relativity time perception presentation ppt

relativity time perception ppt

1. Special RelativitySpecial Relativity
David BermanDavid Berman
Queen Mary CollegeQueen Mary College
University of LondonUniversity of London

2. Symmetries in physicsSymmetries in physics
The key to understanding the laws of nature is to The key to understanding the laws of nature is to
determine what things can depend on. determine what things can depend on.
For example, the force of attraction between For example, the force of attraction between
opposite charges will depend on how far apart opposite charges will depend on how far apart
they are. Yet to describe how far apart they are I they are. Yet to describe how far apart they are I
need to use some coordinates to describe where need to use some coordinates to describe where
the charges are. The coordinate system I use the charges are. The coordinate system I use
CANNOT matter. CANNOT matter.

3. Symmetries in physicsSymmetries in physics
Let’s use Cartesian coordinates.Let’s use Cartesian coordinates.
Object 1 is distance x1 along the x-axis and Object 1 is distance x1 along the x-axis and
distance y1 along the y-axisdistance y1 along the y-axis
Object 2 is distance x2 along the x-axis and Object 2 is distance x2 along the x-axis and
distance y2 along the y-axisdistance y2 along the y-axis
The distance squared between the two objects will The distance squared between the two objects will
be given by:be given by:
222
)21()21( yyxxd 

4. Symmetries in physicsSymmetries in physics
The force is inversely proportional to the distance The force is inversely proportional to the distance
squared.squared.
What transformations can we do that will leave the What transformations can we do that will leave the
distance unchanged?distance unchanged?
Translation: Translation:
byy
axx
byy
axx




22
22
11
11

5. Symmetries in physicsSymmetries in physics
Rotations:Rotations:
2)cos(2)sin(2
2)sin(2)cos(2
1)cos(1)sin(1
1)sin(1)cos(1
yxy
yxx
yxy
yxx









6. Symmetries in physicsSymmetries in physics
We can carry out the transformations We can carry out the transformations
described of translations and rotations and described of translations and rotations and
yet the physical quantity which is the yet the physical quantity which is the
distance between the two charges remains distance between the two charges remains
the samethe same..
That is a symmetry. We carry out a That is a symmetry. We carry out a
transformation and yet the object upon transformation and yet the object upon
which the transformation takes place which the transformation takes place
remains the same or is left remains the same or is left invariantinvariant. .

7. Symmetries in physicsSymmetries in physics
The important quantities in physics are those The important quantities in physics are those
that are that are invariantsinvariants. That is the things that don’t . That is the things that don’t
transform.transform.
Other things will change under transformations Other things will change under transformations
and so will depend typically on our choice of and so will depend typically on our choice of
description, for example which way we are description, for example which way we are
facing.facing.

8. Space and TimeSpace and Time
We live in both space and time. There are the We live in both space and time. There are the
usual three dimensions of space we are used to usual three dimensions of space we are used to
and also one more of time. We perceive time as and also one more of time. We perceive time as
being very different to space though.being very different to space though.
How different is it really? How different is it really?
To arrange a meeting I need to specify a time To arrange a meeting I need to specify a time
and a place. I can describe the place by using and a place. I can describe the place by using
some coordinates and the time by specifying the some coordinates and the time by specifying the
hour of the day (that’s just a time coordinate).hour of the day (that’s just a time coordinate).

9. Space and TimeSpace and Time
Distances in space can given as we have shown.Distances in space can given as we have shown.
Distances in time would also be given by the difference Distances in time would also be given by the difference
of the two times that is:of the two times that is:
12ttt
12
12
yyy
xxx





10. Space and TimeSpace and Time
How do we add up distances in different How do we add up distances in different
directions?directions?
We’ve already seen that it is NOT just the sum We’ve already seen that it is NOT just the sum
of the distances in the different directions rather of the distances in the different directions rather
the total distance is given by:the total distance is given by:
222
yxd 

11. Space and TimeSpace and Time
How do we find the distance in space-time. That is How do we find the distance in space-time. That is
given the distance in space and the distance in time given the distance in space and the distance in time
how can we combine them to give the total distance how can we combine them to give the total distance
in space-time?in space-time?
Wrong guess:Wrong guess:
222
dts 

12. Space and TimeSpace and Time
Einstein had a better Einstein had a better
idea.idea.
He combined space He combined space
and time found the and time found the
right way to describe right way to describe
distances in distances in
spacetime.spacetime.

13. EinsteinEinstein
In 1905, while working as a patent office clerk in In 1905, while working as a patent office clerk in
Bern, published his work on special relativity. Bern, published his work on special relativity.
His insights in that paper were essentially that His insights in that paper were essentially that
space and time should be combined in one space and time should be combined in one
thing, spacetime. He also realised the right way thing, spacetime. He also realised the right way
to construct invariant distances in spacetime.to construct invariant distances in spacetime.
The same year he also published two other key The same year he also published two other key
papers in other areas of physics. It really was an papers in other areas of physics. It really was an
enormous break through year for Einstein.enormous break through year for Einstein.

