Double-Slit Experiment: Exploring SR's Impact on Time

[Marcus de Brun]

Special Relativity dictates that if there is relative motion between two objects; their relative experience of time will change and this is measurable at velocities approaching 'c'.

Within the context of the Double-slit Experiment (with detection): When a given quantum-duality is detected by a detector, is the newly established relationship between 'detector-time' (time as experienced by a detector) and 'quantum-time' (time as experienced by the quantum duality) a valid temporal dimension that is subject to the laws of Special Relativity?

 

[PeroK]

Special Relativity dictates that if there is relative motion between two objects; their relative experience of time will change and this is measurable at velocities approaching 'c'.

Within the context of the Double-slit Experiment (with detection): When a given quantum-duality is detected by a detector, is the newly established relationship between 'detector-time' (time as experienced by a detector) and 'quantum-time' (time as experienced by the quantum duality) a valid temporal dimension that is subject to the laws of Special Relativity?

SR and time dilation, which I assume you are alluding to, are not relevant to the double-slit experiment.

 

[Marcus de Brun]

Why is that? We have a particle (electron) traveling at close to the speed of light. And we have a stationary detector (observer). Can you explain why Special Relativity does not apply to this scenario?

 

[PeroK]

Why is that? We have a particle (electron) traveling at close to the speed of light. And we have a stationary detector (observer). Can you explain why Special Relativity does not apply to this scenario?

The electrons in the double slit are generally not traveling that fast. They don't come out of a high-energy particle accelerator.

In the double slit, all that matters is that the electrons form one pattern when both slits are open; and, another pattern when only one slit is open, or if you detect what slit the electron passes through. None of that requires SR.

You may be interested in:

http://www.cornell.edu/video/richard-feynman-messenger-lecture-6-probability-uncertainty-quantum-mechanical-view-nature

 

[Marcus de Brun]

"None of that requires SR."

With respect Perok, I did not ask if SR is required by any particle in the DS. I asked if the temporal relation between detector at the slit, and the detected electron is subject to the laws of Special Relativity. You say the relationship is excluded from Special Relativity. Please explain why SR might hold for a material observer and a particle moving at any velocity, but does not apply to this case?

Thanks for the Feynman link but I have watched his lectures a number or times already.

M

 

[Dale]

Why is that? We have a particle (electron) traveling at close to the speed of light. And we have a stationary detector (observer). Can you explain why Special Relativity does not apply to this scenario?

Of course SR holds for the double slit experiment, it is built into QED.

But, the electrons are stable. Why would their proper time be relevant at all?

Also, what is a “quantum duality” and how is it detected?

 

[PeroK]

"None of that requires SR."

With respect Perok, I did not ask if SR is required by any particle in the DS. I asked if the temporal relation between detector at the slit, and the detected electron is subject to the laws of Special Relativity. You say the relationship is excluded from Special Relativity. Please explain why SR might hold for a material observer and a particle moving at any velocity, but does not apply to this case?

Thanks

M

If you toss a coin, then you and the coin are in relative motion, but that has no bearing on whether it comes up heads or tails.

There is no "detector time" in the double-slit experiment. The detector checks whether an electron passes through a certain slit. That's it. The detector makes no other measurements.

 

[Mister T]

Why is that? We have a particle (electron) traveling at close to the speed of light. And we have a stationary detector (observer). Can you explain why Special Relativity does not apply to this scenario?

He didn't say it doesn't apply. He said it's not relevant.

It is true that if you measure the time that the electron spends traveling from one place to another, that amount of time will be different in the rest frame of those places than it is in the rest frame of the electron.

But what, if anything, does this have to do with quantum physics?

Your question is not well-formed:

Within the context of the Double-slit Experiment (with detection): When a given quantum-duality is detected by a detector, is the newly established relationship between 'detector-time' (time as experienced by a detector) and 'quantum-time' (time as experienced by the quantum duality) a valid temporal dimension that is subject to the laws of Special Relativity?

For example, what does it mean for a given quantum-duality to be detected by a detector? And what is "time as experienced by the quantum duality"?

 

[Marcus de Brun]

"But, the electrons are stable. Why would their proper time be relevant at all?"

What does it matter if the electron is stable or unstable? It is a particle with mass. It is moving at a velocity relative to the detector.

"Also, what is a “quantum duality” and how is it detected?"

The electron exists as a duality with particle and wave properties. When detected it behaves as a particle, when un-detected it behaves as an interference wave.

If I am traveling in a spaceship at close to the speed of light I might comb my hair and shine my shoes in a half hour of my time. However when I return to Earth only a few seconds of my observer's time has passed.

If I am sitting on an electron combing my hair. At the point of detection SR dictates that whatever I am doing as it appears to a stationary detector must appear to "speed up" or occur within less detector time. Therefore when a detector detects me it will detect me within a contraction of its experience of time. I must be detected to comb my hair more rapidly. Conversly I am compelled to observe the detector within a comensurate expansion of my time.

It does not seem logical to suggest that a detector does not experience time. Everything that exists within spacetime must experience time.

M

 

[PeterDonis]

It is a particle with mass. It is moving at a velocity relative to the detector.

Not if that velocity is not measured. Which it isn't. You need to learn basic QM.

The electron exists as a duality with particle and wave properties. When detected it behaves as a particle, when un-detected it behaves as an interference wave.

This is wrong. Google "electron diffraction": electrons can be experimentally detected as waves. Again, you need to learn basic QM.

If I am traveling in a spaceship at close to the speed of light I might comb my hair and shine my shoes in a half hour of my time. However when I return to Earth only a few seconds of my observer's time has passed.

This is wrong. More time will have passed on Earth than on your ship when you return. You need to learn basic SR.

Your question seems to be based on misunderstandings of both SR and QM.

 

[Nugatory]

The electron exists as a duality with particle and wave properties. When detected it behaves as a particle, when un-detected it behaves as an interference wave.

You have been misled by one of the many popularizations of quantum mechanics written for non-scientists.

That notion of wave-particle duality was briefly considered early in the 20th century, but was abandoned when the modern formalism of quantum mechanics was developed during the 1920s, almost a century ago. Unfortunately, by then the idea had made it into the popular imagination, where it has proven to be as unkillable as invasive plants and urban legends.

If you are serious about thinking about and understanding the double-slit experiment, your best bet would be a modern college-level QM textbook. However, the mathematical price of admission for that is fairly steep; if you haven't had several years of serious college-level math (at least two years of calculus, some differential equations, and solid course in linear algebra) you might give Giancarlo Ghiradi's "Sneaking a look at God's cards" a try.

As this thread is based on a misconception, we can close it now.

 

[robphy]

Possibly interesting:
Controlled double-slit electron diffraction
Roger Bach, Damian Pope,Sy-Hwang Liou, and Herman Batelaan
New Journal of Physics, Volume 15, March 2013

http://iopscience.iop.org/article/10.1088/1367-2630/15/3/033018/meta