De Broglie relation

[Lizwi]

Can a single particle behave as a wave? How?

[studiot]

14 minutes ago, Lizwi said:

Can a single particle behave as a wave? How?

That kinda depends upon what you mean by  a wave.

Mathematically a wave is a solution to the wave equation.

But which wave equation?

In this case you mean the Schrodinger wave equation.

The classical linear wave equation only has periodic  (repetitive) solutions.

These are responsible for the well known repetitive patterns we call 'waves'.

The Schrodinger equation can have non repetitive solutions which would occur with a single isolated particle.

More advanced, non linear 'wave equations' can lead to non repetitive solutions called solitary waves or solitons.

It is possible to model the actions of a single particle upon these.
This is done particularly in optics with photons.

[StringJunky]

1 hour ago, Lizwi said:

Can a single particle behave as a wave? How?

Yes. If you fire a single electron in the two-slit experiment it will interfere with itself.

[swansont]

1 hour ago, Lizwi said:

Can a single particle behave as a wave? How?

Yes, they do. What we call particles have been shown to diffract and interfere, all in accordance with deBroglie's idea.

[Itoero]

Isn't a wave a description of the indeterministic behavior when the 'particle' is not measured?

[Mordred]

 There is numerous probability wave-functions in QM and QFT. Each has its particular application in the case of the De-Broglie wave the relation is the massive particles wavelength to its momentum and mass

[latex]\lambda=\frac{h}{mv}[/latex] this directly relates to the wave-particle duality.

Edited February 14, 2019 by Mordred

[QuantumT]

12 hours ago, Lizwi said:

Can a single particle behave as a wave? How?

Yes. When the DSE is performed with single particles at a time, they also form a wave pattern after a while.

But the problem with "the wave" is that it's unmeasurable, because any attempt to measure it, makes it collapse to a particle (or particles).

This - IMO - makes "the wave!" a philosophical matter, more than a physical one.

[Lizwi]

What makes electrons to diverge after passing through a slit?

[swansont]

3 hours ago, Lizwi said:

What makes electrons to diverge after passing through a slit?

They are waves. That's how waves act. Any kind of slit acts like a quasi-point source, so you get a half of a circular wave emanating from them.

[druS]

On 2/15/2019 at 10:25 AM, QuantumT said:

Yes. When the DSE is performed with single particles at a time, they also form a wave pattern after a while.

But the problem with "the wave" is that it's unmeasurable, because any attempt to measure it, makes it collapse to a particle (or particles).

This - IMO - makes "the wave!" a philosophical matter, more than a physical one.

For goodness sake look at the DSE again, the evidence is all before you. Particles go through one by one. the over time the pattern is a wave interference.   It's nothing to do with philosophy and totally to do with science.

It was unexpected (well it was over 100 years ago) but that doesn't mean it isn't science. Some of the best science has come from the unexpected. Maybe most of the best stuff actually.

[Strange]

On 2/15/2019 at 12:25 AM, QuantumT said:

Yes. When the DSE is performed with single particles at a time, they also form a wave pattern after a while.

They form an interference pattern. A small but vital distinction.

On 2/15/2019 at 12:25 AM, QuantumT said:

But the problem with "the wave" is that it's unmeasurable

The fact that an interference pattern is formed is a measurement of the wave. If you know the distance between the slits, you can calculate the wavelength of the wave from the interference pattern.

2 hours ago, druS said:

It was unexpected (well it was over 100 years ago) but that doesn't mean it isn't science.

Important to note that this was not a "discovery" but a test of a prediction of theory (just in case your comment could be misinterpreted as it being an unexpected result when the experiment was done).

[swansont]

1 hour ago, Strange said:

 Important to note that this was not a "discovery" but a test of a prediction of theory (just in case your comment could be misinterpreted as it being an unexpected result when the experiment was done).

Davisson and Germer confirmed the hypothesis, but that wasn't originally why they were doing the experiment. They started a year before deBroglie presented his thesis. But the theory did indeed come before the experiment showed the results.

[QuantumT]

6 hours ago, druS said:

It's nothing to do with philosophy and totally to do with science.

It was unexpected (well it was over 100 years ago) but that doesn't mean it isn't science.

I never said that "the wave" isn't science. Of course it is!
Philosophy is science, just like physics is. It may not be as popular and respected as physics, but it's still a science branch.

