### In Planck Units: M = t

Refer to Kea's blog for a spectacular photo of the "Great Hexagon of Saturn." Again our Cassini spacecraft has discovered something that old science can't explain. As we have seen, there is more going on inside the planet than meets the eye. This includes an immense magnetic field and polar jets of charged particles, exactly as produced by a Black Hole.

The Northern jet is composed of electrons which spiral tightly around the magnetic field lines. The Southern jet is made of heavier ions, which travel around to the North and follow field lines back in. Earth's Van Allen belts work the same way, with concentric lanes of positive and negative particles travelling in opposite directions. At Saturn's North Pole, the incoming positive stream crowds in on the outgoing negative stream. As nature shows us with the honeycomb, the best way to crowd things together is in hexagons.

Our unit systems are mostly based upon some earthly measure, like the distance a man can reach. Physicists often prefer to use a system based upon some fundamental property of nature. This has led some to use units based upon the "constants" h and c. While Planck units provide a universal system of measurement, they are misleading if you think h and c are constant!

Above are the Planck units of length, time, and mass. As readers of the papers know, speed of light c is proportional with t to the -1/3 power. Since most measurements indicate that the product hc is a constant, Planck value h must be inversely proportional with c, t to the 1/3 power. The behaviour of h is similiar to the solution of a random-walk problem. Some of the Planck units are therefore changing.

The Planck length is actually increasing by t to the 2/3 power. Scale R of the Universe, horizon distance, scale of magnetic fields and even the Schwarzhild radius of a Black Hole increase at exactly the same rate. All these radii increase in a way more logical than the humans who struggle to understand it.

The Planck time turns out to be proportional to the observer's time. If you were a tiny cosmologist at time of 10^{-43} seconds, Planck time would still appear to be 10^{60} times smaller. Hopefully by the time the Universe is 13.7 billion years old you will figure this out. Dr. Lieu (who was at the London conference) found experimentally in a paper (ApJ 585, L77) from 2003 that this "Planck time" is an illusion.

Back when I was enjoying The Blue Mountains, someone noticed that "The Equation" in Planck units is just:

M/M_pl = t/t_pl

Mass of the Universe divided by Planck mass is equal to age of the Universe divided by Planck time. Both sides of the equation are now dimensionless numbers, and both are constant.

Using Planck units, you can write this in even simpler form:

M = t

This must be the simplest equation ever! It is amazing that humans haven't figured this one out yet. Personally I prefer not to use Planck units because they can be so misleading.

The "M = t" was noticed recently by a very well-known blogger. I will not give his name, for he has a "bad boy" image to maintain. Though he has a reputation as the biggest skeptic, he has slowly come over to our side. He may be telling the Harvard string theory group that we are on to something. It would be easy to get angry with others, but there is great value in patience.

## 18 Comments:

Sorry that this is off-topic, but I just noticed it and did not know of any other blog entry that would be better for it. What I noticed is your ClustrMaps map of visitors to your blog, and particularly that you seem to have 1 to 9 visitors from Urumqi, which I think is one of the most interesting cities that I have yet to visit.

My web site has a little bit about Urumqi at

www.valdostamuseum.org/hamsmith/Aug2005Update.html#urumqi

Please feel free to delete this if you want to.

Tony Smith

This comment has been removed by the author.

Louise, it is interesting that in Planck units your formula can be written as simply M = t.

Tony, your page on Urumqi raises the question to my mind: how sustainable is Urumqi's profitability as a manufacturing base?

It's a place thousands of miles from the sea. The goods must be transported therefore by plane, truck, or rail. I can understand how it can profitably service the rest of China and bordering countries, but without access to a shipping port, it surely can't contribute much to foreign trade?

I know the old Silk Road now has an excellent rail service. Presumably Urumqi finds enough trade along that route to make it profitable, without requiring global exports which might need a sea port.

The Chinese bought the blueprints of British Rover cars (when Rover was in financial crisis, shortly before it closed down and went into administration). An uncle in marketing has been to China a few times, advising on their move into the UK automobile industry: they will be manufacturing in Nanjing, near the coast, and shipping cars to the UK from July..

