- #1

- 31

- 0

if the boost rotates an object more into the time dimension, ywo things happen:

it's velocity increases.

it's length contract in the direction of its motion.

does this make sense?

thanks!

- Thread starter jrrship
- Start date

- #1

- 31

- 0

if the boost rotates an object more into the time dimension, ywo things happen:

it's velocity increases.

it's length contract in the direction of its motion.

does this make sense?

thanks!

- #2

- 13,005

- 554

Daniel.

- #3

- 31

- 0

Where are the best resources that talk about boosts?

Thanks!

- #4

- 142

- 0

You may want to have a look at https://www.physicsforums.com/showthread.php?t=103977" on Euclidean Special Relativity in the Independent Research forum. In Euclidean relativity (which is **not** generally accepted by the way and is inconsistent in some details with standard relativity) boosts are indeed rotations in 4D space-time.

Rob

Rob

Last edited by a moderator:

- #5

- 31

- 0

So does that mean that a boost in the x direction means that the object is rotated more into the t direction--does it mean that it has a greater t component, and a smaller x component? is that why it appears shorter?

Where are the best resources that talk about boosts?

Thanks!

- #6

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 956

Could someone please define the word "boost" as it is used here. I don't recognize it.

- #7

- 31

- 0

The way I see it, a "boost" is a rotation in four dimensional space-time.

- #8

- 682

- 1

i don't think it is a real rotation, it's just that if you treat the rapidity like an angle, the Lorentz transformation in terms of rapidity is similar to the equation of rotating except sin becomes sinh and cos becomes cosh (in terms of hyperbolic function).

well, I guess the lorentz transformation does preserve dot product and the determinate does indeed come out to 1... I guess you can call it a rotation in terms of linear algebra.

well, I guess the lorentz transformation does preserve dot product and the determinate does indeed come out to 1... I guess you can call it a rotation in terms of linear algebra.

Last edited:

- #9

Chris Hillman

Science Advisor

- 2,345

- 8

No, but boosts and rotations are linear transformations acting on Minkowski spacetime, in fact Lorentz transformations.is a boost a rotation of a four vector?

Boosts are analogous to rotations but they are not rotations (at least, not in real Lorentzian manifolds).

You can try the textbook by Tristam Needham, Visual Complex Analysis, which happens to have a very nice discussion of the Lorentz group and its Moebius action on the celestial sphere.

- #10

- 31

- 0

A boost, acting on an object, takes a component out of the spatial dimensions and gives it a greater presence in the time dimension.

Hence it appears shorter as it moves.

Is this not true?

- #11

Chris Hillman

Science Advisor

- 2,345

- 8

1. "takes a component out of the spatial dimensions": you probably are thinking of a spacelike hyperplane element and using a boost to boost a vector lying in some an element so that it points out of the hyperplane,

2. "gives it a greater presence in the time dimension": you probably mean "increases its time component".

3. "it appears shorter": "appearance" is tricky in this context. If you mean "visual appearance", this would not be obtained by a simple Lorentz transformation.

- #12

- 31

- 0

A boost that reduces an object's spatial component in the x direction increases its time component.

This is true, right?

Thanks!

- #13

Chris Hillman

Science Advisor

- 2,345

- 8

- #14

- 31

- 0

You say,

"Boosts are analogous but behave a bit differently."

How?

"Boosts are analogous but behave a bit differently."

How?

- #15

- 142

- 0

Perhaps you should have a look at Euclidean SR after all (e.g. http://www.euclideanrelativity.com/simplified/index.htm#four" [Broken]). I'm sure you'll find it interesting, despite it being non-mainstream. Sorry for insisting.A boost that reduces an object's spatial component in the x direction increases its time component.

Rob

Last edited by a moderator:

- #16

Chris Hillman

Science Advisor

- 2,345

- 8

jjrship, you asked how boosts differ from rotations. Well, as I said, both boosts and rotations (acting on Minkowski spacetime) are special cases of Lorentz transformations. (There are many "loxodromic" LTs which are neither a boost or a rotation, but can be built up from boosts and rotations by composition of transformations.) All Lorentz transformations have the property that they always transform a spacelike, null, or past/future pointing timelike vector to a spacelike, null, or past/future pointing timelike vector respectively. Now, a rotation can "turn a spacelike vector all the way around in space", so that through any event in any small neighborhood there exist circles, closed spacelike curves. But a boost cannot "turn a future pointing timelike vector around to become past pointing timelike vector"; closed timelike curves do

- #17

- 5,699

- 990

This may be helpful: google spacetime trigonometry (shameless plug?)

- Last Post

- Replies
- 14

- Views
- 3K

- Last Post

- Replies
- 10

- Views
- 3K

- Last Post

- Replies
- 2

- Views
- 1K

- Last Post

- Replies
- 35

- Views
- 7K

- Replies
- 2

- Views
- 4K

- Last Post

- Replies
- 4

- Views
- 269

- Replies
- 85

- Views
- 10K

- Replies
- 3

- Views
- 1K

- Replies
- 2

- Views
- 2K

- Replies
- 2

- Views
- 754