# The Naked Scientists Forum

### Author Topic: Can this relationship be derived between Schrodinger equation and Doppler shift?  (Read 13117 times)

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #125 on: 19/10/2016 19:49:21 »
Alan - Yes, as you say "The x and y amplitudes are the amplitudes of the original waves."...

These amplitudes of those original waves are causing changes in the distance between the mirrors attached to the tuning forks creating those original waves, and this amplitude of those original waves changes in each of the mirrors at every position in time of the back and forth motions that are occurring at right angles to each other.

It is this part of the process that I wish to discuss and understand the maths of.  In that a pattern is created that is a continuous line, the motions between the mirrors are repetitive...  And in that the motions are repetitive, they constitute a wave form, and a wave form has a period.

Are you with me so far, 'cos if you are I'd like to expand the discussion into translating distances into time periods.  If not, say where your problem is and we will address the problem/s first.

*

Colin - the mechanics that cause a Lissajous figure are occurring in 3 dimensions, it is these mechanics in 3 dimensions that are of interest to me.  That something that is moving in 3 dimensions creates a pattern suggests to me that there are 3 dimensions involved, but if you insist that a Lissajous figure itself is 2 dimensional, then so be it... Actually whether it is or not is incidental to the discussion itself which is about the 3 dimensional mechanics causing the patterns, ok?

As to your statement that says that the mechanics creating the patterns are not occurring in 3 dimensions, either I'm just not understanding what you mean, or you need to think it through more thouroughly.  The mirror is attached to a tuning fork, the fork has a frequency it resonates at when hit, and when hit it rocks back and forth. This action tips the mirror from side to side, or up and down.  These motions 'are' 3 dimensional, and it is these motions that cause the pattern, over time.

...and, I will most certainly have a look at the maths, but to be clear, are you saying that it is the Fourier transformations that are describing the 3 dimensional motions of distance change occurring between the mirrors?
« Last Edit: 19/10/2016 19:51:28 by timey »

#### alancalverd

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #126 on: 19/10/2016 22:06:01 »
By pythagoras, the distance between two points oscillating at right angles to each other is the rest separation plus the square root of the sum of the squares of their positions which at time t are x = a sin ft and y = b sin f't.

You can't "translate distances into time periods" unless there is a known velocity, in whcih case the question is as trivial as navigating by dead reckoning. d = vt.

So you want to know the speed of each mirror at time t. Easy. a cos ft and b cos f't. The calculation of square roots is left as an exercise to the reader, but the answer must be cyclic because there's nowhere else to  go!

« Last Edit: 19/10/2016 22:08:16 by alancalverd »

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #127 on: 19/10/2016 22:43:27 »
In this case translating distances into times wouldn't present a problem, as the light travelling these distances is doing so at constant velocity...

...but the concept of knowing the speed that the mirror is travelling at works well enough, (speed, distance, time formula) and is convenient to the discussion in that it leads to the concept of Doppler shift...

The distance the light is travelling from the first mirror to the second mirror is constantly in flux.  On the forward motion the light is travelling from a surface being pushed forward towards the receiving surface.  On the outward motion the light is travelling from a receding surface.
« Last Edit: 19/10/2016 23:55:40 by timey »

#### alancalverd

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #128 on: 20/10/2016 00:01:49 »
If you are just interested in the Doppler shift from a moving mirror, why not say so?  deltaf = 2v x f/c where v is the instantaneous velocity of the mirror.

#### Colin2B

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #129 on: 20/10/2016 00:13:50 »
As to your statement that says that the mechanics creating the patterns are not occurring in 3 dimensions, either I'm just not understanding what you mean, or you need to think it through more thouroughly.
I can assure you I have thought it through very thoroughly. I have even worked out the best orientation of the fork/mirrors which minimises distortion and tested some ideas with mirrors and laser.

