becaz alpha testing related to acceptence testing, so, 
accepting testing is done infront of client or customer for 
there acceptence. ok, got it .....

Alpha Testing is nothing but Acceptance testing.
So in Alpha testing the Client has to verify 
 The Product is developed according to their 
1.Requirement and Specification.
2.SLA(Service Level Agreement) i.e 
Time Line 
3.DRE (Defect Rate Efficiency)<0.8
DRE = DRE=A/A+B = 0.8
A = Testing Team (Defects by testing team)
B = customer     (    "    "    customer   )
If DRE <=0.8 then good product otherwise not.

If client is missing any thing and they are giving a green 
signal to the product then later on if they are getting any 
error then the product has to come in a new cycle again.

In alpha testing, there in no need of customer. Customers 
are required in beta testing.

Alpha testing is a part of User Acceptance tesing. So 
Customer Side  people are invited for " to provide to the 
customer the feel of the software".

No body invites customer people in alpha testin.Only It is 
done by cusotomer like environment but client will check 
that application weather it is meetingall of their 
requiremens or not.Later testing will be done in real 
customer site with customer people to assess how it is 
working it is called beta testing.

Alpha testing is the one of User Acceptance Testing.
We can conduct user accptanc etesting in 2 ways 1 is alpha 
testing and the other one is beta testing.

Alpha testing is simulated or actual operational testing by 
potential users/customers or an independent test team at 
the developers' site. Alpha testing is often employed for 
off-the-shelf software as a form of internal acceptance 
testing, before the software goes to beta testing.[citation 
needed]