It's interesting that China is succeeding in the manufacturing role that Japan had, and is buying up foreign brands (such as Rover) at competitive prices where it can.

The larger area of China, and larger population, suggest it will go a long way. In particular, it is using coal instead of oil, and (despite the pollution) is relatively safeguarded from oil price increases (although they would still affect shipping costs).

(I should add that the major reasons MG Rover went bust were the high costs of manufacturing in the UK and the competition with low cost imported cars from Japan and elsewhere.)

Hi Louise,

Glad to see you back from your unpleasant adventure.

Just a short comment on Monde's question on the physical significance of R, and nige's thoughts about the nature of c as defined in your theory (comments for the March 30 post, I thought I'd post here as I am rather late for the discussion on that post).

"Scale R of the Universe is distance from that origin, age t multiplied by c"What's the physical significance of R in your model?

R is essentially equal to T (time since the beginning of the universe). This time determines also the size of the universe in the space dimension.

As far as I can understand the situation, from trying various ways that can derive GM=tc^3, one way to understand c is as is a measure of the expansion rate of the universe.What I have come up with up to now (Proper Time Adjusted Special Relativity, which shows, imo at least, that the phenomena of Special Relativity are due to the geometry of the curved expanding universe) seems to suggest that there is such a thing as a "rate of propagation of

timethrough space", and that this rate is none other than c. This would explain why c functions as an upper velocity limit --a material body cannot travel "faster than time". It would not be easy to explain verbally what I mean here, but I have built a Java simulation to show how I think this works (Speed of Light and the "Rate of Propagation of Time"). So essentially c is a measure of the rate of the "flow of time" along the space dimension.You might also want to have a look at The Proper Time of Photons and the Nature of Light, for some thoughts on the proper time of photons, which is always equal to 0, and this seems to suggest that they are always situated at the time moment before the space dimension started expanding, that is, that they may be part of what existed before the material universe came into being.

I know that all this sounds pretty strange, but that is what the mathematics show. I am still trying to make sense of it myself.

Hi Gebar, trying to grasp what you are trying to say ...

Light and speed of light

A light year is the distance light travels in a 'year' (earth year)

Time is the distance light travels

But it takes 1500 earth years for the earth to travel the distance light travels in one light year.

And the earth travels 'around' the Sun, whereas light travels (or appears to travel) in a straight line at short (local) distances, but follows the curvature of space in cosmological distances?

Hi Q9

Light travels in a straight line at short (local) distances, but follows the curvature of space in cosmological distances.If we consider a 2+1 curved expanding universe, represented by the surface of an expanding sphere, "flatlanders" confined on the surface of the sphere will see light travel in straight lines, while for "3D-landers" these straight lines will be grand circles. So light always follows the curvature of space, even in non cosmological distances, but this curvature is only evident to "3D-landers".

What I am saying is that in a flat spacetime (with Galileo transformation), c is infinite and the rate of propagation of time is also infinite. All points of the space dimension are on the same time coordinate. When t changes taking its next value, it changes for the whole extension of the space dimension (for all its points simultaneously). This can be seen as an infinite rate of propagation of time along the space dimension.

In a curved spacetime (which necessarily has a Lorentz transformation), c is finite, and the rate of propagation of time (for an observer who uses a linear (non-polar) coordinate system) is also finite. In such a spacetime, different points have different (proper) time coordinates. As t changes, if we follow a point with a specific proper time coordinate, we will see it moving away from as with the speed of light. That is, if at time t a point of space with proper time t' is situated at a distance of 1 km from us, after 1 second the point of space that has same proper time coordinate t' will be at a distance of 300.000.001 km. And this suggests that time and light are closely connected phenomena.

I think that it is not easy to describe verbally these conjectures, and that's why I have built a number of simulations that attempt to give a clearer picture. You may get a better sense of what I am saying if you view them.

Tony, I looked at your post on Urumqui. Fascinating! At least a few of them have good taste in blogs. Often people in "the West" are oblivious to dynamic changes in Asia. It is disturbing that most Americans can't even name the world's tallest building. At one time even King Kong knew that.

Nige, when the Chinese figure out how to make cars it will be goodbye for US automakers. As I have written, it is due to their shortsightedness that GM has been surpassed by Toyota.

