has.  If the Earth had half the gravity strength, the object would only ''weight' 50kg.  Mass is a product of gravity and not in itself a ''thing''?

You have missed the point completely. What we call mass never changes. The number of protons, neutrons and electrons in an object will not change with a change in gravity. Hence inertial mass remains constant. The force (weight) they exert due to gravity will change with a change in the strength of a gravitational field. The link I posted was not wrong.

#### Thebox

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##### Re: An analysis of the de Broglie equation
« Reply #16 on: 24/05/2016 19:12:08 »

The difference between weight and mass is not trivial.

The link you provided is incorrect, a 100kg mass in space is not 100kg, the object has no mass.

Mass is relative to the object at relative rest in an inertial reference frame, the inertia frame being the provider of how much mass the object has.  If the Earth had half the gravity strength, the object would only ''weight' 50kg.  Mass is a product of gravity and not in itself a ''thing''?

You have missed the point completely. What we call mass never changes. The number of protons, neutrons and electrons in an object will not change with a change in gravity. Hence inertial mass remains constant. The force (weight) they exert due to gravity will change with a change in the strength of a gravitational field. The link I posted was not wrong.

No Jeff. the strong nuclear force remains constant and the sum of all ''charges'', a single particle has no mass,

mass=snf+q =g

You may think I am deluded Jeff, but I am certain that ''you'' have it so wrong.

Let me try to explain, please try to have an open mind and hear me out.  Imagine a single particle ''floating'' around in a vast space where there was no other gravitational influence on the particle, the particle on a set of scales would ''weight'' relatively 0.  There is no force being applied on the particle and the particle is not attracting anything.   Ok let us say I live on a planet that had twice the gravity of the Earth, let us say this single particle on your scales ''weighs'' 1oz.
What would it ''weigh'' on my scales?

#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #17 on: 24/05/2016 20:41:30 »
Up

The difference between weight and mass is not trivial.

The link you provided is incorrect, a 100kg mass in space is not 100kg, the object has no mass.

Mass is relative to the object at relative rest in an inertial reference frame, the inertia frame being the provider of how much mass the object has.  If the Earth had half the gravity strength, the object would only ''weight' 50kg.  Mass is a product of gravity and not in itself a ''thing''?

You have missed the point completely. What we call mass never changes. The number of protons, neutrons and electrons in an object will not change with a change in gravity. Hence inertial mass remains constant. The force (weight) they exert due to gravity will change with a change in the strength of a gravitational field. The link I posted was not wrong.

No Jeff. the strong nuclear force remains constant and the sum of all ''charges'', a single particle has no mass,

mass=snf+q =g

You may think I am deluded Jeff, but I am certain that ''you'' have it so wrong.

Let me try to explain, please try to have an open mind and hear me out.  Imagine a single particle ''floating'' around in a vast space where there was no other gravitational influence on the particle, the particle on a set of scales would ''weight'' relatively 0.  There is no force being applied on the particle and the particle is not attracting anything.   Ok let us say I live on a planet that had twice the gravity of the Earth, let us say this single particle on your scales ''weighs'' 1oz.
What would it ''weigh'' on my scales?

Firstly I would not pass any judgement on your state of mind because that wouldn't be a nice thing to do. You have never been insulting or abusive which is a nice change.

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #18 on: 25/05/2016 04:52:29 »
Jeff, I've been interested to see where you are going with this...

OK so as was pointed out $$\rho\,=\,\frac{h}{\lambda}$$. Therefore in the case of the photon the energy equation becomes $$E\,=\,\frac{\rho{c^2}}{\lambda\nu}$$.

If we take our wavelength as L (1 light second) then we can show that $$E\,=\,\rho{c}\,=\,\frac{hc}{L}\,=\,\frac{h}{t}$$. This 1 hertz wave then shows the direct relationship to the Planck constant.

A particle with mass's energy and frequency increases in a decreasing gravitational field.

A massless photon's energy and frequency decreases in a decreasing gravitational field.

Wavelength is inversely proportional to frequency.

