Can someone falsify this analogy contradicting time dilation?

[misterously]

TL;DR

A spaceship travels at the speed of light from the sun to the earth and back, infinite acceleration and deceleration. Sunlight takes about 8 minutes to reach earth. On the trip to earth, the sun seems to be frozen. On the trip back, sun activity appears to resume and is seen at 2x speed. The ship and its passengers have observed a total of 16 minutes worth of activity in a total of 16 minutes. Where is the time dilation or 'time travel'?

A spaceship travels at the speed of light from the sun to the earth and back, infinite acceleration and deceleration. Sunlight takes about 8 minutes to reach earth. On the trip to earth, the sun seems to be frozen. On the trip back, sun activity appears to resume and is seen at 2x speed. The ship and its passengers have observed a total of 16 minutes worth of activity in a total of 16 minutes. Where is the time dilation or 'time travel'?

 

[Ibix]

You cannot travel at the speed of light. You can ask the same question for a ship travelling at 0.999....9c, though, so I'll assume that instead.

The problem with what you describe is that you are talking about the Newtonian Doppler effect and not considering time dilation at all.

What you have described is simply a version of the so-called Twin Paradox scenario (note: it's not actually a paradox). The usual setup is a pair of twins. One gets into a ship and travels to a distant star at a large fraction on the speed of light and returns home. Due to relativistic effects the travelling twin ages much less than the stay-at-home. This effect is usually called differential aging and is often confused with time dilation, although it is different from time dilation in several respects.

Anyway, your scenario is just the Twin Paradox with the Sun as the stay-at-home and the ship as the travelling twin. Essentially, yes, the traveller receives far more light from the Sun on the return leg than on the outbound leg. If you account for relativistic effects, their clock will also advance almost no time - that's the bit that's missing from your analysis which makes it Newtonian and not relativistic.

We can go in to more detail if you want; it's not overly complicated, just conceptually unfamiliar. But on the face of it the answer is that time dilation is missing from your description because you didn't put it in.

 

[Orodruin]

A spaceship travels at the speed of light

No it doesn’t. Perhaps very close to the speed of light, but not at it.

Sunlight takes about 8 minutes to reach earth.

… in the Earth’s reference frame. Not in a reference frame of a traveler going to or from the Sun.

On the trip to earth, the sun seems to be frozen.

No, it doesn’t. The light that you actually receive from the Sun will be blueshifted and processes on the Sun will look sped up.

On the trip back, sun activity appears to resume and is seen at 2x speed.

No, it will now be redshifted and processes on the Sun will appear to run slower.

The ship and its passengers have observed a total of 16 minutes worth of activity in a total of 16 minutes.

No they don’t. Observers on Earth will see 16 minutes elapse. The observers on the spaceship will be time dilated and observe significantly less time if they are traveling at the speed of light.

Where is the time dilation or 'time travel'?

You simply failed to account for it.

 

[misterously]

If you can add time dilation into this theoretical equation, where I follow your starting point of not travelling at the speed of light, maybe I can better understand what you're trying to convey.

This is the theoretical frame:

- The scenario is the same, a trip from the sun and back
- I am still assuming infinite acceleration and deceleration
- Travelling speed is 0.99c
- In this theoretical example, light takes exactly 8 minutes to travel from the sun to the earth
- The duration of the trip is 16 minutes + 1% or 16 minutes and 9.6 seconds (at 99% c)
- During the trip to earth, we see an extremely slow moving sun (1% activity)
- During the trip back, we see a faster moving sun (perceiving 199% of it's normal activity)
- The ship (travelling twin) has aged 16 minutes and 9.6 seconds
- The other twin (sun) has aged the same.

What other observable factor could introduce time travel?

 

[misterously]

No it doesn’t. Perhaps very close to the speed of light, but not at it.
// I've taken this into account in my other reply

… in the Earth’s reference frame. Not in a reference frame of a traveler going to or from the Sun.

// Let's start at the very beginning then. We are stationary at the surface of the sun. We are racing a photon from the sun to the earth. We travel at 0.99c, so we lose the race, but only by a percentage point. Edit: Since we were very close to the photon at all times, the light impressions from it and surrounding photons all originated from the time of departure from the sun, thus appearing almost frozen, moving only very slowly as they catch up and reach us.

