FAQ RELATIVITY

 2. How much energy is involved when you accelerate a particle to 99.999% of the speed of light? How long does this take? 3. How much energy does it take to get someone ( for instance, Mike 150kg's ) to the speed of light ? Is there a formula that will give me an answer for this ? 4. Y a-t-il des particules qui vont plus vite que la vitesse de la lumiere ? 5. A snapshot of a measuring rod moving at relativistic speeds, shows it to be contracted. But what would a disc spinning at relativistic speeds look like? 6. In the theory of the general relativity, I have heard about the changes in the time and size of objects. Does this happen in reality, or this is only a theory ? 7. As you have to have no mass to travel at the speed of light how does a photon manage to achieve it? Photons have to have mass or how do they manage to 'carry' energy ?

1. When space expanded at the creation of the universe, did time expand as well ? How can we prove that time grows in a linear way?

Time is dependent of physical processes. Time is a word used for indicating change.  We measure it only and exclusively by comparisons.  So we use a very regular process, such as the ticking of a clock, to compare other phenomena with it.  In the same sense space does not exist unless you measure it with a real ruler.  In normal everyday life, we make an easy approximation, which works very well: we think of space and time as existing independently.  The approximation works extremely well because human beings are mainly composed of chemical processes, and these are very slow.  We also live on a small planet in a very ordinary solar system.  There are no black holes close by, and live goes on slowly: 30 meters per second is considered fast (108km/h), whereas light moves at 300'000'000 meters per second, or ten million times faster.

So we cannot prove that time grows linearly, since we decide ourselves how we measure it.  We only know of processes that behave more or less regularly (in our observation).

Now, when you look at something very regular such as the vibration of Cesium atoms in atomic clocks, or even something much more irregular such as the turning of the Earth, you do observe that further away galaxies move away faster than nearer ones.  Even if time were "expanding", space is expanding relative to it (so to speak).  Your expansion of time could only be measured if we had a process that did not itself expand in time.  This process would seem to speed up (since our seconds would get longer and longer).  There is no such process that we know of.  It all hangs together.

Time expansion does not really matter: what matters is to find one set of laws that will explain all effects we observe.  You may then indeed perhaps view them as if time expanded or not, depending on how you interpret them, just as you may view the same object from different perspectives.  As long as the calculations you make with these laws give the same results as what you observe, it's OK.

2. How much energy is involved when you accelerate a particle to 99.999% of the speed of light? How long does this take?

let me try to fill in some details:

-- for a particle with mass m at speed v the energy is going to be the kinetic energy 1/2*mv^2 (where the ^ means "to the power of" and * means times), so in this case it means v squared) .

-- let's say a proton, which weighs 3.3E-27 kg (that is 3.3 divided by 1 with 27 zeroes).

-- I will use exponential notation in order to avoid having to write too many zeroes.  So when you see 3E05 it means a three followed by 5 zeroes or 300'000 and when you see 3E-05 it means the decimal point is on the other side: 0.00003

The mass of our proton is therefore

3.3E-27 kg or 0.0000000000000000000000000033 kg and you can see why I don't want to write the zeroes all the time in what follows.

Since the particle's speed is close to c (the speed of light), the mass also increases; it's no longer the mass that you observe when the particle is at rest.  If the mass at rest is m0, then the mass at speed v will actually be m0/sqrt(1-(v^2/c^2))  where sqrt stands for "square root".  If you remember enough mathematics, you will see that as v comes closer to c the fraction v^2/c^2 will come closer to 1 though it will always remain less than 1.  and 1 minus something close to 1 will be quite small and less than 1. The square root of something smaller than 1 will be a bit closer to 1, but still small.  For the number you give we have actually that v/c = 0.99999  (you said 99.999%) and v^2/c^2 = 0.9999800001000001  and 1-(v^2/c^2) = 0.000019999 and its square root is 0.004472125

so the mass becomes 1/0.004472125 or 223.6 times bigger than it was at rest.  Our proton now weighs 223.6 * 3.3E-27 = 7.38E-25 kilos = m.  It goes at 99.999% of 300000km/s or 29999700m/s = v; hence the kinetic energy 1/2mv^2 is 3.32E-08 joules.  Still very very little!  But of course we are talking about a single proton!

Now think of this:  we make the protons from ordinary hydrogen gas (which is nothing else than atoms than have one proton with one electron, so we just heat it up to strip off the electron).  In 2 grams of hydrogen (two buckets full of gas; nothing really) there are 6.022E+23 atoms (Avogadro's number) which would make for a few toy balloons except that one does no longer use hydrogen in toy balloons, but that is a different issue.

In a cycle of acceleration of LHC, we use 1E+14 protons.  If we did this every second, we would have to cycle for 6.022E+23/1E+14 = 6.022E+09 seconds to use up all the two buckets full of hydrogen gas.  6.022E+9 is actually 6022000000 seconds, or (at 3600 seconds per hour, 24 hours per day, 365.25 days per year) it would take us 191 years to get through it, even if we accelerate 100'000'000'000'000 protons per second!

So the 1E+14 protons per accelerator cycle are an amount of matter that you would not be able to spot, even with a powerful microscope!

