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DentArthurDent
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19 Aug 2014, 5:51 am

I know this is a scince question but I mostly post here so can the mods leave it here?

I have been trying to get my head around this eqaution, and I am getting close, I thought I had it until i tried to explain it to someone and came up very short :D

I have listened to a few books on the subject, and am now onto "why does e=mc2 and why should we care" Brian Cox and Geoffrey Foreshaw. This bit has me confused they are talking about Muons and the fact that they live 29 times longer when sped up to 99.94% of the speed of light, this bit I get, what I don't understand is that from the perspective of the muon the distance it is travelling shrinks by the same amount that its life increases.

I am guessing that this has to do with spacetime and the fact that it is expending more of the spacetime velocity than time. I am rather confused could someone help out here. BTW Maths is not my strong point


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TallyMan
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19 Aug 2014, 6:08 am

It has been many years since I studied this; however, if memory serves correct, everything the muon "sees" is flattened in the direction of travel of the muon. Hence less distance is being traversed from the perspective of the muon. Many of the aspects of relativity or quantum physics are impossible to visualise and you can only use the mathematics to describe what is happening and the mathematics ties up with experimental measurements. e.g. there is a particular particle that is often produced when cosmic rays from the sun hit the earth's upper atmosphere. (May be muons, I've forgotten now). Anyway the particle only has a life of around a fraction of a second but because it is travelling so fast it lives something like 4 seconds instead which means it can actually reach the Earth's surface.


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DentArthurDent
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19 Aug 2014, 6:41 am

TallyMan wrote:
Many of the aspects of relativity or quantum physics are impossible to visualise and you can only use the mathematics to describe what is happening and the mathematics ties up with experimental measurements.


Yes, Agreed. But still I would like to try on this one as I think this may be stumbling bock. I can get how an object shortens when it is close to the the cosmic speed limit, what I don't get is why the chamber the muon is moving in can decrease in length, after all it is only sitting in the time axis, or is it because from the perspective of the muon the chamber is moving at 99.94% of C? and therefore must decrease in size according to the muon?


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TallyMan
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19 Aug 2014, 7:06 am

DentArthurDent wrote:
TallyMan wrote:
Many of the aspects of relativity or quantum physics are impossible to visualise and you can only use the mathematics to describe what is happening and the mathematics ties up with experimental measurements.


Yes, Agreed. But still I would like to try on this one as I think this may be stumbling bock. I can get how an object shortens when it is close to the the cosmic speed limit, what I don't get is why the chamber the muon is moving in can decrease in length, after all it is only sitting in the time axis, or is it because from the perspective of the muon the chamber is moving at 99.94% of C? and therefore must decrease in size according to the muon?


Possibly, I don't know to be honest. I studied this stuff 30 years ago. Jono would be able to give an answer, he's a relatively recent physics graduate.


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ripped
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19 Aug 2014, 8:22 am

Einstein released a paper in 1905 called The Special Theory of Relativity.
Using the speed of light as a basis, Einstein was able to demonstrate mathematically the existence of a permanent direct relationship between solid matter and energy.
E=mc squared is the equation that displays this relationship in summary.

In the maths of Einsteins theories, velocity and matter are simple denominations of the same energy.
The implication being that time is comprised of energy as well. So if you are traveling fast, time is stretched to allow the inflexible mathematics behind these theories to still equate. You cannot alter velocity and not alter time due to the law of the conservation of energy.

But these is a confusion in trying to visualize two perspectives at once.

If you speed up a car to a million MPH, you are crossing through more 'time'. Passing millions of lines on the gridmap while the world stays basically where it is.
An observer on earth looks at his watch one hour after you left. By his calculations you were speeding out past the planets.
After one hour, you pull out your pocket watch in your car.
You have passed a vastly greater amount of space than ground control would have said. Except you are not looking at your watches at the same time.
Due to your differences in velocity, you each occupy a position where time passes at a different rate.

So the muon tank does not decrease in size to anyone.
'Objects shortening' and 'time speeding up' are definitions used to explain the same principles found in the math.
The point being, energy, mass and velocity are as directly related as the three sides of Pythagoras's triangle.



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19 Aug 2014, 8:25 am

Remember one of the key points of relativity ? even Galilean relativity ? is that there?s no such thing as absolute rest. From the perspective¹ of the muon, the Earth is what is moving nearly at the speed of light, so it?s affected by a strong length contraction. To an observer mounted on the muon, clocks sitting on the Earth would appear to run too slow, too (in fact, almost frozen), just like the muon appears to us to run too slowly through time. This seems contradictory only because we tend to believe in an absolute time, but experiments have shown there?s no such thing. Two observers can agree on a common measure of time only when they?re moving with respect to each other very slowly compared with the speed of light.

Spacetime diagrams can be very helpful to visualize these things. The relationship between two observers in relative motion is much like the one between observers which have experienced different rotations, so they don?t have a common forward or upward direction, for example.

____________________________________________

¹ What a human observer would actually see is more complicated, because it depends on the propagation of light at its finite speed; but experiments agree with predictions made according to this abstract picture.


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khaoz
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19 Aug 2014, 3:20 pm

There is actually a book titled "why does E=mc2?" by brian cox and jeff forshaw



DentArthurDent
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20 Aug 2014, 3:18 am

Thanks to all for your replies.

I now understand why if we were to travel at faster than the speed of light we would a reach our destination instantly and therefore violate causation.

It is so hard to prevent the innate belief in absolute time interfering with understanding. I wonder if there will ever be an era when people reason predominately using spacetime rather than space and time?


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