How can you apply Einstein's time dilation formula to radioactive decay?

Question

Determination of earth's age based on radioactive decay is really an Einstein time dilation phenomena?

Answer 1

I guess you want to calculate the average lifetime of a particle, which undergoes a radioactive decay, if this particle is moving with velocity v relative to the observer.

In this case simply apply the formula for the time dilation to the lifetime in it's rest system:

t' = t/sqrt(1-v^2/c^2)

Answer 2

When a particle with the potential to decay (such as a neutron) is accelerated, it's half-life will become longer, i.e. when you consider a lot of fast-moving neutrons, the average time to decay is longer than when you consider a similar batch of neutrons at rest. This is because their "internal clock" moves slower, as predicted by the speciel theory of relativity.

Answer 3

it extremely is an instantaneous quote Einstein mentioned! "It substitute into, of course, a lie what you learn my religous convictions, a lie it extremely is being systematically repeated. i do no longer think in a private God and that i've got by no potential denied this yet have expressed it of course. If something is in me which may be called religious then it relatively is the unbounded admiration for the form of the worldwide as much as now as our technological know-how can demonstrate it."

Answer 4

that's simple. but you're going to need a microwave oven, an spell and speak three rolls of toilet paper and the ability to run around your house counterclockwise really really fast. you got that jack?

Answer 5

Crazy glue?

Answer 6

I don't know the answer to that one, but I do know how to balance a nickel on its side.

Answer 7

The essence of the Special Theory of Relativity is that it connects three distinct quantities to each other: space, time, and proper time. ‘Time’ is also called ‘coordinate time’ or ‘real time’, to distinguish it from ‘proper time’. Proper time is also called clock time, or process time. It is a measure of the amount of physical process that a system undergoes. E.g. proper time for an ordinary mechanical clock is recorded by the number of rotations of the hands of the clock. Alternatively, we might take a gyroscope, or a freely spinning wheel, and measure the number of rotations in a given period. We could also take a chemical process with a natural rate, such as the burning of a candle, and measure the proportion of candle that is burnt over a given period.

Note that these processes are measured by ‘absolute quantities’: the number of times a wheel spins on its axis, or the proportion of candle that has burnt. These give absolute physical quantities, and do not depend upon assigning any coordinate system, as a numerical representation of space or real time does. The numerical coordinate systems we use firstly require a choice of measuring units (meters and seconds, for example). Even more importantly, the measurement of space and real time in STR is relative to the choice of an inertial frame. This choice is partly arbitrary.

Our numerical representation of proper time also requires a choice of units, and we adopt the same units as we use for real time (seconds). But the choice of a coordinate system, based on an inertial frame, does not affect the measurement of proper time. We will consider the concept of coordinate systems and measuring units shortly.

Proper time can be defined in classical mechanics through cyclic processes that have natural periods – for instance, pendulum clocks are based on counting the number of swings of a pendulum. More generally, any natural process in a classical system runs through a sequence of physical states at a certain absolute rate, and this is the ‘proper time rate’ for the system.

In classical physics, two identical types of systems (with identical types of internal construction, and identical initial states) are predicted to have the same proper time rates. That is, they will run through their physical states in perfect correlation with each other.

This holds even if two identical systems are in relative constant motion with respect to each other. For instance, two identical classical clocks would run at the same rate, even if one is kept stationary in a laboratory, while the other is placed in a spaceship traveling at high speed.

This invariance principle is fundamental to classical physics, and it means that in classical physics we can define: Coordinate time = Proper time for all natural systems. For this reason, the distinction between these two concepts of time was hardly recognized in classical physics (although Newton did distinguish them conceptually, regarding ‘real time’ as an absolute temporal flow, and ‘proper time’ as merely a ‘sensible measure’ of real time; see his Scholium).

However, the distinction only gained real significance in the Special Theory of Relativity, which contradicts classical physics by predicting that the rate of proper time for a system varies with its velocity, or motion through space. The relationship is very simple: the faster a system travels through space, the slower its internal processes go. At the maximum possible speed, the speed of light, c, the internal processes in a physical system would stop completely. Indeed, for light itself, the rate of proper time is zero: there is no ‘internal process’ occurring in light. It is as if light is ‘frozen’ in a specific internal state.

