Friday, February 11, 2005

Lee Smolin, Surely You Were Wrong

There have been a heated discussion by Marcus et al:
http://arxiv.org/abs/hep-th/0501191
And an earlier one by Lee Smolin:
http://arxiv.org/abs/hep-th/0311163

What interested those people are the claim that they obtained a dimensionless coupling constant, which equals G*Lambda, i.e., gravity constant times the cosmological constant, the number is claimed to be very small, 10^-120, so that "it becomes amenable for perturbation theory which doesn't break general covariance".

These folks have been completely wrong in this and I am going to talk about why. To start, let me re-write their dimensionless coupling constant in a more explicit form, so omitted parameters like hbar and C can be properly recognized.

In their foot note they said:
"We work in units where c and 16*PI*hbar = 1, so G means 16*PI*hbar*G = lp^2 which is the Planck length"

So, they are claiming a coupling constant:
alpha_g = lp^2/L^2, with lp the Planck length and L the radius of the universe.
Or in another note:
alpha_g = G * hbar /(C^3*L^2)
The units indeed work out to cancel each other to yield a dimensionless number, and that number can be convenient calculated using my natural unit sets:
G = 1/(2N), L = PI*N, hbar = C = 1, N ~= 1.5x10^40
alpha_g = (1/(2N)) /(PI*N)^2 = 1/(2*PI^2*N^3) = 1.5x10^-122
That agrees with their estimate of 10^-120, though they are off by two oders of magnitude. But that small discrepancy is NOT what I am talking about why they were wrong.

The form of
alpha_g = G * hbar /(C^3*L^2) (1)
is wrong, and the result is off by 80 orders of magnitude!!!

Comparing with the EM fine structure constant
alpha = e^2/(hbar*C)
We would expect the gravity coupling constant to take the form
alpha_g = G*M^2/(hbar*C) (2)
Where M is an appropriate characteristic mass.

So far, both the super string camp and LQG camp took the Planck Scale for granted. So they would naturally use M = planck mass as the characteristic mass. You immediately see that that is wrong and is not going any where, since once you plug it in, alpha_g=== 1, which trivializes it to a meanless parameter!!!! The Planck Scale is wrong and leads both camp to no where!

Now, let's see what is the characteristic mass, in the new claim of alpha_g = 10^-120:
alpha_g = G*hbar/(C^3*L^2) = G*M^2/(hbar*C)
M^2 = hbar^2/(C^2*L^2)
or
M*C^2 = hbar * (C/L) = hbar * frequency
We immediately recognize what it is: the characteristic mass energy equals to the mass-energy of a photon, whose wavelength is about equal to the radius of the universe, or in another word, whose period is not 10^-14second, but about equal to the age of the universe!!!! The EM wave corresponding to such a photon are of such low frequency that it has NOT finished oscillation of a single cycle yet since the "birth" of the universe!!!!

What a ridiculously small characteristic mass. No wonder their alpha_g is wrong.

Why do theoretical physicists have to go extreme? They either use the Planck mass, which is ridiculously too high. Or they use the mass-energy of a photon which oscillate at the cycle of age of the universe, which is ridiculously too small!!!

Can't they use a characteristic mass which MAKES SENSE? Such a characteric mass should be the mass scales of elementary particles. My theory says it should be the unit of natural mass unit, which is about 137.036 times the mass of an electron.

Using that correct characteristic mass, the correct alpha_g coupling constant should be
alpha_g = G = 1/(2N) = 3.3x10^-41

Quantoken Zelah said...

Hi Quantoken,

I was reading your blog and you gave an 'alternative' explaination for gravitation redshift. This was that clocks in distant galaxies 'tick' slower than here on earth.

Here are some questions:
1. Why would time tick slower in other galaxies? In particular, what law of nature would explain this phenomena.
2. Why does time ticking slower in other galaxies explain redshift?
3.Do you deny that distant galaxies are moving at high velocities relative to Earth?
4. How do your proposals fit in with the physics principle that the laws of physics are the same through-out the visible universe.

Kind Regards
An amateur mathematician.

6:43 PM Quantoken said...

Zelah:
Here are some questions:
"1. Why would time tick slower in other galaxies? In particular, what law of nature would explain this phenomena."

Why would time in remote galaxies tick at the same pace as ours? If you think about, nobody ever asked that question. People just take it for granted that all clocks tick at the same pace. But there has NOT been a physics law that says clocks must tick at the same pace. Einstein was the first one to open people's mind and re-think the thing we took for granted without a good reason. He pointed out that clocks in different inertial frames, and clocks in gravity fields, all can tick at different pace.

So, certainly it could also be true that clocks separated by really HUGE distances, billions of light years apart, could tick at a different pace as far as our observation goes.

That notion of slower clock at remote locations was NOT proposed to explain Hubble Red shift. It was logically derived from the principle of quantum information conservation. Because I found there is no way I can obtain a conserved total quantum information of the universe through enclosed spacetime, unless BOTH the time and the space are curved. What it means is the remote clocks MUST tick slower.

It happens to explain the Hubble Redshift without the need of relative Doppler movements.

2. Why does time ticking slower in other galaxies explain redshift?

That's because the same light that measures a normal frequence by the remote clock, would measure a lower frequence by our clock, if the remote clock ticks slower than ours. Lower frequence is what we call redshift.

