# I think I have good questions! About superposition and splitting

1. Aug 19, 2009

### Wangf

I am going to crack the quantum mechanics in my free time. :)

correct me if i am wrong. from study. A photon can go both paths in an interferometer.

So what if i put another Interferometer on the upper path, and another interferometer on the lower path. Will the photon split again?
So if i put a serious of inteferometer this way, will the photon continue to split??

My questions, say the "mother" photon is now in both upper and lower paths of an interferometer according to QM, if I continue to put more and more interferometer on "daughter" photon on each path the previous "generation" of photons, will the "daughter" photon continue to split or to have its "daughter" photons in superpositions continously??

My quetions: if not, why? If yes, there must be a level the photon can not forever split? And at how many times it will stop be able to further split?

Also Q: if a photon go to both paths in an interferometer, then the photon in each path is 1/2 the strength or brightness of the original photon, is this right?

Another questions: i also read electrons and atoms can also be superpositions, but if they are in superpositions, has each superpositioned particle have the same length, same mass, same charge as the original "first generation" particle?? if so, where are the additional mass, charge from? (i like to know more than just simply from vacuum, from nothing)

2. Aug 20, 2009

### tiny-tim

Hi Wangf!
I'll bet that it cracks you first!

(quantum mechanics has more time than you have, and you can only use serial processing, while it can use quantum processing! )
It can split indefinitely … remember, it's not the photon itself that is splitting, but the wave function of the photon.
No, there's only one photon … "the photon in each path" makes no sense.
Again, only one particle.

3. Aug 20, 2009

### mary_and_mark

i am new to QM too. My question is:

If a photon pass a vertical polarizer, then we can say that this photon is spin vertially. According the collapse explanation, it will keep the moving direction after being measured.

But some experiments showed that if we put a horizontal polarizer after the vertical one, still some particals can pass. although i know the particals states are decided by wave function. But how to explain the collapse?

it will be appreciated if someone explain this too me.

4. Aug 20, 2009

### Staff: Mentor

Which experiments are you referring to?

5. Aug 20, 2009

### mary_and_mark

6. Aug 20, 2009

### Wangf

That will indicates to me QM is incomplete

7. Aug 20, 2009

### kote

Given certain assumptions (that you seem to be making), QM is incomplete. This is certainly a reasonable view. Claims to the contrary are based on (also very reasonable) semantic arguments that suggest we redefine "reality" so that it is theoretically within the limits of our knowledge.

8. Aug 20, 2009

### tiny-tim

Why?

9. Aug 20, 2009

### Wangf

Because the basic of QM is that nothing can split forever. If a photon can continously split in a series of half-silver mirrors, it must be a level it cannot further split.

That what is the basic meaning of quantum...

Correct me if I am wrong.

I still have question: in the first post, will the strength/brightness of the photon in each path of the interferometer be 1/2 of the original photon? if so, if photon can continously split, will its split photon be 1/2 x 1/2 X1/2 ...... the strength of the 'grand- grand- grand..... mother" photon??

10. Aug 20, 2009

### Dmitry67

Again, there is ONLY ONE photon.
It always has the same energy.
The wavefunction of the photon splits. Please dont imagine a particle fall in pieces. This is absolutely wrong.

I can give you an example. I have 1 winnign lottery ticket. I give 1000 people tickets and only one wins. So I 'split' the victory in 1000 pieces. So every man has 1/1000 chance of the victory. But the victory itself is only one and it never splits. You can 'split' the victory between 1000'000 men or 1'000'000'000 - there are absolutely no limits. The same for the photon.

11. Aug 20, 2009

### tiny-tim

You are wrong!

"quantum" means that any particular detector needs a minimum level of energy in order to detect something.

if the photon is not intercepted before the paths have rejoined, then there was no detection, and no contradiction of the "quantum" principle.

there's only one photon … "the photon in each path" makes no sense.

12. Aug 20, 2009

### Wangf

Thanks all. So I understand from what you guys say, before detection, the photon can split forever.... if there is a detection, photon will only be one photon particle.

i still doubt "wave function" can split forever. I believe no body did an experiment to prove wave function can split forever or not.

I think, maybe, if some scientist set up a very long series of half-silver mirror, and they might see the interference pattern suddenly disappear.

I don't believe wave function can split forever. If I set up thousands or million/billions of half-silver mirror to continue to split "wave function", there may be at a level the photon just cannot be in same path same time and the interference pattern suddenly disappear! Viola, new level of QM. )

13. Aug 20, 2009

### Dmitry67

The Nature makes that experiment many times when you look at stars. When you see a star your eye detects photons from the star's photosphere. They are emitted in random direction. So photon from a star in Andromeda can hit your eye, my eye, a rock in Australia, hit the Moon, Jupiter, other stars, even in the Galaxies on the other side of the Andromeda. So that single photon can have a chance to hit an enourmous surface - everywhere, hitting any atom in a huge volume. We are not talking about billions. We are talking about MUCH bigger numbers. And the 'splitting' does not show any non-linear effects so far.