At this point, we should mention that the concept of proper time appears more strongly in quantum mechanics than in classical mechanics, through the intrinsically ‘wave-like’ nature of quantum particles. In classical physics, single point-particles are simple things, and do not have any ‘internal state’ that represents proper time, but in quantum mechanics, the most fundamental particles have an intrinsic proper time, represented by an internal frequency. This is directly related to the wave-like nature of quantum particles. For radioactive systems, the rate of radioactive decay is a measure of proper time. Note that the amount of decay of a substance can be measured in an absolute sense. For light, treated as a quantum mechanical particle (the photon), the rate of proper time is zero, and this is because it has no mass. But for quantum mechanical particles with mass, there is always a finite ‘intrinsic’ proper time rate, represented by the ‘phase’ of the quantum wave. Classical particles do not have any correlate of this feature, which is responsible for quantum interference effects and other non-classical ‘wave-like’ behavior.
So far, we have only examined the most basic part of STR: the valid STR transformations for space, time, and proper time, and the way these three quantities are connected together. This is the most fundamental part of the theory. It represents relativistic kinematics. It already has very powerful implications. But the fully developed theory is far more extensive: it results from Einstein’s idea that the Lorentz transformations represent a universal invariance, applicable to all physics. Einstein formulated this in 1905: “The laws of physics are invariant under Lorentz transformations (when going from one inertial system to another arbitrarily chosen inertial system)”. Adopting this general principle, he explored the ramifications for the concepts of mass, energy, momentum, and force.

The most famous result is Einstein’s equation for energy: E = mc². This involves the extension of the Lorentz transformation to mass. Einstein found that when we Lorentz transform a stationary particle with original rest-mass m0, to set it in motion with a velocity V, we cannot regard it as maintaining the same total mass. Instead, its mass becomes larger: m = γm0, with γ defined as above. This is another deep contradiction with classical physics.

Einstein showed that this requires us to reformulate our concept of energy. In classical physics, kinetic energy is given by: E = ½ mv². In STR, there is a more general definition of energy, as: E = mc². A stationary particle then has a basic ‘rest mass energy’ of m0c². When it is set in motion, its energy is increased purely by the increase in mass, and this is kinetic energy. So we find in STR that: Kinetic Energy = mc²-m0c² = (γ-1)m0c²
Many nuclei are radioactive. This means they are unstable, and will eventually decay by emitting a particle, transforming the nucleus into another nucleus, or into a lower energy state. A chain of decays takes place until a stable nucleus is reached.
Conservation of nucleon number means that the total number of nucleons (neutrons + protons) must be the same before and after a decay.

There are three common types of radioactive decay, alpha, beta, and gamma. The difference between them is the particle emitted by the nucleus during the decay process.
Therefore, For low velocities, with: v << c, it is easily shown that: (γ-1)c² is very close to ½v², so this corresponds to the classical result in the classical limit of low energies. But for high energies, the behavior of particles is very different. The discovery that there is an underlying energy of m0c² simply from rest-mass is what made nuclear reactors and nuclear bombs possible: they convert tiny amounts of rest mass into vast amounts of thermal energy.

The main application Einstein explored first was the theory of electromagnetism, and his most famous paper, in which he defined STR in 1905, is called “Electrodynamics of Moving Bodies”. In fact, Lorentz, Poincare and others already knew that they needed to apply the Lorentz transformation to Maxwell’s theory of classical electromagnetism, and had succeeded a few years earlier in formulating a theory which is extremely similar to Einstein’s in its predictions. Some important experimental verification of this was also available before Einstein’s work (most famously, the Michelson-Morley experiment). But his theory went much further. He radically reformulated the concepts that we use to analyse force, energy, momentum, and so forth. In this sense, his new theory was primarily a philosophical and conceptual achievement, rather than a new experimental discovery of the kind traditionally regarded as the epitome of empirical science.

He also attributed his universal ‘principle of relativity’ to the very nature of space and time itself. With important contributions by Minkowski, this gave rise to the modern view that physics is based on an inseparable combination of space and time, called space-time. Minkowski treated this as a kind of ‘geometric’ entity, based on regarding our Equation 1 as a ‘metric equation’ describing the geometric nature of space-time. This view is called the ‘geometric explanation’ of relativity theory, and this approach led Einstein even deeper into modern physics, when he applied this new conception to the theory of gravity, and discovered a generalised theory of space-time.

The nature of this ‘geometric explanation’ of the connection between space, time, and proper time is one of the most fascinating topics in the philosophy of physics. But it involves the General Theory of Relativity, which goes beyond STR.