We have travelled 149 million kilometers (distance between sun and earth). For simplicity's sake, let's put the speed of light (c) at 300.000km/s.

The ray of light has reached the earth in 496.66 seconds
We have reached the earth in 491.7 seconds

The rest of the example follows my logic in my previous reply.

Also, I think you mixed up redshift and blueshift. Redshift is when objects move further apart. If you travel to the sun, its image should blueshift and vice versa

 

[Ibix]

In this theoretical example, light takes exactly 8 minutes to travel from the sun to the earth

...according to clocks at rest with respect to the Sun.

The duration of the trip is 16 minutes + 1% or 16 minutes and 9.6 seconds (at 99% c)

... according to clocks at rest with respect to the Sun.

During the trip to earth, we see an extremely slow moving sun (1% activity)

No, about 7%.

During the trip back, we see a faster moving sun (perceiving 199% of it's normal activity)

No, anout 1400%.

The ship (travelling twin) has aged 16 minutes and 9.6 seconds

No, about 2.3 minutes.

The other twin (sun) has aged the same.

No, about 16 minutes

There is not a single universal notion of time in relativity. Different observers and different frames measure different times and distances between events. Not realising this (especially not realising that different frames may disagree about whether spatially separated events were simultaneous or not) is the key reason people become confused about relativity.

 

[Ibix]

No, it doesn’t. The light that you actually receive from the Sun will be blueshifted and processes on the Sun will look sped up.

No, it will now be redshifted and processes on the Sun will appear to run slower.

I suspect you misread the OP. The trip is Sun-Earth-Sun - I think you read Earth-Sun-Earth.

 

[misterously]

...according to clocks at rest with respect to the Sun.

... according to clocks at rest with respect to the Sun.

Since you're saying there is no constant, I will leave this alone for now and focus on where you assert the differential

No, about 7%.

No, anout 1400%.

Which is here. You are saying that on the trip back to the sun we are seeing a factor of 200 more activity than we saw on our trip leaving the sun to earth. How did you reach these numbers, 7% and 1400%?

No, about 2.3 minutes.

No, about 16 minutes

There is not a single universal notion of time in relativity. Different observers and different frames measure different times and distances between events. Not realising this (especially not realising that different frames may disagree about whether spatially separated events were simultaneous or not) is the key reason people become confused about relativity.

 

[Ibix]

Which is here. You are saying that on the trip back to the sun we are seeing a factor of 200 more activity than we saw on our trip leaving the sun to earth. How did you reach these numbers, 7% and 1400%?

The relativistic Doppler factor, which is $\sqrt{\frac{c\pm v}{c\mp v}}$ (whether you have + on the top and - on the bottom or vice versa depends which way you are travelling). That allows for both time dilation and the naive Newtonian Doppler, which is the effect of distance change. Note that 0.07×14=1.

"Activity" is a fairly loose term. That factor will tell you about things like the frequency change of light and the change in rotation rate of the Sun, but it's not inconceivable that you've got something in mind that works differently. That's why it's usually better to specify exactly what you intend to measure. For example, since you are interested in time, the most direct thing to do would be to leave a clock on the Sun and eatch it through a telescope. Its apparent rate will be reduced by the factor I stated.

 

[Orodruin]

If you travel to the sun, its image should blueshift and vice versa

The mixup was in the travel directions. I read starting at Earth, which also seems more natural.

I suspect you misread the OP. The trip is Sun-Earth-Sun - I think you read Earth-Sun-Earth.

Yes, this.

thus appearing almost frozen, moving only very slowly as they catch up and reach us.

If sufficiently redshifted, yes.

The ray of light has reached the earth in 496.66 seconds
We have reached the earth in 491.7 seconds

All in the reference frame of the Earth. This says nothing about the time experienced by the travellers.

The rest of your example also ignores time dilation effects so there is no wonder you end up with a faulty result.

 

[Orodruin]

The relativistic Doppler factor, which is $\sqrt{\frac{c\pm v}{c\mp v}}$ (whether you have + on the top and - on the bottom or vice versa depends which way you are travelling).

