Personal identity (Metaph.), the persistent and continuous unity of the individual person, which is attested by consciousness. - Dictionary.com

How can we prove that we are the same person a minute or even second in the future when time is constantly changing and actions or words, thoughts and memories are changed as time progresses.

The problem of memory:
As I age and time continues the memories of the past become vague and unclear. Sometimes my memories are even the the point of irrational when I've filled in the missing spaces with things that make sense to keep the story in a flow without consciously meaning to. If I do not remember my younger self, Is It I who was living then? In the moments of my life where I periodically take actions that are not true to myself, without recalling them, was it my true self or identity that has committed these such actions? A photograph exists where I am painting but, I've never painted a portrait in my life.

The Problem of Thought:
I never seem to remember my thoughts that I have had five minutes ago, therefore is my need to write everything down. Could thoughts possibly make up a persons identity? Add in a new piece of information that can alter your mind or opinion in a split second. Your thoughts have changed. Your identity has changed.

The Problem of Actions:
Much similar to the problem of thought, it's also changing with time. Just because you have choose to walk instead of drive, does this factor into your identity. An Action that counteracts with your cognitive thought, an incompatibility and everything is thrown off.

The Split-Brain.
Our brains are split into two independently working hemispheres. So scientifically speaking, which hemisphere of your brain gives you identity? Is it both? no, It is none.

We do not have personal identity.
We follow the social contract and live according to our actions of today and haunting of the past based on the need for a workable society.

Therefore I am nothing.