# The Naked Scientists Forum

### Author Topic: Can an electron be in two places at the same time?  (Read 34095 times)

#### Bill S

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##### Re: Can an electron be in two places at the same time?
« Reply #75 on: 11/02/2015 17:21:45 »
John. you were not directing us to Louis Savain, were you?

#### Ethos_

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##### Re: Can an electron be in two places at the same time?
« Reply #76 on: 11/02/2015 17:42:08 »
John. you were not directing us to Louis Savain, were you?
Louis Savain...........Rebel Scientist?......or Crackpot!

#### PmbPhy

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##### Re: Can an electron be in two places at the same time?
« Reply #77 on: 11/02/2015 21:03:33 »
Quote from: jccc
Still think light is particle?
You've never been in a laboratory and watched or ran these experiments so you don't know what you're talking about. Anybody who knows the results knows that if the light source is dim enough then light arrives at the screen in clumps. That means that it appears as specks of light, e.g. the light is localized in space and interacts with light detectors in a finite localized location, not spread out all over the place. The stronger the source of light the more it appears to be spread out in space like a wave.

#### Bill S

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##### Re: Can an electron be in two places at the same time?
« Reply #78 on: 12/02/2015 16:02:16 »
The following is a quote from the Haifa Lectures (Mendel Sachs)

“But if both slits are open, the wave function for the electron penetrating screen S1 is the superposition of states, (ψ1 + ψ2), so that the probability density for the electron wave reaching screen S2 is |(ψ1 + ψ2)|2 = |ψ1|2 + |ψ2|2 + (ψ 1*ψ2 + ψ1ψ 2*). The first two terms above are the partial probability densities that the electron will pass through slit s1 or slit s2. The third term (the cross product) is the ‘interference’ part of the scattering. It shows up on screen S2 as a diffraction pattern.”

I understand that this explains the diffraction pattern produced by electrons, and I know (in a general way) what ψ1 and ψ2 are. However I run into trouble with the next bit of math [|(ψ1 + ψ2)|2 = |ψ1|2 + |ψ2|2 + (ψ 1*ψ2 + ψ1ψ 2*).] especially the last part.

I would really appreciate a guide for the mathematically challenged.

#### JohnDuffield

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##### Re: Can an electron be in two places at the same time?
« Reply #79 on: 12/02/2015 18:12:16 »
Are you suggesting that we should not view time as the fourth dimension? Because if your idea is correct, space/time would only be an abstraction.
I'm suggesting you should view time as a dimension in the sense of measure, but not in the sense of freedom of motion. Time isn't on a par with space. In a metric signature we say (-+++). I can hop forward a metre but you can't hop forward a second.

The dimensions of space are evident and we need no motion to understand their reality. And they consist of three dimensions.
No problem.

Motion is the evidence that the fourth dimension is also a reality.
There's no problem with motion. That's evident too. But note that a clock "clocks up" some kind of regular cyclical motion and shows you some cumulative result called the time. It's a cumulative measure of motion. When some guy in some science fiction movie has some gizmo to stop time, what he actually stops is motion.

And the path thru it is as real as the other three.
But you can't move through motion. You can move through space, but not through motion, and not through time, and not through spacetime. Louis Savain is right about that.
« Last Edit: 12/02/2015 19:10:39 by JohnDuffield »

#### yor_on

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##### Re: Can an electron be in two places at the same time?
« Reply #80 on: 12/02/2015 18:57:43 »
The reality is space and motion. That's motion through space, not spaceitme. Spacetime is a combination of space and time, but it's an abstract thing.
Are you suggesting that we should not view time as the fourth dimension? Because if your idea is correct, space/time would only be an abstraction.

The dimensions of space are evident and we need no motion to understand their reality. And they consist of three dimensions.

Motion is the evidence that the fourth dimension is also a reality. And the path thru it is as real as the other three.

I must respectfully disagree with your position on this issue John.

Still think light is particle?

It's a duality, depending on observer and experiment. If you want everything involved to become 'observers' of each other, then that's ok by me.

#### Ethos_

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##### Re: Can an electron be in two places at the same time?
« Reply #81 on: 12/02/2015 18:59:55 »
But you can't move through motion. You can move through space, but not through motion, and not through time, and not through spacetime.
I wasn't suggesting that one could move through "motion", that would make no sense. But it is possible to move through time. We are moving through time as I write this sentence. And we can also move through it in other more dramatic ways. Time dilation has been recognized for many years and proved with the advent of space travel. When you make the remark that we can't move through time, I find myself wondering how you could make such a statement. You are obviously an intelligent individual judging from your previous posts on different subjects. But I am frankly astounded to hear you make the statement; "You can move through space but not through time."
« Last Edit: 12/02/2015 19:04:58 by Ethos_ »

#### jeffreyH

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##### Re: Can an electron be in two places at the same time?
« Reply #82 on: 12/02/2015 19:21:28 »
You effectively can't move through time as this indicates a choice in the matter. Unlike space, through which motion can be determined and there are degrees of freedom, time passes without giving the choice of whether to 'move' with it or not. The only thing that can be done is to affect the rate at which time passes in a forward temporal direction. We can do things to affect the rate of change. However we would be unable to tell if any change has actually occurred because all measurements would remain consistent locally. So in this respect I have to agree with John.