I would add to this that the relativistic Doppler factor is just the Newtonian Doppler factor $(1 \pm v/c)$ that the OP is using modified by the time dilation factor, which the OP is ignoring:
$$
(1 \pm v/c) \gamma = \frac{1\pm v/c}{\sqrt{1 - v^2/c^2}}
=
\sqrt{\frac{(1 \pm v/c)^2}{(1 - v/c)(1 + v/c)}} = \sqrt{\frac{1 \pm v/c}{1 \mp v/c}} = \sqrt{\frac{c\pm v}{c \mp v}}
$$

 

[Orodruin]

... and to summarize:

There is no time dilation in the OP's scenario because OP assumes that there is no time dilation - contrary to the predictions of relativity.

 

[Ibix]

OP: I wonder if you've fallen into the trap of thinking that time dilation and relativistic effects have something to do with light travel time and are expecting them to just drop out of thinking about what you can see in a trip like the one you are considering.

In fact, relativity has absolutely nothing to do with light travel times. It is true that we often discuss experiments involving light pulses to investigate relativity because the kinematics of light pulses are easier to handle than those of sub-light objects. But that sometimes gives people the impression that it's the light travel time that's important. It's not - it's just that the speed $c$ (at which light happens to travel) has the unusual property that everyone always measures it to be the same. The consequences of this turn out to be far-reaching, including that time is a much more varied concept than in Newtonian physics.

 

[ersmith]

Also, time dilation has actually been observed in a large number of real experiments. If a thought experiment contradicts an actual real world experiment, the thought experiment is clearly flawed. Others have tried already to show you the flaw, but it boils down to assuming that there's just one universal time. There isn't.

 

[Dale]

Another way to approach the problem is using the spacetime interval: $$c^2 d\tau^2=c^2 dt^2 -dx^2-dy^2-dz^2$$ Using time in seconds and distance in light seconds so that $c=1$ we get for the first leg of the journey $$\tau=\sqrt{484.8^2-480.0^2}=68$$ and for the second leg of the journey $$\tau=\sqrt{484.8^2-(-480.0)^2}=68$$ So the total journey is 136 seconds for the ships. Or as @Ibix said about 2.3 minutes.

His Doppler shift approach is probably more directly relevant to your thinking here, but I like using the spacetime interval whenever possible since it is the foundational equation of relativity

 

[PeroK]

// Let's start at the very beginning then.

This thread seems pointless as you've misunderstood what the special theory of relativity says. And, in particular, what time dilation means.

You ought to start with reputable source. The first chapter of Morin's book is free online here:

https://scholar.harvard.edu/david-morin/special-relativity

 

[PeterDonis]

If you can add time dilation into this theoretical equation

Time dilation is already in the correct theoretical equation. If it isn't in yours, then yours is wrong.

 

[Ibix]

Since we were very close to the photon at all times, the light impressions from it and surrounding photons all originated from the time of departure from the sun, thus appearing almost frozen, moving only very slowly as they catch up and reach us.

I missed this post - I think I was writing the reply below it.

The quoted part is horribly wrong. Realising that there was no consistent way to describe light moving slowly past him is one of the things that led Einstein to what became the second postulate of relativity: light always overtakes you at $c$ relative to you. You never see it "creeping" past you.

The observer on the spaceship sees the Earth and the Sun rushing along at $0.99c$ while light from the Sun does $c$ in the other direction. It's never a case of "almost" keeping up with light, not by your own measures.

 

[misterously]

Thanks everyone for your answers!

I missed this post - I think I was writing the reply below it.

The quoted part is horribly wrong. Realising that there was no consistent way to describe light moving slowly past him is one of the things that led Einstein to what became the second postulate of relativity: light always overtakes you at $c$ relative to you. You never see it "creeping" past you.

The observer on the spaceship sees the Earth and the Sun rushing along at $0.99c$ while light from the Sun does $c$ in the other direction. It's never a case of "almost" keeping up with light, not by your own measures.

Is there any way to explain why that is, or at least to describe how this was proven?

 

[Ibix]

Is there any way to explain why that is, or at least to describe how this was proven?

The theoretical basis at the time was that Maxwell's equations can be used to describe an EM wave moving at $c$ but not at any other speed. For about forty years that was taken to mean that Maxwell's equations were incomplete, but experimental evidence mounted that this wasn't the case - de Sitter's observations of double stars, Fizeau's experiments with light in flowing water, and the Michelson-Morley experiment are probably the best known (and the Wikipedia pages are a decent introduction).