When considering how massless particle like the photon relate can be shown by the following relationships.

$$E\,=\,\lambda\nu{m}v\,=\,0$$

Where setting mass equal to zero gives the desired result as expected. This indicates a very different relationship between the photon and time dilation.

Apart from the fact that the direction of change in frequency and energy for a photon within a gravitational gradient is contrary the direction of change in frequency and energy within a gravitational gradient for a particle with mass:

Changes in the gravitational field have a far 'lesser' effect of change upon a particle with mass's energy and frequency, than they do upon a photons energy and frequency.

This presents a further illogicality.  Surely a particle with mass would be more greatly affected by changes in the gravitational field, not less?

#### Thebox

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##### Re: An analysis of the de Broglie equation
« Reply #19 on: 25/05/2016 06:49:25 »

Yes indeed, relative to you on Earth the ''mass'' of your measured particle is 1oz relative to the gravitational influence of the Earth, relative to me on my planet, the particle has 2oz of ''mass''.

The problem is Jeff science should not be measuring ''mass'' in kg which is equal to Newton's, ''mass'' should be a measurement of ''charge'' and ''likes''.

In comparison to what science does, I could say the volume and density of an object is equal to it's ''mass'', this also would be explaining a different thing than protons, neutrons, etc, and the internal ''force'' .

I have noticed this in science Jeff, several things mean the same thing but are explained differently when they mean the same thing.

Another example is force normal, inertia, kE and so on, science does this a lot. The inertia of an object is it's ''mass'' and so on, science has made ''mountains'' out of ''mole hills'' and continues to do it, although the ''box'' contains lots of different words that science say means different things, the words in the box are mostly the same ''colour''.

I understand the same as you that ''mass'' is Protons etc, But I will never understand in a million years why science persists in measuring ''mass'' in Kg which is a metric ''weight'' equal to Newton's rather than mass= the summation of all energies within.

#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #20 on: 25/05/2016 11:02:11 »
Technically relativistic mass is akin to the sum of all the energies. As we apply forces to speed things up it becomes harder as relativistic mass increases. For gravity this seems not to be an issue. Density as well as mass MUST have an effect on gravity's ability to accelerate objects otherwise there can be no boson for the gravitational field. You need to think about that one very carefully to understand.

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #21 on: 25/05/2016 13:03:01 »
Technically relativistic mass is akin to the sum of all the energies.

So - presumably if we take our caesium atomic clock and accelerate it up to relativistic speeds in a uniform gravitational field, the additional kinetic energy will increase the frequency of cycles?

...this cannot be correct because an increase in the frequency of cycles of a caesium atomic clock would of course register an 'increase' in the rate of the clocks time, and not the decrease in rate of time that is observed of an accelerated clock...

I found this and thought it might interest you Jeff:

http://web.mit.edu/lululiu/Public/pixx/not-pixx/photoelectric.pdf

#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #22 on: 25/05/2016 19:54:17 »
Technically relativistic mass is akin to the sum of all the energies.

So - presumably if we take our caesium atomic clock and accelerate it up to relativistic speeds in a uniform gravitational field, the additional kinetic energy will increase the frequency of cycles?

...this cannot be correct because an increase in the frequency of cycles of a caesium atomic clock would of course register an 'increase' in the rate of the clocks time, and not the decrease in rate of time that is observed of an accelerated clock...

I found this and thought it might interest you Jeff:

http://web.mit.edu/lululiu/Public/pixx/not-pixx/photoelectric.pdf

Thanks for the pdf. I skimmed through it but didn't take much in. I can't answer your questions above as I do not have the knowledge to do so. I was reading up on particle physics a while back but stopped just before being admitted to hospital. I haven't done much reading since. I have variable days at the moment.

#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #23 on: 25/05/2016 23:41:47 »
I have read the pdf. It reiterates what was originally done to find Planck's constant I believe. The linear plot is the most fascinating element. Once you can determine that direct a relationship you know you are on to something.

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #24 on: 26/05/2016 12:24:51 »
Jeff - I remember you saying that you'd been in hospital last year.  A problem with breathing if I recall correctly.  Sorry to hear that you are not fully recovered.

Your welcome for the PDF.  Planck derived his constant via the black body experiment which used thermal equilibrium and the resulting light emissions.  These MIT undergraduates are testing the constant via the photoelectric effect.