The mirror is attached to a tuning fork, the fork has a frequency it resonates at when hit, and when hit it rocks back and forth. This action tips the mirror from side to side, or up and down.  These motions 'are' 3 dimensional, and it is these motions that cause the pattern, over time.
You need to separate out the motion which creates the lissajous and the motion which doesn't. I have taken to calling them lateral and longitudinal in order to keep them clear in my mind.
If the mirror is attached to the side of the fork it does, as you say, rock - like a lever pivoted at the bottom of the arm. This creates 2 movements. First, a change of angle of incidence between the beam and the mirror, this creates a changing angle of reflection or deflection causing the beam to sweep up and down - I call this the lateral movement. This sweeping, vertical movement is passed to the second mirror which vibrating at right angles to the first adds a horizontal movement. It is the combination of these 2 dimensional movements - up/down, side to side - which creates the lissajous figures. No third dimension is required - think about the double pendulum, 2 dimensions of movement.
In addition, as you say, the rocking of the arm causes a movement along the path of the beam (longitudinal) shortening  and lengthening the distance between the forks. This causes, as Alan rightly said,  a very small timing jitter in the beam, it also causes a very small alternating Doppler Shift in the beam.
The jitter causes a very slight variation in the dwell time as the beam traces out the lissajous (remember how the sand can pile up less when the pendulum speeds up) and if it were possible to measure it there would be a very slight variation of brightness over the curve. The Doppler, again if you could measure it, would cause slight variation to the colour of the beam at various sectors of the curve. However, both of these effects are so small that it is impossible to see them.
There is also a a very, very slight distortion of the curves due to the angle of incidence of the mirror relative to the beam not twisting in the same plane but following a slight curve, I haven't plotted this out but I think it slightly distorts the extremes of the loops, but again it is below measurable level.
As I said before, every mechanical system introduces some distortion, but this system produces very little.
It's worth noting that on the net there are diagrams showing some setups with the mirror attached to the end of a tine facing upwards with the beam shining down onto it, in this case the forward back motion is virtually eliminated and yet lissajous curves are still produced.
As you can see I have thought it through, but why do I expect you won't be convinced?

...and, I will most certainly have a look at the maths, but to be clear, are you saying that it is the Fourier transformations that are describing the 3 dimensional motions of distance change occurring between the mirrors?
No, you were asking about 2 waves being combined to create a third. If you want to look at 3 dimensional motion between the mirrors forget Fourier it won't help you.

Note- I see Alan has responded while I was typing. He understands.

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #130 on: 20/10/2016 00:17:52 »
If you are just interested in the Doppler shift from a moving mirror, why not say so?  deltaf = 2v x f/c where v is the instantaneous velocity of the mirror.

What interests me is that the 'speed' of a Doppler shift can be translated into a period of time via the speed distance time  formula where light is the travelling phenomenon, but enough of this for the moment...
So long as we can agree that Doppler shifts are occurring in the passage of the lights optical path?

Edit: To clarify, I am not referring to a frequency change in the light...  A Mossbauer effect of receiving a gamma ray conducted horizontally in a uniform gravity field will not respond differently if the gamma ray emitter is attached to a vibrating speaker cone.  The photon will still be received.
« Last Edit: 20/10/2016 00:39:48 by timey »

#### Colin2B

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #131 on: 20/10/2016 08:53:07 »
So long as we can agree that Doppler shifts are occurring in the passage of the lights optical path?
Alan agreed this back in #41 and pointed out that it doesn't affect the lissajous patterns.

#### alancalverd

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #132 on: 20/10/2016 10:29:26 »

What interests me is that the 'speed' of a Doppler shift can be translated into a period of time via the speed distance time  formula where light is the travelling phenomenon, but enough of this for the moment...
This sentence is meaningless.

Quote
So long as we can agree that Doppler shifts are occurring in the passage of the lights optical path?
obviously

Quote
Edit: To clarify, I am not referring to a frequency change in the light...
but that is exactly what a Doppler shift is!

