Understanding Bohr's Theory: Spacetime & Energy Momentum Relations Explained

[PGaccount]

The spacetime and energy momentum relations can be written as

t² - x² = s²
P⁺P^- = m²

Niels Bohr says that "the spacetime or energy momentum relations must be applied at least twice, otherwise they are not defined". Does anyone know what he means by this?

 

[haushofer]

Where did Bohr say that and in which context?

 

[Matterwave]

Sometimes, if you are referring to very old texts (e.g. Bohr) you might notice a big difference between the language and frameworks used there and that used in modern physics. A lot has changed in the last 100 years. There's not just concepts which were proven wrong (e.g. the Bohr atom), but also concepts which got re-framed (e.g. reletivistic mass) in such a way that reading an old source might confuse a modern physicist. You would have to provide a lot more context to your statements in order for anybody to be able to answer your question.

 

[PGaccount]

"Now I don't know if you agree, but this complementary point of view is really obvious, you see — it's completely obvious. And that is, therefore, the solution of the thing. Bohm, for instance, writes that we can measure a lot of things, but he has misunderstood because one can measure anything. One can measure the moment of an electron and its position just by letting it fall on a photographic plate. Then we know where it is, and we also know what the momentum is there because we can measure the momentum before. But all of these things are of no interest; the point is that in any experiment then you must use the space time relations, or energy and momentum relations at least two times, otherwise they are not defined. And. then that is what the whole thing comes to. It's only that you disturb the classical relations in the' definition, and then that is all that we need and want"

 

[sweet springs]

Though I have no idea about "twice" you mention, I suspect it "squared". Both the formula you menioned include squared quantity.

 

[PeterDonis]

Then we know where it is, and we also know what the momentum is there because we can measure the momentum before.

No, we don't know the momentum after measuring the position, because measuring the position changes the momentum. Likewise, measuring the momentum changes the position.

 

[bahamagreen]

"...at least two times...", may be just a reminder of the proper way to make classical measurements in science. The carpenter sets the ruler's edge at one end of a board and takes a single measurement by reading somewhere down the ruler, but a classical scientist places the ruler down arbitrarily and reads the ruler at two locations, estimates the last digit of each, and gets a value from their difference (and two measurement errors rather than the carpenter's single error). Likewise the track coach clicks his stopwatch and takes a single measurement of where the watch's hand stopped, rather than taking two measures and figuring the difference.

Maybe when Bohr is stating "...what the momentum is there because we can measure the momentum before." he is meaning - what the momentum is there because we (have measured) the momentum before (with a previous electron in the same prepared state)... so that the individual measurements of momentum and position must require measures, one of each, on two electrons (and where "an electron" is being used as a particle class name, not literally meaning a single individual electron).

Maybe he is seeing this as complementary because the classical measure is two measurements of the single thing, but the quantum measure is single measurements on two things (two instances of same prepared state). This may be what he means by "...disturb the classical relations in the definition,..."

 

[PGaccount]

Consider an electron in a magnetic field. If the velocity is in the page, and the magnetic field is out of the page, then the electron will move in a circle whose radius depends on its momentum. So when it falls on the plate, we are essentially measuring the radius, and so we know what momentum is there. How does this fit with the uncertainty principle?

 

[PGaccount]

Pic

 

[Ibix]

So you have an electron gun emitting electrons to the right, which travel clockwise until they hit a plate?

That's easy. Your gun has a finite size, so you do not know either the exact launch position or launch momentum (including direction!) of the electron. So you do not know the radius exactly. Narrowing the gun will increase the uncertainty about launch direction (it's a diffraction effect). Widening it decreases the momentum uncertainty (less significant diffraction) but increases your position uncertainty. Either way you have uncertainty about the radius and hence your momentum measure.

 

[Klystron]

Consider an electron in a magnetic field. If the velocity is in the page, and the magnetic field is out of the page, then the electron will move in a circle whose radius depends on its momentum. So when it falls on the plate, we are essentially measuring the radius, and so we know what momentum is there. How does this fit with the uncertainty principle?

Perhaps the OP is using a special/different orientation but this experiment should result in cycloidal electron rotation. The attached diagram which appears similar to your picture demonstrates the distinction.

 

[PGaccount]

has anyone figured this out by 11? what does he mean by twice? what are the "energy-momentum and space-time relations" he is referring to? Does it have something to do with the fact that the action

S = -m∫ ds

involves a mass point interacting with a field ds²?