Although the error bar was not within acceptable scientific range, I thought you might find the potential linearity aspect interesting.  What I found interesting was the fact that they showed that the cut off point was correlating with the energy associated with frequency, and not kinetic energy.

The question I asked concerning accelerating a caesium atomic clock to relativistic speeds in a uniform gravitational field, and if the resulting rise in kinetic energy would increase the frequency of cycles of the caesium atom, which of course would be incorrect, because this would register an increase in the rate of time and not the decrease in rate of time observed of an accelerated clock:
I'm almost 100% certain (subject to being wrong ) that there isn't 'anyone' who can answer this question Jeff, but I hereby challenge 'all' the experts and moderators on this forum to try!

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #25 on: 26/05/2016 17:54:19 »
Also Jeff - I know you said you are not reading much at mo, and this one is a bit of a longer read at a grand total of 38 pages, but if you get a chance it's a good read up till the last few pages.

http://em01.powweb.com/sciencetoday/planckunits/planck_unit.pdf

The long and short of this one is that there are 2 derivable values for square root.  Most of the Planck values are derived using one means, but a couple are using the alternate means.

I'm a bit fuzzy on the legitimacy of this claim of there being 2 means of deriving a value from square root, so if this does take your interest and you have an opinion, I'd be grateful to know it...

#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #26 on: 26/05/2016 19:08:54 »
It didn't make much sense. I could understand if it was talking about positive and negative results from a square root. I would ignore it if I were you.

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #27 on: 26/05/2016 20:51:57 »
I think he is talking about the square root of the speed of light, and that if you move the decimal point to portray the speed of light in kilometres, instead of metres, a different value emerges via square root when calculating meters than with kilometres, despite the fact that the actual distance is the same. (I haven't checked to see if this is true, but I doubt someone would write 38 pages based on this sole premiss if the premiss for the calculation was not correct.)

He goes on to show that Planck's charge constant has been calculated using the position of the decimal point of the speed of light contrary to the position the decimal point has been used to calculate the majority of the other related constants.

If you go to page 9 you will see a table of what the Planck constants values are when worked out by the means of both positions of the decimal point.
This table may well be quite interesting when related back to the data the MIT undergraduates were recording in the link I previously posted...

#### alancalverd

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##### Re: An analysis of the de Broglie equation
« Reply #28 on: 26/05/2016 22:46:34 »
A particle with mass's energy and frequency increases in a decreasing gravitational field.

A massless photon's energy and frequency decreases in a decreasing gravitational field.

I think what you mean by the second statement is that the frequency of a photon originating in a stronger gravitational field and  seen by an observer in a weaker gravitational field is lower than that of a photon emitted by the same process in the lower field.

But the first statement baffles me. The kinetic energy of any massive particle increases as it enters a stronger gravitational field (stuff accelerates at g as it falls, and g is bigger as you get closer to the earth )  therefore it must decrease as it leaves the stronger field (what goes up generally stops and then comes down). It's the essential difference between a projectile and a rocket. Now if you want to associate a deBroglie wavelength with kinetic energy, it must behave in exactly the same way as a photon wavelength.
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#### alancalverd

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##### Re: An analysis of the de Broglie equation
« Reply #29 on: 26/05/2016 23:13:07 »
The question I asked concerning accelerating a caesium atomic clock to relativistic speeds in a uniform gravitational field, and if the resulting rise in kinetic energy would increase the frequency of cycles of the caesium atom, which of course would be incorrect, because this would register an increase in the rate of time and not the decrease in rate of time observed of an accelerated clock:

If the source and observer are in the same uniform gravitational field, the only effect will be due to their relative motion

From Wikipedia (or any textbook)
Quote
When two observers are in relative uniform motion and uninfluenced by any gravitational mass, the point of view of each will be that the other's (moving) clock is ticking at a slower rate than the local clock. The faster the relative velocity, the greater the magnitude of time dilation. This case is sometimes called special relativistic time dilation.

which is what we observe with flying clocks and clocks in a low earth orbit.

