Just in the past two days, I've seen two extreme examples of people writing on science issues when they've no business doing so - because their scribblings are totally baseless and effectively nonsense. Yet for some reason, any Joe Schmoe - who may never even have taken a General Science course (far less a physics course)- thinks he can write about any old science topic that strikes his fancy. These folks need a definite reality check!

Now, am I saying here that no one who isn't formally qualified in science (say with an advanced degree) can write about a science topic? No! A person who's never seen a physics book in college can still write on a physics topic, but it's incumbent on him to first do his research! If he's going to expound on special relativity, then carefully read about it before making wild claims. The same applies for anyone purporting to write on topics such as evolution or climate change. Thus, merely because these topics happen to be 'hot wire' political issues doesn't mean anyone can just write whatever he or she wishes. Science has laws and principles, as well as technical definitions, and if these are flouted then the content is useless.

Anyway, the first example of pseudo-scientific blather appeared in the Letters section of the recent

**Mensa Bulletin**. In a way, this is more or less excusable because editors of magazines, even Mensa's, aren't trained to parse the accuracy of content before printing it. Thus, any guy can write all kinds of tripe on special or general relativity and get a hearing.

In this case, letter writer Neil Slater really goes out for the long ball, with his sundry whacks mainly at Einstein's special theory. He claims first that:

*The time was ripe for any number of physicists to publish the Special theory. Einstein just happened to be at the right place in history."*

In a way, he's correct because Einstein's resolution of the contradiction in the Galilean addition law for velocities, e.g. u(x)' = u(x) - v, had to await the Michelson-Morley experiment and its negative results, i.e. showing the speed of light c was the same whether a light source approached the Earth or moved away from it. Whereas, by the Galilean form, the person would conclude the relative velocity is greater when the source is approaching and less when it is receding, by analogy with classical relativistic mechanics on Earth.

Thus, if a car is moving at 40 mph toward another car that is moving opposite to it, also at 40 mph, then we conclude each car is approaching the other at: 40 mph + 40 mph = 80 mph. In like manner, if Earth and a light source are approaching, with Earth moving at 66,000 mph in its orbit, and light moving at 669,600,000 mph toward it then we expect the result to be

**the addition of the two speeds**. But the Michelson-Morley experiment showed this was not the case, and that the relative speed was still the velocity of light - no addition of Earth's velocity to it!

This then is the experiment that had to transpire before a resolution of the Galilean velocity addition law could arrive. Before the M-M experiment, no one would have been able to resolve it, neither Fitzgerald, or Lorentz or anyone else. Einstein's resolution was remarkably simple and became known as

*The Principle of relativity*

:

**"All the laws of physics are the same in all inertial reference frames"**Or to put a more specific touch to it:

**The speed of light is the same in all inertial refefence frames.**

It was this principle, ultimately traced to the negative result of the Michelson-Morley experiment, which enabled Einstein to forge his particular set of transformations. This then led to the unified entity of

**space-time**or the space-time continuum, which was his singular breakthrough. The essence of the concept is displayed in Fig. 1 and is based upon on an invariant quantity called

**interval**denoted as

**s**. We see then that for two different frames of reference f1(d, it), f2(d' it')the interval is exactly the same, hence invariant for all observers. In each case we have: s^2 = d^2 - c^2t^2. Note that d' corresponds to contracted length and hence to expanded time (it').

Let's now go on to Slater's next comment which is:

*"In simplest form one cannot be sure where or when any object exists"*

But this is palpable nonsense. If this were true, then we'd never be able to measure precisely the path of muons for example, or show they were subject to time dilation! We wouldn't, in effect, know where or "when" they are so wouldn't be able to compare them! Consider then, the case of a muon formed high in the atmosphere and travelling at 0.99c for a distance of 4.6 km before it decays: e.g.

muon -> (e-) + neutrino + (anti-neutrino)

How long does the muon survive as measured in its own rest frame, and how far does the muon travel as measured in its own frame? If time dilation applies, we expect that the time in its own rest frame will be significantly longer than for a stationary observer (e.g. on Earth's surface) observing it. We also expect its distance traveled will be much shorter! Given a proper time, t': and t = t'/ y

where y = [1 - v^2/c^2]^1/2 then t' = ty

So the proper time t' = t, where t = x/c = (4.6 x 10^3 m/s)/ 2.98 x 10^8 m/s)

= 1.55 x 10^-5 s

which is the muon lifetime

**relative to an observer on Earth**.

and so: t' = ( 1.55 x 10^-5 s) (o,141) = 2.18 x 10^-6 s or ~ 2.2 us (micro-seconds)

which is the commonly observed lifetime for muons in their frame of reference.

