Doubly Special Relativity

[CraigS]

Take a look at this addition to Special Relativity:

Doubly special relativity

Now, doubly special relativity, proposes that not only is the speed of light always the same regardless of your frame of reference, but Planck units of mass and energy are also always the same. This means that relativistic effects (like mass appearing to increase on the train) do not occur at the Planck (i.e. very small) scale – although at larger scales, doubly special relativity should deliver results indistinguishable from conventional special relativity.

It turns out that at the Planck scale e = m, even though at macro scales e=mc^2. And at the Planck scale, a Planck mass is 2.17645 × 10^-8 kg ... supposedly the mass of a flea’s egg … and has a Schwarzschild radius of a Planck length … meaning that if you compressed this mass into such a tiny volume, it would become a very small black hole containing one Planck unit of energy.

To put it another way, at the Planck scale, gravity becomes a significant force in quantum physics. Although really, all we are saying that is that there is one Planck unit of gravitational force between two Planck masses when separated by a Planck length … and by the way, a Planck length is the distance that light moves within one unit of Planck time!

Here we go … those damned mathematicians at it again …. ...

It all sounds terribly exciting, but this line of thinking has been criticized as being just a trick to make the math work better, by removing important information about the physical systems under consideration.

Interesting article. The idea that a Planck length can be considered an invariable constant independent of an observer’s frame of reference, whilst light speed isn't, is one of those counterintuitive thingys ..

Cheers

[Robh (Rob)]

Hi Craig,

Thanks for that. Highly enlightening and revolutionary if true.

From some examination, here's a rundown on some of the Planck facts.
The Planck constant h was first used to give the energy of a photon.
E = hv where v is the frequency of the electromagnetic wave.

The Planck length = sqr(hG/c^3) where h is the reduced Planck's constant (h = Planck's constant /pi), G the gravitational constant and c the speed of light.
The Planck length is about 10^-20 of the diameter of a proton.

Some exerpts from wikipedia:
" The physical significance of the Planck length, if any, is not yet known."
"Because it is so tiny, there is no hope of directly probing this length scale in the foreseeable future."
It does go on to say that lengths of special significance in quantum gravity are likely to be small multiples of the Planck length.

The Planck energy is supposed to be the maximum possible energy that can fit into a region of the scale of a Planck length.

Planck units are designed to normalise the physical constants h, G and c to 1, where h is Planck's constant, G the gravitational constant and c the speed of light.
E = mc^2 simplifies to E = m or the Planck energy and mass are numerically equal.

So it appears that this normalisation is true regardless of the claims of doubly special relativity.

Doubly special relativity's unique claim is that c and Planck units of mass and energy are observer independent or invariant regardless of your reference frame. Fascinating.

Regards, Rob

[CraigS]

Yep .. great stuff, Rob ... thanks.

(I wasn't aware that Planck units are designed to normalise the physical constants ..).

The reference frame invariance makes it a beauty though, eh ? !

Cheers & Rgds

[Robh (Rob)]

Originally Posted by CraigS

Yep .. great stuff, Rob ... thanks.

(I wasn't aware that Planck units are designed to normalise the physical constants ..).

The reference frame invariance makes it a beauty though, eh ? !

Cheers & Rgds

Craig,

Have a look at this list at
http://en.wikipedia.org/wiki/Planck_units
under the heading
Planck units simplify key equations

I don't get it all but it makes interesting reading.
Regards, Rob

[CraigS]

Originally Posted by Robh

Craig,

Have a look at this list at
http://en.wikipedia.org/wiki/Planck_units
under the heading
Planck units simplify key equations

I don't get it all but it makes interesting reading.
Regards, Rob

Rob;
Its got me beaten .. need to refer this to a higher authority .. where are those mathematicians when ya need em ?

Cheers

[sjastro]

Originally Posted by CraigS

Rob;
Its got me beaten .. need to refer this to a higher authority .. where are those mathematicians when ya need em ?

Cheers

Perhaps it's easier to comprehend using a more down to Earth example.