Quote
if the resulting rise in kinetic energy would increase the frequency of cycles of the caesium atom
That's a big "if" and has no foundation. Once the clock is moving at a constant speed, it has no idea that it is moving except in relation to another clock, so there's no reason why its atoms should behave any differently from when it was "stationary".

And I'm afraid the "Planck unit" paper has all the hallmarks of a crank. The discovery that
√100 ≠ 10√10 should not surprise anyone over the age of 12.

It would be really bitchy and nitpicky for me to point out the glaring omissions from the MIT students' paper, so I'll leave that to others. Suffice it to say that when I was teaching this experiment to undergraduates 50 years ago, they would not have been let off without a stern warning!
« Last Edit: 26/05/2016 23:23:25 by alancalverd »
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#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #30 on: 27/05/2016 00:27:47 »
A caesium atomic clocks frequency increases in a decreasing gravitational field relative to a clock at ground level.  No kinetic energy involved when the 2 clocks are held stationary relative to each other. ie: 1 meter apart in elevation for instance.
(See NIST 2010 ground level relativity tests)
Any particle with mass held 1 meter higher in elevation from another identical particle will therefore have a higher frequency than the lower particle...no?

A photon's frequency decreases travelling into a decreasing gravitational field.  It is doing so whether anyone observes it or not.

The only difference between the 2 scenarios apart from the photon having no mass is the fact of its velocity, (whereas I have held the particles with mass, discussed previously, stationary relative to each other and the gravitational field.).

You are giving the photon relativistic mass via kinetic energy to calculate g and stating the rate of time as being slowed by the relativistic speed and mass.

But these concepts don't tally up logistically when you take your caesium atomic clock, and accelerating it to relativistic speeds in a uniform gravitational field, ask yourself will the clocks frequency increase as its energy increases?  Because this would of course register an increase in the clocks rate of time which cannot be correct, because an accelerated clock's rate of time is observed to slow...

Alan, in reply to your second post, whenever I have made any reference to a change in the rate of time, please know that this is relative to a stationary caesium atomic clock at ground level registering the frequency associated with the 'standard second'.

With regards to the rest of your post, be bitchy if that's what you enjoy.  I had indeed thought that this was not the alancalverd way, (sad sigh), but go ahead, 'tis a free country...

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #31 on: 27/05/2016 02:29:04 »
Quote
if the resulting rise in kinetic energy would increase the frequency of cycles of the caesium atom
That's a big "if" and has no foundation. Once the clock is moving at a constant speed, it has no idea that it is moving except in relation to another clock, so there's no reason why its atoms should behave any differently from when it was "stationary".

Huh? ...If a ceasium atomic clock registers a faster or slower rate of time, then it's energy and frequency are changing...

The point being Alan, that accelerating the caesium atomic clock to relativistic speeds in a uniform gravitational field will add relativistic mass via kinetic energy, which will increase the particles energy e=mc2, and its frequency will increase, and that atomic clock will register an increase in its rate of time relative to an identical stationary clock registering a standard second, which is not what is observed.  An accelerated caesium atomic clock's rate of time will decrease relative to a stationary clock, and this very much involves the accelerated clocks frequency, and therefore it's energy decreasing, relative to the stationary clock.

Turn this concept vertically into a decreasing gravitation field whereby the caesium atomic clocks energy and frequency already increases in the decreasing gravitational field, and the kinetic energy and therefore the additional relativistic mass is still adding energy via e=mc2.  The faster it travels the more energy it has, it's frequency and therefore the rate of time the clock is registering will get even faster, not slower. (I'm pretty sure my logic is sound)

Special relativity states a slowing of time at speed relative to the stationary, and this is observed, but the logic of relativistic mass falls apart when looking at how the frequency of cycles of a caesium atomic clock is energy dependent.

And... why would a gravitational field affect a photon given relativistic mass in a contrary direction to how it affects any other particle?

#### alancalverd

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##### Re: An analysis of the de Broglie equation
« Reply #32 on: 27/05/2016 09:38:58 »
Huh? ...If a ceasium atomic clock registers a faster or slower rate of time, then it's energy and frequency are changing...
No it won't "register" a different time. As far as the observer next to the clock is concerned, it is working perfectly. Gravitational shift and motion shift are only apparent to an observer in a different gravitational potential or moving with respect to the clock.

