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Author Topic: An analysis of the de Broglie equation  (Read 23545 times)

Offline alancalverd

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Re: An analysis of the de Broglie equation
« Reply #50 on: 28/05/2016 10:01:32 »
I don't know why you keep referring to the phenomenon as though it were an illusion based on observer dependency.
I don't. It isn't an illusion.

We are talking about relativity here. What you see depends on your speed or gravitational potential relative to what you are looking at. There are no absolutes.

A clock cannot "register" a different time from what it is generating, by definition, but another clock can see the difference between them.
 

Offline timey

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Re: An analysis of the de Broglie equation
« Reply #51 on: 28/05/2016 11:17:45 »
Granted Alan... But when NIST place 2 atomic clocks 1 meter apart in elevation - given that the NIST clock operative is likely more than 3 feet tall, both clocks are indeed in the same reference frame as the observer, and are observed by that observer to be running at different rates.

So - I fail to see the relevance of bringing up the relativity aspect when discussing the mechanics of the clock, and questioning if the naturally resonating frequency of the caesium atoms, (being 9,192,631,770 Hz), of the ground level clock, increases or decreases for the clock held at 1 meter elevation relative to the clock on the ground...
« Last Edit: 28/05/2016 11:36:48 by timey »
 

Offline alancalverd

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Re: An analysis of the de Broglie equation
« Reply #52 on: 28/05/2016 11:38:25 »
The observer, in effect, writes down the numbers appearing on the clock faces (it's actually simpler than that - you measure the phase difference accumulated over millions of cycles, between the two signals, and you find it varies in such a way that the higher clock is clearly running faster*).

We define time (and therefore frequency) as what comes out of a standard clock. Relativity says that what comes out of a standard clock will be blueshifted with respect to another if it is at a greater altitude. And it is.

Nothing to do with the mechanics of the clock, which in this case is gravity-invariant. How do we know?  Because (a) if you turn the clock upside down, you get the same answer (b) the calculated relativistic G-blueshift is exactly what is measured and (c) you get the same answer (though with less precision) with rubidium clocks and hydrogen masers, which have very different mechanisms.

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both clocks are indeed in the same reference frame as the observer
They are not moving with respect to each other, but the upper clock is at a higher gravitational potential - that's what we mean by "altitude". General relativity is the business of equating a gravitational field to a moving frame of reference.

*It doesn't matter where you measure the phase difference. If you subtract the lower signal from the received upper signal, you can see that the upper clock is running faster. If you do it the other way around, you can see that the lower clock is running slower. 

« Last Edit: 28/05/2016 11:42:16 by alancalverd »
 

Offline timey

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Re: An analysis of the de Broglie equation
« Reply #53 on: 28/05/2016 12:21:43 »
Understood!

But you see how the clock at ground level is calibrated at the frequency of  9,192,631,770 Hz, because that is the natural resonating frequency of the caesium atom, what I am asking is:

Do the caesium atoms of the clock elevated 1 meter in elevation relative to the clock on the ground still resonate at 9,192,631,770 Hz, or does this frequency change?

And if the frequency does change from 9,192,631,770 Hz for the elevated clock, does it increase, or decrease?
 

Offline jeffreyH

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Re: An analysis of the de Broglie equation
« Reply #54 on: 28/05/2016 14:50:50 »
The scale by which a unique frame of reference can be defined has a limit at the Planck scale. So two clocks at a separation of 1 metre elevation must be considered to be in unique and different frames of reference, since the gravitational gradient varies between the two. Simply because two objects are in the same room does not necessarily mean the frames of reference they occupy are identical.
 

Offline timey

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Re: An analysis of the de Broglie equation
« Reply #55 on: 28/05/2016 15:58:34 »
Ok, yes the clocks are in different frames of reference, but only 1 meter apart.

My question:

The calibrated frequency of the caesium atoms of the mechanism of the atomic clock on the ground, this being 9,192,631,770 Hz... Do the caesium atoms of the clock elevated at 1 meter operate at a frequency of 9,192,631,770 Hz, or does the elevated position of the clock at 1 meter change this operating frequency?

If the elevated position of the clock does cause this frequency of 9,192,631,770 Hz to change, ie: gravitationally shift, is the frequency an increased frequency, or a decreased frequency in relation to 9,192,631,770 Hz?
 

Offline jeffreyH

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Re: An analysis of the de Broglie equation
« Reply #56 on: 28/05/2016 16:30:23 »
What answer are you expecting?
 

