"In the particle's reference frame, the photon would move away from it at the speed of light."
For some reason I've never been able to wrap my head around this. Anyone know a good explanation for this stuff?
For some reason I've never been able to wrap my head around this. Anyone know a good explanation for this stuff?
You are kind of like that car. You (and everything else) are always moving at the speed of light, but through spaceTIME, not through space. When you move through space you are not changing your speed through spacetime, you are only changing your direction. The faster you move through space, the slower you move through time, and vice versa.
If I am an outside observer measuring your position with a very long ruler and your time with my wristwatch, all while watching your dashboard clock, I have access to three numbers. (Your clock, my watch, your position on my long ruler.)
There are three ways to compare these numbers. If I compare my watch to your position down the ruler, I will obtain "classical speed." The behavior of this number is very confusing when it is high.
I may also compare your dashboard clock with my ruler position, or your dashboard clock with my watch. Both of these can lead to a "speed," in the sense of one number changing at a certian rate with respect to another.
If Vx is the rate of change of the ruler position with respect to your dashboard clock, and Vt is the rate of change of my wristwatch with respect to your dashboard clock, and c is the speed of light, then it turns out to be always true that c^2*Vt^2 - Vx^2 = c^2. If you graph this you will see that it is a hyperbola.
In the parent's example, the car situation would obey V(north)^2 + V(south)^2 = 100mph^2. If you graph that it is a circle, as it differs from the above by the minus sign.
There's no explanation "needed". Light photons move at a constant speed from any viewpoint. Its just a fact that is experimentally confirmed.
Perhaps what you need is an experiment that proves this to be true. But those experiments don't offer you any "explanation", they just will prove what you already have been told.
https://en.wikipedia.org/wiki/Relativity_of_simultaneity
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One thing that helped me understand it all is that "Reality" is a wave that propagates out. We call it "the speed of light", but its far more accurate to call it "The speed of reality" or perhaps "The speed of causality".
Basically, when A causes B, that "event" takes time to propagate to other locations. This means that different observers sees the event happen at different times.
For example: the galaxies 3-billion light years away from us appear to be forming today. We know the information is 3-billion years old, but reality itself is warped. Because the reality from 3-billion years ago was 3-billion light years away, its basically happening right now from our point of view (The "wave of reality" is finally reaching us).
Calling it the "speed of light" is confusing for multiple reasons. Just call it the "speed of reality" (and light in a vacuum happens to travel at this speed) and in my eyes, it becomes way easier to understand.
Hand-waving isn't an explanation, it's a distraction.
As another poster described: Why do Magnets attract each other, but sometimes repel each other?
Well, we can list a ton of consequences, make up stories about negative charge and positive charge (but then why do THOSE things attract / repel each other??). We can craft mathematical laws that describes the nature of this attraction.
But at the end of the day, its just a fact you have to accept. Reality has these things called magnets: they're made up of things that attract each other.
Similarly: Reality itself moves at a certain speed. Physicists call that speed "The Speed of Light". From everyone's point of view, reality propagates out like a wave, and space itself warps to keep things consistent. Its weird. But that's just how the world works.
Step 1 is accepting the fact. Step 2 is performing calculations so that we can start taking advantage of those relativistic effects in engineering and design.
Saying that the laws of the universe don't (or can't) have explanations is not the same as saying they are intuitive to everyone. Ultimately, some of those facts you just have to accept. It is extremely difficult to have any useful analogy or explanation that attempts to explain why light always travels at the speed of light in any reference frame.
The consequences can definitely be explained well, but the fundamental laws really can't.
EDIT:
John von Neumann's quote about math reflects my view about this kind of fundamental physics:
> in mathematics you don't understand things. You just get used to them.
The Lorenz-Factor(γ) for a velovity approaching c approaches infinity. Thus, from the reference frame of a particle at c, the time dialation: ΔT = γ*Δt, also becomes infinite. 2 ticks on a clock (Δt) of an ordinary observer, take an infinite amout of time in the reference frame (ΔT).
This doesn't prove or explain anything, but the fact that we can't handle infinities very well, in our casual thinking.
Instead you simply have to deal with towers of abstractions, understand the experiments. It is counter-intuitive to claim we also couldn't see photons, but really, the disconnect between theory and phenomenology is rather large. I guess we are only really interested in the weak-electromagnetic force. And that's a probabilistic theory thanks to quantum mechanics. Discrete systems are macroscopic simplifications for didactic and deductive reasons.
