/sci/ - Science & Math

http://en.wikipedia.org/wiki/Time_dilation

>>1140281
First off, you can't move anything with mass at 100% C. It doesn't work. You need infinite energy to make it happen. Newton was wrong when he said you could do that. The kinetic energy you add to the system has to be moved too.
Second, yes. That's why time slows.

Add a fourth dimension to space, called time. Particles are 1-dimensional paths, and events are 0-dimensional points. Meters and seconds are now the same type of unit, with one second equal to 299792458 meters.

Almost all the familiar rules of geometry still work. There is one important caveat: 4-dimensional distances, called intervals, can be either real or imaginary numbers. If the interval is imaginary, it is called spacelike; if it is real, it is called timelike. You can compute the interval between any two events by measuring the time and 3-dimensional distance between the events, and then plugging the two intervals into the Pythagorean theorem:

<div class="math">interval = \sqrt{(time\;interval)^2 + (distance\;interval)^2} = \sqrt{(time)^2 - (distance)^2}</div>

Note that to convert the 3-dimensional distance to a 4-dimensional interval, we have multiplied it by <span class="math">\sqrt{-1}[/spoiler].

The interval between two events along the path of an object is called proper time. If the object is a clock, proper time is how much time passes on the clock between the two events.

When you choose the coordinate system, the unit time vector can point in whatever direction you want, as long as intervals in that direction are timelike. Events which are simultaneous (happen at equal values of time) in one coordinate system will generally not be simultaneous in other coordinate systems.

You can do trigonometry in spacetime, but sometimes the angles will be imaginary. An imaginary angle is called a rapidity, and the values of the trigonometric functions are given by the hyperbolic trig functions.

Every particle has a 4-momentum vector which is tangent to the particle's path and has a magnitude equal to the particle's mass. Given a coordinate system, the time component of 4-momentum is called energy, and the spatial components are called momentum. 4-momentum is conserved.

Electric fields rotate charged particles in the xt, yt, and zt planes; magnetic fields rotate them in the xy, xz, and yz planes. The angle (or rapidity) that the particle's momentum rotates per proper time is equal to the charge of the particle times the value of the field divided by the particle's mass. The electric and magnetic fields together form a four-dimensional object called the Faraday tensor.

>>1140281

Trollfag IMO.

>>1140372

1. Let's assume for this example that mass is not an issue.

2. I'm still puzzled. Wouldn't it be more accurate to say that above certain speeds we can't measure time properly (rather than saying it slowed down)?


>>1140380
>>1140388
These two post are way to advanced for me.

>>1140308
Thxs for the good intention anon, but I already read this.

>>1140400
C'mon man. I'm really trying to grasp this concept, not trolling (to troll It's easier to make a atheism vs religion thread or something like that).

Also: nice doubles.

>>1140402
You should give them a try anyway. Those two posts are a summary of the modern understanding of special relativity. You are not expected to understand all of it, but a lot of it is just the geometry you already know.

>>1140436
I read them, more than once. I still don't understand them.

>>1140281
For a more direct answer, it's traditional when teaching students special relativity to derive things from Einstein's two postulates like he did in the original paper. This is what your professor is doing with the light clock example. But deriving a concept isn't the same as understanding it. To understand special relativity, you want to learn the geometric picture.

>>1140455
Could you be more specific about what doesn't make sense so I can try to improve my explanation?

would it be actully somehow possible to negate the mass or something with antigravity or whatever. i have no clue what im talking about.. just curious

all i know that if someone movies at the speed of light we would need infinite energy.. but can we just take the mass away or something?

>>1140281
Off topic, but where are you from?

>>1140462
Does that means I'm screwed till the next semester?

>>1140469
Well... I just started taking physics in college so most of the math is beyond my understanding still (most = 99% lol).

---------

Perhaps it would be better if we start with a definition: What is time? (yes, I read the wikipedia article)

>>1140481
There isn't any known way to remove all the mass of an object, but massless objects do travel at the speed of light. Nothing moves faster, though.

Since everything that "can happen" is related to the speed of light, and that varies, the assumption that "time itself" changes holds for all our math and experiments.

