Light-clock and time dilation [was: Hydrogen atom expressed mathematically]

[erik giles]

[Note from mentor: this thread was originally posted in the Quantum Physics forum.]

I am looking for a way to mathematically express the orbit of an electron around the nucleus of a hydrogen atom, while the atom is stationary as well as in motion.

Note the orbit of the electron is 3 dimensional. Any suggestions as to what tool I ought to be using?

Thanks,
Erik

 

[PeroK]

I am looking for a way to mathematically express the orbit of an electron around the nucleus of a hydrogen atom, while the atom is stationary as well as in motion.

Note the orbit of the electron is 3 dimensional. Any suggestions as to what tool I ought to be using?

Thanks,
Erik

The electron doesn't orbit the nucleus in the classical sense.

Try looking up "spherical harmonics".

 

[erik giles]

Thanks! Will do. I do know the orbit is stepwise / quantized at specific levels.

 

[Nugatory]

Google for "Schrödinger equation hydrogen atom". Fasten your seatbelt - it's going to be a bumpy ride.

 

[erik giles]

Excellent thank you.

 

[strangerep]

Any suggestions as to what tool I ought to be using?

An actual textbook on QM.

(From your opening post, I'm guessing you haven't studied one yet?)

 

[erik giles]

I have but I am doing it based on specific needs for specific problems. Don't have enough time to do it the right way.

 

[strangerep]

I have but I am doing it based on specific needs for specific problems.

I have no idea what this means.

Strange that you didn't mention which QM textbook(s) you have studied.

Don't have enough time to do it the right way.

And... you don't even have enough time to read how to solve the problem??

 

[Vanadium 50]

you don't even have enough time to read how to solve the problem??

Which makes one wonder what would be gained if we were to hand him the answer - as it is the same answer the texts have.

 

[erik giles]

I think I did not clearly explain the problem I am working on. I am working to better understand time dilation.

One of the illustrations I found is the light clock. While it does mathematically explain the concept of time dilation, the photons of light observed in the green line (D) cannot be the same as the photons observed in the dotted line (L), since the direction of light is not affected by the motion of the light source.

IE, either the light was projected in direction L, or direction D. In the case of a moving target, depending on its velocity, we would see a left curving line L. Can you help me understand this diagram better?

My idea was to plot the motion of a hydrogen atom parallel to the path of the photon which is why I asked about the mathematical expression of the hydrogen atom.

Thanks.

 

[PeroK]

I think I did not clearly explain the problem I am working on. I am working to better understand time dilation.

One of the illustrations I found is the light clock. While it does mathematically explain the concept of time dilation, the photons of light observed in the green line (D) cannot be the same as the photons observed in the dotted line (L), since the direction of light is not affected by the motion of the light source.

IE, either the light was projected in direction L, or direction D. In the case of a moving target, depending on its velocity, we would see a left curving line L. Can you help me understand this diagram better?

My idea was to plot the motion of a hydrogen atom parallel to the path of the photon which is why I asked about the mathematical expression of the hydrogen atom.

Thanks.
View attachment 215649

The green dotted line L in the second diagram is somewhat confusing. The diagram on the left is the path of the light to one observer (the one moving with the clock). The diagram on the right is the path of the light to a second observer, for whom the clock is moving to the right.

How you got from there to the model of the hydrogen atom is indeed a crooked path!

 

[erik giles]

Here's what a light clock would actually do. So I think the diagram above is incorrect.

 

[PeroK]

Here's what a light clock would actually do. So I think the diagram above is incorrect.

Think about tossing a coin on an aeroplane. Does the coin fly backwards and hit the rear of the cabin? Or, does the coin behave normally to someone on the plane?

What path does the coin take to an observer on the ground?

If the coin is in the air for 0.5s, then by my calculations the plane and the coin will have traveled about 150m horizontally while it was tossed. Yet, both observers see the coin leave and return to the passenger's hand.

In this respect, a moving light clock would be no different. Both observers would see the light bounce between the top and bottom. But, one observer would see the whole apparatus move horizontally while this was happening.

The critical difference is that the coin can (and does) have a different velocity in the two frames. But, the invariance of the speed of light means that light cannot move faster to one observer than the other. And this leads to a serious fresh analysis of the concepts of classical physics, including the universality of time itself.