Offline timey

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Re: An analysis of the de Broglie equation
« Reply #57 on: 28/05/2016 16:49:45 »

The NIST site states that the frequency of cycles increases for the elevated clock...

Unless there is some other meaning to the phrase of terminology?  Not impossible, hence the question...
 

Offline alancalverd

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Re: An analysis of the de Broglie equation
« Reply #58 on: 28/05/2016 17:36:56 »
To be absolutely pedantic, the cesium clock isn't calibrated. It is the universal standard against which all other timepieces are calibrated, so it defines the second, because all cesium clocks operate at the same frequency, everywhere.

Frequency is the number of cycles per unit time. In a lower gravitational field* time speeds up. So if the frequency of the space clock is constant, the number of space clock cycles seen by an observer on the earth in one earth clock second is larger.

Now 3 ft is, in human terms, a significant change in gravitational potential. If you drop a brick on your foot, it really hurts.  But in cosmic terms it's a very small change, so you need two very precise clocks to measure it by time dilation. That said, it's fundamental to the means by which we measure GPS altitude, so if your clock is really good, you can land a plane by it.


*and here's a source of confusion - if the gravitational field is divergent, as with the earth's field, a higher altitude -> lower field strength  = higher gravitational potential. But don't worry about it, it's just a sign convention.
« Last Edit: 28/05/2016 17:40:56 by alancalverd »
 

Offline timey

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Re: An analysis of the de Broglie equation
« Reply #59 on: 28/05/2016 18:21:50 »
When the clock is set up and placed in situ, the microwave beam that the ball of cooled caesium atoms is tossed up through 'must' be calibrated, ie: tweaked.  They know that they have tweaked the microwave beam to the correct frequency that the caesium atom naturally resonates at - this being the frequency of 9,192,631,770 Hz - when the caesium atoms tossed up in the chamber through this microwave beam emit light.

The NIST site states that the clock in the weaker gravity field has an increased frequency of cycles and runs at a faster rate.
« Last Edit: 28/05/2016 18:24:44 by timey »
 

Offline alancalverd

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Re: An analysis of the de Broglie equation
« Reply #60 on: 28/05/2016 19:50:56 »
"Faster" compared with what? (Hint - the one on the ground!) And I don't think NIST uses the term "frequency of cycles", just "frequency". 

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A caesium standard or caesium atomic clock is a primary frequency standard in which electronic transitions between the two hyperfine ground states of caesium-133 atoms are used to control the output frequency. The first caesium clock was built by Louis Essen in 1955 at the National Physical Laboratory in the UK.[1]
The cesium atom determines the frequency of the microwave source.

 
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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.

The difference betwen definition and calibration is significant to professional nitpickers like standards physicists.
 

Offline timey

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Re: An analysis of the de Broglie equation
« Reply #61 on: 28/05/2016 20:47:05 »
Be that as it may Alan, the only part of the process that I am concerned with is the frequency of the elevated clock being greater than the clock that is on the on the ground in the stronger gravitational field.

Remember that the caesium atom has been chosen because it's natural resonating frequency is equal to a second as defined by the movements of the earth around the sun, not because it is the definition of the phenomenon of time itself.  It is only a measurement.

The frequency of the caesium atom increases in the weaker gravitational field due to the addition of gravity potential?
 

Offline alancalverd

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Re: An analysis of the de Broglie equation
« Reply #62 on: 29/05/2016 00:19:34 »
Remember that the caesium atom has been chosen because it's natural resonating frequency is equal to a second as defined by the movements of the earth around the sun,
Only if you believe that  9,192,631,770 = 1, and I think you may be alone in that belief.

Those who know a bit more would say that cesium is chosen because 9 GHz microwaves are easy to generate and manipulate, and the cesium ground state hyperfine transition is very stable and easy to identify within the cesium absorption spectrum. The magic number was chosen as the best estimate of the length of an astronomical ephemeris second in terms of the frequency of a cesium clock, and from that moment on, the clock defined the second and all astronomical measurements became secondary measures.   

Not a good idea to talk about the "frequency of the cesium atom" lest deBroglie fans think you  mean the deBroglie frequency of the atom, which depends on its kinetic energy. The hyperfine splitting energy doesn't.

As the energy (and hence frequency: E=hf) of the cesium clock transition is fixed, the phenomenon of one clock running fast or slow compared with another is due to the relativistic gravitational and/or motion dilation of time between observers.   
 
