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ON TIME An Introduction into the theory behind Albert Einsteins Special Relativity

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Relativity in a nutshell… Qn: What would a beam of light look like if you were to race alongside it? According to Newton, one could catch up to any moving object if one could travel fast enough. Einstein realised that if that were to happen, the wave would appear to be frozen in time This is against the laws of physics.

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Relativity in a nutshell… Einstein observed that the speed of light in vacuo appeared to be some sort of cosmic speed limit that nothing can surpass- a cosmological constant This is because the speed of light is absolute in all frames of reference - it always appears to be the same regardless of ones speed This led to the creation of the Special Theory of Relativity in 1905.

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Time Dilation Remember that the speed of light is constant in all frames of reference- but how does this work? Imagine an electron travelling at 0.8c racing alongside a stream of photons Photons From your frame of reference, you would see the electron almost keeping up with the photons…

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Time Dilation BUT from the electrons frame of reference, no matter how fast it can travel, the photons will seem to be racing ahead at their usual pace (=c). This is because the speed of light is the same in all frames of reference. Photons ???! …This is the time dilation effect. Time itself had slowed down for the electron!

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Time Dilation The time dilation effect: The faster an object travels, the slower time passes for it. Let us now take the path that an object at rest and a moving object trace through time. Time elapses slower for the moving object as compared to the object at rest. OROR OMOM 1s

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Time Dilation Because time now passes by more slowly for the electron (due to its high speed) as compared to the photons, from the electrons frame of reference it would then appear to be travelling much more slowly compared to the photons This is because light is not subject to time dilation. (Principle of non-invariance)

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Distance/Time comparison Time comparison: 1s.: Due to time dilation, when 5s have elapsed for the photon, only 3s have elapsed for the electron travelling at 0.8c, from its frame of reference. Distance comparison: D/s 1s

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Time Dilation The time dilation factor, or Lorentz factor, can be calculated using the formula (1- v 2 /c 2 ) -1/2 E.g. For the electron travelling at 0.8c, the Lorentz factor would be (1-0.8 2 /1.0 2 ) -1/2 = 1.67, i.e. when one second has elapsed for the electron, 1.67 seconds would have elapsed for the photon (or for any other object at rest, for that matter.)

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Muon Decay Muons are inherently unstable particles that decay in a matter of a microseconds Muons created by cosmic-ray impacts in the upper atmosphere can travel all the way deep underground. Their presence is recorded by Geiger counters. Yet, in the time taken for a muon to decay, even light travels less than a kilometre. So why are these muons able to travel such a great distance (~20km) to ground level?

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Muon Decay This is because the time dilation effect results in the muons appearing to age slower than they should! When a few microseconds have elapsed for the muon, much more time would have elapsed for an observer at rest.

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Length Contraction The length contraction effect: The faster an object travels, the shorter it appears to be to an observer at rest. The distance travelled by the object will also appear to be shortened from the objects frame of reference. The length contraction factor can be calculated using the formula (1-v 2 /c 2 ) 1/2, where the result would be the apparent length of the object in comparison to the actual length of the object.

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Length Contraction To demonstrate this effect, lets say a familiar-looking electron (0.8c!) wants to travel from Point A to Point B, 240 000m away. From a stationary observers frame of reference: Distance travelled in one second The electron would have taken 1 second to travel from A to B since 0.8 X 300 000m (distance travelled by light in one second) = 240 000m.

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Length Contraction But, due to time dilation, when 1 second has elapsed for the observer, only 0.6 seconds would have elapsed for the electron. Also, due to length contraction, the electron would have perceived itself to have only travelled (1-0.8 2 /1.0 2 ) 1/2 = 0.6 times the actual distance of 240 000m

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Length Contraction From its frame of reference, the electron would have travelled only 0.6 X 240 000 = 144 000m 144 000m/0.6s = 240 000 m s -1 = 0.8c Hence, the resulting velocity would still remain unchanged. This is because velocity is an inherent property of an object and cannot be changed without the presence of an external force. This shows how time dilation and length contraction are interrelated.