[Strange]

52 minutes ago, QuantumT said:

I never said that "the wave" isn't science. Of course it is!
Philosophy is science, just like physics is. It may not be as popular and respected as physics, but it's still a science branch.

Definitely not.

Philosophy is not evidence based, in the same way that science is. It is (should be) a rigorous discipline and may use mathematics (particularly formal logic and set theory) but that's about where the similarity ends.

Philosophy is important for describing and defining how science works (and, sometimes, why it doesn't).

With regard to your statement about waves, the question of whether the waves are "real" or not is a philosophical one, not a scientific one. (As is the question about what "real" means.)

Science deals with things we can measure. We can measure the wave and so it is real as far as science is concerned.

[QuantumT]

1 hour ago, QuantumT said:

it's still a science branch.

I got that backwards. Science is a branch of philosophy. The relation between the two is nicely described here.

I agree with you, Strange.

[studiot]

On 2/15/2019 at 8:01 AM, Lizwi said:

What makes electrons to diverge after passing through a slit?

 

On 2/14/2019 at 11:25 PM, QuantumT said:

Yes. When the DSE is performed with single particles at a time, they also form a wave pattern after a while.

But the problem with "the wave" is that it's unmeasurable, because any attempt to measure it, makes it collapse to a particle (or particles).

This - IMO - makes "the wave!" a philosophical matter, more than a physical one.

This is primarily to help QuantumT and Liz.

One characteristic of waves that is briefly mentioned when they are first taught, but then generally forgotton about is the connection between space and time.

Consider the following experiment.

You send a continuous sine wave signal down a telephone line and perform the following two measurements.

At your end of the line you attach a voltmeter and monitor the signal over a period of time at this point on the telephone line.

Your measurements will plot out the first curve on my attachment.

Then you stretch out a long tape measure along the telephone line and attach a series of voltmeters along the line, starting from your original one.

All at the same instant you record the measurement on each voltmeter and

Your measurements will plot out the second curve on my attachment.

 

Do you notice something very important?

 

They are the same pattern.

 

In fact with any wave you will always get a (the same) pattern in space as you do in time.

 

So for the double slit if you get a pattern of electron arrivals in time, you can expect a similar pattern in space.

 

[Strange]

1 hour ago, QuantumT said:

I got that backwards. Science is a branch of philosophy.

I would disagree with that as well (except historically). But further discussion would be off topic!

[QuantumT]

1 hour ago, studiot said:

You send a continuous sine wave signal down a telephone line and perform the following two measurements.

At your end of the line you attach a voltmeter and monitor the signal over a period of time at this point on the telephone line.

Your measurements will plot out the first curve on my attachment.

Then you stretch out a long tape measure along the telephone line and attach a series of voltmeters along the line, starting from your original one.

All at the same instant you record the measurement on each voltmeter and

Your measurements will plot out the second curve on my attachment.

 

Do you notice something very important?

 

They are the same pattern.

 

In fact with any wave you will always get a (the same) pattern in space as you do in time.

 

So for the double slit if you get a pattern of electron arrivals in time, you can expect a similar pattern in space.

Seems quite logic.

[studiot]

1 hour ago, QuantumT said:

Seems quite logic.

Is that all you want to say about it?

[QuantumT]

6 minutes ago, studiot said:

Is that all you want to say about it?

It is about the interference pattern, isn't it? And that no matter how slowly (time) the particles arrive, they form the same pattern (space). Time and space can't be separated.

Or did I get it wrong (again)? 

[studiot]

15 minutes ago, QuantumT said:

It is about the interference pattern, isn't it? And that no matter how slowly (time) the particles arrive, they form the same pattern (space). Time and space can't be separated.

Or did I get it wrong (again)? 

You got it right.

I was trying to put the maths into words and pictures.

This guy does it better.

I just posted a link in another thread.

Watch these videos.

 

Edited February 20, 2019 by studiot

[druS]

On 2/20/2019 at 10:10 PM, Strange said:

They form an interference pattern. A small but vital distinction.

Thank you. I will get there with the language of science. In time.

[Strange]

26 minutes ago, druS said:

Thank you. I will get there with the language of science. In time.

Potentially confusing because the interference pattern is, itself, wave-like!