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Offline timey

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Re: An analysis of the de Broglie equation
« Reply #63 on: 29/05/2016 01:16:11 »
I very rarely believe anything these days.  Belief is illogical.  I have read that a caesium atoms transitions at the frequency of 9,192,631,770 Hz defines the length of 1 standard second, and have yet found no evidence to suggest anything otherwise.

If the frequency of the atoms of the elevated clock is greater than the frequency of the atoms of the clock at ground level, then the E=hf transitions of the caesium atom are not fixed.  E will increase or decrease as frequency increases or decreases.

In the NIST ground level relativity tests both clocks are held stationary with regards to each other, so kinetic energy cannot be responsible for the difference in frequency between the clocks... and logically speaking if the clock at 1 meter elevation were to zoom off horizontally at speed - adding the subsequent kinetic energy would further increase the frequency and the atomic clock would register a further increase in time, and not the decrease in rate of time as is observed.

The De Broglie hypothesis holds that a particles energy is proportional to frequency, and momentum is calculated via velocity and mass.  The fact that lights mass is calculated via kinetic energy is confusing, but as far as I am aware, a particles frequency is mass related, and it is a particles mass that is velocity related.
 

Offline alancalverd

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Re: An analysis of the de Broglie equation
« Reply #64 on: 29/05/2016 09:58:19 »

 then the E=hf transitions of the caesium atom are not fixed.  E will increase or decrease as frequency increases or decreases.

That's the difference between classical mechanics and quantum mechanics + relativity. QM sensibly says E is fixed because the atom has no idea where it is, and the electrostatic forces inside an atom are much larger than any possible perturbation. Relativity says time is compressed or expanded by gravitation. Common sense says the observer next to the clock doesn't see any change, because he has no other reference. Calculation says an observer at a different gravitational potential will see a difference between the clocks. Experiment says that is exactly what happens. 

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In the NIST ground level relativity tests both clocks are held stationary with regards to each other, so kinetic energy cannot be responsible for the difference in frequency between the clocks... and logically speaking if the clock at 1 meter elevation were to zoom off horizontally at speed - adding the subsequent kinetic energy would further increase the frequency and the atomic clock would register a further increase in time, and not the decrease in rate of time as is observed.
"Ground level" is not "1 meter above ground". Even a cheap GPS like the 200 gadget in my tatty old Cessna can tell the difference, thanks to gravitational time dilation. Relative velocity time dilation is not the same phenomenon as gravitational dilation, as you know (we've discussed this before). Other experiments have shown (indeed you have quoted them) that relative motion slows time, exactly as predicted.

It's interesting to calculate both effects for an orbiting astronaut (low earth orbit, speed dominates, received frequency decreases) and a GPS satellite (high orbit, gravitational shift dominates, frequency increases). There will be some orbital distance at which the effects cancel and a "space clock" keeps time with a "ground clock" - just like your favorite Pound-Rebka experiment!

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[The De Broglie hypothesis holds that a particles energy is proportional to frequency, and momentum is calculated via velocity and mass.  The fact that lights mass is calculated via kinetic energy is confusing, but as far as I am aware, a particles frequency is mass related, and it is a particles mass that is velocity related.
Not quite true, but wholly irrelevant. Maybe next time! But you will confuse yourself less by sticking to the usual terminology: the frequency of a cesium clock (9 gigahertz microwaves, lower than optical)  is not the deBroglie frequency of a cesium atom (way up with cosmic gamma radiation) 
« Last Edit: 29/05/2016 10:10:57 by alancalverd »
 

Offline timey

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Re: An analysis of the de Broglie equation
« Reply #65 on: 29/05/2016 11:16:18 »
The difference between quantum and relativity, and the fact they cannot be reconciled with each other is exactly the region I'm interested in...

Nope ground level is not 1 meter above ground!!!  NIST used 2 clocks, one on the ground (sea level presumably) and one at 1 meter elevation...  If the clock elevated at 1 meter zoomed off horizontally at speed was the consideration...  (I could have zoomed the ground level clock off at speed, but it wouldn't have made for such a good working visualisation due to drag factor. ;)...)

Yes, I am aware that my description of frequency being mass related and mass being velocity related is "not quite true"... this being because e=mc2...