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Gravitational Timewarping Motion is not the only thing that causes time dilation to occur– the effect of gravity can slow time down as well. The stronger the gravitational influence, the slower time passes by. This is in part due to Einsteins equivalence principle which states that the effects of acceleration are equal to the effects of gravitation.

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Gravitational Timewarping When a light-emitting body accelerates away from you, the light that reaches you will be continuously red-shifted (i.e. its frequency will be lowered) due to the Doppler effect. Replace the accelerating body with a gravitational body, and this would mean that light travelling away from the body will undergo a lowering in frequency as well.

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Gravitational Timewarping Since frequency is a measure of the number of waves per second, a lowering of frequency as a result of the gravitational red-shift would also mean a reduction in the number of waves per second. If the number of waves per second is reduced as light travels away from the gravitational object, this would mean that time itself is speeded up as the distance increases.

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Gravitational Timewarping 1 s As the number of waves per second decreases with increasing distance from the gravitational body, a reverse time dilation effect occurs… …the length of one second appears to get shorter and shorter as time speeds up.

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Moving On… …So is the secret to outlasting your peers running around very fast in the basement? Anyway, now that were done with the key aspects of Special Relativity, let us now move on to more abstract ideas of time and space…

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The Speed of Time: A Theory Some of you might be wondering: why is it that makes light so special? Why is the speed of light absolute in all frames of reference? Why isnt light affected by relativity? As for now, the answer is: we dont know. But for the moment, heres our take on the matter.

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The Speed of Time: A Theory Suppose that there is actually more than one type of time: Time as the fourth dimension (or the time that we know it), and time as a temporal force that can travel alongside us as we trace out our passage through 4 th dimensional time. Most of us would think that we experience the passage of time due to our movement forward in 4D time. The speed of our movement through time would depend on the speed of our motion through 3D space.

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The Speed of Time: A Theory But what if I told you that there exists a temporal force that also travels alongside us as we travel forward on our timeline? This temporal force would consist of particles of time known as temporons, which are 10 -45 s (quantum) units of time. We would then experience the passage of time due to the passage of these temporons through us.

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The Speed of Time: A Theory Now, an observer at rest would experience the full effects of these temporons zipping through him Since he is not moving and the temporons are moving at a very high speed, time passes by quickly for him. But suppose he starts to move. The temporons would now pass by slower relative to him in his frame of reference, and thus, time would appear to be slowed down, or dilated!

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The Speed of Time: A Theory As he moves faster and faster, time gets more and more dilated. According to the Lorentz formula, when one reaches the speed of light, time is dilated completely and thus time would then logically stop. This is where the magic of this theory comes in: A potential explanation for the non-invariance of light!

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The Speed of Time: A Theory According to the theory, we experience time passing by when temporons pass through us. If we travelled at the speed of light and if time were to stop, however, this would mean that no temporons are passing us by! Now suppose these temporons actually travel at a specific speed: the speed of light.

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The Speed of Time: A Theory This would mean that when WE travel at the speed of light, no temporons would then be able to pass through us since we are travelling at the same speed as they are! The result would be a time stoppage– exactly the result predicted by time dilation! Now…what would happen if we then chose to travel faster than the speed of light???

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The Speed of Time: A Theory According to the theory, we would theoretically be able to catch up with the temporons racing in front of us and experience time in reverse! This effect has also been predicted by the Lorentz formula! So, is it really possible to travel backwards in time? Could this theory in fact be the explanation for time dilation, and therefore, the principle of non-invariance after all?

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ONLY TIME WILL TELL. …Questions, anyone?

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Page 1 Phys 320 - Baski Relativity I Topic #9: Special Relativity I Transformation of Variables between Reference Frames –Non-relativistic Galilean Transformation.

Page 1 Phys 320 - Baski Relativity I Topic #9: Special Relativity I Transformation of Variables between Reference Frames –Non-relativistic Galilean Transformation.

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