Would you, especially physicists, further explain this formula?

Question

dS = Sqrt( (dx)2 + (dy)2 + (dz)2 + c(da)2 )
I just want to learn more about relativity, I love Physics!

Answer 1

It looks like a different version of the formula defining the relativistic 'interval' between two points (events in spacetime):

ds² = dx² + dy² + dz² - c²dt² (c = the speed of light)

This formula, called the 'metric', defines the 'interval' between two points. The 'interval' in 4-dimensional spacetime is the quantity analogous to the distance between two points in the 3D space we are familiar with. The 'd' symbol indicates 'differential', meaning that the two points are close together, strictly, infinitesimally close together.

Recall that distance r in flat, 3D Euclidean space is defined by:

dr² = dx² + dy² + dz²

So in the flat, 4D space of (special) relativity:

ds² = dr² - c²dt² i.e. interval² = (spatial distance)² - c² (time difference)²

The negative sign in front of the time term means that there can be (and are) points in 4D spacetime with finite 3D distance separating them, that have zero 4D interval separating them. This is different from regular 3D space, where the only way to have zero distance between two points, is to have the points coincident ('on top of each other').

This zero-interval condition is true if and only if dr = c dt, i.e. if and only if c = dr/dt, i.e. if and only if the two points can be connected by a beam of light.

Another way of thinking about this zero-interval condition is that two points separated in space, that can be connected by a beam of light, are 'on top of each other' in 4D spacetime, because they have zero interval separating them.

So consider a photon that happened to leave the Andromeda Galaxy 2 million years ago (and 2 million light years from Earth) and entered your eye one night as you gazed up into the sky, and was absorbed in your retina. Those two events (points in spacetime) share a photon: The emission of the photon in Andromeda Galaxy, 2 million years ago, and the absorption of that same photon in your eye, that evening. Therefore for these two events dr = c dt and therefore these two events have zero interval (zero '4D distance') between them, and so relativistically speaking, are 'right on top of each other'. Your eye was literally 'touching' the Andromeda Galaxy that night.

The interval separating two points, unlike the distance or time separating two points, is invariant and will be observed to be the same for observers in all locations and in all states of motion. Analogously, in 3D space, the distance between two points is invariant, although the component x, y and z coordinate differences between two points can be different for observers with different (x,y,z) coordinate systems.

The invariance of the 4D spacetime intervals separating events, and the relative nature of the spatial and temporal coordinates of events (which depend on the state of motion of the observer), is what Hermann Minkowski was referring to when he said that, after Relativity: "Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."

It's the interval between two events, not their separation in space or time, which is the same for all observers and therefore objectively real. Space and time coordinates for events in spacetime are subjective, and depend on the viewpoint (location and motion) of the observer, but the intervals separating events are objectively real, and are calculated to be the same for all observers.

Relativity does NOT say that 'everything is relative', and therefore that objective reality does not exist.

Rather it says that we all have our own points of view, and that these differing views of one reality (differing coordinate systems describing space and time) can be related to each other objectively in well defined ways through the Lorentz transformation equations.

Answer 2

THE physicists do`nt ecplain the relativity cose no one sponsores resurches on a blind hunt ennymore.
and while the same theory make the constant C (speed of light) it self relative. als:
dS = Sqrt( (dx)2 + (dy)2 + (dz)2 + c(da)2 )

dS = Sqrt( (dx)2 + (dy)2 + (dz)2 + (Sqrt( (dx)2 + (dy)2 + (dz)2 + c(da)2 ))(da)2 )


and thenn again:

dS = Sqrt( (dx)2 + (dy)2 + (dz)2 + (Sqrt( (dx)2 + (dy)2 + (dz)2 + (Sqrt( (dx)2 + (dy)2 + (dz)2 + c(da)2 ))(da)2 ))(da)2 )
whair the C is C in C whair the C in C is Sqrt( (dx)2 + (dy)2 + (dz)2 + c(da)2 ) whair again c is Sqrt( (dx)2 + (dy)2 + (dz)2 + c(da)2 ).

Answer 3

This appears to be an attempt to represent the metric of interval in spacetime. Spacetime was introduced by Minkowski who realized that the apparent differencies in time and space that observers moving with respect to each other see can be resolved by taking the interval between events as a combintation of space and time, rather than each separately. In ordinary three-dimensions we consider the interval between events to be defined by their separation in space plus their separation in time, expressed as

s^2 = x^2 + y^2 + z^2 (space interval) and t (time interval)

The Minkowski interval replaces this with a new interval defined as:

s^2 = x^2 + y^2 +z^2 - (c*t)^2 where c = light velocity.

When moving observers apply that measurement to the same events, they will agree on the result. If they consider the space and time separately, they will not agree. Therefore the conclusion that events exist in a four-dimensional world which is real, but our observations of that world are incomplete.

Answer 4

how old are you definitely reply me. i am a physicist. only then according to your level would i reply to you. write to me on [e-mail]

Answer 5

hmmmm.....

actually i dont have an answer