14. SpacetimeSpacetime
The distance in spacetime is given by:The distance in spacetime is given by:
222
tds 

15. SpacetimeSpacetime
When we measure distances we use the same When we measure distances we use the same
units for x and y. If we didn’t then we could units for x and y. If we didn’t then we could
convert between units in the distance formula convert between units in the distance formula
like so:like so:
With w the ratio of the two different units. With w the ratio of the two different units.
Instead we pick w=1 and use the same units for Instead we pick w=1 and use the same units for
our x and y distances.our x and y distances.
2222
ywxd 

16. SpacetimeSpacetime
For spacetime, what is the choice of units of For spacetime, what is the choice of units of
time that will set w=1 and give us the equivalent time that will set w=1 and give us the equivalent
unit for time as for space?unit for time as for space?
If we measure space in meters then we should If we measure space in meters then we should
measure time in light meters. (More about this measure time in light meters. (More about this
later).later).

17. SpacetimeSpacetime
Given that the distance in spacetime is given Given that the distance in spacetime is given
by:by:
What are the transformations that leave this What are the transformations that leave this
distance invariant? What is the symmetry? That distance invariant? What is the symmetry? That
is how can we transform space and time so that is how can we transform space and time so that
the distance in spacetime remains the same.the distance in spacetime remains the same.
222
tds 

18. SpacetimeSpacetime
LorentzLorentz realised that realised that
there was a symmetry there was a symmetry
in nature where you in nature where you
could transform space could transform space
and time distances in and time distances in
the following way.the following way.

19. Lorentz TransformationsLorentz Transformations
2
1
1
)(
)(
v
b
vxtbt
vtxbx





20. Lorentz TransformationsLorentz Transformations
Spatial distances can shortenSpatial distances can shorten
Time distances can also shortenTime distances can also shorten
The spacetime distance is the same that is it is The spacetime distance is the same that is it is
invariant under these transformations.invariant under these transformations.
v is a velocityv is a velocity
Units are chosen such that time is measured in Units are chosen such that time is measured in
light meters.light meters.

21. Lorentz TransformationsLorentz Transformations
Distances in space will depend on the velocity of Distances in space will depend on the velocity of
the observer.the observer.
Distances in time will depend on the velocity of Distances in time will depend on the velocity of
the observer.the observer.
This is just like saying that spatial distance in This is just like saying that spatial distance in
one direction depends on which way you are one direction depends on which way you are
facing.facing.
The equivalent to the angle you are facing is The equivalent to the angle you are facing is
velocity you are moving at. velocity you are moving at.

22. ExperimentsExperiments
Thousands of Thousands of
experiments have experiments have
been done checking been done checking
the Lorentz the Lorentz
transformations and transformations and
the altering of time the altering of time
and space depending and space depending
on velocity.on velocity.

23. ExperimentsExperiments
Lifetime of elementary Lifetime of elementary
particlesparticles
Orbiting atomic clocksOrbiting atomic clocks
Collider physicsCollider physics
Michaelson Morley Michaelson Morley
experiment: Speed of experiment: Speed of
light is constant no light is constant no
matter what your matter what your
velocityvelocity

24. ExperimentsExperiments
In the experiment carried out by Michaelson and In the experiment carried out by Michaelson and
Morley an attempt was made to measure speed Morley an attempt was made to measure speed
of light parallel to the motion of the earth and at of light parallel to the motion of the earth and at
right angles to the motion of the earth.right angles to the motion of the earth.
According to our usual notions of how velocities According to our usual notions of how velocities
add there should have been a difference.add there should have been a difference.
They found the speed of light was the same They found the speed of light was the same
whether it was directed alongs the earth’s whether it was directed alongs the earth’s
motion or not. This agrees with relativity, the motion or not. This agrees with relativity, the
speed of light is the same no matter how fast speed of light is the same no matter how fast
you are going!you are going!

25. ConsequencesConsequences
How big is a light meter?How big is a light meter?
Speed of light is about 300000000m/sSpeed of light is about 300000000m/s
One light meter is about 0.0000000033333 sOne light meter is about 0.0000000033333 s
To convert to velocities measured in m/s we To convert to velocities measured in m/s we
need to divide by c- the speed of light a big need to divide by c- the speed of light a big
number.number.
Most velocities in every day are much much less Most velocities in every day are much much less
than the speed of light which is why we don’t than the speed of light which is why we don’t
notice the Lorentz transformations in ordinary notice the Lorentz transformations in ordinary
life.life.

26. ConsequencesConsequences
Notice that v/c can’t be 1 or the Lorentz Notice that v/c can’t be 1 or the Lorentz
transformation become infinite and time transformation become infinite and time
and space become infinitely transformed.and space become infinitely transformed.
We can’t travel faster than the speed of We can’t travel faster than the speed of
light.light.

27. ConsequencesConsequences
Just as space and time Just as space and time rotate rotate into each other so do into each other so do
other physical quantities. What matter is the invariant other physical quantities. What matter is the invariant
quantity.quantity.
Energy and Momentum also transform into each other Energy and Momentum also transform into each other
under Lorentz transformations. The invariant quantity is:under Lorentz transformations. The invariant quantity is:
222
pEm 

28. ConsequencesConsequences
Putting back in c, the speed of light so that energy and Putting back in c, the speed of light so that energy and
momentum would be measured in SI units this equation momentum would be measured in SI units this equation
becomes:becomes:
If p is zero we get the celebrated equation:If p is zero we get the celebrated equation:

22242
cpEcm 
2
mcE

29. ConclusionsConclusions
Space and time should be combined to Space and time should be combined to
spacetime a single entity.spacetime a single entity.
The invariant measure of distance on spacetime The invariant measure of distance on spacetime
isis
With the unit the light meter.With the unit the light meter.
Lorentz transformations leave this distance Lorentz transformations leave this distance
invariant.invariant.
222
tds 