# The Naked Scientists Forum

### Author Topic: An analysis of the de Broglie equation  (Read 22093 times)

#### alancalverd

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##### Re: An analysis of the de Broglie equation
« Reply #225 on: 25/06/2016 01:48:12 »
vc=f

A moment's reflection on the dimensional analysis of this statement will show you that it is nonsense.

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #226 on: 25/06/2016 02:52:19 »
Aha - (chuckle) - and so we can see exactly why I am requiring help with the maths.

Come on Alan, my maths may not be correct, but my intended direction of calculation is surely obvious.  I'm trying to calculate the acceleration of gravity as an 'inverted time dilation' time aspect.  Or - the velocity of Doppler redshift as an 'inverted time dilation' time aspect.

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #227 on: 25/06/2016 07:56:44 »
As I see it, from my untrained perspective:

The acceleration of gravity is given in meters per second squared.

The speed of light is 299 792 458 meters per second.

This means that the distance of 299 792 458 meters can be held constant to a second.

If we divide 299 792 458 meters by 299 792 458 meters, we arrive at 1 meter.

If we divide 1 meter by the speed of light, we can find that the speed of light covers 1 meter in 3.335+ ...is it a millionth of a second?

By adding the meters per second squared of the acceleration of gravity  to the distance of 299 792 458 meters and then dividing by the speed of light, we will arrive at a 1 point something measure of a meter.

Divide 1 point something meters by the speed of light.  Take this result and subtract 3.335+... from it.  The remaining fraction of a second is by how much a second gets 'longer' every 299 792 458 meters in height in the 'open space' gravitational field of the particular mass you are calculating for.

Matching these extra millionth (?) of second to extra length in wavelength of light in the weaker gravity field would of course be peachy.

#### alancalverd

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##### Re: An analysis of the de Broglie equation
« Reply #228 on: 25/06/2016 08:53:11 »
If we divide 299 792 458 meters by 299 792 458 meters, we arrive at 1 meter.
No. You get 1, a dimensionless number.

If you ignore dimensions you will end up believing your own rhetoric.

According to you, a pint of water divided by a pint of water is 1 pint, and a pint of whisky divided by a pint of whisky is 1 pint, so you might as well drink whisky if you are thirsty, or water if you want to get drunk.
« Last Edit: 25/06/2016 08:57:53 by alancalverd »

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #229 on: 25/06/2016 09:28:13 »
As I see it, from my untrained perspective:

The acceleration of gravity is given in meters per second squared.

The speed of light is 299 792 458 meters per second.

This means that the distance of 299 792 458 meters can be held constant to a second.

If we divide 299 792 458 meters by 299 792 458 meters, we arrive at 1 meter.

If we divide 1 meter by the speed of light, we can find that the speed of light covers 1 meter in 3.335+ ...is it a millionth of a second?

By adding the meters per second squared of the acceleration of gravity  to the distance of 299 792 458 meters and then dividing by the speed of light, we will arrive at a 1 point something measure of a meter.

Divide 1 point something meters by the speed of light.  Take this result and subtract 3.335+... from it.  The remaining fraction of a second is by how much a second gets 'longer' every 299 792 458 meters in height in the 'open space' gravitational field of the particular mass you are calculating for.

Matching these extra millionth (?) of second to extra length in wavelength of light in the weaker gravity field would of course be peachy.

Bearing in mind that a second of time is defined by the gravitational field, at ground level, Earth...

Calculating for a greater gravity field than earth (ie: a greater acceleration than 9.807 m/s²) would require maths that resulted in a meter be less than 1... In which case you subtract 9.807 meters squared from the higher acceleration of gravity, and minus the result from 299 792 458 meters, and then divide the result by 299 792 458 meters for a 0 point something of a meter.

Then divide the 0 point something of a meter by speed of light.  Take result and minus 3.335+ millionth of second for a negative result.  This is by how much a second is shorter in a greater gravity field to Earth.

Of course anything with mass will be GR time dilation affected in a mass in relation to mass relationship.
« Last Edit: 25/06/2016 10:05:22 by timey »

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #230 on: 25/06/2016 09:32:54 »
If we divide 299 792 458 meters by 299 792 458 meters, we arrive at 1 meter.
No. You get 1, a dimensionless number.

If you ignore dimensions you will end up believing your own rhetoric.

According to you, a pint of water divided by a pint of water is 1 pint, and a pint of whisky divided by a pint of whisky is 1 pint, so you might as well drink whisky if you are thirsty, or water if you want to get drunk.

I see square root 1 used in many of the related calculations...

Can you please explain what dimension square root 1 is?

