A) a photon travels at the speed of light because it is massless, right? But doesn’t E=mc² teach us that mass and energy are somewhat interchangeable? How can a photon have energy but no mass?
B) I’m willing to accept it as fact when smarter people tell me that FTL is impossible because, amongst other things, it will break causality. It makes perfect sense to me that the universe needs to have some unbreakable rules for things to remain consistent. But I’ve never been able to grasp exactly why it would break causality.
But doesn’t E=mc² teach us that mass and energy are somewhat interchangeable?
There are two ways to read that equation. Either you use the instant mass, that changes with the object’s speed and has an undefined result for anything moving at the speed of light (this is the one Einstein wrote in awe about), or you use the rest mass and that’s the half of the equation that doesn’t consider the object’s speed (this is the one everybody actually uses).
On the second case, the complete equation is E² = (mc²)² + (pc)² where p is the momentum.
But I’ve never been able to grasp exactly why it would break causality.
It’s what I might call inferred logic. It’s not that traveling faster than light “breaks causality” it’s that light is observed to be constant in all reference frames. From that observation you build a system of motion which requires that nothing can travel faster than light. In that mathematical system, if you break that rule then the math says that you must go backwards in time to go faster than light.
So the “causality” is a side effect of the math system you created based around the rule that light is constant in all reference systems.
It’s like if you created a math system where you observed A=1 and let B=1 and state that A+B=2. Then someone says but what if A+B = -1. Your reply would be that means B = -2 because we observed A = 1 and B can be anything so if we add A + B and get -1 B must be -2. If B represented time you’d say, “Well that means you have negative time!” But it’s just the math and if you give physically impossible inputs you get physically impossible outputs.
A) from a photon’s perspective extrapolating relativity, zero time passes from when it is created to when it is absorbed. Essentially the two points are connected and the interaction is pure causality. This is part of the quantum nature of matter and can be understood as the manifestation of the probability of the two points interacting. An outside observer in three dimensional space doesn’t see the folds in higher dimensions that allow these interactions. We observe a time difference from the source to the target but our observation itself requires similar prabalistic folds in higher dimensions to make such observations, so the effect is never in isolation but as a combination that cancels the paradox. Of course I’m just making this all up, but it sounds good, eh? I’m a little bit high. Sorry.
I kind of despise the time cone answer because it doesn’t actually answer the question. It transforms the question into a picture and uses the picture as the answer which is circular logic.
“Why do thrown objects fall in a parabola?”
“See here’s a graph of a equation. If the object is outside the graph it’s not on the parabola and that’s why thrown objects fall in a parabola shape.”
I don’t think in this case the logic is circular, it just explains how the light cone shows that FTL breaks causality, and assumes that you’ll learn the math behind the light cone somewhere else. Maybe the author assumes the light cone can be better learned from other sources
Whilst we’re at it can someone explain;
A) a photon travels at the speed of light because it is massless, right? But doesn’t E=mc² teach us that mass and energy are somewhat interchangeable? How can a photon have energy but no mass?
B) I’m willing to accept it as fact when smarter people tell me that FTL is impossible because, amongst other things, it will break causality. It makes perfect sense to me that the universe needs to have some unbreakable rules for things to remain consistent. But I’ve never been able to grasp exactly why it would break causality.
There are two ways to read that equation. Either you use the instant mass, that changes with the object’s speed and has an undefined result for anything moving at the speed of light (this is the one Einstein wrote in awe about), or you use the rest mass and that’s the half of the equation that doesn’t consider the object’s speed (this is the one everybody actually uses).
On the second case, the complete equation is E² = (mc²)² + (pc)² where p is the momentum.
It’s what I might call inferred logic. It’s not that traveling faster than light “breaks causality” it’s that light is observed to be constant in all reference frames. From that observation you build a system of motion which requires that nothing can travel faster than light. In that mathematical system, if you break that rule then the math says that you must go backwards in time to go faster than light.
So the “causality” is a side effect of the math system you created based around the rule that light is constant in all reference systems.
It’s like if you created a math system where you observed A=1 and let B=1 and state that A+B=2. Then someone says but what if A+B = -1. Your reply would be that means B = -2 because we observed A = 1 and B can be anything so if we add A + B and get -1 B must be -2. If B represented time you’d say, “Well that means you have negative time!” But it’s just the math and if you give physically impossible inputs you get physically impossible outputs.
A) from a photon’s perspective extrapolating relativity, zero time passes from when it is created to when it is absorbed. Essentially the two points are connected and the interaction is pure causality. This is part of the quantum nature of matter and can be understood as the manifestation of the probability of the two points interacting. An outside observer in three dimensional space doesn’t see the folds in higher dimensions that allow these interactions. We observe a time difference from the source to the target but our observation itself requires similar prabalistic folds in higher dimensions to make such observations, so the effect is never in isolation but as a combination that cancels the paradox. Of course I’m just making this all up, but it sounds good, eh? I’m a little bit high. Sorry.
A) https://www.youtube.com/watch?v=wiBsfvW5AWY
B) https://www.youtube.com/watch?v=i88ipC8GebA
And just for good measure on a more intuitive understanding of special relativity, https://www.youtube.com/watch?v=Zkv8sW6y3sY
I love this guy’s videos; the best I have ever seen difficult physics concepts explained, based on intuition and not equations.
Is this floatheadphysics? I was gonna link him, haha. I discovered him like a week ago and it’s been so fun.
Regarding B someone linked this a week or so ago. It’s kind of technical but it does explain it https://www.physicsmatt.com/blog/2016/8/25/why-ftl-implies-time-travel
I kind of despise the time cone answer because it doesn’t actually answer the question. It transforms the question into a picture and uses the picture as the answer which is circular logic.
“Why do thrown objects fall in a parabola?”
“See here’s a graph of a equation. If the object is outside the graph it’s not on the parabola and that’s why thrown objects fall in a parabola shape.”
I don’t think in this case the logic is circular, it just explains how the light cone shows that FTL breaks causality, and assumes that you’ll learn the math behind the light cone somewhere else. Maybe the author assumes the light cone can be better learned from other sources