Gebar, I am glad that your ideas are attracting interest too.

Hey, I was that 'somebody' who wrote The Equation in Planck units!

Anyway, I still think that a lot of work needs to be done before it is really meaningful.

You ought to have a look at the recent preprint of George Ellis about 'Varying Speed of Light Cosmologies'. He has a lot of relevant questions as well as references to previous works by Albrecht, Barrow, Magueijo, Moffat etc.

E.g. 'In order to be viable, any VSL theory involving a variable speed of photon travel must of necessity be based on some other method of measuring spatial distances than radar. So the question for any specific proposed VSL theory is, What viable alternative proposal for distance measurement is made?'

This is really equivalent to saying, how could 'varying c' be measured, unless some *dimensionless* quantities are varying.

Sections 5 and 6 are particularly important.

"Any VSL theory involving a change in the speed of photon travel must eventually propose some other equations than standard Maxwell's equations to govern electromagnetism, and show how this leads to a varying physical speed of light associated with a wavelike solution to these equations" ...

"If it is to be specifically c that is varying, you must vary it in all places where it occurs in the physical equations, which is many places; but where it occurs in the equations depends on the units used, so it is not obvious how to do this coherently and uniquely"

- simply by changing the units, you can get different results out of 'varying c'. Eg if you say

kappa = 8 pi G/c^4

then kappa should vary with 1/c^4, yes?

But if you decide to use a quantity G' instead of G, such that G'= G/c^4, then you have

kappa = 8 pi G'

now how does this vary? Unclear.

Basically 'variation' of factors of c that appear in some equations is not physically meaningful, because you can redefine the quantities which you think are constant to absorb any number of powers of c.

That is why I am always saying that you should find a way to reformulate things in a way that does not depend on units.

Even better if you could write down a cosmological metric and dynamical equations and derive the propagation of light through space and cosmological distances as is done in usual GR.

Nice to hear from you, Thomas. I acknowledge your thoughtful comment from August. Certainly there is a lot of work to be done. Finding a usefu standard of distance measurement may be difficult. It may be necessary to define distances in terms of time.

Elsewhere I have used $\kappa = 8 \pi G$, which has caused some argument.

Other have borught up whether dimensionless values change. In the case of alpha, it is very likely constant. That also explains Lieu and Hillman's result that "Planck time" is an illusion.

No one has yet asked, since c is related to $\epsilon_0$ and $\mu_o$, does the permissivity or permeability change? I think it is the latter, meaning that the scale of magnetic fields also increases as t^{2/3}.

Hi Gebar,

I did take a browse thru your wiki-style site.

I was trying to get to grips with the concept of the relation between time & (speed of) light.

light travelling between two points on earth will follow the curvature of earth, if it could travel thru (the centre of the) earth it would reach the other side faster than travelling along the surface...

And in telecoms we bounce light off satelites - of course these are short distances for the speed of light.

But 'light' travelling to Mars or from Mars to Earth would travel in a straight line, not in any curved orbit - unless you mean of course that in 20 mins Mars will have moved (in Space) therefore by the time light reaches Mars it will have travelled in a curve rather than a straight line.

However, coming back to Time and Light (speed of).

We have defined atomic time

And Space Time is defined by motion

No motion (movement) no Time.

Though of course one has to question what was the speed of Time when the 'universe' was expanding - could billions of years have passed in a few seconds

After all we can recreate diamonds in a lab - in lab time - simulating geological forces and replacing geological times.

On a parallel note Hydrogen line

The lowest orbital energy state of atomic hydrogen has hyperfine splitting arising from the spins of the proton and electron changing from a parallel to antiparallel configuration.

This transition is highly forbidden with an extremely small probability. This means that

the time for a single isolated atom of neutral hydrogen to undergo this transition is around 10 million years and so is unlikely to be seen in a laboratory on Earth.However, as the total number of atoms of neutral hydrogen in the interstellar medium is very large, this emission line is easily observed by radio telescopes.

Also, the lifetime can be considerably shortened by collisions with other hydrogen atoms and interaction with the cosmic microwave background.

Hi Quasar9

I just saw your answer to my previous comments.

