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04:08The Uncertainty Principle
Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He mathematically...
00:59Uncertainty: Overview
In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
02:49Second Law of Thermodynamics
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
00:59Propagation of Uncertainty from Random Error
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
01:14Probability in Statistics
Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
01:18Principle of Equivalence
According to Albert Einstein (1897-1955), free-falling and feeling weightless are intrinsically linked. If a person were in free-fall under gravity, for example, diving towards the Earth from an airplane, they would feel completely weightless. Similarly, a person descending in a lift may feel partially weightless. Broadly speaking, it is assumed that an object in a uniform gravitational field and an object undergoing constant acceleration in the absence of gravity are under the same...
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Curious and sublime: the connection between uncertainty and probability in physics.
1Faculty of Philosophy, University of Oxford, 10 Merton Street, Oxford OX1 4JJ, UK. harvey.brown@philosophy.ox.ac.uk
Summary
The link between probability and uncertainty in physics may be less certain than previously thought. Quantum mechanics, particularly the Everett interpretation, challenges this long-held assumption, suggesting a tenuous connection.
Area of Science:
- Quantum Physics
- Foundations of Physics
Background:
- The traditional view in physics links probability directly with uncertainty.
- This connection has been a cornerstone of physical theories for centuries.
Purpose of the Study:
- To re-evaluate the fundamental relationship between probability and uncertainty in light of quantum mechanics.
- To explore the implications of the Everett interpretation for this relationship.
Main Methods:
- Conceptual analysis of quantum mechanics.
- Examination of the Everett (many-worlds) interpretation.
- Philosophical inquiry into the nature of probability.
Main Results:
- The Everett interpretation of quantum mechanics suggests probability may not inherently imply uncertainty.
- This challenges the classical understanding of probability in physical systems.
- The role of probability in quantum mechanics might be understood differently.
Conclusions:
- The established link between probability and uncertainty in physics is potentially tenuous.
- Quantum mechanics, via the Everett interpretation, offers an alternative perspective.
- Further investigation is needed to fully understand probability in quantum contexts.