In any case all that comment results in is that it takes 3.335+ millionth (?) of a second for the speed of light to cover 1 meter, which is correct. (Given that millionth is correct)

And... don't mean to be funny but If you divide a number by itself all you are saying is that there is the number you are using 'amount' of 1 thing. (edit: and in the instance you comment on, that 1 thing is a meter)

Have you anything to say about any other part of the post?
« Last Edit: 25/06/2016 09:55:44 by timey »

#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #231 on: 25/06/2016 11:20:37 »
Read up on dimensional analysis. Then you will see exactly what Alan means. It is one of the most beneficial things you will ever do for you understanding of physics.

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#### alancalverd

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##### Re: An analysis of the de Broglie equation
« Reply #232 on: 25/06/2016 12:59:00 »
Quote
Bearing in mind that a second of time is defined by the gravitational field, at ground level, Earth...

No. It is the time that elapses during 9,192,631,770 cycles of the radiation produced by the transition between two levels of the cesium 133 atom. Anywhere and everywhere.

#### Ethos_

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##### Re: An analysis of the de Broglie equation
« Reply #233 on: 25/06/2016 14:48:01 »
Read up on dimensional analysis. Then you will see exactly what Alan means. It is one of the most beneficial things you will ever do for you understanding of physics.

#### Colin2B

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##### Re: An analysis of the de Broglie equation
« Reply #234 on: 25/06/2016 15:22:01 »
I agree with Alan, Jeff, and Ethos about dimensional analysis, it really helps with thinking and analysis. Just to get you started:

Can you please explain what dimension square root 1 is?
It depends what units you are working in. It can be dimensionless or it can use the units you are working with eg for 1meter the units would be √m usually written m½.

And... don't mean to be funny but If you divide a number by itself all you are saying is that there is the number you are using 'amount' of 1 thing. (edit: and in the instance you comment on, that 1 thing is a meter)
No, that 1 thing is not a meter. By dividing meters by meters you create a dimensionless ratio or scaling factor (remember Jeff talking about sigma in a different context?). This ratio can be applied to quantities that are not in meters.

It's important to get these basics in place otherwise you will either lose credibility and people will miss the point you are making, or you will mislead yourself into the wrong conclusions.

#### alancalverd

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##### Re: An analysis of the de Broglie equation
« Reply #235 on: 25/06/2016 15:36:58 »
I used to teach dimensional analysis to Arts undergraduates who had never taken a public examination in any science. After about 2 hours' instruction, I set them an "A" level (university entrance) physics paper. They all achieved a pass grade - enough to start an apprenticeship - just by carefully analysing the questions. And this was in the 1960s when A levels were difficult and apprenticeships were worth having!

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #236 on: 25/06/2016 17:20:06 »
Excuse me - but I defined 299 792 458 as being meters, and then divided it by 299 792 458 meters.  The answer is 1 meter.

Then I defined my use of this calculation by dividing 1 meter by the speed of light to calculate what fraction of a second it takes the speed of light to travel 1 meter.

It would appear that my first division of meters by meters is arbitrary, but it is just a means of setting the scene for the meters per second squared of the acceleration of gravity to be added to the meters it takes the speed of light to travel 1 second.

The reason for the calculation of adding the meters per second to the meters covered in 1 second by the speed of light, is to find out how much of a fraction of a second longer it takes the speed of light to cover the distance of the 1 point something meter.

All I am doing is using the time distance speed formula to transpose the acceleration of gravity into an inverted time dilation aspect.  This concept ultimately holds distance as a constant and the rate of the 'inverted time dilation' as the variable, which means that the geometry of 'space' is flat, and it is 'inverted time dilation causing curvature,

Now then guys, in that I am 'changing the dimensions of the universe from an expanding universe to a slowly contracting universe, as per my model, if you think these 'NEW' dimensions are going to be instantly recognisable to you, then you's are not really as clever as I am giving you credit for.

If dimensional analysis is such a favourable tool, why not get involved and 'apply' it to the matter in hand without bias to the fact that the concept is new and foreign to you, instead of using the mention of dimensional analysis to discount the subject matter?

Surely this would be of more intellectual interest than the constant reminding me that my idea is not dimensionally 'usual' to your pre- conditioned pallets?

#### alancalverd

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##### Re: An analysis of the de Broglie equation
« Reply #237 on: 25/06/2016 18:33:40 »
For as long as you divide apples by oranges to get chickens, nobody will take you seriously.

We know the speed of light, whether expressed in meters per second or millifurlongs per microfortnight, and the only preconception that underpins relativity is that c is constant. So far, it has worked very well.

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #238 on: 25/06/2016 18:49:09 »
...and exactly what part of the fact that I am also holding the speed of light constant have you not understood?