14. Aug 20, 2009

### Wangf

Thanks. May i still ask: i am wondering if one photon each time, will the it be able to split forever before detection?

15. Aug 20, 2009

### Dmitry67

Forever is a very strong word. So far there are absolutely no indication that it can not split forever.

By the way, do you understand, that even in the 2-slit experiment, photon 'splits' not into 2, but into billions? If it hits a screen behind 2 slits, it leaves a track in one spot. If there are say 10000x10000 spots then it has 100 millions of different options?

16. Aug 20, 2009

### DrChinese

That leads me to a question...

Say that photon is spreading out into spacetime. Presumably the collapse of its wavefunction occurs when some interaction occurs that might be associated with a measurement or observation.

We see photons from the early universe (CNBR) all the time. So when we do, their wavefunction is just now collapsing after billions of years. Clearly then, they missed opportunities to have their WF collapse at many earlier points in time. Can other photons - ones that are "missed" yet again today - propagate into the future indefinitely? I.e. with no end detection whatsoever? Or is it that those photons do have an end point, it just happens to be in the future sometime/somewhere? Is my question clear?

In other words, if those photons can go on forever with no end point in their life, there must be a lot of wavefunctions spread out all over the place waiting to collapse. Imagine the wavefunctions of all the neutrinos out there! Those would be passing through us all the time just like the neutrino itself would. Kinda weird to think about.

17. Aug 20, 2009

### Wangf

Did anyone do an experiment on this? Shooting one photon each time with some time gap between each ones, will you see photon go thru 100 million holes/slits same time?

18. Aug 20, 2009

### Dmitry67

DrChinese, I was asking the same question a long time ago in another context. Yes, many photons (I believe, most of the photons) will never ever find their absorbers. It is a problem for the Transactional Interpretation.

19. Aug 20, 2009

### Dmitry67

Shooting photons (and not only photons) with gaps - done
Photosensitive screen behind gives photon millions different chances - done.

I dont understand what you are tring to do. May be after 100th split photons are converted into flying unicorns? To claim things like this you must have something much stronger then your personal disbelief that photon can split infinitely.

20. Aug 20, 2009

### jambaugh

Here's a general comment about understanding the nature of superposition. "Being in superposition" is not a property of the quantum (photon or electron or ...).
It is a relationship between the description of the specific quantum and our choice of standard representation. More precisely superposition is a property of certain modes of preparation for a quantum relative to other modes of preparation.

For example:

A left-hand circularly polarized photon is in a superposition of vertical and horizontal polarization. It is not in superposition (or in a trivial one) with respect to left-hand and right hand circular polarization.
Likewise a vertically polarized photon is in a superposition of left-hand and right-hand circular polarizations.

(More precisely the mode of producing L-C photons is a superposition of the modes of producing V and H photons, while the mode of producing V photons is a superposition of the modes of producing L-C and R-C photons.)

If you understand the Hilbert space vectors (kets or wavefunctions) as referring not to the state of the quanta but to the mode of producing those quanta then you will be well ahead of the game.
[Disclaimer: This is the CI version of things, you may get different versions from Pilot-Wave-ists and Many-World-ers.]

So with this in mind be careful about saying in e.g. a double slit experiment that "the photon went through both the left and right slits". Rather you should say the photon mode you see after the defraction is in a superposition of one for a photon which definitely went through the left and for one which definitely went through the right.

This is where it gets "tricky" talking about what is or what happens away from the measuring events. Avoid declaritive statements about the actual photon itself except when refering to measured values. You see in Classical Mechanics saying "an e-m wave was emitted by a vertical polarizer" and "the wave is vertically polarized" are equivalent. So even in QM we often use the second form to shorthand the first form.

In the end every quantum is in exactly one mode and we invoke superposition only when that mode isn't one we prefer to work with. In this sense it is "ok" to say in a double slit experiment "the photon passed through the pair of slits" without qualifying (even to say "both" which implies passing through only one is a consistent alternative.) You might think of it as picking a frame of reference for that photon wherein the double slit is a single channel through which it may pass (or not).

To get a sense of this idea think of a (very) weak analogy where you cross your eyes to get left and right stereoscopic images to merge into a single 3-D image. The depth of a point in this image is meaningless if you think in terms of just left or right but rather is a composite of relative information from both.