# How many subjects are there in modern physics

## introduction¶

### Sizes and units¶

Units of measurement play an important role in physics:

- Every physical quantity corresponds to a measurable property of an object or state, for example length, mass, time, speed, energy, temperature, etc.
- Every physical quantity is made up of a numerical value and a unit of measurement:

Physical quantities are usually designated with Latin or Greek letters in italics, whereas units should be written in non-italics for visual differentiation. In the formula display one writes for a quantity also the following:

For example, if the physical quantity is mass of an object so is if the mass is given in the unit “kilograms”. Weighs the object Kilograms, that's how it is for this object ; so overall you can in this case write (the mal symbol between numerical value and unit is usually not written explicitly).

- Quantities can only be added or subtracted if their units match. First of all, individual units may have to be converted accordingly.
- Sizes can always be multiplied with one another or divided by one another. The result is obtained by applying the calculation rule both to the numerical values and to the units of the individual quantities.

*Examples:*

Scalar and vector quantities

Some physical quantities, for example mass and temperature, do not have a preferred spatial direction, so their effect is the same in all spatial directions. By specifying *one* Such so-called “scalar” quantities are adequately described by the numerical value and the associated unit of measurement.

Scalar quantities are, for example, mass, temperature, volume, electrical charge, and others.

Other physical quantities, such as force and speed, always have a clear direction in space. Such quantities are represented in drawings by arrows (vectors), in physical formulas by a small arrow above the formula symbol. In three-dimensional space, too, are ultimately *three* Numerical values and the associated unit of measurement are necessary to adequately describe the physical effect of these so-called "vectorial" quantities in the respective spatial directions. [2]

Vector quantities are, for example, force, acceleration, speed, and others.

International units

By using clearly defined units of measurement, measurement results can also be reproduced and compared at a different time, in a different location and / or in a different language.

In 1960, at a symposium, the following seven units were defined as the international system of units :

From these seven "SI units", the other units (which are also relevant in practice) can only be derived by means of multiplication or division.

An overview of units recognized in Germany and internationally and their conversions is available free of charge as a brochure (PDF) from the Physikalisch-Technische Bundesanstalt.

Powers of ten

Depending on the subject of investigation, the numerical values of measurement results can differ by several orders of magnitude - for example, a planet has a considerably greater mass than a single atom, and an insulator has an electrical resistance many times greater than a conductor. In order to still be able to use the usual units of measurement - for example to indicate the mass of a body in kilograms - so-called “powers of ten” have been introduced for the sake of clarity. The following applies here, for example:

The last expression was set arbitrarily; however, this definition has the advantage that the number of zeros in the result can be read off directly from the exponent.

When specifying powers of ten, negative exponents are also common, for example:

Instead of one could too write, the minus sign in the exponent only indicates that the respective (tens) power is in the denominator. [3] The number in the exponent indicates how many zeros appear in the result; the comma must be placed after the first zero.

There are linguistic abbreviations for the individual powers of ten, for example the prefix “kilo” stands for the factor respectively ; so you can, for example, for also write. Some of these potencies are listed in the table below.

A major benefit of powers of ten is that they are based on the relationship just have them offset against each other. For example, to specify a length of decimetres in millimeters to convert, it is sufficient to include the respective numerical value to multiply. Many pocket calculators even have their own key for this purpose, the one with or is marked with, and can save some typing. [4] By using powers of ten, you don't have to "push the comma" (including the possible source of error that a zero is overlooked).

Another benefit to using powers of ten is that because of the relationship It is also easy to convert square or cubic units: You replace the respective prefix with the respective power of ten, and then exponentiate both the unit and the prefactor.

*Examples:*

How many square millimeters are equal to one square meter?

For the conversion between and applies:

Thus, for one square meter:

When converting, the unit to be converted was first put in brackets and the prefix of ten was replaced by the corresponding power of ten; then both the power of ten and the unit were squared.

What fraction of a cubic meter is a cubic centimeter?

For the conversion between and applies:

Thus, for one cubic meter:

The conversion in the other direction works in the same way; the "conversion factor" remains the same, the exponent of the power of ten then only has the opposite sign.

Measurement error

Physical measurements are made by comparing the size to be measured with a scale calibrated in the corresponding unit (meter stick, scale, thermometer, voltmeter and ammeter, etc.). Electrical measurement methods are often used, which make the measurement results easy to read by means of digital displays.

However, it must always be noted that the measured values determined can be incorrect. A basic distinction is made between systematic and random ("statistical") measurement errors:

*Systematic*Errors result from incorrectly set measuring equipment. For example, if a thermometer is incorrectly calibrated, the temperature displayed will inevitably deviate from the actual temperature.Systematic errors occur again with every repeated measurement; they often ensure a constant deviation from the actual value (if, for example, the scale of a ruler with instead of begins).

*Statistical*Errors can be traced back to fluctuations in the size to be measured in punctual measurements with measuring sensors, measuring delays and reading inaccuracies (with non-digital displays) or inaccurate electronic sensors (with digital measuring devices).

The following applies to each individual measurement:

or shorter:

Such an explicit representation of a measurement result ultimately represents a probability statement. This usually means that the actual value has a probability of within the interval is located.

Systematic errors occur again with every measurement; they can be minimized and sometimes even completely avoided by clever experimental methods. Accidental mistakes can never be completely avoided; one tries to keep them as low as possible through repeated measurements and statistical methods.

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