I tried to link Mahayana emptiness to Theravada emptiness in this question.
Here's what I learnt about Mahayana emptiness:
According to Mahayana Madhyamaka emptiness (shunyata), all phenomena
is empty of intrinsic essence (svabhava), and even this emptiness
itself is empty of intrinsic essence. However, this intrinsic essence
appears to be the essence given to phenomena by reification or
objectification-classification (papanca). So this means that my mental
idea of how some phenomena is, is not how it actually is.
Now, Nirvana is not a sankhara (conditioned and/or compounded thing)
but it is also empty, in the sense that it is empty of the essence
given to it by reification. So this means that my mental idea of how
Nirvana is, is not how it actually is.
Even "emptiness is empty" means that my mental idea of how Mahayana
emptiness is, is not how it actually is.
This is interesting, because it does not mean that a chair, a dog and
Nirvana are mind-independently unreal or non-existent according to
Madhyamaka. Rather, the mental idea that I have of a chair, a dog and
Nirvana is unreal or non-existent.
And then about Theravada emptiness:
Now in Theravada, all suffering is related to clinging. Clinging is
always related to the self. According to Sutta
Nipata 4.14, the root of all reification or
objectification-classification (papañca) is "I am the thinker".
Also from MN 1, an arahant who is fully liberated from suffering would
see phenomena as they truly are, without reification where his mental
idea of phenomena associates it with his self (of persons). This is
apparently also known as tathata.
According to the Suñña Sutta, the five aggregates are empty of a self
(of persons), including that they have no association with self (of
persons). All reified mental ideas are mental fabrications (sankhara),
so they too are empty of a self (of persons).
Now linking Theravada emptiness with Mahayana emptiness:
So, linking the Mahayana Madhyamaka emptiness to the Theravada
emptiness, I can say that all phenomena is empty of a mentally reified
intrinsic essence, where this reification or
objectification-classification is rooted in "I am the thinker".
Thanissaro Bhikkhu explains this as "the perception, 'I am the
thinker' lies at the root of these classifications in that it reads
into the immediate present a set of distinctions — I/not-I;
being/not-being; thinker/thought; identity/non-identity — that then
can proliferate into mental and physical conflict." I take it here
that "I am the thinker" creates a duality between self (of persons)
and non-self (of persons) that creates mental and physical conflict.
So, since Mahayana emptiness says that all phenomena is empty of
mentally reified essence, and since all reification is rooted in a
self (of persons), and Theravada emptiness states that all phenomena
is empty of a self (of persons), then these two definitions of
emptiness could be logically linked in this way.
Furthermore, the enlightened one who sees the Theravada emptiness of
all phenomena through wisdom, will also simultaneously see the
Mahayana emptiness of all phenomena, due to having his reification
(papanca) ended, due to having his fetters concerning a self (of
persons) uprooted. So, the enlightened one sees things as they truly
are, which apparently is called tathata.
So, according to both Theravada and Mahayana, basically, Buddhism as a whole, it does not matter whether a chair or table or space or time or Nirvana or a cat or a tree are REALLY existing or not. All these things are definitely empty of the intrinsic essence given to it by mental reification.
There is more explanation in this answer.
For e.g. a dish of a meal consisting of meat may look like delicious food to a meat eater. At the same time it looks repulsive to a vegan. To a honey bee, it looks like a pile of dirt, because that's not its food.
So, the question is not whether delicious meal exists or repulsive food exists or dirt exists, in real life or just in your mind. That thing is simply empty of the essence given to it by the minds of a meat eater, a vegan and a honey bee.
In a way, you can say that the delicious meal only exists in the mind of the meat eater, and it does not exist outside. The repulsive food only exists in the mind of the vegan, and it does not exist outside. The piece of dirt only exists in the mind of the honey bee, and it does not exist outside. What is that which exists outside? Does it matter what it is? Does it matter how it exists?
Both Mahayana and Theravada are quite the same in my opinion. The only difference is that they focus on different perspectives of the same thing.
To the question, "How do time and space REALLY exist?", I answer, "not how you think it exists." That's the most accurate answer of Buddhism, from both Mahayana and Theravada, in my opinion.
The historical Buddha valued pragmatism over metaphysics. See the Parable of the Poisoned Arrow.