Quote
And... why would a gravitational field affect a photon given relativistic mass in a contrary direction to how it affects any other particle?
It doesn't, as I explained earlier. The kinetic energy of a particle increases as it accelerates towards a massive body (everyday gravitation), and the frequency of a photon increases as it travels towards a massive body (blue shift). According to Einstein, they are the same phenomenon. But what did he know, eh?

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The only difference between the 2 scenarios apart from the photon having no mass is the fact of its velocity
That, in the words of the prophet, is one hell of a difference. See above.

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A caesium atomic clocks frequency increases in a decreasing gravitational field relative to a clock at ground level.  No kinetic energy involved when the 2 clocks are held stationary relative to each other. ie: 1 meter apart in elevation for instance.
You have spotted the difference between gravitational shift and relative velocity shift. No dispute there.

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Any particle with mass held 1 meter higher in elevation from another identical particle will therefore have a higher frequency than the lower particle...no?
What do you mean by the frequency of a particle?
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#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #33 on: 27/05/2016 12:51:24 »
The De Broglie hypothesis gives all particles a wavelength, frequency and energy.

You say a particle's kinetic energy increases as it falls to earth:  looking at a caesium atom, if it is falling towards earth and its kinetic energy increases, it's mass increases with the additional energy via e=mc2 and its frequency will 'increase' as a result.  An increase in the frequency of cycles of a caesium atom 'is' an 'increase' in the rate of time.

There is nothing written above that is not true to accepted physics.

Yet the observed behaviour of a caesium atomic clock is that it will run at a slower rate relative to a standard second when accelerated, and will run at a slower rate relative the rate it runs at in the weaker gravitational field when exposed to an increase in gravitational field. (NIST 2010 ground level, non accelerated, relativity tests)

Therefore, all particles with mass's wavelength, according to NIST tests in relation to the De Broglie hypothesis, will increase, ie: lengthen, as their energy, and therefore their frequency reduces in an increasing gravitational field.

Lights wavelength decreases in an increasing gravitational field.

I don't think I can be any clearer, and repose my question:  Why is the photon's direction of change in wavelength the opposite to a particle with mass's direction of change in wavelength when exposed to changes in the gravitational field?
« Last Edit: 27/05/2016 12:54:49 by timey »

#### alancalverd

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##### Re: An analysis of the de Broglie equation
« Reply #34 on: 27/05/2016 13:16:11 »
You say a particle's kinetic energy increases as it falls to earth:  looking at a caesium atom, if it is falling towards earth and its kinetic energy increases, it's mass increases with the additional energy via e=mc2 and its frequency will 'increase' as a result.  An increase in the frequency of cycles of a caesium atom 'is' an 'increase' in the rate of time.
The misunderstanding is in the mechanism of the cesium clock. It has noting to do with the mass of the atom, only the energy difference in the hyperfine ground states of its electron cloud. This is unaffected by gravitation or movement.
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#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #35 on: 27/05/2016 14:10:22 »
But a caesium atomic clock's frequency of cycles does change with changes in a gravitational field, and it does change when subject to motion relative to a stationary clock.  This caesium atomic clock's transitions from ground state and back is the method by which we record time and each change in the rate of time comes complete with a specific frequency in hertz.  If the frequency of those cycles increases, the rate of time is faster, and if the frequency of those cycles decreases, the rate of time is slower.

For the frequency of cycles: ie waves per second, to increase - there must be an increase in energy.

An increase in energy, according to GR and e=mc2, includes an increase in mass...

#### alancalverd

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##### Re: An analysis of the de Broglie equation
« Reply #36 on: 27/05/2016 14:42:17 »
No it doesn't! From the point if view of an observer in the same field, the clock is working perfectly because the energy levels of the cesium ground state haven't changed. They are only dependent on the charge and mass of the electrons and protons, not on the ambient gravitational field. But the observer at a different gravitational potential sees the clock as running faster or slower because the field alters the curvature of spacetime.

