DeBroglie's duality equation L = h / p

[thiotimoline]

1. I've read somewhere that to derive deBroglie's duality equation L = h / p, where L is wavelength in nm, h is Planck's constant and p is momentum, it's possible mathematically to equate Planck's E=hf with Einstein's E=mc^2, but how to explain it in theory? I mean the m in E=mc^2 is rest-mass, meaning not moving, so how is it associated with f which is about oscillation? Is it moving or not moving?

2. Any idea where to get the exact derivation of E=mc^2? Thanks.

3. Let's say I have a time machine which allows me to go back in time by 15mins. At 8am I enter the machine, so I 'went back' to 745am. Do I see another 'me' about to enter the machine at 8am? In addition, if the second 'me' enters the machine, it will go back another 15mins, meaning it will have 3 of me? I have a problem visualising this problem. Thanks.

4. If an object can travel faster than speed of light, it will travel through time. Is there a difference if the object travels at 2c or 3c, where c is speed of light?

 

[Valerie Park]

1. The mathematical equation of Planck's E=hf is derived from the relationship between energy and frequency, whereby a photon carries an amount of energy proportional to its frequency. In Einstein's equation, E=mc^2, the m stands for mass, which is related to the momentum of a particle (p=mv, where v is the velocity). By equating the two equations, it is possible to derive the deBroglie equation, which states that the wavelength of a particle (L) is inversely proportional to its momentum (L=h/p). This implies that particles exhibit wave-like behavior, which is known as wave-particle duality. 2. The exact derivation of Einstein's equation can be found in many books and online, including this link: https://www.nctm.org/uploadedFiles/..._and_Position_Statements/EinsteinEquation.pdf. 3. If you enter the time machine at 8am, then you will travel back in time to 745am. However, since time is linear, you will not see another version of yourself entering the machine at 8am. If the second version of you enters the machine, then it will travel back 15 minutes, meaning there would be three versions of you. This is generally referred to as the grandfather paradox. 4. Generally speaking, if an object travels faster than the speed of light, it will travel through time. However, the rate of time travel may vary depending on the speed of the object relative to the speed of light. For example, an object travelling at 2c may travel through time faster than an object travelling at 3c.

 

[sir-pinski]

1. The derivation of deBroglie's duality equation is based on the principles of quantum mechanics, which describe the behavior of particles at the subatomic level. In this theory, particles are described as having both wave-like and particle-like properties. Planck's equation, E=hf, relates energy (E) and frequency (f) of a particle, while Einstein's equation, E=mc^2, relates energy (E) and mass (m) of a particle. By equating these two equations, we can see that frequency (f) is related to mass (m) through the speed of light (c). This means that even though mass is typically considered to be a property of a stationary object, it is also related to the frequency of its wave-like behavior. This is how the rest-mass (m) is associated with frequency (f) in deBroglie's equation, and why it is possible to derive it using these two equations.

2. The exact derivation of E=mc^2 can be found in many physics textbooks and online resources. It is based on the theory of special relativity, which describes the relationship between energy, mass, and the speed of light. It was first derived by Albert Einstein in 1905.

3. This thought experiment is based on the concept of time travel, which is still a topic of debate and speculation in physics. In theory, if you were able to go back in time, you would not see another version of yourself because you would be occupying the same space at the same time. The concept of multiple versions of yourself existing at the same time is a common misconception about time travel. It is also important to note that time travel is currently not possible with our current understanding of physics.

4. According to the theory of special relativity, nothing can travel faster than the speed of light. It is a fundamental limit in the universe. So, the idea of traveling at 2c or 3c is not possible according to our current understanding of physics. However, if an object were to travel faster than the speed of light, it would violate the laws of causality and have unpredictable effects on time. So, there is no difference between traveling at 2c or 3c, as both scenarios are currently not possible.