Edit:  The lower microwave region kicks the energy and therefore the frequency of the caesium atom up an energy level.  (Quantum). At elevation the frequency of the atom increases (gravity potential, Relativity).   The energy level of the atom increases the frequency and the wavelength gets shorter (De Broglie hypothesis)

I can see the possibility that an increase in frequency can be associated with an increase in the rate of time (caesium atom behaviour at increased frequency in a weaker gravitational field) and that a lower frequency such as experienced by light in a weaker gravitational field can be indicative of a decrease in the rate of time.

Ditch the notion of energy mass equivalence... and under this remit calculation of wavelength is time related and quantum can then be calculated as to a particles position and momentum simultaneously and without recourse to probability...
 

Offline alancalverd

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Re: An analysis of the de Broglie equation
« Reply #66 on: 29/05/2016 12:23:39 »
Difficut to know where to begin to lead you out of this snowdrift of pseudoscience, so let's ignore the stuff about cesium atoms (why not? you have ignored what I told you!) and start with 
Ditch the notion of energy mass equivalence... and under this remit calculation of wavelength is time related and quantum can then be calculated as to a particles position and momentum simultaneously and without recourse to probability...

You will know from your wide and deep reading on the subject, or even Wikipedia, that mass-energy equivalence does not enter into derivation of, or the equation for, gravitational redshift, nor relative velocity shift. Nor does probablity or quantum mechanics. Relativistic shifts and time dilation are purely classical, continuum, deterministic phenomena.

Keep it simple. In general, truth is found through simplicity.
 

Offline timey

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Re: An analysis of the de Broglie equation
« Reply #67 on: 29/05/2016 13:34:04 »
I'm not ignoring what you have told me...  What I am doing is employing a technique that solicitors use when cross examining witnesses.  I read a book on it.  One leads the discussion to the area one wishes to illuminate.  I forget what the technique is called, I'm out at mo, but will look at the book when I get back later and tell you.

I have read extensively on all of the things that you have 'told me'.  I might not know how to manipulate mathematics but I do have a good understanding of current physics and  therefore please understand that when I make deviations from current physics I do so purposefully.

You seem to be unconcerned that physics is divided into 2 working hypothesis that cannot be reconciled with each other.  I observe a universe that is working as a whole.  The reason I observe this is because the universe does work as a whole, therefore there must be a 'bridge' between quantum and the observed effects of gravitational shift and energy change that are currently Relativity.  It is the goal of theoretical physicists worldwide to reconcile these theories with each other, and it is widely accepted among these physicists that in order to do so, alternatives must be considered.

Perhaps you are confusing the consideration of alternatives to be a 'snowdrift of pseudoscience'?  Or perhaps there is no confusion and you could then rename your board of New Theories as such, instead of 'New Theories'?

Keep it simple:  In a universe where we know that gravity has an effect on particles, and quantum is the world of particles, why is it that these equations you mention do not relate to each other?

Going back to the caesium atom, it's energy level and frequency increase in the weaker gravitational field.  Are you measuring what the rate of time is for that location of weaker gravity field, or are you merely measuring what the rate of time is for the caesium atom via the gravitational shift of an increase in energy, and therefore an increase in frequency, it has suffered in the weaker gravitational field?
 

Offline alancalverd

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Re: An analysis of the de Broglie equation
« Reply #68 on: 29/05/2016 15:54:00 »
In a universe where we know that gravity has an effect on particles, and quantum is the world of particles, why is it that these equations you mention do not relate to each other?

The only equations I have mentioned, of gravitational and velocity shift, are very closely related to each other. Neither has any implied or observed quantum implications as they are both continuum phenomena. Hence no need for a bridge of any sort. 

"Quantum is the world of particles" is journalism or philosophy, not physics.

There is a legitimate question as to why gravitation is not quantised, and the answer is that we don't know, or the quanta are very small, but the question is irrelevant to the present discussion.

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Going back to the caesium atom, it's energy level and frequency increase in the weaker gravitational field.
beware of snow. The potential energy of an atom increases as it moves up the gravitational well. The deBroglie frequency of an atom depends on its momentum, which can be any value you like, or zero if it isn't moving. Neither has anything to do with the clock frequency, which is a function of the electronic structure of the atom, not its environment or relative speed. That's why we use cesium clocks, hydrogen spectra, mossbauer photons and the like, to investigate relativistic frequency shifts. 
 

Offline timey

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Re: An analysis of the de Broglie equation
« Reply #69 on: 29/05/2016 17:54:58 »
All particles are in motion!  When a particle is described as having a rest mass, all this means is that the particle is at rest relative to the earth's motion. ie: it is moving with the earth.

