Relativity again!!!!
Relativity again
Earth (and sun) are 26 000 light years from the galactic centre and travelling at 220km/sec around the galaxy (orbital speed). We take about 230 million years to rotate once around the galaxy which is 100 000 light years across.
One last discussion regarding General Relativity and a particular point in space is that when you are at that point all physical laws (distance and time) look normal to you. You are not aware that anything is different if you move from one point to another. You have to realise that to see the differences between points in space you have to have the “God’s eye view” of being able to compare these parameters. Wherever you are the physical laws as YOU PERCEIVE THEM (eg the speed of light) are the same. If we were at significantly different gravitational potentials (General Relativity) in space you would measure distance with the identical ruler that I gave you when we parted and with the identical clock I gave you departed and we would both be happy that the speed of light was correctly worked out as 300 000 km per second. But a higher Being with both perspectives at once would see that your rod was longer than mine but that your clock ticked slower than mine giving us both satisfaction that our parameters are “normal”. In the case of general relativity we can take this distant perspective as seen from Earth because the black hole with it’s different gravitational potential or space density is a physical reality and not just a perceptual one as with Special Relativity. To solve this perceptual problem and unify Special end General Relativity, it would be necessary to follow the moving frame of reference with your own frame of reference, This may sound improbable, but visualise following a moving target with a camera which has your co-ordinate system imprinted on the lense. This gives you the moving frame of reference’s perspective, shortened rods and dilated time, but viewed from your reference. This sounds wierd, but this is exactly what is happening when you observe a distant star. You think that it is standing still and you focus your telescope on it as though it is standing still, but according to our definition of gravity space is moving into it at one heck of a speed … so you get the shortened rods and time dilation just like you would if you followed the frame of reference in special relativity. This is crucial to grasp if the following chapter is to be made any sense of.
The other aspect we have to consider regarding λ and Λ is the effects of Special Relativity. Now that we have defined a fabric for space the common “Doppler” effect becomes the obvious way to understand special relativity. Let’s say you came back from your sojourn into space clocking 70% of the speed of light. You decide to impress your girlfriend with a high speed fly-past. As you pass us our “λ – factor” (or gravitational potential or Space Density) is the same as yours and thus we are on the same “space contour”. I should clock your speed as 70% of the speed of light, right? This is true only because we are within the same space density with regard to General relativity and Special Relativity warping of space due to your speed are not visible to me.
If I were standing on earth and you were travelling near our black hole I would clock your speed as MUCH slower. The warping of space due to travelling at speeds comparable to the speed of light (Special Relativity) has to be superimposed on the warping due to gravitation General Relativity). This means that we have the two forms of relativity working together to define the density of space as you see it. This does not pose a problem because of the difference of scale between the two systems, but has some interesting theoretical implications.
We have stated previously that I proposed total equivalence between the warping of space due to gravity and that of a mass travelling at speeds comparable to the speed of light (relativistic speeds). To repeat the basis for the analogy: mass travelling through space is equivalent to space travelling into mass (gravity). Any mass travelling at the speed of light will be equivalent to a black hole in mass/energy and space curvature (this is not possible but nearing that situation is realistic). Remember in this discussion that only our figment of imagination called a black hole can absorb space at the speed of light. Smaller or lesser objects will absorb space at a MUCH slower rate and thus be analogous to a much slower speed. This equivalence being accepted I am going to investigate using Lorentz’s equations to approximate the curvature of space
- near a black hole,
- on earth and
- in distant, open space.