Fundamentally, what had happened was that Maxwell had built a theory that was consistent with the as-yet undiscovered Einstein theory of relativity, and was not compatible with Newton and Galileo's relativity. Einstein was the first to realise that, although others such as Lorentz and Poincare had already developed a lot of the maths, just not realised quite how far reaching the implications were.

 

[Orodruin]

and was not compatible with Newton and Galileo's relativity

Well, not at face value. There were certainly a lot of attempts to reconcile them, particularly related to aether theories where the assumption was that Maxwell’s equations would only hold in the aether rest frame.

Let us not forget that the wave equation for oscillations of a string is invariant under Lorentz transformations using the wave speed instead of the speed of light. That does not necessarily imply that oscillations of a string are fundamentally incompatible with Newtonian physics and Galilei transformations.

 

[Ibix]

There were certainly a lot of attempts to reconcile them, particularly related to aether theories where the assumption was that Maxwell’s equations would only hold in the aether rest frame.

Yes - that's the part I was meaning by "taken to mean that Maxwell's equations were incomplete". But one by one experiments knocked the ideas down until relativity came along.

 

[Orodruin]

Yes - that's the part I was meaning by "taken to mean that Maxwell's equations were incomplete". But one by one experiments knocked the ideas down until relativity came along.

My point was that Maxwell’s theory of light as such was not

Maxwell had built a theory that [snip] was not compatible with Newton and Galileo's relativity.

(Snip for my removal of additional text)
The EM theory could certainly be reconciled with Newtonian physics and there was no a priori contraction. However, such reconciliations failed experimental tests.

 

[pervect]

My favorite approach is the Bondi k-calculus (which is of course just algebra, not calculus). See for instance https://en.wikipedia.org/wiki/Bondi_k-calculus

The doppler shift factor is just "k". We'll work an example where k=10 for simplicity.

This corresponds to a velocity of (k^2 - 1) / (k^2 + 1) * c, or 99/101 of the speed of light, approximately .98 c.

If an object travels with this velocity for 100 seconds in its own frame away from a beacon that emits one pulse a second, for 100 seconds (again, as measured by its own clock) it will receive 10 pulses on the outbound trip. This happens because the beacon is redshifted so it appears to emit one pulse every 10 seconds, and 1 pulse every 10 seconds for 100 seconds is 10 pulses.

[add]For some reason , when I wrote this, I called the "beacon" frame the "earth" frame, and the object the "spaceship" frame. SOrry for being a bit careless with the analogy.

On the inbound trip, the doppler shift will multiply the frequency by 10, rather than divide it by 10, so the ship will receive 1000 pulses on the inbound trip.

Thee total number of pulses received, on the round trip is the sum of the number of pulses received on the inbound trip plus the number of pulses received on the outbound trip, for a total of 1010 pulses, received over 200 seconds.

This is what happens in the object's frame. Now, what happens in the Earth frame?

The time dilation factor is 1/sqrt(1-v^2/c^2), this turns out to be alternatively and more easily expressed as being equal to (k + 1/k)/2, which turns out to be 5.05. So, in the Earth frame the ship travels outward for 505 seconds, not 100 seconds. And it travels inbound for 505 seconds. So the total travel time is 1010 seconds, during which 1010 pulses are emitted.

So, everyone agrees that the beacon emits 1010 pulses. In the beacon frame, this occurs over 1010 seconds, in the object frame it occurs in 200 seconds, due to the time dilation factor of slightly over 5:1.

 

[pines-demon]

I agree with you @Orodruin but this:

No, it doesn’t. The light that you actually receive from the Sun will be blueshifted and processes on the Sun will look sped up.

Wouldn't the Sun look slower as it moving relative to your ship?

No, it will now be redshifted and processes on the Sun will appear to run slower.

As in this case?

 

[Orodruin]

Wouldn't the Sun look slower as it moving relative to your ship?

It depends on what you mean by ”look”. If you correct for things such as light travel time, yes, the Sun is time dilated. However, we were talking about how the Sun was actually seen by someone in the spaceship, it will be blueshifted - meaning events that occur 1 s apart on the Sun will be received by the observer with a time difference less than 1 s.