When the speed of light changes, every reaction every molecule wobble and surely every event on a large scale changes with it, to be consistent.

to rephrase: the light clock example is used because it is the simplest possible way to detect the passing of time.
Since moving reference frames need to be consistent (what happens in one also happens in another) we need time to slow down for funkyness NOT to happen

To OP I recommend picking up a college textbook on the subject if you haven't already, when you get to this high a level of science it really does split into a binary "know all the math and concepts like a real physicist"/"has no understanding whatsoever".

I don't know relativity yet, but I can say fairly confidently that yes, the lightclock thought experiment makes no fucking sense to a layman, but in context it's probably perfectly valid. The trouble is that "in context" entails alot of complicated stuff in physics.

>>1140486
I'm from San Juan, Puerto Rico.

>>1140495
I'm curious: How do we know this? How can we be sure *nothing* travels faster than light?

>>1140493
Time is what a clock measures. It is a property of a path between two events in spacetime.

>>1140507

i think the "nothing travels faster than light" is a slight simplification. particles w/ speeds > c have been theorized, and accorting to QM, v <= c only needs to be true on average

>>1140499
Can you elaborate a bit? How does the speed of light changes?

>>1140501
I have, trust me, I read a lot. But I'm nowhere near high level science yet. I'm just starting with the basics now.

>>1140507
We're never sure of anything in physics. We just have theories that we can compare to reality, and the theory called special relativity tells us that nothing moves faster than light. The reason is that if an object moves faster than light, you can find a coordinate system in which its departure happens before its arrival, leading to the possibility of grandfather paradoxes.

>>1140535
Well then, and again I don't know relativity yet so I can't say for sure, but I suspect you will not understand this subject until you work your way methodically through all of the basics and up to relativity, just like in a college course.

Like I said, when you reach this level, I think intuitive layman's understandings simply do not exist. You either know exactly how it works or you don't know how it works at all.

>>1140521
huh? Don't mean to be rude, but that definition sucks. I mean, it doesn't say anything...

>>1140533
But if moving an object with mass to light speed requires infinite energy... how much energy would it be required to travel faster than that?

could light travel faster then light?

>>1140535
I don't think what >>1140499 was saying is consistent with special relativity. The invariant speed c (which light travels at in a vacuum) does not change according to special relativity.

>>1140535

Saying that the speed of light changes is a bit off, but here goes.

If you shine a light in a stationary box from one side to the other, the light travels the width of the box, say "x".
If the box is moving in the same direction as the light,
the light travels the distance "x" , plus the distance the far wall of the box has traveled (say "y" ) , right?

Now, since we record time by our light clock, one "tick" will now take the time light uses to travel x+y.
But since this is the fastest possible speed, and every other photon inside the box also needs to travel the extra distance in the "x" direction, it is self-consistant.
The net effect inside the moving box is nothing, but from the outside the light uses more time from one side to the other, and time appears to move slower

>>1140281
So do you get it yet OP? What problems are you having still?

>>1140558
I'm not sure what you want me to say. Time is a fundamental concept on which the rest of the theory is built. How would you go about defining distance?

If you are moving at C with your back to the direction of motion, and you are looking at a clock, it will appear to stand still because the light from its face will never reach you. However, it is moving normally.

>>1140582
While true, that has nothing to due with time dilation.

>>1140551
>you can find a coordinate system in which its departure happens before its arrival,
Wouldn't it be more accurate to say that we detect it's departure before its arrival?

Also: when I say "certain" I don't mean in the "religious-100%-blind-faith" sense, I mean in the "as-far-as-we-know" sense. ;-)

>>1140557
Yeah, that's the way it seems. I'm still trying though. Maybe in 2-3 years I'll be telling people the same thing you're telling me.

>>1140560
wat

>>1140566
Why do we say light is faster in a vacuum? What do non-vacuum environments have that slow it down?

>>1140582
While true (except the part where you claim the clock is moving normally), that has nothing to due with time dilation.

>>1140281
WTF? NO, JUST NO!

Imagine we are in a ship, moving fast, we still have a clock in there, hence we are still measuring time. Why would you think we cant measure time? ALL YOU NEED IF A FUCKING CLOCK!

>>1140617

Think about that question.
In a non-vacuum there are atoms.

A lot of them, meaning that light collides with at least some. The absorbtion and reemission of a photon takes time, small as it may be, so the light uses more time than if it can pass freely.

