Random Thoughts About Relativity

Facts About Relativity  

In order to introduce some of my ideas, it will be good for the reader to become familiar with some of the weird behavior of particles traveling at very high speed, high enough to invoke relativistic effects.

As seen by a stationary observer:

1) The closer a moving object gets to the speed of light, the slower its moving clock gets.

At the speed of light, it is zero – to the moving object, everything is simultaneous.  Start, Splat. The moving object sees the outside world as distorted, getting shorter in length, and at c, the length from here to there is zero, no matter how far the stationary observer measures it.  Photons live in a go-splat world.

2) The closer a moving object gets to the speed of light, the shorter its length gets.

At the speed of light, it has zero length to the stationary observer, but normal length to the moving object.  Everything seems normal to the moving object  until it gets to c – the problem for the moving object at c is that there is no time to seem normal – everything is instantaneous.

3) The closer a moving object gets to the speed of light, the larger its mass gets due to kinetic energy increase (for objects that have mass).

At the speed of light, an object with mass would have infinite mass.   This rules out object with mass ever getting up to c.  Photons do not have mass so they can move at the speed of light.   Nothing with mass can go that fast.

4) The closer a moving object gets to the speed of light, the more energy you have to use to get it there.

You have to give more and more energy to the object to get it  closer and closer to the speed of light. Energy equals mass times speed of light squared.  At the speed of light, the energy required is infinite.  You can never push an object with mass that hard.

What is the equation that describes the way in which time slows down as you approach the speed of light?

The equation is known as the time dilation equation and is:

Δ t = Δ T/ √[ 1 – (v/c)²]    Time dilation

Where  Δ t is the moving object time ticks and Δ T is the stationary object time ticks, v is the velocity and c is the speed of light.

When the velocity approaches c, the term v/c becomes very close to 1 and then the term Δ t becomes very large because the right side is divided by a very small number approaching zero.  This means that the distance between clock ticks gets very long for the moving object.   Time begins to stand still as it reaches the speed of light because the distance between tics becomes infinite.

What happens to space (in direction of motion)?

Δ x = Δ X/√[ 1 – (v/c)²]      Space distortion

Where  Δ x is the ruler mark as measured by the moving object and Δ X is the ruler mark as measured by the stationary object.

When the velocity approaches c, the right hand term approaches infinity.  essentially, a unit measure, such as an inch for the moving object would stretch millions of miles as measured by the stationary object at speeds near c.  

conversely, a foot long ruler moving near c would be invisibly short as seen by the stationary object – a term called foreshortening. 

Conversely again, the stationary object would seem impossibly close and impossibly short to the moving object near c.  At c, neither could see the other even with the best of instruments until they collide, which would be instantaneous for the moving object.  (To do so would imply that the image was moving faster than c.)

 So someone (very small and massless) sitting on a photon would think they see time normally, but the time of flight would seem to pass instantly from time started to time finished because no time would elapse (Δt very large).   Of course there would be no time to measure time (or even think about it) because the photon would instantly hit the other end of its path, no matter how far away that is.

Someone sitting and watching nearby would see time normally (from their perspective), but in their case, ΔT would be very short (time interval ticks near 0) and they would seem to age quickly compared to the someone riding on a photon.

The total time of flight might seem 100 years to an observer, but seem instantaneous for one traveling at the speed of a photon. The observer would age instantly according to the one moving fast, and the observer would think the one moving quickly didn’t age at all.   Weird isn’t it?  Weird but true.

Similarly, distance gets shorter as an object approaches c as seen by the observer and longer for the observer as seen by the object that is moving fast.

In other words, the time that passes in one time frame (Δ t) is the time that passes in another (Δ T) divided by the square root of 1 minus the velocity squared divided by the speed of light squared.

Enough of this – keep in mind that photons don’t have time to age, and photons arrive the instant they are emitted.  A photon emitted in the furthest star that we can see by telescope arrives the instant it is emitted.   (From the photon’s point of view).   They live an instantaneous “go-splat” life.

From our point of view it may have taken billions of years to get here.  Both viewpoints are valid.  That is the weird nature of relativistic speeds.  Time and space are distorted. 

One last thing:  Effect of speed on atoms:

Atoms are flattened in the direction of their motion.  Normally about 10 -8 cm in diameter they change from a sphere to a flattened disk as they approach the speed of light (from our stationary perspective only).

Particle accelerators have to be designed to account for both time dilation and space contraction in order to work. 

Atoms have mass so they can never reach the speed of light, but particle accelerators push particles, including atoms, to very high speeds that require design changes to keep them on track around their path – changes that involve the equations above.

Next – some of the quantum weirdness explained, example by example from the earlier posts.

Quantum Weirdness in Entangled Particles

Entangled Particles

Selecting which atom we use with careful attention to its excitation states can create entangled particles.  Some atoms emit two photons at a time or very closely together, one in one direction, the other in the opposite direction.  These photons also have a property that one spins or is polarized in one direction and the other always spins or is polarized at right angles to the first.  They come in pairs such that if we conduct an experiment on one to determine its orientation, the other’s orientation becomes known at once.   They are “entangled”.

 

Figure 10 – Entangled Particles   

All of this was involved in a famous dispute between Einstein and Bohr where Einstein devised a series of thought experiments to prove quantum measurement theory defective and Bohr devised answers. 

The weirdness, if you want to call it that, is the premise that the act of measurement of one actually defines both of them and so one might be thousands of miles away when you measure the first and the other instantly is converted, regardless of the distance between them, to the complement of the first.   Action-at-a-distance that occurs faster than the speed of light?

Some would argue (me for instance) that this is more of a hat trick, not unlike where a machine randomly puts a quarter under one hat or the other, and always a nickel under a second one.  You don’t know in advance which contains which.  Does the discovery that one hat has a quarter actually change the other into a nickel or was it always that way?  Some would say that since it is impossible to know what is under each hat, the discovery of the quarter was determined by the act of measuring (lifting the hat) and the other coin only became a nickel at that instant.   Is this action at a distance? 

It is easy to say that the measurement of the first particle only uncovers the true nature of the first particle and the deduction of the nature of the second particle is not a case of weirdness at all.   They were that way at the start.

However, this is a hotly debated subject and many consider this a real effect and a real problem.  That is, they consider the particles (which are called Einstein‑‑ Podolsky‑Rosen (EPR) pairs) to have a happy-go-lucky existence in which the properties are undetermined until measured.   Measure the polarization of one – and the second instantly takes the other polarization.

A useful feature of entangled particles is the notion that you could encrypt data using these particles such that if anyone attempted to intercept and read them somewhere in their path, the act of reading would destroy the message.

So there you have it – Weird behavior at a distance, maybe across the universe.

Next:  Some Random Thoughts About Relativity