Time is independent of how you measure it, but very dependent on where you measure it.
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#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #37 on: 27/05/2016 15:22:40 »
Well Alan - the reason the observer of the clock doesn't see any change in the atoms of the clock, when in in motion with the clock, or when in the same gravitational potential as the clock, is because the atoms that make up the physique of the observer are also affected as the clock is by the motion, or gravitational potential.  This is why astronauts who have been exposed to a faster rate of motion and a different gravity potential are reported to have aged more slowly.

http://www.techinsider.io/do-astronauts-age-slower-than-people-on-earth-2015-8

#### alancalverd

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##### Re: An analysis of the de Broglie equation
« Reply #38 on: 27/05/2016 17:03:28 »
A good article, including

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That's because of time-dilation effects. First, time appears to move slower near massive objects because the object's gravitational force bends space-time....

....nothing about the atoms of the clock. Which is why the time dilation effect is exactly the same for all massless photons as it is for electron transitions in an atom, and for all clocks (including rubidium, which preceded cesium). Gravity affects time. And remember that  the frequency of a cesium clock has nothing to do with the mass of, or gravitational pull on, its atoms. It's an entirely quantum-mechanical function of the electron orbitals. If the actual frequency was affected by gravity, the perceived frequency would presumably depend on the chemical makeup of the observer, but it doesn't.
« Last Edit: 27/05/2016 17:05:40 by alancalverd »
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#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #39 on: 27/05/2016 17:59:47 »
Time is a measure of the rate of change of a system. Systems within distinct frames of reference may exhibit different rates of change when observations are made from a frame that is separated from the combined system. So that the remote observer records the rate of change of two atomic clocks as being different. You would never experience this within a frame local to a particular clock. This is the point which often confuses. All lab frames must appear 'normal'.

#### Thebox

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##### Re: An analysis of the de Broglie equation
« Reply #40 on: 27/05/2016 18:05:15 »
Time is a measure of the rate of change of a system.

Abstract time is a measure of the rate of change of a system, do not mistake abstract for ''timeless'' time of space.

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #41 on: 27/05/2016 18:07:52 »
A good article, including

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That's because of time-dilation effects. First, time appears to move slower near massive objects because the object's gravitational force bends space-time....

....nothing about the atoms of the clock. Which is why the time dilation effect is exactly the same for all massless photons as it is for electron transitions in an atom, and for all clocks (including rubidium, which preceded cesium). Gravity affects time. And remember that  the frequency of a cesium clock has nothing to do with the mass of, or gravitational pull on, its atoms. It's an entirely quantum-mechanical function of the electron orbitals. If the actual frequency was affected by gravity, the perceived frequency would presumably depend on the chemical makeup of the observer, but it doesn't.

Because space time bends space is the typical layman oriented fob off use of terminology employed by physicists who think the proper explanation is beyond the understanding of their listener.

So you are saying that the mechanism atoms of the clock are not affected by gravity, that the electron clouds are not affected by gravity, and the only thing that is affecting these mechanism of the atomic clock are the factor of what time is doing in the location of the clock?

Yet it is proved that changes in the gravitational field cause the frequency and wavelength of all particles to shift due to a change in their energy.  The fact of all particles having frequency and wavelength is the premiss of the De Broglie hypothesis and forms the basis of quantum mechanics. (quantum mechanics hasn't as yet been linked to gravity).

The gravitational field shift's the 'energy' of the particle with mass, and the frequency of wavelength per standard second, in the same fashion that it shifts the energy of photon's, and their frequency. (albeit photon's are affected in a contrary direction)

Then, according to GR, e=mc2 will cause a change in mass...

- but you are correct in that the chemical make up of the observer will have no bearing on their perception of a time registered on a clock using the frequency of caesium atoms to measure time, in much the same way that a tall person will not perceive a meter to be any longer or shorter than a smaller person will.  A measure of time is a measurement, and the measure of all time considerations in physics are set by the length of a standard second.  How the atoms of an observer's own physical make up interact with the mechanism atoms of the clock would not be perceivable to the observer in the slightest.  There is a case for the atoms of the observer affecting the mechanism atoms of the clock though, but this effect would not be of the type to initiate the correct shift in their energy transitions from ground state and back cycles.  That would require a 'specific' shift of exactly the correct  and matching frequency, such as a gravitational shift, or a velocity related shift.  And yes, as far as the atom is concerned it will be transiting from its ground state and back again no matter where in a gravitational field you place it, and no matter what speed you subject it to... but relative to the clock registering a standard second at earth's ground level, and at the velocity of earth's transit through space, any change in reference frame is a change in that reference frames clocks ground state energy and frequency - as far as we are concerned on earth and by our earth standard measurements.