OK, the clock is moving normally from its point of view. Time dilation is experienced through others, not by yourself.

>>1140617
>>you can find a coordinate system in which its departure happens before its arrival,
>Wouldn't it be more accurate to say that we detect it's departure before its arrival?
No. It may seem strange to you, but according to special relativity, it is possible for event A to happen before event B in one coordinate system, but for event B to happen before event A in another coordinate system.

>>1140567
Ahhh... it's so refreshing to read my question written so eloquently.

So time just "seems" to slow down? It doesn't "actually" slows? (i.e. is time dependent on the speed of light at these speed or some external standard?)

>>1140571
I think my main problem is that I'm asking a lot of question with complicated answers. Answers that require more science knowledge that I have to be able to fully understand.

>>1140582
Will I still age in that scenario?

>>1140574
I don't know man. I'm just asking, really. A lot of the definitions of "fundamental" stuff in science puzzle me.

>>1140619
wat

>>1140507
How did your professor tell you anything if the UPR is closed?

>>1140641
Ohh... I think I get it. It's the bouncing between objects that slows it down (like the stations on a train ride?)

Question: light still moves between atoms (in what little gap there may be between them) as if on a vacuum right?)

>>1140650
I think I'll have to read about coordinate systems to understand your answer... I'm not familiar with the concept.

>>1140689
YOUR A FUCKING FAGGOT!

>>1140674
>Implying I go to UPR

I go to the "Universidad del Sagrado Corazón" (yes, they have science classes in a Catholic university).

>>1140650
Grandfather paradox is bullshit since the coordinate system is based relative to the source.
It is a logical fallacy.

>>1140617
2-3 years? Wat?

I'm working through textbooks on my own and unless it gets much, much tougher later on I'll probably have finished the chapters on Relativity within 2 months. If you set your mind to it and have good reading material, 2-3 years is an absurdly pessimistic prediction.

>>1140662

The problem here is I think you abstract an philosophic "time" that is outside everything.

In our world, time is exactly the passing of that photon, or some other event. There isnt an "outside" clock that keeps "absolute" time.

So the concept of "actually slowing down" and "seemingly slowing" down makes no sense.

Think about it this way. If you are inside the moving box, another box which you were viewing the whole mess from earlier and you thought were stationary is now moving instead. which one is right? since we can´t tell which one is ACTUALLY stationary they both need to be.

Which is why we have special relativity. Alot of the weirder examples are just more advanced consequences of this simple scenario, and being consequences of the math involved hold true

>>1140707
What are you studying?

>>1140711
Hope you're right anon. I just estimated the time it would take me to complete my bachelors degree.

>>1140713
>since we can´t tell which one is ACTUALLY stationary they both need to be.
Really? Why can't we just say: we don't know which one is moving since we have no point of reference?

>>1140716
I'm studying business management, but I'm taking as many science classes as I can (all my electives, and probably a few more just because).

Also: Why would you sage my thread man?

Let me revise what I said about time a little, and maybe it will be a bit more comprehensible:

In Newtonian physics time is something external and universal. We have to abandon this concept of time.

In special relativity, there are two concepts of time which we have to worry about:

(1) Proper time is an intrinsic property of an object and two events that happen to that object. It is what a clock measures.

(2) Coordinate time is a function of an event and a coordinate system. It is a lot like the Newtonian concept of time, except that there is more than one version of it; it is not universal.

>>1140741
Because unknown to you, there are people who don't feel their post warrant a bump and use sage the way it's meant to be used, instead of as a "thread voting tool".

>>1140728

I meant they both need to be "true", not they both need to be stationary. pardon my english.

That is infact exactly what we say.

But if we want to be able to make predictions about how things work, we sometimes need to postulate simple principles we cannot prove in themselves, but when the consequences we derive are consistent with everything we observe, asking wether they are true from a philosophical point of view is not necessary.

>>1140689
Your professor is probably calling spacetime coordinate systems "reference frames." I try to avoid that terminology because it tends to lead to the common misconception expressed in >>1140582 which claims that things like time dilation are perspective effects.

>>1140775
But to add to that, yes, you should do some reading about coordinate systems, both in three and four dimensions; even if you never use relativity in your life, you will need to be very familiar with coordinate systems in order to understand the rest of physics.