3.Do you deny that distant galaxies are moving at high velocities relative to Earth?

Yes I deny that. There is NOT a systematic relative movement that's correlated to distance. Other that Hubble Redshift, there is NOT a second independent evidence proving such movement at all. If you measure the distance of a galaxy at one time, and do the same measurement a few years later, and discovered that the distance has increased. That would constitute a secondary evidence confirming the movement.

No such independent verification exists. Certainly I do recognize that even if the movement is real, it may not be possible to detect the distance change in just a few years. But fact remains that there has been NO evidence of any actual distance change.

With Hubble Redshift the ONLY and INDIRECT evidence of any recessing movement, and with the redshift itself having a better alternative explanation, I do not think there is any reason to continue to believe the remote galaxies are moving away.

4. How do your proposals fit in with the physics principle that the laws of physics are the same through-out the visible universe.

In my theory, the laws of physics are certainly still the same at all space and time locations. You would NOT be able to do any experiment which tells you your absolute location and time. Keep in mind that the time dilation is relative: The remote galaxy would also observe our clock as slower than theirs.

On the other hand, the popular Big Bang theory breaks the universality of physics laws completely. In their theory, there will be an absolute time which can be discovered through experiment, that is the time since Big Bang. Physics laws are no longer universal, they have the so called running physics constant, where constants like alpha would change over time. And even energy is no longer conserved!!! They break all known physics laws and have made no verifiable prediction so far. That's crackpot despite they being the mainstream.

Quantoken

12:38 AM Zelah said...

Thank you for your detailed reply. Now, the problem here is the interpretation of ( General Relativity / Special Relativty ) vs Conservation of Quantum Information.

I've considered your response, and still have some questions. Assuming Isotropic spacetime here are my results. I will assume that your invariant is not the Speed Of Light (SOL) which thereby leads GR to be Lorentz Invariant, but the Invariant will be Quantum Information which I will assume to be Von Neumann Information. Please respond if the above is not correct.

Here is the standard explaination of redshift. The redshift is not a doppler effect, rather (FW models) Space itself expanding. Also, in standard SR/GR, time is not same for observers in different inertial frames!

The real reason that time is the same for all observers in cosmology is that it is assumed! I.E SpaceTime (ST) is assumed to be Isotropic and homogeneous. Now, if you believe that time is ticking differently in other parts of the universe, then either the matter density is different in this part of the universe, or empty space itself is different! Now for a question.

How does conservation of information change the matter density or empty space in different parts of the universe?

Also, Please provide model of how information links to matter (I assume that the entropy of a photon is 1)!

An amateur mathematican

8:55 PM Quantoken said...

In my frame of theory, quantum information conservation is more fundamental, and all other conservation or invariant laws are the derivative results from quantum information conservation.

But NO, light speed (SOL) will still be constant and invariant, observed by all observer! This invariant is NOT by physics laws, but by pure definition of space and time. i.e., the light speed is the very ruler that measures distance and convert between distance and time.

How could you measure any variation of a ruler itself using the ruler itself? You can not. Since light speed is the very ruler for distance and speed measurements, it never varies by definition.

The nature provides us with three rulers, which once fixed, can be used measured any physics quantity, from time, distance, to mass/energy. These three rulers must be invariant, or we do not even have a ruler to rely on for any meaningful measurements.

The three natural rulers are:
1.The speed of light in vacuum, which allows us to compare the scale of distance and time. We still need a ruler for either the time or the distance to be able to measure both.

2.The Planck constant hbar. This ruler allows us to measure mass or energy, once another ruler is provided to measure either the distance or time.

3.A third ruler is needed to measure either the distance or the time. I find this ruler to be another physics constant, parallel to hbar. I find it could be either the fundamental mass unit, which happen to equal to electron mass divided by alpha. Or it could be the natural unit of length, which equals to the electron classical radius.

Those three fundamental rulers are absolutely invariant throughout the whole universe because they are the basis that we can make meaningful measurements and different measurements can be brought together to compare. Without them we would have to rely on actual physical rulers made of matters, which are unreliable and could be change due to condensed matter physics.

Time can NOT be assumed to be the same for all observers. You must have a physical way of verifying it, instead of blindly assume it. The spacetime is still isotropic and homogeneous with a none-equal time, since such inequality is relative and symmetric.

As I said the remote galaxies will also think our clocks are slower than theirs. The whole thing is relative. If you go any where in the universe, you will make the same observation that galaxies further away from you the observer all seem to run slower clocks. So this does NOT break the homogeneousity or isotropicity of the universe.

How do you know whether the remote galaxies run the same clock or not? You have to use something to measureit. The only thing you can rely on is light beacons. The photons from the same spectrum line must measure the same frequence if the clocks are running at same pace. So the difference measured (i.e., redshift), indicates a different clock speed.

Certainly that does not exclude the possibility that red shift was really caused by relative movement. Both time dilation, space expansion, or relative movements can explain the same Hubble redshift. But once you consider quantum information conservation, which is fundamental, then the only plausble explanation is time dilation and fixed size closed spacetime.

Quantum information conservation has its root deep in the existing quantum theory, which says you can not go from a pure state into a mixed state. Which means the total number of possible quantum states is a fixed number.

Quantoken

2:50 PM Zelah said...