You say that the De Broglie frequency* of an atom is dependent on momentum.  Momentum is calculated via mass and velocity.  Frequency is calculated via energy... and e=mc2.

Are you saying that there is a distinction between how the energies that supposedly contribute to the mass of a particle, or atom, interact with gravity?

You are saying that the clock frequency is a function of the electrons making up the structure of the atom.  Breaking the atom down to its particle structure, the electron has energy, frequency, wavelength...and mass.

Why is the 'we don't know' aspect of physics irrelevant to a discussion that attempts to offer an answer to unknowns, or at least gives a 'reason for cause' for observables that may then be discussed?

If a photon gravitationally shifts in energy, any particle is gravitationally shifting in energy!

*(What is the difference between a De Broglie frequency of an atom, and the frequency of light?  And if a De Broglie frequency differs from another type of frequency, what is this other type of frequency?)
 

Offline alancalverd

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Re: An analysis of the de Broglie equation
« Reply #70 on: 29/05/2016 18:47:10 »
All particles are in motion!  When a particle is described as having a rest mass, all this means is that the particle is at rest relative to the earth's motion. ie: it is moving with the earth.
Alas, this planet is of no cosmic significance. Pmb prefers the term "proper mass", but I think the term "invariant mass" is more descriptive. It's the bit that doesn't depend on speed.   

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You say that the De Broglie frequency* of an atom is dependent on momentum.  Momentum is calculated via mass and velocity.  Frequency is calculated via energy... and e=mc2.{/quote]. As you wish. But if you put in the numbers, you will see that the deBroglie frequency of Cs133 is several orders of magnitude higher than the hyperfine transition frequency that drives the clocks.

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Are you saying that there is a distinction between how the energies that supposedly contribute to the mass of a particle, or atom, interact with gravity?
no

[quoote]You are saying that the clock frequency is a function of the electrons making up the structure of the atom.  Breaking the atom down to its particle structure, the electron has energy, frequency, wavelength...and mass.
Yep. And it's only the quantised energy that matters here.

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Why is the 'we don't know' aspect of physics irrelevant to a discussion that attempts to offer an answer to unknowns, or at least gives a 'reason for cause' for observables that may then be discussed?
because in this instance, the cause is known.

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If a photon gravitationally shifts in energy, any particle is gravitationally shifting in energy!
True, but irrelevant.

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*(What is the difference between a De Broglie frequency of an atom, and the frequency of light?  And if a De Broglie frequency differs from another type of frequency, what is this other type of frequency?)
I'll leave you to calculate or look up the numbers. Hint: the answer is "enormous"!
 

Offline timey

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Re: An analysis of the de Broglie equation
« Reply #71 on: 29/05/2016 19:09:20 »
Why is the fact of an electron gravitationally shifting irrelevant, if the electron's quantised energy transition is shifting the frequency of the clock in the weaker gravitational field?

I did not mean the 'value' of the supposed difference between a De-Broglie frequency of a particle with mass and the frequency of light, just the fact that lights frequency reduces in a weaker gravitational field and a particle with mass, it's frequency increases in a weaker gravitational field.

You also implied that a De Broglie frequency differs from frequency of another kind.  I wanted to know what this other frequency related to, if it is not associated with the energy of the particle, as the De Broglie frequency is...
 

Offline jeffreyH

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Re: An analysis of the de Broglie equation
« Reply #73 on: 29/05/2016 20:41:27 »
So instead of saying that it is the caesium atom's energy, or the electron's energy that has been gravitationally shifted in the weaker gravitational field for an increase in frequency, it would be more terminologically correct to say that the energy of the hyperfine structure transition of the caesium atoms has gravitationally shifted in the weaker gravitational field for an increase in frequency?
 

Offline alancalverd

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Re: An analysis of the de Broglie equation
« Reply #74 on: 29/05/2016 22:35:04 »
No. As far as the observer in the weaker field is concerned. there has been no change in anything.

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just the fact that lights frequency reduces in a weaker gravitational field and a particle with mass, it's frequency increases in a weaker gravitational field.
If you keep repeating this you may convince yourself, but nobody else. One more time: the frequency of electromagnetic radiation as seen by an observer in a weaker gravitational field is lower than that seen by an observer at the source.

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While gravitational redshift refers to what is seen, gravitational time dilation refers to what is deduced to be "really" happening once observational effects are taken into account.

Now what do you mean by the frequency of a particle?
 

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Re: An analysis of the de Broglie equation
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