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I recently had lunch with a coworker who suggested that I pose a new physics thought experiment every week, and see what readers think of it.

So, this is the first installment!

The other day, I was looking at Einstein's special theory of relativity, especially the formula for length contraction that goes like this:

where capital X is the original length for an object, v is its velocity, c is the speed of light, and lower case x is the resulting apparent length of the object due to special relativity.

So what happens to x if the object is going faster than the speed of light (v >c)?  Would the object disappear from our view, but become apparent somewhere else?  After all,  according to the formula, if you go faster than light, your apparent length is an imaginary number!

I know that Einstein's laws make it difficult to go faster than the speed of light (especially because of the special theory of relativity with respect to mass).  But not impossible if you are willing to grant that quantum mechanics' assertion that time is quantized (that there is a smallest instant of time that cannot be subdivided) is correct.

To be a bit more explicit, the smallest instant possible according to quantum mechanics is Planck Time which is about:

A neutron weighs about:

1.6749 × 10-27 kg

And the speed of light is about:

3×108 m/s

So altogether we need about  27.08921 x 10 25  joules to get a neutron to the speed of light inside a Planck Time time interval...  (My math may be wrong here - I studied math not physics.  But the point is that the amount of energy needed is not infinite.)

BTW, the amount of energy emitted by the Sun every second is about 4 x 1026Joules.  (See here)

So it is possible then for an object to go faster than the speed of light by applying more energy than this specified amount...  I think if we grant this as possible we get some interesting results.

1. This might explain the inflationary hypothesis with repect to the Big Bang Theory....  Objects going faster than the speed of light may be undergoing a translation across imaginary axes until they finally slow down enough to go slower than the speed of light.  And then some of the matter might get "stuck" in the imaginary plane.

2. Which might also explain why we observer energy fluctuations at the subatomic level.  Physicists have always pondered where this energy comes from....  Perhaps these are further consequences of the Big Bang.

Anyway, I found this to be an interesting consequence of a literal interpretation of quantum mechanics and special relativity.

I am very much interested in your comments!

Jonathan

 

Posted on Saturday, December 1, 2007 5:20 PM Personal , Physics , Thought Experiments | Back to top


Comments on this post: Thought Experiment Sunday

# re: Thought Experiment Sunday
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I have nothing to add to the discourse other than to say I really enjoy the content. I hope you keep it up.
Left by Anthony Trudeau on Dec 02, 2007 9:13 AM

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