B Being on a different IRF, wouldn't light appear to slow?

[WhoCares]

I realize the basics of general and special relativity, and I picked up a copy of "Relativity" by Albert Einstein, though there's one question I just couldn't find the answer to despite my hours of surfing online. I understand the basics of inertial reference frames, length contraction, and time dilation. There must be something I'm misunderstanding or some essential piece I'm missing due to only knowing the basics.

So, for any observer, c must always be 299,792,458 m/s, and due to this fact, other inertial reference frames appear to have a "slow clock" and shorten along their direction of motion.

If I were running at .99c next to a beam of light, then general relativity tells me that, from my perspective, this light would appear to be going .01c. However, special relativity makes up for that through time dilation and length contraction. But, because v=d/t, wouldn't light, from my IRF, appear to slow down even further due to it appearing to be covering even less distance in greater time?

If, by approaching c, all other IRFs appear to slow down, wouldn't light itself appear to slow below c?

 

[Orodruin]

then general relativity tells me that, from my perspective, this light would appear to be going .01c.

No it doesn't. Where did you get this impression from?

 

[Ibix]

If, by approaching c, all other IRFs appear to slow down, wouldn't light itself appear to slow below c?

Since the length contraction and time dilation formulae are derived by assuming the speed of light is constant, clearly the answer is no.

general relativity tells me that, from my perspective, this light would appear to be going .01c.

General relativity tells you no such thing. Did you mean Galilean relativity?

 

[WhoCares]

No it doesn't. Where did you get this impression from?

Sorry, I may not have made myself clear. I was saying, without special relativity, if I were to run at a speed of 296,794,533.42 km/s next to an object traveling at a speed of 299,792,458 km/s, it would appear to be traveling 2,997,924.58 km/s.

Since the length contraction and time dilation formulae are derived by assuming the speed of light is constant, clearly the answer is no.

I understand the answer is no, that's why in my original post I said there must be something I'm misunderstanding. I'm inquiring as to why other IRF's would appear to slow down in this scenario, though light would not.

General relativity tells you no such thing. Did you mean Galilean relativity?

Probably; my mistake.

 

[Dragon27]

But, because v=d/t, wouldn't light, from my IRF, appear to slow down even further due to it appearing to be covering even less distance in greater time?

When you say "I understand the basics", you're just deluding yourself. You can't say that you understand time dilation if you think you can just replace $t$ with a bigger number in a random formula and get "the time dilation", because that's not how time dilation works. You should learn the basics properly, with space-time diagrams, events, lorentz transformations and stuff, so that you could analyze a situation in a precise manner by identifying events in space-time and calculating their coordinates in different frames of reference.

 

[WhoCares]

When you say "I understand the basics", you're just deluding yourself. You can't say that you understand time dilation if you think you can just replace $t$ with a bigger number in a random formula and get "the time dilation", because that's not how time dilation works. You should learn the basics properly, with space-time diagrams, events, lorentz transformations and stuff, so that you could analyze a situation in a precise manner by identifying events in space-time and calculating their coordinates in different frames of reference.

Okay! I'll look into all of that stuff. I'm only in high school so I'll have to figure out how much of that I can figure out on my own, but thank you for the help.

By the way, I wasn't plugging t into that formula to get "the time dilation." I was using that fraction to express that the denominator, t, would have to get smaller rather than larger to increase velocity, v.

 

[Ibix]

I'm inquiring as to why other IRF's would appear to slow down in this scenario, though light would not.

In general, they don't. If I regard myself as stationary and you as doing 0.9c then you regard me as doing 0.9c. Also, "an inertial reference frame traveling at the speed of light", which seems to be implied by the sentence I quoted is nonsense.

Are you trying to ask why objects with velocities less than c have different velocities in different inertial frames, but light does not? Ultimately the answer is "because we assume that to be true and the predictions we make when we assume that turn out to be right". One of the predictions is the Lorentz transforms which you can use to derive the relativistic velocity addition formula, which tells you that if I see you traveling at u and something else traveling at v, you will see that thing traveling at v', where $$v'=\frac {v-u}{1-uv/c^2}$$For any non-zero u you like, $v'\neq v$ unless $v=c$.

 

[Dragon27]

By the way, I wasn't plugging t into that formula to get "the time dilation." I was using that fraction to express that the denominator, t, would have to get smaller rather than larger to increase velocity, v.

Yeah, I thought that you thought that by time dilation $t$ in $v=s/t$ would just get bigger, and therefore $v$ would get smaller (ever more so, because $s$ would decrease, too). It's wrong. Time dilation says that a clock moving at some speed $v$ would tick at a slower rate, than if it weren't moving at all.
The time difference between two events (like the time difference between the beginning and the end of the flight of light) in a new frame of reference in general depends also on the distance between two events (in the old frame of reference).

I'm only in high school

One of the best elementary books on SR is Spacetime Physics by Taylor and Wheeler. Should be accessible at a high-school level.

 

[Ibix]

By the way, I wasn't plugging t into that formula to get "the time dilation." I was using that fraction to express that the denominator, t, would have to get smaller rather than larger to increase velocity, v.

Unfortunately there's a third relativistic effect called the "relativity of simultaneity" that invalidates this approach. My measurement of the length of a moving object requires me to measure the position of the ends of the object simultaneously. The relativity of simultaneity means that you, in another frame, don't agree that I measured simultaneously. So my measurements of the length of your ruler are irrelevant to you. Simply dividing them by my meaurement of your clock's tick rate is, therefore, also irrelevant to you.

You do need to learn to use the Lorentz transforms. Look up the "light clock" thought experiment. You can derive the Lorentz transforms from this with nothing more complex than Pythagoras' Theorem.

 

[WhoCares]

One of the best elementary books on SR is Spacetime Physics by Taylor and Wheeler. Should be accessible at a high-school level.

Thank you! I'll give it a read.

Unfortunately there's a third relativistic effect called the "relativity of simultaneity" that invalidates this approach. My measurement of the length of a moving object requires me to measure the position of the ends of the object simultaneously. The relativity of simultaneity means that you, in another frame, don't agree that I measured simultaneously. So my measurements of the length of your ruler are irrelevant to you. Simply dividing them by my meaurement of your clock's tick rate is, therefore, also irrelevant to you.

You do need to learn to use the Lorentz transforms. Look up the "light clock" thought experiment. You can derive the Lorentz transforms from this with nothing more complex than Pythagoras' Theorem.

I had already read about the light clock thought experiment and played around with the Lorentz transformations, I just for some reason hadn't thought about the fact that the relativity of simultaneity would apply to the scenario I gave. I was simply plugging .01c into the formula to test my original scenario and dividing the length that 299,792,458 meters contracted to by the amount of time 1 second contracted to (both from my perspective). I did finally apply the coordinate transformation formulas and realize both the error in my math and my logic.

I know it probably seems silly to everyone else and now I feel stupid for having dismissed relativity of simultaneity, but I wanted to say thank you for teaching me something.

 

[Orodruin]

I would say that at least 99% of the layman misconceptions about relativity are based on blindly trying to apply time dilation and length contraction without any thought on what they mean or how they are derived and not taking the relativity of simultaneity into account. You are not alone.