Einstein Vs Bohr and Heisenberg

[Shark Bait]

Einstein's theoretical challange as retold by Stuart Clark, author of 'The Day Without Yesterday'.

Background: Einstein was not a fan of quantum theory and the uncertainty principle. Apparently he came up with a thought experiment for Bohr and Heisenberg.

Quote p217: 'It concerns the trade-off between knowing the energy of a process and the duration of the process.'

P218: "Imagine a box filled with light and placed on a weighing machine. Next to the box is a clock. The box opens at a particular time and a single photon is emitted. The weight of the box instantly changes, and that will give us the precise amount of energy released. The clock will have told us exactly when the photon was emitted. Both can therefore be known with certainty. There is no uncertainty between energy and time.'

'If the uncertainty principle is true, you should be able to give me a theoretical reason why the clock will be affected by the release of the photon. How can those two things be physically related?'

According to Clark, Bohr came up with a solution for Einstein:

P219: 'You have given me a sleepless night,' Bohr said to Einstein, 'but I have an answer for you. When the photon leaves the box, the box will weigh less. It will therefore rise a little on the scales.' Einstein inclined his head in agreement. 'At its new height it will feel a weaker pull of Earth's gravity than before. According to general relativity, the rate at which time passes is dependent upon the strength of the gravitational field. So, time for the box slows down during the emission of the photon. In other words, the emission of the photon causes time to pass at a differnet rate after the release than before. The difference in this rate introduces an uncertainty into the measurement of the clock standing beside the apparatus. As you see, Albert, the uncertainty predicted by general relativity is exactly the same as predicted by Heisenberg's principle. You forgot your own theory.'

I don't know if how Clark retold this story is historically accurate but the details of the challenge got my cogs turning:

Even though this is a theoretical challenge, light is without mass. How could the box register a lower weight?
As time slows down for the box, my understanding is that time for the released photon speeds up.
Edit: Apologies, this thread probably belongs in the Amateur Science section of the forum.

[TrevorW]

http://www.desy.de/user/projects/Physics/Relativity/SR/light_mass.html

more thought

[raymo]

As I understand it, something has to have some mass in order to be
affected by gravity, as light is in gravitational lensing.
raymo

[Astro_Bot]

2c:

Photons are massless. The path taken by the particle is affected by the curvature of spacetime, which is caused by mass/energy - the effect is called gravity - General Relativity is the theory that applies.

As to the box experiment, I have no idea, but perhaps it has to do with how the reference frames are constructed.

And then there's quantum gravity ........ too hard!


An additional thought:

Consider a black hole, from which no light can escape. It's not that the massless photon is "pulled on" by gravity, it's that the curvature of spacetime is so tight that any path the photon takes curves back inside the black hole. Alternatively, you could think of it as the speed of light being fixed in all inertial reference frames (Special Relativity) and the photon never achieves "escape velocity" from the black hole - escape velocity is independent of vehicle mass.

[Shark Bait]

Thanks Trevor, the article covers the specific situation covered as quoted from the book, as well as dealing with the point raised by raymo. It will take some time before I can digest it all. With time, I hope some of it sticks and becomes clear in my mind.



I recently finished Fred Watson's book 'Star-Craving Mad' and he did a great job of explaining General and Special Relativity in a way that seemed to make sense. That must have been an illusion as I will now have to read it all over again.

The article you recently posted on Quantum Theory was tough going. I have read it through and it requires some thought before trying again. Getting to grips with these topics must be one of the hardest things to do. Some of it seems near impossible to visualise. There must be those who have done so, for the technology to continues to advance. Simply brilliant.

[Astro_Bot]

I didn't mean to make it sound like I actually understand stuff. ;)

None of this is easy, and I'm sure I had to read my relativity book a few times before I grasped the small portion of it that I did. :)

My short post isn't complete - it really is only 2c worth. So, for example, to be more strictly correct, even though a photon is definitely a massless particle, and has zero mass "in the real world", in Relativity, it has relativistic mass and momentum! More here (http://en.wikipedia.org/wiki/Relativistic_mass).

[Astro_Bot]

An afterthought ...