What I am proposing would not be a possibility if the speed of light was not held constant.
« Last Edit: 25/06/2016 18:53:48 by timey »

#### alancalverd

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##### Re: An analysis of the de Broglie equation
« Reply #239 on: 25/06/2016 19:48:55 »
Excuse me - but I defined 299 792 458 as being meters, and then divided it by 299 792 458 meters.  The answer is 1 meter.
No. 299...meters divided by 299...meters is 1, not 1 meter.

Quote
Then I defined my use of this calculation by dividing 1 meter by the speed of light to calculate what fraction of a second it takes the speed of light to travel 1 meter.

Quote
It would appear that my first division of meters by meters is arbitrary, but it is just a means of setting the scene for the meters per second squared of the acceleration of gravity to be added to the meters it takes the speed of light to travel 1 second.
so now you are adding meters per second2 to meters. If carpet is £10 per square meter, please add ninepence and tell us what the answer means.

Quote
The reason for the calculation of adding the meters per second to the meters covered in 1 second by the speed of light, is to find out how much of a fraction of a second longer it takes the speed of light to cover the distance of the 1 point something meter.
Obviously, (nought point something)/c

Quote
All I am doing is using the time distance speed formula to transpose the acceleration of gravity into an inverted time dilation aspect.  This concept ultimately holds distance as a constant and the rate of the 'inverted time dilation' as the variable, which means that the geometry of 'space' is flat, and it is 'inverted time dilation causing curvature,
uite [possibly, but you won't demonstrate anything by muddled dimensionality.

Quote
Now then guys, in that I am 'changing the dimensions of the universe from an expanding universe to a slowly contracting universe, as per my model, if you think these 'NEW' dimensions are going to be instantly recognisable to you, then you's are not really as clever as I am giving you credit for.
what new dimensions will you be using, pray? I would recommend that you sort out the  ordinary ones first, then flip into inverted ("k") space once you have achieved dimensional balance. k-space mathematics is quite simple and selfconsistent but it won't tolerate dimensional imbalance!

Quote
If dimensional analysis is such a favourable tool, why not get involved and 'apply' it to the matter in hand without bias to the fact that the concept is new and foreign to you, instead of using the mention of dimensional analysis to discount the subject matter?
Many have tried, but you keep ignoring us.

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #240 on: 25/06/2016 20:26:28 »
If you are trying to dimensionally analyse my proposal, I must have missed your explanation of why it is dimensionally incorrect.

I'm afraid your analogies of apples and oranges, and putting the words of alcoholic water, and non alcoholic whisky in my mouth (for what reason?) have completely passed me by...

The acceleration of gravity is a dimension.  A mathematical process via the time distance speed formula in relation to the constancy of the speed of light is employed.  The result is a dimension of this proposed inverted time dilation.

The mathematical process to arrive at this dimension of inverted time dilation is not a dimension.  I am not suggesting that the time distance speed formula in relation to the constant speed of light is a dimension, anymore than using square root 1 as a mathematical process suggests that square root 1 is a dimension.

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #241 on: 25/06/2016 21:05:27 »
OK - to be hopefully be more 'usual' in the mathematical process employed:

1 meter times speed of light = 299 792 458 meters

1 meter divided by speed of light = 3.3ish nano seconds.

Add meters per second squared of acceleration of gravity to 299 792 458 meters.
Divide by speed of light.
Subtract 3.3 nano seconds from result.

Is the problematic term gone?

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#### alancalverd

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##### Re: An analysis of the de Broglie equation
« Reply #242 on: 26/06/2016 00:04:45 »

The acceleration of gravity is a dimension.
No it isn't. It is a number with two dimensions, L2T-2.

#### Ethos_

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##### Re: An analysis of the de Broglie equation
« Reply #243 on: 26/06/2016 00:06:31 »
Quote from Wiki:

"Checking equations that involve dimensions."

"The factor-label method can also be used on any mathematical equation to check whether or not the dimensional units on the left hand side of the equation are the same as the dimensional units on the right hand side of the equation. Having the same units on both sides of an equation does not guarantee that the equation is correct."

Having different units on both sides guarantees that the equation is in error.
As a general rule, seeking a balanced equation should result in a ratio on one side of the equation equal to the other side. This results in a ratio equal to a ratio relationship. Not one meter, kilo, or second but the number (1).

If this is not sufficient an explanation, please look up Dimensional analysis at Wiki.
You may also want to look up the term: Dimensionless numbers.

