Either way, NASA is already exploiting it. I guess, next they’ll find a way to glitch through the very fabric of the universe to teleport to a distant galaxy without moving at all or even using any energy.
In short, even though photons have no mass, they still have momentum proportional to their energy, given by the formula p=E/c. Because photons have no mass, all of the momentum of a photon actually comes from its energy and frequency as described by the Planck-Einstein relation E=hf.
But how do you apply this with Lorentz’ transformation (i.e. relativistic factors)? You cannot approach the speed of light without considering relativism. It is known that p = gamma * m * v where p is momentum, gamma is the gamma factor given by sqrt(1/(1-(v^2/c^2))), m is mass and v is velocity. If you study the gamma factor, you’ll realize that it approaches infinite as v approaches c, the speed of light. Since we are actually dealing with light here, where v = c we are breaking the equation. Momentum cannot be defined for any mass which moves at the speed of light. It’s asymptotic at that speed.
Also note that the same goes for E = mc^2. At relativistic speeds, also this equation needs to consider the gamma factor. So those classical equations break down for light.
The answer is that photons don’t have mass, but they have energy. There is a good explanation a bit further up in this thread on how this is possible.
Radiation pressure does not have anything to do with mass-energy equivalence. 1), the energy for this process does not come from the conversion of electric energy into mass, and 2) having a momentum is not a property tied to massive particles. All electromagnetic waves carry momentum according to Maxwell’s theory of electromagnetism, and its transfer is fully explained by his equations and results from the interaction of the EM wave with matter, i.e., absorption and reflection. Each such interaction will transfer momentum to the massive object. This is classical physics, you don’t need any Einstein relativity to explain electromagnetic phenomena because his theories only become relevant for very massive bodies and their movement, and nuclear reactions.
When I saw this reply it had a point score of 0, which means somebody downvoted the post.
When a user is freely admitting a lack of expertise, and defers to another user who seems to know better, I would say it’s extremely rude to downvote that reply.
This is an example of a user going out of their way to humbly rescind their previous statements when it appears they were mistaken (this is admirable and not a thing that usually happens on the Internet). They didn’t do it for their own benefit, but for the benefit of the community, to not leave misleading or incorrect information in the comments.
So to sum up, downvoting a selfless act is pretty shitty and not good for the community.
in fairness, I was terse in my original response and probably came off as insincere. Thank you though. I try not to leave up misinformed statements when it turns out to be a learning moment.
Sounds like a bug.
It’s a feature.
Either way, NASA is already exploiting it. I guess, next they’ll find a way to glitch through the very fabric of the universe to teleport to a distant galaxy without moving at all or even using any energy.
Must be a problem with floating point precision.
Infinite energy glitch
Yeah, why do masless particles have momentum? And please not because law X says so.
In short, even though photons have no mass, they still have momentum proportional to their energy, given by the formula p=E/c. Because photons have no mass, all of the momentum of a photon actually comes from its energy and frequency as described by the Planck-Einstein relation E=hf.
From here: https://profoundphysics.com/if-photons-have-no-mass-how-can-they-have-momentum/
Essentially, momentum is a function of energy, not mass. It’s just that massive objects have way more momentum than massless ones.
Thanks! That’s the critical piece of information.
Because they have mass. They don’t have “mass at rest”, but they are never at rest anyway.
Do you remember that famous
E = mc^2equation? Everything that has energy has mass.But how do you apply this with Lorentz’ transformation (i.e. relativistic factors)? You cannot approach the speed of light without considering relativism. It is known that
p = gamma * m * vwhere p is momentum, gamma is the gamma factor given bysqrt(1/(1 - (v^2/c^2))), m is mass and v is velocity. If you study the gamma factor, you’ll realize that it approaches infinite as v approaches c, the speed of light. Since we are actually dealing with light here, wherev = cwe are breaking the equation. Momentum cannot be defined for any mass which moves at the speed of light. It’s asymptotic at that speed.Also note that the same goes for
E = mc^2. At relativistic speeds, also this equation needs to consider the gamma factor. So those classical equations break down for light.The answer is that photons don’t have mass, but they have energy. There is a good explanation a bit further up in this thread on how this is possible.
The one that you multiply with gamma is the rest mass, not the total mass.
To be short,
p = m_0 * γ * v, wherem_0is the rest mass. Put that in your equation and look what happens.So photons only have no mass if they don’t move? Do they even exist if they don’t move?
No. Or, at least not from our point of view.
They only exist moving at the speed at light. All particles with no rest mass only exist moving at the speed of light.
So photons do have mass?
only as long as they exist
Else they don’t. We are talking quantum here.
Energy is mass
deleted by creator
Radiation pressure does not have anything to do with mass-energy equivalence. 1), the energy for this process does not come from the conversion of electric energy into mass, and 2) having a momentum is not a property tied to massive particles. All electromagnetic waves carry momentum according to Maxwell’s theory of electromagnetism, and its transfer is fully explained by his equations and results from the interaction of the EM wave with matter, i.e., absorption and reflection. Each such interaction will transfer momentum to the massive object. This is classical physics, you don’t need any Einstein relativity to explain electromagnetic phenomena because his theories only become relevant for very massive bodies and their movement, and nuclear reactions.
ok, that’s quite far over my head but I will take your word for it
Ok, a side note on etiquette here.
When I saw this reply it had a point score of 0, which means somebody downvoted the post.
When a user is freely admitting a lack of expertise, and defers to another user who seems to know better, I would say it’s extremely rude to downvote that reply.
This is an example of a user going out of their way to humbly rescind their previous statements when it appears they were mistaken (this is admirable and not a thing that usually happens on the Internet). They didn’t do it for their own benefit, but for the benefit of the community, to not leave misleading or incorrect information in the comments.
So to sum up, downvoting a selfless act is pretty shitty and not good for the community.
in fairness, I was terse in my original response and probably came off as insincere. Thank you though. I try not to leave up misinformed statements when it turns out to be a learning moment.