#### Thebox

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##### Re: An analysis of the de Broglie equation
« Reply #42 on: 27/05/2016 18:13:39 »
This caesium atomic clock's transitions from ground state and back is the method by which we record time and each change in the rate of time comes complete with a specific frequency in hertz.

There is no change in the rate of time, the change is the measured change of frequency, nothing to do with the ''rate'' of time.

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If the frequency of those cycles increases, the rate of time is faster, and if the frequency of those cycles decreases, the rate of time is slower.

No, the rate of cycles is slower that is that, the ''rate'' of time is not slower or faster, the rate of the Caesium atom is nothing to do with time.
« Last Edit: 27/05/2016 18:18:31 by Thebox »

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #43 on: 27/05/2016 22:45:01 »
Quote wiki:
""Caesium clocks are the most accurate commercially produced time and frequency standards, and serve as the primary standard for the definition of the second in SI (the metric system). By definition, radiation produced by the transition between the two hyperfine ground states of caesium (in the absence of external influences such as the Earth's magnetic field) has a frequency of exactly 9,192,631,770 Hz. That value was chosen so that the caesium second equalled, to the limit of human measuring ability in 1960 when it was adopted, the existing standard ephemeris second based on the Earth's orbit around the Sun.[2] ""

And here is a description of the mechanics:

http://www.wired.com/2014/04/nist-atomic-clock/

The caesium atom resonates at the natural frequency of 9,192,631,770 Hz.   Presumably when gravitational time dilation is discussed and the frequency of cycles of the caesium atom increases for a faster rate of time, the natural frequency of the atom being 9,192,631,770 Hz increases?

If this natural frequency of the caesium atom decreases for a faster rate of time in a weaker gravitational field, then I do apologise Alan for completely wasting your time.

If this natural frequency of the caesium atom increases for a faster rate of time in a weaker gravitational field, then again I ask you, why does the caesium atoms frequency and energy increase for a shorter wavelength in a weaker gravitational field, when a photon's frequency and energy decreases for a longer wavelength in a weaker gravitational field?
« Last Edit: 27/05/2016 22:48:16 by timey »

#### alancalverd

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##### Re: An analysis of the de Broglie equation
« Reply #44 on: 27/05/2016 22:58:25 »
So you are saying that the mechanism atoms of the clock are not affected by gravity, that the electron clouds are not affected by gravity, and the only thing that is affecting these mechanism of the atomic clock are the factor of what time is doing in the location of the clock?
Yes, to the extent that the hyperfine ground state energy difference is not dependent on the local gravitational field.

Good reference! Note that
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Cesium atoms in fountain clocks actually experience time differently at the top of the 3-foot chamber than at the bottom.
No suggestion that the atom undergoes any change, but that time is indeed warped by gravity.

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If this natural frequency of the caesium atom increases for a faster rate of time in a weaker gravitational field, then again I ask you, why does the caesium atoms frequency and energy increase for a shorter wavelength in a decreasing gravitational field, when a photon's frequency and energy decreases for a longer wavelength in a weaker gravitational field?
Once again, it doesn't. A clock - any clock - in a weaker gravitational field will appear to run faster than one in a stronger field. The red/blue shift is exactly the same for a photon, because they are all subject to the same physics. If you start with an incorrect premise, you can end up in all sorts of trouble. As my old navigation instructor said "always start from where you are, then you won't get lost before you take off."
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#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #45 on: 27/05/2016 23:15:10 »
I am starting from the premiss that NIST conducted ground level atomic clock testing of gravitational time dilation.  The clocks didn't just 'appear' be running at different rates of time.  I don't know why you keep referring to the phenomenon as though it were an illusion based on observer dependency.  The experiment stated that an atomic clock at 1 meter elevation registered an increase in frequency of cycles and the clocks rate of time was running faster relative to the identical clock placed 1 meter below it at ground level.  Both clocks could be observed simultaneously by 1 individual.