#### JohnDuffield

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##### Re: Can an electron be in two places at the same time?
« Reply #83 on: 12/02/2015 19:31:56 »
I wasn't suggesting that one could move through "motion", that would make no sense. But it is possible to move through time. We are moving through time as I write this sentence.
Cross my heart and hope to die Ethos, that's just a figure of speech. Let's forget about the motion of the Earth and the Sun and the Galaxy. Let's say you're sitting in your chair, motionless. Why do you think you're "moving through time"? Because all around you, things are moving. If I were to snap my gedanken fingers and stop all the motion inside your body and brain such that you were in total stasis, then when I snapped my fingers again a hundred years later, you might claim you'd travelled through time. But you didn't actually travel through time. You didn't travel anywhere. You didn't move at all. Instead everything else did. And that motion was through space.

And we can also move through it in other more dramatic ways. Time dilation has been recognized for many years and proved with the advent of space travel.
There's no issue with time dilation. That's where your rate of local motion is less than mine. But it isn't time travel. You don't end up in the middle of last week. You could set off in some fast rocket on some out and back trip, and I could watch you every step of the way. You never leave the present.

When you make the remark that we can't move through time, I find myself wondering how you could make such a statement. You are obviously an intelligent individual judging from your previous posts on different subjects. But I am frankly astounded to hear you make the statement; "You can move through space but not through time."
It's true Ethos. I can hold my hands up a foot apart and show you the gap, the space between them. I can also waggle my hands and show you motion - my hand is at one location, then another, et cetera, and you can be confident that my hand is moving through space. But if I stop moving my hand, in what sense is it moving through time? It's just a figure of speech I'm afraid. That's what A World without Time: The Forgotten Legacy of Godel and Einstein is all about. Time is something like heat. Heat is real. So is time. A hundred years will kill you just as surely as a hundred degrees C.  But just as you don't literally climb to a higher temperature, you don't literally  travel through time.
« Last Edit: 12/02/2015 19:33:33 by JohnDuffield »

#### JohnDuffield

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##### Re: Can an electron be in two places at the same time?
« Reply #84 on: 12/02/2015 19:35:44 »
John. you were not directing us to Louis Savain, were you?
No, I meant to be directing you to A World without Time: The Forgotten Legacy of Godel and Einstein. But my URL was a google search on "no motion in spacetime". My bad. Louis Savain has Einstein on his crackpot list, saying this:

"I placed Albert Einstein at the bottom of the list because he, of all people, should have known better. The man needs no introduction, of course, but why is he on the list? Because he (reluctantly but who cares?) agreed with his good friend, Kurt Gödel, that the spacetime of general relativity allows time travel to the past via closed time-like loops..."

That's wrong. In A World without Time you can read how Gödel worked out that time cannot pass if you can visit the past, and that time travel is not possible. Wheeler conflated a temporal circle with a cycle. You can't actually travel around a closed-timelike curve, just as you can't actually fly along a worldline.

#### Bill S

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##### Re: Can an electron be in two places at the same time?
« Reply #85 on: 12/02/2015 19:51:56 »
Quote from: John
You can't actually travel around a closed-timelike curve,

Amen!!!!  Instinctively I believed that, but knowing that neither belief, nor instinct, leads to good science (unless you are Einstein) I have devoted a lot of time and effort to trying to prove myself wrong.  No success yet.

#### chiralSPO

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##### Re: Can an electron be in two places at the same time?
« Reply #86 on: 12/02/2015 20:00:49 »
Motion through time is a potentially unfortunate figure of speech. But in some sense it is correct. If we think of spacetime as a four-dimensional (mathematical) space, where any point is defined by three spatial coordinates and one temporal coordinate, and if we consider changing an object's spatial coordinates as motion through space, then why not consider changing the temporal coordinate as motion through time?

I think it is a very important point, though, to consider that typically there is little relative "motion" along the timeline, and we only observe "now" so it is usually pretty useless to think about the time coordinates of objects. It is useful to think about the time coordinates of events though...

#### Ethos_

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##### Re: Can an electron be in two places at the same time?
« Reply #87 on: 12/02/2015 20:03:56 »
But just as you don't literally climb to a higher temperature, you don't literally  travel through time.
OK,......but would it then be accurate to say: "The advance of time has moved the location of our reality." Because for time to be a dimension, it should progress in a linear fashion.
« Last Edit: 12/02/2015 20:09:26 by Ethos_ »

#### Bill S

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##### Re: Can an electron be in two places at the same time?
« Reply #88 on: 12/02/2015 20:18:30 »
Quote from: Ethos
Because for time to be a dimension, it should progress in a linear fashion.

