The Uncertainty of Time in Quantum Mechanics

[newjerseyrunner]

I was thinking about the double slit experiment and I know that if you let electrons go through one slit on the other it'll produce a pattern like a particle and if you let it go through both it'll act like a wave. I also know that if you observe the electron at the hole, the ones you observe will act like particles and the ones you miss will act like a wave. I also am fairly certain (correct me if I'm wrong) if you allow the electron to go though either hole without observing it at the hole, but observe it after the hole, it doesn't appear to act as though it went through the slits as a wave then turned into one when you observed it, it acts as though it's been a particle the whole time.
First off, do I have the premise right?

Then I know that electrons have no real fixed point in space, they giggle around randomly and have a statistical probability of being in some location at a given time.

I was trying to think of how the electron acts when it's observed after it's already supposedly gone through the holes and it seemed as though it must have first gone through as a wave, been observed, then gone backwards in time and changed to a particle, and I know nothing's supposed to go backwards in time due to causality.

So like they don't have a definite position in space until observed, do they also not have a definite position in time? I think that makes sense based on the concept of spacetime.

 

[ZapperZ]

I was thinking about the double slit experiment and I know that if you let electrons go through one slit on the other it'll produce a pattern like a particle and if you let it go through both it'll act like a wave. I also know that if you observe the electron at the hole, the ones you observe will act like particles and the ones you miss will act like a wave. I also am fairly certain (correct me if I'm wrong) if you allow the electron to go though either hole without observing it at the hole, but observe it after the hole, it doesn't appear to act as though it went through the slits as a wave then turned into one when you observed it, it acts as though it's been a particle the whole time.
First off, do I have the premise right?

Then I know that electrons have no real fixed point in space, they giggle around randomly and have a statistical probability of being in some location at a given time.

I was trying to think of how the electron acts when it's observed after it's already supposedly gone through the holes and it seemed as though it must have first gone through as a wave, been observed, then gone backwards in time and changed to a particle, and I know nothing's supposed to go backwards in time due to causality.

So like they don't have a definite position in space until observed, do they also not have a definite position in time? I think that makes sense based on the concept of spacetime.

There are HUGE problems with your scenario here.

1. What do you mean by "jiggle"? You have only given some handwaving, vague idea without any meaningful description. This is verging on personal theory, which is prohibited by the PF Rules.

2. We KNOW what happens when electrons "jiggle" sinusoidally. We do this all the time at various synchrotron light sources when electrons pass through an insertion device called undulator and wigglers. They RADIATE EM waves. Now, can you tell me where is this radiation given off by your "jiggling" electrons?

Zz.

 

[newjerseyrunner]

I'm just asking if they don't have a defined location in space, or do they not have a defined position in spacetime? Let me rephrase my question: an electron exists around a proton, it's position is described as a a statistical function: 1s, 2s, 2p, 2p. I'm asking is it known or not that the sum of the probability is exactly one, or can there be discrete times where it doesn't exist at all or other times where it exists in two locations at the same time? I read recently that Drs. S. Haroche and D. Wineland won a nobel prize for proving they can exist in two locations at once.

 

[ZapperZ]

I'm just asking if they don't have a defined location in space, or do they not have a defined position in spacetime?

No, if you look at your post again, you did not just ask! You also hypothesized about electrons "jiggling". Be very careful when you throw out things like that, because if we take it at face value, you are implying a boat-load of things!

Let me rephrase my question: an electron exists around a proton, it's position is described as a a statistical function: 1s, 2s, 2p, 2p.

These are not "positions"! These are orbital angular momentum states. The positions are described the combination of the Radial and Angular parts of the wavefunction.

I'm asking is it known or not that the sum of the probability is exactly one, or can there be discrete times where it doesn't exist at all or other times where it exists in two locations at the same time? I read recently that Drs. S. Haroche and D. Wineland won a nobel prize for proving they can exist in two locations at once.

You are asking a more generalized question about the concept of "Superposition". There are already tons and tons of threads on this, having titles ranging from "Schrödinger Cat" to "Double slits" to "Measurement Problem/Wavefunction collapse". Look them up! But please refrain from proposing anything until you've actually understood the physics.

Zz.

 

[bhobba]

I read recently that Drs. S. Haroche and D. Wineland won a nobel prize for proving they can exist in two locations at once.

May I suggest you reread it because QM does not say that. Whenever its observed it is found only in one location - never two. When its not observed the theory is silent about what's going on.