Actually, the quantum and relativistic worlds are real and it's the "everyday world around us" that's an illusion! :D

[raymo]

Again, as I understand it, there is no proof that photons are massless;
and if they are massless, maybe they would not interact with spacetime,
and ignore the curves and sail straight through them without deviating. Just
another thought to toss into the cauldron of complexity that is the
universe. I suppose the fact that photons travel at the speed that they do
comes close to proof of their mass,[assuming that relativity is correct, that is].
raymo

[Astro_Bot]

No, really, they are massless. As hard as it is to understand, relativisitic mass is a function of energy but still equals zero in the reference frame of the photon.


It's all about the reference frames. As far as the photon is concerned, it follows a geodesic path - a straight line when viewed from each point along the line - but from the point of view of an external observer, the path is curved (which is equal to the curvature of spacetime).

Relativity has been demonstrated to be correct by many experiments and observations .... but is still (apparently) neither complete nor sufficient (to explain everything going on in the universe).

Tell me when your head explodes. :D

[sjastro]

I don't know if how Clark retold this story is historically accurate but the details of the challenge got my cogs turning:
[LIST=1]
Even though this is a theoretical challenge, light is without mass. How could the box register a lower weight?

To answer this question one needs to note the differences between Newton's concept of gravity as opposed to Einstein's and how it impacts on "weight" and mass.
The equations describing Newton's concept of gravity are linear. From a physical viewpoint the gravitational force between 2 masses is the same as breaking up one of the the masses into pieces and adding up the individual forces between each piece and the unbroken mass. In other words the whole is equal to the sum of its parts.
From a GR perspective the equations are no longer linear, in this case one would find the whole is now less than the sum of its parts.
The "missing mass" is taken up by the binding energy required to break up the mass into pieces. This energy also contributes to the total force. In fact energy in general contributes to mass via the equation E=mc^2.
This has been experimentally confirmed. One finds for example the mass/energy of the helium atom is less than the sum of its constituent protons, neutrons and electrons.

In Einstein's example the photon carries away a certain amount of energy which is related to its wavelength hence the box will be lighter.

Regards

Steven

[Shark Bait]

Thanks for taking the time to prepare your explanation Steven. I am continuing in my attempts to gain a deeper understanding of General / Special Relativity and Quantum Mechanics. To help with this, I now have another book, this one written by Brian Greene - The Fabric of the Cosmos. My hope is that this book will fill in some of the gaps, although I can see where this is all going. If I am to achieve my goal, it will require a serious upgrade in my mathematical abilities.

[sjastro]

If photons have mass then the scattering of a photon by another particle would follow the same physics as the scattering of particles in general, namely the energy and momentum changes of a scattered particle is a function of its velocity. Here energy and momentum are related to the particle's mass.

The situation with photons is very different. They do not undergo velocity changes after scattering. In this case the energy and momentum is related to the photon's wavelength. Energy and momentum changes occur due to a change in the scattered photon's wavelength.

Regards

Steven

[sjastro]

Without wishing to come across as pedantic this is only true if the black hole mass is fairly small. The radius of the event horizon is proportional to the black hole mass. For small masses, the radius is close enough to the physical singularity for space-time curvature (and other nasties such as tidal forces) to be significant.

For massive black holes such as the billion plus solar mass at the centre of our galaxy the event horizon is so far out that space-time curvature is very small.

To explain why photons cannot escape from inside the blacks holes horizon irrespective of its mass requires the use of Minkowski space-time diagrams (http://en.wikipedia.org/wiki/Minkowski_diagram).

Unfortunately a full blown explanation is beyond the scope of this forum as well as the science forum and probably requires at least third year applied maths or physics to make sense of it.

I'll try to explain it as non mathematically as possible.
Using the attachment as a reference an observer is located in the present on a hypersurface. Anything above the plane is in the observers future, below it is in the observers past.
The light cones are analogous to an intense light flash which starts off as a point initially (in the present) and spreads out as time increases. This is the future light cone. The past light cone is simply running the flash backwards in time.
A photon can also be considered to be an "observer" in this case.

A property of the past and future light cones is that well away from a black hole horizon the cones are aligned "vertically". As a photon approaches a black hole the future light cones progressively tilts towards the event horizon. On the event horizon, the photons future light cone is inside the horizon, the past light cone points outwards. Essentially what it means for any object, photon or otherwise inside the event horizon, it would have to travel backwards in time in order to escape.
For an observer outside the horizon this is course will never be seen.

Regards

Steven