Relativity

Stage 2 physics

Relativity

The sheer and absolute brilliance of Einstein was not (only) his new developments, but that he could bring together the physics of over 3 hundred years and notice not only the similarities but to see commonality of the anomalies across a range of different physical discoveries.

In bringing together the work of a large number of physicists, a key area that underpins the Special Theory of Relativity is Galileo's work on reference frames. Galileo noted that observations are always in respect to the observer and that two observers can make different (and correct) observations of the same thing. However, the laws of physics will not change for each observer.
Einstein formulated this into the Principle of relativity which states that;

The laws of physics are the same for all observers in uniform motion

This is known as the First postulate of relativity

Definitions

An Inertial frame of reference is one where the observer is in uniform motion (no acceleration)
An Accelerated frame of reference is one where the observer is accelerating (velocity is changing)
NOTE: it is all about the observer and not about what is being observed
Also, all frames of referece are equivalent or equally valid. There is no 'correct' or preferred frame of reference.

The second postulate is that the

speed of light is the same for all observers

Spacetime

Every object travels a path in spacetime. 3 coordinates in space and 1 in time. For example. at 9.00pm you were at latitude; 34.921230, longitude; 138.599503 at a height of 46.00m (your 1 time and 3 space coordinates).

Even if you stand still, your path through time continues, one second at a time. When you move, your position in space changes.

In this way, you only ever occupy a point in space time for less than a second.

Time dilation

Time slows down as an object speeds up when compared to a stationary observer
Note, time also slows down as gravity increases to the point that time stops at the event horizon of a black hole.

Simultaneity and Causality

Since time can be different for every observer, an interaction that occurs at a specific time according to one observer may happen at a different time according to another observer
However, every observer will agree to the series of events or 'causes' that led to an interaction

Length contraction

The length of a moving object will contract in the direction of movement as seen by a stationary observer
Note, if you are moving with the object, you will not see the contraction
In the same way, with time contraction, if you are moving with the object, you will not notice a 'slowing' of your time. It is only when you make a comparison that you will find that less time has 'ticked by' for you

Rest mass vs relative mass

As an object accelerates toward the speed of light, its mass increases. Actually, it is its momentum which increases, however, since we normally consider

momentum = mass x velocity

If momentum has increased by more than the increase in velocity, we would say that the increase must be in an increase in mass. This gives us the concept of 'relative mass'.

However, we should more properly consider a change in momentum with relativistic momentum given by the formula;

Why cant we travel faster than the speed of light?

Relativistic momentum.

As per the equation above, as you increase velocity toward the speed of light, momentum increases toward infinty. To increase the momentum of an object, you must 'do work' on it. If the momentum is increasing toward infinity, then the amount of work required is also increasing toward infinity. Work is a change in energy, therefore, to increase the velocity of an object to the speed of light, you must supply infintie energy.

Not happening.

What about things like the alcubierre drive?

The alcubierre drive is not about going faster than the speed of light, it is about shrinking space. The concept is good, large masses like the sun shrink space or curve space. However, given that the sun only curves space very slightly, the alcubierre drive will require an enourmous amount of energy to have a signifcant effecton the space around it.

Okay, what about time travel?

No, because ... Causality.

Remember above, no two observers may agree about the time of an interaction, but if they can observe it (see notes in the lectures), then they will agree to the events that caused it. This chain of causality is continuous and agreed to by ALL observers. It is a chain of events in spacetime. It is impossible to jump in or out of a chain of causality in spacetime.

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