When they describe an increase in the frequency of cycles for a faster rate of time, are they describing an increase in the frequency that the caesium atom resonates with naturally at ground level or not?

That's a good place to start from...

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #46 on: 27/05/2016 23:59:22 »
How's about you chiralSPO?  Or evan.au?  Would you be willing to engage in a direct question?

Does the natural resonating frequency of a caesium atom at ground level, this being 9,192,631,770 Hz, increase when the atomic clock is elevated in a weaker gravitational field, or does it decrease?
« Last Edit: 28/05/2016 00:05:23 by timey »

#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #47 on: 28/05/2016 01:54:34 »
How's about you chiralSPO?  Or evan.au?  Would you be willing to engage in a direct question?

Does the natural resonating frequency of a caesium atom at ground level, this being 9,192,631,770 Hz, increase when the atomic clock is elevated in a weaker gravitational field, or does it decrease?

What are you measurements with respect to? The ground level frame or the frame of the caesium atom.

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #48 on: 28/05/2016 03:28:10 »
The 2010 NIST ground level relativity tests placed 2 identical caesium atomic clocks 1 meter apart in elevation.  The clock at ground level is described as recording the duration of a standard second via the caesium atoms naturally resonating frequency of 9,192,631,770 Hz.
The clock at 1 meter elevation is described as increasing in its frequency of cycles and running at a faster rate of time relative to the clock at ground level.

So in answer to your question Jeff, I'm looking at the different measurement of frequency for both these clocks caesium atoms reference frames.

Due to the doubt Alan has seeded in my mind regarding the question about a particle with mass's frequency increasing or decreasing in a weaker gravitational field, relative to ground level, I am trying to confirm if this description of an increase in the caesium atoms frequency of cycles means that the frequency of the caesium atoms has increased at elevation in the weaker gravitational field.

If the frequency of the caesium atom increases in the weaker gravitational field - and I'm pretty sure if it does then it must be due the addition of  potential energy - then the caesium atomic clock is registering a faster rate of time when in a higher energy state, which does not correspond to current physics, extra energy being equivalent to extra mass and therefore synonymous with a slowing of the rate of time.  And... also casts aspersions on the concept of a clock experiencing velocity, relative to the stationary clock, requiring a further addition of kinetic energy for a slowing of time.  This being because an addition of energy will increase the frequency of the caesium atoms and the clock will register an increase in the rate of time, relative to the stationary clock, which again does not correspond with current physics.

If the naturally resonating frequency of the caesium atom remains unchanged by, or decreases in the weaker gravitational field, and the description given of an increase in the frequency of cycles for the atomic clocks increase in rate of time is not related to the caesium atoms frequency as per the De Broglie hypothesis whereby wavelength is inversely proportional to frequency,  I owe Alan an apology for wasting his time, you too probably, and I shall in future only ever deem to discuss the weather and horses.

#### Thebox

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##### Re: An analysis of the de Broglie equation
« Reply #49 on: 28/05/2016 08:14:17 »
The 2010 NIST ground level relativity tests placed 2 identical caesium atomic clocks 1 meter apart in elevation.  The clock at ground level is described as recording the duration of a standard second via the caesium atoms naturally resonating frequency of 9,192,631,770 Hz.
The clock at 1 meter elevation is described as increasing in its frequency of cycles and running at a faster rate of time relative to the clock at ground level.

Quite hilarious, I am truly beginning to think that the entire world is ''thick''.   For one last time and ''the love of God'', THE CAESIUM ATOM IS NOT IN DIRECT RELATIONSHIP TO TIME AND HAS NOTHING WHAT SO EVER TO DO WITH TIME,

When the frequency rate of the Caesium is slower or faster that is that , you can't say the Caesium runs at a faster rate of time or slower rate of time, you people are all ''mad''.

« Last Edit: 28/05/2016 08:17:58 by Thebox »