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FRIDAY, 16 JULY 2010 UPDATED

Wacky Thoughts On Time

 

 

The Lorentz Contraction

Why things look contracted when you travel at high speed.

This is the effect that an observer moving in relation to an object will observe it to be contracted along the direction of motion. This is by the following factor.
 
 
Where l' is the length observed by the moving observer, l is the length measured when at rest with respect to the object, v is the velocity of the observer, and c is the speed of light. If v is expressed as a fraction of the speed of light, then it does not matter about the units it's expressed in.
 
So why don't people stood on the pavement look thinner the faster you drive past them? This is because the length of contraction has very little effect at small velocities. Contraction only really begins to take effect as you approach the speed of light.
 
We drive through town at about 30 miles per hour (48 km/hour). The speed of light is about 670 million miles per hour (one thousand million km/hour). Fast. In our cars, we are traveling at a fraction of the speed of light, so you observe objects contracted by a fraction. Far too small to notice.
 
For instance, when driving at 30 miles per hour past a very big man, with a 1 metre waist, he will appear slimmer by less than the size of an atomic nucleus.
 
 

 

The Dilation of Time

Why astronauts traveling for a year at high speed in space return to Earth to find that 20 years have passed.

Time in a moving system will be observed by a stationary observer to be running slower by the following factor.
 
 
This reciprocates the Lorentz Contraction equation. Like the Loretz contraction, effects are negligible for small velocities. The effects increase exponentially as velocity of the system approaches the speed of light. In simpler terms, this is the effect that a space traveler has when flying through space at high speeds has aged much slower than his colleagues on earth.
 
The closer we get to the speed of light, the greater the dilation. If we could travel at 0.99 times the speed of light (very close to the speed of light), every day in the system would mean that nearly twenty thousand years would pass for the observer at rest.
 
Time dilation is small for the velocities that we travel at on Earth. However it is possible to measure with accurate instruments. This is because time dilation affects the rate at which time passes, and the total discrepancy between stationary and moving clocks increases throughout the voyage.
 
For every second you age on earth, an astronaut orbiting the earth in space (at a velocity of 7700 metres per second), will age 3 nanoseconds less. After a year in space, like some Russian cosmonauts have been, this dilation adds up to 3.8 seconds per year. If a watch has been synchronised with one on Earth before they went into orbit, this discrepancy will actually show in the watch in space and the watch on Earth.
 
In more practical terms, if you begin work at 21 years old and retire at 65 years old, you will have spent 44 years working. If you spent your working life cycling 9 miles to work at an average speed of 18 miles per hour, you will age shorter than if you traveled by car at an average speed of 40 miles per hour - by about 3 nanoseconds.
 
The end result of this is that you could extend your life by 3 nanoseconds by driving to work instead of cycling.
 
 

 

The Doppler Shift

Why racing car's engine noise changes pitch as it speeds past you.

The wavelength of light, sound or any other kind of propagating energy measured by a moving observer will be shifted by a factor of.
 
 
This is where V the velocity at which the observer is receding or approaching from the source, and C is the speed at which the wave propagates.
 
The Doppler shift in sound waves is a common occurrence. We can hear this when we stand by the side of a road and hear an ambulance approaching with it's siren blaring out. The sound of the siren will be increasingly shifted to a higher pitch as the ambulance approaches us. The siren will then quite abruptly peak and lower it's pitch as it passes by us and recedes.
 
If a train travels at 120km/hour, it is roughly one tenth the speed of sound. The Doppler formula will calculate the the frequency of the sound of an approaching the train will be a 10% higher pitch, and the sound of the train receding will be shifted to a 10% lower pitch. This is roughly the difference between two adjacent white keys on a piano.
 
The reason that we notice the Doppler shift in sound and not light is due to the massive difference between the velocity of sound waves and the velocity of light waves.
 
If we could travel fast enough to notice the Doppler shift in light, we would see red traffic signals Doppler shifted so that they appear to have changed to green before they actually change. This could cause traffic accidents. But not nearly as many accidents that it would cause by having to travel at about a quarter of the speed of light to notice the traffic signal changes.
 
 

 

The Aberration of Light

Why light will appear to be curved, or at an angle the faster you go.

Aberration of light is predicted by classical (Newtonian) physics. This is unlike Lorentz contraction and the dilation of time, which are relativistic effects. Aberration was first demonstrated two years before Newton's death in 1725. Special relativity modifies the classical formula, with differing results for objects moving at a substantial fraction of the speed of light.
 
Classical Aberration of Light.
This can be demonstrated by an example of rain. For example, we are in a stationary car in the rain, and rain drops come down in a straight line at their terminal velocity of 60km/hour. As we drive off in the car and get up to 60km/hour, the rain will appear to be falling toward us at a 45 degree angle, since our speed is equivalent to the velocity of the falling rain. The faster we go, the more acute the angle of the rain. If we get up to 250km/hour (on the German Autobahn of course!), we are traveling four times the speed of the rain, so the rain appears to be almost horizontal.
 
The aberration of light is exactly the same, except that light travels about 18 million times faster than rain. So we would need to travel much faster than 250km/hour to notice. For example, the same Autobahn above has roadside lights, where light is emitted in a beam vertically towards the ground. At 250km/hour, the photons of light emitted toward the ground will slant just like the raindrops due to the cars motion. However the angle is 18 million times smatter than the rain, so it may be difficult to notice.
 
Therefore if
 
Relativistic Aberration of Light.
Classical physics predicts that if we travel at the speed of light, we would measure the aberration of light from a source relative to our direction of travel to be 45 degrees. This Relativistic aberration predictions agree very closely to classical aberration predictions for velocities much less than the speed of light. It's only as you approach the speed of light that special relativistic effects become apparent. Where classical physics predicts an aberration of 45 degrees, special relativity shows the aberration to increase without bound. This is because no material object can attain the speed of light.
 
If you could travel close to the speed of light, the observational effect of relativistic aberration would be strange. Light rays arriving from any direction (other than directly opposite to the direction of motion) would be seen to approach a point directly in front of the moving observer.
 
POSTED BY NEIL WOOD AT 12:31 FRIDAY 16/07/2010
UPDATED 16:58 FRIDAY 11/05/2012
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