I'm not sure I follow the logic of that.  Tensed time should progress, but tensless (untensed) time has more in common with spatial dimensions, and that is static.

#### Ethos_

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##### Re: Can an electron be in two places at the same time?
« Reply #89 on: 12/02/2015 20:20:52 »
Motion through time is a potentially unfortunate figure of speech. But in some sense it is correct. If we think of spacetime as a four-dimensional (mathematical) space, where any point is defined by three spatial coordinates and one temporal coordinate, and if we consider changing an object's spatial coordinates as motion through space, then why not consider changing the temporal coordinate as motion through time?

I think it is a very important point, though, to consider that typically there is little relative "motion" along the timeline, and we only observe "now" so it is usually pretty useless to think about the time coordinates of objects. It is useful to think about the time coordinates of events though...
Well said my friend. The passage of these events is how we understand the change and as those changes take place, we experience them passing before us. It may be a little off mark to suggest motion through time but time is surely passing. And as it passes, it is moving us to a new reality.
« Last Edit: 12/02/2015 20:28:06 by Ethos_ »

#### Ethos_

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##### Re: Can an electron be in two places at the same time?
« Reply #90 on: 12/02/2015 20:31:35 »
Quote from: Ethos
Because for time to be a dimension, it should progress in a linear fashion.

I'm not sure I follow the logic of that.
The reason I find that logical comes from; The passage of time is a collection of changing events in a region lying between the past and the future. Just as the region lying between two points of width, length, or height are dimensions, so is the region lying between the past and future. And as such, a linear dimension as defined by a region lying between two points or locations. Time qualifies in that respect because each moment, each Planck moment places us in a different location in time. And because space and time can't be logically separated, a new location in space/time.
« Last Edit: 12/02/2015 23:44:25 by Ethos_ »

#### Bill S

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##### Re: Can an electron be in two places at the same time?
« Reply #91 on: 14/02/2015 18:43:59 »
Is there no mathematician in this thread?

#### JohnDuffield

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##### Re: Can an electron be in two places at the same time?
« Reply #92 on: 15/02/2015 14:37:02 »
Amen!!!!  Instinctively I believed that, but knowing that neither belief, nor instinct, leads to good science (unless you are Einstein) I have devoted a lot of time and effort to trying to prove myself wrong.  No success yet.
I think Groundhog Day is illuminating. If I were to propose some closed timelike curve where the worldline is 24 hours long, most people think they'd live the same day over and over again. But that isn't how it is. It's more like your life lasted 24 hours. So it's more like Mayfly Day. Only it's causeless. Like you hatched from your own egg or something equally weird. In no way does this rather surreal abstract notion offer any prospect of time travel.

#### JohnDuffield

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##### Re: Can an electron be in two places at the same time?
« Reply #93 on: 15/02/2015 15:09:32 »
Motion through time is a potentially unfortunate figure of speech. But in some sense it is correct. If we think of spacetime as a four-dimensional (mathematical) space, where any point is defined by three spatial coordinates and one temporal coordinate, and if we consider changing an object's spatial coordinates as motion through space, then why not consider changing the temporal coordinate as motion through time?
Because that isn't what actually happens, and as (amateur?) physicists we want to make sure that our descriptions match reality.

I think it is a very important point, though, to consider that typically there is little relative "motion" along the timeline, and we only observe "now" so it is usually pretty useless to think about the time coordinates of objects. It is useful to think about the time coordinates of events though...
It certainly is. Spacetime "works". But it isn't some actual thing that you can wander around at will. Ours is a world of space and motion. We can move around space, but time is just a cumulative measure of motion. The universe as we know it has been here for 13.8 billion light years. All that is, is a measure of how far light would have moved since the big bang.

Quote from: Ethos_
OK,......but would it then be accurate to say: "The advance of time has moved the location of our reality." .
That doesn't sound accurate. The advance of time is fair enough, but moved the location of our reality doesn't sound right. The location of our reality is our little patch of this universe. And the reality is that we live in a world of space and motion.

Quote from: Ethos_
Because for time to be a dimension, it should progress in a linear fashion
I don't think there's much issue with that, provided you appreciate that time is derived from the motion of things, and that there is no actual thing called time doing the progressing.

Quote from: Ethos_
The passage of these events is how we understand the change and as those changes take place, we experience them passing before us. It may be a little off mark to suggest motion through time but time is surely passing. And as it passes, it is moving us to a new reality.
There no issue with events happening and changes taking place. But they don't actually pass. Nor does time. That's just a figure of speech. And whilst the present is not the same as the past, we haven't actually moved through time to go from one to the other. The place is the same place, things in it have been moving and changing, that's all.