 

[erik giles]

Think about tossing a coin on an aeroplane. Does the coin fly backwards and hit the rear of the cabin? Or, does the coin behave normally to someone on the plane?

What path does the coin take to an observer on the ground?

If the coin is in the air for 0.5s, then by my calculations the plane and the coin will have traveled about 150m horizontally while it was tossed. Yet, both observers see the coin leave and return to the passenger's hand.

In this respect, a moving light clock would be no different. Both observers would see the light bounce between the top and bottom. But, one observer would see the whole apparatus move horiziontally while this was happening.

The critical difference is that the coin can (and does) have a different velocity in the two frames. But, the invariance of the speed of light means that light cannot move faster to one observer than the other. And this leads to a serious fresh analysis of the concepts of classical physics, including the universality of time itself.

Thanks, yes I agree completely regarding the path of the coin, totally get that.

I was going to use a hydrogen atom in place of the coin for another reason.

However, here is what I am getting at. While the path of the coin does indeed change with the motion of the aircraft, a photon in the same situation does not. A photon emitted within the confines of an aircraft would deflect (even though very slightly) perpendicular to the path of the aircraft. This would hold true even at low velocities.
So, I am not seeing how the light clock thought experiment could be correct. The cesium clocks they use for these experiments depend on the rate of decay of the cesium to measure time, not the motion of a photon between to points.

 

[PeroK]

Thanks, yes I agree completely regarding the path of the coin, totally get that.

I was going to use a hydrogen atom in place of the coin for another reason.

However, here is what I am getting at. While the path of the coin does indeed change with the motion of the aircraft, a photon in the same situation does not. A photon emitted within the confines of an aircraft would deflect (even though very slightly) perpendicular to the path of the aircraft. This would hold true even at low velocities.
So, I am not seeing how the light clock thought experiment could be correct. The cesium clocks they use for these experiments depend on the rate of decay of the cesium to measure time, not the motion of a photon between to points.

Your missing the point:

I hope you are not one of these people who think that the velocity of light is independent of the source? It's the speed of light that is invariant. The direction can't be invariant.

The light clock is taken as a example clock. This shows time dilation. It is then inferred that the issue is with time itself - not with any specific clock and that time dilation applies however time is measured.

 

[erik giles]

Adding the coin to the experiment (which I had planned on adding an H atom, but the coin will do).
The coin as you pointed out keeps its relative position with the stationary observer, but the photon deflects.
This is why the light clock thought experiment in the other diagram is incorrect. It gives the light photon a bit of a 'homing mechanism' in that it deflects to follow the intended target.

The light clock diagram does not apply to time dilation, in my opinion, as it is based on incorrect assumptions.

 

[erik giles]

Your missing the point:

I hope you are not one of these people who think that the velocity of light is independent of the source? It's the speed of light that is invariant. The direction can't be invariant.

The light clock is taken as a example clock. This shows time dilation. It is then inferred that the issue is with time itself - not with any specific clock and that time dilation applies however time is measured.

I think you have missed the point. Are you telling me that a projected light beam will always hit a target along its original line of motion, even if the target moves? What if there are two targets? One moving and one not? Will it hit both?

 

[erik giles]

IE, once an individual photon has left the emitter, its path is no longer affected by the emitter.

 

[PeroK]

Adding the coin to the experiment (which I had planned on adding an H atom, but the coin will do).
The coin as you pointed out keeps its relative position with the stationary observer, but the photon deflects.
This is why the light clock thought experiment in the other diagram is incorrect. It gives the light photon a bit of a 'homing mechanism' in that it deflects to follow the intended target.

The light clock diagram does not apply to time dilation, in my opinion, as it is based on incorrect assumptions.

There is no homing mechanism. "Straight up" is frame dependent. What is straight up for the passenger on the plane is not straight up to someone on the ground. The light ray goes "straight up" relative to the clock. That is not "straight up" to someone for whom the clock is moving.

The "moving" clock has no idea that it's moving. It's simply firing a light beam up and down.

 

[erik giles]

There is no homing mechanism. "Straight up" is frame dependent. What is straight up for the passenger on the plane is not straight up to someone on the ground. The light ray goes "straight up" relative to the clock. That is not "straight up" to someone for whom the clock is moving.

