What is called the uniformity of space time, and what does space time uniformity mean

The so-called spatial uniformity means this: (after you select a reference frame), if you measure it at different positions in the reference frame, its length is the same, for example, if you measure its length in this place in x=1, y=0, z=0, and you measure it in another place, where the coordinates are x=2, 1, 0, then its length is also in meters. This means that it is spatially homogeneous.

The so-called time uniformity means that the passage of time is uniform, and it does not say that time passes faster and faster or slower, for example, you measure the period of a single pendulum an hour ago, whether it is seconds, and after an hour, measure the period of a single pendulum, or seconds.

The so-called linearity of space is the uniformity of space in practice, so to speak, and the homogeneity of space is the meaning, for example, if you take a meter ruler and rotate it 30 degrees in a certain direction, it is still one meter. That's what it means. It means that the nature of space is the same in all directions.

Spatiotemporal uniformity, which requires that the coordinate transformation between two reference frames that do uniform linear motion is a linear transformation, i.e., there is only one relationship (i.e., a linear relationship). x is just with x'x= (x'+vt') x'= (x-vt) i.e. there is a coefficient in front of the transformation coordinates. When we find this coefficient, we find its transformation relation.

Finally, it explains why spatiotemporal uniformity requires that the transformation be linear, because the assumption is not a linear relationship, such as a quadratic relationship, that is, x and x'is proportional to the quadratic of , then there is x'=k*x*x+kvt'where k is the coefficient of scale, in the x-coordinate system, put it on the x-axis, we measure a meter ruler with its two endpoints x1 and x2 respectively, and then in another coordinate system where it does a uniform linear motion along the x-axis, it has been assumed that x1 is assumed according to the assumption'=k*x*x+kvt' x2'=k *x2 *x2+kvt'Get it to be x2 in length'-x1'=k(x2*x2-x1*x1), obviously if the position of x1 is different when it is placed for the first time, then the length of the pen measured in the second coordinate system is also different, which is not consistent with the uniformity of space-time.

Of course, this is not a strict proof, but I just want to give you an example of why the space-time uniformity requires the transformation to be linear, and if it is a linear transformation, then it is obtained in another coordinate system x2'-x1'=k(x2-x1)。where x2-x1=1, so x2'-x1'=k is a constant, and it doesn't matter if you put a ruler on **.

The core of special relativity kinematics is the Lorentz transform.

With these two new axioms, the very important Lorentz transform relation is derived very naturally. Discuss the role of a photon emitted from t=0 x=0 in the system and 'system (at t=0 'the system coincides with the system and later ' moves in the x-axis direction with v. ), according to:

1. Spatiotemporal uniformity: x= (x'+vt')

2. Principle of relativity: x'= (x-vt).

3. The principle of invariance of the speed of light: x=ct

x’=ct’

Among them: the condition of space-time uniformity is not a new principle, a fixed object placed in any position in space is the same length at any time, which is very intuitive, from simple reasoning can know that the coordinate transformation of uniform space-time is linear. Because if as:

x=ax'2+bt', then the length of an object is measured at any moment (dt'=0): dx=2ax'dx'It can be seen that placing any dx in the system in a different x' is a different length for the system.

That is, the space is uneven, which is counterintuitive. Since 'and is equivalent, ' is changed to 'has x= (x'+vt'), then there must be x'= (x - vt) when the system changes to ', so it can be seen that the principle of relativity is fair to different inertial frames. Finally, the two relationships given by the principle of invariance of the speed of light seem incomprehensible, but they are supported by experiments.

Solving the 4 equations in this way immediately gives and Lorentz transform:

Department Department 'Department.

x=γ(x’+vt’) x’=γ(x - vt)y=y’ y’=y

z=z’ z’=z

t= (t'+vx' c2) t'= (t-vx c2) The Lorentz transform unifies space-time and motion, and unifies the high-speed world and the low-speed case of classical mechanics. When v <

Space-time uniformity means that there is no bending, like the density of a glass of water.

Linearity means that the equation of space is temporary.

Isotropy means that it is the same up and down, left and right, and there is no difference.

Uniform explanation.

1) [even;well-distributed;uniform] The number of parts of things is the same distribution Uniform rain (2) [regular] Zheng Xian The interval of time is equal Breathing evenly Detailed explanation (1).It means that the distribution of the number of parts of a thing is equal. "The Surprise of the First Moment" Volume 25:

In the past three years, I have accumulated a certain amount of surplus funds, and you and I have divided the source evenly into two parts. You took one point, and you sent it to Panu for me. Ye Shengtao, "Diaphragm Yi and Him":

The sound of the pendulum is exceptionally crisp , producing an even tone. ” 2).Refers to proper sparseness.

Qing Li Dou "Yangzhou Pure Cong State Painting Boat Record Hongqiao Record": calligraphy moist, flesh and bone even. ”

The word decomposition mean mean , and by extension, harmonize: equilibrium. Neck and neck.

Average. All, all, all of them are safe. The unit of measurement in the Han Dynasty in China was equal to 2,500 stones.

Ancient with "rhyme", harmonious sound. Junzhong Ancient musical instrument. Ancient Tong "Jun", the wheel of the pottery.

Explanation of uniform uniform ú average, so that average: uniform. Symmetry (坣).

Draw one out and give it to someone else or do something else: Mix (give a portion to someone else). Spread evenly.

Radical : 勹.