Yet each of these protons has an energy of 3.32E-08 joules.  That is 3.32E-08 * 1E+14 = 3.32E+06 joules.  How much is that?  Let's take a five ton truck (a removal van, say, loaded with your furniture).  If it travels down the motorway at the speed limit of 120km/h it goes at 120000m/3600s = 33.33 meters per second.  Using 1/2mv^2 again, we get that it has an energy of 2.78E+06 joules, or LESS than our indiscernible bunch of protons!

In actual fact, in the Large Hadron Collider (LHC) we get a little closer to the speed of light and the planned energy in the proton bunch at LHC is equivalent to the energy in an intercity train at full speed.  You better stay out of the way...  But LHC is underground, so not to worry.

Here is another equivalent:  the energy of each single proton, 3.32E-08 joules, which is very very small, is still what you feel when a fly lands on your skin.

Now I'm still not finished:  what we just calculated is the actual energy that is in the particles, but in order to get them there we push them with electromagnetic fields and most of the energy is wasted because we don't have a very good grip on that tiny bunch as you may imagine.

In the old Super Proton Synchrotron (SPS) the time it takes to get up to this 99.999% speed is 10 seconds, but in the LHC, where we go further, the time is limited by the power converters needed to feed the magnets whose magnetic fields keep the protons in a circular orbit.  Because those are slow, we need an extra 25 minutes to get the final energy.  The energy stored in the magnetic field of the LHC is itself much larger than that of the circulating proton bunches; it is more comparable with that of an aircraft carrier at full steam.  And you just cannot take that much electricity off the grid at once...

3. How much energy does it take to get someone ( for instance, Mike 150kg's ) to the speed of light ? Is there a formula that will give me an answer for this ?

'An infinite amount of energy' is the correct answer. No massive particle can be accelerated to the speed of light, and the protons at CERN are no exception - their speed is almost, but not quite, the speed of light. Only massless particles can travel at the speed of light.
A good URL to
consult is http://math.ucr.edu/home/baez/physics/

At CERN we always clearly indicate that a particle is going at 0.999999... times c (or however close it is). The energy it then has is the energy that was used to speed it up from rest.

E^2 = p^2 c^2 + m^2 c^4 => E_spent = (gamma-1) m c^2

where gamma = ( 1 / sqrt( 1 - (v/c)^2) )

Pick v/c, define m in [GeV/c^2], and there you go. You

can calculate it for one proton (m = 1 GeV/c^2), and set

100 kg = 10^29 protons.

Also have a look at

http://www.physicsguy.com/ftl/html/FTL_intro.html

4. Y a-t-il des particules qui vont plus vite que la vitesse de la lumiere ?

Dans le cosmos on aurait observe des particules qui vont plus vite que la vitesse de la lumiere. Des particules díorigine naturelle, pas celles que líon peut observer dans les laboratoires.

On n'a jamais observÈ des particules plus rapides que la vitesse de la lumiËre. Ni dans la nature, ni  au laboratoire. Mais si on fait les calculs selon Feynman, il y a une faible possibilitÈ pour une particule d'aller plus vite (et aussi plus lentement).  Seulement, on doit faire la somme de toutes ces probabilitÈs pour arriver a ce qui se passe vraiment, et le rÈsultat est toujours infÈrieur ou Ègal ý la vitesse de la lumiËre.

5. A snapshot of a measuring rod moving at relativistic speeds, shows it to be contracted. But what would a disc spinning at relativistic speeds look like? Its circumference would be Lorentz contracted all the way round but its radius would not. The ratio is no longer Pi.

Neither the radius nor the circumference are moving in inertial reference frames. So, special relativity does not apply. In order to give precise answers to your questions, one has to use general relativity, and this may perhaps be a little far fetched?

6. In the theory of the general relativity, I have heard about the changes in the time and size of objects. Does this happen in reality, or this is only a theory?

I think you are thinking of effects already seen in the theory of special relativity, with time dilation and length contraction of objects at high velocity. A good introduction to the concepts can be found here:

http://www.physicsguy.com/ftl/index.html

7. The speed of light is the fastest velocity achievable, and to reach this velocity you have to have no mass (because as you increase your velocity to near the speed of light your mass increases as well eventually requiring infinite energy). As you have to have no mass to travel at the speed of light how does a photon manage to achieve it? Photons have to have mass or how do they manage to 'carry' energy?

Photons are bunches of energy.

Your problem stems from the use of the phrase "to reach a certain speed", as this implies that you start with a fairly heavy thing at rest, then push it until it "reaches a certain speed".

But that is true only for things that have a rest mass.  Photons never travel slower, you cannot change their speed.  They start off (from the electron that emits them when it falls back to a lower energy level in an excited atom, for example,) already at the speed of light.  That's just how it is.

So photons have no rest mass, but they carry energy and that energy is certainly subject to the force of gravity.

Another confusion stemming from the observations of everyday life is that we see so much "matter": solid stuff lying around.  But inside it, at the particle level, there are only bunches of energy interacting, some so knotted on themselves that they can be thought of as "standing still" and having rest mass.

Even when I say "inside" I'm not entirely accurate, since there is nothing else than the particles "inside".

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