Consider the difference between density and SG (specific gravity).
Density is mass/volume or in terms of dimensional analysis M/L^3 where M is mass and L is length.

SG is the ratio of the density of the substance to a reference substance (usually water). Since the numerator is M/L^3 and the denominator is M/L^3, the terms cancel out and SG is therefore a dimensionless unit.

Hence the density of water at 20C is 1 g/cc and SG is 1 relative to water.
Or the density of gold is 19.3g/cc and SG is 19.3 relative to water.

In the case of SG relative to water, the SG of any substance can be written as a constant multipled by the SG of water (at 20C).

As with arbitrarily setting the SG of water to equal 1, one can for example assign c=1 as a fundamental planck unit and express velocity in terms of the planck unit.

Regards

Steven

[CraigS]

Thanks for that Steven;
Ok .. so that's what I relate to as being similar/the same as normalisation in statistics. So in this case, it is just normalisation using a Planck Unit as the basis. (?)

Thanks kindly, Cheers

[sjastro]

Originally Posted by CraigS

Thanks for that Steven;
Ok .. so that's what I relate to as being similar/the same as normalisation in statistics. So in this case, it is just normalisation using a Planck Unit as the basis. (?)

Thanks kindly, Cheers

Craig,

The Planck units do form a basis but the reasons for normalization are different when compared to say statistics.

In Quantum Mechanics a normalised wavefunction has a physical significance as the probabilty of finding a particle confined in space equals 1. Hence the normalisation process for a wavefunction involves integrating the wavefunction over the entire space and setting the result to equal one. This allows any integration constants to be determined.

The primary objective of using Planck units and normalising them is to make the mathematics easier to handle.

Regards

Steven

[CraigS]

Originally Posted by sjastro

This allows any integration constants to be determined.

The primary objective of using Planck units and normalising them is to make the mathematics easier to handle.

So apart from making the maths easier to handle, it also helps to determine the constants.
I'd imagine determining the constants would be pretty interesting and could tell us very interesting things (??)
(I'm close to being out of my depth here )

Cheers

[sjastro]

Originally Posted by CraigS

So apart from making the maths easier to handle, it also helps to determine the constants.
I'd imagine determining the constants would be pretty interesting and could tell us very interesting things (??)
(I'm close to being out of my depth here )

Cheers

There two different issues here Craig.

The integration constants relate to the normalization of a wavefunction, in Quantum Mechanics. It doesn't simplify the mathematics.

Normalising the Planck units allows a simpler mathematical format to be used, particularly in Quantum Field theory. One of the problems in mathematics is not only the computational side, but writing the mathematics down can be horrendously complicated.
A simpler format allows the logical structure to be more easily discerned and errors in the mathematics to be detected.

Regards

Steven

[CraigS]

Originally Posted by sjastro

There two different issues here Craig.

The integration constants relate to the normalization of a wavefunction, in Quantum Mechanics. It doesn't simplify the mathematics.

Normalising the Planck units allows a simpler mathematical format to be used, particularly in Quantum Field theory. One of the problems in mathematics is not only the computational side, but writing the mathematics down can be horrendously complicated.
A simpler format allows the logical structure to be more easily discerned and errors in the mathematics to be detected.

Regards

Steven

OK .. got it … and so … coming back to the original article, I agree that it all sounds pretty interesting.

It also seems like a good idea to 'make the math work better', in spite of 'the usual' criticism about maths/renormalisation etc.

As Rob inferred in another thread, if it all gets too complicated, what else could they do, in order to 'see the trees from the forest' ?
(Perhaps a rhetorical question, here).

Cheers

[snas (Stuart)]

Craig

I am greatly indebted to you for informing me as to the fact that
2.17645 × 10^-8 kg is supposedly the mass of a flea’s egg.

Now when I have a client in my veterinary consultation room, I can tell them how much flea eggs weigh.

Who would have thought that IIS would be the source for information as to the mass of a flea egg?

Stuart