Unifying Relativity and Quantum Mechanics: The Challenge of Planck Units

[Andru10]

Are Planck units the same in all frames of reference ? If so, shouldn't the theory of relativity be modified to account for this ? (same as considering the speed of light the same in all reference frames) Because in it's current form, for a large enough velocity, through length contraction we can obtain a length shorter than the Planck length.

 

[Force1]

Are Planck units the same in all frames of reference ? If so, shouldn't the theory of relativity be modified to account for this ? (same as considering the speed of light the same in all reference frames) Because in it's current form, for a large enough velocity, through length contraction we can obtain a length shorter than the Planck length.

Unless you are accelerating or deccelerating, you cannot determine if you are at rest or in motion relative to any other frame. Therefore, in your frame, regardless of your relative motion, Planck measures are the same as in any rest frame.

If you are talking about length contraction observed in a frame that is in motion relative to your frame, then Planck length would appear contracted in the frame that is moving relative to your frame.

 

[Andru10]

If you are talking about length contraction observed in a frame that is in motion relative to your frame, then Planck length would appear contracted in the frame that is moving relative to your frame.

And if the contracted Planck length (relative to my frame) is shorter than the Planck length (in my frame) how could I measure/observe it ?
According to wiki: Current theory suggests that one Planck length is the smallest distance or size about which anything can be known.

 

[nicksauce]

Are Planck units the same in all frames of reference ? If so, shouldn't the theory of relativity be modified to account for this ?

This is, as I understand it, the basis for doubly-special relativity.

See: http://en.wikipedia.org/wiki/Doubly_special_relativity

 

[Force1]

And if the contracted Planck length (relative to my frame) is shorter than the Planck length (in my frame) how could I measure/observe it ?
According to wiki: Current theory suggests that one Planck length is the smallest distance or size about which anything can be known.

I see what you are getting at.

Even though the derivation of the Planck measures represents them that way, they are really tools that enable us to do mathematical calculations about relationships. Then it depends on the theoretical perspective in which you are using the measures. GR will use them to define a universe in spacetime which is a point lattice geometry where you move from one point to another in Planck increments.

If you take that perspective and discuss the length contraction in a frame moving in relation to your frame then you are dealing with the relativistic conservation of momentum, i.e. special relativity.

 

[Andru10]

This is, as I understand it, the basis for doubly-special relativity.

See: http://en.wikipedia.org/wiki/Doubly_special_relativity

Thanks, I didn't know this theory existed :)

 

[Naty1]

Good question andru.
DSR is a neat idea to keep in mind but note that Wiki cautions:

The theory is highly speculative as of first publishing in 2002, as it relies on no experimental evidence so far.

Here are a few comments of Brian Green, THE FABRIC OF THE COSMOS:
(p 350)

If string theory is correct... the usual concepts of space and time simply don't apply on scales finer than the Planck scale. ..the concepts of space and time segue into notions for which "shrinking smaller" is as meaningless as asking "Is the number nine happy?"...

You can get a feel for this by checking out "T duality" in string theory...easy to understand in concept...

Things at sub Planck scales may be too energetic, too chaotic reflecting "quantum foam" jitters that jumbles everything together...

Utlimately the answer to your question is "we don't know": it's one manifestation of the conflict between relativity and quantum mechanics.

 

[Andru10]

Good question andru.
DSR is a neat idea to keep in mind but note that Wiki cautions:

Here are a few comments of Brian Green, THE FABRIC OF THE COSMOS:
(p 350)


You can get a feel for this by checking out "T duality" in string theory...easy to understand in concept...

Things at sub Planck scales may be too energetic, too chaotic reflecting "quantum foam" jitters that jumbles everything together...

Utlimately the answer to your question is "we don't know": it's one manifestation of the conflict between relativity and quantum mechanics.

Thank you! This is very interesting.