The "moving" clock has no idea that it's moving. It's simply firing a light beam up and down.

Yes I know. But please answer one question - will an individual photon emitted at T 0 hit the target at T+15?

If yes, the photon has a homing mechanism.
If no, then the photon has deflected and the light clock thought experiment is invalid.

 

[erik giles]

IE, regardless of any frame you observe from, the photon will miss unless aimed at a different angle. In which case we have a different photon path.

 

[PeroK]

Yes I know. But please answer one question - will an individual photon emitted at T 0 hit the target at T+15?

If yes, the photon has a homing mechanism.
If no, then the photon has deflected and the light clock thought experiment is invalid.

A photon will hit the target if the emitter is configured correctly. It's easiest to look at this in the rest frame of the emitter. And, if it hits the target in that frame it must hit the target in all frames, as hitting the target is a physical fact. Some people like to imagine that if it hits the target a bomb goes off. A bomb going off is not frame dependent.

 

[PeroK]

IE, regardless of any frame you observe from, the photon will miss unless aimed at a different angle. In which case we have a different photon path.

The path of the photon is physically the same in all frames - it must be; anything else would be physically absurd. But, if one frame is moving with respect to another then the description of that physical path will differ. One observer's "vertical" is another observer's "at an angle".

In this respect light is no different from a coin or hydrogen atom.

Where light is different is that the speed is invariant. The speed of light is the same for all observers.

 

[PeroK]

IE, regardless of any frame you observe from, the photon will miss unless aimed at a different angle. In which case we have a different photon path.

Here's a way to look at it. Imagine that the light clock has a narrow cylinder joining the emitter to the target. The light either stays within the cylinder (and hits the target) or it doesn't. And, if it stays in the cylinder to one observer, it must stay in the cylinder to all observers. Again, think that the photon touching the sides of the cylinder would set off a bomb if you like.

To an observer for whom the light clock is at rest, the light path is vertical: up a stationary cylinder.

But, to other observers the cylinder is moving (perhaps close to light speed) horizontally. So, to those observers, the light is traveling at an angle.

Anything else is a fundamental geometric contradiction.

 

[erik giles]

Under you reasoning, any photon emitted, if pointing at the target at the time of emission, will always hit the target regardless of distance of motion of the target.

Therefore, please review this thought experiment with two targets. Can you tell me, which target an individual photon hit at T+15? I hope you are not one of those people who thinks a photon can hit both targets. It's okay if you are stumped, this is the point of the physics forum.

 

[PeroK]

Under you reasoning, any photon emitted, if pointing at the target at the time of emission, will always hit the target regardless of distance of motion of the target.

Therefore, please review this thought experiment with two targets. Can you tell me, which target an individual photon hit at T+15? I hope you are not one of those people who thinks a photon can hit both targets. It's okay if you are stumped, this is the point of the physics forum.

I'm sorry if that is your attitude. You'll need to find someone else to waste their valuable time trying to teach you something you don't really want to learn.

Your misapprehensions about this experiment are actually quite common. You shouldn't mistake beginner's errors for insights that a hundred years of professional physicists have missed.

 

[erik giles]

Which target will an individual photon hit? Target one or two?

It is very clear to me now that you can't answer that. You all should not have been sarcastic and condescending towards me at my original question regarding the hydrogen atom, since you are now stumped by my question. Questioning my level of research, etc, in such a way is counter to the purpose of this forum.

At the end of this, it is clear that you do understand time dilation and so do I. The true issue is, the light clock thought experiment is invalid, which was my original thesis when I asked about the hydrogen atom.

I predict that you will not answer the question. You will either go silent or make another remark about my attitude, when it was you who started with the attitude at my original post.

 

[A. Neumaier]

the photons of light observed in the green line (D) cannot be the same as the photons observed in the dotted line (L)

A photon can have a wave function concentrated on many rays simultaneously.

 

[erik giles]

Agreed. Can you tell me which target an individual photon would hit at T+15?

 

[erik giles]

Agreed. Can you tell me which target an individual photon would hit at T+15?

IE, I am not questioning special relativity itself, rather, the validity of the light clock thought experiment.