The distance traveled is: L = x/y = (4.6 x 10^3 m) (0.141) = 649 m

Using only L, one might suppose the muons

**would never reach Earth's surface**since the path length is too short. But it is precisely time dilation that accounts for the fact a large number DO reach the Earth and are detected. Hence, Slater is incorrect because he hasn't factored in time dilation for the frame of reference and object, which is exactly what enables us to assay "where" and "when" an object exists! That muon path lengths can differ then, vis-a-vis the frames observed in, discloses Slater's take is pseudo-scientific nonsense.

The same principle as the above can be used to ascertain potential space journeys for any astronauts traveling to other planets at near light speeds. Consider, for example, two astronauts traveling to Proxima Centauri at 4.2 Ly distance. If their craft manages to travel at 0.95c nearly all the way, then:

How much time would elapse on the clocks of Earth observers?

Well, this would be: (4.2 Ly)/ 0.95c = 4.4 yrs.

However, the astronauts would disagree -- so how much actual time would elapse on THEIR clocks? Well, for the traveling twin (A),the time elapsed is:

t(A) = t(B)[1 - v^2/c^2]^1/2 = (4.4 yrs.) [1 - (0.95c)^2/c^2]^1/2 = 1.37 yrs.

This also refutes the next claim of Slater's which was:

"

*It doesn't take a lot of imagination to see the passing of time appears to be interrelated with an increase in the rate of time and an increase in distance/*

However, we already showed this is false via the above Twin A and B example for ostensibly traveling the same distance to Proxima Centauri but ending up with different travel times. Thus, the rate of time passage is not so simply related to distance. not unless one factors in putative length contraction in one frame of reference relative to the other, and hence factors time dilation also!

More nonsense from Slater follows:

"

*Also it isn't hard to show that two or more items can coexist in time and space, as can be observed by any outside party"*

Really? Then I'd like him to please prove to me that another entity (e.g. alien?) is occupying the same time and space coordinates as I am. He can't. Moreover, it's total nonsense, because that effectively would mean a ZERO interval (e.g. s = 0 ) shared by reference frames! If s = 0 then we have no relativistic transformations and can't compute any dimensional differences! The whole basis for special relativity is that the interval

**s**is non-zero and hence Slater's rumination is plain poppycock.

But when one is spouting nonsense he's usually on a roll. Slater again:

*"At a distance accelerate away from an object and you will move into what you perceive is the past. This might let you become contemporaneous with your great, great grandmother (at a distance)"*

But no matter how fast one accelerates "from an object" there is no way one is going into the past. Ask the Shuttle astronauts now prepared to accelerate from Earth on the last Shuttle mission. There is no way they will travel into the past or meet their great great grandmothers! The reason is that simple displaced acceleration isn't enough. One must be able to traverse from an event in current time, t, to the past light cone of the event (see Fig. 2). So how in hell can one do this? One way is by using the same twin paradox format.

For the case of a total trip to return to Earth, we therefore see (keeping all assumptions in place) the total time as measured by the Earth twin will be:

2 t(B) = 2 (4.4 yrs.) = 8.8 yrs. While for traveling twin A:

t(A) = 2 t(A) = 2 (1.37 yrs) = 2.74 yrs. or call it 2.7 years.

Thus, on returning home, the traveling twin (A) will be: 8.8 yrs - 2.7 yrs. = 6.1 yrs.

**younger than the twin that remained on Earth**. This calculation, note, is totally consistent with the one we did to work out the time for muons' duration in their rest frame if they completed a path of 4.6 km. It can also easily be worked out, again from the muon example, that the distance to Proxima as computed by the twin A will be 1.31 Ly. (Since L(A) = 1.31 Ly/0.95c = 1.37 yrs)

Thus, on the Twin A's arrival back at Earth one would have the putative evidence for his traveling (partially) into a past light cone, since this would yield an age 6.1 years younger than his stationary twin. More technically, A moves from his past light cone (conferred by virtue of his travels) to a future light cone shared with his twin B. (See Fig. 3). The time differential (in their ages) is what gives away the light cone divergence in their frames of reference.

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