Then using this warped space as the status quo of the fabric of space at that point, again apply the Lorentz equations to moving bodies within that space. Lets see where that takes us:
Hey! Does this look familiar or what? Imagine the time amplitude reducing with the distance of wavelength as in the picture showing inflation earlier in our discussions … this may work!!!!! These are the classical curves that Lorentz’s equations delivered when I fed in the speeds in kilometres per second. Notice that the distance (x’) and time (t’) adjustment factors have been place on the same graph and both relate to unity. For example they show how a measuring unit (kilometres in this case) will warp from one kilometre at 10,000 km per second to say half a kilometre at 250,000 km/sec (the speed of light being 300,000km/sec) In the same example time would warp from one second travelling at 10,000km/sec to about 1.8 sec at 250,000 km/sec. This is classical special relativity physics and mathematics and is one of the most awesome discoveries that man has made. Einstein popularised and conceptualised these equations, but Lorentz’s genius has to be credited.
NOW, let’s start playing. We have discussed our intent to pursue the equivalence of space warping due to speed and that of gravity. We will say that the warp on the left (near the speed of light) is equivalent to a black hole space warp and the warp on the right is equivalent to “open space” with minimal space warp. We must also do the equivalence thing and replace the speeds on the bottom axis with distance (light years) away from the black hole. Lastly we have to adjust the two graphs to make both cross unity (one) on the warp axis at a point between the black hole and deep space. This is because we are on earth and our observation point is here where our measuring sticks are one (second, kilometre etc) and our time (seconds) is one. All warping can then be compared to the space density around the earth. This position will be chosen about half way as an approximation of where the earth lies in our extended galaxy (extended by dark matter and energy, remember). Like this:
This is the equivalence model that we can now work with. This is the background warping of space that general relativity predicts. From this model it is easy to draw concentric rings of equally dense space around the black hole with decreasing amplitude (time) and increasing distance (wavelength) as proposed by our inflation model described earlier. Every point in space has a “warp factor” or space density as we discussed in earlier chapters on curvature of space. Remember the “λ” or warp factor that is determined by the cosmological constant (Λ) and the formula
λ = Λ m bh/r2
This diagram describes the warp factor at various distances from the black hole and gives the warp in terms of space (wavelength) and time (amplitude) particular to that point in space. What more could we ask for?
I will state the obvious for clarity: As we move away from earth toward open space
- a meter will get longer and
- time will get shorter,
whereas if we move toward the black hole
- our meter long rod will get shorter and
- a second will get exponentially longer.
No wonder they say that it will take an eternity to fall into a black hole!!!!!!!!!!!!
One last observation before we go off into dream world even further. If you use these warp factors to determine the speed of light we get the following:
This tallies with our earlier observations that light or any electromagnetic emissions from a black hole are travelling at virtually zero km/sec (from the earth perspective) and in open space about 400,000km/sec, even faster than the 300,000 km/sec that we see near the earth. It must be stressed however that this is a “God’s eye” view and when you are there you will measure with your “warped” measuring stick and clock that light is travelling at the “normal” 300,000 km/sec. This conclusion of Einstein’s certainly makes him the man.
As an insert here I would like to try to introduce the Lorentz equations into our sinusoidal wave formula. It is interesting to note that sin maximises its amplitude to unity and the Lorentz equations display the deviation from unity. Let’s stick to the “earth adjusted” version of our graphs to retain an “earth perspective”.
This is awesome!!!!! Notice how the time warp (amplitude) increases near the Black hole while the distance or space (wavelength) shortens accordingly. This is really the first time that our theory of magnetic waves being the fabric of space has been expressed in terms of conventional physics. The amplitude of the sinusoidal electromagnetic wave does really reflect the time warp and the wavelength the distance measure of space.
Let’s first take an ad break!
OK, we’re back.
The next step in our journey is going to be the effect of special relativity (in other words, travelling at speeds near that of light – relativistic speeds) on top of this warped space picture of general relativity. As discussed earlier we are going to apply Lorentz’s equations in the way that they were intended this time. We will use them to determine the effect of speed on time and distance. This application will reveal the classical warping when applied to our model when we consider space near the earth, because we have adjusted the model to reflect the warp around our area of space as unity or one. This is what space scientists work with daily and has been practically proven over and over. Without these transformations even our satellites for GPS would not give accurate readings. Where our speculations come in however is that we will apply these Lorentz Transformations to our postulated space density model not only near the earth but also near the black hole of our galaxy as well as the open space about 87,000 light years from the galaxy centre. Here goes.
