Newtons Law

[Bettina]

I was on a game forum and someone raised the issue that Newtons law of gravity is not a law anymore because of "Minkowski's Space". I said it was still a law and when I googled it everywhere I still see Newtons law of gravity as still a law. Is it still?

 

Bettina

[J.C.MacSwell]

I was on a game forum and someone raised the issue that Newtons law of gravity is not a law anymore because of "Minkowski's Space". I said it was still a law and when I googled it everywhere I still see Newtons law of gravity as still a law. Is it still?

 

Bettina

 

I think that in the strictest scientific sense it is not, although 400 years from now it will still be taught as Newton's Law of Gravity.

 

Law or not, you still have to obey it here on Earth!

[swansont]

I think that in the strictest scientific sense it is not' date=' although 400 years from now it will still be taught as Newton's Law of Gravity.

 

Law or not, you still have to obey it here on Earth! [/quote']

 

 

In the scientific sense a law is a simple relationship that has been observed to hold under certain conditions. It's still a law.

[CPL.Luke]

besides minkowski space doesn't have gravity

[J.C.MacSwell]

In the scientific sense a law is a simple relationship that has been observed to hold under certain conditions. It's still a law.

 

In that case it's permanently a law...

 

 

But if we are "fast" enough we can break it!

[MetaFrizzics]

Newtonian Gravitation is passe'.

The latest thing is Relational Mechanics.

[5614]

So is Minkowski's Space a:

1) Hypothetical area where there is low gravity

or

2) A real place which is a significant distance from the nearerst body, meaning low gravity?

or

3) A very small area?

[timo]

or

4) The spacetime of special relativity? (just added this so that you have a correct answer to chose from, even though the statement Bettina found doesn´t make much sense, then).

[5614]

I thought that Minkowski's Space wasn't everywhere due to the amount of gravity... so where might you find this flat spacetime of special relativity? Because I thought it can't be everywhere due to gravity, or the amount of gravity.

[timo]

There is no gravity in special relativity, that´s my point. Newtonian mechanics violates special relativity because of it´s instantaneous changes in the gravitational field (the time between cause and effect is not limited by the speed of light).

[MetaFrizzics]

I thought that Minkowski's Space wasn't everywhere due to the amount of gravity... so where might you find this flat spacetime of special relativity? Because I thought it can't be everywhere due to gravity, or the amount of gravity.

True: Minkowski Spacetime is Special Relativity, which is an Electromagnetic theory having a flat metric. It is considered the 'local' spacetime embedded in General Relativity, which is supposed to handle the slight curvature of space over vast distances (usually). Spacetime is only significantly bent over short distances near massive objects like black holes or suns.

 

So here, 'locally' means any distance smaller than Solar-System spans, and the 'big picture' means orbital distortion around massive objects like the sun.

[Severian]

I was on a game forum and someone raised the issue that Newtons law of gravity is not a law anymore because of "Minkowski's Space". I said it was still a law and when I googled it everywhere I still see Newtons law of gravity as still a law. Is it still?

 

Bettina

 

Newton's Law of gravity is non-relativistic' date=' which means that it is not compatible with special relativity. It will not hold for objects travelling at high speeds relative to each other, but is a good approximation for objects which travel slowly (so Newton's apple is fine).

 

Part of special relativity is the introduction of space-time, unifying space and time together by saying that any event can be specified by its co-ordinates (c*t,x,y,z) where t=time, (x,y,z)=usual space co-ordinates and c is the speed of light (included to make the dimensions work).

 

The 'distance' between two events (0,0,0,0) and (c*t,x,y,z) (I put one of them at the origin for simplicity) is simply given by a rule called the 'metric'. Euclidean space-time has the most obvious 'distance' to choose, namely

 

c[sup']2[/sup]t²+x²+y²+z²

 

which is sort of analagous to a distance in 3d space: x²+y²+z². Unfortunately(?) this rule is not compatible with special relativity, since the distance changes depending on how fast the observer moves. We really want a rule for distance which is not dependent on what the observer is up to.

 

Minkowski space-time is a space time which has such a distance rule (metric). In Minkowski space, the space-time separation of the two events is

 

c²t²-x²-y²-z²

 

Notice the minus signs. It is this metric which defines what we mean by Minkowski space.

 

So far this has nothing to do with gravity, except to note that Newton's law isn't compatible with the Minkowski metric. However, Einstein's General Relativity was an attempt to make a law of gravity which is compatible with special relativity's principles. In GR, the presence of energy/mass actually changes the metric itself - it changes the rule by which we measure distance, and this makes it look like there is a gravitational force (even though things are really travelling in straight lines).