Gravity is next to the other three basic forces. That's a simple dualism. So time stands still for the photon, but space bends. And we can't fully explain how.
And don't get me started on infinity. It's just a number big enough for all intents and purposes. Conversely, it's pretty simple to think about the opposite: Nothing. So if you you take an infinite amount of time to observe a clock at light speed from your inertial frame of reference, it will just not move at all -- there are no "2 ticks". Corollary: A photon doesn't experience time at all. And this holds in quantum mechanics, because a photon doesn't exist until observed. A photon is thus the measure of interaction, a delta on our clock. Colloquially, time is the order of events -- if nothing happens, time stands still.
For sake of the argument: If you just switch the photon and observer in your example, the photon in infinite time wouldn't "see" any time pass on the outside observers clock. He wouldn't move. But this is just too simplistic, you have two points in space that practically can't move, because they don't
From the frame of reference of a photon, the environment would
> 2 ticks on a clock (ΔT) at c, take an infinite amout of time in the reference frame of an ordinary observer (Δt).
Extending the thought, you are trying to multiply infinity by infinity. As you said, we cannot handle infinities. I guess that is because there can be only one, one singularity, one universe. That's why the speed of light is set at unit-interval.
Sounds like the Matrix.
Sounds like a register.
Sounds like a processor tick.
I know of no way to make it intuitive though. Things improve slightly if you replace speed with 'rapidity' which places the speed of light at infinity, but then you get that objects with infinite rapidity don't travel instantly from one place to another (although this is true in some frames of reference).
Those concepts are connected by the speed of light in vacuum, yes, but there is no logical reason for that. This was an educated guess, and was confirmed by observation it's not a conclusion.
Einstein started to formulate special relativity theory starting from an assumption that a "ball of light" won't change its shape for non-inertial (no accelerarion) observers regardless of their respective speed. I.e. constant speed of light was the reason not a result of this theory.
(Duh. This got lenghty.)
Actually I can't even parse the first two sentences, and the third seems to refute something I never claimed.
Time stands still for the photon and is super slow for the particle. Super slow is still infinitely away from 0. In the article example from the particles view, 0.000..1 seconds pass for the photon to be 1cm ahead being the photon is so fast. From our view however that same small time is dilated to the 200k years.
Say a particle and I are moving along like so:
-----[photon @ speed of light]-->
-----[me @ 50% speed of light]-->
-----[other car]-->
-----[my car]-->
That's how I've understood the explanation for relativity. But it must be a very wrong understanding - because that whole idea breaks down when the other car is going along a different vector to me! In this situation:
<----[other car @ 100km/h]--
-----[my car @ 50km/h]-->
https://en.wikipedia.org/wiki/Lorentz_transformation
Your measurement of time and space will always adjust to ensure light travels at a constant speed.
Time dilates, length contracts. So perhaps it would "look" like the car travelled a smaller distance over a longer period of time that what you expected, from your frame of reference, versus a third observer who can see you both.
Enough with the metaphors already, the measurements don't do anything, you, or rather phyisicists and the like do measurements, and they adjust numbers normalized to c=1 because how else would you do it. There is no way to synchronize clocks because of the CAP theorem, nevermind relativity.
This is what allows the photon to appear to continue to travel at the speed of light from the particles frame of reference.
If the particle was carrying a clock, and we could watch it tick as it flew away from us, it would appear to be ticking super slowly, the second hand would take forever to move.
Conversely if we had a giant clock and the particle could watch it as it flew away from us, it would appear to be ticking super fast, it would look as though we were travelling far into the future.
The same is also true if an object is close to a very large gravity well. If someone could stand next to the event horizon of a black hole and hold a giant clock, from our point of view, their clock would appear to tick very slowly. From their point of view, it would tick normally, but our clock would rapidly tick far into the future. The universe around them would quickly travel into the future.
Time and space are elastic to allow the speed of light to remain constant.
Feynman talks interestingly about the nature of these facts:
When Time Breaks Down | Space Time | PBS Digital Studios
At about 4:30 is when they talk about light speed, but you should watch before then to understand what is going on.
Or perhaps it’s better to just say that the concept of reference points hits an asymptote at velocity c, so it simply doesn’t make sense to talk about the reference frame of a photon.
Does that somehow link the emission time of the two given that there is a reference frame in which they are equivalent?
What is interesting from photon's frame of reference is the image of the rest of the world.