Monday 26 September 2011
Saturday 30 July 2011
Friday 15 July 2011
Thursday 7 July 2011
Pulling together the work @QMULphysicsacademy and the proof of Special Realtivity: - I have proved it for myself!
Through my experiment at QMUL I have gathered my own data that proves Einstein's Special Theory of realtivity. Over a 46 hour period we detected nearly two million muons. Without relativity we would only have expected to see about twenty!!
Time Dilation
• If two identical, synchronised clocks are placed
side by side they will read the same time for as
long as they both remain side by side.
• However if one of the clocks is moving, it will show
that less time has elapsed (i.e. time has slowed
down) than the stationary clock.
• This effect is called time dilation.
• It has been confirmed by experiment.
• Two highly accurate atomic clocks were
synchronised. One was placed in a jet aircraft and
the other in a laboratory on Earth. After the jet
returned (having travelled at 1000 km/hr), the
travelling clock was a tiny fraction of a second
behind the Earth clock.
Proof – A Thought Experiment:
• Within a truck moving with velocity v, a light pulse is transmitted, reflected by a
mirror and received!
• Truck's frame of reference i.e. observed within the truck, the light pulse travels a
distance of 2L in time t0.
• Earth's frame of reference i.e. observed outside the truck, the light pulse travels
2x.
• Light travels a longer distance but at the same speed ⇒ longer time taken t ≥ t0.
t0 = 2L/c
⇒
L = ct0/2
t = 2x/c
⇒
x = ct/2
• Using x2 = L2 + (vt/2) 2 sub for t and t0
• t - relativistic time i.e. measured in a frame of reference moving relative to object.
• t0 - rest time i.e. measured in the same frame as (at rest with) the object.
• Relativity factor:
As v ≤ c, t ≥ t0.
• Time dilation is significant at relativistic speeds i.e. v
→ c, γ → ∞ i.e. t → ∞.
Actual Experiment - Muon Decay Experiment
• Muons are produced in the upper layers of the Earth’s atmosphere.
• They travel close to the speed of light (99% c).
• But they have very short life-times i.e. a half-life of 2
μs.
• Classically, very few muons would be expected to reach the Earth’s surface;
most would have decayed by that time.
• But with time dilation, the half-life of muons increase (time slows down!).
• Measure count rates of muons at top and bottom of a mountain.
• For an observer on the ground, a higher than expected count rate is measured –
fewer have decayed because of the longer half-life.
Worked Example
• Muons travel at 0.99c.
• Muons should take
t = s/v = 6000 / (0.99 × 3 × 108) = 20
μs to reach Earth’s surface.
• They have a half-life of 2
μs.
• So (20
μs / 2 μs =) 10 half-lives should occur in this time.
• Expect 1/210 muons to reach Earth’s surface.
• If 1000 muons are detected in the upper layers of
the Earth’s atmosphere then expect:
1 muon to be detected at the Earth’s
surface.
• With time dilation, the half-life increases to
t =
γ t0 = × 2 μs = 7.09 × 2 μs = 14 μs
• So (20
μs / 14 μs =) 1.4 half-lives occur.
• Observe 1/21.4 muons to reach Earth’s surface.
380 muons are detected at the Earth’s
surface.
• A higher than expected count rate is detected!
My understanding of special realtivity
Special Theory of Relativity I
Frame of Reference
• It is a set of axes that defines the position of any point in space at any instant of
time.
• The frame can be at rest or moving at a constant velocity or accelerating.
• An inertial frame is a non-accelerated frame of reference.
Newtonian Relativity
• Two observers who are moving relative to each other will disagree about their
measurements of velocity.
• Absolute motion cannot be determined.
• Motion is always measured relative to a frame of reference e.g. Earth's frame.
• The laws of motion are the same in any inertial frame of reference.
• But not the laws of electromagnetism e.g. the speed of light is different in different
inertial frames of reference.
Einstein's Relativity
• There are two postulates (suggestions).
• First: all the laws of physics are the same in any inertial frame of reference.
• Second: hence the speed of light is the same in any inertial frame of reference.
• This theory predicts that two observers who are moving relative to each other will
disagree about their measurements of time and distance.
• Absolute time and distance cannot be measured; only relative time/distance.
physics academy @QMUL
During the week of the 4th July I have been attending a physics academy at Queen Mary. This has been a chance to explore a range of topics I wouldn't otherwise cover and to work with both students and researchers.
We received lectures in condensed matter physics, particle physics and one on solar physics.
I chose to do a project on detecting muons. I will be presenting my presentation tomorrow.
Here is a quick example of some of the content:
We have been using a scintillator to detect these in a lab. Here is a pic:
We managed to measure the half life of a muon pretty accurately (our experimental value was 2.185μs, close to the accepted value of 2.2) so this was pretty pleasing.
I will try to put some more of what we have been doing soon
take care
Obi
x
We received lectures in condensed matter physics, particle physics and one on solar physics.
I chose to do a project on detecting muons. I will be presenting my presentation tomorrow.
Here is a quick example of some of the content:
We have been using a scintillator to detect these in a lab. Here is a pic:
We managed to measure the half life of a muon pretty accurately (our experimental value was 2.185μs, close to the accepted value of 2.2) so this was pretty pleasing.
I will try to put some more of what we have been doing soon
take care
Obi
x
First Post
Hi everyone
This is my first post and I'd just like to just introduce myself and my blog.
I plan on posting stuff that I experience and learn as a physics student. I am currently studying A levels and I am hoping to apply to Oxford to read physics next year.
These posts will hopefully contain content that I have either found interesting or that has taken me a while to get my head round, and I will try to explain some of the main ideas in the way I have understood them, and hopefully a way you can too!
Anyway, I am a novice blogger, but I hope that people who read this will at least be a little intrigued!
All the best
Obi
x
This is my first post and I'd just like to just introduce myself and my blog.
I plan on posting stuff that I experience and learn as a physics student. I am currently studying A levels and I am hoping to apply to Oxford to read physics next year.
These posts will hopefully contain content that I have either found interesting or that has taken me a while to get my head round, and I will try to explain some of the main ideas in the way I have understood them, and hopefully a way you can too!
Anyway, I am a novice blogger, but I hope that people who read this will at least be a little intrigued!
All the best
Obi
x
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