« Last Edit: 26/06/2016 00:28:35 by Ethos_ »

#### alancalverd

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##### Re: An analysis of the de Broglie equation
« Reply #244 on: 26/06/2016 00:07:14 »
1 meter times speed of light = 299 792 458 meters
No, it is a meaningless jumble of dimensions L2T-1

The rest is unworthy poppycock. I can't describe it as numerology because you haven't referred to the Great Pyramid or Fibonacci, but I'm sure you will, eventually.

Please ensure brain is in motion before engaging typing finger.
« Last Edit: 26/06/2016 00:14:09 by alancalverd »

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #245 on: 26/06/2016 00:57:54 »
On the basis Alan that - I have fully explained to you the circumstances of the fact that it's not that I'm not proficient in maths.  It's that I've 'never' done any at-all, as I did not get schooled beyond primary school education - you are being incredibly unfair in that you are demanding that I know dimensional analysis in relation to algebraic mathematics, (and I am trying), especially in relation to the fact that it is because I 'don't' know these things that I have asked for HELP!  If I knew them I wouldn't need any.

It is indeed blatantly bloody obvious what I'm trying to do, and 'confusingly' your input is slanted towards the critique of the attempts of a completely qualification-less person, when you could be employing the advantage of your degree to the purpose of assistance. Bit disappointing really!

Dimensional analysis of above calculation:

L is equal to 299 792 458 meters
M is equal to gravitational acceleration
T is equal to L+M/c (edit: minus 3.3ish nano seconds)

Am I on the right track?

L1=T1
L2=T2
« Last Edit: 26/06/2016 01:27:10 by timey »

#### Ethos_

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##### Re: An analysis of the de Broglie equation
« Reply #246 on: 26/06/2016 01:08:33 »
On the basis Alan that - I have fully explained to you the circumstances of the fact that it's not that I'm not proficient in maths.  It's that I've 'never' done any at-all, as I did not get schooled beyond primary school education - not only are you being incredibly unfair in that you are demanding that I know dimensional analysis in relation to algebraic mathematics, (and I am trying) especially in relation to the fact that it is because of I 'don't' know these things that I have asked for HELP!  If I knew them I wouldn't need any.

It is indeed blatantly bloody obvious what I'm trying to do, and 'confusingly' your input is slanted towards the critique of the attempts of a completely qualification-less person, when you could be employing the advantage of your degree to the purpose of assistance. Bit disappointing really!

Dimensional analysis of above calculation:

L is equal to 299 792 458 meters
M is equal to gravitational acceleration
T is equal to L+M/c

Am I on the right track?

L1 = T1
L2=T2
Alan is only trying to show you where your math is wrong Timey. If you are weak in math, it might be advisable for you quit using it to describe your hypothesis. If you continue to use math that turns out to be in error, please don't be upset when it's pointed out to you. You've asked for help and help is what alan and many others are attempting to give you.

#### jeffreyH

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##### Re: An analysis of the de Broglie equation
« Reply #247 on: 26/06/2016 01:33:46 »
L is length in units of metres. T is time in units of seconds. M is mass in units of kilograms. Speed is therefore in units of L/T or metres per second. If we were to multiply a speed by time we would then have (L*T)/T. If we have the same unit in the numerator as in the denominator they cancel. So the 2 Ts cancel and we are left with a length. So if we have 2 metres per second and multiply by 2 seconds we end up with a length of 4 metres. Sit down with a cuppa and read this through a few times.

#### timey

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##### Re: An analysis of the de Broglie equation
« Reply #248 on: 26/06/2016 02:06:41 »
Well - yes Jeff.  I've read the dimensional analysis link that Alan provided last summer.

But how do you apply it to this proposed inverted time?  It presents problems when dealing with a T that is variable in relation to M and L.  I didn't need a cup of tea, nor even more than 30 seconds pass to work this out.

I have given L in meters (in height)
I have given M in terms of g
I have given T in terms of inverted time dilation in fractions of a standard second (for M of, or less than g of earth)

As far as the 'principle' of dimensional analysis goes, in that L1 is equal to T1 under any circumstance of M, (albeit inclusive of the given limitation beyond which an altered calculation is required) the equation or mathematical process has proportional dimensions.
« Last Edit: 26/06/2016 02:13:52 by timey »

#### alancalverd

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##### Re: An analysis of the de Broglie equation
« Reply #249 on: 26/06/2016 10:14:39 »
On the basis Alan that - I have fully explained to you the circumstances of the fact that it's not that I'm not proficient in maths.

There was a time when I wasn't proficient in aviation, but out of courtesy to other users of the sky, I took the trouble to learn the basics before charging into Heathrow's airspace and telling everyone else that they didn't understand.

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##### Re: An analysis of the de Broglie equation
« Reply #249 on: 26/06/2016 10:14:39 »