Quote
A Mossbauer effect of receiving a gamma ray conducted horizontally in a uniform gravity field will not respond differently if the gamma ray emitter is attached to a vibrating speaker cone.  The photon will still be received.
only at those times where v(cone) = 0 i.e. at the max and min displacement,  when there's no Doppler shift. That's the whole point of the experiment.
[/quote]

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #133 on: 20/10/2016 12:03:12 »
No, it is not meaningless Alan...  The speed that the mirror moves forward with is inherent with a distance.  The mirror only moves so far forward... Subtract the distance that it moves forward from the original distance, divide this distance by speed of light and you have a time value.  The light didn't travel that distance, therefore the time it takes to complete the shorter distance is lesser.  Subtract time value from the original time.
A backward motion will do the opposite and add time to the distance.

Yes - the frequency of light changes in a gravitational gradient and this effect is thought to be due to Doppler shift, because distance between source and receiver is expanding or contracting.  The frequency of the Doppler shift denotes the speed at which the expansion or contraction is occurring...

But we can see in the mechanics of the movement between the mirrors that the light does not travel the distance that is behind the moving forward mirror, nor the distance behind the moving back mirror, and neither of these forward or backward speeds can add or subtract from the velocity of the light.

Adding a vibration to the gamma ray emitter of the Mossbauer simply means the light has a little less time (forward motion), or a little more time (backward motion), in which to travel to the destination.

The Pound Rebka is a vertical experiment...  Have you got any experimental data on a Mossbauer conducted on the 'horizontal' that states frequency change in the gamma ray via this vibration.  I have never come across any myself...
Provide me evidence of this and I'll be packing up my 'New Theory' on new theories as a waste of time!

#### alancalverd

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #134 on: 20/10/2016 17:36:56 »
Come on, lass, this is going backwards into the mists of incomprehension that you left at least a year ago!

No, it is not meaningless Alan...  The speed that the mirror moves forward with is inherent with a distance.
Please don't talk bollocks! The speed of the mirror is a cos ft. What on earth does "inherent with a distance" mean?
Quote
The mirror only moves so far forward... Subtract the distance that it moves forward from the original distance, divide this distance by speed of light and you have a time value.  The light didn't travel that distance, therefore the time it takes to complete the shorter distance is lesser.  Subtract time value from the original time.
A backward motion will do the opposite and add time to the distance.
No! A thousand times no! It adds distance to the  distance, and time to the time. If you start arbitrarily mixing dimensions you will mislead yourself and look very silly.

Quote
Yes - the frequency of light changes in a gravitational gradient and this effect is thought to be due to Doppler shift, because distance between source and receiver is expanding or contracting.  The frequency of the Doppler shift denotes the speed at which the expansion or contraction is occurring...
utter bollocks.

Quote
But we can see in the mechanics of the movement between the mirrors that the light does not travel the distance that is behind the moving forward mirror, nor the distance behind the moving back mirror, and neither of these forward or backward speeds can add or subtract from the velocity of the light.
as far as we know, c is constant

Quote
Adding a vibration to the gamma ray emitter of the Mossbauer simply means the light has a little less time (forward motion), or a little more time (backward motion), in which to travel to the destination.
No. The photon has no idea of its destination. Moving  the emitter adds energy, and since c is constant, this must appear as a change in frequency.

Quote
The Pound Rebka is a vertical experiment...  Have you got any experimental data on a Mossbauer conducted on the 'horizontal' that states frequency change in the gamma ray via this vibration.  I have never come across any myself...
Provide me evidence of this and I'll be packing up my 'New Theory' on new theories as a waste of time!
PR alone results in equal and opposite values to the gravitational shift between up and down, so horizontal = no shift.

Sorry, I can't go on responding to this drivel. I thought you had read and understood the Pound-Rebka experiment. You certainly claimed to have done so. Why have you suddenly started writing utter nonsense about it, and now Mossbauer too?