Thanks
Bill

 

[mfb]

I was trying to think of how the electron acts when it's observed after it's already supposedly gone through the holes and it seemed as though it must have first gone through as a wave, been observed, then gone backwards in time and changed to a particle

No, and that idea does not make sense.

 

[watcher]

i think the op is referring to the interpretation of delayed choice quantum eraser experiment

 

[bahamagreen]

I think the OP is asking about the uncertainty principle... he is using the word "jiggling" to classically characterize a particle's probability with respect to position and wondering if the concept extends to time... that a particle does not absolutely exist in the present instant but has some probability that it is ahead or behind with respect to "now". The probability of the "now" particle would need to include the overlapping probabilities of other times close behind and ahead of the present moment.

Is the Schroedinger equation's answer to this ultimately "Yes"?

 

[Khashishi]

You should see this thread https://www.physicsforums.com/threads/do-elementary-particles-jiggle-like-atoms.712089/

 

[Nugatory]

I think the OP is asking about the uncertainty principle... he is using the word "jiggling" to classically characterize a particle's probability with respect to position and wondering if the concept extends to time... that a particle does not absolutely exist in the present instant but has some probability that it is ahead or behind with respect to "now". The probability of the "now" particle would need to include the overlapping probabilities of other times close behind and ahead of the present moment.

Is the Schroedinger equation's answer to this ultimately "Yes"?

No.
Time is not an observable so is not subject to the probabilistic treatment of observables and the uncertainty principle doesn't apply. Instead, it appears as a parameter, one of the arguments of the wave function, and always has a definite value. Any uncertainty about where a particle is at particular moment is captured in the position uncertainty - if you don't know exactly where a moving object is, you don't know exactly when it will arrive at a particular location.

 

[bahamagreen]

The idea that time is not an observable is new to me... I don't know what you mean by that.
The OP mentioned jiggling in spacetime,

"So like they don't have a definite position in space until observed, do they also not have a definite position in time? I think that makes sense based on the concept of spacetime."

I've wondered similarly... If the worldline for a particle has position and time components, and the position components are subject to uncertainty but the time component is not (if all that is correct so far...); how is the worldline characterized with respect to uncertainty? Does it have uncertainty because of the position components, or no uncertainty because of the time component, or is the uncertainty only applicable for the position but not time components, or does uncertainty as a concept not apply to worldlines? If worldlines are not subject to uncertainty, how is it that the particle represented by the worldline is?

 

[jtbell]

The idea that time is not an observable is new to me... I don't know what you mean by that.

There is a position operator, a momentum operator, an angular momentum operator, etc... but there is no time operator. You cannot calculate things like expectation values for time.

 

[Nugatory]

The idea that time is not an observable is new to me... I don't know what you mean by that.

You'll cover this in the first few days of an introductory QM class.

One of the basic principles of quantum mechanics is that a system is represented by a state function that evolves over time according to the Schrödinger equation. That makes time one of the inputs - there is never any question or uncertainty about the answer to the question "What is the value of the wave function at time $t$?".

Another is that observables are represented by Hermitian operators (a particular class of mathematical objects) that act on the state function in ways that let us calculate the probability of getting various results when we measure that particular observable. Position, angular momentum, spin, energy, momentum are examples of observables. But time is not; it shows up in the mathematical equivalent of "If we were to measure the value of observable X at time t, what is the statistical distribution of X values would we find?"

 

[Nugatory]

I've wondered similarly... If the worldline for a particle has position and time components, and the position components are subject to uncertainty but the time component is not (if all that is correct so far...); how is the worldline characterized with respect to uncertainty? Does it have uncertainty because of the position components, or no uncertainty because of the time component, or is the uncertainty only applicable for the position but not time components, or does uncertainty as a concept not apply to worldlines? If worldlines are not subject to uncertainty, how is it that the particle represented by the worldline is?

If you're talking worldlines, you're talking relativistic quantum mechanics, and that's a whole different story. First step is to treat position and time the same way (unlike non-relativistic QM where, as I said above, time is an input parameter and position is an observable) because otherwise we face the sorts of difficulties you've mentioned.
However, that takes us into mathematical deep water very quickly. You can get a feel for just how deep by looking at the first few pages (the Preface for students, and then the half-dozen pages starting at page 19) of Srednicki's book: http://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf

I picked that one because it's easily accessible online and the approach is very much aligned with your question, not because it has greater merit than any other quantum field theory text.