>>1140746
How and why did Einstein "made up" those two new concepts of time?

Those concepts are new to me so instead of asking tons of shit I'm reading the wikipedia articles now.

>>1140755
:'-(

>>1140764
Makes sense. Finally, a post I can fully understand.

You win 10 internetz.

>>1140775
Yeah, he uses that term.

>>1140796
I'm on it right now. Wont be able to finish today though, it's too much.

When I have more questions I'll comeback. You guys have been nice and even though I still don't get a ton of shit at least I've been pointed in the right direction.

>>1140806
Also, there's no need to feel sad or offended in an anonymous site.

I just wanted you to know that it's nothing personal or against you, I just don't feel my post important enough to bump the thread for everyone to see.

>>1140836
We're good. no hard feelings.

>>1140806
>Those concepts are new to me so instead of asking tons of shit I'm reading the wikipedia articles now.

Oh, watch out ... the wiki article on "coordinate time" is mostly about general relativity (gravitation). You don't need to understand its contents and might have a hard time doing so without learning special relativity first. What you mostly need to get is that a coordinate system in spacetime has four axes, x, y, z, and t, and in special relativity coordinate time is the proper time measured along the t axis. (In general relativity it is more complicated, hence the wiki article.)

When you approach the speed of light, weird things start to happen...

Mass increases

Time dilation increases

Rate of Event changes.

If two flashlighs are beaming passed each other surely they are going at 2x lightspeed? Right?

WRONG.

The two photons moving away from each other at lightspeed are not doing 2c but 1c... why?

rate of event. If only you could bullet-time slow it down to see....

IF the mirror is moving away from the lightsource, it won't alter the fundamental speed of light (unless you change its medium like air, glass or water)

You will however alter the reflected photons FREQUENCY. This is known as doppler shifting. If its RED its MOVING AWAY
If its BLUE its MOVING TOWARDS.
Red Shift (not Russian soldiers)
Blue Shift (not Half Life)
If something moves away from the lightsource the photons don't lose velocity, they lose frequency energy.
IF you batton a photon at someone, again the velocity doesn't change either, but the frequency increases!!!

>>1140863
Ok. Thxs 3 the warning.

Also: how do you make/visualize a 4d graph?

>>1140866
Is that how we can measure the distance of stars and other astronomical objects?

>>1140866

Yes, but that is because we always define c to be the incoming speed of a photon - there is not other way to do it.

The red/blueshift is needed to keep for energy to be consistent with the time dilation effects.

and yes, that is how we measure our relative speed to far stars

>>1140896

A 3D graph that changes with time. It doesnt really imagine well, just as a 4D coordinate system doesnt seem intuitive - theres not place for the fourth axis.

But the numbers work (x,y,z,t) no problem

>>1140925
thxs.

>>1140934
we can render 3d graphs in 2d planes. Could we render 4d graphs in 3d planes?

>>1140934
>>1140952
parametrics?

>>1140952

In a sense. You could let the fourth dimension be for instance colour.
(not so uncommon in engineering etc)
Imagine a sphere with density (t component ) 1/r^2 -
Plotted in space, the coordinates for any given point would be (x,y,z, 1/r^2) - the last component could be plotted as color. Dense is white in the middle - turning to black as you go away from the origin.

instant 4D :D

>>1140995
very ingenuous solution.

>>1140952
In many problems, only one or two dimensions of space matter. For example, when things are traveling along a straight line, you only need one spatial dimension. Then you can make a 2D plot of the one spatial dimension you need and time.

>>1140995
Yes I agree with your colour being an additional dimension theory..
only colour applies to a very narrow part of the Electromagnetic Spectrum.
It would be fairer to say that pitch is the additional dimension then it applies to all waves.

>>1141029

the idea here was 4D visualization.

If it is not to be visualized the numbers do more than enough work themselves.
Any size not included in the existing three dimensions could be the fourth. or fifth.


(using dimensionality in the mathematical sense here, otherwise absolutely anything can be a dimension)

If you really want to get into some crazy-ass 4D stuff, you can try to visualize it through analogs and by looking up stuff about tesseracts and hypercubes.

If you want to save yourself the headache, though, just imagine additional dimensions as just additional parameters; that's all you need for the numbers to work.