Maybe you'd prefer to delete the entire post, and I will do likewise with this one, to save embarrassment?
« Last Edit: 20/10/2016 17:41:15 by alancalverd »

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #135 on: 20/10/2016 18:28:32 »
Alan - you can leave the post as is... You might not comprehend the notion that if the speed of light is involved, that a distance and a time are the same thing, are interchangeable, and more to the point can be confused with each other, but someone might...

You are correct in that you thought I had read and understood the Pound Rebka.  I have, 'extensively' and do understand that the Doppler shift is thought to add or subtract energy for a 'longer' or 'shorter' wavelength.

What of it?  Am I not allowed to call 'anything' into question?  Am I just to accept what is spoon fed to me parrot style without engaging brain?

If you have experimental data that describes the use of a speaker in a horizontal Mossbauer experiment that confirms the frequency change on the horizontal, then fair enough!  As I said, my curiosity then over and done with.

Do you?  'Cos as said last post, I haven't been able to find any...

#### Colin2B

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #136 on: 20/10/2016 19:09:09 »
You are correct in that you thought I had read and understood the Pound Rebka.  I have, 'extensively' and do understand that the Doppler shift is thought to add or subtract energy for a 'longer' or 'shorter' wavelength.
You may think that, but it is not what you said. Alan is questioning:
the frequency of light changes in a gravitational gradient and this effect is thought to be due to Doppler shift, because distance between source and receiver is expanding or contracting.
which is not true.

#### alancalverd

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #137 on: 20/10/2016 19:58:49 »

If you have experimental data that describes the use of a speaker in a horizontal Mossbauer experiment that confirms the frequency change on the horizontal, then fair enough!  As I said, my curiosity then over and done with.

Do you?  'Cos as said last post, I haven't been able to find any...

Obviously not, because there is no frequency shift in the horizontal plane. http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/mossb.html describes a classic demonstration that any movement reduces the absorption.

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #138 on: 20/10/2016 20:28:24 »
You are correct in that you thought I had read and understood the Pound Rebka.  I have, 'extensively' and do understand that the Doppler shift is thought to add or subtract energy for a 'longer' or 'shorter' wavelength.
You may think that, but it is not what you said. Alan is questioning:
the frequency of light changes in a gravitational gradient and this effect is thought to be due to Doppler shift, because distance between source and receiver is expanding or contracting.
which is not true.

Before I answer your post, just want to say from one sensitive soul to another, that on my reading through of your posts that it is difficult for me to multi mlquote...so I dont, I took on board your description of a light source moving closer to the screen, and further back from the screen in relation to Doppler shift, and found your analogy of longditudal and lattititudal waves rather inspired.  Thank you.

Alan is not questioning anything.  He is saying bollocks, drivel, and that we sorted this out last year.  No we didn't... Although I can appreciate that Alan does not read every post I make, nobody posted the data I have asked for last year either.

The frequency of light does change in a gravitational gradient.  It is thought that the Doppler shift created by the velocity of the light source (star) moving away from point of observation (earth), ie: a distance expanding - or moving towards point of observation, ie: a distance contracting, changes the wave length of the light.

Where have I gone wrong?

Edit: just saw Alan's post, looking at that now.

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #139 on: 20/10/2016 22:09:28 »
Alan - I just cannot get that link to load, but I gather from the short description you gave that introducing motion to the gamma ray emitter results in less absorption.

This will be the case in both the vertical experiment, where this effect would be factored in, and a horizontal replication of the vertical experiment.
In the horizontal experiment, whereas no motion is introduced to the gamma ray emitter, a rate or percentage of absorption is observed.
Replicating this horizontal experimental on the vertical, where again no motion is introduced to the gamma ray emitter, results in this rate of absorption being zero (?). It is only when the motion is introduced to the gamma ray emitter and the frequency of this motion is cancelled out, that the gamma ray is received by the Mossbauer.
To complete the experiment definitively, (in my mind anyway) one would need to replicate the vertical experiment, where motion is introduced to the gamma ray emitter on the horizontal... where by the remit of the vertical experiment, introducing the motion to the gamma ray emitter should shift the frequency of the gamma ray and the Mossbauer will not be able to receive...
If the Mossbauer does not receive, this confirms the premises of the understanding of Doppler shift in relation to distance.
If the Mossbauer still receives the gamma ray, one must then re-examine the current understanding of introducing a Doppler shift to the gamma ray on the vertical, and the fact that the Mossbauer only then receives it.

