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Shift vector in x axis (Lorentz boost)

vanessatse (27)
The rest of my code seem to work alright without the section on the "Lorentz boost". I'm not sure how I should approach this - I have to shift my 4-vector by "boosting it". Am I on the right track? - what should I return in the Boost function and how should I call it in the main? Thanks!


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#include<iostream>
#include<cmath>
using namespace std;

//=============================================================================
//Vector 3
//=============================================================================

class Vector3
	{
		// Friends 
		//Prototypes overloading of << operator
		friend ostream & operator << (ostream &os, const Vector3 &v3);
		
	protected:
		double x; double y; double z;
		
	public:
		double xi; double yi; double zi;
		
		//Default constructor
		Vector3(){x=y=z=0;}
		
		//parameterised constructor
		Vector3(double xi, double yi, double zi)
		{x=xi; y=yi; z=zi;}
		
		//destructor
		~Vector3(){};
		
		//Acessor functions
		double Getx() const {return x;}
		double Gety() const {return y;}
		double Getz() const {return z;}
		
		//Scalar product function
		double scalar(Vector3 v3) const
		{
			double temp;
			temp=x*v3.Getx()+y*v3.Gety()+z*v3.Getz();
			return temp;
		}
		
		//Overload () operator
		Vector3 operator() (double a, double b,double c)
		{return Vector3(a,b,c);}
	};

//Overload << operator for Vector3
ostream & operator<<(ostream & os, const Vector3 &v3)
{
	os<<"("<<v3.Getx()<<","<<v3.Gety()<<","<<v3.Getz()<<")"<<endl;
	return os;
}
//=============================================================================
// Vector 4
//=============================================================================

//Overload << operator for Vector4
class Vector4 : public Vector3
	{
		friend ostream & operator<<(ostream & os, const Vector4 &v4);
		
	protected:
		double a; double b; double c; double ct;
		
	public:
		double ai; double bi; double ci; double cti;
		
		//Default constructor
		Vector4(){a=b=c=ct=0;} 
		
		//Paramaterised constructor
		Vector4(double ai, double bi, double ci, double cti) 
		{a=ai; b=bi; c=ci; ct=cti;}
		
		~Vector4(){}; //destructor
		
		//Accessor functions
		double Getx(){return a;}
		double Gety(){return b;}
		double Getz(){return c;}
		double Getct(){return ct;}
		
		//Scalar product function
		double scalar(Vector4 v4) const
		{
			double temp;
			temp=a*v4.Getx()+b*v4.Gety()+c*v4.Getz()+ct*v4.Getct();
			return temp;
		}
		
		//Lorentz boost functions
		double Boost(Vector4 v4) const
		{
			double Beta; double Gamma; 
			double BOOSTct; double BOOSTx; double BOOSTy; double BOOSTz; 
			double const LightSpeed=3e8; double const Velocity=2.8e8;
			Beta=Velocity/LightSpeed;
			Gamma=1/sqrt(1-Beta*Beta);
			BOOSTct=Gamma*(ct-Beta*a);
			BOOSTx=Gamma*(a-Beta*ct);
			BOOSTy=b;
			BOOSTz=c;
			
			
		}
		
		//double scalar
		
	};

ostream & operator << (ostream & os, Vector4 &v4)
{
	os<<"("<<v4.Getx()<<","<<v4.Gety()<<","<<v4.Getz()<<","<<v4.Getct()<<")"<<endl;
	return os;
}

//=============================================================================
int main(void)
{
	Vector3 v1;
	cout<<v1<<endl;
	
	Vector3 v2(1,2,3);
	cout<<v2<<endl;
	
	Vector3 v3(10,11,12);
	cout<<v3<<endl;
	
	cout<<"Scalar product of Vector 2 and 3:"<<endl;
	cout<<v2.scalar(v3)<<endl;
	
	
	Vector4 v4(2,3,4,5);
	cout<<v4<<endl;
	
	Vector4 v5(6,7,8,9);
	cout<<v5<<endl;
	
	cout<<"Scalar product of Vector 4 and 5:"<<endl;
	cout<<v4.scalar(v5)<<endl;
	

	
}
closed account (D80DSL3A)
I'm not sure what you mean by "boost". 4-vectors can be added just as 3-vectors can be, element by element. Perhaps your Boost function should return the sum of two Vector4 objects?
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Vector4 Boost(Vector4 v4) const
{
    return Vector4( a+v4.a, b+v4.b, c+v4.c, ct+v4.ct);
}

It looks like you are applying a Lorentz transformation there currently, but to what?

I think your scalar() function calculation is wrong. Squared length is:
temp=ct*v4.Getct()-( a*v4.Getx()+b*v4.Gety()+c*v4.Getz() );

Other problems with your code. You have multiple duplication of data members (x,y,z:xi,yi,zi) in the Vector3 base class. What are xi,yi,zi for?
You then add another full set of coordinates in the Vector4 class (a,b,c,ct:ai,bi,cti) instead of using the xi,yi,zi inherited from Vector3.
I'm not sure what a call to getX() would get you. There is a version of getX() in each class, but they are non-virtual, differing only in their const-ness on the calling object. If the const (base) version gets called it will return the uninitialized value of x for a Vector4 object. Quite messy.
vanessatse (27)
I've added this to the Lorentz transformation part. But i'm not sure what to return after this function. I need a vector to be returned but my function only returns a double, right?


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		double LorentzTransformation(Vector4 v5) const
		{
			double Beta; double Gamma; 
			double TRANSct; double TRANSx; double TRANSy; double TRANSz; 
			double const LightSpeed=3e8; double const Velocity=2.8e8;
			Beta=Velocity/LightSpeed;
			Gamma=1/sqrt(1-Beta*Beta);
			TRANSct=Gamma*(v5.Getct()-Beta*v5.Getx());
			TRANSx=Gamma*(v5.Getx()-Beta*v5.Getct());
			TRANSy=v5.Gety();
			TRANSz=v5.Getz();
		}
closed account (D80DSL3A)
OK. I think you're trying to apply the transformation to the calling Vector4 object (4-vector in unprimed frame) to produce the 4-vector in the primed (observers) frame of reference. The needed parameter would be the relative velocity between the reference frames. If the relative motion is along the x-axis only then a double would do.

It's been a lot of years since I studied relativity (college years), but here's my next guess at what you're looking for:
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// transform applied using the calling Vector4 object (this).
Vector4 LorentzTransformation(double v) const// v is relative velocity along the x-axis.
{
    const double LightSpeed=3e8;// defining constant    
    double Beta = v/LightSpeed;
    double Gamma = 1/sqrt(1-Beta*Beta);

    // apply transformation and return result vPrime
    Vector4 vPrime;
    vPrime.ct = Gamma*( Getct()-Beta*Getx() );
    vPrime.a = Gamma*( Getx()-Beta*Getct() );
    vPrime.b = Gety();
    vPrime.c = Getz();
    return vPrime;
}

EDIT: comments in code.
Also, in review I see the term 'boost' is appropriate. Your function name was fine.
Last edited on
vanessatse (27)
Thank you for your help. I had to remove the "const" after "Vector4 LorentzTransformation(double v)" in order to remove the error that popped up. Is that still ok?

Then I tried calling the function in my main but I am having trouble here.

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double a; double v;
	a=v4.LorentzTransformation( v);
	v=1.2;
	cout<<"Lorentz transformation of Vector 5:"<<v4<<endl;

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