Zero-Point Field and Gravity Relations

[Spyman]

I have a few questions concerning the relation between gravity and the zero-point field but to avoid ending up with a complicated thread and depending of the answers I will ask them one and one.

 

1) Is the strength of the zero-point field inside a volume of space related to the gravitational potential inside the same volume ?

 

Would for instance the force between the plates in a Casimir experiment get stronger or weaker if the experiment where done in the spacestation instead of on the surface of Earth ?

 

The reason for asking is the Unruh effect which seems to indicate at least a possibility thereof.

 

Unruh demonstrated that the very notion of vacuum depends on the path of the observer through spacetime. From the viewpoint of the accelerating observer, the vacuum of the inertial observer will look like a state containing many particles in thermal equilibrium — a warm gas.

 

So the temperature of vacuum, seen by a particle accelerated by the Earth's gravitational acceleration of g = 9.81 m/s², is only 4×10-20 K.

 

http://en.wikipedia.org/wiki/Unruh_effect

[solo]

I have a few questions concerning the relation between gravity and the zero-point field but to avoid ending up with a complicated thread and depending of the answers I will ask them one and one.

 

1) Is the strength of the zero-point field inside a volume of space related to the gravitational potential inside the same volume ?

Most assuredly; Because, as this article points out, there is no space empty of field. Understanding that gravity bends and distorts space time, one could rightly assume that the zero-point field would also be affected by the gravitational field.....................solo

[Spyman]

Hi solo and Welcome to SFN !

 

Now about your answer, can you extend it a little ?

 

Would the force between the Casimir plates change ?

[solo]

Hi solo and Welcome to SFN !

Many thanks for the warm welcome Spyman.

 

Now about your answer, can you extend it a little ?

 

Would the force between the Casimir plates change ?

The following speculations are just that, speculations because I have no experimental data to offer regarding any official research. Nevertheless, remembering that even though the Casimir plates produce only a very small gravitational influence, a gravitational effect is none-the-less a factor. Keeping this in mind, one must assume a slight curving or bending of the vacuum field itself. At this small scale however, detection would be extremely difficult............solo

[Spyman]

The following speculations are just that, speculations because I have no experimental data to offer regarding any official research. Nevertheless, remembering that even though the Casimir plates produce only a very small gravitational influence, a gravitational effect is none-the-less a factor. Keeping this in mind, one must assume a slight curving or bending of the vacuum field itself. At this small scale however, detection would be extremely difficult............solo

I interpret your 'speculation' as: Yes, the force should increase but very tiny.

 

Tiny as it is, (between the surface of Earth and the spacestation), it will have big influence where the gravity is very strong, for instance on the Hawking radiation at the event horizon of a black hole.

 

Or say that a scientist on a spacecraft, far away in a big 'empty' void between galaxies, would perform a Casimir experiment and in the middle the pilot would push the engines to the maximum, causing an enormous acceleration, would the plates crumble and break from the 'warping' of space ?

 

For an experimental test of the Unruh effect it is planned to use accelerations up to 10^26 m/s², which would give a temperature of about 400,000 K.

 

Would the spacecraft be heated by friction against space and keep the thermal energy when the engines goes off ?

 

My 'intuition' tells me that there should be some other effect exact equaling, that extra force. Take both the distance and the zero-point field between the plates for instance, they would also be affected. But relativity plays a large role here and I lack enough knowledge to evaluate the effects...

[Spyman]

Okay, 116 reads and only one 'speculation' excluding me...

 

...and I would like an explanation so I'm going to bump this thread. -> B U M P !

 

Is the Unruh effect frame dependent or an absolute effect of the zero-point field ?

[5614]

Is the Unruh effect frame dependent or an absolute effect of the zero-point field ?

From the first paragraph of the site you linked to:

The quantum state which is seen as ground state for observers in inertial systems is seen as a thermodynamic equilibrium for the uniformly accelerated observer.

As observers in different frames disagree on an observation, surely it is frame dependant.

[Spyman]

LOL ! Obviously I am so confused that I am not able to express my question...

 

And thats my own fault, so I guess I have to rephrase it again.

 

To start: If the zero-point field is a field in space and if space curves the field have to curve with it, so if the curving is relative to frames then it is also frame dependent.

I think both solo and 5614 is correct so far...

 

Let's put it this way:

 

2 identical spacecrafts are in a huge void so the difference in gravitational acceleration would be small enough to be neglected.

 

One ship is accelerating at twice the rate as the other.

 

In both ships the Casimir force is measured in identically experiments but the setup for the experiments are done in their own respective frames.

 

Will the crews in their own frames measure an identical strength of the force ?

[Severian]

I think your original question and your example are both very amibiguous. The Casimir effect is normally examined under conditions of zero 'background field', ie a true vacuum with no sources. Obviously if you put a charge on the plates, they will feel an electromagnetic attraction or repulsion, but that is not what we are after.

 

In your example, you have applied a field between the plates in one experiment and not in the other. The accelerating ship is sitting in a gravitational potential, so obviously the force between the plates will be different. But this is also true if I apply an electromagnetic field, so nothing new there.

 

I think what you are really trying to ask is, examining a pair of plates infinitely far from any gravitational source (impossible of course, but nevermind that), if I could switch off gravity (altogether, no gravitons of any form) would the casimir force between the plates change?

 

This is a bit difficult to say, since the Casimir effect is a quantum effect but we don't have a quantum theory of gravity. My gut feeling is that it would in principle change the force. After all, the Casimir effect happens by plucking out vitural particle anti-particle pairs from the vacuum and pulling them towards the plate. In principle, since the plates have mass (or more precisely energy) this can happen using gravitons. If those gravitons are missing, then there is no effect from them.

 

However, this effect would be very very small. Gravity (we think) is many many orders of magnitude weaker than the other forces, so I very much doubt this would be measurable unless you had very very big plates!

 

What does this have to do with the value of the zero point energy? (This is another difficult topic, since we don't undestand it either!) Well, the zero point energy provides a cosmological constant, which you can think of as a uniform curvature of space. So, if there is a cosmological constant, the true vacuum (without any gravitational sources) already has a gravitational field, so the casimir force will change.

 

However, that is cheating since the casimir force is supposed to be in zero field (a true vacuum), so to be fair you would need to place gravitational sources in such a way that the effect of the cosmo constant is cancelled out...

[Spyman]

Hi Severian,

 

I intended to make long reply, but I only ended up with a mess, so...

In your example, you have applied a field between the plates in one experiment and not in the other.

One ship is accelerating at twice the rate as the other.

Both ships is accelerating.

[Severian]

Both ships is accelerating.

 

There is still a gravitational potential difference between the ships if they are accelerating at different rates.

[Spyman]

There is still a gravitational potential difference between the ships if they are accelerating at different rates.

YES !

 

Will the crews in their own frames measure an identical strength of the force ?

Am I correct if I interpret your answer as: The force is stronger in the ship with greater acceleration ?

(Measured in their own respective frames.)

[Spyman]

AAARGH !!! <slaps hand in forehead>

 

But at least I am slowly catching on...

 

I think what you are really trying to ask is...

 

Well, the zero point energy provides a cosmological constant, which you can think of as a uniform curvature of space. So, if there is a cosmological constant, the true vacuum (without any gravitational sources) already has a gravitational field, so the casimir force will change.

My missing 'link': The Cosmological Constant.

 

You actually nailed it down good Severian - Thank you !