#### Colin2B

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #140 on: 21/10/2016 00:10:41 »
Thank you.

The frequency of light does change in a gravitational gradient.  It is thought that the Doppler shift created by the velocity of the light source (star) moving away from point of observation (earth), ie: a distance expanding - or moving towards point of observation, ie: a distance contracting, changes the wave length of the light.

Where have I gone wrong?
Both of your statements are true.
Doppler is created by a moving star relative to detector.
Frequency does change in a gravitational gradient, but it changes even when source and detector are stationary relative to each other, so no Doppler in that case.

I'll let you and Alan discuss the subject as there is obviously some history I'm not aware of.

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #141 on: 21/10/2016 01:02:16 »
Yes me too :)

*

As to history Colin, I remember reading way back Alan saying somewhere that he only comes in 2 modes: Intellectual thug...and (scratches head), hmmm...I can't for the life of me remember the other mode...(chuckle) ...

But for anyone who might not realise, do not think that my getting gloves off and going a few rounds with Alan means that I do not respect him.  It's quite the opposite actually.

#### alancalverd

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #142 on: 21/10/2016 07:03:55 »
Timey: RTFM. I'm out.

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #143 on: 21/10/2016 11:41:21 »
Only trouble is that the manual comes with a post script that clearly states that it is incomplete and cannot provide a full picture of the universe. Hence a bunch of frustrated physicists who are still mulling over the same unsolved problems that incite the same conversations repetitiously day in day out.

For anyone who can appreciate a conversation that deviates from the norm... that attempts to approach a problem stated in the manual by taking logical steps to unpick the physical mechanics of experiment and understand that there are symmetries that must be adhered to...
ie: That if shaking a gamma ray emitter on the vertical causes a frequency shift in the gamma ray, that shaking it in the horizontal will do the same... And because the gravitational shift will not re-shift the frequency of that shaken gamma ray on the horizontal, because the gravity field is uniform(ish) on the horizontal, that the Mossbauer on the horizontal will not be able to receive it!  The gamma ray will not have the correct energy level to be received!

« Last Edit: 21/10/2016 11:47:20 by timey »

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #144 on: 21/10/2016 14:29:33 »
The link Alan provided loaded for me today, so let's examine said manual.

http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/mossb.html#c1

Quote:
"The Mossbauer effect involves the emission and absorption of gamma rays from the excited states of a nucleus. When an excited nucleus emits a gamma ray, it must recoil in order to conserve momentum since the gamma ray photon has momentum. But this takes energy, and the gamma photon has less energy by about 1 eV for a 100 keV photon. The sharpness of an energy state in a potential target nucleus has a natural line width on the order of 10-5 eV, so that the shift in the photon energy prevents the target nucleus from absorbing the gamma photon.

Mossbauer discovered that by placing emitting and absorbing nuclei in a crystal, you could use the crystal lattice for recoil, lessening the recoil energy loss to the point that these extremely sharp emission and absorption lines would overlap so that absorption was observed. An important result was that you now had an extremely sensitive detector for energy shifts - a motion of either source or absorber with velocities on the order of millimeters per second was enough to detune the absorption."
Unquote

So - examining this stage by stage:

Quote:
" When an excited nucleus emits a gamma ray, it must recoil in order to conserve momentum since the gamma ray photon has momentum."
Unquote

...And the gamma ray photon is not absorbed by the target nucleus...

By adding the crystal lattice this recoil motion is reduced - so we are seeing a backward motion of recoil being eliminated by the addition of the crystal lattice.  Now we have overlapping line widths, and the gamma ray can be absorbed by the target nucleus.