Quote from: Ethos_
The passage of time is a collection of changing events in a region lying between the past and the future.
There's no problem with the events or change, but there is no actual "region" lying between the past and the future.

Quote from: Ethos_
Just as the region lying between two points of width, length, or height are dimensions, so is the region lying between the past and future.
Only they aren't the same. You can move around those spatial dimensions, and as you do your blood moves, your heart moves, electrochemical signals in your brain moves, things move in your clock, and the hands of your clock moves too. We then infer the time dimension from all this motion, but there is no real "region" between the past and present and future.

Quote from: Ethos_
And as such, a linear dimension as defined by a region lying between two points or locations. Time qualifies in that respect because each moment, each Planck moment places us in a different location in time. And because space and time can't be logically separated, a new location in space/time.
The point to remember is that your measurements of space and time both employ the motion of light, such that when you move fast through space you measure time and space different to me. And note that you're moving through space, and so is the light.

#### PmbPhy

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##### Re: Can an electron be in two places at the same time?
« Reply #94 on: 15/02/2015 15:56:30 »
Is there no mathematician in this thread?

#### Bill S

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##### Re: Can an electron be in two places at the same time?
« Reply #95 on: 15/02/2015 21:29:03 »
Quote from: Pete

Thanks, Pete, can I direct your attention to #78?

#### PmbPhy

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##### Re: Can an electron be in two places at the same time?
« Reply #96 on: 16/02/2015 00:33:26 »
Quote from: Bill S
Thanks, Pete, can I direct your attention to #78?
Sure, buddy. It's simple. First we note how [ψ|2 is defined, i.e.

[ψ|2 = ψ*ψ

Therefore

1 + ψ2|2 = (ψ1 + ψ2)*(ψ1 + ψ2)

Note we note that the complex conjugate of a sum is the sum of the complex conjugates, i.e.

1 + ψ2)* = ψ1* + ψ2*

Now we multiply it all out

1 + ψ2|2 = (ψ1 + ψ2 )*(ψ1 + ψ2)

= (ψ1* + ψ2*)(ψ1 + ψ2)

= ψ11 + ψ12 + ψ21 + ψ22

= |ψ1|2 + |ψ2|2 + (ψ12 + ψ21)

Therefore

1 + ψ2|2 = |ψ1|2 + |ψ2|2 + (ψ12 + ψ21)

Simple, huh? :)
« Last Edit: 16/02/2015 00:38:01 by PmbPhy »

#### PmbPhy

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##### Re: Can an electron be in two places at the same time?
« Reply #97 on: 16/02/2015 00:39:52 »
Quote from: JohnDuffield
The point to remember is that your measurements of space and time both employ the motion of light, such that when you move fast through space you measure time and space different to me. And note that you're moving through space, and so is the light.
Wrong yet again. While measurements of events in spacetime can be done using light it's not a necessity.

#### Bill S

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##### Re: Can an electron be in two places at the same time?
« Reply #98 on: 16/02/2015 17:19:57 »
Quote from: Pete
Simple, huh? :)

If you say so!

I was puzzled by the vertical lines which seem to be used as though they were brackets.  I understand that they imply the absolute value of the figure they enclose.  The nearest I could come to understanding the absolute value of a number was that it signifies the distance of that number from zero.  I’m hard pressed to think of a calculation in which this distinction between value and absolute value might be significant.

3 = 1+1+1

|3| = 0+1+1+1 ?????

#### JohnDuffield

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##### Re: Can an electron be in two places at the same time?
« Reply #99 on: 16/02/2015 21:48:43 »
Wrong yet again. While measurements of events in spacetime can be done using light it's not a necessity.
We use radar to measure distances, and our most accurate clocks are optical clocks. If you want to use a ruler and mechanical clock that's fine by me, but you will note that both consist of matter that has an electromagnetic nature. Hence the wiki article on gravitational time dilation referred to light and matter sharing the same essence. You can still see this on this  A-level page: "...electromagnetic radiation and matter may be equally affected, since they are made of the same essence...

Quote from: Bill S
If you say so!
As you have doubtless learned already, on its own, maths doesn't really help with this sort of thing. What really helps, is experiment. That's not to say maths is futile. The refractive index in electron optics and the principles of dynamics by Ehrenberg and Siday was heavy on maths. It dates from 1949, and it predicted what we nowadays call the Aharanov-Bohm effect. The electron wave isn't just something you can diffract. You can refract electrons too. Here's a picture from the paper, which I'm afraid is behind a paywall:
« Last Edit: 16/02/2015 21:56:16 by JohnDuffield »

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##### Re: Can an electron be in two places at the same time?
« Reply #99 on: 16/02/2015 21:48:43 »