But 'light' travelling to Mars or from Mars to Earth would travel in a straight line, not in any curved orbit - unless you mean of course that in 20 mins Mars will have moved (in Space) therefore by the time light reaches Mars it will have travelled in a curve rather than a straight line.Well, yes and no. Light always follows geodesics. If a spacetime is flat, these geodesics are straight lines no matter where you look at them from. If a spacetime is curved, the geodesics look like straight lines for those who inhabit this spacetime, but they look like curved lines for someone who can perceive the extra dimension in which spacetime curves. In the Earth-Mars case, we have the total curvature of the universe, since it is closed, and we also have the curvature created by the gravitation fields of the Sun, Earth, Mars, and even the other planets of the solar system, not to mention the galaxy. So if someone who could perceive the curvature of spacetime looked at an Earth-Mars light ray, he would see a very wiggly line indeed. It would follow the shortest possible pathway between the two planets, but it would not be straight (think of a line drawn on an elastic surface that has depressions due to weights placed on it).

Now, in order to visualize this, you need an extrinsic description of spacetime curvature, which is something that has not been studied much. Theoretical physics is almost exclusively based on the intrinsic description of curvature through tensors.

About the relation between time and the speed of light. Time propagates with the speed of light. One simple way to understand this is to think that if you stand still, your time has the "normal" flow rate, as your speed increases your time slows down, and if you could travel with the speed of light, time would stand still for you. (Or to be more exact, it would look so to a "stationary" observer.) So maybe time and light are closely connected phenomena.

One more thing. I think that the strange phenomena that appear when the velocity of an object approaches the speed of light are due to the fact that it essentially approaches the "speed of time". It just so happens that light is the only "thing" that can reach the highest speed allowed in our spacetime, the speed of time.

I also suspect that in fact the speed of light is infinite and we only catch up with it when the propagation (passage) of our time allows us, so that it looks like it has this finite speed. So when a "light producing event" happens, it "lights up" a whole flat plane. However, our curved world only intersects with this flat plane at certain points, so that instead of seeing a whole lighted flat plane, we see an expanding circle of light (for a 2+1 expanding spherical universe), or an expanding sphere of light (for a 3+1 expanding closed universe). For the 2+1 case, imagine an expanding sphere that is intersected by a stationary plane. Their instersection is a circle on the surface of the sphere, and as the sphere expands, this circle expands too.

Hi Gebar,

thanks for coming back to me.

But I was thinking like shooting at a bird in the sky, you aim at where the bird is going to be ...

Same with directing light at Mars, you aim at where Mars is going to be in twenty minutes ... incidentally that earth has also moved in space means the light sent back from Mars would have to be focused to where earth is going to be 20 minutes after it leaves Mars.

But with further distance objects. The light from a distant star is reaching us in a 'straight' line from where the Star was when it emitted the light ...

albeit it may have zig-zagged and bounced of all sorts of dust on the way (delaying the journey).

I do appreciate the concept of travelling at the speed of light

After all as in Tron, one were an photo-electron travelling down the cable (or wireless) to the destination on the Internet almost at the speed of light ...

one would almost instantly be there (at short earth distances)

But at longer distances, it would be like looking out of a window on a bullet train ... what is close would be a blur (much blurrier still at the speed of light) yet if one were to focus on some point on the 'horizon' - say on the Sun, one would simply travel round the Sun in approximately a third of a day (earth day) rather than over 365 days as the earth completes its annual solar orbit.

Incidentally do photons from the Sun not (mostly) travel to earth in a straight line once they have left the surface of the Sun?

Yes, of course you are right about having to "aim" ahead in order for a photon to hit a distant target.

Ah, Tron, one of my favorite movies at the time.

About how things would look if you were to "travel light, almost at the speed of light", you might like to have a look here. You may find especially interesting the "head-light" effect.

And finally, about how photons travel after they leave the Sun: their path would curve due to gravity, so some of them that normally would miss the Earth passing a little ahead or a little behind it, they will in fact hit it, because their path will curve towards the Earth due to gravity. This effect would be much more pronounced if we aimed a photon at the Sun. It is as if you are trying to hit a target that attracts your bullets, you would hit it even if your aim was a bit off.

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