In adding motion to the gamma ray emitter, it makes logical sense that adding a backward motion would ensure that the gamma ray will not be absorbed.  Or that adding a backward motion to the target nucleus would elicit the same physical effect...

So effectively the motion added to the gamma ray emitter could be viewed as adding in the same effect that the crystal lattice took out, and the result is that we see the absorption reduced.

In the vertical experiment, when whatever it is in the gravity field cancelled out the added effect of adding in motion, absorption is observed.  It is only when this added motion is matched to whatever it is in the gravity field that is cancelling out this added motion, that absorption will be observed.

The motion added has an associated distance. ie: the distance the speaker cone moves back and forth, (or mirror, where Lissajous is concerned)...  This distance, in respect to the speed of light 'can' be translated into a period of time.  Therefore in the vertical experiment it could be viewed that in adding a backward movement, that this is in effect adding time to the journey of the gamma ray, and that what is being matched by the gravity field is a time related matter, and not distance related.  The mechanics of the motions between the mirrors of the Lissajous are suggestive that this may be the case.

A perspective that would require you to consider that a gravity field itself, ie: the space surrounding a body of mass is inherent with a gravitational time dilation factor of its own, separate from GR time dilation, and that this factor of time dilation causes time to get increasingly slower (for the empty space only) with distance from mass.
« Last Edit: 21/10/2016 14:37:56 by timey »

#### jeffreyH

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #145 on: 21/10/2016 14:39:17 »

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #146 on: 21/10/2016 15:14:37 »
Sure - stick with your vastly overcomplicated quantum computations and your search for dark energy.  And be as unpleasant as you like while you do it... Its hardly original behaviour.

I can fully understand why it is that so many of the people who 'have' made controversial and game changing contribution to physics and science have had such a miserable time of it in their lives.

The history books are full of exactly this kind of blatant unwillingness even to make a consideration of alternatives, a type of almost religiously slanted dogma that has historically driven many intelligently oriented minds to starvation, illness, and even suicide.

So do I take it that there is nobody here who can take a conversation beyond textbook parroting.  No-one who can look at the physics of experiment asymmetrically, and no person who can observe or observe anyone else observe anything other than what is written in the text book without lapsing into rudeness, and hateful prejudice?

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #147 on: 21/10/2016 15:26:20 »
If Einstein had not been looking for a steady state universe he would not have added a cosmological constant, which he then retracted in light of Hubble's redshift 'velocities'.  He would have been forced to consider a contracting universe...

Now line me up and shoot me down for it as is your wont, but that is what I am considering, and it is indeed a highly logical approach!

#### jeffreyH

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #148 on: 21/10/2016 15:45:28 »
I am getting very tired of watching you insult the people that are trying to help you. You may find it amusing in your own passive aggressive way. I don't.

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #149 on: 21/10/2016 16:20:40 »
I am getting very tired of watching you insult the people that are trying to help you. You may find it amusing in your own passive aggressive way. I don't.

And I am getting very tired of you commenting on anything apart from the topic of the thread...

I have insulted nobody.  I am stating facts.  Nobody here wishes to discuss anything in terms that are not already written in a text book.  This is understandable, because if something is not written in a text book, then you guys have not been taught what we are talking about.

It is a fact that this seems to present a problem for all of you to some degree and manifests itself in different ways dependant upon the character of the person I'm talking to...  You seem to relish any opportunity to give anyone else reading the impression that you are of the intelligence to be able to discern between sense and nonsense, and really do seem to enjoy being belittling...otherwise why would you do it?

Alan and Colin, I feel, can see that I am in possession of a degree of intelligence, but become frustrated at their lack of understanding (due partly to my having difficulty explaining myself) of the concepts I'm trying to impart.

Now 'if' you do actually wish to comment on the topic of the thread, be my guest...

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #149 on: 21/10/2016 16:20:40 »