The first thing that strikes me is that the speed of light as perceived from earth is only 40,000 km/sec. Remember that the pilot near the black hole (poor chap!) does not see it like this. He still sees the speed of light as 300,000 km/sec … that is the reality!!!!!!!!!!!!!!! It is only from OUR perspective that we see it skewed. When he travels at 40,000km/sec according to him, he is not breaking the light barrier, not even near. To us it seems that he is travelling only about 2,000 km/sec. In fact, according to us he cannot exceed 40,000km/sec even if he is measuring his speed at 290,000km/sec!
Let’s look at the same sum done on our own doorstep.
This looks more like we are used to. The speed of light is 300,000 km /sec which is right. As the pilot starts travelling faster his measure speed is the same as how we clock him. Even though we are in the same gravitational space warp, his rods and clocks are affected by special relativitywhich we are not aware of.
Before we try to make any deductions lets look at the last example of our fortunate/unfortunate pilot attempting the same objective of reaching the speed of light in non mass-warped space about 87,000 light years away from the black hole.
Although from earth we calculate the speed of light at 600,000 km/sec in this distance stretched and time limited space, our pilot can still only reach 300,000 km/sec on his speedometer.
I feel sorry for this poor guy because no matter where he is, all measurements we apply will disprove his claim of having adhered to the 300 000km/sec speed limit, yet all his instruments will show irrevocably that he did in fact conform. Who is delusional here???
None of this is can be new to space physicists!? I have performed these approximations merely for the purpose of relating the findings to our model of space fabric to the classical weirdness of relativity. The inherent incorporation of distance and time warp within our space model gives us a different measure of perception when applying relativity principles. Without our new background understanding of space and its electromagnetic makeup the complexity of relativity is a theoretical conundrum that we have to take with a pinch of salt and a large dollop of faith.
Please remember whenever we discuss extremes of any speed, distance, time or process that it is the purpose of this article to refute infinities and singularities and long before these situations arise, there is another process or negative feedback that takes over. As an example in point, a black hole cannot just continue growing indefinitely … as the heat generated by the accretion increases, so inflation will increase to compensate. Remember that the mass that a black hole absorbs at any time during the accretion cycle is only a miniscule percentage of the visible and accreted mass (i.e. only a miniscule percentage of a small percentage (about 2%) of the galaxy. The radiation will balance this absorption as larger or smaller stars enter the black hole.
Let’s use our model to determine how we observe the rotation curve of our galaxy. This means that we compare the expected speeds of rotation to actual observed speeds in our warped space. Surprise … the rotational curve is flattened and the observed speeds vary from about 180 km/sec to 240km/sec. Actual observations put this speed at between 200 and 240km/sec. Do you realise what this means? It means that the main argument for the existence of Dark Matter is not necessary to explain these flattened curves!!!!!!!! Actually this comes as no surprise because the person on the rotating planet measures the velocity of his planet as the correct speed to maintain it’s orbit, but from a distance our judgement of a slower rotation is made because we measure the radius of his orbit with the spectacles of our own gravitational potential. All physical attributes of our observations will be seen and measured according to the difference in gravitational potentials of the observer and the observed. This applies even if the path that the light has travelled has been through denser and then less dense space, the observed difference between the two parties remains the same. (See however “Red Shift” due to light passing galaxies)
Wow, this finding does not exclude dark matter in my mind, but my conclusion of the size of its mass/energy must be more moderate. Perhaps we should change our ratios of the mass/energy in our universe even further. Remember that we earlier disputed the necessity for such a large percentage of dark energy and contended that there could not be more dark energy than mass? Well now I am probably going to shock you even further, because I would like to suggest that in stead of the classical 4:22:76 of matter: dark matter: dark energy we should now look at something more like 50:40:10.
|
Summary of Postulates relating to this Section
|
